deliverable d1.2 power system analysis and key … · report page 2 of 206 disclaimer the...

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............................................................................................................................................................

Acronym: MIGRATE – Massive InteGRATion of power Electronic devices

Grant Agreement Number: 691800

Horizon 2020 – LCE-6: Transmission Grid and Wholesale Market

Funding Scheme: Collaborative Project

............................................................................................................................................................

Deliverable D1.2

Power System Analysis and Key

Performance Indicators

Date: 31.01.2018

Contact: [email protected]

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Disclaimer The information, documentation and figures in this deliverable are written by the MIGRATE project

consortium under EC grant agreement No 691800 and do not necessarily reflect the views of the European Commission. The European Commission is not liable for any use that may be made of the information contained herein.

Dissemination level:

Public

Restricted to other programme participants (including the Commission Services)

Restricted to bodies determined by the MIGRATE project

Confidential to MIGRATE project and Commission Services X

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Document info sheet Document name: Power System Analysis Approaches and Key Performance Indicators

Responsible partner: TUD1

WP: 1

Task: 1.2/1.4

Deliverable number: 1.2

Revision: 2.0

Revision date: 31.01.2018

Name Company Name Company

Authors:

J.L. Rueda Torres

E. Rakhshani

D. Wang

B. Tuinema

N. Farrokhseresht

D. Gusain

A. Perilla

J. Mola Jimenez

V. Sewdien

S. Rüberg

TUD

TUD

TUD

TUD

TUD

TUD

TUD

TUD

TenneT2

TenneT3

T. Breithaupt

D. Herwig

F. Goudarzi

A. Pawellek

A. Neufeld

R. Meyer

L. Hofmann

A. Mertens

M. Val Escudero

J. Kilter

LUH4

LUH

LUH

LUH

LUH

LUH

LUH

LUH

EirGrid5

Elering6

Task leader: J.L. Rueda Torres TUD

WP leader: S. Rüberg TenneT

Revision history log

Revision Date of release Author Summary of

changes

0.0 – Draft 30.06.2017 TUD, LUH,

TenneT, EirGrid Initial draft

1.0 – Draft 03.10.2017 TUD, LUH,

TenneT, EirGrid First complete draft

2.0 31.01.2018 TUD, LUH,

TenneT, EirGrid

Comments from T1.2/T1.4 partners

are addressed

1 Delft University of Technology, The Netherlands 2 TenneT TSO B.V., The Netherlands 3 TenneT TSO GmbH, Germany 4 Leibniz Universität Hannover, Germany 5 EirGrid, Ireland 6 Elering, Estonia

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Executive Summary

This Deliverable is devoted to the study of four model problems, which describe the modelling and

simulation needs to enable a suitable (i.e. accurate) recreation of a given stability phenomenon

when the studied system is close to or in an unstable condition. The model problems are defined

based on the top ranked stability issues listed in Deliverable D1.1 (‘Report on Systemic Issues’).

These issues were evaluated by Transmission System Operators (TSOs) of the MIGRATE

consortium and other members of the European Network of Transmission System Operators for

Electricity (ENTSO-E). Among the model problems are the frequency performance within the

inertial response time window of the frequency containment period, large-disturbance rotor angle

stability, small-disturbance voltage stability, and sub-synchronous controller interactions.

Chapter 1 revises the main findings from deliverable D1.1 and outlines the scope of the work

carried out in tasks T1.2 (‘Power system analysis approaches and development of KPIs to measure

the distance to instability’) and T1.4 (‘Development and use of a small set of generic test cases

able to grasp system stability issues raised by the growing PE connection into any control zone’). In

Chapter 2, the current state-of-the-art modelling in power systems and the capabilities of Power

Electronics-Interfaced Generation (PEIG) is revised and discussed. At the end of this chapter, a

manufacturer survey about expected future capabilities of Power Electronic (PE) converters with

respect to the grid codes is discussed. It is pointed out that the technical feasibility of many non-

exhaustive requirements depends on the concrete specifications demanded by the relevant TSO,

which is of significant importance for requirements that may demand an energy storage. The

overall consent of the interviewed manufacturers was that the benefit of each requirement for a

particular grid application has to be weighed against the cost of implementation and testing.

The development of a set of generic test cases and the implementation of transition scenarios in

the Great Britain and Irish systems are presented in Chapter 3. Three generic test cases are

introduced. The generic test cases are based on existing benchmark systems for power system

stability studies available in literature. These benchmark systems were modified to account for high

penetration levels of wind power generation and to evaluate the impacts on the stability

performance due to the decrease of the number of conventional power plants connected to the grid.

The first generic test case is used in Chapter 4 to study the frequency performance, considering the

inertial response time window (1-30 seconds from the time of occurrence of an imbalance),

whereas the second one is used to study the large-disturbance rotor angle stability and the small-

disturbance voltage stability. The third generic test case is used to study sub-synchronous

controller interactions. This chapter also shows a simple methodology to exploit information from

power system planning to create different transition scenarios, which constitute different topologies

and entail different composition of generation and demand for future situations of a power system

that undergoes a dramatic transformation from synchronous generation dominated behaviour to

PEIG dominated behaviour. The methodology is applied to the Great Britain system, which is used

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together with the model of the Irish system for testing the Key Performance Indicators (KPIs)

proposed in Chapter 4.

In Chapter 4, the notion of KPI is introduced. Here, a KPI constitutes a way to map the values of a

system variable or set of system variables (e.g. kinetic energy) onto the actual value of a stability

indicator (e.g. frequency nadir), thus allowing to estimate the distance to instability. The distance

to instability is an indication of the stability status of the system and how the system will move

from stable status to the stability limit (i.e. threshold defined by the operator for the stability

indicator) as a consequence of changes in the key variables. Methods to determine the KPIs based

on offline simulations are proposed. DIgSILENT PowerFactory and PSCAD are used to perform RMS

simulations and EMT simulations, respectively. Widely used indicators for the assessment of the

frequency performance within the inertial response time window of the frequency containment

period, and the assessment of the large-disturbance rotor angle stability are integrated into the

proposed KPIs for these phenomena, whereas new indicators are proposed and integrated into the

KPIs for small-disturbance voltage stability and sub-synchronous controller interactions. Numerical

results obtained by using the generic test cases provide insight into the stability performance of

systems with high penetration levels of PEIG, whereas the tests conducted by using the Great

Britain system (further assessment of frequency performance in the frequency containment period,

large-disturbance rotor angle stability, and small-disturbance voltage stability) and the Irish

system (additional case study concerning frequency performance in the frequency containment

period) shed light into the feasibility and effectiveness of the proposed KPIs when applied to larger

size systems. This chapter also provides recommendations for future studies and application of the

KPIs in power system operation.

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Contents

Executive Summary .................................................................................... 4

Contents ................................................................................................... 6

List of Figures ............................................................................................ 9

List of Tables ........................................................................................... 14

Abbreviations ........................................................................................... 16

1 Introduction ....................................................................................... 19

1.1 Motivation ................................................................................... 19

1.2 Deliverable 1.2 in the Context of MIGRATE and WP1 ........................ 19

1.3 Main Findings from Deliverable 1.1 ................................................ 20

1.4 Scope, Objectives and Approach of Tasks 1.2 and 1.4 ...................... 22

1.5 Outline of Deliverable 1.2 ............................................................. 23

2 State-of-the-Art Power System Modelling and Simulation ......................... 24

2.1 Introduction ................................................................................ 24

2.2 Power System Modelling ............................................................... 24

2.3 Power System Simulation Practices ................................................ 27

2.3.1 Simulation of Power System Dynamic Response .................... 27

2.3.2 Review on Current TSO Practices ........................................ 28

2.4 Manufacturer Review of PE Capabilities and Network Codes............... 30

2.5 Conclusions ................................................................................. 37

3 Modelling of Transmission Systems with high Penetration of PE Devices ..... 39

3.1 Introduction ................................................................................ 39

3.2 Development of Generic Test Cases ............................................... 39

3.2.1 General Description of Generic Test Cases ............................ 39

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3.2.2 Power System Modelling in RMS and EMT ............................. 40

3.2.3 Generic Test Case 1: Frequency Performance in the Frequency

Containment Period ........................................................... 53

3.2.4 Generic Test Case 2: Large-Disturbance Rotor Angle Stability

and Small-Disturbance Voltage Stability ............................... 56

3.2.5 Generic Test Case 3: Sub-synchronous Controller Interactions 59

3.3 Development of Realistic Test Cases of Medium Size ........................ 60

3.3.1 Development of Transition Scenarios ................................... 60

3.3.2 Implementation into the GB Test System ............................. 63

3.3.3 Implementation into the Irish Test System ........................... 72

4 Study of Power System Stability ........................................................... 81

4.1 Introduction ................................................................................ 81

4.2 KPI for Assessment of Frequency Performance ................................ 82

4.2.1 Frequency Performance in Containment Period ..................... 83

4.2.2 Analysis of ROCOF and NADIR using Generic Test Case 1 ....... 86

4.2.3 Proposition of KPI for Assessment of Frequency Performance 102

4.2.4 Recommendations and Usage in Control Room ................... 111

4.2.5 Validation with the Irish System ....................................... 113

4.3 KPI for Large-Disturbance Rotor Angle Stability ............................. 120

4.3.1 Introduction ................................................................... 120

4.3.2 Decision Trees Background ............................................... 122

4.3.3 Background of MVMO ...................................................... 125

4.3.4 Outline of the Proposed Method of Selecting Key Variables ... 125

4.3.5 Test Results with Generic Test Case 2 ................................ 128

4.3.6 Test Results on the GB System ......................................... 135

4.3.7 Conclusions and Recommendations ................................... 141

4.4 KPI for Small-Disturbance Voltage Stability ................................... 143

4.4.1 Introduction ................................................................... 143

4.4.2 Definitions ...................................................................... 144

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4.4.3 Proposed Indicator: Calculation Procedure .......................... 149

4.4.4 Results for Generic Test Case 2......................................... 151

4.4.5 Validation on the GB Power System ................................... 154


4.5 KPI for Sub-Synchronous Controller Interactions ........................... 158

4.5.1 Introduction ................................................................... 158

4.5.2 Assumptions ................................................................... 159

4.5.3 Definitions ...................................................................... 160

4.5.4 Calculation Procedure ...................................................... 162

4.5.5 Results for different Case Studies ...................................... 169


4.5.7 Control Room Implementation .......................................... 175

A Generic Test Cases ............................................................................ 176

B Transition Scenario Implementation .................................................... 183

B.1 Implementation into the GB Test System ...................................... 183

B.2 Implementation into the Irish Test System ................................... 188

C Assessment of KPIs in the Irish System – Supplementary Information ..... 194

C.1 Generation Dispatches – WINTER PEAK ........................................ 194

C.2 Generation Dispatches – SUMMER PEAK ....................................... 196

D Use of Inertia for Frequency Stability KPI ............................................. 198

Bibliography .......................................................................................... 199

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List of Figures

Figure 2.1 Classification of transients according to their classical time frame t, their

eigenvalue groups 𝜆 and their expansion [8]. ......................................................... 26

Figure 2.2 Phenomena time scales in electric power systems [11]. ........................................... 26

Figure 3.1 Overview of the model problem. ........................................................................... 40

Figure 3.2 General example of the DSL components implementation. ....................................... 42

Figure 3.3 Controller structure of the wind turbine model in PowerFactory. ............................... 44

Figure 3.4 External data file selection of wind turbines in PowerFactory. ................................... 45

Figure 3.5 Interface for the connection of the wind model to the grid. ...................................... 45

Figure 3.6 Structure of WP controller proposed by IEC 61400-27-1. ......................................... 46

Figure 3.7 Grid interface of a wind park with two types of wind turbines. ................................. 47

Figure 3.8 Performance of active power injected into the grid for the wind turbine models (WT

type 4 in red and WT type 3 in green) in the GB test system. ................................... 47

Figure 3.9 Single 3.6 MW DFIG connected to an equivalent voltage source through a 50x unit

multiplier. .......................................................................................................... 49

Figure 3.10 Electrical structure of DFIG electromechanical system. ............................... 50

Figure 3.11 (a) initialisation of Detailed DFIG Model and (b) detailed DFIG Response

to 150 ms 3-phase SC at the PCC. ........................................................................ 51

Figure 3.12 Overview of the external network connection. ........................................... 51

Figure 3.13 Overview of the type-4 wind turbine module. ............................................ 52

Figure 3.14 Initialisation of Detailed Type 4 Model. ..................................................... 52

Figure 3.15 Modified PST16 benchmark system. ......................................................... 53

Figure 3.16 Simplified overview load dispatch scenarios (modified PST16 system). ......... 55

Figure 3.17 Modified generic test case 2. ................................................................... 57

Figure 3.18 Modified IEEE 9 Bus System – Single Line Diagram. ................................... 58

Figure 3.19 Generic Test Case SSCI – Single Line Diagram. ......................................... 59

Figure 3.20 Extended Model for SSCI – Single Line Diagram. ....................................... 60

Figure 3.21 The S-curve model of transitions. ............................................................ 61

Figure 3.22 Great Britain reduced transmission system (from [49] - Figure 3.1, pp.

74). ........................................................................................................... 64

Figure 3.23 Overview of matching process with the work flow. ..................................... 65

Figure 3.24 Mapping of the 5 ETYS regions onto the 29 zone network model. ................. 65

Figure 3.25 Steps to relate the National Grid information with the existing reduced GB

model. ........................................................................................................... 66

Figure 3.26 Development of conventional generation and PEIG (Gone Green & No

Progression). ..................................................................................................... 67

Figure 3.27 Node bus structure in the reduced GB system (from [49] - Figure 3.2, pp.

76). ........................................................................................................... 69

Figure 3.28 PowerFactory Data manager with the 9 transition scenarios archives. ........... 69

Figure 3.29 Procedure to create transition scenarios in the GB system. .......................... 70

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Figure 3.30 Connection of offshore wind park to the grid. ............................................ 71

Figure 3.31 Connection of onshore wind park to the grid. ............................................ 71

Figure 3.32 Connection of synchronous generators to the grid in all scenarios. ............... 72

Figure 3.33 All Island Transmission System (July 2016) [55]. ...................................... 74

Figure 3.34 Visualisation of the Irish Grid in the PowerFactory model. ........................... 76

Figure 3.35 Visualisation of a Transmission Station in the model of the Irish system. ...... 77

Figure 3.36 Location of aggregated wind farms in the model of the Irish system. ............ 80

Figure 4.1 Approach for the study of power system stability. ................................................... 81

Figure 4.2 Definition of key performance indicator: (a) Estimation of distance to instability

from clearly defined relationship; (b) Estimation of distance to instability based on

inference (no clearly defined relationship).............................................................. 82

Figure 4.3 Illustration of different slopes for different values of inertia. ..................................... 83

Figure 4.4 Illustration of the required points for ROCOF computation. NADIR is highlighted. ........ 85

Figure 4.5 Procedure for automated simulation and data extraction by combining

PowerFactory, Python, Matlab, and Excel. SS_DB stands for database of initial

conditions (steady-state), whereas time_DB stands for database of time responses

of system variables. ............................................................................................ 87

Figure 4.6 Frequency responses, Case 1: Conventional power plants with synchronous

generation in all areas. ........................................................................................ 89

Figure 4.7 Frequency responses, Case 5: Areas A and C with all conventional plants in

operation, Area B with only one conventional plant in operation. .............................. 89

Figure 4.8 Frequency responses, Case 10: Area A with all conventional plants in operation,

Area B with 100% penetration of wind generation, Area C with only one

conventional plant in operation............................................................................. 90

Figure 4.9 Frequency of the voltage at node 21, Case 10: Area B with 100% penetration of

wind generation. ................................................................................................ 90

Figure 4.10 Procedure for data processing of frequency response and calculation of

ROCOF and NADIR by using Matlab and Microsoft Excel. .......................................... 92

Figure 4.11 Synchronous generators’ frequency response to an imbalance caused by

10% generation loss, the frequency associated to the COI is shown by the red

dotted line. ........................................................................................................ 93

Figure 4.12 Frequency of the COI. The time window for ROCOF computation is

highlighted in red. .............................................................................................. 93

Figure 4.13 ROCOF vs kinetic energy for different dispatch configurations. Generic test

case 1. ........................................................................................................... 94

Figure 4.14 NADIR vs kinetic energy for different dispatch configurations. Generic test

case 1. ........................................................................................................... 95

Figure 4.15 ROCOF in generic test case1, Summer profile. Effect of ZIP load. ................. 96

Figure 4.16 NADIR in generic test case1, Summer profile. Effect of ZIP load. ................. 97

Figure 4.17. ROCOF in generic test case1, winter profile. Effect of ZIP load. .................... 98

Figure 4.18. NADIR in generic test case1, winter profile. Effect of ZIP load...................... 98

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Figure 4.19 ROCOF in generic test case1, summer profile. Different composition of ZIP

load. ........................................................................................................... 98

Figure 4.20 NADIR in generic test case1, summer profile. Different composition of ZIP

load. ........................................................................................................... 99

Figure 4.21 ROCOF in generic test case1, summer profile. Effect of induction motors. ... 100

Figure 4.22 NADIR in generic test case1, summer profile. Effect of induction motors. .... 101

Figure 4.23 ROCOF in generic test case1, summer profile. Effect of active distribution

networks. ........................................................................................................ 101

Figure 4.24 NADIR in generic test case1, summer profile. Effect of active distribution

networks. ........................................................................................................ 102

Figure 4.25 ROCOF vs kinetic energy, (for GG2020 Scenario, Winter profile). ............... 103

Figure 4.26 NADIR vs kinetic energy, (for GG2020 Scenario, Winter profile)................. 104

Figure 4.27 ROCOF for different load models and different wind penetration (GG2020

Winter). ......................................................................................................... 104

Figure 4.28 NADIR for different loads and different wind penetrations (GG2020

Winter) . ........................................................................................................ 105

Figure 4.29 ROCOF vs kinetic energy, (for GG2020 Scenario, Summer profile). ............ 105

Figure 4.30 NADIR vs kinetic energy, (for GG2020 Scenario, Summer profile). ............. 106

Figure 4.31 ROCOF vs kinetic energy for GG2020. .................................................... 106

Figure 4.32 NADIR vs kinetic energy for GG2020. ..................................................... 107

Figure 4.33 System performance for GG2020: (a) frequency of the COI for GG2020

with G11 outage at 26 s; (b) time derivative of frequency of the COI; (c) variation

of losses over time [MW]. .................................................................................. 108

Figure 4.34 Mapping of ROCOF vs kinetic energy for frequency performance KPI. ......... 110

Figure 4.35 Mapping of NADIR vs kinetic energy for frequency performance KPI. .......... 110

Figure 4.36 SMAPD vs kinetic energy for frequency performance KPI. ......................... 111

Figure 4.37 Implementation of the proposed frequency based KPI in control room. IED

stands for intelligent electronic device. ................................................................ 112

Figure 4.38 Visualisation of winter peak generation dispatches vs system kinetic

energy (MWs) as a function of wind generation. ................................................... 115

Figure 4.39 ROCOF vs System kinetic energy relationship, Summer and Winter

scenarios. ........................................................................................................ 117

Figure 4.40 Structure of a decision tree. .................................................................. 123

Figure 4.41 Flow chart of MVMO. ............................................................................ 124

Figure 4.42 Key variable selection. .......................................................................... 126

Figure 4.43 Illustration of decision trees. ................................................................. 127

Figure 4.44 Innovation of the proposed method. ....................................................... 128

Figure 4.45 Errors of decision trees for modified generic test case 2. ........................... 130

Figure 4.46 Response of G1. .................................................................................. 132

Figure 4.47 Response of wind farm. ........................................................................ 132

Figure 4.48 The influence of wind farm on rotor angle stability of G2. .......................... 133

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Figure 4.49 (left) Estimation using 59 variables; (right) Estimation using 8 key

variables . ....................................................................................................... 134

Figure 4.50 (left) Estimation using 59 variables; (right) Estimation using 8 key

variables. ........................................................................................................ 134

Figure 4.51 Errors of decision trees. Scenario 2020 of GB system. .............................. 137

Figure 4.52 (left) Results with 98 variables; (right) Results with 11 key variables. O =

Estimation; X = Simulation. ............................................................................... 138

Figure 4.53 G1 angle with a fault duration of 0.271 s. ............................................... 139

Figure 4.54 G1 angle with a fault duration of 0.272 s. ............................................... 139


Estimation; X = Simulation. ............................................................................... 140


Estimation; X : Simulation. ................................................................................ 140

Figure 4.57 Proposed implementation for decision trees. ............................................ 142

Figure 4.59 SNSP* Example. ................................................................................... 146

Figure 4.60 Test model for voltage stability. ............................................................. 148

Figure 4.61 Data Generation for the Calculation of N-VISI. ......................................... 150

Figure 4.62 Manual Data Processing: Steps for N-VISI calculations. ............................ 150

Figure 4.63 Results of V/V0 and SCC Analyses for Generic Test Case........................... 151

Figure 4.64 Critical P and SCC vs PE2L ratio. ............................................................ 152

Figure 4.65 PV and N-VISI Curves for Bus 5. ............................................................ 153

Figure 4.66 N-VISI Curves for Bus 5. ...................................................................... 154

Figure 4.67 N-VISI Curves for GB Bus 5 (GG2020).................................................... 155

Figure 4.68 N-VISI Curves for GB Bus 5. ................................................................. 155

Figure 4.69 Power System Boundaries. .................................................................... 160

Figure 4.70 Zero Crossing Over and Impedance Dip Observation. ............................... 161

Figure 4.71 Wind Turbine Damping. ........................................................................ 162

Figure 4.72 Calculation Procedure SSCI. .................................................................. 163

Figure 4.73 White Noise Excitation Implementation. .................................................. 165

Figure 4.74 Impedance Scan Comparison: Passive Impedance Scan vs White Noise

Excitation. ....................................................................................................... 166

Figure 4.75 SSCI Process 1: Grid Side Analysis......................................................... 167

Figure 4.76 SSCI – Process 2. ................................................................................ 168

Figure 4.77 SSCI – Process 3. ................................................................................ 169

Figure 4.78 Grid Side Analysis. ............................................................................... 170

Figure 4.79 Zero Crossing over for 3 Cases. ............................................................. 170

Figure 4.80 Wind Speed Influence on Damping (fR = 22 Hz). ...................................... 171

Figure 4.81 Active Power Reference Influence on Damping (fR = 22 Hz). ..................... 172

Figure 4.82 Impact of Wind Farm Size on Damping. .................................................. 173

Figure 4.83 Net Damping for fR = 22 Hz................................................................... 173

Figure 4.84 Comparison between Stable and SSCI Situation. ...................................... 174

Figure A.1 Excitation system used in steam and hydro power units. ....................................... 177

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Figure A.2 Block diagram for TGOV1 steam turbines. ............................................................ 178

Figure A.3 Block diagram for HYGOV hydro turbines. ............................................................ 178

Figure A.4 Power System Stabiliser block diagram. .............................................................. 179

Figure A.5 Flow chart of adopted approach to run simulations. OC_db stands for operating

condition data base, whereas time_DB is the data base of time responses. .............. 181

Figure A.6 Flow chart to get the elements that cause the biggest impact in steady state

conditions. SS_DB stands for data base of steady-state results. PFI denotes power

flow indicator, a measure of the loading of each component. .................................. 182

Figure B.1 Power flow in the Scottish transmission network ([46] - Figure 3.4, pp 31). ............. 184

Figure B.2 Power Flow in the North England transmission network ([46] - Figure 3.5, pp 54). ... 184

Figure B.3 Dynamic representation of general load. .............................................................. 193

Figure D.1 ROCOF vs Inertia, generic test case 1. ................................................................ 198

Figure D.2 NADIR vs Inertia, generic test case 1. ................................................................. 198

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List of Tables

Table 1.1 Ranking and categorisation of identified stability issues [2]. ..................................... 21

Table 1.2 Model problems and related stability issues............................................................ 22

Table 2.1 Overview of the discussed requirements and their assigned category; Brackets ()

indicate technology dependence or partial applicability. ........................................... 31

Table 2.2 Availability of several grid features with regard to different technologies. .................. 37

Table 3.1 Power system modelling in PowerFactory. .............................................................. 41

Table 3.2 Power system modelling in PSCAD. ....................................................................... 48

Table 3.3 DFIG General Parameters. ................................................................................... 50

Table 3.4 Wind turbine T4 General Parameters. .................................................................... 52

Table 3.5 Load and generation distribution in the PST 16 benchmark system. .......................... 54

Table 3.6 Wind parks and active power generation rating (modified PST16 system). ................. 54

Table 3.7 Initial conditions for the analysis of large-disturbance rotor angle stability. ................ 57

Table 3.8 IEEE 9 Bus System – Initial Conditions. ................................................................. 58

Table 3.9 Ratio of wind generation installation. Based on the information provided in [50]......... 67

Table 3.10 Total load demand in the GB system over the years. ............................................... 68

Table 3.11 Line data for offshore wind park connection. .......................................................... 71

Table 3.12 Transformer data for offshore wind park connection. ............................................... 71

Table 3.13 SVS data (biggest value) for offshore wind park connection. .................................... 71

Table 3.14 Generation and Load Data in Ireland baseline model. .............................................. 78

Table 4.1 Synchronous generator dispatch for Winter season (in MW). .................................... 88

Table 4.2 Recorded system states..................................................................................... 129

Table 4.3 Decision tree parameters. .................................................................................. 130

Table 4.4 Weight factors obtained when training decision trees with modified generic test

case2. ............................................................................................................. 131

Table 4.5 Synchronous power and wind power. .................................................................. 135

Table 4.6 Wind penetration levels. .................................................................................... 135

Table 4.7 Recorded variables in the north area. .................................................................. 136

Table 4.8 Decision tree parameters. .................................................................................. 136

Table 4.9 Selected key variables. Scenario 2020 of GB system. ............................................ 137

Table 4.10 SNSP Comparison. ............................................................................................ 147

Table 4.11 Classification of Interactions in Power Systems..................................................... 158

Table 4.12 Definition of Parameters. ................................................................................... 161

Table 4.13 Impedance Scanning Methods. ........................................................................... 163

Table 4.14 Grid Side Damping. ........................................................................................... 171

Table 4.15 Wind Farm Side Damping. ................................................................................. 172

Table A.1 Synchronous generators typical parameters (ElmSym) in generic test case 1. .......... 176

Table A.2 Synchronous generators typical parameters (TypSym) in generic test case 1. .......... 176

Table A.3 Excitation system typical parameters in generic test case 1. .................................. 177

Table A.4 Steam turbine governor typical parameters in generic test case 1........................... 179

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Table A.5 Hydro turbine governor typical parameters in generic test case 1. .......................... 179

Table A.6 PSS typical parameters in generic test case 1. ..................................................... 180

Table A.7 SVSs typical values in generic test case 1. ........................................................... 180

Table A.8 Two-winding transformer typical values in generic test case 1. ............................... 180

Table A.9 General load typical values in generic test case 1. ................................................ 180

Table A.10 Transmission lines typical values in generic test case 1. ........................................ 180

Table B.1 Foreseen Grid Reinforcements in GB Transmission System. ................................... 183

Table B.2 Mapping of NOA Boundaries and ETYS Regions to 29 Zone Network Model. .............. 185

Table B.3 Installed capacity for the 29 zones for the Gone Green scenario. ............................ 186

Table B.4 Installed capacity for the 29 zones for the No Progression scenario. ........................ 187

Table B.5 Ireland ”Slow Change” Scenario. ........................................................................ 188

Table B.6 Ireland ”Low Carbon Living” Scenario. ................................................................. 189

Table B.7 IEEEX1 AVR model: typical parameters. .............................................................. 190

Table B.8 HYGOV governor model: typical parameters. ....................................................... 190

Table B.9 IEEEG2 governor model: typical parameters. ....................................................... 191

Table B.10 WP controller – WP Q control module. ................................................................. 191

Table B.11 Type 3 and 4 WT controller – Q control module. ................................................... 192

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Abbreviations

AC

Alternating Current

AMI Angle-based Stability Margin Index

ADN Active Distribution Networks

AGC

Automatic Generation Control

aRACI Additional Reactive and Active Current Injection

aRCI Additional Reactive Current Injection

AVM

Average Value Models

AVR

Automatic Voltage Regulator

CCGT Combined Cycle Gas Turbine

CCI Clustered Controller Interactions

CHP

Combined Heat and Power

CI Controller Interactions

COI Centre of Inertia

D (D1.1) Deliverable (Deliverable 1.1)

DC

Direct Current

DE Dynamic Equivalent

DER Distributed Energy Resources

DFA Detrended Fluctuation Analysis

DFIG Doubly-Fed Induction Generator

DG Distributed Generation

DSL DIgSILENT Simulation Language

DSM Demand Side Management

DSO Distribution System Operator

EHV

Extra-High Voltage

EMS Energy Management System

EMT

Electromagnetic Transient

EMTP

Electromagnetic Transients Program

ENTSO-E

European Network of Transmission System Operators

FACTS

Flexible Alternating Current Transmission System

FCR

Frequency Containment Reserve

FFR Fast Frequency Response

FRR

Frequency Restoration Reserve

FRT Fault-Ride-Through

HV

High Voltage

HVAC High Voltage Alternating Current

HVDC

High voltage Direct Current

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HV-gate High-Value-Gate

IEEE

Institute of Electrical and Electronics Engineers

IGBT

Insulated Gate Bipolar Transistor

IL Interruptible Load

KPI Key Performance Indicator

LCC

Line commutated converter

LFSM-O

Limited Frequency Sensitive Mode – Overfrequency

LFSM-U

Limited Frequency Sensitive Mode – Underfrequency

LSC Line Side Converter

LV

Low Voltage

(n)-LVRT (no) Low Voltage Ride Through

MIC Maximum Import Capacity

MMC

Modular Multilevel Converter

MSC Machine Side Converter

MV Medium Voltage

MVMO Mean Variance Mapping Optimisation

N-VISI Normalised Voltage Instability Sensitivity Index

ODSA Online Dynamic Security Assessment

OEL

Overexcitation Limiter

OHL

Overhead Line

PE

Power Electronics

PE2L Power Electronics to Load Index

PEIG Power Electronics-Interfaced Generation

PEID Power Electronics-Interfaced Device

PLL Phase-Locked Loop

PMU Phasor Measurement Unit

PNI Parallel Network Interface

POR Primary Operating Reserve

PSS

Power System Stabiliser

PV

Photovoltaics

QSVI Quasi-Stationary Voltage Index

RG CE

Regional Group Continental Europe

RMS

Root Mean Square

ROCOF

Rate of Change of Frequency

RTDVA Real-Time Dynamic Vulnerability Assessment

SCADA

Supervisory Control and Data Acquisition

SM

Submodules

SMADP Sum of Maximum Active Power Deviation

SNSP System Non-Synchronous Penetration

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SSC Short Circuit Capacity

SSCI Sub-Synchronous Controller Interactions

SSR Sub-Synchronous Resonance

SSSC

Static Synchronous Series Compensators

SSTI Sub-Synchronous Torsional Interaction

STATCOM Static Synchronous Compensators

SVC

Static var Compensator

T (T1.1) Task (Task 1.1)

TCR

Thyristor-controlled Reactors

TCSC

Thyristor-controlled Series Compensators

TSC

Thyristor-switched Capacitors

TSI Transient Stability Index

TSO

Transmission System Operator

TSR

Thyristor-switched Reactors

UEL

Underexcitation Limiters

UFLS

Underfrequency Load Shedding

UMEC

Unified Magnetic Equivalent Circuit

UPFC

Unified Power Flow Controllers

VSC

Voltage-Source Converter

WAMS

Wide Area Monitoring System

WECC

Western Electricity Coordinating Council

WNE White Noise Excitation

WP (WP1) Work Package (Work Package 1)

WSAT Wind Security Assessment Tool (EirGrid)

WTG

Wind Turbine Generator

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1 Introduction

1.1 Motivation In the future, Power Electronics (PE) will be applied more often in power systems to connect load

and (renewable) generation. As PE-interfaced generation and load behave differently than

conventional generation and load, it is of importance to study the possible impact of increasing

amounts of PE on the dynamics and stability of the power system. Also, power system analysis

methods need to be reviewed in terms of their feasibility to sufficiently reflect the performance

characteristics of a given power system with a high PE penetration. This is done in the MIGRATE

project.

1.2 Deliverable 1.2 in the Context of MIGRATE and WP1

Work Package 1 (WP1) of the MIGRATE project addresses power system stability issues of

transmission grids under high penetration of Power Electronics (PE). It thereby focusses on the

period in which the transition from a 0% PE-based power system to a 60-70% PE-based power

system takes place. During this transition period, PE is introduced in the current High-Voltage

Alternating Current (HVAC) infrastructure and operated considering existing rules and requirements,

and with technology either being currently or shortly available.

The main objectives of WP1 are [1]:

1. To identify and prioritise the stability-related issues faced by the TSOs considering different

network topologies, geographical locations and penetration levels of PE (generators, HVDC

converters, FACTS, loads, etc.).

2. To develop novel approaches and methodologies able to analyse and mitigate the impacts of PE

penetration on power system stability based on simulations, laboratory scale experiments and

PMU measurement methods (data supplied by WP2).

3. To propose control strategies so as to further tune and coordinate existing system controls in

order to maximise the penetration level of PE considering the current operating rules, the

existing control and protection devices and the available degrees of freedom in the network

codes (RfG and HVDC grid codes as well as the DCC).

4. To validate the use of a monitoring approach of the PE penetration based on online PMU

measurement methods developed in WP2.

The first objective was addressed in Task 1.1 (T1.1) and Deliverable 1.1 (D1.1). The first objective

is further elaborated in tasks T1.2 and T1.4, of which the results are described in this deliverable

(i.e. D1.2). This Deliverable thereby mainly contributes to Objective 1 and lays the ground work for

Objective 2 of the MIGRATE project [1]:

O1: ‘To develop a methodology to be shared by TSOs which allows an improved

understanding and monitoring of the system dynamic behaviour (as PE penetration grows

when connecting new generation and load technologies) and an assessment of the time to

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reach unmanageable system stability issues of any control zone of the pan-European

transmission system (using existing technologies and present grid codes)’

O2: ‘To design and implement pilot tests with relevant use cases which

demonstrate, mainly in the UK and Iceland, how existing infrastructures of PMU

sensors can support the real life monitoring and control of the possible stability

issues as defined within the above (O1) methodology.’

1.3 Main Findings from Deliverable 1.1 In Deliverable 1.1 [2], the research results of Task 1.1 were described. The main objectives were:

To identify and prioritise power system stability issues brought by the increasing penetration of

PE in the different control zones covered by the TSOs of the consortium.

To assess, in collaboration with PE manufacturers, the capabilities of existing (and to be

deployed in the near future) grid-connected PE devices considering requirements imposed by

the existing network codes, and establish the extent of potential improvement of current system

control practices and infrastructure (without modifying the control hardware) in order to

facilitate the integration of PE devices within the framework of the existing network codes.

In order to identify all power system stability issues brought by the increasing penetration of PE in

the different control zones covered by the TSOs of the consortium, a questionnaire was issued to

all MIGRATE TSOs and the majority of TSOs within ENTSO-E. The results obtained from the TSO

questionnaire were complemented by a literature survey. Based on these two sources, eleven

power system stability issues were identified and described in detail. In order to prioritise the

identified issues, a second questionnaire was issued to all TSOs within the MIGRATE consortium.

The stability issues were assessed with respect to three dimensions of impact: severity, probability

and expected timeframe. As a result of these ratings, the issues were ranked with respect to their

overall impact on power system stability. Rank 1 identifies the issue with the largest overall impact.

The ranking results are shown in Table 1.1.

The stability issues with the highest priority were developed into “model problems”. Each model

problem describes the modelling and simulation needs to enable a suitable (i.e. accurate)

recreation of a given stability phenomenon, when the studied system is close to or in an unstable

condition. Each KPI presented in Chapter 4 is developed based on the corresponding model

problem. The state-of-the-art modelling and simulation approaches were documented as well,

together with the modifications in the state-of-the-art modelling and simulation required due to

increasing PE penetration.

Furthermore, a high level description of the model problems was given as a starting point for

further analysis in Deliverable 1.2. Basically, there will be four model problems: for frequency

performance in the frequency containment period, for large-disturbance rotor angle stability, for

small-disturbance voltage stability and for sub-synchronous controller interactions. The stability

issues with the lowest ranking will not particularly be investigated in the remaining tasks of WP1.

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The literature review and discussions with industry experts within the MIGRATE consortium

revealed that there is lack of consensus on a clear and unique definition of harmonic stability nor of

a generic test case.

Table 1.1 Ranking and categorisation of identified stability issues [2].

Rank Stability category Issue

1 Frequency stability Issue 3: Decrease of inertia

2 Not classified1 Issue 11: Resonances due to cables and PE

3 Rotor angle stability Issue 2: Reduction of transient stability margins

4 Frequency stability Issue 4: Missing or wrong participation of PE-connected

generators and loads in frequency containment

5 Not classified1 Issue 10: PE controller interaction with each other and passive

AC components

6 Voltage stability Issue 5: Loss of PE devices in the context of fault-ride-through

capability

7 Voltage stability Issue 7: Lack of reactive power

8 Rotor angle stability Issue 1: Introduction of new power oscillations and/or reduced

damping of existing power oscillations

9 Voltage stability Issue 8: Excess of reactive power

10 Voltage stability Issue 6: Voltage-dip-induced frequency dip

11 Voltage stability Issue 9: Altered static and dynamic voltage dependence of loads 1The term “Not classified” refers to non-appearance of the reported issue as a formal category of existing and widely accepted classification of power system stability phenomena [3].

Table 1.2 gives an overview of the model problems and related stability issues. It must be

mentioned that stability issue 11: “Resonances due to cables and PE” is a power quality issue and

is therefore a topic addressed in WP5. Only four model problems are developed in T1.4 and a

description of the modelling aspects is given in Chapter 3, whereas simulation results (T1.2) are

shown in Chapter 4 of D1.2.

In Deliverable D1.1, the requirements for grid-connected PE devices were described as well. The

network codes identified to be most relevant for the grid connection of PE are:

Network Code on requirements for grid connection of generators (NC RfG),

Network Code on requirements for grid connection of high voltage direct current

systems and direct current-connected power park modules (NC HVDC),

Network Code on Demand Connection (NC DCC)

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Table 1.2 Model problems and related stability issues.

Model problem Stability issue

“model problem for

frequency performance

in the frequency

containment period”

Issue 3: Decrease of inertia

Issue 4: Missing or wrong participation of PE-connected generators

and loads in frequency containment


large-disturbance rotor

angle stability”

Issue 2: Reduction of transient stability margins


small-disturbance

voltage stability”

Issue 5: Loss of devices in the context of fault-ride-through capability

Issue 7: Lack of reactive power


sub-synchronous

controller interactions”

Issue 10: PE controller interaction with each other and passive AC

components

Based on the requirements stated therein, the capabilities of PE-interfaced generation were

preliminarily assessed. For this, each requirement was categorised while each category meant a

qualitative evaluation of the necessary attention to meet the respective requirement. Many

requirements were assessed to be already met by current PE devices or to require little action.

Requirements which demand an active power reserve may impose larger effort. However, for a

more comprehensive and precise assessment, manufacturer collaboration is required. It was

decided to extend the research considering capabilities of grid-connected PE devices and potential

improvement of current system control practices and infrastructure and to present the results of

this research in Deliverable D1.2.

1.4 Scope, Objectives and Approach of Tasks 1.2 and 1.4 The results of Task 1.1 and Deliverable 1.1 are used to analyse the most critical stability issues

related to PE and to develop adequate Key Performance Indicators (KPIs) to measure the distance

to instability. This work is mainly performed in Task 1.2, of which the objectives are:

To extensively use the portfolio of existing numerical simulation methods in order to address

each of the model problems and to understand the sources of instability.

To propose adequate KPIs for estimating the distance to instability and for determining the

maximum penetration of PE.

To propose a final list of available models and methods to address the identified model problems.

To provide information on the performance of the used methods when conducting transient

stability analysis of each identified instability phenomenon and associated model problem.

Task T1.2 concerns with the development of KPIs for assessing the distance to instability for each

model problem listed in Table 1.2. In Task 1.4, generic test cases and transition scenarios are

developed, which are used to study the model problems. The main objectives of T1.4 are:

To create a few generic test cases to study the identified model problems and stability issues.

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To develop a baseline test case based on existing systems (Great Britain & Ireland), and

describe future transition scenarios for PE, to be progressively integrated until 2030.

To select a reduced set of manageable generic KPIs, based on the KPIs as developed in T1.2.

Task T1.4 starts with the identified stability issues from task T1.1 and combines them into several

models problems, thereby mainly following the traditional classification of stability phenomena.

These models problems are then developed into a few generic test cases, used to study the specific

stability phenomena. Two test systems are prepared for validation purposes, i.e. the Great Britain

and the Ireland system. Transition scenarios up to 2030 are described and implemented into the

Great Britain system to reflect the increase of PE in the future, whereas for the Irish test system

scenarios (in which wind generation was gradually increased) were developed based on the

baseline case of 2016.

1.5 Outline of Deliverable 1.2 This report is organised as follows. In chapter 2, the state-of-the-art of power system modelling

and simulation practices are described. This chapter also describes a review of the capabilities of PE

with respect to network code requirements. In chapter 3, the simulation approach for power

systems with PE is discussed. First, the generic test cases are developed for the four model

problems, as initially described in D1.1. Secondly, transition scenarios for analysing the impact of

increasing levels of PE are defined and implemented. Chapter 4 discusses the current practice of

indicators and development of different KPIs to measure the distance to instability. The KPIs are

developed per model problem.

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2 State-of-the-Art Power System Modelling and

Simulation

2.1 Introduction

This chapter provides an overview of the state-of-the-art in modelling and simulation of power

systems in terms of stability analysis of the five highest-ranked stability issues (see Table 1.1). The

description is mainly based on standard literature, recent grid studies, standards and power system

simulation software documentation. It is complemented by answers of experts of various European

Transmission System Operators (TSOs) to the TSO questionnaire (as described in [2]) and by

current scientific publications. Since the development process of specific power system models is

not only dependent on the scope of the study but also on various other factors like the specific

system’s characteristics, the availability of model parameters and personnel resources, state-of-

the-art system models typically vary within a certain range.

First, fundamental characteristics of power systems and the subsequent classification of power

system dynamic responses into different time ranges resulting in different power system modelling

approaches are described in Section 2.2. Subsequently, system modelling approaches of the

presented device models are briefly described in Section 2.3. The description is complemented by a

summary of the TSO questionnaire answers about their current way of conducting dynamic grid

studies and device modelling. Next, a section is presented with a manufacturer review of PE

capabilities and network code requirements in Section 2.4. Conclusions are drawn in Section 2.5.

2.2 Power System Modelling

Under steady-state conditions, the Root Mean Square (RMS), i.e. phasor, values of all variables

describing a power system during a certain period of time are constant and in a constant relation to

each other. In steady-state operation, the power system can be modelled using considerably

simplified models of components, so-called steady-state models. In steady-state analyses, like

power flow analysis, algebraic equations are used to represent the network elements and the

overall network is expressed by basic nodal equations. By this, the system dynamics, expressed

through differential equations, can be neglected.

Following a perturbation, such as sudden changes in generation, load, or network topology (e.g.

switching or short circuits), the state variables vary very quickly over the course of time. In such

cases, the dynamic and transient behaviour of the power system in the time domain must be

considered. In order to analyse this system behaviour, the devices and their associated controllers

have to be modelled in more detail compared to steady-state conditions. Modelling depth is

strongly dependent on the simulation purpose. In time-domain modelling, the time-dependent

behaviour of each single network element (the dynamics of the power system) is represented

through differential equations and partial differential equations for lines which are solved using

step-by-step numerical integration techniques [4].

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A fundamental characteristic of a power system is the multi-time scale character [5], [6]. This has

to be considered and exploited to improve computational efficiency of the simulation algorithms.

The underlying fact of this characteristic implies that the interactions between different energy

storages like inductances, capacitances or rotating masses of the electric power system model

show different dynamic phenomena with different speeds which can clearly be distinguished. Thus,

the time scale of transients in such models can be separated using e.g. singular perturbation

method discussed in [7]. Based on this methodology, the slower variables are assumed to be

constant during the fast transients. Furthermore, the fast transients are assumed to be already

decayed, if the slower phenomena are the subject of investigation [6].

In this respect, it should be noted that in most cases, the analysis of the fast phenomena is locally

limited (in terms of the grid area that needs to be studied), while the analysis of the slower ones is

associated with relatively larger grid areas. For instance, in [8], the following three time scales of

the power system are defined:

Short-time range involves fast electromagnetic transients (0.5-500 kHz) caused by energy

exchange between inductive and capacitive energy storages within the electrical network with

the milliseconds range as the time frame of interest.

Medium-time range involves slower interactions between inductive energy storages, rotor

windings and mechanical energy storages. These energy exchanges are referred to as electro-

magneto-mechanical transients (1-100 Hz) with a time frame of interest of seconds.

Long-time range involves exclusively interactions between long-term mechanical energy

storages, such as secondary reserves. These so-called electromechanical transients (0.5-5 Hz)

have the time frame of interest in the minute range.

Figure 2.1 depicts the three time scales described above, their respective eigenfrequencies, their

characteristic transients and their affected network areas. In time-domain simulations, the

representation of the passive electrical network is crucial. To analyse long- and medium-time range

dynamic phenomena, the passive electrical network is sufficiently characterised by its steady-state

behaviour. Therefore, they are generally categorised as quasi-steady-state phenomena (e.g.

transient stability, control procedures, low-frequency oscillation behaviour) and are simulated using

RMS component models. Here, the passive electrical network is represented by steady-state

models and solely the fundamental oscillation of voltages and currents is considered through their

RMS. If the analysis of fast electromagnetic transients (e.g. switching surges, lighting strikes,

ferroresonances7) is the topic of investigation, the power system area of interest is simulated using

electromagnetic transient (EMT) models with a high level of detail. In EMT simulations, in addition

to the dynamics considered in RMS simulations, the dynamic behaviour of passive network

elements is also taken into consideration. Thus, voltages and currents are expressed by their

instantaneous values [9]. Figure 2.2 shows various phenomena and their time scales in electric

power systems.

7 Ferroresonance refers to all oscillation phenomena between non-linear inductances (power transformers, voltage measurement inductive transformers, etc.) and capacitors (cables, long lines, etc.) [10].

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1: individual devices around the fault location2: network areas around the fault location3: large network areas

Electro-magnetic

Short-time range

Medium-time range

Long-time range

Expansion

Time in s

Normalized eigenvalue

Electromechanical

Electro-Magneto-mechanic

Figure 2.1 Classification of transients according to their classical time frame t, their eigenvalue

groups |𝜆| and their expansion [8].

10-7 10-5 10-3 0.1 10 103 105

(sec)

Switching Surges

Lightning Propogation

Stator Transients and Subsynchronous Resonance

TransientStability

Governor and LoadFrequency Control

Boiler and LongTerm Dynamics

10-7 10-5 10-3 0.1 10 103 105

(sec)

Switching Surges

Lightning Propogation

Stator Transients and Subsynchronous Resonance

TransientStability

Governor and LoadFrequency Control

Boiler and LongTerm Dynamics

Figure 2.2 Phenomena time scales in electric power systems [11].

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Another essential factor in time-domain simulations is the length of the integration time step which

is linked to the smallest time constants of the system. Due to the higher frequencies that have to

be covered in EMT studies compared to RMS studies, the time steps in EMT simulations need to be

considerably shorter. This is why the passive network elements in EMT simulations are modelled by

their dynamic representation. The dynamic phenomena in medium-time and long-time range can

also be simulated using EMT simulation. The calculation time would increase unnecessarily in this

case. Hence, for an efficient simulation of a certain phenomenon, it is necessary to adjust the

integration time step. For long-term simulations, it is advantageous that computer programmes

support a simulation step size control which increases the step size automatically after fast

transients have decayed [9].

2.3 Power System Simulation Practices

2.3.1 Simulation of Power System Dynamic Response

As mentioned in Section 2.2, in order to analyse long- and medium-time range dynamic

phenomena (quasi-steady-state phenomena), the steady-state representation of passive electrical

networks in the frequency domain is sufficiently accurate (i.e. a set of linear algebraic equations).

In long-time range studies, the performance of transformer tap changers and phase-shifting angle

controls cause variations in the network admittance matrix as a function of bus voltages and time.

In short-time range simulations, the passive electrical network is represented through its EMT

models (i.e. a set of differential and partial differential equations). Static loads are represented also

through algebraic equations and can be represented as part of the network equations (network

admittance matrix) in case of quasi-steady-state studies. The dynamic behaviour of the various

dynamic devices (e.g. generating units, dynamic loads, HVDC converters, static var compensators,

synchronous condensers, their respective controls, etc.) is represented through linear or non-linear

differential equation systems [12]. The network equations, the equations of the dynamic devices

and the equations of the non-linear static loads are interfaced by means of equivalent current

injections of the devices and the non-linear loads with the network. The current injections from the

dynamic devices are dependent on their state variables [13]. The resulting overall system

equations can be solved for each time step as an algebraic-differential equation system can be

solved using a wide range of approaches depending on the modelling details and the numerical

methods [12].

The numerical methods for solving the differential equation system are categorised in implicit (e.g.

trapezoidal rule) and explicit methods (e.g. Euler, Runge-Kutta methods). In [12], a general

description of these methods is provided. A comparison between discretisation using implicit multi-

step methods and numerical integration using explicit methods leads to the following advantages

and disadvantages:

- In contrast to implicit methods which solve the non-linear differential equation systems

iteratively, the numerical integration using explicit numerical methods requires generally lesser

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computation time per time step. However, to avoid instabilities, the time steps have to remain

small [13].

- Because of the better stability properties of the implicit methods, the step size can be increased

considerably after decaying the fast transients. Therefore, regarding the long-time range

simulations, these methods exhibit major advantages. In these methods, the higher

computation time per time step will be compensated through a lower number of time steps [13].

The standard programs to simulate transients in the power system can be roughly categorised into

programs to analyse electromechanical transients (medium- and long-time range) and programs to

study electromagnetic transients (short-time range). Electromechanical transient programs (e.g.

PSS/E or EUROSTAG) use a steady-state network model. EUROSTAG is capable to analyse the

whole range of electromechanical transients (from a few seconds to minutes), because of its time

step adjustment feature. In principle, electromagnetic transient programs (e.g. EMTDC8) can also

analyse electromechanical phenomena. However, it will not be efficient, because they include a

highly detailed network model whose analysis demands very small time steps. NETOMAC and

DIgSILENT can analyse both electromagnetic and electromechanical transients, because they

support a highly detailed transient as well as a steady-state network model. Other important

factors to be considered with respect to simulation programs are speed and robustness of their

numerical methods as well as completeness of their model library [13].

2.3.2 Review on Current TSO Practices

Since power system stability assessment is a crucial task for every TSO, their current way of

performing dynamic network studies strongly determines the state-of-the-art. The following

summarises the answers of 21 ENTSO-E TSOs given to a questionnaire issued in Q2/2016 9

regarding state-of-the-art modelling and simulation of power system stability.

How are dynamic studies currently performed: RMS or EMT?

Dynamic studies regarding power system stability are predominantly performed in RMS. Classical

stability aspects like frequency stability, voltage stability and rotor angle stability are exclusively

studied using RMS simulation environments. Most (but not all) of the TSOs perform EMT studies as

well, but mostly to study specific phenomena of certain devices like harmonics, saturation effects,

transient overvoltages and switching of extra-high voltage (EHV) cables (often in the planning

stage). However, few TSOs mentioned controller interactions between HVDC converters and WTG

converters or between WTG converters connected to nearby buses to be within the scope of EMT

simulations.

What is the frequency for performing these studies?

The frequency varies widely. Most TSOs perform RMS stability studies a few times a year as part of

the long-term system planning and/or triggered by events. However, one TSO mentions that it

8 EMTDC: Electromagnetic Transients including DC. 9 For more information on the questionnaire and a summary covering the full questionnaire please refer to MIGRATE Deliverable 1.1 “Report on systemic issues” [2].

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performs RMS dynamic studies in real-time every 15 minutes. The connection of new equipment is

also accompanied by dynamic studies; both RMS and EMT (most often mentioned are HVDC

converters, large wind farms and FACTS).

What stability aspects are being studied?

All classical stability aspects are mentioned in the answers, but most of the TSOs focus on

phenomena they decided to monitor more closely due to special characteristics in their control

zones. In this context, transient stability is most often mentioned, but voltage stability and small-

signal rotor angle stability are often monitored too. Frequency stability is mentioned least often,

but this may be due to the fact that frequency stability is often studied by ENTSO for the whole

regional groups’ synchronous areas. Controller interactions, which have been defined in D1.1 to be

a stability issue, are also mentioned.

What is the geographical size of the grid model you use for the different stability aspects?

Most TSOs of Regional Group Continental Europe (RG CE) use a model of their own control zone

and a (sometimes simplified) representation of their neighbouring control zones for RMS studies.

Some use the ENTSO-E CE dynamic study model covering the whole synchronous area. TSOs of

other RGs typically model the whole synchronous area (except for RG Baltic, where the

neighbouring countries, which are no ENTSO-E members, are not fully represented). Few TSOs

gave an answer differentiated with respect to stability phenomena. However, the answers given

imply a larger size for small-signal rotor angle stability and frequency stability and a smaller size

for transient stability and voltage stability. The geographical size of models for EMT studies

strongly depends on the scope of the study. In general, the geographical size is smaller, often

focusing on few devices and buses.

Which utilities are modelled in which detail? Which control systems are modelled in which detail?

RMS:

Generally, the whole own EHV and sometimes HV network is modelled (overhead lines (OHLs),

cables and transformers). Most TSOs also mention models for SVC and HVDC converters/links

(generic or vendor). Little information is given about the level of detail applied to other control

zones. As some TSOs use a mutual dynamic model, the OHL, cables and transformers are probably

modelled in a similar level of detail. Likewise, little information is given about modelling the

surroundings of the area of detailed modelling. One TSO mentions to use a simplified

representation available from its supervisory control and data acquisition (SCADA) system.

Network protection – if mentioned – is modelled through contingency definitions. Underfrequency

Load Shedding (UFLS) is mentioned to be modelled but without further specification.

Usually, all power plants with synchronous generators are modelled in detail (some TSOs mention

certain thresholds between 5 MW and 100 MW above which the generators are modelled in detail).

Normally, these include models of the synchronous generator, the turbine governor, the turbine,

the excitation system (including PSS) and the AVR. Some TSOs mention to model excitation

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limiters and protection schemes as well. Several TSOs model large wind farms, usually with generic

models10.

One TSO also models smaller wind clusters and Combined Heat and Power (CHP) clusters with

aggregated models. Typically, the models are more detailed and specific for the TSO’s own control

zone. Generation in neighbouring control zones is often modelled less detailed and parameterised

less specifically.

EMT

Little information is given about the level of detail of EMT models. In general, EMT models are more

detailed and more often provided by the respective device manufacturer or owner.

How is the load currently being modelled for your dynamic studies? Do you have generic models? If so, how is the parameterisation being done? Do you have user defined load models? If so, how is the parameterisation being done?

Usually, the load is modelled as static load, most often with a breakdown into constant power,

constant current and constant admittance components (ZIP load), but some TSOs just use constant

impedance loads. This includes some voltage dependency of the loads. Frequency dependency is

not mentioned by most of the TSOs. User defined load models are normally not used, except in

specific situations for some large industrial loads. One TSO mentions that distributed generation is

modelled separately from the loads (while it is assumed that usually distributed generation is

included in the load model representing the distribution grid it is connected to) for distribution grids

with distributed generation.

2.4 Manufacturer Review of PE Capabilities and Network Codes

Within Deliverable D1.1 [2], several Network Codes where summarised and a list of requirements

for grid-connected Power Electronics (PE) was derived. This list was then preliminarily assessed

from an academic point of view with regard to technical feasibility and impact on PE manufacturers.

The results emphasised that requirements, which could demand additional energy storage, could

cause greater efforts by the manufacturers and that several requirements are broadly defined,

leading to uncertainties regarding the consequences for the minimum required capabilities.

Within the framework of Deliverable 1.2, ABB, Enercon, Siemens Energy Management, SMA and

Woodward were consulted as representative manufacturers of a variety of typical grid-connected

PE devices. During the discussion, the manufacturers commented on the preliminary assessment

done in D1.1 and provided an assessment of the new requirements from their point of view as well

as comments on additional PE capabilities, which are not required yet, but are available. For each

additional feature, an assessment whether it can be activated with little cost or whether it requires

10 One TSO explicitly mentions to use WECC 2nd generation model: Electric Power Research Institute (EPRI), “Specification of the Second Generation Generic Models for Wind Turbine Generators,” 2014. [available Online].

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an elaborate development process has to be made. In addition, general aspects of grid operation

with a high share of PE devices were discussed.

In this section, the anonymised results of these discussions are summarised, in order to reflect the

manufacturer’s comments regarding PE capabilities within the framework of the Network Codes. It

therefore reflects the opinion of the manufacturers, not necessarily the authors’ opinion. During the

talks, the requirements have been discussed individually. However, it proved feasible to group

several requirements and categorise them. The discussed requirements and their assigned

category within this section are depicted in Table 2.1.

Many requirements match existing technology or require minor adjustments. These are categorised

as already implemented. Requirements, which are not considered to pose difficulties, but which

have not been implemented yet, are marked as firmware modifications. Changes to the systems,

requiring major hardware or software extensions are described as system extensions. System

resizing describes requirements, like new voltage ranges, which may lead to a redesign of system

components. Several requirements may ask for additional power and therefore a power reserve or

energy storage can become necessary, depending on the concrete specification by the relevant

TSO. Some manufacturers stressed that technical capabilities will only be available in the field if

the operators of the plants either have to provide them compulsory (due to Network Code

requirements), or it is financially attractive to them.

Table 2.1 Overview of the discussed requirements and their assigned category; Brackets () indicate technology dependence or partial applicability.

Group

Requirement

Exh

au

sti

ve

req

uir

em

en

t

Alr

ead

y

imp

lem

en

ted

/

min

or c

on

cern

Fir

mw

are

mo

dif

icati

on

Syste

m

resiz

ing

Syste

m

exte

nsio

n

Po

wer r

eserve/

en

erg

y s

tora

ge

Frequency ranges X X (X)

Rate of change of frequency withstand

capability X

Limited frequency sensitive mode –

overfrequency X X

Constant output at target active power X X

Maximum active power reduction at

underfrequency X

Active power controllability and control range X X

Limited frequency sensitive mode –

underfrequency X X

Frequency sensitive mode X X

Frequency restoration control X

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Group

Requirement

Exh

au

sti

ve

req

uir

em

en

t

Alr

ead

y

imp

lem

en

ted

/

min

or c

on

cern

Fir

mw

are

mo

dif

icati

on

Syste

m

resiz

ing

Syste

m

exte

nsio

n

Po

wer r

eserve/

en

erg

y s

tora

ge

Disconnection of load due to underfrequency X X

Fault-ride-through capability of power-

generating modules connected below 110 kV X

Fault-ride-through capability of power-

generating modules connected at 110 kV or

above

X

Loss of stability11 X

Rate of change of active power X (X)

Steady-state stability1 X X

Auto-reclosures X (X)

Black start capability11 (X) X X

Capability to take part in isolated network

operation11 (X) X

Quick re-synchronisation11 X

Voltage ranges X X

Synthetic inertia capability11 (X) X X

Post-fault active power recovery X

Provision of fast fault current11 X

Priority to active or reactive power

contribution (X) (X)

Reactive power capability at maximum active

power X

Reactive power capability below maximum

active power X

Reactive power control modes X

Power oscillation damping control (X) X

System Resizing

Several requirements can be addressed by the inverter’s sizing, i.e. expanded 𝑈-𝑄/𝑃max-profiles

require higher rated modules for the same active power rating of the inverter. In addition, the new

frequency ranges are generally considered to be a minor concern for PE devices, but may require

modification of auxiliary systems like pumps. With the expected deviations from nominal grid

frequency, the tuning of filter components may have to be revalidated. The larger frequency

11 The requirement was considered to be not sufficiently specified, allowing different interpretations.

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deviations at higher harmonics may impair the output filter’s effectiveness or even excite parallel

resonances within the filter, causing large currents. The new voltage ranges do not match the

existing portfolio of available voltage classes of devices, causing an oversizing of components or

extra redesign effort. This is especially important for high-voltage facilities, as the required

minimum times at a voltage of 1.15 pu could lead to significantly oversized insulations.

Firmware Modifications

Features like Limited Frequency Sensitive Mode – Overfrequency (LFSM-O) or the priority of

reactive/active power contribution are considered to be technically feasible, but have to be

implemented. LFSM-O could be challenging for systems with a power source which cannot be

powered down dynamically, which is especially important when considering technologies apart from

Wind, PV or HVDC systems.

Even though some requirements can be fulfilled with firmware modifications, every new or updated

feature increases cost. Each modification needs to be thoroughly tested and certified, if required,

which was mentioned to be the most time-consuming part of implementation.

System Extension

Synthetic inertia capability, black start capability and the capability to take part in islanded

operation can cause significant effort in order to be implemented. It is important to note that these

requirements are non-exhaustive12 and they only apply, if demanded by the relevant TSO13. The

unspecific character of these requirements led to different interpretations of what is demanded

from PE devices.

It is important to distinguish between participating in islanded network operation and guiding

islanded network operation. Taking part in islanded operation was not considered to be generally

implemented in installed devices, but technically feasible. Guiding an isolated network is impacted

by the power capability of the grid forming entity14. Larger power sources have greater influence

on the isolated network operation, but are not necessarily designed for this operation. Therefore,

guiding isolated network operation is considered as more complex and technically challenging, as

there can be other power generating entities of larger power capacity within the isolated network

which do not operate as part of the grid forming collective and need to be synchronised. An

additional remark was made regarding devices connected at distribution level. The requirements

set by the Distribution System Operator (DSO) often demand the immediate disconnection in case

of islanded operation due to health and safety reasons. The priorities of the requirements should be

specified.

Black start capability strongly depends on the system’s power source. Additionally, modifications to

the auxiliary systems or energy storages could become necessary. The concepts are not generally

12 They are subject to further - more detailed - specification by the relevant TSO 13 Regulation (EU) 2016/631 14 Single or group of power generating units, collectively forming the grid

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implemented in existing hardware, but are imaginable for suitable technologies in the future, e.g.

Photovoltaics (PV). Technologies for isolated network operation or black start capabilities are

already available from microgrid concepts, uninterruptable power supplies or are already

implemented in High-Voltage Direct Current (HVDC) stations. Wind turbines and PV, as installed

today, lack energy storages and/or grid forming capability can therefore not black start directly or

at all times. As soon as the local grid is energised by another power source, they could contribute

to the black start.

Synthetic inertia can be requested to mimic the frequency-response reserve of conventional

generators. Some TSOs tend towards an implementation based on the rate of change of frequency,

but currently an implementation based on the deviation of frequency is accepted in many cases. If

an implementation based on the deviation of frequency is accepted, this requirement could also be

fulfilled by operating in a fast Frequency Sensitive Mode (FSM). An implementation based on the

rate of change of frequency may pose some difficulties regarding the filtering effect of the applied

calculation method, especially when considering existing Phase-Locked Loop (PLL) technology. A

detection time of 50 to 70 ms was mentioned for changes in frequency, but which strongly depends

on the implementation. It is assumed to be demanding to design an effective and robust synthetic

inertia based on this without getting susceptible to inadvertent reaction in case of fault events that

affect the frequency measurement. If the inverter operates as a voltage source, the initial reaction

could be very fast, but its current needs to be controlled strictly to never exceed the maximum

currents admitted by the PE. If concepts for synthetic inertia are used, which draw additional power

from the rotational energy of the system - thereby slowing it down [14] - additional specifications

for tolerances and recovery periods are needed.

Power oscillation damping control is already implemented in HVDC converters, but not in other PE

devices.

Power Source / Energy Storage

Many requirements can be interpreted in such a way that they make an energy storage system or

power reserve necessary. FSM and Limited Frequency Sensitive Mode – Underfrequency (LFSM-U)

require the capability to increase the output power. The LFSM-U requirement accounts for the

operating conditions of the device and the availability of prime energy. ENTSO-E described the

possibility that only power-generating units operating below maximum available power activate

LFSM-U [15].

Power reserves can be implemented by energy storages or by reducing the output power below the

maximum available power in normal operation. HVDC links have a power reserve implemented,

decreasing the transmission line’s capacity. Other concepts, i.e. using the rotational energy of a

wind turbine, allow an increased output power for a limited time, without additional energy

storages or withholding power. Actively operating below the maximum available power requires a

determination of the maximum power point at the present operating conditions. Depending on the

power source, this estimation is already possible or technically challenging.

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Limiting the rate of change of active power in upward direction is usually already implemented. The

limitation in downward direction is generally not expected to be demanded from volatile energy

sources and would likely make an energy storage system necessary. Limiting the rate of change of

active power in upward direction can decrease the yield, if power peaks cannot be fed into the grid.

If additional storages are necessary or power is withheld actively, the investment cost of the PE

devices rise and/or the yield decreases.

Additional Comments from the Manufacturers

In addition to the already described requirements, comments were made to features that are

already implemented in PE devices and other topics regarding technical capabilities of grid-

connected PE devices.

Fault-ride-through capability is implemented by all manufacturers. This also applies to type 3

wind turbines. The variety of existing Fault-Ride-Through (FRT) profiles increases the effort of

implementation and testing.

The rate of change of frequency withstand capability of PE devices is generally mentioned to be

higher than the requirement for HVDC converter stations, but it has to be noted that a high rate

of change of frequency is likely to occur in correlation with power imbalances within the grid. If

the PE-connected power generating module operates in FSM during the high rate of change of

frequency, a sufficiently dynamic power source is required. Additionally, the demanded

dynamics for FSM are not specified sufficiently.

The specifications to determine frequency were considered to be insufficiently precise by some

manufacturers. Depending on the implementation and filter settings, varying results of the rate

of change of frequencies can be generated. This is especially important, if the phase angle at

the connection point jumps.

PE devices allow a wide and dynamic control of active and reactive power. In general, the

necessary control interfaces are already implemented in the firmware of existing devices. In

order to control a great number of PE devices within the grid, appropriate communication

infrastructure has to be provided.

The disconnection of load is uncomplicated for PE devices, and it was mentioned that HVDC

links can even initiate a fast power reversal, if necessary.

The requirement to automatically disconnect in case of angular instability or loss of control was

interpreted in different ways. One interpretation was correlated to angular stability, which is

already implemented in the devices implicitly. In case of large deviations between the detected

and actual phase angle, overcurrents will occur and the device disconnects. Active detection

methods for persisting output oscillations are not implemented. Another interpretation was with

regard to active and reactive power controllability. Depending on the grid quality and present

configuration, e.g. the amount of power injected by devices in close electrical proximity, not all

operating points in the PQ diagram can be operated stably, with regard to other system

limitations, i.e. voltage ranges. It is assessed to be difficult to determine the present distance to

unstable operating conditions within the PQ diagram

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Auto-reclosures can be handled by all manufactures, if these are limited to a period of a few

seconds. For larger facilities, i.e. HVDC systems, this requirement is unproblematic, as the

facility is connected via multiple paralleled lines. For system sizing and design, more precise

specifications including type, distance and number of faults would be advantageous.

The interpretation of quick resynchronisation showed differences from manufacturer to

manufacturer. A common understanding was that resynchronisation can be done significantly

faster than conventional generation, if the protection devices are set up appropriately.

Several manufacturers mentioned rise times of fast fault currents around 30 ms. A discussed

rise time of 10 ms was considered to be difficult to implement with state-of-the-art control

concepts. Converters operating as voltage sources could react very quickly in fault conditions.

The provided fault current was often assessed to be 1.2 to 1.3 times the nominal current. There

are also devices that provide a fault current equal to the nominal current. Some devices are

designed to provide this overcurrent permanently, whereas other devices cannot. An important

note was that PE devices are often not operating at maximum capacity, which is why the

effective short circuit ratio is likely to be much higher than 1.2 to 1.3 times the presently infeed

current in most situations.

One manufacturer mentioned that today’s network codes and requirements are designed with

grid-feeding controls in mind and impede the implementation of novel control techniques,

especially with regard to harmonic content. Some requirements and characteristic parameters

were designed considering stiff grids and may need reassessment for applicability in weak grids.

It was also mentioned that the new codes are rather a step towards decentralised generation

than to renewable energy sources. Further, the question was raised, whether it may be more

cost-efficient to aggregate some of the features in larger, specialised facilities, i.e. energy

storage systems or reactive power provision.

Table 2.2 shows a selected number of features and whether they are available in different

technologies. As the discussed HVDC technology is a transmission system only, the remarks for

voltage source converter HVDC systems assume that the HVDC link is energised and power is

available at the other point of connection.

The technical feasibility of many non-exhaustive requirements depends on the concrete

specifications demanded by the relevant TSO, which is of significant importance for requirements

that may demand an energy storage, i.e. frequency sensitive modes. As long as active power

increments are expected only when additional power is available, these requirements are

considered to be technical feasible. If active power increments are demanded at any time, either

additional energy storages are needed to increase power for a limited period or an active power

reserve has to be created by withholding available power. This increases the investment cost or

decreases yield.

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Table 2.2 Availability of several grid features with regard to different technologies.

Type of generation

Requirement

Win

d

PV

HV

DC

15(V

SC

)

Active power controllability and control range

Limited frequency sensitive mode – underfrequency ●/16 ●/16

Frequency sensitive mode ●/16 ●/16

Frequency restoration control ●/16 ●/16

Priority to active or reactive power contribution ●

Quick re-synchronisation

Black start capability 16 ●16

Capability to take part in isolated network operation17 ● ●

Synthetic inertia capability ●16 ●16

Power oscillation damping control ● ●

: Already possible with existing technology, but may require minor modifications

● : Not implemented at the moment, but considered technically feasible

: Only implementable with great effort/cost

Voltage source converter based HVDC systems are capable of providing manifold advantageous

features for grid stability. It has to be kept in mind that HVDC converter stations usually are large

facilities with high power rating and computing power. Some advanced control features may not be

transferable to a great number of small power generating units without additional investment in

processing hardware, communication and implementation effort. Nevertheless, e.g. VSC based

battery systems could provide similar advantageous features.

Different concepts of PE generation to take part in islanded operation are currently investigated

broadly, i.e. microgrids. The overall consent of all manufacturers was that the benefit of each

requirement for the particular grid application has to be weighed against the cost of


2.5 Conclusions

In this chapter, the state-of-the-art modelling of power systems and the capabilities of Power

Electronics (PE) were described. The analysis of the state-of-the-art in power system modelling and

simulation showed that stability analyses of large power systems typically are performed using

RMS models. The concrete modelling depth and geographical extent of the grid model differ

15 With regard to HVDC interconnections between asynchronous grids; available features of embedded

HVDC links may vary. 16 The technical feasibility and necessary effort depends on whether an additional energy storage or

power reserve is requested by the relevant TSO, as it would greatly increase investment cost and/or yield. As long as fluctuations of available primary energy are accepted, the requirements are technically feasible.

17 With respect to the distinction between “taking part” and “guiding” isolated network operation.

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depending on the analysed stability phenomenon and grid area under study and data availability.

However, stability phenomena significantly influenced or even caused by PE devices might not be

sufficiently analysable with RMS models, e.g. PE controller interactions. The state-of-the-art must

therefore be scrutinised with respect to the effects of increasing PE penetration. The validity of key

assumptions justifying RMS simulations must be reviewed as well as the validity of the applied

component models.

In a manufacturer review, the capabilities of PE with respect to the network code were discussed.

The technical feasibility of many non-exhaustive requirements depends on the concrete

specifications demanded by the relevant TSO, which is of significant importance for requirements

that may demand an energy storage. Voltage source converter based HVDC systems are capable of

providing manifold advantageous features for grid stability, but it has to be kept in mind that some

advanced control features may not be transferable to a great number of small power generating

units without additional investment in processing hardware, communication and implementation.

Different concepts of PE generation are currently and broadly researched and the benefit of each

requirement for the particular grid application has to be weighed against the cost of


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3 Modelling of Transmission Systems with high

Penetration of PE Devices

3.1 Introduction

The MIGRATE project has four main objectives of which the first one is related to the development

of a methodology to be shared with TSOs that allows an improved understanding and monitoring of

the system dynamic behaviour [1]. This specific objective requires a systematic study approach

that can be reproduced by all partners of the consortium, and for such purpose the definition of

"model problems” is relevant. The model problems describe the modelling, case study and

simulation/quantification used to analyse a specific stability phenomenon. In Section 3.2, the

modelling approach and characteristics of the set of generic test cases developed based upon

existing benchmark systems for stability studies is provided. The case study and simulation results

are presented in Chapter 4, which use the generic test cases for investigation of the impact of PE

on the phenomena listed in Table 1.2 (Chapter 1) and to define the features of the methodology to

be used for the determination of the KPIs. To study the impact of increasing levels of Power

Electronics on the Great Britain system, transition scenarios from 2016 until 2030 are developed

based on a reduced size model of the GB system, whereas the situation in the year 2016 is

considered in a relatively detailed model of the Irish system. These implementations are presented

in Section 3.3. In Chapter 4, the outcomes of the tests of the proposed KPIs on the GB and Irish

systems are provided.

3.2 Development of Generic Test Cases

3.2.1 General Description of Generic Test Cases

The model problems, as defined in deliverable D1.1 of MIGRATE, are the descriptions of the

modelling and simulation needs to ensure accurate recreation of a given stability phenomenon

when the studied system is close to, or in, an unstable condition [2]. A model problem has three

main aspects: the modelling, case study and simulation/quantification. Figure 3.1 shows an

overview of the model problem definition. It can be seen that the modelling aspect describes how

the system and its components are modelled. The case study specifies the grid topology and

conditions under which instability occurs, while the simulation/quantification aspect describes how

the simulation is performed and how the results are assessed. The detailed information provided is

intended to fulfil Objective 1 as stated in the MIGRATE Grant Agreement, where the modelling

technique of all elements is required to be known in order to understand the dynamics of the

considered system and to allow the reproducibility of the tests [1].

This chapter introduces generic test cases and validation systems to study the stability behaviour

of power systems for the selected phenomena shown in Table 1.2 (Chapter 1). As modelling of

these systems and their elements are essential for this, in this chapter special attention is paid to

the Modelling aspect of the model problem. Concerning the case study aspect, the grid topology

and (initial) operating conditions under which instability can occur are the parts that will be

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discussed in this chapter as well. As the conditions under which instability occurs can only be

determined by analysing the systems with the stability KPIs, part of the case study aspect will be

described in Chapter 4. The simulation/quantification aspect of the model problem is specific for

the particular study and used indicators, and will therefore be discussed in Chapter 4 as well.

Figure 3.1 Overview of the model problem.

In the following sections, generic test cases will be developed. These generic test cases consider

the specific stability phenomena, typically classified as the study of frequency, rotor angle and

voltage stability [3]. Sub-synchronous controller interactions are a fourth category considered in

this research. Each particular phenomenon must be studied separately for better understanding of

the roots and propagation of stability threats.

3.2.2 Power System Modelling in RMS and EMT

The modelling aspect refers to the representation of the electrical system, the considered devices

and their associated controllers that will be implemented for the stability studies. Frequency, rotor

angle and voltage stability are studied with RMS simulations in DIgSILENT PowerFactory, while

sub-synchronous controller interactions are studied with EMT simulations in PSCAD. The following

sections describe the general modelling in PowerFactory and PSCAD, where special attention is paid

to the modelling of wind turbines.

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Modelling in PowerFactory

Frequency, rotor angle and voltage stability are studied by implementing models for RMS

simulations in PowerFactory. Table 3.1 gives an overview of the selected elements in DIgSILENT

PowerFactory 2016 for implementing the generic test cases as well as the GB system and the Irish

system. Particular modelling aspects are highlighted in the subsection describing each system in

the remainder of this chapter.

Table 3.1 Power system modelling in PowerFactory.

Element Details Reference

Synchronous generator ElmSym / TypSym (6th-order)

(controllers: AVR, GOV, PSS)

[16]

Automatic Voltage Regulator (AVR) Modified IEEE Type 1 (avr_IEET1A.BlkDef

model taken from the library of standard

models)

[17]

Turbine governors (GOV) Steam (gov_TGOV1.BlkDef model taken

from the library of standard models) /

Hydro (gov_HYGOV.BlkDef model taken

from the library of standard models)

[17]

Power System Stabiliser (PSS) Speed input stabiliser (user defined model

based on pss_PSS1A.BlkDef model taken

from the library of standard models)

[12], [17]

Static Var System (SVS) ElmSvs [18]

Two-winding transformer ElmTr2 / TypTr2 (3-phase) [19]

General loads ElmLod, TypLod [20]

Transmission lines ElmLne / TypLne

(PI-circuit, lumped parameters)

[21]

Nodes connecting lines, generators,

loads, etc. to the network

ElmTerm [22]

Phase-Locked Loop (PLL) ELMPhi_pll (first-order or second-order

generic models might be used)

[23], [24]

More details and typical parameters for the generic test cases can be found in Appendix A.

To describe the overall approach for interconnecting the necessary elements to perform RMS

simulation, a simple example is given in this section. Consider a system with two synchronous

machines and one Wind Park model (WP) in a network with auxiliary PLL block for measuring the

frequency. The synchronous machines in the network have auxiliary components such as AVRs,

PSS and governor systems and the same holds for the WP, which has a measurement unit,

mechanical part and P/Q controllers. The hierarchical structure of DIgSILENT Simulation Language

(DSL) is used to generate a model of the auxiliary components attached to each device and to

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ensure correct execution of time domain simulations. The hierarchical levels defined by DSL are

associated to Model Definition, Common Model, Composite Frame, and Composite Model.

In this example, as well as in all implemented models (generic test cases, GB system, Irish

System), all synchronous machines in the network have a similar structure, defined as Composite

Frame in PowerFactory, which defines slots for how the AVR, the PSS and the governor system are

connected to the machine. A Composite Frame as shown in Figure 3.2 for all the synchronous

machines and the WP model can be defined. This composite frame is located in the User Defined

Models folder inside the project Library. The Composite Frame can be conceived as some kind of

draft (which can be easily modified), that is called from an object called Composite Model, which

constitutes some kind of mask that actually allows to PowerFactory to select the model of the

device or machine and its associated auxiliary components (i.e. controller, protection devices, and

objects for external data exchange) to be considered in the simulation functions. These composite

models are located inside the Network Data folder.

NETWORK

Static Generator

(WP)

Mechanical Model

Synchronous Generator1

Exc. 1

LFC

PSS

AVR


Exc. 1

LFC

PSS

AVR

Common Models Common Models

Composite Model 3Composite Model 2Composite Model 1

ControlP, Q, Pitch Measurments

Library


Exc. 1

LFC

PSS

AVR

Composite Frame

Static Generator

(WP)

ControlP, Q, Pitch Measurments

Composite FrameAVR PSS GOV

P,Q controller

WP Control

Inertia Emulation

Model definitions

Input data

Input data

Mechanical Model

PLL

Figure 3.2 General example of the DSL components implementation.

Model Definitions are block diagrams that define the skeleton of auxiliary models. AVR, PSS and

governor models are defined as model definitions and stored in the User Defined Models folder

inside the project Library similar to composite frames. Each Model Definition includes the transfer

functions and control systems equations to be implemented. PowerFactory provides macros with

most of standard transfer functions. The macros allow defining input signals, output signals,

parameters, internal variables, state equations, state variables, and minimum/maximum limits. In

this example, for each of the two synchronous machine’s Composite Models, the AVR (and PSS,

governors) may have different values of parameters. Common models are objects that fill up the

slots in the Composite Model for each machine, creating an integrated model in the time domain.

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The structure of Common Models is borrowed from Model Definitions. Thus, each of the AVR, PSS,

and governor Common Models picks up its respective model blueprint (or structure) from the Model

Definition. To summarise: Composite Models borrow their structure from Composite Frames and

Common Models borrow their structure from Model Definitions. Common Models are filled in slots

available in Composite Models. The above example is visualised in Figure 3.2.

Wind Turbine Model in PowerFactory

The wind turbine models used in MIGRATE WP1 were developed in DIgSILENT PowerFactory by

Energynautics GmbH based on the standard IEC 61400-27 series [25]. The developed model is

embedded into a single structure following the principles of DSL, and is used to represent different

types of turbines, being possible to change the type of the wind turbine (Type 3A, 3B or 4) by

changing the generator system. This section gives a brief explanation of the models included in the

generic test cases which are used in RMS simulations, also showing some simulation results that

illustrate the model performance (i.e. initialisation and dynamic response to a disturbance).

Single Wind Turbine Model in PowerFactory

The structure of wind turbine model is presented in Figure 3.3 [26]. The main features of the

model are described as follows:

─ In the measurement part of this model, the blocks Frequency, PowerMeasurement and

VoltageMeasurement are connected directly to the terminals of the wind turbine and put out the

corresponding measurement data. Those measurement values and the currents from the

Generator Block are used for initialising the model.

─ The Generator Block contains the PowerFactory element “Static Generator”, and works as a

current source. The Generator System block is taken from IEC 61400-27-1 [26], [27].

─ The mechanical part is represented by the Aerodynamic block, which calculates the mechanical

power on the turbine, and the Mechanical block, which contains a two mass or single mass

oscillator. The Two mass model is based on IEC 61400-27-1 [27].

─ Input part: the block Wind speed gives the wind speed. It must contain an external file with

wind measurement data in m/s. As an alternative to wind speed as input, the maximal available

power can be used as input by using Power input. In Input choice and back calculation one of

the two input options can be chosen.

─ In the control part, the block P control is based on P control Type 3 from [25]. In this study, it is

used for both Type 3 and 4 wind turbines. The Pitch angle control block is taken mainly from

[25]. The input pemuin is added to pWTref (the active power reference value) when emulated

inertia is activated. There are several possibilities for power control depending on the frequency

inserted. These possibilities are P choice and reduction (power reduction with overfrequency)

[28], Delta control [29], and Emulated Inertia based on [30]. These all influence the output

power depending on the measured frequency.

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Figure 3.3 Controller structure of the wind turbine model in PowerFactory.

Type 3

and 4

Contr

olle

r: 5

.5.4

.2 (

2015)

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we

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asu

rem

en

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r: 5

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2015)

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co

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co

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P a

nd Q

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Some of the input slots require external data (P setpoint, X setpoint, cosphi setpoint, Wind speed

and Power input). For all of these slots, an instance of the PowerFactory type “Measurement File”

(ElmFile) has been created. Those measurement files refer to an external csv-file that contains a

time dependent value. For example, the measurement file for wind speed is inserted in the Wind

speed slot. The first column of the csv-file contains a value for the time (in seconds) and the

second column contains a value for the wind speed (in m/s). All other csv-files that are used by

other measurement files have the same structure. The user can update the csv-files as desired to

create a different wind speed profile. Figure 3.4 shows an example on how to call an external file.

Figure 3.4 External data file selection of wind turbines in PowerFactory.

The template of the model consists of the complete wind turbine including a mechanical part,

generator, controllers and a transformer. The interface which connects the power plant to the grid

model is shown in Figure 3.5. As wind generator, the built in PowerFactory module Static Generator

(ElmGenstat) is used. A two winding transformer (ElmTr2, [19]) is also used.

Figure 3.5 Interface for the connection of the wind model to the grid.

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Wind Park (WP) model

As it is well known, the use of a single wind turbine is not considered in transmission systems

because of its practicality and low power generation. Instead, the use of a group of wind turbines

at the same location to produce larger amounts of electric power is widely implemented and a

trend in developed countries. This last concept is called a Wind Park (WP) or wind farm.

The WP model aggregates many wind turbines of the same type into one model with one

overarching controller frame, which represents an increased efficiency in the use of computational

resources. Also, an important difference between the software based model between the WP and

wind turbine is that the former controls the active and reactive power at the Point of Common

Coupling (PCC) and not at the terminals of the wind turbine. The general structure of the wind park

control used in PowerFactory is shown in Figure 3.6.

Figure 3.6 Structure of WP controller proposed by IEC 61400-27-1.

As shown in Figure 3.6, the blocks Power measurement, Frequency measurement and Voltage

measurement are connected to the PCC. Hence, the external files that are inserted in P setpoint WP,

X setpoint WP and Cosphi setpoint WP give reference values for the PCC [25].

The interface to the grid, when simulating a whole wind park is depicted in Figure 3.7. Only the

part marked by the red rectangle is part of the template. Therefore, for grid integration, the wind

turbines have to be added separately by inserting the wind turbine templates.

WP control and communication frame:

Communication..Comm delay fo..

Frequency..Phase Mea..

P setpoint WPP setpoint WP

X setpoint WPX Setpoint WP

Cosphi setpoint WPCosphi setpoint WP

WP Q controlWP Q control

Activ eActiv e

Communication..Comm linear f . . xPDre..

y1=

0...

y1=0...

cosp

h..

yo=1...

pWPre..

xWPre..

Communication..Comm linear f . .

Grid measurem..Grid measurem..

pWP

fi..

qWP

fi..

uWP

fi..

FWPU

V..

xPDre..

pPD

re..

fWP

fi..

pWPfi..

qWPfi..

uWPfi..

fWPfi..

p=1.0..

q=-0...

u=1.0..

pPDre..

fmeas..


Power mea..PQ Measur..

Voltage m..Voltage M..

WP P controlWP P control


0

1

2

3

0

1

2

3


0

1

2

3

0

1

2

3


0

1

0

1

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SIL

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pW

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.

DIg

SIL

EN

T

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Figure 3.7 Grid interface of a wind park with two types of wind turbines.

Figure 3.8 Performance of active power injected into the grid for the wind turbine models (WT

type 4 in red and WT type 3 in green) in the GB test system.

15.00012.0009.00006.00003.00000.0000 [s]

382.0

381.0

380.0

379.0

378.0

z\WT11a: Total Active Power in MW

7.085 s380.701 MW

15.00012.0009.00006.00003.00000.0000 [s]

558.0

556.0

554.0

552.0

550.0

z\WT19: Total Active Power in MW

6.665 s552.000 MW

DIg

SIL

EN

T

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The initialisation dynamic response of the both Type 3 and Type 4 wind turbine models during a

disturbance, integrated in GB system, is shown in Figure 3.8. The used GB system is the baseline

model in 2016 (see Section 3.3.2) and both tested wind turbines are located in zone 11 (Type 4)

and zone 19 (Type 3) of the GB system, i.e. North England and East England, respectively. The

upper plot of Figure 3.8 shows the active power response of the Type 3 wind turbine in zone 19

and the lower plot shows the active power response of the Type 4 wind turbine in zone 11. As it

can be seen, stable initialisation is achieved at t=4 seconds. In this simulation case, a generation

outage (2.2 GW) occurs at t=8s and stable output for both wind turbines is reached at t=12s. As

can be seen, the active power response is able to follow the power reference of the wind turbine.

Modelling in PSCAD

Controller Interactions are studied by implementing models for EMT simulations in PSCAD. Table

3.2 gives an overview of the selected elements in PSCAD for implementing the generic test case.

All these components are available in the Master Library of PSCAD. Additional libraries might be

required when simulating certain user specific models (such as the wind turbines discussed in the

next section). These libraries complement the Master Library.

Table 3.2 Power system modelling in PSCAD.

Element Details Reference

Voltage Source Three Phase Voltage Source Model 2

(Source Impedance Type: Ideal (R=0)

[31], [32]

Resistance

Inductance

Capacitance

Resistor

Inductor

Capacitor

A combination of these 3 elements can be used to

represent a very basic model of a transmission line

Two-winding transformer Three Phase 2 Winding Transformer

Transmission lines Bergeron Model (The Bergeron Model is a very

simple, constant frequency model based on

travelling waves)

Frequency Dependent Model (The Frequency

Dependent Model uses curve fitting to duplicate the

frequency response of a line or cable. It is the most

advanced time domain model available as it

represents the full frequency dependence of all line

parameters (including the effect of a frequency

dependent transform))

EMT Wind Turbine Models

For the MIGRATE project, Manitoba HVDC RC developed wind turbine type 3 and type 4 models.

This section gives a brief overview of those models. Within the EMT implementation two different

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variations are provided. The complete model including the power electronic converters and an

average model, where the power electronic converters have been replaced with equivalent

voltage/current sources. These models are generic and most of its controls are based on the IEC

standards 61400-27-1 [26], [27]. Full details on these models as well as comparisons between the

two modelling techniques are presented for different realistic operating scenarios in [33].

DFIG Type 3 Model

The PSCAD generic DFIG model presented here has been setup for a single 3.6 MW machine

connected to a 50 Hz equivalent voltage source. A machine multiplier component can be used to

scale up the machine and thus simulate a collection of machines with only one wind generator, as it

is shown in Figure 3.9.

Figure 3.9 Single 3.6 MW DFIG connected to an equivalent voltage source through a 50x unit

multiplier.

The DFIG is an electromechanical system with electrical, mechanical and controls components. The

DFIG model is presented as a two-part system, with a mechanical subsystem, in charge of

converting the maximum power available from the wind into torque, and an electrical subsystem,

in charge of delivering such power into the electrical system (Figure 3.10). The interface

component in this system is the induction generator, which converts the mechanical energy into

electrical energy. The general parameters for the implemented DFIG model are presented in Table

3.3.

0.0602 [ohm] 0.001916

R=0

DFIGav

SCR 10X/R = 10

BRK

BRK

Dblk

x n

n

*

BRK

d/dt50.0

P = 180.4Q = 2.972V = 33.21

V

A

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Figure 3.10 Electrical structure of DFIG electromechanical system.

Table 3.3 DFIG General Parameters.

Parameters Value

Cut in wind speed 3 m/s

Cut out wind speed 25 m/s

Nominal wind speed 10.2 m/s

Machine rating 4 MVA

Nominal frequency 50 Hz

Machine terminal voltage 0.9 kV

The initialisation of the detailed model is shown in Figure 3.11a. Stable operation is achieved at

t=5 seconds. In Figure 3.11b, the response of the detailed DFIG is shown for a 3-phase short

circuit of 150 milliseconds at the point of common coupling. The short circuit is applied at t=10

seconds; stable operation is achieved at t=20 seconds.

DFIG

Converters

Mechanical Model AC_sys

BRK#1

4.2 [MVA]

33/0.69/0.9

#3

#2

1000

V

A

*-1.0

V

A

S2TMODE

& Controls& Controls

GRID

ConverterConverter

GENERATOR

RABCSABC

S

TL

N

I M

W

CTRL

Istator

W0

WindTRQ

Wm

Vw

W0 Tm

Wind to torque

Pref

Ppu

Start

pu

Pitch

W0

W0

Wpu

V

A

VI_m

TurbStart

Signals

Pitch

Pg_pu

Two-Mass Model

Paero

TE w_WTR

wgenReset

W0

S2TMODE

A

B

Ctrl

Ctrl=1

T2ms

1

W0

T2ms

A

B

Ctrl

Ctrl=1

wWTR_Two_Mass

A

B

Ctrl

Ctrl = 1

WpuWpu_Mch

T2ms

Wpu

TE*

-1.0

Vwind_out

V

A

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Figure 3.11 (a) initialisation of Detailed DFIG Model and (b) detailed DFIG Response to 150 ms 3-phase SC at the PCC.

Full Converter (Type 4) Model

The type-4 wind turbine is connected to an external electrical network (Figure 3.12) and can be

modified as required to represent a specific network situation.

Figure 3.12 Overview of the external network connection.

The type-4 wind turbine model is shown in Figure 3.13 and contains the following components:

─ Line Side and Machine Side Converters (LSC & MSC)

─ Converter dq Controllers (LSC & MSC)

─ Turbine Controller Modules (including emulated inertia and pitch angle control modules)

─ Multi-Mass Model

─ Two-Dimensional Aerodynamic Model

─ Wind turbine Transformer and Machine Models

Details of all the components can be found in [33].

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Figure 3.13 Overview of the type-4 wind turbine module.

The general parameters for the implemented type-4 model are presented in Table 3.4 The

initialisation of the detailed model is shown in Figure 3.14. Stable operation is achieved at t=8 sec.

Table 3.4 Wind turbine T4 General Parameters.

Parameters Value

Cut in wind speed 3 m/s

Cut out wind speed 25 m/s

Nominal wind speed 10.2 m/s

Machine rating 6 MW

Nominal frequency 50 Hz

Machine terminal voltage 0.9 kV

Figure 3.14 Initialisation of Detailed Type 4 Model.

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3.2.3 Generic Test Case 1: Frequency Performance in the Frequency

Containment Period

The PST16 Benchmark System

This generic test case was developed for the study of frequency performance in the frequency

containment period (i.e. the period after unbalance occurrence up to 30 seconds) and is based on

the PST16 benchmark system as described in [34], [35] and [36]. This system is suitable for

different kind of stability studies (frequency, rotor angle and voltage), as stated in [34].

Furthermore, the three interconnected areas in the system have weak connections because of the

length of the tie lines, which makes this system suitable for low-frequency oscillations studies as

well.

Figure 3.15 shows the diagram of the modified PST16 benchmark system as used in the MIGRATE

project. The grid consists of three strongly meshed areas, 66 buses, 16 generators, 28

transformers, and 51 transmission lines. Long transmission lines interconnect the areas (i.e.

200 km transmission lines). The loads are concentrated in area C and power is transferred from

area A and B to area C through two long tie-lines.

Figure 3.15 Modified PST16 benchmark system.

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The PST16 benchmark system considers 5 hydro power, 7 thermal (coal), and 4 nuclear units. The

11 latter are located in areas B and C. Table 3.5 shows the disposition of load and generation in

the system.

Table 3.5 Load and generation distribution in the PST 16 benchmark system.

Load (MW) Generation (MW)

Area A 2000 4840

Area B 6100 5652

Area C 7465 5450

Total 15565 15941

Adaptation of PST16 System with Wind Power Generation

The PST16 benchmark system is adopted to develop KPIs for frequency performance in the

frequency containment period. The 11 thermal and nuclear units in the original system are located

in areas B and C. Thus, following the objectives of the European countries to decommission

greenhouse gases, new wind parks are likely to be installed in the areas with thermal units. Area A

is not altered due to the hydro unit dominance there. The wind turbines and wind park controllers

are the main elements to take into account as Power Electronics-Interfaced Generation (PEIG).

Figure 3.15 shows the benchmark system with the wind park installations applied. Table 3.6 shows

the installed capacity of the wind parks. Since it is expected that wind turbine type 4 will

predominate in the future [37], it was decided to follow this trend in the modelling. The allocation

of the wind turbine types was done randomly. The names of the wind parks are indicated in Figure

3.15.

Table 3.6 Wind parks and active power generation rating (modified PST16 system).

Wind park name and zone Technology Active power (MW)

WP_2B Type 4 2413.4

WP_3B Type 4 1407.6

WP_8B Type 4 904.7

WP_10B Type 3 954.0

WP_02C Type 4 1306.6

WP_10C Type 4 855.4

WP_12C Type 4 1156.2

WP_14C Type 4 855.4

Total 9853.5

The wind parks were installed with the same capacity as the synchronous generators on their Point

of Common Coupling (PCC), with the intention to study a change in the power share in the system

but also to study when a wind park completely replaces a synchronous generator without modifying

the overall power generation profile. Such approach has been widely used in existing stability

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studies [38], since it allows to get a high level insight into the effects of increasing levels of power

electronics-interfaced generation. However, for detailed connection studies, carried out by system

operators, the exact location and grid topology is necessary to get more detailed insights of the

connection on the operation of the power system.

There are three load demand cases taken into account: Winter (100%), Spring (80%) and Summer

(60%), where 100% represents almost 16 GW. For each case, several dispatch scenarios are

studied, where the main variation is done in the power share between synchronous and wind

generation. This means that under each season several simulations are run, where only the power

share is changed (the power flow direction is not altered). To better visualise the dispatch

scenarios, Figure 3.16 shows a simplified overview. In each simulation case, a set of operating

scenarios is created such that the wind generation progressively takes over the synchronous units18,

specifically the thermal and nuclear ones. More details about the dispatch scenarios can be found in

Chapter 4 and Appendix A.

Summer

Load 60%

Operational Scenario1

...

...

...

Spring

Load 80%

Winter

Load 100%

Modified 16 PST benchmark

system in PowerFactory



Operational ScenarioN

...





...





...

Figure 3.16 Simplified overview load dispatch scenarios (modified PST16 system).

18 Wind power generation that replaces conventional plants does not entail operation of the wind power plant at nominal power, so the efficiency and realistic wind speed inputs are taken into account.

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Description of Operating Conditions

The case study describes the operating conditions under which conditions of instability can occur. A

heuristic approach is followed to stress the test system such that insight on the hazards can be

revealed. This approach will make a complete scan on the system behaviour. The methodology

followed runs a large amount of simulations with different power share from PEIG with three

different load demand profiles, corresponding to winter, spring and summer time. The objective is

to perform a sensitivity analysis, which will contribute to understand the possible sources of

frequency instability for high penetration of renewables.

For a more detailed discussion of the approach for the development of load scenarios and operating

conditions, it is referred to Appendix A.

It was considered to perform the simulations under the following circumstances:

─ No change in topology.

─ Line out-of-service. The tie-line selected to be out-of-service is the one connecting area A with

area C (tie line A-C in Figure 3.15) as it was found that this is the worst case scenario.

Besides the different grid topologies and power dispatch, the RMS simulations are performed by

setting a power imbalance of 6.3% and 13%. This is achieved by tripping the following generators:

─ A1aG and A1bG

─ A2aG and A2bG

─ A1aG or A1bG or A2aG or A2bG (one at a time).

No short circuits, line outages or any other types of events are considered because the normative

contingency for interconnected operation in continental Europe is the tripping of two of the largest

generating facilities connected to the same busbar (for frequency studies) [39].

3.2.4 Generic Test Case 2: Large-Disturbance Rotor Angle Stability and Small-

Disturbance Voltage Stability

The IEEE 9-bus system [40], which is well known as the P.M. Anderson 9-bus model, is used to

assess the large-disturbance rotor angle stability and small-disturbance voltage stability of RES-

dominated power systems. The system consists of 3 synchronous generators with IEEE type 1

exciters, 6 transmission lines, and 3 constant impedance loads. Small modifications are made to

make this test system suitable for studying these two stability phenomena.

Large-Disturbance Rotor Angle Stability

For Large-Disturbance rotor angle stability, the modified 9-bus test system is shown in Figure 3.17.

As shown in the single line diagram, generator G1 is replaced by a wind turbine type 3. In the rotor

angle stability studies, G3 is selected as the reference generator. The angle of generator G2 is

observed to investigate large-disturbance rotor angle stability. The system steady-state (initial

conditions) information is provided in Table 3.7.

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G3

2

G2

G1

3

1

5

4

987

6

L7

Load A

Load C

Load B

Figure 3.17 Modified generic test case 2.

Table 3.7 Initial conditions for the analysis of large-disturbance rotor angle stability.

Component Active power (MW) Reactive power (Mvar)

Generator G1 70.5 24

Generator G2 190 6.7

Generator G3 75 48.9

Load A 80 45

Load B 90 30

Load C 160 60

Small-Disturbance Voltage Stability

The single line diagram of the modified 9-bus system is given in Figure 3.18. The small size of the

model makes it particularly suitable for investigating voltage stability, as observed changes/results

can be assessed and explained relatively easily. The power system is modelled in DIgSILENT

PowerFactory and steady state analysis is used for the assessment of small-disturbance voltage

stability. Small-disturbance voltage stability is defined as the ability of any power system to

maintain steady voltages when subjected to small perturbations such as incremental changes in

system load [12]. The small-disturbance voltage stability relates to issue 7 (i.e. Lack of Reactive

Power) of the TSO questionnaire of deliverable D1.1 [2]. The concern is that increasing demand in

the power system will increase the reactive power needs and displacement of conventional

generation by PEIG might result in a lack of reactive power provision.

In order to assess the influence of increasing levels of RES on the small-disturbance voltage

stability, the IEEE 9 bus system is modified to include wind turbine generators type 3 and type 4 at

buses 4, 7, and 9 (marked in orange). The wind turbines used are the ones developed by

Energynautics and are the same as in generic test 1 [25].

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Figure 3.18 Modified IEEE 9 Bus System – Single Line Diagram.

Another implemented modification is the use of 10 parallel machines for generators G2 and G3.

The machine ratings are changed to 1/10th of their initial values. To assess the impact of small-

disturbance voltage stability, the parallel generators at bus 2 are switched off one by one. The RES

is increased with the same amount. After all parallel machines at bus 2 are switched off, the

parallel machines at bus 3 are decreased. The initial conditions of the loads and generators are

given in Table 3.8.

Table 3.8 IEEE 9 Bus System – Initial Conditions.

Component Active Power (MW) Reactive Power (MVAr)

Generator G1 72 28

Generator G2 163 5

Generator G3 85 -11

Load A 125 50

Load B 90 30

Load C 100 35

G1

1

10

Load A

5

G2

72 8

Load C

Load B

G3

9 3

6

4

WT T3

WT T4

WT T3

WT T3

WT T4

WT T4

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3.2.5 Generic Test Case 3: Sub-synchronous Controller Interactions

A series compensated overhead line can produce oscillations in the sub-synchronous frequency

range. When this overhead line is electrically close to a PEID (mainly WT T3), these oscillations can

grow if the damping of the system is not large enough. This can occur when the PEID exhibits a

negative resistance behaviour in which the negative resistance is larger than the positive resistance

of the network. This interaction between the PEID and the series compensated line is defined as

Sub-Synchronous Controller Interaction (SSCI). As no mechanical devices are involved in the

resonance, this phenomenon is a purely electrical oscillation. Due to this nature oscillations can

grow substantially in a short time.

The generic test case for Sub-Synchronous Controller Interactions (SSCI) is based on the IEEE First

Benchmark Model for Sub-Synchronous Resonance (SSR) [41] and is shown in Figure 3.19. This

generic test case is used to get basic insight into the parameters that influence the SSCI

occurrence.

Figure 3.19 Generic Test Case SSCI – Single Line Diagram.

More elaborated simulations are carried out using the model of Figure 3.20, in which more wind

turbines are present. The model of Figure 3.20 uses parallel network interfaces to enable

acceptable simulation times. Therefore, the connections of the lines ‘TLine_1’ to ‘TLine_3’ go to

three separate cases containing detailed wind turbine models. The values of the RLC components

can be altered with the aim of achieving a certain network behaviour (e.g. damping or a specific

level of series compensation). An EMT environment is necessary for investigating the controller

interactions, as an RMS environment cannot model the devices in enough detail. An RMS based

software is not capable of illustrating correct sub synchronous or harmonic phenomena due to

modelling simplifications. As the EMT wind models provided by Manitoba HVDC RC are developed in

PSCAD, the generic test case is modelled using PSCAD/EMTDC, with a solution time step of 25 µs.

0.0602 [ohm] 0.001916

R=0

SCR 10X/R = 10

DFIGPCC

1.0 [uF]

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Figure 3.20 Extended Model for SSCI – Single Line Diagram.

3.3 Development of Realistic Test Cases of Medium Size

After using the Generic Test Cases described in Section 3.2 for the development and initial testing

of the power system analysis methodologies laid out in Chapter 4, the adapted methodologies are

applied to more realistic, medium-sized power grids along with realistic Transition Scenarios for the

migration from the status quo to a PE dominated power system. These Realistic Test Cases are

based on the GB and the Irish test system.

3.3.1 Development of Transition Scenarios

What is a Transition?

A transition is defined as ‘a change from one form or type to another, or the process by which this

happens’ [43]. Within the MIGRATE project, transition scenarios are used to describe the changes

in the electricity landscape over time, i.e. increasing levels of installed Power Electronics-Interfaced

Generation (PEIG). The aim is to assess the impact of these changes in the transmission grid.

Transitions have 5 main characteristics [44]:

1. A transition is a co-evolution process:

This is a process in which some domains continuously adapt to and influence each other, leading

to interdependencies. As an illustration, one can examine the influence of environmental policies

on the generation segment.

2. A transition is a multi-actor process:

At least 2 domains, with different actors, are required in a transition. Within the electricity

transition, several actors are involved, e.g. policy makers, manufacturers, generators,

consumers, transmission system operators, etc.

3. A transition is a radical shift from one system to another:

Radical here refers to the scope of the shift, rather than its speed. The shift may be sudden,

slow, or in a step-wise fashion. In the example of an electricity transition, the shift is from a

conventional generation dominated system to a PE dominated power system.

0.0602 [ohm] 0.001916

fR=0

SCR 10X/R = 10

Freq_sys

d/dt

TLin

e_1

TLine_1

12 to

4

5

1WPre

f

BRKn

Punit_

base

Punit_

base

BRKn

WPre

f

1

12 to

4

5

TLine_2

TLin

e_2

TLin

e_3

TLine_3

1

2 t

o 4 5

1

WPre

f

BRKn

Punit_base

1.0 [uF]

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4. A transition is a long-term process:

A time frame of 30-50 years is generally considered. This interval takes into account the time

required for the breakthrough of innovations, as well as for making these innovations embedded

in the system.

5. A transition is macroscopic:

Because transitions have a co-evolution and multi-actor nature, it affects several domains.

Therefore it is macroscopic. With decreasing levels of conventional generators, the electricity

network will be operated differently (e.g. operational limits based on stability instead of thermal

capacity, new ancillary services), energy will be traded differently (e.g. renewable energy feed-

in tariffs), etc.

A transition is, qualitatively, usually depicted using the S-curve as shown in Figure 3.21. The x-axis

contains the time, whereas the y-axis contains some sort of indicator for the change in the system.

As an example the installed PE-based generation is chosen as indicator for system change in the

picture below.

Figure 3.21 The S-curve model of transitions.

In the S-curve, 4 stages can be observed:

─ Predevelopment: in this stage innovations are being developed; the status quo does not change

visibly.

─ Take-off: innovations are already developed in this stage; the state of the art starts to change.

─ Acceleration: innovations are being embedded in the system; the system is undergoing a

paradigm shift.

─ Stabilisation: the speed of the system change (i.e. installed PE in the graph) decreases and a

new equilibrium is reached; the system successfully adapted to the change.

It should be noted that the S-curve is not a fixed pathway and that the phases are only conceptual:

the S-curve cannot be used to predict the specific course of transitions.

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Use of Transition in MIGRATE

One of the main objectives for this task of the project is to develop and use a small set of generic

test cases able to grasp system stability issues raised by the growing power electronic connection

into any given zone. However, the results of the generic test cases should be compared with the

expected situation in Ireland and Great Britain (GB). These comparisons will be provided as a

validation of relevant model characteristics as the analysis of angular and frequency stability

challenges [1]. The mentioned "expected situations", or scenarios, must represent a transition

between current situation of the transmission system and expected situation in the future.

The transition scenarios are a set of models where the expected installed generation capacity (i.e.

conventional and PEIG), load demand, power flows and possible grid reinforcements for the years

2016, 2020, 2025, 2030, and 2035, are configured in a reduced model of the Great Britain (GB)

system. These scenarios were built upon an original GB reduced model. Such original model was

built considering a scenario for the year 2013, thus it was upgraded using the information available

in “UK electricity transmission, Electricity Ten Year Statement 2016” by National Grid [45], [46].

The main objective of these scenarios is to be used as validation systems to assess the impact of

increasing levels of PE penetration in the transmission grid.

Proposed Framework

In the framework described next, it is proposed to analyse the transition of the electricity system

using 3 underlying transitions:

1. Network transition (N)

For this transition, the focus is on development in network topologies and the increased use of

PE-based devices for the network such as HVDC and STATCOMs. The assumption is that the

network development will face the slowest transition because of the very long lead times (as a

result of public opposition, technical challenges, regulatory requirements, etc.) involved in

realising such projects.

2. Generation transition (G)

The focus here is the transition from conventional, synchronous machine-based generation to

more PE-dominated generation (wind parks and PV parks). The assumption is that this

transition will be the fastest as a result of subsidy schemes for RES and because of the fact that

the generation is an open market segment. One important parameter is the fraction of PEIG

that is connected to the transmission grid (vs. the distribution grid)

3. Load transition (L)

This transition deals with how the load will evolve throughout time. A moderate transition speed

is expected. It is expected that the load increase will not be proportional to the increase in

population, because of energy efficiency measures in (domestic) appliances. Two important

parameters here are the load profile and the load composition.

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3.3.2 Implementation into the GB Test System

Implementation of the Transition Scenarios

For the implementation of the transition scenarios in the Great Britain (GB) power system,

information on the 3 types of transitions defined above is gathered. For future network

development, the publication Network Options Assessment by National Grid [45] has been used as

inspiration. For the transition in generation, the Electricity Ten Year Statement [46] and Scenario

Outlook and Adequacy Forecast 2015 [47] were used. The Future Energy Scenarios document by

National Grid [48] was used to obtain an overall overview of the developments in GB.

The detailed GB power system is too complex and too big to be used in repetitive time domain

simulations. A fully represented system would have hundreds of substations with highly detailed

transmission line modelling, such that for performing the analysis defining boundaries is very

important. A boundary "splits the entire (Great Britain) system into adjacent parts, crossing critical

circuit paths that carry power between the areas where power flow limitations may be

encountered" [46]. There are at least 20 reported boundaries in the current GB transmission

system.

To reduce the complexity of the system, a dynamic equivalent with reduced number of variables

must be defined such that some simplifications are made. There is no computational overburden

and the dynamic response of the reduced model resembles the full GB system in a way that the

analysis of results can be comparable to that of the full system. This way, the use of the so-called

reduced model can provide great advantages for the study of the concepts of interests while

intending them to be used in the GB system.

In [49], L. Shen from University of Manchester has developed a reduced model based on steady-

state data provided by the University of Strathclyde which was validated against a solved AC power

flow reference case provided by National Grid Electricity Transmissions. The main structure of the

network is shown in Figure 3.22, where each of the 29 substations represents a grouped level of

generation, load demand and losses.

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Figure 3.22 Great Britain reduced transmission system (from [49] - Figure 3.1, pp. 74).

In the ETYS 2016 document [46], the developments are clearly described for each boundary with

their respective power generation and demand. Therefore, a comparison can be made between

Figure 3.22 and the ETYS GB information where the matching substations reveal how to scale the

power. The procedure can be explained visually as in Figure 3.23.

As shown in Figure 3.24, the boundaries that were found to coincide with substations in the

reduced model are of the most interest and are associated with one of the five regions of the Great

Britain island: Scotland, North England, West England, East England and South England. Then, the

information published in [45]-[46] by National Grid about the scaling power demand and

generation over the years for the entire island can be divided between these 5 regions, which are

related to some interesting boundaries, as mentioned above.

This way, each one of the 29 substations in the reduced model can be scaled up accordingly to

their associated boundary, while the overall summation of each power demand and generation in

each substation will add up the total expected growth of the GB system. A graphical illustration of

the procedure just explained can be seen in Figure 3.25.

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Figure 3.23 Overview of matching process with the work flow.

Figure 3.24 Mapping of the 5 ETYS regions onto the 29 zone network model.

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Figure 3.25 Steps to relate the National Grid information with the existing reduced GB model.

Step four of Figure 3.25, "Estimate generation dispatch", was done by following two principles:

1. Power Electronics-Interfaced Generation (only wind turbines considered in this work) have

priority over synchronous generation due to environmental and economic reasons.

2. The power flow direction was kept at all times, i.e. from north to south and from east to west

(when applicable), see also Appendix B.1.

To accomplish a proper dispatch profile, the generation dispatch at northern regions was kept

bigger than the load demanded locally, while at southern substations the generation was kept

significantly below the demanded power.

For the implementation of the transition scenario in the GB system, it was chosen to select the two

extremes, i.e. Gone Green (GG) and No Progression (NP), in order to study the worst case

scenarios. The Gone Green scenario is based on the assumption that all renewable generation and

environmental targets are achieved: 15% of all energy from RES by 2020, and 80% reduction in

greenhouse gasses by 2050. The No Progression scenario is based on the assumption that only

new units that are already under construction, or too far advanced to be cancelled, are

commissioned. Figure 3.26 shows the development of the conventional generation and the Power

Electronics-Interfaced Generation (PEIG) over time for the Gone Green and No Progression

scenarios. In Appendix B.1, more details can be found regarding the division over the 29 zones in

the reduced GB model.

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Figure 3.26 Development of conventional generation and PEIG (Gone Green & No Progression).

Each particular choice of the wind generation per zone was made by taking into account the

proximity to the shore of each substation to define on whether the generation might be on- or

offshore, and by using the wind speed map published by English authorities to estimate the size of

the wind park. The expected ratio of onshore/offshore wind generation is shown in Table 3.9. With

the data shown in the table, it is possible to scale the synchronous generation and to install the

wind parks at the designated places in the model, while keeping the expected ratio of

onshore/offshore wind generation.

Table 3.9 Ratio of wind generation installation. Based on the information provided in [50].

Gone Green 2016 2020 2025 2030 2035

On-Shore (%) 53 41 32 32 32

Off-Shore (%) 47 59 68 68 68

No Progression 2016 2020 2025 2030 2035

On-Shore (%) 50 50 50 50

Off-Shore (%) 50 50 50 50

After the implementation in PowerFactory, the power dispatch profile for each generator is

configured in order to supply the demand as shown in Table 3.10. The dispatch setting of

generators must comply with the main power flows in the network (see also Appendix B.1), as it is

desirable to have the scenarios in their most representative form of the real GB system. For the

purpose of stability studies, wind generation is dispatched at maximum of its capabilities in order

to create a worst case scenario as required by the Task objectives [1]. The dispatch values of each

generator along the years can be found in Appendix B.1.

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Table 3.10 Total load demand in the GB system over the years.

2016 2020 2025 2030 2035

Gone Green [GW] 52.450 48.749 49.349 52.900 57.050

No Progression [GW] 52.450 49.249 46.850 44.850 44.949

The scaling of generation and demand causes the need to reinforce the grid capabilities either in

topology (new lines, capacitors, STATCOMS, etc.) or in rated capacity of the existing elements. To

do so the NOA document [45] was consulted and used as inspiration to apply any required

reinforcement. The word “inspiration” is crucial to understand the use of the mentioned document

because in the frame of this research, it is nearly impossible to execute the actions mentioned

there because it is too detailed about real existing lines or equipment, which means it mentions

elements or zones that are not represented in the reduced model.

The way to proceed is to implement the scaling in generation and demand, and to analyse the

required reinforcements in the GB model afterwards. Once this is done, a double check of those

required activities is contrasted with the NOA study to corroborate the similarity in nature (i.e. in

NOA also similar actions are executed, although maybe not in the same region or substation).

Implementation in PowerFactory

The model of the GB system in PowerFactory is a reduced model, which consists of five areas:

Scotland, North England, West England, East England and South England [51]. The model is

organised into 29 zones, each one comprising one bus, one conventional power plant represent the

dominant type of generation in the zone, and a load. The generators are represented by using the

sixth order model, whereas the loads are represented with the static ZIP model, which is set to

work as a constant power model (worst case). The buses are interconnected through 99

transmission lines (49 double-circuit lines, and one single-circuit line). These transmission lines

represent the main routes for the power flows across the GB system.

In the reduced model of the GB system, each substation is constructed based on the topology

shown in Figure 3.27. All the elements connected to the node bus have representative values, i.e.

they are grouped elements that include others that were not represented in the network. In this

way, the generators and loads have larger ratings than normal commercial generators or single

loads. The load models used in the GB system are 100% static loads, modelled as constant power

loads (both P and Q). The parameters of the ZIP model in PowerFactory were taken from [52].

The transition scenarios are a set of 9 PowerFactory files (pfd extension files) as shown in Figure

3.28, shared with the MIGRATE consortium under the internal communication memo "Great Britain

transition scenarios in DIgSILENT - PowerFactory" on 07-04-2017.

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Figure 3.27 Node bus structure in the reduced GB system (from [49] - Figure 3.2, pp. 76).

The procedure for developing the baseline scenario (year 2016), similarly to all the other cases,

starts by setting the installed capacity of the synchronous machines and wind generation. This is

done by changing the number of parallel machines or the rating capabilities of the type model,

while for the latter the information of onshore/offshore installation is of major relevance because

the offshore wind parks have different topology than the onshore ones.

The dispatched generation and load demand is implemented in PowerFactory after determining the

installed capacity (as shown in the tables in B.1). Subsequently, a power flow calculations is

executed to perform an element inspection where the overloaded parts or buses with undesired

voltage deviations are identified, so the necessary corrective actions (reactive power

compensation) can be taken. Figure 3.29 shows the procedure used for the creation of the baseline

scenario, and the transition scenarios.

Figure 3.28 PowerFactory Data manager with the 9 transition scenarios archives.

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As mentioned in the previous paragraphs, the onshore and offshore topologies of the

interconnection of the wind parks are different. The topologies used for the wind parks’ installation

are shown in Figure 3.30 and Figure 3.31 for offshore and onshore, respectively. A distance for the

transmission lines of 70 km was assigned to submarine cables due to the limited information

available about the offshore installation in Great Britain, a design consideration was to take all

these as near-shore generation units. The offshore topology was based on the wind park

connection displayed in [54], where real-world parameters for each element in the grid connection

and control systems were also taken. The information for the transformers, submarine cables and

some typical values for the Static Var Compensators (SVCs) are put together in Table 3.11, Table

3.12 and Table 3.13.

Start

Update values of installed capacity of wind parks and conventional power plants

Set values of load demand and generation dispatch

Run power flow calculation

Identify overloaded elements and buses with

voltage limit violation

Overload or voltage

violations?End

Take corrective actions

Yes No

Figure 3.29 Procedure to create transition scenarios in the GB system.

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Figure 3.30 Connection of offshore wind park to the grid.

Table 3.11 Line data for offshore wind park connection.

Component Impedance Capacitance

150 kV sub.cable 0.046+j0.113 Ω/km 241.0 nF/km

Table 3.12 Transformer data for offshore wind park connection.

Transformer type Voltage Rated power Impedance

Wind turbine trafo (for Type 4 turbines) 0.4/33 kV 1000 MVA 0.06

Wind turbine trafo (for Type 3 turbines) 0.66/33 kV 1000 MVA 0.06

Table 3.13 SVS data (biggest value) for offshore wind park connection.

Q Reactance (>0) Mvar = 1121 Q per Capacitor unit (<0) Mvar = -337.12

The SVSs described in Table 3.13 are meant to compensate the charging reactive power of the

cables, and thus, to minimise the steady state voltage deviation from bus bars at 150 kV. The

number of parallel cables displayed in the offshore schematic depends on the power level to be

transmitted, since to the cables used in this work have fixed ampacities of either of 2 or 2.66 kA.

Figure 3.31 Connection of onshore wind park to the grid.

On the other hand, Figure 3.32 shows a schematic of the way of connection of all the synchronous

generators, as it was defined by the researchers of the University of Manchester in [49].

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The high voltage side of the substation, in its majority, is at 400 kV with 26 out of 31 existing

nodes at this voltage level. Four nodes are at 275 kV and one at 138 kV [53]. Figure 3.30 and

Figure 3.31 show at the far right the Point of Common Coupling (PCC), which compared to Figure

3.32 is the high voltage side of the substation. This implies that the wind parks and synchronous

generators are one next to the other, both connected at the HV side of the substation.

Following the information determined for each transition scenario, once the load demand,

synchronous and wind generation are scaled up, the topology of the grid must be reinforced. It is

important to remember that the design is for the worst-case scenario, which is the load demand at

100% of winter peak, for which the reinforcement actions are validated against this highly stressed

scenario. However, as it was explained previously, the reinforcements cannot be taken literally

from [45] but inspired on it. The most frequent actions taken were:

─ Adding parallel transformers

─ Adding parallel lines

─ Adding Static Var Systems (SVS), in Voltage ControlMode (set point at 1.0 pu)

─ Replacing existing lines by another with higher ratings

─ Replacing existing transformers by another with higher ratings

Figure 3.32 Connection of synchronous generators to the grid in all scenarios.

3.3.3 Implementation into the Irish Test System

This section describes the implementation of the baseline case (2016) in the Irish system. This

model has been developed in PowerFactory 2016 using steady state system data publically

available [55] and additional generic dynamic data. The purpose of the model is to reproduce the

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stability problems identified with the generic test cases (in Section 3.2) and to facilitate detailed

investigations of the dynamic behaviour in a real system. In no way should this model be

interpreted as a true representation of the Irish power system at any particular point in time or

should be used for the purposes of replicating specific events in the grid. While accurate, many

simplifications had to be made for technical and commercial reasons. Therefore, the results

produced with this model will give a typical and meaningful (rather than exact) picture of the

performance of a small isolated system with large share of PE based generation, like in Ireland.

Current Situation

The Ireland and Northern Ireland power system is a synchronous island system with limited HVDC

interconnection to Great Britain. This single synchronous power system has a forecasted peak

demand of approximately 7000 MW and an expected installed capacity of dispatchable conventional

generation of 9500 MW by 2020.

European legislation has mandated that at least 20% of the European Union’s final energy

consumption should come from renewable energy by 2020. In Ireland, the electricity sector has

been mandated to deliver the majority of this renewable energy contribution and has set an

electrical energy target of 40% from renewable resources by 2020. Wind power will be the

dominant resource in meeting the targets with approximately 37%.

The transmission system in Ireland is operated at 400 kV, 220 kV and 110 kV. The transmission

system in Northern Ireland is operated at 275 kV and 110 kV. The two transmission systems are

connected by means of one 275 kV double circuit. The 400 kV, 275 kV and 220 kV networks form

the backbone of the all-island transmission system. Typically large generation stations (greater

than 100 MW) are connected to the 220 kV, 275 kV or 400 kV networks. The 110 kV circuits

provide parallel paths to the 220 kV, 275 kV and 400 kV networks and are the most extensive

elements of the all-island transmission system.

The transmission system is generally comprised of overhead lines. There are exceptions to this,

such as in the city centres of Belfast, Cork and Dublin, where underground cables are exclusively

used. Moreover, increasing amounts of underground cables are being installed in remote areas

(such as the South West) to facilitate connections of wind farms to the nearest grid infrastructure.

The East West HVDC Interconnector links the electricity grids in Ireland and Wales, while the Moyle

HVDC Interconnector links the electricity grids in Northern Ireland and Scotland. Figure 3.33 shows

a geographical map of the existing transmission grid at the beginning of July 2016.

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Figure 3.33 All Island Transmission System (July 2016) [55].

Northern

Ireland

KILTOY

CATHALEEN'S

FALL

BINBANE

DRUMKEEN

MEENTYCAT

SORNE

HILL

TRILLICK

DRYBRIDGE

LOUTH

MEATH

HILL

MULLAGHARLIN

NAVAN

SLIGO

TAWNAGHMORE

MOY

CASTLEBAR

RICHMOND

CARRICK

- ON -

SHANNON

BELLACORICK

GILRA

ARIGNA

TONROE

CORRACLASSY

CUNGHILL

CORDERRY

FLAGFORD

GARVAGH

SHANKILL

ARVA

RATRUSSAN

ENNIS

DALLOW

PORTLAOISE

CRANE

CARLOW

KILKENNY

THURLES

CAHIR

DOON

ANNER

BALLYDINE

MALLOW

CHARLEVILLE

RATHKEALE

TARBERT

BUTLERSTOWN

DUNGARVAN

BLAKE

TULLABRACK

MUNGRET

MONETEEN

FASSAROE

POLLAPHUCA

IKERRIN

LISHEEN

OUGHTRAGH

TRALEE

DUNFIRTH

KILLOTERAN

KILLONAN

STRATFORD

BALLYBEG

TIPPERARY

GLENLARA

ATHY

PROSPECT

MONREAD

TRIEN

AHANE

ARDNACRUSHA

LIMERICK

CASTLEFARM

SEALROCK

WATERFORD

TYNAGH

SINGLAND

CLAHANE

DERRYBRIEN

AGANNYGAL

AUGHINISH

WEXFORD

KILTEEL

BALLYWATER

GREAT

ISLAND

CULLENAGH

TURLOUGH

HILL

CARRICKMINES

SEE

DUBLIN

AREA

NORTH WALL

SHELLYBANKSIRISHTOWN

OLDSTREET

FINGLAS

BARODA

NEWBRIDGE

HUNTSTOWN

MONEYPOINT

KELLIS

ARKLOW

PLATIN

KNOCKUMBER

GORMAN

BALTRASNA

GLASMORECORDUFF

WOODLAND

ATHLONE

CASHLA

GALWAY

LANESBORO

THORNSBERRY

CLOON

SOMERSET

CUSHALING

DALTON

SALTHILL

DERRYIRON

SHANNONBRIDGE

KINNEGAD

MULLINGAR

BANDON

DUNMANWAY

MACROOM

BRINNY

KNOCKRAHAKILBARRY

RAFFEENAGHADA

MARINA

CARRIGADROHIDCOOLROE

BALLYLICKEY

CLONKEEN

COOMAGEARLAHY

GARROW

GLANLEE

GLANAGOW

INNISCARRA SEE

CORK

AREA

CLASHAVOON

BARRYMORE

KNOCKEARAGH BOGGERAGH

DROMADA

SHELTON

ABBEY

Ireland

KILTEEL

COOKSTOWN

HAROLD’S

CROSS

RYEBROOK

FINGLAS

INCHICORE

MACETOWN

GRIFFINRATH

MAYNOOTH

McDERMOTTRINAWADE

WOLFE TONE

CITYWEST

CABRA

GRANGE

CASTLE

HUNTSTOWN

KILMORECOLLEGE

PARK

NANGOR

WOODLAND

GLASMORE

CORDUFF

GRANGE

NORTH WALLSHELLYBANKS

IRISHTOWN

ARTANE

TANEY

RINGSEND

POTTERY ROADCENTRAL PARK

PELLETSTOWN

KILMAHUD

DARDISTOWN

POPPINTREE

CROMCASTLE

FRANCIS ST.

NORTH

QUAYS

POOLBEG

DUBLIN AREA

MILLTOWN

MISERY

HILL

BLACKROCK

CARRICKMINES

CORK AREA

LOUGHMAHON

CORK

HARBOURAGHADA

WHITEGATE

MIDLETON

KNOCKRAHA

OLDCOURT

CASTLEVIEW

COW’S

CROSS

LONGPOINT

GLANAGOW

BARNAHELYRAFFEEN

RINGASKIDDY

KILBARRY

MARINA

LIBERTY

STREET

TRABEG

CORK

CITY

COBH

LODGEWOOD

CAUTEEN

CASTLEDOCKRILL

CARROWBEG

GORTAWEE

LISDRUM

CLIFF

GOLAGH

BALLYMENA

LOGUESTOWN

COLERAINE

LIMAVADY

COOLKEERAGH

KILLYMALLAGHT

SLIEVE KIRK

LISAGHMORE

SPRINGTOWN

STRABANE

OMAGH

ENNISKILLEN

AGHYOULE

MAGHERAFELT

TAMNAMOREDUNGANNON

DRUMNAKELLY

NEWRY

BANBRIDGE

WARINGSTOWN

LISBURN

BALLYNAHINCH

ANTRIM

KELLSLARNE

KILROOT

MAGHERAKEEL

CASTLEREAGH

HANNAHSTOWN

TANDRAGEE

Northern

Ireland

GLENREE

BANOGE

NENAGH

SRANANAGH

PORTAN

EAST-WEST

INTERCONNECTOR

PORTAN

Transmission System400 kV, 275 kV, 220 kV and 110 kV2016

LEGENDTransmission

Connected Generation400 kV Lines

275 kV Lines

220 kV Lines

110 kV Lines

HVDC Cables

220 kV Cables

110 kV Cables

400 kV Stations

275 kV Stations

220 kV Stations

110 kV Stations

Phase Shifting Transformer

CLOGHRAN

CRORYKILL

HILL

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FORTUNESTOWN

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Scenario Implementation in PowerFactory

The baseline model of the Irish grid is based on a data freeze of July 2016 [55]. Figure 3.34 shows

the schematic grid representation in PowerFactory, where the colours differentiate its seven

Areas/Zones. This model represents in detail all transmission stations and circuits in Ireland. The

Northern Ireland transmission grid has not been included in the model. This means that the grid,

as modelled, is electrically smaller and weaker than the real all-island system. Consequently, the

stability issues associated with integration of large shares of PE will be exacerbated, which will

simplify detection and analysis.

The physical layout of all transmission stations has been represented in detail, as shown in Figure

3.35. This facilitates the simulation of operational switching measures that can be evaluated for the

purposes of system stability. Examples of these measures include station sectionalising to redirect

flows and avoid network congestion or to manage fault levels. The model comprises a total of 238

stations and 1334 busbars.

The PowerFactory model is structured in seven geographical Areas. The breakdown of generation

and demand for each area is included in Table 3.14. It can be seen that the bulk of the load is

concentrated in Dublin. Conventional generation is mostly located in Dublin, Cork (South West) and

the Shannon Estuary (Mid-West), with direct access to high capacity 400 kV and 220 kV

transmission circuits. Wind generation is mostly located in the west coast of Ireland, where wind

resources are abundant but transmission infrastructure is scarce. Initially, most of the wind farms

were connected to 110 kV or the distribution networks. However, network congestion and stability

considerations are driving transmission network reinforcements to redirect the wind power towards

the 220 kV and 400 kV network. These reinforcements have been implemented in the model.

Two scenarios have been selected in the Irish test system: the ”Slow Change” scenario and

the ”Low Carbon Living” scenario. A detailed description of these scenarios can be found in [56],

and a summary is included in Appendix B.2.

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Figure 3.34 Visualisation of the Irish Grid in the PowerFactory model.

2

1

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Figure 3.35 Visualisation of a Transmission Station in the model of the Irish system.

Modelling in PowerFactory

Synchronous Generators

There are 55 synchronous generators represented in detail in the model. This portfolio

encompasses a wide range of machines with different sizes and characteristics. As an example, the

rated apparent power varies from large Combined Cycle Gas Turbines (CCGTs) of 570 MVA to small

hydro plants of 15-20 MVA. Similarly, normalised inertia constants range from 10 s to 1.3 s. The

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synchronous generators are represented in PowerFactory using ElmSym elements and TypSym

type library components. The model parameters correspond to the physical characteristics of each

unit as provided by the manufacturers in their technical datasheets.

Table 3.14 Generation and Load Data in Ireland baseline model.

Area Conventional Generation

[MW]

Wind Generation

[MW]

Demand

[MVA]

DUBLIN 2078 0 1815

MID-WEST 2090 168 413

MIDLANDS 472 414 486

NORTH-EAST 0 201 430

NORTH-WEST 264 609 756

SOUTH-EAST 431 144 580

SOUTH-WEST 1516 1210 756

Generic benchmark controllers have been implemented to represent the dynamic behaviour of

turbine governors and Automatic Voltage Regulators (AVR). These models have been tuned to

produce “reasonable” responses, similar to those observed in real-time operation. It should be

noted that the tuning has been based on professional experience, but validation against actual

responses during system disturbances has not been performed. As such, the dynamic response of

these machines must be interpreted as “typical” rather than exact replica of the conventional

generation portfolio installed in Ireland.

The standard IEEEX1 AVR model was used to represent the excitation system for all synchronous

generators. The standard HYGOV model was used to represent the speed governor in all hydro

plants. The standard IEEEG2 model was used to represent the speed governor in all other

conventional plants. Typical parameters for the controllers can be found in Appendix B.2.

Wind Farms

Wind farms were represented with the new generic models developed by Energynautics for the

MIGRATE project [25]. At the time of data freeze, there were 131 wind farms connected in Ireland.

Implementation of the new generic models in such large volume was soon identified to be

inefficient from a computational point of view. Therefore, model aggregation was performed to

reduce the models to a practical volume. Thirty five individual wind farms were finally represented.

Figure 3.36 shows the geographical location of the aggregated wind farms in the model. The

cumulative amount of installed wind capacity on each area is included in Table 3.14. For simplicity,

all wind farms were represented with the Type 3-A dynamic model using the default parameters

provided by Energynautics. However, some settings had to be changed in order to activate the

voltage control functionality, which is a Grid Code requirement for all generators connected at

transmission voltage levels (i.e. 110 kV and above) [57]. The relevant parameter settings for that

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functionality can be found in Appendix B.2. Wind farms connected to the distribution network were

configured with fixed power factor.

Load

The general load, as forecasted for each transmission station [55], was represented at the low

voltage side of the TSO/DSO interface transformers. This is typically at 38 kV, 20 kV or 10 kV.

Industrial load connected at transmission level was represented in detail with their contracted

Maximum Import Capacity (MIC) behind the grid connected transformer. The ElmLod element and

TypLod type components available in PowerFactory were used. A total of 266 individual loads are

represented in the model.

The loads were represented as the maximum winter peak value (5000 MW) and scaling factors

were used to simulate lower demand scenarios like summer peak (4000 MW) or summer valley

(1750 MW). For dynamic simulations, the voltage and frequency dependency of the load is

captured with a 50% static load and 50% dynamic load assumption. The parameters used in the

simulations can be found in Appendix B.2.

Other Transmission Network Components

All other transmission network elements like lines, cables, transformers, reactors, capacitor banks,

etc, were represented using standard library components from PowerFactory. The lines and cables

were represented using the actual physical characteristics of the conductors and geometry of the

towers/cables. This approach allows accurate computation of mutual coupling between parallel

circuits. Individual sections of non-homogeneous circuits were represented in detail and connected

in series. This resulted in a total of 1076 line elements and 257 cable system elements. All circuits

were represented with Lumped Parameters (PI model). Two and three winding transformers were

represented in detail using the technical datasheet parameters from each unit. A total of 685

transformers are represented in the model.

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Figure 3.36 Location of aggregated wind farms in the model of the Irish system.

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4 Study of Power System Stability

4.1 Introduction

The overall approach used to conduct the study of each stability issue listed in Table 1.2 in

Chapter 1 is schematically illustrated in Figure 4.1. The generic test cases, the reduced size

representation of the GB system and the detailed representation of the Irish system, which were

introduced in Chapter 3, constitute the main inputs to the platform that is used for modelling and

simulation. The modelling, simulation, and scripting functionalities of DIgSILENT PowerFactory are

used in the study and assessment of the frequency performance in the frequency containment

period, large-disturbance rotor angle stability, and small-disturbance voltage stability. PSCAD is the

preferred tool for the study and assessment of sub-synchronous controller interactions. A selected

set of operating conditions (e.g. profile of load and generation dispatch that entails a highly loaded

system) and disturbances of interest (e.g. outage of the biggest power plant), i.e. the worst case

(when the system is prone to instability), is defined in the corresponding platform to ascertain the

consequences of increasing penetration levels of PE-interfaced wind power generation. This

information can be defined by each operator or planner based on the operational experience and is

system dependent.

ModellingSystem layout, component parameters

Selected operating conditions and disturbances

SimulationStability indicatorTime response of system variables

DIgSILENT PowerFactory (RMS simulations)PSCAD (EMT simulations)

Figure 4.1 Approach for the study of power system stability.

For each stability phenomenon, the most widely used indicator (in academia and industry) is

evaluated by using the generic test cases. The GB system is used to further evaluate the indicators

concerning frequency performance in the frequency containment period, large-disturbance rotor

angle stability, and small-disturbance voltage stability. Additional tests concerning frequency

performance in the frequency containment period and large-disturbance rotor angle stability are

done by using the Irish system. Basically, the suitability (to capture the resulting stability degree)

of the indicator is investigated before integrating it into the notion of Key Performance Indicator

(KPI), which is introduced subsequently. Other tools like Python, Matlab, and Microsoft Excel are

used to automate the execution of simulations, data processing, and calculation of indicators from

the time response of selected system variables (e.g. kinetic energy of the system). The rationale

behind the selection of the system variables is addressed as well.

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Simply put, a KPI is expected to map the values of a system variable or set of system variables

onto the actual value of a stability indicator (i.e. a metric that quantifies numerically the status of

the system in terms of stability, e.g. ROCOF, NADIR, critical clearing time, etc.). The KPI allows

estimating distance and the tendency of the system to move from a stable condition to the stability

limit. Figure 4.2 shows two possible methods of structuring a KPI. The first one illustrates the case

when a simple (e.g. single valued) relationship can be established such that a characteristic curve

can be used to map the values of a system variable into the corresponding values of a stability

indicator. The second method concerns with the case when it is not possible to find a simple

relationship between a system variable and a stability indicator. This case can occur when the non-

linearity associated to the dynamic performance of a power system is excited. Therefore, an

estimation method is needed to infer the value of a stability indicator that will result as a

consequence of having different values of a system variable or set of variables. As it will be shown

in the next sections, the KPI is determined based on offline simulations (accuracy dependent on

suitability of the used system model). Nevertheless, it might be possible to use them in

combination with measurements from the Energy Management System to assist the operators in

the control room19 . The KPI is also a valuable tool for stability assessment in power system

planning studies.

Key system variable

Stability indicator

Mapping Curve

(a)

Key system variable 1

Key system variable 2

Key system variable N

...Estimation

methodStability indicator

(b)

Figure 4.2 Definition of key performance indicator: (a) Estimation of distance to instability from clearly defined relationship; (b) Estimation of distance to instability based on inference (no clearly defined relationship).

4.2 KPI for Assessment of Frequency Performance

According to the prioritisation of topics of interest indicated in Chapter 1, Table 1.1 and Table 1.2,

the decrease of inertia (which entails a major impact in the time frame of inertial response after a

system contingency such as the occurrence of an active-power imbalance) was ranked as the topic

of highest interest. The issue related to missing or wrong participation of PE-connected generators

and loads in the frequency containment period has also been considered among the topics of

19 The development of the KPIs described is done from the power system analysis point-of-view. Whether and how the proposed KPIs can be evaluated and displayed in the Energy Management System in real-time will be addressed in WP2 of the MIGRATE project.

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highest interest. Therefore, the research outcomes presented in this chapter are related to the time

frame concerning the containment period. The frequency performance in other time frames (e.g.

frequency restoration period) is out of the scope of D1.2.

4.2.1 Frequency Performance in Containment Period

In this section, ROCOF and NADIR are the indicators evaluated to obtain insight about their

suitability with respect to their application in the study of systems with high penetration of

PE-interfaced generation. ROCOF and NADIR are the most widely used indicators by TSOs

worldwide to assess the frequency performance in the frequency containment period [58], [59].

Rate Of Change Of Frequency

The Rate of Change of Frequency (ROCOF) constitutes the frequency gradient after an imbalance

event of active power generation and load demand [60]. The frequency starts to deviate from the

rated value as an immediate result of a generation loss. Figure 4.3 illustrates the variation of the

frequency, as an example, for the variation of the frequency for different values of inertia in

generic test case 1.

Figure 4.3 Illustration of different slopes for different values of inertia.

The ROCOF, which results during the first instants after the time of occurrence of an event (e.g.

generator outage) that causes imbalance in a power system, is defined as follows [39]:

where f stands for frequency (in Hz).

ROCOF =𝑑𝑓

𝑑𝑡 (4.1)

NADIR

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For a synchronous generator, the first time derivative of the frequency, 𝑑𝑓

𝑑𝑡 , can be determined from

the per-unit formulation of its swing equation [12], that is:

where:

∆𝑃 = the change of the active power (e.g. amount of MW lost due to a generator outage)

f0 = the nominal frequency (Hz)

H𝑖 = the inertia constant of the generator (s)

TN−𝑖 = the acceleration time constant (s)

(i.e. time in seconds it takes to accelerate a generator from standstill to nominal speed)

SB−𝑖 = the nominal apparent power of the generator (MVA) [61]

i = the i-th generator among n generators in the system

The relationship between the kinetic energy stored in the rotating masses (MWs), Ekin−𝑖 , at

nominal speed and the inertia constant H𝑖 of a synchronous generator is defined by [62], [63].

The total kinetic energy of the system is computed by [63]:

where n is the number of synchronous generators in the system.

Equation (4.5) is determined by substituting equation (4.3) into (4.2). It can be seen that the

ROCOF is inversely proportional to the kinetic energy (as it does with the inertia constant in

equation (4.2)).

Motivated by equation (4.5), an approximation of ROCOF, as shown in equation (4.6) is suggested

in [64] and [65] for qualitative assessment of the frequency performance within the time window

of the system inertial response.

𝑑𝑓

𝑑𝑡=

∆PSB−𝑖2H𝑖

f0 =

∆PSB−𝑖TN−𝑖

f0 (4.2)

Ekin−𝑖 = H𝑖 ∙ SB−𝑖 (4.3)

Ekin−sys = ∑ Ekin−𝑖𝑛

𝑖=1 (4.4)

𝑑𝑓

𝑑𝑡=

∆P

2 ∙ Ekin−𝑖f0 (4.5)

ROCOF =∆Psys

2(Ekin−sys − Ekin−lost)f0 (4.6)

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where ∆Psys and Ekin−lost stand for change in system active power and kinetic energy lost due to the

sudden disconnection of a generator, respectively.

It is worth highlighting that the swing equation concerns exclusively with the rotor motion of an

individual synchronous generator. Therefore, for a multi-machine system, an equivalent generating

unit is defined to represent the average behaviour of n synchronous generators. The equivalent

generating unit is known in existing literature as Centre of Inertia (COI).

According to [66], the frequency of the COI is defined as

where 𝑓𝑖(𝑡) is the time frequency response of the i-th generator, recorded for a given time window.

The ROCOF is estimated from the frequency of the COI, by considering a time window of 500 ms

following the disturbance [67]. It is worth recalling that the analysis done in this section focuses on

the assessment of the frequency performance in the containment period, time window of inertial

response of synchronous generators. In this context, a significant variation of the ROCOF is

expected to happen once a critical imbalance (e.g. outage of the largest generation units) occurs in

the system. Thus, in such conditions, the ROCOF is calculated as follows:

1. Compute the frequency Centre Of Inertia (COI) according to equation (4.7) [66]-[67].

2. Get the time of the event (𝑡1). See Figure 4.4 for a graphical illustration.

3. Find the index of an intermediate time 𝑡2 such that, for instance, 𝑡2 = 𝑡1 + 0.5 s.

4. Make a linear fitting to 𝑓𝐶𝑂𝐼(𝑡) in 𝑡 ∈ [𝑡1 , 𝑡2].

5. Get the slope of the linear function as ROCOF.

Figure 4.4 Illustration of the required points for ROCOF computation. NADIR is highlighted.

𝑓𝐶𝑂𝐼(𝑡) =∑ H𝑖SB−𝑖 𝑓𝑖(𝑡)𝑛𝑖=1

∑ H𝑖SB−𝑖𝑛𝑖=1

(4.7)

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The normative contingencies for the interconnected operation in Continental Europe, as defined by

ENTSO-E in [39] and [59] for the ROCOF computation is the tripping of the two largest generation

units connected to the same busbar. The maximum value of ROCOF allowed in the Great Britain

system is 125 mHz/s, whereas for continental Europe values between 500 mHz/s and 1 Hz/s have

been recorded [59].

It should be mentioned that in this study, the frequency of the COI in the system under study is

used for the calculation of ROCOF. Although being out of scope of D1.2, because the focus is on a

systemic issue, it is worth pointing out that in case of having a system with several regions with

different inertia characteristics, the same methodology based on frequency of the COI can be

applied for each of the regions.

NADIR

This indicator corresponds to the lower frequency value obtained after a power imbalance which

depends on the system inertia, the response of the available frequency containment reserves, the

size and location of the disturbance, and the pre-disturbance operating conditions. In Figure 4.3,

this value is highlighted with a dot of the corresponding colour for each curve, and is pointed out in

Figure 4.4 as well [68].

The criterion that defines the limit for NADIR is expressed as

𝑓𝑁𝑎𝑑𝑖𝑟 ≥ 𝑓𝑚𝑖𝑛 (4.8)

where fmin is the minimum acceptable frequency defined in the grid code.

This indicator has a high relevance in the frequency control procedures because a low value (lower

than 47.5 Hz) might violate the security thresholds and a blackout can hardly be avoided [39] due

to the disconnection of generation units at this frequency. However, in order to avoid load shedding,

the maximum frequency deviation is defined as -800 mHz in continental Europe as stated in

sections A-D2.3 and A-D2.4 of [59], which represents a NADIR of 49.2 Hz.

4.2.2 Analysis of ROCOF and NADIR using Generic Test Case 1

Automating Data Extraction and Processing

The power system dynamics is simulated by using DIgSILENT PowerFactory. This software allows

an interaction with Python which can be exploited to automate the execution of simulation and data

extraction. Thus, the Python-PowerFactory interface is used to call the set of defined dispatch

scenarios (cf. Figure 3.16 in Chapter 3) from an external file (Excel data base). Matlab scripts are

used to process the data obtained from the simulations in PowerFactory and calculate the ROCOF

and NADIR. The overall procedure is schematically shown in Figure 4.5. Please note that the user

has the option to customise the process to automatically define different system topologies.

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Start

Run RMS simulation time_DB

All Dispatch

cases?

i++

Finish

Load dispatch cases

i=1

Select dispatch case(i)

Dispatch cases

...

Load Case1

Ld1

Ld2

...

D1

D2

Ldn Dn

... CaseM

... ...

D1

D2

Dn

...

......

Gen Case1

G01

G02

...

D1

D2

Gn Dn

... CaseM

... ...

D1

D2

Dn

...

...

...

Yes

Branch

outage?

No

Set line out of

service

No

Yes

SS_DB

Set event

Automated

simulation and data

extraction

Data Processing

Run load flow

Figure 4.5 Procedure for automated simulation and data extraction by combining PowerFactory, Python, Matlab, and Excel. SS_DB stands for database of initial conditions (steady-state), whereas time_DB stands for database of time responses of system variables.

An example of dispatch scenarios is shown in Table 4.1, where the synchronous generators’

dispatch for winter season is shown. The character X indicates that a synchronous generator is out

of service. This table represents several situations, where the synchronous generation dispatch

changes due to the shift from low to high share from wind generation. It is worth clarifying that

synchronous generators in Area A belong to hydro power plants (another type of renewable energy

based power plant) and are kept as base plants in all operational scenarios. Besides, it is

highlighted that the diversity of dispatches shown in Table 4.1 entail different levels of inertia (also

different levels of kinetic energy) and different geographical spread of power electronic interfaced

wind generation within Area B as well as within Area C. The load information is selected according

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to the seasons presented in Chapter 3, Section 3.2.3, for generic test case1 (Winter, Spring or

Summer) as 100%, 80% or 60% of Winter peak load. The procedure of creating different

operational scenarios illustrated in Figure 3.16.

Table 4.1 Synchronous generator dispatch for Winter season (in MW).

Operational scenario

Sync Gen 1 2 3 4 5 6 7 8 9 10

A1aG 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

A1bG 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

A2aG 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

A2bG 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

A3G 400 400 400 400 400 400 400 400 400 400

A6G 440 440 440 440 440 440 440 440 440 440

B10G 950 X X X X X X X X X

B2aG 1200 1200 X X X X X X X X

B2bG 1200 1200 1200 X X X X X X X

B3G 1401.7 1401.7 1401.7 1401.7 X X X X X X

B8G 900 900 900 900 900 X X X X X

C10G 850 850 850 850 850 850 X X X X

C12G 1150 1150 1150 1150 1150 1150 1150 X X X

C14G 850 850 850 850 850 850 850 850 X X

C2G 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0 X

C7G 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0 1300.0

Total generation (Synchronous) 15941.7 14991.7 13791.7 12591.7 11190 10290 9440 8290 7440 6140

Total losses 215.5 216.05 220.21 224.37 229.12 229.17 229.23 228.94 228.95 232.93

Total Load 15565 15565 15565 15565 15565 15565 15565 15565 15565 15565

To illustrate the effects of increasing of wind penetration, the following three cases for Winter

(Case 1, Case 5 and Case10 according the dispatches in Table 4.1) are analysed. In Case 1, the

whole system is fully supplied by conventional power plants with synchronous generators. In

Case 5, Areas A and C remain with all plants with synchronous generators in operation, whereas

Area B has only one plant with synchronous generators in operation and the other plants are

replaced by wind power plants. In Case10, Area A still remains with all plants with synchronous

generators in operation, Area B has 100 % of penetration of wind generation, and Area C has only

one plant with synchronous generators in operation and the other plants are replaced by wind

power plants. In all cases the imbalance is caused by the sudden outage of the conventional power

plant A1bG in Area A (which represents 6.3% of total generation).

As shown in Figure 4.6 (Case 1), since all the areas are based on synchronous generation, the

frequency of the COI and the values of system indicators (ROCOF/NADIR) are affected by all three

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areas. Note also that inter-area low frequency oscillations involving the three areas are highly

excited by the occurrence of the imbalance.

Figure 4.6 Frequency responses, Case 1: Conventional power plants with synchronous generation in all areas.

Figure 4.7 Frequency responses, Case 5: Areas A and C with all conventional plants in operation, Area B with only one conventional plant in operation.

In Figure 4.7 (Case 5), as it happens in Figure 4.6, the synchronous generators in Area A

experience a higher frequency gradient, since they are located in the Area in which the imbalance

occurs. A similar observation was reported in [65]. Additionally, note in Figure 4.7 that the

frequency of the COI is mainly affected by Areas A and C, and it can also be seen that the

remaining synchronous generation in Area B follows the average (i.e. experiences less frequency

gradient than generators in Area A). In this case, the inter-area low frequency oscillations are less

excited, whereas ROCOF and NADIR worsen significantly.

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Figure 4.8 Frequency responses, Case 10: Area A with all conventional plants in operation, Area B with 100% penetration of wind generation, Area C with only one conventional plant in operation.

Lastly, note in Figure 4.8 (Case 10) that all remaining synchronous generators follow very closely

the COI, whereas the inter-area oscillations are not excited, the ROCOF and NADIR worsen even

more w.r.t Case 5, and the frequency performance deteriorates dramatically after the NADIR. For

sake of illustration, the measured frequency in Case 10 for one bus of Area B (which has no

synchronous generators) is shown in Figure 4.9. This corresponds with the measured frequency of

the voltage in node 21 (the common coupling node of wind park 10B, cf. Figure 3.15). It can be

seen that the frequency response in Area B follows very closely the frequency of the COI.

Figure 4.9 Frequency of the voltage at node 21, Case 10: Area B with 100% penetration of wind generation.

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The remainder of this section focuses on three aspects:

1. Analysis of ROCOF and NADIR by using generic test case 1 (cf. Section 3.2.3). The ROCOF and

NADIR resulting from different levels of kinetic energy of the system (due to different levels of

inertia as a consequence of different wind penetration levels) and the effects of different load

model parameters on ROCOF and NADIR are investigated.

2. Further investigation on the findings from generic test case 1 by using an academic (reduced

size) model of the GB system (cf. Section 3.3.2) provided by the University of Manchester and

proposition of a methodology for KPI for frequency performance in the frequency containment

period

3. Additional tests based on the Irish system (cf. Section 3.3.3).

Calculation of ROCOF and Frequency NADIR

The computational procedure to determine the ROCOF and NADIR for the simulations run in this

work is shown in Figure 4.10. Once the data base with the generators frequency response is

obtained (time_ DB block in Figure 4.10) in the data extraction step (cf. Figure 4.5), the raw data

is migrated to MATLAB to begin the processing. The structure of the data base is such that there

exists one csv-file per each simulation case, for which the entire set of simulations needs to be

examined. Each csv-file has the time series and the corresponding frequency values associated to

the dynamic response of each active (i.e. in service) synchronous generator in the system.

Therefore, this information is used to compute the fCOI(t), from which the ROCOF is obtained.

As mentioned in Section 4.2.1, the common practice is to compute the frequency of the Centre-Of-

Inertia (COI), which constitutes an equivalent representation of the frequency response of the

entire system. In other words, each system can be seen as a single generator with an equivalent

inertia and its representative centroid frequency.

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Start

time_DB Load frequency data

i=1

Load results for

case(i)

Compute:

,

1

,

1

( )

( )

n

i base i i

iCOI n

i base i

i

H S PMf t

f t

H S PM

Get:

- time of event ( )

- NADIR and when occurs ( )1t

Find index:

Linear fitting to in ( )COIf t

ROCOF = slope of

linear function

Save values in row # iCASE ROCOF

1

2

...

0.119

M

NADIR

49.5

All cases?

i++

Export table to EXCEL

Finish

NO

YES

To locate NADIR

Use the MATLAB

function findpeaks()

in: 1( ) ( )COIg t f t t

Select highest maxima*

as NADIR.

*The maxima values of g(t) are the minima of frequency function.

t3

t2 = 500 ms

Figure 4.10 Procedure for data processing of frequency response and calculation of ROCOF and NADIR by using Matlab and Microsoft Excel.

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Figure 4.11 shows the frequency response of all generators in the generic test case 1 when a

generator unit that entails 10% of total generated active power gets suddenly out of service. The

event occurs at t=26 s.

Figure 4.11 Synchronous generators’ frequency response to an imbalance caused by 10%

generation loss, the frequency associated to the COI is shown by the red dotted line.

In the investigations done with all systems considered in this deliverable, the time window where

the slope of the frequency is computed is fixed to 0.5 s after the occurrence of the disturbance. As

shown in Figure 4.4, the window defined by [t1, t2] is the period of interest for ROCOF computation.

A linear fitting on in this time window will represent a suitable approximation of the actual rate of

change of frequency as can be seen in Figure 4.12.

Figure 4.12 Frequency of the COI. The time window for ROCOF computation is highlighted in red.

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Recalling Figure 4.4 and Figure 4.10, after a linear fitting is done, the slope of such a function is

stored as the ROCOF for the automatically analysed simulation case. This information is stored in a

table, which is exported to Microsoft Excel once all simulations are done.

Recalling Figure 4.5, complementary information to the dispatch scenarios defines the conditions

for getting the system profile:

─ Topological changes: No.

─ Event: Generator outage.

─ Name of element (cf. Figure 3.15 in Chapter 3): A1bG (represents 6.3% of total generation).

─ Load demand: Winter, Spring and Summer (cf. Figure 3.16 in Chapter 3).

The normative contingency for continental Europe, according to [39], is the generator outage of

the two biggest generation units at one busbar. However, this does not apply directly to generic

test case 1, because it leads to instability. Therefore, the outage of one of the biggest generation

plant (A1bG, cf. Figure 3.15 in Chapter 3) is considered.

Figure 4.13 shows all simulations (for different load demand levels) plotted together and it clearly

reveals different values of ROCOF for the same level of kinetic energy. It is observed that the trend

of ROCOF is such that the values are higher when the inertia or kinetic energy is low, which

happens when wind generation replaces synchronous generators. This means that it is possible to

establish a clear (single valued) relationship between the frequency response of the system and

the overall system kinetic energy. However, when the system load demand increases, the

frequency tends to respond more abruptly (although with the same trend), which is observed in

Figure 4.13 even though the kinetic energy might be the same.

Figure 4.13 ROCOF vs kinetic energy for different dispatch configurations. Generic test case 1.

0

0,05

0,1

0,15

0,2

0,25

0,3

15000 35000 55000 75000 95000 115000 135000 155000 175000

RO

CO

F [

Hz/

s]

Kinetic energy [MWs]

Winter

Spring

Summer

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In the results, the increasing behaviour of ROCOF was expected as it has been widely documented

that the reduction of inertia of kinetic energy causes a higher rate of change of frequency. Also, as

shown in Figure 4.14, the NADIR has a negative correlation with ROCOF, i.e. the higher the ROCOF

the lower the NADIR, which is also an expected result since the ROCOF measures how fast the

frequency drops.

Figure 4.14 NADIR vs kinetic energy for different dispatch configurations. Generic test case 1.

Impact of the Load Models

According to the presented information in the CIGRE working group report on a general overview

on load modeling and aggregation [69], and also the conducted survey on international industry

practice on load modeling in [70], the common model of load (known as ZIP model) to show its

voltage dependency consists of three polynomial terms as shown by equation (4.9). Each term has

one exponential component representing different types of load models [71]:

𝑃 = 𝑃0 (𝑎𝑃. (𝑣

𝑣0)𝑒_𝑎𝑃 + 𝑏𝑃. (

𝑣

𝑣0)𝑒_𝑏𝑃 + (1 − 𝑎𝑃 − 𝑏𝑃). (

𝑣

𝑣0)𝑒_𝑐𝑃) (4.9)

where 𝑣 is the instantaneous measured magnitude of load bus voltage and 𝑣0 is the initial operating

point magnitude of voltage from power flow calculation.

Other parameters like 𝑒_𝑎𝑃, 𝑒_𝑏𝑃 and 𝑒_𝑐𝑃 are the exponential coefficients to account for a certain

voltage dependency on the static load model. 𝑎𝑃 and 𝑏𝑃 are combinatory coefficients for having

different combinations within the ZIP model. Thus, different characteristics of the ZIP model can be

achieved by selecting different values for 𝑒_𝑎𝑃, 𝑒_𝑏𝑃 and 𝑒𝑐𝑃 . According to [12], the typical values

for constant power, constant current and constant impedance are 0, 1, and 2 respectively.

As indicated in the survey in [70], different load models have been proposed for consideration in

power system stability. The exponential recovery load model is reported as an alternative model in

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15000 35000 55000 75000 95000 115000 135000 155000 175000

NA

DIR

[H

z]


Winter

Spring

Summer

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[72]. Also as mentioned in [70], constant power and constant current load models account for

about 42% of all used models. In Europe, around 52% of the used models for power system

dynamic studies are constant P and ZIP models. In general, the constant power PQ load model is

still the most widely used in the majority of power system stability studies (as it is the most

conservative approach).

Study Case

In correspondence with the analysis done in the previous subsection, a generator outage event,

taking out generator A1bG (cf. Figure 3.15 in Chapter 3) with active power output of 120 MW,

accounting for approximately 6.3% of the total generation, is considered to study the impact of the

load model on the values of ROCOF and NADIR. The disturbance occurs at t=26 s, and the

simulation is run for a total of 45 s.

Results

The first case is when the load model is static but varied between a constant power load (P),

constant current load (I), constant impedance load (Z). The two scenarios taken for this case are

one with no wind and one with 61% (of the total generation) wind. The results are as shown in

Figure 4.15 and Figure 4.16.

Figure 4.15 ROCOF in generic test case1, Summer profile. Effect of ZIP load.

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0,0980

0,0982

Const_Z Const_I Const_P

Hz/

s

0% Wind; 100% SM Connected 61% Wind; 56% SM Connected

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Figure 4.16 NADIR in generic test case1, Summer profile. Effect of ZIP load.

It can be seen from these graphs that different load models give some insights into the importance

of load modelling. For both the high and the low wind scenario, it can be seen that the worst

results are obtained for constant power loads. This is because the power requirement of the load

remains constant despite the network conditions, unlike constant current (linear voltage

relationship) and constant impedance (quadratic voltage relationship). This means that for constant

power load scenarios, the current increases, which causes more strain on network and hence,

worse system indicators [53]. Under non-constant voltage relationship (as in constant I and

constant Z loads), the voltage drop in the system reduces the amount of power required by the

such loads in the system. Which means, after occurrence of the disturbance, the voltage profile will

be affected in some buses and due to the voltage dependency of loads, the loads are adjusted as

well. Power electronics-interfaced loads, when well regulated, behave as constant power loads [73].

As more and more loads are being PE-interfaced in form of motor drives, ac-dc converters, the

worst case scenario can be effectively represented by constant power load models. This is

supported by the analysis in Section 4.2.3 as well. A similar effect can be seen in the winter

scenarios where the system is more highly loaded. Figure 4.17 and Figure 4.18 below corroborate

this fact.

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Hz


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0,1480


Hz/

s

Low Wind High Wind

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Figure 4.17. ROCOF in generic test case1, winter profile. Effect of ZIP load.

Figure 4.18. NADIR in generic test case1, winter profile. Effect of ZIP load.

Henceforth, the analysis is carried out on the summer case where the system is slightly less loaded

than the winter case. The results and trends however, apply in a similar capacity to other loading

cases too. Now, the constant power is taken as the base case (worst case scenario). It is compared

against a mixture of loads, since the actual system is a mixture of loads. The base case is

compared against cases when the ZIP load compositions are 40% (constant Z), 40% (constant I),

20% (constant P), and 20% (constant Z), 40% (constant I), 40% (constant P) respectively.

Figure 4.19 ROCOF in generic test case1, summer profile. Different composition of ZIP load.

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Hz

Low Wind High Wind

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0,0978

BASE CASE Z,I,P :40%,40%,20%

Z,I,P :20%,40%,40%

Hz/

s

Hz/

s


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Figure 4.20 NADIR in generic test case1, summer profile. Different composition of ZIP load.

From Figure 4.19 and Figure 4.20, as expected, the mixture of loads is better than in the base case.

However, as the percentage of constant power load is increased, the ROCOF and NADIR indicators

get worse (although the difference between the two additional scenarios is not much). This is

expected since the load moves more towards a constant power characteristic.

For the next case, the ZIP ratio is kept as 20%, 40%, 40% to have a load profile closer to constant

power, but also a mixture of other loads. Next, the inclusion of induction motor loads in the system

is analysed. Most of the load in the power system is industrial load (mostly induction motor load).

The amount of induction motor load in the system is varied in steps of 25% between 0 and 75%.

Figure 4.21 and Figure 4.22 show an interesting characteristic in this case. It is necessary to

differentiate the scales in this case for the two scenarios of high and low wind since the results’

profiles cannot be correctly visualised otherwise. On the left y axis is the scale for the low wind

scenario while on the right is for the scenario of high wind penetration. It is observed that the

system progressively becomes worse when more and more induction motors are added. ROCOF is

increased while the NADIR is decreased. This can be explained by induction motor operating

characteristics themselves. Induction motor operating characteristics are directly related to system

frequency. Any change in system frequency directly reflects on the motor speed. In an induction

motor, the frequency determines the speed (and therefore inertia) unlike the synchronous motor,

where the speed (and therefore inertia) determines the frequency. As already mentioned, it is

essential to analyse the impact of induction motor load since it is dominant. This analyses gives is

good indication of the importance of addition of dynamic load. Note also that the impact of a high

amount of induction motors is more prominent in a system with high penetration of power

electronics-interfaced generation. By contrast, the impact is small in a system dominated by

conventional plants with synchronous generators, which have a better voltage regulation behaviour

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BASE CASE Z,I,P : 40%,40%,20%Z,I,P : 20%,40%,40%

Hz

Hz


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(w.r.t. voltage regulation capability of power electronics-interfaced generation), and this prevents

high variability of the voltage magnitudes of the buses to which loads are connected.

Figure 4.21 ROCOF in generic test case1, summer profile. Effect of induction motors.

However, recently most of the induction motor loads are being interfaced by PE-based drives.

Hence, it is needed to include the effect of having PE in the system. For this purpose, in the next

analysis the induction motor percentage is set to a conservative 25% and includes PE-based

aggregated load. This load model is a composite load model derived from [53], and can effectively

be used to aggregate distributed generation and PE-interfaced load.

In an initial study, it is attempted to replace the conventional loads in area C of generic test case 1

(i.e. the area with the highest load and least wind generation). For one scenario, 1 conventional

load is replaced with aggregated Distributed Generation and load (DG-load), and for the second

scenario, 3 conventional loads are replaced with aggregated DG-loads. The results are shown in

Figure 4.23 and Figure 4.24. From these figures, the inclusion of Distributed Energy Resources

(DER) seems to have a positive impact on the system’s ROCOF and NADIR. This can be attributed

to the fact that the DER contribute to reduce the system active power loss even in case of

disturbances. This is in strong contrast to earlier cases where DGs were seen as ‘static negative

loads’, disconnected in event of disturbances (e.g. voltage below 0.8 pu). The DER model used in

[53] has a complex control structure that is able to aggregate large amounts of technologically

diverse DGs (non-LVRT, LVRT, aRCI, aRACI supporting) effectively and produce aggregated

behaviour that can reflect the support from DGs to the grid. It is thus recommended that

conventional loads should be replaced with composite load models.

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0% 25% 50% 75%

Hz/

s


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Figure 4.22 NADIR in generic test case1, summer profile. Effect of induction motors.

Figure 4.23 ROCOF in generic test case1, summer profile. Effect of active distribution networks.

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0% 25% 50% 75%

Hz


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0,320

0,1005

0,1010

0,1015

0,1020

0,1025

0,1030

0,1035

0,1040

0,1045

0,1050

0,1055

Base Case 1 DER 3 DERs

Hz/

s


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Figure 4.24 NADIR in generic test case1, summer profile. Effect of active distribution networks.

4.2.3 Proposition of KPI for Assessment of Frequency Performance

Based on the findings with generic test case 1The main stability indicators used for the proposed

frequency KPI in this study are ROCOF and NADIR. Because, as shown with generic test case 1,

these indicators are still suitable for assessment with high penetration levels of wind power and

also considering the impact of load modelling. As indicated in Section 4.1, the proposed KPI is

expected to map the values of system variables onto the actual value of a stability indicator

(ROCOF/NADIR). Here, the key system variable is the system kinetic energy, whereas load power

deviations and losses deviations are studied in this section to ascertain their influence. It should be

noted that, inertia can be used as an alternative, provided that a reliable estimate is available to

ensure enough confidence in the monitoring task in the control room. According to the fundamental

physics of the motion, system inertia can be derived according to the moment of inertia of all

rotating masses synchronously rotating in the system which will result in system kinetic energy.

As a result of previous analysis with generic test case 1, it is important to point out that it is

necessary to ascertain other system variables (in addition to the level of kinetic energy of the

system) which can give more insight on the frequency behaviour in the frequency containment

period (changes in ROCOF and NADIR). For sake of further analysis, recalling equation (4.2),

ROCOF and kinetic energy have an inverse relationship, i.e. lower kinetic energy leads to a higher

value of ROCOF. This relationship can be considered as the main factor in frequency performance

assessment in the frequency containment period. But in order to get more insight about the fact of

having different values of ROCOF for the same level of kinetic energy and in different loading levels

with different generation dispatch and COI (cf. Figure 4.13), analysis of additional variables mainly

from the grid side parameters might be beneficial. These additional variables can be related to

those elements which can affect the variation of power mismatch (∆𝑃 in equation (4.2)).

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One of those system key variables is the load power variation (∆𝑃𝐿), for which an initial analysis

was presented in previous section for generic test case 1. Considering equation (4.7), different load

models to investigate its effect on system response can be performed [71], [74].

It should be noted that the losses through the entire system shall also be considered in addition to

the power system load. The term losses refers to the active power losses associated to the

elements in the transmission network (e.g. resistance of a transmission line). The total active

power losses are part of the active power balance equation of the system, and they can vary as a

consequence of the change in the power flow profile (reflected in change of currents’ magnitude

through the branches of the transmission network). Therefore, the other parameter to perform

further analysis in the frequency containment period is related to the losses in the grid (∆𝑃𝐿𝑜𝑠𝑠).

Analysis related to the effects of this system variable, and finally the implementation of the

frequency performance KPI is discussed and presented in the following paragraphs.

Key System Variable Effects

For better understanding and detailed analysis of the effects of loads and losses, more analysis, as

a complementary part of Section 4.2.2, is performed. In this part of the analysis, the GB test

system is used. In order to have a fair comparison, the same system conditions and the same

faults with the GG2020 and winter and summer profiles are applied. Therefore, a generator outage

(G11 in the North England area), which entails approximately around 7% of total generation, is

considered. This disturbance occurs at t=26 s, and the simulation time is 36 s.

Variations of system indicators, ROCOF and NADIR, for different levels of kinetic energy and with

different load modelling (constant P, constant I, constant Z) are presented in Figure 4.25 and

Figure 4.26. Like in the analysis of generic test case 1, it is corroborated that the constant power

load model entails a more pessimistic ROCOF and NADIR.

Figure 4.25 ROCOF vs kinetic energy, (for GG2020 Scenario, Winter profile).

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According to the obtained results in Figure 4.26, the changes of NADIR show an increasing trend

from a system with low inertia to a system with higher inertia. In the first operational scenario

(system with 223 GWs kinetic energy), the value of NADIR is slightly higher than the values

corresponding to the next four operational scenarios. The main reason is due to high power output

of remaining synchronous generators. For sake of further analysis, only conditions with the highest

and lowest inertia/kinetic energy are presented in Figure 4.27 and Figure 4.28. The two conditions

are based on the case of low wind penetration (around 17%) and high wind penetration (around

40%) of the total generation. These figures allow to appreciate the effect of constant power model,

which is evident for the winter load profile of the GB system in the year 2020.

Figure 4.26 NADIR vs kinetic energy, (for GG2020 Scenario, Winter profile).

Figure 4.27 ROCOF for different load models and different wind penetration (GG2020 Winter).

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The same analysis is performed for the summer profile of GG2020 with the GB test system. This

time, the loading of the system is reduced to 60% compared to the winter profile. The comparisons

for different load models and their effects on the ROCOF and NADIR for different levels of kinetic

energy are shown in Figure 4.29 and Figure 4.30. According to the results, ROCOF is not changing

a lot but slightly higher differences are observed in the values of NADIR (cf. Figure 4.30). Despite

of this fact, it can be inferred that for lower loading levels, the effect of the constant power model

is more noticeable in the NADIR.

For sake of comparative illustration, the ROCOF and NADIR, for different loading profiles (modelled

by a constant power model) in winter and summer are summarised in Figure 4.31 and Figure 4.32.

From the analysis done in Figure 4.25 to Figure 4.30, the reason behind the difference in values of

ROCOF and NADIR for the same kinetic energy level can be associated to the voltage dependency

of the load, which is more critical (i.e. results in higher ROCOF) in higher loading conditions.

Figure 4.28 NADIR for different loads and different wind penetrations (GG2020 Winter).

Figure 4.29 ROCOF vs kinetic energy, (for GG2020 Scenario, Summer profile).

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As it is well known, the total electrical power provided by the generators in a system must be equal

to the total electrical power demand consumed by the network. This includes the electrical loads

together with all the losses in the transmission network. Any change in this equilibrium that

disrupts the steady-state operation of the power system is considered as a power imbalance which

leads the generators to decelerate, exciting an oscillatory behaviour [74]. The current in the

transmission network also oscillates with the same frequency as the generators. The current

through a certain transmission element causes ohmic losses, which are part of the consumed

power. Therefore, the variation of losses during an imbalance can also be considered another key

system variable helping to understand the frequency performance in the containment period. As

discussed in Section 4.2.3, these losses can be obtained from the state estimator available in the

EMS of each control room considering SCADA/synchrophasor measurements technologies [75]-[76].

Figure 4.30 NADIR vs kinetic energy, (for GG2020 Scenario, Summer profile).

Figure 4.31 ROCOF vs kinetic energy for GG2020.

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This aspect becomes clearer considering the results shown in Figure 4.33. To capture the time

variation of the losses, two scenarios from GG2020, for winter and summer, are considered. And

the same fault as in the previous analysis is applied. In Figure 4.33a, the frequency of the COI is

depicted for winter and summer profiles, whereas the time derivative of the frequency of the COI

and the time variation of power losses are in Figure 4.33b and Figure 4.33c. The time derivative of

frequency of the COI (shown in Figure 4.33b) is derived by applying the derivative term of the

frequency of the COI (shown in Figure 4.33a). Note that when the derivative of the frequency of

the COI changes abruptly due to the imbalance, a similar pattern occurs for the ohmic losses. This

finding is in agreement with what was proven in [74], i.e. fluctuations of frequency of the COI are

dictated by the oscillations in the transmission network's ohmic losses.

Figure 4.32 NADIR vs kinetic energy for GG2020.

From the findings presented in this subsection, it is proposed to define a KPI for the assessment of

frequency performance in the containment period which maps information from key system

variables (i.e. inertia/kinetic energy, losses and load power) to well-known indicators (i.e.

ROCOF/NADIR). The procedure for implementation is explained in the following paragraphs.

Assumptions

The main assumptions which have been taken into account for the KPI for assessment of frequency

performance in the containment period are summarised as follows:

─ Synchronous generators are the main (predominant) source of system inertia in the frequency

containment period.

─ The loads are represented by a constant power model.

─ The droop of governors does not change.

─ PEIG connected at transmission level and only wind turbines type 3 and type 4 are considered.

These components do not possess a function for fast frequency response (to recreate the worst

case of ineffective or wrong participation in the frequency containment period).

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Figure 4.33 System performance for GG2020: (a) frequency of the COI for GG2020 with G11

outage at 26 s; (b) time derivative of frequency of the COI; (c) variation of losses over time [MW].

Calculation Procedure

The following steps shall be followed:

1. Generate a set of different dispatches for the test grid which cover the most important scenarios

with different ranges of kinetic energy (i.e. considering not only change of power share, but also

disconnection of synchronous generators).

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─ These set of dispatches can be used as the input to the procedure shown in Figure 4.5 and

Figure 4.10.

2. For each dispatch, compute the ROCOF and NADIR based on the frequency of the COI in the

system, which can be used to determine the trend of ROCOF/NADIR vs the level of system

kinetic energy.

3. For each dispatch, calculate the Sum of Maximum Active Power Deviation (SMAPD) of load and

losses, which reflects the effect of the active power consumption in the system on the system

active power balance, according to the following procedure:

─ Step1: record the time series (for the considered simulation time window) of the losses and

active power demand in the system.

─ Step2: SMAPD is the sum of the maximum values of active power load and losses

(aggregated system generation output) throughout the power system with respect to their

pre-disturbance value (before the occurrence of imbalance). The calculation of the SMAPD

can be performed in the same time window of calculation of the ROCOF, i.e. 0.5 sec after the

occurrence of the imbalance.

─ Step3: create the characteristic curve of SMAPD vs level of system inertia/kinetic energy.

4. Use the obtained mappings from previous steps 2 and 3, to assess the frequency performance

in the frequency containment period. For instance, if a given dispatch is planned for a given

loading condition, then, from the relational curves, the operator can estimate whether the

corresponding values of ROCOF/NADIR respect the thresholds defined in its grid code

requirements.

KPI implementation with the GB Test System

The calculation procedure described in the previous paragraphs has been implemented in the GB

test system for different scenarios (2016 as baseline, GG2020 and GG2030). All the analysis in this

subsection is applied for the system with the same conditions as previously:

─ Season: Summer, i.e. load peak at 60%.

─ Topological change: No.

─ Event: Generator outage representing 7% of the total system generation.

The first part of this KPI implementation is to obtain the mapping from system kinetic energy into

ROCOF/NADIR as shown in Figure 4.34 and Figure 4.35. It means, a set of feasible dispatches

covering different wind penetration levels is obtained and based on that, all ROCOF/NADIR values

are calculated and depicted.

As shown in Figure 4.34 and Figure 4.35, the blue points are related to the baseline scenario which

has more synchronous generators with less wind (i.e. wind penetration from 5 to 15%), the red

values are related to the GG2020 scenario (wind penetration from 15% to 40%) and the green

values are related to the GG2030 scenario (60% to 78% of wind penetration). Since most of the

synchronous generators are in service in the baseline scenario, more variety of feasible kinetic

energy is obtained for this case. From a simple visual inspection of the mapping trends for different

scenarios of the GB system, we can observe that the baseline scenario shows a more flat

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relationship ROCOF/NADIR vs kinetic energy, whereas for 2020 and 2030 more radical changes in

system indicators ROCOF and NADIR with respect to the kinetic energy level are observed20.

Figure 4.34 Mapping of ROCOF vs kinetic energy for frequency performance KPI.

Figure 4.35 Mapping of NADIR vs kinetic energy for frequency performance KPI.

20 As it was explained in Section 4.2.1, i.e. equation (4.3), the inertia H [s] is proportionally related to the Kinetic Energy [MW.s]. Therefore the figure ROCOF/Nadir vs Kinetic Energy, can alternatively defined as ROCOF/Nadir vs Inertia. This is illustrated in Appendix D, which shows the figures ROCOF/Nadir vs Inertia for Generic Test Case 1 (cf. Section 4.2.2, Figure 4.13 and Figure 4.14).

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As shown in the mapping of Figure 4.34 and Figure 4.35, in most of the cases each level of system

kinetic energy may be related to a single value of ROCOF/NADIR, but in some cases (different

scenarios) two values of ROCOF/NADIR may be associated to the same level of inertia/kinetic

energy. The reason behind the difference in ROCOF/NADIR for different loading levels (e.g. winter

and summer) is shown in Figure 4.33 and load effects analyses, which illustrates that the variation

of the frequency of the COI is correlated with the time variation of the system load and losses

corresponding to a given loading level. For example, note that if the value of the estimated system

kinetic energy is more than 288000 MWs, then its related value of ROCOF can be estimated directly

by the mapping obtained in Figure 4.34. But if the value of the system kinetic energy is around

225000 MWs, then for the same system kinetic energy, depending on the system

loading/operational scenario (GG2020 or GG2030), and different values of ROCOF can be

associated. In such case, additional mapping from SMAPD can help to choose the right value of

ROCOF. The judgment in this case is as follows: if the SMAPD is around 400 MW, the mapping of

SMAPD vs kinetic energy for GG2020 in Figure 4.36 (values in red colour) should be used to select

the ROCOF from the corresponding curve in the mapping ROCOF vs kinetic energy of Figure 4.34

(also in red, GG2020 scenario). This part of analysis gives more insight about the changing of

ROCOF/NADIR in different seasons/operational scenarios.

Figure 4.36 SMAPD vs kinetic energy for frequency performance KPI.

4.2.4 Recommendations and Usage in Control Room

The KPI for the assessment of the frequency performance in the frequency containment period,

which is based on mapping curves determined via offline simulations can be used for the

assessment in the control room as illustrated in Figure 4.37. Note that the figure suggests that

mapping curves (ROCOF/NADIR vs kinetic energy and SMAPD vs kinetic energy) shall be

determined offline, based on a suitable model of the system (i.e. responses obtained via offline

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simulations have high resemblance with actual measured responses), for a selected number of

disturbances, each one evaluated for a number of dispatches (which entail variation of the power

share and system kinetic energy). Thus, a disturbance indicator (e.g. selecting the type of

disturbance that actually happens based on an alert signal from protection devices) can be used to

select the mapping curves, whereas information (actual kinetic energy, active power demand,

active power losses) from the energy Management System (EMS) is passed through the mapping

curves to estimate the ROCOF/NADIR. The procedure for determining the mapping curves was

introduced in Section 4.2.3. As illustrated in Figure 4.25 to Figure 4.36, the information

ROCOF/NADIR vs kinetic energy and SMAPD vs kinetic energy can be used in a complementary

manner to estimate the value of ROCOF/NADIR for a given loading level and generation dispatch.

Therefore, the decision block shown in Figure 4.37 suggests that the operators can also assess

what will happen with ROCOF in case an operational action (e.g. planned generator outage) is

taken and an imbalance is likely to occur in such operating conditions.

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Figure 4.37 Implementation of the proposed frequency based KPI in control room. IED stands for intelligent electronic device.

The main limitation of this approach concerns with the use of a model implemented in a selected

software package. The lack of accuracy of the model to recreate the real behaviour can lead to

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misleading results. Nevertheless, there has been a significant progress on model identification from

synchrophasor measurements [77]. Thus, the models used by operators can be improved and

updated regularly to ensure reliable (from numerical accuracy point of view) simulation results.

Moreover, the computing effort associated to the execution of offline simulations may be of concern

for large size systems. Nevertheless, the adoption of high performance computing in power system

simulation software packages can help to significantly reduce the computing time [78], [79].

A reliable estimator of the system kinetic energy is needed. An approach to estimate the kinetic

energy from synchrophasor data is explored in WP2 of MIGRATE. The estimation of total load active

power demand and active power losses can be done based on the state estimator, which is usually

based on SCADA measurements (1 sample per 2-6 seconds [75]). However, recent proposals have

been made to also consider synchrophasor measurements by sampling each 200 to 500 ms [76].

4.2.5 Validation with the Irish System

This section describes EirGrid’s assessment of the new frequency stability KPI in the Irish system.

The assumptions, methodology, and outcomes of the assessment are discussed next.

Assumptions

The only source of reserve in the system comes from synchronous generators. This assumption is

consistent with work performed for the KPI development and the assessment in the GB system,

therefore it is used here to harmonise the analysis and compare outcomes. However, it must be

noted that this assumption neglects the possible contribution to frequency control from PE based

sources like batteries, wind, PV, flywheels, HVDC, etc. It is understood that these effects will be

assessed in Task 1.6 as part of the development of mitigation measures.

The operation of ROCOF protection relays normally installed in embedded generators was not

included in the simulations. This simplification was made to facilitate a better observability and

understanding of the system dynamics following a large power imbalance. Inclusion of these

protection relays would result in cascade tripping that will mask the physical behaviour of the

system. Similarly, Under-Frequency Load Shedding (UFLS), Interruptible Load (IL) and Demand

Side Management (DSM) schemes have not been included in the simulations

Methodology

System Demand

In order to assess the relationship between frequency stability and the system loading, two

demand scenarios are assessed side by side: Winter Peak (5 GW) and Summer Peak (4 GW).

Network topology and synchronous generation capacity remain the same in both operational cases.

HVDC interconnector flows are set to 350 MW import in the Winter Peak cases and 350 MW export

in the Summer Peak cases.

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Development of Scenarios

In order to systematically assess the impact of increased levels of PE based generation in the Irish

system, a series of scenarios have been developed using the Baseline case described in Section

3.3.3. Each simulation series is comprised of 12 distinct sub-cases in which the level of PE based

generation (i.e. wind) is increased from 0 MW to 2750 MW in steps of 250 MW. The wind turbine

generators (WTG) are set at their maximum rated output in all scenarios and the incremental wind

output is introduced by scaling the number of WTGs in the model.

In total, 24 scenarios are assessed: 12 for Winter Peak and 12 for Summer Peak. In each scenario,

the generation output of the synchronous machines is reduced appropriately to balance the fixed

level of demand. When the output of a synchronous machine drops below its rated minimum load,

this machine is taken offline and its remaining output is re-dispatched to other online units.

Common to all scenarios is the output of “Longpoint AD2” synchronous generator (425 MW), which

is tripped to generate the power imbalance in the simulations. Therefore, the dispatch of this unit is

left constant to assess all simulation results in equal terms. The dispatch of this machine

represents 8.5% of the Winter Peak load and 10.6% of the Summer Peak load.

A detailed breakdown of all generation dispatches (Summer and Winter) with the output of each

unit is tabulated in Appendix B.2. In these tables, each column represents a single generation

dispatch scenario. For each synchronous machine, an “X” means that the generator is offline

whereas a number indicates the dispatched output in MW.

The generation dispatches developed for Winter Peak are illustrated in Figure 4.38. This graph

shows the kinetic energy of the system as a function of the wind generation. A description of the

dispatches follows:

─ For scenarios #1 (0 MW wind) to #4 (750 MW wind), the combined wind output is not too

significant and it can be accommodated by simply reducing the output of some synchronous

generators, but no unit is taken off-line. As a result, Figure 4.38 shows that the system kinetic

energy does not change (i.e. the same rotating mass is present in these four cases).

─ Scenarios #5 (1000 MW wind) to #12 (2750 MW wind) represent cases where the increasing

level of wind generation displaces synchronous machines, which have to be taken offline. Now

the graph shows that the system kinetic energy is continuously falling, as expected. The rate at

which the kinetic energy drops on each scenario depends on the size and characteristics of the

unit(s) that is taken offline at each step.

The generation dispatches developed for the Summer Peak case follow similar trends as the Winter

Peak and they are not illustrated here for simplicity. It should be noted that the selected scenarios

did not attempt to follow an economic dispatch. However, a “pseudo” merit-order approach was

assumed, based on knowledge of the Irish system, whereby the most efficient and must-run plant

was decommissioned last.

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Figure 4.38 Visualisation of winter peak generation dispatches vs system kinetic energy (MWs) as a function of wind generation.

The scenarios described above represent a possible transition path for wind penetration into the

Irish system from 0% up to 55% (or 68%) of the system demand for the Winter Peak (or Summer

Peak) case. In terms of SNSP21 levels, these equate to 62% and 63% for Winter Peak and Summer

Peak respectively.

Intuitively, it can be stated that the selected scenarios do not constitute a unique transition path

and many different combinations of generation commitment patterns can be produced for a defined

generation portfolio. In practice, the generation dispatch adopted in real-time operations is the

result of a combined number of constraints such as market rules, network congestion, plant

availability, stability limitations, etc.

Although the selected scenarios represent a limited number of snapshots for a transition, it will be

demonstrated that they can provide sufficient insight into the system dynamics during power

imbalances and facilitate an effective assessment of the KPI for assessment of frequency

performance in the frequency containment period.

The implementation of the generation dispatches in the PowerFactory model is done with a Python

script, which performs the procedure shown in Fig. 4.5.

21 The System Non-Synchronous Penetration (SNSP) is a measure of the non-synchronous generation on the

system at an instant in time. It is defined as the non-synchronous generation and net interconnector imports

divided by the demand and net interconnector exports (where “Demand” includes pump storage consumption

when in pumping mode). This indicator is used by EirGrid in real time operations. At the time of writing, a 60%

limit for SNSP is currently in place for system security reasons, with a trial for 65% coming soon.

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Dynamic Simulations

The main objective of this assessment is to understand the dynamic behaviour of the system

frequency during a severe power imbalance and how it is affected by the increased penetration of

PE based generation (and associated displacement of conventional generation plant). This

investigation is performed by running RMS time-domain simulations for all scenarios, subject to the

same disturbance.

For the purposes of this assessment, the trip of 425 MW of synchronous generation (“Longpoint

AD2” unit) is defined as the reference disturbance. This event has been selected for the following

reasons:

─ It represents the loss of the largest single infeed in the selected scenarios. Therefore, it

generates the largest power imbalance.

─ It results in the disconnection of the largest amount of inertia in a single event. Therefore, it

reduces the ability of the system to slow down the falling frequency.

The main variable of interest in these simulations is the frequency output for each synchronous

generator. These frequency traces are combined into a centre-of-inertia (COI) as described in

Section 4.2.1. The frequency NADIR and ROCOF conclusions apply to the combined COI for the

entire system.

Other steady-state variables like circuit loading and generation dispatch are also monitored and

extracted from the PowerFactory simulations as described in Section 4.2.2.

The above processes are automated with two scripts:

─ DataExtraction_Freq.py: Python scrip that runs through the defined list of scenarios in

PowerFactory, performs the dynamic simulation for each scenario and extracts the selected

variables into csv output files.

─ RoCoF_Nadir.m and SS_proces.m: Matlab scripts that post-process the PowerFactory simulation

outputs and generate the indices described in Section 4.2.1.

Simulation findings

This subsection presents the outcome of the dynamic simulations performed with the Irish system

model. Analysis of the results suggests slightly higher values of ROCOF and lower frequency NADIR

in the Summer Peak scenarios than in the equivalent Winter Peak scenarios. This behaviour is

expected and can be explained by the reduced number of synchronous generators required to meet

the lower load. The summer scenarios have less inertia and less load damping than the winter ones,

therefore the frequency excursions are more pronounced in terms of rate of decay and amplitude.

For simplicity, this section will only present the Summer Peak results. The Winter Peak results

follow the same trend, but they are less severe.

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The direct relationship between initial ROCOF and system inertia has been long documented in

literature [12] and has also been the focus of many recent studies [80]-[83]. This correlation is

further examined here, based on the dynamic simulation results produced with the Irish system

model.

Figure 4.39 shows ROCOF vs System Kinetic Energy. For completeness Winter Peak and Summer

Peak scenarios are included in the graph. Therefore, the impact of the system loading conditions

can now be visualised in one single plot. The following observations can be made:

─ For the same system loading conditions the relationship between ROCOF and System Kinetic

Energy is single-valued.

─ The relationship between ROCOF and System Kinetic Energy is almost linear.

The above features make the system Kinetic Energy (or alternatively the system inertia) a very

good system variable to ascertain the expected initial ROCOF for a defined size of contingency.

Figure 4.39 ROCOF vs System kinetic energy relationship, Summer and Winter scenarios.

Despite the good correlation observed between ROCOF and System Kinetic Energy, a perfect linear

relationship is not present in the simulation results. Furthermore, a dependency (albeit minor) with

system demand is observed.

Preliminary investigations suggest that the small differences between the summer and winter

results are caused by the damping effect introduced by the load. This damping has two

components: (i) load reduction due to voltage dip and (ii) load reduction due to frequency dip [84],

[85]. Both effects combine to reduce the level of power imbalance, and therefore improve the

frequency response.

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This observation aligns with the analytical expression (equation (4.6)) derived from the well know

swing equation under the assumption of no load damping. The linearity of the equation disappears

if a damping coefficient is added to reflect the load dependency with voltage and frequency.

Further research work is recommended to better understand this process.

In practice, the use of equation (4.6) in Ireland has shown very good correlation with

measurements of actual system disturbances. It is acknowledged that the equation lacks

information about the inertia of the load and associated damping effects, therefore the results are

generally on the conservative side. However, this provides and inherent safety margin for the

secure and reliable operation of the system.

Caveats

The dynamic studies presented in this section have been based on a limited number of scenarios,

therefore this cannot be interpreted as an exhaustive study into the dynamic performance of a real

power system. It is worth highlighting some of the assumptions and simplifications made in the

analysis and their impact on results:

─ Generic models were used to represent the governors and AVR controllers for all synchronous

generators. These models were tuned to produce typical and realistic responses based on

experience. However, their response has not been validated against system disturbances. The

results, thus, cannot be interpreted as a true reflection of the performance of the Irish system.

─ A simplified dynamic representation of the load has been adopted for this analysis. Accurate

load dynamic models are currently under development within the MIGRATE project (in Task 1.3),

but not yet available at the time of writing. Some sensitivity analyses were performed with the

Irish model to investigate the impact of the load representation (dynamic and static). These

analyses showed that the load representation had a distinct impact on the frequency response

of the system. However, the trends shown in Figure 4.38 and Figure 4.39 were not altered. This

finding emphasises the need for accurate dynamic load modelling but it does not contradict the

conclusions related to correlations between initial ROCOF and System Kinetic energy.

─ The operation of ROCOF protection relays normally installed in embedded generators was not

included in the simulations. This simplification was made to facilitate a better observability and

understanding of the system dynamics following a large power imbalance. Inclusion of these

protection relays would result in cascade tripping that will mask the physical behaviour of the

system. Therefore, the conclusions related to the linear relationship between initial ROCOF and

Kinetic Energy are only applicable outside the range of operation of these protection relays. The

goal is to avoid tripping of generation, either by adjusting the protection settings or by adopting

an alternative protection scheme.

─ Similarly, Under-Frequency Load Shedding (UFLS), Interruptible Load (IL) and Demand Side

Management (DSM) schemes have not been included in the simulations. These schemes are

designed to reduce the power imbalance and arrest the falling frequency. However, they are not

fast enough to influence the initial ROCOF. Therefore, the conclusions from the studies are still

valid.

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─ The only source of mitigation to the falling of frequency in the model comes from synchronous

generators. This assumption is consistent with the context (i.e. reduction of system inertia and

no participation of PE interfaced sources) defined in D1.1 [2] for frequency performance in the

containment period work performed for the KPI development (Section 4.2.3) and the

assessment in the GB system, therefore it is used here to harmonise the analysis and compare

outcomes. However, it must be noted that this assumption neglects the possible contribution to

frequency control from PE based sources like batteries, wind, PV, flywheels, HVDC, etc. Some of

these technologies could act fast enough to affect the initial ROCOF, therefore the relationship

between ROCOF and System Kinetic Energy may change. The challenge will be to identify how

much of that new source of restoring power (in addition to the inertial response from

synchronous machines) is required to maintain system stability in conditions of very low system

inertia. It is understood that these effects will be assessed in Task 1.6 as part of the

development of mitigation measures.

─ Generic models for wind generation were developed by Energynautics as part of the MIGRATE

project. These WTG models were integrated in the PowerFactory model of the Irish system.

Parameter setting and configuration for these models were advised by Energynautics. From a

limited number of tests performed in the Irish system model, the response of the generic WTG

models was in line with typical performance requirements in Grid Codes.

The above assumptions and simplifications need to be considered when analysing the results.

Indeed, the study findings and conclusions presented in this section must be interpreted from a

qualitative, rather than quantitative, point of view.

Conclusions and Recommendations

This section has presented EirGrid’s assessment of the performance and suitability of the new KPI

proposed for assessment of frequency stability in the frequency containment period in Section

4.2.3.

Dynamic simulations of the Irish system have been performed to assess the suitability of the new

KPI. While based on a limited number of scenarios, the studies have provided adequate insight into

the system dynamics during the frequency containment period.

Kinetic Energy has shown to be directly related to the initial ROCOF and it is currently used in

Ireland with great success. However, as the level of PE based generation increases, the depleted

system inertia will cause the frequency to fall too fast for conventional controllers to act in time.

Therefore, fast delivery of power will be required in order to arrest the rapid falling frequency. The

speed of operation of this reserve (either POR of FFR) needs be accounted for in a reliable and

robust KPI.

A complex interaction between system inertia, FFR and POR is expected. The main challenge will be

to understand and capture those interactions into a simple, concise and reliable indicator. It is

recommended that further research work is undertaken in this direction to derive a reliable KPI

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that reflects the key behaviour of the system during the frequency containment period. This KPI

should be robust enough to predict initial ROCOF and, most importantly, frequency Nadir.

Given the small size of the Irish system, locational variations of inertia are not significant. This,

however, will not apply to large interconnected systems like the pan-European grid. It is

recommended that further research work is performed to understand the propagation of frequency

instabilities through large networks and to investigate the concept of regional inertia [66].

4.3 KPI for Large-Disturbance Rotor Angle Stability

4.3.1 Introduction

Large-disturbance rotor angle stability (also known as transient stability) concerns the ability of the

synchronous generators of an interconnected power system to remain in synchronism after being

subjected to a large disturbance, such as a three-phase short circuit on a transmission line or a tie-

line tripping [3]. When such a disturbance occurs, the equilibrium between the mechanical and the

electrical torque in each synchronous generator is altered, resulting in large excursions (swings) of

the rotor angles (which are influenced by the non-linear power-angle relationship). If the angular

swings are not too large and attenuated, the system can reach a (new) steady-state operation

condition again and is considered stable. Unstable conditions occur when some generators lose

their synchronism with other generators due to too large or increasing angular swings, which is an

indication that the system cannot absorb the kinetic energy corresponding to the rotor speed

differences [3].

Large-disturbance rotor angle instability can lead to generator outages, load shedding, tripping of

major transmission lines and even blackouts. Significant research efforts have been devoted to

develop methods to continuously monitor and estimate the degree of large-disturbance rotor angle

stability in systems dominated by synchronous generators [86], [87]. Nevertheless, the massive

integration of renewable generation involves a phase out of synchronous generators, challenging

the large-disturbance rotor angle stability of the remaining ones, which have to cope with the

variability of operating conditions introduced by renewable generation22.

The critical clearing time [88], maximum angle difference [89], and area-based centre-of-inertia

referred rotor angle [90], constitute the most widely used indicators in the current state-of-the-art

on assessment of the impact of increasing penetration of renewables on large-disturbance rotor

angle stability. These indicators are determined from signal records (generated via offline time

domain simulations or obtained from synchrophasor measurements), and there is evidence that

these indicators can still be suitable, cf. the application of the critical clearing time in [91].

Therefore, a comparative assessment among them is out of the scope of the work presented in this

section. The maximum angle difference indicator is chosen in this work due to the reduced

22 The massive penetration of power electronic interfaced renewable generation entails a reduction of the system inertia and the short circuit capacity levels. This is also reflected in the severity of fault currents.

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computing effort and conceptual simplicity. Any of the other two indicators can be used in the

proposed KPI as well. Alternative indicators, determined by using simplified models and usually

without performing time domain simulations (e.g. equal area criterion [12]) have been also

proposed in existing literature. They only allow providing a qualitative assessment (intuitive

insight) and therefore are not considered in this work.

The second fundamental question to be answered is how to structure a KPI which helps in

quantifying the effect of the change of one or more key variables on the distance to large-

disturbance rotor angle instability. In order to evaluate such a KPI, two things are needed:

1. Large-disturbance rotor angle stability margin. It is quantified based on the acceptable

maximum angle difference ∆𝛿max (like 180 degrees [3]), namely:

where ∆𝛿 is the angle difference between any two generators. This factor defines the extent of

large-disturbance rotor angle stability, and enables system operators to estimate the distance

from the current operation condition to the instability border (namely ∆𝛿max 180). The margin

can also be defined by using an alternative expression, like (360 − ∆𝛿)/(360 + ∆𝛿 ) in [89].

2. Mapping from key variables to large-disturbance rotor angle stability margin, that is to say, if

key variables are measured, how could it be possible to know the maximum angular difference?

Unlike the assessment of frequency performance due to the inertial response in the frequency

containment period (which is dominated by the level of inertia in the system), the non-linear

nature of large-disturbance rotor angle stability and the influence of more than one or two

variables does not allow defining a simple mapping curve. Therefore, an estimation method is

needed to infer the maximum angle difference associated to a set of selected key variables. The

most popular methods to estimate large-disturbance rotor angle stability margin come from the

field artificial intelligence [92], [93]. Particularly a random forest consisting of Decision Trees

(DTs) is adopted here because of the good interpretability (or transparency) and easy

implementation. Other methods, like support vector machine based regressor, can also be used.

Decision trees estimate the angle of any generator selected by the operators, and calculate the

maximum angle difference, namely max∆𝛿, and then estimate the margin. Nevertheless, the

research effort devoted to this section is focused on two essential and aspects:

─ investigating what could be the smallest set of key system variables needed to estimate the

maximum angular difference in a system with high penetration levels of renewables;

─ jointly tackling the problem of key variable selection and the design of the selected artificial

intelligence method. So far, the problem of key variable selection has been treated

separately in existing literature. The method described below can be easily applied for cases

in which other artificial intelligence methods are preferred. From a practical point of view,

the operator can select all variables monitored with available PMU devices. At least, the bus

voltage magnitude and angle can be selected as candidate key variables for the decision

tree The application of MVMO will indicated which variables are the most representative

Margin = ∆𝛿max −max∆𝛿 (4.10)

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(high observability). Data series (time responses) collected with available PMU devices can

be used instead of data generated via offline simulations.

The remainder of this section reports the work for selecting key variables to estimate large-

disturbance rotor angle stability of power systems with high penetration of renewable generation.

Simply put, the estimation accuracy that can be achieved by using decision trees is used to

investigate the influence of system variables on large-disturbance rotor angle stability. A weight

factor is given to each variable. An optimisation method, Mean–Variance Mapping Optimisation

(MVMO), is adopted to optimise weight factors to minimise the errors of decision trees. In the list

of weight factors corresponding to the minimum error, the variables with the largest weight factors

are considered as the key variables. Decision trees built with key variables are considered as the

optimal performance trees and are used to estimate large-disturbance rotor angle stability.

Next, the background of decision trees and MVMO is first introduced. Then the proposed method of

selecting key variables to estimate large-disturbance rotor angle stability is described. The method

is first demonstrated on a modified version of the generic test case 2, which was introduced in

Section 3.2.4, to illustrate its implementation. Finally, the method is tested on GB system to

ascertain its feasibility and efficiency when applied to a larger size system.

4.3.2 Decision Trees Background

Decision Trees are one of the most popular classifiers, which are used in various disciplines such as

statistics, machine learning, pattern recognition, data mining, etc. Decision trees are successful

because they provide a clear, documentable and discussible model of how the classification is made

[94], [95]. The model maps a new observation into a most appropriate class, whose average of

outputs is considered as the output of this new observation.

As shown in Figure 4.40, a decision tree is a graphical description of a well-defined decision

problem, which is composed of a root node, branches, internal nodes and leaves [94]. The root

node is the starting point of the tree, without any incoming branch. The internal nodes constitute

nodes with incoming branches and outgoing branches. Each internal node splits its sample set into

two or more sub-classes according to a certain splitting criterion. A branch is a connection

descending from an upper (parent) node to a lower (child) node. The nodes with incoming

branches but without outgoing branches are called leaf nodes. Each leaf node is assigned a target

value or a decision as its output. Here, the maximum angular difference is considered as the output

of leaf node. Essentially, a path from a root node to a leaf node is a series of if-else rules, which

make the internal logic and reasoning process easy to comprehend. A decision tree is built in the

way that the training samples are recursively split into smaller left and right groups in a top-down

manner by selecting a certain splitting at a node, until the stopping criterion is met.

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Figure 4.40 Structure of a decision tree.

When a new observation is collected, it will be navigated from a root node down to a leaf node,

according to the splitting used at each node. The leaf node includes a set of samples who have

similar characteristics to this new observation. Therefore the average of outputs of these similar

samples is considered as approximately the estimation for the new observation. As far as large-

disturbance rotor angle stability is concerned, the output of a leaf node is defined as the average of

maximum angle differences associated to L samples in this leaf node [96].

where:

∆𝛿est = the estimated maximum angle difference for the new observation

l = the lth sample in the leaf node

The key task in the design of the decision trees is to select the proper splitting at each node so that

the training samples are classified. Here, the method named CART is selected because it tends to

build simple binary trees which can clearly show the relationship between measured system states

and maximum angular differences [96].

Like any artificial intelligence method, good accuracy of decision trees requires enough training

samples (i.e. sets of numerical values of the system variables used as inputs of the decision tree).

With the samples obtained by using an accurate model in power system simulations, decision trees

can identify the link between system states and large disturbance rotor angle stability. But

numerous samples will slow down the computing speed of the decision trees. Therefore, the

training (exploration) and testing (exploitation) of decision trees should be well balanced. Moreover,

during the training process, the selection of input variables also has a big influence on the accuracy

of decision trees. Here, this topic is dealt with by using an optimisation method, MVMO, which is

described next.

∆𝛿est =∑ ∆𝛿𝑙𝐿𝑙=1

𝐿 (4.11)

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Yes

No

Start

Initialize algorithm and optimization problem parameters

Normalize optimization variables in vector x to range [0, 1]

Fitness evaluation by using de-normalized variables

StopTermination criteria satisfied?

---

Ranking Fitness x1 x2 ... xD

1st best

2nd best

...

F1

F2

Last best FA

Mean --- ...

Shape ---

d-factor ---

1x

1s2x Dx

2s Ds...

1d 2d Dd...

Optimization

Variables

Store n-best population

Parent assignment

The first ranked solution xbest is chosen as parent

Offspring generation

Selection: Select m (m<D) dimensions of x

For selected m dimensions, calculation

of h-function variables si1, si2 and x1

Mapping:

i

i1

i2

x

s

s

*i=x rand

1

0

newix

1

Crossover: Use the values of xbest for the

remaining dimensions of x

Offspring

generation

Figure 4.41 Flow chart of MVMO.

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4.3.3 Background of MVMO

MVMO belongs to the family of evolutionary optimisation algorithms. Its main feature is its unique

search mechanism for exploring the possible values of the optimisation variables within a

normalised range of search space. It also adopts a single parent-offspring approach (i.e. a single

solution vector is iteratively evolved). Moreover, the n-best solution vectors achieved so far are

stored and ranked based on their fitness value in an archive, which is recurrently updated. The

mean and variance of each optimisation variable within the best solution vector achieved so far are

computed from the archive and used to guide the generation of new solutions. The first ranked

solution in the archive is selected as starting point to generate a new solution. Next, a non-linear

mapping function is applied to selected optimisation variables. The selection is based on a random-

sequential approach. The mean and variance of each selected optimisation variable are inputs to

the mapping function, which generates new values for these variables. The non-linear shape of the

mapping function is automatically adapted over the iterations to move from search exploration

(generating solutions in different regions of the search space) to search exploitation (intensifying

the search within a region of the search space in which the optimum solution is located). As a

result, MVMO exhibits fast convergence characteristics and efficiently avoids premature

convergence [97], [98]. The overall process is illustrated in Figure 4.41. The iterative process is

automatically executed until a predefined termination criterion (e.g. a fixed number of fitness

evaluations) is fulfilled.

4.3.4 Outline of the Proposed Method of Selecting Key Variables

The selection of key variables is shown in Figure 4.42. Based on operational experience, a group of

L candidates of key variables (which can be directly obtained or derived from phasor measurement

units, like generator output power) is defined. Then, considering a combination of uncertainties

defining different operating conditions (e.g. different generator dispatch and load profile, different

fault clearing times), training samples are generated. An initial weight factor is given to each

candidate variable. Then, a group of decision trees is built and its accuracy is tested. For this

purpose, the accuracy error is defined as the sum of deviations between estimated and simulated

maximum angular differences associated to a set of samples.

where:

∆𝛿est.𝑘 : the estimated angle difference

∆𝛿sim.𝑘 : the simulated angle difference

k : kth test, k=1,2,…, K

The errors and trees are sent to MVMO, which will optimise the weight factor for each candidate

variable, and then rebuild the decision trees and test them again until the stopping criterion (e.g.

an accuracy threshold) is met. The above optimisation of weight factor can be described by the

model in the following equation:

Err = ∑(max∆𝛿est.𝑘 −max∆𝛿sim.𝑘)

𝐾

𝑘=1

(4.12)

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subject to:

where L is the total number of weight factors; 𝑤𝑙min and 𝑤𝑙

max are respectively 0 and 1 in the work

carried out in this section.

Finally, MVMO method provides a sequence of weight factors from the largest to the smallest. The

system operator can decide how many variables are selected. Selecting more variables means

more measurements and smaller estimation errors of decision trees. Selecting less variables means

less measurements and larger errors of decision trees.

Figure 4.42 Key variable selection.

From Figure 4.42, when obtaining key variables (loop MVMO-build decision trees), a group of

decision trees are built. For sake of illustration, Figure 4.43 shows one part of a designed decision

tree, taking generic test case 2 as example. Overall, it is worth pointing out that decision trees

have rules that are built upon input-output data obtained from simulations of the power system.

The rules constitute the knowledge extracted from the samples of inputs (e.g. generator speed S2,

bus voltage magnitude V9 and V5, etc.) and output (stability indicator, e.g. rotor angle margin,

which corresponds to the sampled inputs).

minimize Err (𝐖) (4.13)

𝐖 = [𝑤1, 𝑤2, , … , 𝑤L] (4.14)

𝑤𝑙min ≤ 𝑤𝑙 ≤ 𝑤𝑙

max , 𝑙 = 1, 2, … , L (4.15)

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S2, V9 Q89, …V5

If S2 > Sth

Yes No

If V9 > Vth

Yes

Margin1

If Q89 > Qth

Margin2

YesNo

If V5 > Vth

Margin3

Yes

Margin4

NoNo

. . .

. . .

. . .

The green part

is the rest of

the decision tree

(more rules)

S2: : G2 speed;

V9 : Bus 9 voltage magnitude;

Q89: Line 8-9 reactive power;

V5 : Bus 5 voltage magnitude;

Figure 4.43 Illustration of decision trees.

Innovation of the Proposed Method

The innovation of the proposed method resides into the two following aspects:

1. Traditionally, decision trees are used to estimate an indicator for large-disturbance rotor angle

stability for a fixed (pre-defined) set of variables [99]. Here decision trees are used to select a

small set of key variables for the estimation of the indicator by accounting for the impact on the

resulting estimation error. Key variables mean the variables which allows unveiling the influence

of wind power on large disturbance rotor angle stability. This is reasonable because if decision

trees use the key variables that are most closely related to the large-disturbance rotor angle

stability performance as inputs, the estimation accuracy is expected to be higher. Therefore, the

variables allowing obtaining the smallest estimation errors are considered as the key variables.

2. Unlike the current practice, the training of the decision trees and the selection of the key

variables are done at the same time and automatically. The workflow of the proposed method is

shown in Figure 4.44. The typical way of using decision trees (at the top half) is to first select a

group of variables of interest for large-disturbance rotor angle stability. The rules for splitting

samples are figured out and decision trees are built. Then, decision trees are tested to

investigate their performance. According to the performance, the researcher decides whether or

not to adjust the rules for splitting samples. If yes, the new rules are sent to decision trees and

new trees are built. Similarly, the performance of the new trees is tested and the procedure is

repeated until the performance of the decision trees is satisfactory.

In the proposed method (cf. lower part of Figure 4.44), the human interference is replaced by an

optimisation algorithm (MVMO). The user of this method can decide to input any variables

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(engineering judgment from operational experience) to the decision trees, together with initial

weight factors (defined in the range [0,1]). MVMO is responsible to optimise the weight factors to

reduce the errors of the decision trees. The new weight factors are sent to the decision trees again.

And MVMO continues to optimise them until the stopping criterion is satisfied. The list of weight

factors will tell the user what the key variables are, and at the same time, the decision trees

corresponding to the minimum error are considered as the finally trained trees.

4.3.5 Test Results with Generic Test Case 2

The proposed method is first illustrated on a variant of generic test case 2, namely the modified

version of generic test case 2 (cf. Section 3.2.4). Generator G1 is replaced by a wind turbine type 3.

G3 is selected as the reference generator. The angle of generator G2 is observed to investigate

large-disturbance rotor angle stability.

Figure 4.44 Innovation of the proposed method.

In the first step of designing decision trees, enough samples should be collected. In order to collect

samples, the following uncertainties are considered to generate different operation conditions.

─ Fault location. A three-phase short circuit fault is applied on different locations [1%, 50%, 99%]

in each of six transmission lines of generic test case 2 at different percentages of the line length.

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─ Fault duration. Different fault durations, namely [0.35s, 0.36s, 0.37s, 0.38s, 0.39s, 0.40s,

0.41s, 0.42s, 0.43s, 0.44s, 0.45s], are considered to simulate the severity of fault.

─ Inertia constant of G2. This factor determines how quickly G2 accelerates/decelerates due to

the imbalance of electrical and mechanical torque. Two values, 3.3s and 3.4s are selected in

this part. It is worth pointing out that, due to the fact that the inertia constants of the

generators of the 9 bus system are small (<5 s), this small change in the value of the inertia

constant can cause the 9 bus system to transit from large-disturbance rotor angle stability to

large-disturbance rotor angle instability for some combinations of fault location and fault

duration.

The different fault locations will cause different power imbalances at the terminal of generator G2,

and thus influence its transient stability in a different way. Therefore, to better estimate the

transient stability of generator G2, the samples representing different fault locations are

incorporated in the training. Moreover, the inertia of generator G2 is closely related to the

accelerating speed of generator G2. Therefore, the uncertainties of these three elements are used

to create stable and unstable samples for decision trees. In total, 396 samples (combinations of 3

samples of fault location in 6 transmission lines, 11 samples of fault duration, 2 samples of inertia

constant of G2) are collected. Each of them is simulated in PowerFactory 2016. Generally speaking,

the amount of samples depends on how many uncertainties are investigated and the system size.

In practical terms, the expert knowledge (e.g. network topology, most critical faults, loading levels,

and generation dispatch) of system operators can help to define the minimum number of samples

which could eventually bring the system close to or even cause large-disturbance rotor angle

instability.

For each sample, system states are recorded for developing decision trees. A group of variables

that possibly influence large-disturbance rotor angle stability is selected as the candidates for key

variables, as shown in Table 4.2. The post-disturbance time response (measured at fault clearing

time) of them are collected for decision trees training and testing.

Table 4.2 Recorded system states.

Component States

G2, G3 Terminal voltage

Current injected to the grid

Active power and reactive power

Speed, angle and accelerating speed

Bus Voltage magnitude and angle

Transmission

line

Active power

Reactive power

The variables listed in Table 4.2 are used as the inputs of decision trees. In practice, the generator

speed, the rotor angle and the accelerating speed can be approximately represented by the

frequency, the angle, and the ROCOF of the terminal bus. 59 variables are selected. The algorithms

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of decision trees, as well as MVMO, are programmed in Matlab. Totally, 100 trees are built to form

a random tree forest. The parameters of the decision trees are given in Table 4.3.

Table 4.3 Decision tree parameters.

Tree number Leaf size Attribute number

100 1 59

The initial weight factor for each variable in For each sample, system states are recorded for

developing decision trees. A group of variables that possibly influence large-disturbance rotor

angle stability is selected as the candidates for key variables, as shown in Table 4.2. The post-

disturbance time response (measured at fault clearing time) of them are collected for decision

trees training and testing.

Table 4.2 is 0.5. The upper bound of the weight factor is 1, and the lower bound is 0. It will

influence decision trees to select one variable as the input, or not. A variable with a weight factor 0

entails that it is removed from the inputs of decision trees. 60 tests are generated to investigate

the errors of decision trees.

The tests, decision trees, and weight factors are provided to MVMO, which is responsible to

optimise the weight factors. The optimised errors after 200 iterations are shown in Figure 4.45.

Figure 4.45 Errors of decision trees for modified generic test case 2.

Here, it is seen that by regulating the weight factors, the errors of decision trees are reduced

gradually. The weight factors of 58 variables are obtained and ranked from the biggest from the

smallest. Table 4.4 lists the first 8 biggest weight factors and 2 smallest weight factors.

The 1st, 4th and 6th variables are associated to post-disturbance time response (measured at fault

clearing time) of generator G2. They represent the influence of the fault on the generator dynamics.

The fault changes G2 terminal voltage (variable 4) and thus changes the active power of G2. So G2

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starts to accelerate (variable 1) and its rotor angle (variable 6) increases. When the rotor angle

exceeds the critical value, G2 accelerates again and loses large-disturbance rotor angle stability.

The rest are related to the reactive power flow. These variables influence the terminal bus voltage

of generator 2 and its active power output. In this way, they will influence rotor angle stability of

generator 2.

Bus 9 voltage has a big influence on the large disturbance rotor angle stability of G2. Here,

generator 3 is the reference generator. And the wind turbine operates with given power factors, 1

(unite power factor) and 0.9 (lagging). Therefore, the voltage magnitude of bus 9 decides how

much reactive power will be sent to bus 8 which connects to the largest load of system, 160 MW.

The bus 8 voltage will decide the real load quantity after a disturbance. Furthermore, it will

influence the loading level of G2 and its large disturbance rotor angle stability.

The Line 5-7 reactive power and Bus 5 voltage, namely the 5th and 7th variables in Table 4.5, are

considered as the key variables describing the influence of wind farm on the rotor angle stability of

generator 2.

Table 4.4 Weight factors obtained when training decision trees with modified generic test case2.

Number Weight factor State

1 0.94 G2 speed

2 0.88 Bus 9 voltage magnitude

3 0.86 Line 8-9 reactive power

4 0.83 G2 terminal voltage magnitude

5 0.82 Line 5-7 reactive power

6 0.81 G2 angle



.

.

.

.

.

.

.

.

.


58 0.0047 G3 speed

First, the response of generator 1 (shown in Figure 4.46) and the response of the wind farm

(shown in Figure 4.47) are compared, in terms of PCC voltage, active power and reactive power

after a three phase short circuit in Line 7-8. It is seen that the active power of the wind farm (the

red line in Figure 4.47) restores faster than synchronous generator 1 (the red line in Figure 4.46),

with less power oscillations. On the other hand, generator 1 is able to provide a little more reactive

power after the disturbance (the black line in Figure 4.46), than the wind farm (the black line in

Figure 4.47). Therefore, the voltage of PCC (the blue line in Figure 4.46) restores faster too.

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Figure 4.46 Response of G1.

Figure 4.47 Response of wind farm.

The key variables’ (Line5-7 reactive power’s and Bus 5 voltage’s) ability of representing the

influence of wind farm on the rotor angle stability of generator 2 is illustrated through the following

3 cases:

─ Wind farm runs at a power factor (cosΦ) 0.9

─ Wind farm runs at a power factor (cosΦ) 0.95

─ Wind farm runs at a power factor(cosΦ) 1

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Figure 4.48a shows the reactive power produced by the wind farm. The larger the power factor

(cosΦ) is, the less the reactive power is. Correspondingly, the Bus 5 voltage is lower, as shown in

Figure 4.48b. The Line 5-7 (shown in Figure 4.48c) transfers more reactive power from the

terminal bus of G2 to the load bus (namely Bus 5). The lower the terminal voltage of generator 2 is,

the less active power it outputs. Therefore the rotor angle stability is worse, as shown in Figure

4.48d. When the power factor (cosΦ) is 1, the generator 2 loses rotor angle stability.

(a) (b)

(c) (d)

Figure 4.48 The influence of wind farm on rotor angle stability of G2.

It is worth clarifying that when the rotor angle exceeds 180 degrees (or 3.14 radians),

PowerFactory restarts the angle from -180 degrees (or -3.14 radians). Therefore, the solid black

line in Figure 4.48d shall not be misunderstood as a stable case.

Here, the first 8 variables with the largest weight factors are selected as key variables. They are

taken as the inputs of decision trees. The estimation accuracy is compared with the estimation

accuracy of decision trees which use all 58 variables as the inputs. The purpose is to show if the

proposed method selects correctly the key variables for assessment of large-disturbance rotor

angle stability, that is, the decision trees using the 8 key variables is expected to have the similar

estimation accuracy as decision trees using all 58 variables. Indeed, the operator can decide to

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select more variables or less according to the errors of decision trees calculated by Equation (4.12).

Equation (4.12) is defined to quantify the errors of decision trees for one group of key variables, in

order to give system operators the confidence about the selected variables. The error calculation is

automatically carried out to reduce the operators' working load. The operator can add or remove

some variables and observe the evolution of errors until they are confident in the selected variables.

Selecting more variables means more measurements and better accuracy of decision trees.

Selecting less variables means less measurements and worse accuracy of decision trees.

Next, the estimation errors obtained by using all 58 variables and by using the above 8 key

variables as inputs of decision trees are compared in Figure 4.49 and Figure 4.50. Two different

fault locations (not considered in the training) and five fault duration (not considered in the

training) in six transmission lines, as well as one different value of inertia constant of G2 (not

considered in the training) are used.

Figure 4.49 (left) Estimation using 59 variables; (right) Estimation using 8 key variables .

In Figure 4.49, it is seen that the estimation by using 8 variables has nearly the same accuracy as

the estimation done by using 59 variables. Their errors are further compared in Figure 4.50.

Figure 4.50 (left) Estimation using 59 variables; (right) Estimation using 8 key variables.

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Figure 4.50 shows that using 8 key variables increases the estimation errors but the errors are still

small.

4.3.6 Test Results on the GB System

Selection of Key Variables and Building of the Decision Trees

The proposed method is further tested on the GB system. Scenario 2020 introduced Section 3.3.2

is used. The GB system has three sub-areas, the north, the centre and the south. Considering the

computation burden for the whole GB system, the sub-area of the north is selected as one example

to demonstrate the proposed method.

In this case, more wind penetration levels and different dispatches between synchronous

generators are considered to analyse the influence of wind power and power flow distribution

among synchronous generators on large-disturbance rotor angle stability. The following

uncertainties are considered to generate different operation conditions.

─ Fault duration. One three phase short circuit fault is applied to tie line 6-9a. Indeed, the GB

system is fairly (rotor angle) stable for large-disturbances. So in order to generate unstable

samples, the fault duration is selected in a range from 0.2s to 0.3s. After this fault, the power

plant G1 in Zone 1 may lose rotor angle stability.

─ Dispatches among synchronous generators. In the north area, there are 4 synchronous power

plants. Different dispatches between four power plants are generated. Because of the regulation

of generator units, the inertia of different zones is changed.

─ Wind penetration levels of the north area. The initial output of synchronous generators and wind

turbines are listed in Table 4.5.

Table 4.5 Synchronous power and wind power.

Zone1 Zone2 Zone3 Zone4 Zone5 Zone6 Zone7 Zone8

Synchronous

power (MW) 964 0 0 0 1020 0 1077 1077

Wind power

(MW) 912 912 853 852 890 890 852 852

Based on the power outputs in Table 4.5, part of synchronous generators are decommissioned and

replaced by wind generators. The wind penetration levels used to generate samples for decision

trees are listed in Table 4.6.

Table 4.6 Wind penetration levels.

Level 1 Level 2 Level 3 Level 4 Level 5

Penetration(%) 63 68 72 77 82

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In total, 633 samples are collected, which include 97 dispatches. For each samples, the following

states are recorded as the candidates for key variables.

Table 4.7 Recorded variables in the north area.

Component States

G1,G5,G7,G8 Terminal voltage

Current injected to the grid

Active power & reactive power

Speed, angle, accelerating speed &

inertia

Buses GT1, GT5, GT7, GT8 Voltage magnitude & angle

25 Transmission lines in

the north

Active power

Reactive power

98 variables are selected. These variables represent the post-fault power flow and the generator

status. The bus voltages and transmission line powers define the post–fault power flow. The

terminal voltage, current, and power of generators are related to the electrical torque, which is

influenced by the electrical distance between the generator and the fault. The inertia is one

important factor which influences the post-fault rotor accelerating speed. The speed, angle, and

accelerating speed describe the rotor motion.

The parameters of the decision trees are defined as in Table 4.8. Totally, 100 trees are built to

form a random forest. For each tree, one leaf node only includes one sample. Each variable can be

selected as a property to split a group of samples. Therefore, 98 attributes are used.

Table 4.8 Decision tree parameters.

Tree number Leaf size Attribute number

100 1 98

An initial weight factor, 0.5, is given to each variable. The upper bound of the weight factor is 1,

and the lower bound is 0. The convergence of the optimisation process to find the optimal weight

factors after 1000 iterations is depicted in Figure 4.51. It takes nearly 72 hours to converge on a

computer with Intel I5-2400 and 4G RAM. But it is worth mentioning that this is one-shoot offline

optimisation (i.e. a single run of MVMO – cf. Figure 4.42) and by using only one core of the

computer. Once obtaining the sequence of weight factors, the users need not repeat the

optimisation.

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Figure 4.51 Errors of decision trees. Scenario 2020 of GB system.

The error is reduced almost 50% after 1000 iterations. Corresponding to the minimum error, the

first 10 variables with the largest weight factors are listed in Table 4.9.

Table 4.9 Selected key variables. Scenario 2020 of GB system.

Number Weight factor State

1 0.98 GT1 bus voltage magnitude

2 0.96 Line 4-5a reactive power

3 0.94 GT1 current magnitude

4 0.91 GT7 voltage magnitude

5 0.87 G1 speed

6 0.85 Line 6-9a active power

7 0.82 Line1-3a active power

8 0.81 Line4-6b active power

9 0.8 GT8 active power

10 0.79 Line2-4b reactive power

11 0.76 GT5 reactive power

From Table 4.9, it can be seen that large-disturbance rotor angle stability is influenced by:

─ The loading level of generator 1, namely the voltage (variable 1) and the current (variable 3).

These two variables determine the active power output of generator 1.

─ The kinetic energy of generator 1, namely the speed (variable 5). The variable represents the

accelerating energy obtained by generator 1 during the fault. In practice, it can be

approximately represented by the terminal bus frequency.

─ The reactive power distribution after the fault, namely the 2nd, 4th, 10th and 11th variables. It is

verified that after the fault, the terminal voltage of generator 1 reduces so that generator 1

cannot output the active power normally. There is not enough reactive power support, so the

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reactive power flows from other zones to Zone 1. These 4 variables influence the flow of

reactive power to Zone 1.

─ The active power sent out from the north area, namely, the 6th, 7th, 8th, and 9th variables. The

fault prevents the active power transfer from the north area to the centre area, which causes

the generators in Zone 1 to accelerate. Therefore the quantity of active power output will

influence the severity of the fault, and further influence large-disturbance rotor angle stability.

Next, decision trees are built using the above 11 key variables, and are tested under different

operation scenarios. The obtained results are compared against the results obtained using all 98

variables to show that the proposed method can efficiently select key variables for large-

disturbance rotor angle stability assessment.

Test Results

65% wind Penetration

60 tests are made for this penetration level. From Figure 4.52, it can be seen that the estimation

done by using 11 key variables also provides similar accuracy as the estimation done by using 98

variables.

Figure 4.52 (left) Results with 98 variables; (right) Results with 11 key variables. O = Estimation;

X = Simulation.

Another point noticed here is that there are some points with relatively large estimation errors.

This is caused by the sudden transition from rotor angle stability to rotor angle instability due to a

minor change of fault duration, which is shown in Figure 4.53 and Figure 4.54. Indeed, GB system

is fairly stable for large disturbances. Therefore, in order to generate unstable samples, the fault

duration is increased from 0.2s to 0.3s. With the increasing of fault duration, GB system becomes

more prone to instability. For example, in the border between rotor angle stability and instability, if

the fault duration is slightly changed from 0.271s to 0.272s, the difference of one millisecond

causes rotor angle instability (please see Figure 4.54). On the edge to instability, usually the

artificial intelligence based methods have relatively large errors.

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Figure 4.53 G1 angle with a fault duration of 0.271 s.

Figure 4.54 G1 angle with a fault duration of 0.272 s.

The case in Figure 4.54 is unstable. This figure shows a first swing instability. It is worth clarifying

that when the angle exceeds 180 degrees, PowerFactory restarts the angle from -180 degrees.

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70% wind penetration

46 tests are made for this penetration level. The results are shown in Figure 4.55. It can be seen

that the estimation done by using 11 key variables still gets the same accuracy as the estimation

done using all variables.

Figure 4.55 (left) Results with 98 variables; (right) Results with 11 key variables. O = Estimation; X = Simulation.

Moreover, in this case, tests are classified into two categories, stable tests and unstable tests (cf.

upper and lower points in Figure 4.55). The decision trees give good estimations. Different from

Figure 4.52, which shows the performance of proposed KPI at the critical edge, Figure 4.55 shows

results for stable cases and unstable cases.

79% wind penetration

In this case, more synchronous generators are decommissioned. Wind penetration nearly reaches

80% in the north area. For all used 48 tests, rotor angle instability occurs. Figure 4.56

demonstrates that using all variables and using 11 key variables, both provide good estimations.

Figure 4.56 (left) Results with 98 variables; (right) Results with 11 key variables. O = Estimation; X : Simulation.

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4.3.7 Conclusions and Recommendations

This section presented the KPI developed for the assessment of large-disturbance rotor angle

stability. The two most important innovations of this work are:

─ The accuracy of decision trees is used to select key variables to estimate the maximum angular

deviation. Taking key variables as the inputs of decision trees entails a good accuracy.

─ The selection of key variables and the optimisation of decision trees are made at the same time

via a weight factor. The weight factor is optimised by MVMO.

The presented results on 9 bus system and GB system show that the proposed method is efficient

and feasible. It selects correctly a few of key variables for decision trees, and at the same time

keeps a good estimation accuracy for large-disturbance rotor angle stability. It is noted that on the

edge to instability, decision trees may have some relatively large errors. This is a common

challenge for all artificial intelligence based methods. More research effort should be put into

solving the misjudgement on the border between stability and instability.

Before using this method in real power systems, adequate tests are necessary. To ensure a

satisfactory performance, a minimum number of samples of possible system operating conditions

and disturbances are needed for training the decision trees. This is a general requirement for

artificial intelligence based methods. That is to say, if artificial intelligence based methods do not

obtain enough good knowledge from the samples, they could probably fail to give correct

estimations. A simple approach can be used to define the minimum number of samples: select a

set of few critical faults. The possible faults in real systems are numerous, but not every fault

causes transient instability. Therefore, the faults which never cause large-disturbance rotor angle

instability as well as the faults which always (in any operating condition) cause large-disturbance

rotor angle instability can be neglected for decision trees. The focus can be put on faults which do

not cause large-disturbance rotor angle instability in normal operation conditions, but may cause

large-disturbance rotor angle instability in stressed operation conditions. Such approach was

illustrated in this report.

On the other hand, any independent test should be made by using values of the system variables

which are in the range of collected samples. That is to say, if a complete new and different

operation condition, which has radically different characteristics with respect to the considered

samples, is tested, maybe decision trees obtained by the proposed method cannot give a good

estimation. Two possible solutions can be taken to improve the performance: enrich the used

sample database, namely, providing more knowledge to decision trees to make them smarter, or

adding self-learning skills to decision trees.

Once decision trees meet the requirement of system operators with respect to acceptable accuracy,

they can be used for large-disturbance rotor angle stability monitoring and control. One possible

implementation is shown in Figure 4.57. First, with the help of off-line training (cf. Figure 4.42),

different groups of decision trees are obtained for different faults. In practice, when a fault occurs,

Disturbance indicator will send the fault information to a classifier. This classifier will select the

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corresponding group of decision trees, like group 1, group 2. PMU measurements are also sent to

the selected group of decision trees. Decision trees will output the large disturbance rotor angle

stability indicator, like Margin 1, Margin 2, etc.

Disturbance indicator -

IED

.

.

.

Group 1

Group 2

Group n

Margin 1

Margin 2

Margin n

Classifier of

Decision trees

PMU measurement

Off-line

decision trees

training

(cf. Fig. 4.41)

Figure 4.57 Proposed implementation for decision trees.

Figure 4.58 gives an example of a possible application. In the example, there are n key variables

and a group of decision trees to estimate the maximum angle difference 𝛿𝑖 − 𝛿𝑗 . The first key

variable is perturbed from K1 to K’1 and other key variables are kept constant. The decision trees

are executed to obtain the resulting increment of angle difference ∆(𝛿𝑖 − 𝛿𝑗). The sensitivity of angle

difference to K1 is defined as:

𝑆K1 =∆(𝛿𝑖 − 𝛿𝑗)

𝐾1′ − 𝐾1

(4.16)

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The user can investigate key variables one by one and get a series of 𝑆KPI𝑖 (sensitivity matrix).

Based on the list of sensitivity, it will be possible to first regulate the key variables with the largest

sensitivities in order to improve large-disturbance rotor angle stability of the system, and at the

same time minimise the number control of actions. The monitored signals from the real power

system (monitored by PMU devices) can be used in combination with the sensitivity matrix to

estimate the distance to instability (because the real power system is constantly disturbed by

fluctuating load and fluctuating generation)

Figure 4.58 Decision tree based sensitivity analysis

4.4 KPI for Small-Disturbance Voltage Stability

4.4.1 Introduction

One of the topics identified by TSOs as a potential issue in the future is the lack of reactive power

due to increasing levels of PE penetration [2]. Voltage instability appears mostly as a progressive

drop of voltages. This can be initiated by either a short-term, large disturbance event (e.g. short

circuit) or a long-term, small disturbance event (gradual load increase). Most events leading to

voltage instability are long-term in nature (in contrast to e.g. frequency stability).

With the increasing levels of PE penetration in the power system, conventional synchronous

machines are being displaced. With less and less conventional generation available, the voltage

control capabilities as well as the strength of the power system might decrease. This chapter

presents the development of a new indicator for small-disturbance voltage stability, the Normalised

Voltage Instability Sensitivity Index (N-VISI)23.

The following design criteria are imposed on the new indicator:

─ The indicator should evaluate and visually depict the impact of increasing levels of renewables

on the voltage stability.

23 The reduction of the level of short circuit capacity due to massive penetration of power electronic interfaced renewable generation could alter the amplitude and waveform of instantaneous voltages and currents when severe faults occur. This issue is studied based on EMT simulations.

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─ The indicator or its calculation process should preferably identify weak nodes in the system in

order to carry out further analysis on specific buses.

─ The indicator should give insight in the distance to instability.

─ The indicator should be relatively easy implementable for control room applications.

For the long-term voltage stability assessment, it is assumed that the wind turbines have a fixed

active power output.

4.4.2 Definitions

Power Electronics-Interfaced Generation (PEIG) is defined here as infeed that is connected to the

grid using PE. This can be generation and import through HVDC. Power Electronics-Interfaced

Device (PEID) is defined here as any device that is connected to the grid using PE. This can be

generation, loads, HVDC converters, etc.

System Non-Synchronous Penetration (SNSP)

The System Non-Synchronous Penetration (SNSP), as defined in [100] is an indication of the ratio

of PEIG over the system load and HVDC export and is defined as:

where:

Pwind = the wind generation in the system (MW)

PHVDC(import) = the import through HVDC interconnections (MW)

Pload = the system demand (MW)

PHVDC(export) = the export through HVDC interconnections (MW)

Whereas this indicator is a useful one in terms of expressing the relative PEIG in a system, the

results presented in [100] illustrate values of SNSPs larger than 100%. Based on the above

formula this means that the sum of wind generation and HVDC imports is larger than the sum of

the demand and HVDC exports.

As this is not possible in a balanced power system, a modified SNSP index (SNSP*) is derived to

indicate the level of PEIG in a system. The aim is to derive a mathematical expression for the

SNSP* where SNSP* is defined as the ratio of the PE infeed (i.e. PEIG) over the total system

demand. It is assumed that the power system is balanced at all times, i.e. the total generation

(synchronous as well as non-synchronous) is equal to the total demand, ergo SNSP* is defined as:

SNSP = 𝑃𝑤𝑖𝑛𝑑 + 𝑃𝐻𝑉𝐷𝐶(𝑖𝑚𝑝𝑜𝑟𝑡)

𝑃𝑙𝑜𝑎𝑑 + 𝑃𝐻𝑉𝐷𝐶(𝑒𝑥𝑝𝑜𝑟𝑡) (4.17)

𝑆𝑁𝑆𝑃∗ =𝑃𝐸𝐼𝐺

𝑃𝑙𝑜𝑎𝑑=

𝑃𝐸𝐼𝐺

𝑃𝐸𝐼𝐺 + 𝐶𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛

(4.18)

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Whereas equations (4.17) and (4.18) are in essence the same, the definition in equation (4.18) is

helpful in deriving step by step equation (4.24).

In terms of energy exchanges (imports and exports), a power system can conceptually have 5

possible independent operating states: no exchanges (case 1), AC export (case 2), AC import

(case 3), DC export (case 4), and DC import (case 5). In case 1, SNSP* is therefore defined as:

In case 2, there is an AC export out of the system, which acts as an extra load on the system.

Assuming fixed Pwind and Pload this means that conventional generation will increase to cover this

extra demand. SNSP* is now defined as:

When there is an AC import (case 3) and fixed Pwind and Pload the conventional generation decreases

by the amount of the AC import. SNSP* is then defined as:

In the case of a DC export and fixed Pwind and Pload (case 4), the conventional generation will

increase again in order to cover the extra demand. The increase in the output of the conventional

generation is equal to the value of the DC export. SNSP* is now defined as:

In the last case, the system has a DC import (case 5). Again Pwind and Pload are assumed fixed. The

DC import is categorised as PEIG and therefore the SNSP* is now defined as:

An example of all these 5 cases is given in Figure 4.59.

𝑆𝑁𝑆𝑃∗ =𝑃𝑤𝑖𝑛𝑑

𝑃𝑙𝑜𝑎𝑑 − 𝑃𝑤𝑖𝑛𝑑

(4.19)


𝑃𝑙𝑜𝑎𝑑 − 𝑃𝑤𝑖𝑛𝑑 + 𝐴𝐶𝑒𝑥𝑝𝑜𝑟𝑡 (4.20)


𝑃𝑙𝑜𝑎𝑑 − 𝑃𝑤𝑖𝑛𝑑 − 𝐴𝐶𝑖𝑚𝑝𝑜𝑟𝑡 (4.21)


𝑃𝑙𝑜𝑎𝑑 − 𝑃𝑤𝑖𝑛𝑑 + 𝐷𝐶𝑒𝑥𝑝𝑜𝑟𝑡 (4.22)

𝑆𝑁𝑆𝑃∗ =𝑃𝑤𝑖𝑛𝑑 + 𝐷𝐶𝑖𝑚𝑝𝑜𝑟𝑡

𝑃𝑙𝑜𝑎𝑑 − 𝑃𝑤𝑖𝑛𝑑 + 𝐷𝐶𝑒𝑥𝑝𝑜𝑟𝑡 (4.23)

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Figure 4.59 SNSP* Example.

Combining the above cases would yield the following generic mathematical definition for SNSP*:

Another simple index ‘PE to load’ ratio (PE2L) is proposed and is defined as the part of the load (i.e.

the demand in the system excluding AC imports, AC exports, and DC exports) that is covered by

PEIG. The mathematical expression for PE2L is:

where:

∑Pwind = the total wind generation

∑PDC,import = the total imports from HVDC interconnections

Pload,system = the load of the system (excluding exports and AC imports)

The goal of this indicator is to get insight in which part of the load is supplied by PEIG. In contrast

to the SNSP* this indicator can be larger than 1, as exports are excluded. A value larger than 1

implies the infeed from PEIG is larger than the load and that the remaining energy is exported.

CASE 1Pwind = 500 MWLoad = 1000 MW





AC export = 250 MW

AC import = 250 MW

DC export = 250 MW

DC import = 250 MW

PEID = 500 + 0 = 500Conv. Gen. = 1000 – 500 = 500

𝑆𝑁𝑆𝑃∗ = 500

500+ 500= 0.5

PEID = 500 + 0 = 500Conv. Gen. = 1000 – 500 + 250 = 750

𝑆𝑁𝑆𝑃∗ = 500

500+ 50= 0.

PEID = 500 + 0 = 500Conv. Gen. = 1000 – 500 - 250 = 250

𝑆𝑁𝑆𝑃∗ = 500

500+ 250= 0.6

PEID = 500 + 0 = 500Conv. Gen. = 1000 – 500 + 250 = 750

𝑆𝑁𝑆𝑃∗ = 500

500+ 50= 0.

PEID = 500 + 250 = 750Conv. Gen. = 1000 – 500 - 250 = 250

𝑆𝑁𝑆𝑃∗ = 500+ 250

500+ 250+ 250= 0. 5

𝑆𝑁𝑆𝑃∗ =∑𝑃𝑤𝑖𝑛𝑑 + ∑𝑃𝐷𝐶,𝑖𝑚𝑝𝑜𝑟𝑡

𝑃𝑙𝑜𝑎𝑑,𝑠𝑦𝑠𝑡𝑒𝑚 + ∑𝑃𝐴𝐶,𝑒𝑥𝑝𝑜𝑟𝑡 + ∑𝑃𝐷𝐶,𝑒𝑥𝑝𝑜𝑟𝑡 − ∑𝑃𝐴𝐶,𝑖𝑚𝑝𝑜𝑟𝑡

(4.24)

𝑃𝐸2𝐿 = ∑𝑃𝑤𝑖𝑛𝑑 + ∑𝑃𝐷𝐶,𝑖𝑚𝑝𝑜𝑟𝑡

𝑃𝑙𝑜𝑎𝑑,𝑠𝑦𝑠𝑡𝑒𝑚

(4.25)

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A comparison between the modified SNSP (SNSP*), the original SNSP, and the PE2L index is given

in Table 4.10. The difference in the indices, arising for case 2 and case 3, can be explained by the

fact that the definition for SNSP does not contain the AC exchanges.

Table 4.10 SNSP Comparison.

Case SNSP* PE2L SNSP

Case 1 0.5 0.5 0.5

Case 2 0.4 0.5 0.5

Case 3 0.67 0.5 0.5

Case 4 0.4 0.5 0.4

Case 5 0.75 0.75 0.75

V/V0

The V/V0 index [101], [102], is a rather simple index that determines the weakest bus in a power

system. It is the ratio between the actual bus voltage V and a reference voltage V0. The actual bus

voltage V is known from power flow studies (offline) or state estimation (online). V0 is the voltage

at the same bus but with all loads set to 0. This voltage is obtained using power flow simulations.

The ratio V/V0 gives the voltage stability index. The value can be between 1 and 0 and the lower

the index, the weaker that specific bus is.

The V/V0 indices across the buses create a voltage stability map of the power system, allowing for

immediate detection of weak nodes. Detection of weak areas in the system is beneficial and even

more for larger systems. Another advantage of this index is that it has practically no computational

burden on the system, and can therefore be carried out more frequently (e.g. for load increases,

redispatch, topology changes, etc.). This index has been used for online voltage stability

monitoring (identification of weak buses) since 1995 [103].

The results from the V/V0 analysis have been validated using Short Circuit Capacity (SCC)

calculations for the generic test case. In more than 80% of the simulated cases, the V/V0 method

correctly identified the 3 worst buses of the system (compared with the results from the SCC

calculations).

PV Curve

The Power-Voltage characteristic at buses, also known as PV curves, is a popular method especially

in the industry for determining the small-disturbance voltage stability of power systems [104]. The

mathematical formulation for the PV curve is derived as follows. Assume the 2 bus system as given

in Figure 4.60.

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Figure 4.60 Test model for voltage stability.

VS is the sending end voltage and has a phase displacement 𝜑1 compared to a reference signal:

VS=𝑉𝑆∠𝜑1 . VR is the receiving end voltage and has a phase displacement 𝜑2 : VR=𝑉𝑅∠𝜑2 . The

transmission line has a complex impedance Z, consisting of a resistance R and reactance X. Also,

the following relationships exist:

Let 𝜑2 − 𝜑1 = 𝜃 be the load angle 𝑆 =𝑉𝑅𝑉𝑆𝑒

−𝑗(𝜃−𝜓)

𝑍−

𝑉𝑅2𝑒𝑗𝜓

𝑍

Also: 𝑒−𝑗𝜃 = 𝑐𝑜𝑠𝜃 − 𝑗𝑠𝑖𝑛𝜃 and 𝑒𝑗𝜃 = 𝑐𝑜𝑠𝜃 + 𝑗𝑠𝑖𝑛𝜃 therefore:

AC

R + jX

BUS 1 BUS 2S = P + jQ

VS VR

𝑍 = 𝑅 + 𝑗𝑋 = 𝑍𝑒𝑗𝜓 (4.26)

𝑉𝑆 = 𝑉𝑆𝑒−𝑗𝜑1 (4.27)

𝑉𝑅 = 𝑉𝑅𝑒−𝑗𝜑2 (4.28)

𝐼 = 𝑉𝑆 − 𝑉𝑅

𝑍

(4.29)

𝑆 = 𝑉𝑅𝐼∗ ⇒ 𝑆 = 𝑆 = 𝑉𝑅 (

𝑉𝑆 − 𝑉𝑅

𝑅 + 𝑗𝑋)

∗

(4.30)

𝑆 = 𝑉𝑅𝑒−𝑗𝜑2 (

𝑉𝑆𝑒𝑗𝜑1 − 𝑉𝑅𝑒

𝑗𝜑2

𝑍𝑒−𝑗𝜓) (4.31)

𝑆 =𝑉𝑅𝑉𝑆𝑍

(cos (𝜃 − 𝜓) − 𝑗𝑠𝑖𝑛(𝜃 − 𝜓)) −𝑉𝑅

2

𝑍(𝑐𝑜𝑠𝜓 + 𝑗𝑠𝑖𝑛𝜓)

(4.32)


cos(𝜃 − 𝜓) − 𝑗𝑉𝑅𝑉𝑆𝑍

𝑠𝑖𝑛(𝜃 − 𝜓) −𝑉𝑅

2

𝑍𝑐𝑜𝑠𝜓 − 𝑗

𝑉𝑅2

𝑍𝑠𝑖𝑛𝜓)

(4.33)


cos(𝜃 − 𝜓) −𝑉𝑅

2

𝑍𝑐𝑜𝑠𝜓 + 𝑗 (

−𝑉𝑅𝑉𝑆𝑍

𝑠𝑖𝑛(𝜃 − 𝜓) −𝑉𝑅

2

𝑍𝑠𝑖𝑛𝜓) (4.34)

𝑃 = 𝑅𝑒(𝑆) =𝑉𝑅𝑉𝑆𝑍

cos(𝜃 − 𝜓) −𝑉𝑅

2

𝑍𝑐𝑜𝑠𝜓 ⇒

𝑐𝑜𝑠𝜓

𝑍𝑉𝑅

2 −𝑉𝑆 cos(𝜃 − 𝜓)

𝑍𝑉𝑅 + 𝑃 = 0

(4.35)

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For the active power equation, which is a second order equation for VR, the sending end voltage,

the load angle, and the line impedance can be assumed constant. Solving the equation for the

receiving end voltage, the influence of increasing active power transfers P on the receiving end

voltage VR can be investigated. When this is plotted for several values of P, the PV curve is

obtained.

The major strengths of the PV curve are its robustness, computational efficiency, and easy

implementation as a control room application. The shortcomings are in the fact that the PV curve

assumes a constant load angle (with increasing loads) as explained above. It also does not directly

give information on the ‘speed’ to instability, especially with increasing levels of PE2L.

The KPI that is proposed in this chapter aims at keeping the strengths of the PV curve while

addressing the shortcomings. The proposed procedure will also identify the weak buses in a system,

so that these buses can be targeted for further analysis.

4.4.3 Proposed Indicator: Calculation Procedure

The Normalised Voltage Instability Sensitivity Index (N-VISI) is proposed as a new indicator for

assessing small-disturbance voltage stability. The flowchart in Figure 4.61 illustrates the required

steps to populate the data for the calculation of the N-VISI. As a first step the V/V0 analysis and

SCC calculations are carried out (please refer to Section 4.4.2 for more the details on the V/V0

index). The V/V0 index gives the weakest bus (or set of weakest buses) in the power system. For

this identified bus, a set of power flows is solved while increasing the load uniformly across the

system until divergence of the power flow solution occurs. For every power flow solution, the

changes in voltage and load are recorded for manual data processing. These steps are repeated for

a defined set of weak buses. These steps are automated using python.

Figure 4.62 illustrates the steps for the manual data processing. The N-VISI itself is the result of

the manual data processing steps. Once the loads and corresponding voltages are recorded for the

set of weak buses, curve fitting is applied to obtain a mathematical function of the P-V relationship.

As shown in the previous section, this relationship is non-linear. Therefore, polynomial regression

has been used for curve fitting. The first derivative of the polynomial is then calculated and

represents the ‘speed’ towards the nose point (instability point). For each of the load levels defined

in the previous step, the derivative (i.e. the sensitivity) is calculated. As these sensitivities have a

wide range for different cases, they are normalised for comparison purposes. Therefore the index

N-VISI can have a value between 0 and 1: the higher the index, the faster the nose point is

reached, ergo the less stable the system becomes24.

24 It should be mentioned that the effect of variations in tap position of transformers or compensation devices on the N-VISI is not explicitly taken in into account. However, as these variations alter the operating condition, the N-VISI can be easily calculated for these operating conditions as well.

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Figure 4.61 Data Generation for the Calculation of N-VISI.

Figure 4.62 Manual Data Processing: Steps for N-VISI calculations.

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4.4.4 Results for Generic Test Case 2

The processes described in the previous section have been implemented for generic test case 2.

For voltage stability, this is the IEEE 9 bus system in which certain modifications are done (for

more details, see Section 3.2.4).

As a first step, the V/V0 and SCC analyses were done. The results are presented for 3 cases in

Figure 4.63. The Base Case represents a conventional power system with no PEIG. The Increased

PE case is a representation of a RES-dominated power system with a PE2L ratio of approximately

70%. In this case the wind generation displaces the conventional generator G2 at bus 2. In the

Reduced SG (reduced synchronous generation) case the conventional generator G2 at bus 2 is

disconnected again. No wind generation is connected to the grid at this moment, i.e. the power

balance is maintained by increased production of the remaining conventional generators.

Figure 4.63 Results of V/V0 and SCC Analyses for Generic Test Case.

Compared to the Base Case, one can observe that in the Increased PE case the V/V0 index

decreases for several buses. The largest relative decrease can be observed for bus 2 and bus 7.

This can be explained by the fact that bus 2 contains generator G2, which is switched off in the

Increased PE case. A step up transformer connects G2 to bus 7, which therefore is also directly

influenced by the state of G2. Buses 5, 6 and 8 are load buses.

Bus 5 has the lowest V/V0 index and is therefore the weakest bus. This bus has the largest active

and reactive power load. When switching off G2, the reactive power has to be provided by the

remaining conventional generators. The increased reactive power transfer leads to lower voltages

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in this case. As bus 6 is located between G1 and G3, the absence of G2 is not affecting the bus

voltage.

The short circuit analysis carried out on the three cases reveals that the Reduced SG case has the

lowest short circuit capacity. Although G2 is also switched off in the Increased PE case, the WTs in

this case deliver a small amount of short circuit current, resulting in an overall higher short circuit

capacity compared to the Reduced SG case.

Both methods, the V/V0 as well as the SCC, identify buses 5, 6, and 8 as the weakest buses (bus 2

and 7 are not considered because of the switching off of the conventional generator).

For bus 5 the SCC is given for different PE2L ratios in Figure 4.64. In the same figure the

development of the critical load with increasing levels of PE2L is illustrated. The critical load is

defined as the maximum load that can be accommodated by the system while maintaining

acceptable voltage levels at all buses. Increasing the load even further would result in a voltage

collapse. Generators G2 and G3 are modelled as 10 parallel machines. With increasing levels of

PEIG, the number of parallel machines is reduced, starting with generator G2.

Figure 4.64 Critical P and SCC vs PE2L ratio.

The general trend is a decreasing one: the critical load as well as the SCC decrease with increasing

PE2L ratios. Increasing PE2L ratios displaces conventional generation. This reduces the long-term

voltage support available from conventional generation. Also, as conventional generators have

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higher short circuit capabilities, displacement of these units by PEIG results in decreasing SCC. At

around 60% PE2L ratio, generator G2 is completely switched off. This causes the change on the

slope of the curves (generators G2 and G3 are not identical).

For different PE2L levels the PV curves and the N-VISI are calculated and presented in Figure 4.65

for bus 5 of the generic test case. It should be noted that the N-VISI does not represent any

physical variable of the power system, as is the case with other voltage stability indicators [105],

[106], [107]. It is rather a normalised metric between 0 and 1, where 1 represents an instable

system. The coloured lines in the figure are iso-PE2L ratio lines (i.e. operating points across lines

with the same colour have the same PE2L ratio). It can immediately be observed that the N-VISI

index is more effective in terms of illustrating the impact of increasing levels of PE2L levels. It

shows from the initial loading of the system (315 MW) already how stable the system is in terms of

different PE2L levels, something which is difficult to assess using the PV curves (voltage collapse

can occur at voltages close to 1 p.u.). For each loading level the distance to instability can be read

from the N-VISI curves.

Figure 4.65 PV and N-VISI Curves for Bus 5.

The impact of changing operating conditions on the voltage stability is shown in Figure 4.66.

Starting at operating point A, an indication of how stable the system is compared to other

operating conditions (increased of loading or PE2L ratios) can be perceived. Operating point A

represents an initial operating state with a certain load and 0% RES (PE2L ratio is 0). Compared to

operating point A, the load in operating point B is increased, whereas the PE2L ratio is still 0%.

When the operating point changes from A to B, the effect of the load increase is observed by

moving along the blue trajectory.

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The load in operating point C is identical to operating point A; the PE2L ratio now is 100%. When

the operating point changes from A to C, this symbolises an increase in the PE2L ratio. The effect

of this change on the voltage stability is observed by moving from the blue line to the purple line.

In operating point D the load as well as the PE2L ratio is changed.

Figure 4.66 N-VISI Curves for Bus 5.

As can be seen from the results of the N-VISI this new indicator not only gives insight into the

distance to instability, but also illustrates effectively the impact of system changes (PE2L ratio and

load) on the voltage stability. As the N-VISI uses the complete set of data of each PV curve, the

faster decrease of e.g. the yellow line (63% PE2L ratio), and the earlier collapse of the purple line

(100% PE2L ratio) are also taken into account in the respective N-VISI. That is why the N-VISI for

the 100% PE2L ratio is higher from the initial loading already.

4.4.5 Validation on the GB Power System

The same processes as defined in the previous sections are implemented in the GB system. Based

on the V/V0 results, the results for bus 15 are presented in Figure 4.67. In this figure, scenario

GG2020 is used as a starting point. The N-VISI analysis is carried out on this case. As a next step,

the PE2L ratio is increased to 40% and afterwards to 50%. It can be observed that for the 40%

case the voltage stability is improved. This has to do with the dispatch: wind generation is

increased in the near vicinity, leading to an increased margin for reactive power control of

conventional generation. In the 45% case the changes in the network are done electrically far from

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bus 15 (mainly at buses 25, 27 and 28). The effect of these changes on the voltage stability at bus

15 is relatively small.

Figure 4.67 N-VISI Curves for GB Bus 5 (GG2020).

Figure 4.68 N-VISI Curves for GB Bus 5.

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The N-VISI curves for bus 15 are shown in Figure 4.68. It should be mentioned that whereas in the

previous results the PE2L ratio was increased on the same network, the results shown in Figure

4.68 are based on 3 different cases of the Gone Green scenarios. The years 2020, 2025, and 2030

of the Gone Green scenarios are analysed. Based on the previous results, one would expect the

voltage stability to deteriorate with increasing levels of PE2L.

There are 2 reasons why the opposite is happening here:

1. When looking at the generation at node 15, it is observed that 1 GW of wind farms is connected

at this node for the scenario GG2030. The increased wind generation results in decreased

output of the conventional generators, which results in an increased margin for reactive power

control. Therefore more load can be accommodated. This is reflected in N-VISI curve.

2. The number of conventional generation at node 15 is increased in the GG2030 scenario. The

effect is the same: the margin for reactive power control from conventional generation is

increased, resulting in a more stable system.

These results show what is confirmed in [103] as well: indicators based on sensitivities change

more dynamically if changes occur electrically close to the bus under investigation. When changes

such as load increase or even the dispatch changes at a bus that is electrically far from the bus

under investigation, the effect is rather small. This confirms the rather local impact of voltage

stability, in contrast to frequency stability.

As proven here with the analysis, this index can also be used for investigation and understanding

how the voltage stability changes for different planning scenarios (GG2020 scenario versus

GG2030 scenario).


The aim of this chapter was to develop a new KPI for voltage stability. The Normalised Voltage

Instability Sensitivity Index (N-VISI) is developed and proposed. This index has the following

advantages:

─ It gives information on the distance to instability in terms of sensitivities.

─ The influence of changes in the system (PE2L ratios and load) on the voltage stability can be

illustrated in a comprehensive manner.

─ The process for calculating the N-VISI defines the weak buses in the system by using the V/V0

analysis.

─ Using the V/V0 method for each iteration can show how the weak buses in the power system

shift as a result of specific actions.

─ It has been shown that the index is also useful in analysing and understanding how voltage

stability changes for different planning scenarios (GG2020 vs GG2030).

The following disadvantages have been observed with the N-VISI:

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─ The load increase is modelled based on a uniform load increase across all the load buses. A new

operating point based on an asymmetrical load increase would require carrying out new

analyses.

─ The index is situation specific. Changes in the network topology, dispatch or loading will require

new calculations.

However, because the required calculations are based on steady state simulations and can be

performed fast, this is not seen as a major issue.

Roadmap for Control Room Implementation

The N-VISI index developed in this chapter can be implemented in the control room. For each step

in the calculation process the requirements are presented as follows. The V/V0 analysis requires

two inputs. The actual bus voltages are known in the SCADA. For calculating the V0 voltages, the

actual grid topology is required, which can be retrieved from the SCADA as well. A steady state

power flow program is required to calculate the V0 voltages, after which the V/V0 analysis can be

conducted. Next, a set of weak buses is selected based on the V/V0 indices and for each bus N-

VISI curves are calculated for different levels of PE2L ratios25.

The steady state power flow program can be used to simulate the P-V characteristics at each of the

identified buses and for each of the PE2L ratios. The PE2L ratios can be defined based on the

operational planning schedules (network topology, dispatched generation, exports, and imports)

which are known in advance. In order to calculate the N-VISIs, a software capable of doing the

defined mathematical operations (polynomial regression and derivative calculation) is required.

Once the N-VISIs are calculated, a visualisation tool is needed to illustrate the current operating

point on the iso-PE2L lines of the N-VISI vs Load graphs.

However, for implementing the KPI for real time operations, there are a number of challenges:

1. Determining the PE2L ratio in real time is practically impossible at this moment. The reason for

this is that the transmission system operator can only observe the vertical load (i.e. load at the

transformer between TSO and DSO. Installed RES generation on DSO level is subtracted from

the real, actual demand).

2. As the power system in reality is in quasi steady state, control room engineers need to define

thresholds based on their operational experience (e.g. minimum observed change in load) for

activation of the N-VISI calculations.

Future Work

Voltage stability is local phenomenon. With the replacement of transmission system connected

conventional power plants by transmission- and distribution system connected RES, the distribution

system is changing towards an active distribution network. Active distribution networks can support

25 Whereas the aim of the selection of buses is to concentrate on weak parts of the system, it should be mentioned that the N-VISI can be calculated for all the buses in the system.

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to a certain extent the secure operation of the power system (including voltage stability) [108].

With decreasing reactive power controllability in the transmission system on the one hand, and

increasing reactive power controllability in the distribution system on the other hand, the impact of

distribution system connected RES should be further investigated. As TSOs have limited knowledge

of the RES availability at distribution level, a strong cooperation between the TSO and DSO will be

required, when harnessing the reactive power support from distribution system connected RES.

This is a topic for further research.

4.5 KPI for Sub-Synchronous Controller Interactions

This section discusses the development of an indicator for determining the ‘distance’ to instability

for controller interactions. The phenomenon of Controller Interactions (CI) has no distance to

instability in the form that exists for the classical power system phenomena. This is a result of the

mechanisms leading to CI, which will be explained in the subsequent subsections. The distance to

CI proposed in this section could theoretically be used to predict the occurrence of CI.

4.5.1 Introduction

The motivation of investigating the current issue is that participants of the TSO questionnaire

(deliverable D1.1 [2]) mentioned ‘PE controller interaction with each other and passive AC

components’ as one of the problems resulting from increasing penetration of PE in the transmission

system. This issue ranked 5th in terms of severity, probability and timeframe.

When analysing this problem, it should be observed that these are technically 2 independent issues.

The first is the interaction of PE controllers with passive AC components. The second is the problem

of controller interactions of PE devices among each other.

In Table 4.11, a classification of the possible interactions between conventional generators, series

capacitors and Power Electronic-Interfaced Devices (PEID) in power systems is shown.

Table 4.11 Classification of Interactions in Power Systems.

Conventional Generator Series Capacitor PEID

Conventional Generator Inter area oscillations SSR SSTI

Series Capacitor SSR

SSCI

PEID SSTI SSCI CCI

The interaction between conventional generators can result in oscillations. Oscillations resulting

from a single generator are called local modes, whereas oscillations associated with groups of

generators are called interarea modes [109]. These interactions involve the mechanical shaft of the

generators and are therefore categorised as electromechanical oscillations.

The interactions between a turbine-generator and a series capacitor (e.g. a series compensated

transmission line) is defined as Sub-Synchronous Resonance (SSR). A resonance is defined as ‘the

enhancement of the response of a physical system to a periodic excitation when the excitation

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frequency is equal to a natural frequency of the system [110]. The interaction results in either

electrical oscillations (induction generator effect, see [111]) or electromechanical oscillations

(torsional interactions, see [112]).

Sub-Synchronous Torsional Interaction (SSTI) is a phenomenon associated with the interaction

between a turbine-generator and PEID. The torsional resonances in the turbine-generator shaft get

amplified due to the negative resistance of the power electronic controls in that specific sub-

synchronous frequency region [113]. As the shaft dynamics are part of the interactions, SSTI is

also categorised as an electromechanical phenomenon.

A series compensated overhead line can produce oscillations in the sub-synchronous frequency

range. When this overhead line is electrically close to a PEID (mainly WT T3), these oscillations can

grow if the damping of the system is not large enough. This can occur when the PEID exhibits a

negative resistance behaviour in which the negative resistance is larger than the positive resistance

of the network. This interaction between the PEID and the series compensated line is defined as

Sub-Synchronous Controller Interaction (SSCI). As no mechanical devices are involved in the

resonance, this phenomenon is a purely electrical oscillation. Due to this nature oscillations can

grow substantially in a short time (less than 1 second, see ERCOT case study [114]).

The last category in Table 4.11 is the interaction between PEIDs among each other. In this case,

fast controllers that are electrically close to each other can interact when both devices are

regulating the voltage at the same bus. A change in the voltage at this bus will cause a reaction of

the two (or more) devices, trying to regulate the voltage. Devices with fast controllers (mainly PE)

will rapidly increase and decrease their reactive power output, what could lead to reactive power

hunting. This effect is expected to be more present at weak points of common coupling.

In literature no suitable name was found for this phenomenon. As it deals with a cluster of

controllers that are electrically close, the term Clustered Controller Interactions (CCI) is proposed.

The focus of the assessments carried out in this deliverable is on SSCI.

4.5.2 Assumptions

For the scope of this deliverable, the following assumptions are made:

─ The wind farms contain identical wind turbines. This assumption facilitates the implementation

of simulations in PSCAD, as in the framework of the MIGRATE project one wind turbine type 3

(WT T3) EMT model and one wind turbine type 4 (WT T4) EMT model have been developed.

─ In the investigated cases cables do not result in SSCI since the resonance frequency is larger

than the nominal frequency. Similar results are achieved in [115].

─ The grid side is modelled as a passive network.

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4.5.3 Definitions

For the sake of common understanding this section provides some definitions. Figure 4.69

illustrates the boundaries of the power system as they are used throughout this section. The grid

side is also referred to as the network side or system side and is defined as the transmission

system to which the wind farm will be connected. In this figure, the grid side represents the

equivalence of a passive transmission system. The point of common coupling is the interconnection

point of the wind farm to the grid side. The wind turbine side or wind farm side contains the wind

turbines with all associated controls and collector systems.

For SSCI to occur, there are 2 necessary requirements [116]:

1. Zero reactance at a sub synchronous frequency

This happens when the inductive reactance and the capacitive reactance are of equal magnitude,

causing electrical energy to oscillate between the magnetic field of the inductor and the electric

field of the capacitor (positive reactance is inductive and negative reactance is capacitive). The

first step in SSCI investigation is the analysis of whether or not a network series resonance

could occur. A series resonance in the electrical system can be observed by a dip in the

impedance Z or a zero crossing over of the reactance X26. This is illustrated for the network of

the model problem in Figure 4.70. The grid impedances in the model problem are chosen in

such a way that the SSCI phenomenon can be observed and analysed.

Figure 4.69 Power System Boundaries.

In Table 4.12 the definition of the parameters used in this section are given.

26 The theoretical foundation behind the reactance crossover can be found in [118].

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Table 4.12 Definition of Parameters.

Parameter Definition

fR Resonance frequency at the network side

fNOM Nominal frequency of the system (50/60 Hz)

R(fR) Grid side electrical damping at the resonant frequency

VW Wind speed

VW,CUT IN Cut in speed of wind turbines

VW,CUT OUT Cut out speed of wind turbines

RVw(fR) Electrical damping of wind turbines at wind speed VW and

resonant frequency fR

PREF Active power output reference of wind farm

Figure 4.70 Zero Crossing Over and Impedance Dip Observation.

2. Net negative resistance

Power electronic devices can exhibit negative damping across certain frequency ranges. This is

an inherent characteristic of PE devices and their controls. If the negative resistance is larger in

magnitude than the damping provided by the grid, the net resistance is negative, which could

lead to amplification of oscillations. Figure 4.71 illustrates the damping provided by a wind

turbine for the sub synchronous frequency range.

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Figure 4.71 Wind Turbine Damping.

4.5.4 Calculation Procedure

As discussed in the previous section, the occurrence of SSCI is dependent on the network topology

and the damping of the system and the wind farm. In this section it will be shown that the wind

speed and the active power set point of the wind farm influence the magnitude of the damping on

the wind farm side. Therefore the distance to instability (i.e. distance to SSCI occurrence) can be

measured in terms of these parameters. The procedure for monitoring the distance to SSCI,

containing three processes and illustrated in Figure 4.72, is explained in this section. As impedance

scanning is a major part of the required analysis, the available impedance scanning methods are

given in Table 4.13 and are briefly discussed.

The applicability of four impedance scan methods is assessed based on the system behaviour

(linear or non-linear), the required type of analysis (steady state or time domain), the required

number of simulations, and the computational effort.

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Figure 4.72 Calculation Procedure SSCI.

Table 4.13 Impedance Scanning Methods.

Scanning Method System Analysis type # of Simulation

Runs

Computational

effort

Passive Impedance Scan Linear Steady state 1 Low

Sinusoidal Excitation Linear Time domain 1 per frequency

of interest Low

Impulse Excitation Linear Time domain 1 Low

White Noise Excitation Non-linear Time domain 1 High

The passive impedance scan is well known and used for impedance scanning of passive networks.

With one simulation run, the user gets an overview of the impedances across a wide frequency

range. The required analysis is a steady state simulation. Sinusoidal excitation, impulse excitation,

and white noise excitation use a time domain simulation to get insights in the impedance. White

Noise Excitation (WNE) is the only method that can be used to assess the non-linear behaviour of

devices. These non-linearities however require large computational efforts and result in long

simulation times [117].

Determine N possible

topologies + contingencies

Perform frequency scan for N

cases

For each case determine fR

and R(fR)

Case fR (Hz) RCASE (Ohms)

Case 1

…

…

…

Case N

EMS/SCADA

Matching topology?

Matching PWIND?

Monitor VW

NO

NO

NO

STOP

PROCESS 1 PROCESS 3

YES

YES

YES

fR < fNOM ? STOP

For VW ∈ [VW, CUT IN; VW, CUT OUT]:

Conduct Frequency Scan of WT

RVw(fR) < 0 ?

Net negative

resistance?

Record combination of case and wind speed

VW

STOP

NO

NO

PROCESS 2

YES

YES

PREF = 0.1

Wind Speed RVw

PREF = …

Wind Speed RVw

PREF = 1.0

Wind Speed RVw

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The WNE application in PSCAD consists of 2 modules: the harmonic injection module and the

harmonic measurement module. The harmonic injection can either be a current or voltage injection.

The implemented module contains a spectral voltage injection. The following parameters need to

be defined in this module:

─ Magnitude of the injected voltage ‘Hmag’

The ‘magnitude of the injected signal’ should be large enough to trigger a stable response of the

PEID, yet small enough not to cause any instabilities. Values between 5-10% are suggested.

─ Phase of the injected voltage ‘Ph’ in degrees

This parameter creates a phase shift for each of the injected signals. This spreads out the signal

energy due to which a larger voltage can be injected, without perturbation of the steady state

condition [119].

─ Minimum frequency

─ Maximum frequency

─ Increment of the frequency

The ‘minimum and maximum frequency’ determines the frequency range of interest for the SSCI

investigation, whereas the increment fixes the interval.

The harmonic measurement module measures the current flowing out of the PEID. From the

injected voltages and measured currents the impedance is calculated for each of the frequencies

defined in the harmonic injection module. The parameters that need to be defined here are:

─ Time to record

─ File name

As can be seen from Figure 4.73, the ‘time to record’ is very crucial in terms of accuracy of the

results. After starting the simulations, the model needs to initialise. Only after the breaker that

connects the wind turbine to the network is closed and the transients are stabilised, the currents

can be recorded and processed. It is worth mentioning that this time required for the transients to

stabilise is dependent on the wind speed, active power set point, and the size of the wind farm.

The ‘file name’ is the name of the text file containing the amplitudes and phases of the impedances

at each frequency in the range defined in the harmonic injection module.

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Figure 4.73 White Noise Excitation Implementation.

For the analysis suggested and carried out in this section, the passive impedance scan and the

white noise excitation method are used for determining the impedances. Figure 4.74 shows the

results of the passive impedance scan and the white noise excitation methods for a passive

network. It can be concluded from this figure that the results are similar when either method is

used on a passive network. This is in line with the results found in [120].

0.0602 [ohm] 0.001916

R=0

SCR 10X/R = 10

DFIGPCCHarm Injectionb a

Harm Measureb a

Bus1D

harm_injection_1...

180

0

Ph

0

deg

10

0

Hmag

0.1

Harmonic Imp

Array - 63VaM

IaM

VaP IaP

Record arreay to fileAL

BL

Array size - 63

@ t - 6.0 sZm

Phm

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

y

freq res Ia

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Figure 4.74 Impedance Scan Comparison: Passive Impedance Scan vs White Noise Excitation.

The monitoring of SSCI occurrence is defined in 3 processes: the grid side analysis (process 1), the

wind farm side analysis (process 2), and the SSCI monitoring (process 3). Each of these processes

is briefly discussed next.

Process1: Grid side analysis

Process 1 facilitates the frequency scan of the grid. The main goal here is to identify the system

damping at the resonance frequencies of the grid, as seen from the point of common coupling. In

this process it is important to include all relevant grid topologies (including post contingency grid

topologies) that could lead to sub synchronous resonances.

The passive impedance scan can be used for determining the resonance frequencies as well as the

damping on the system side. The justification for using this impedance scanning method is that the

grid is modelled as a passive network.

These analyses will yield a look-up table as shown in Figure 4.75. This table contains for the

defined N grid topologies (Case 1 – Case N) the corresponding resonance frequency (fR) and

associated damping (RCASE). This look-up table will then be used in process 3 for monitoring

purposes.

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Figure 4.75 SSCI Process 1: Grid Side Analysis.

Process 2: Wind farm side analysis

The main goal of process 2 is to investigate whether or not the wind farm exhibit negative damping

behaviour at the grid resonance frequency. And if so, how big this damping is. In case the damping

from the wind turbines is negative and larger in amplitude than the grid damping, oscillations

originating the grid will get amplified by the wind turbine controls.

In order to investigate this behaviour an impedance scan is required for several wind speeds,

preferably across the interval where there is an active power output from the wind turbines (i.e.

between cut in and cut out speed). From these scans, the wind turbine damping is determined. In

case the wind turbine damping is negative and larger than the grid damping, the values (wind

Determine N possible

topologies + contingencies

Perform frequency scan for N

cases

For each case determine fR

and R(fR)

Case fR (Hz) RCASE (Ohms)

Case 1

…

…

…

Case N

NO

PROCESS 1

YES

fR < fNOM ? STOP

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speed and damping) are recorded and a look-up table is created (see Figure 4.76). This process is

repeated for several levels of active power output of the wind turbines.

Because the wind turbines are active, non-linear components, the passive impedance scan cannot

be used. Instead, the white noise excitation method with harmonic voltage injection is used. As WT

Type 4 wind farms are immune against SSCI ([121], [122], [123]), the focus of the current

analysis is limited to WT Type 3 wind farms.

Figure 4.76 SSCI – Process 2.

Process 3: SSCI monitoring:

The first two processes created look-up tables containing conditions where SSCI might occur. In

the last process the aim is to monitor the system in real-time using these tables. First, the

EMS/SCADA system is used to determine whether the actual grid topology matches one of the N

cases of the took up table created in process 1. Matching topology implies the existence of a

resonance in the sub synchronous frequency range.

For VW ∈ [VW, CUT IN; VW, CUT OUT]:

Conduct Frequency Scan of WT

RVw(fR) < 0 ?

Net negative

resistance?

Record combination of case and wind speed

VW

STOP

NO

NO

PROCESS 2

YES

YES

PREF = 0.1

Wind Speed RVw

PREF = …

Wind Speed RVw

PREF = 1.0

Wind Speed RVw

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The next step is to monitor the active power output level of the wind turbines. In case there is a

match with the look up table created in process 2, the operator should monitor the wind speed and

take the necessary mitigation measures when the wind speed approaches the negative resistance

region for that specific active power output level.

Figure 4.77 SSCI – Process 3.

4.5.5 Results for different Case Studies

The results presented in this chapter are of qualitative nature, because of the following reasons:

─ The WT T3 PSCAD models used are generic models developed for the MIGRATE project. The

investigation for SSCI occurrence requires manufacturer models in which at least the controls

are modelled in detail. As these controls are vendor specific, the results presented here will not

match with those when using vendor’s models. However, the general conclusions should be the

same.

─ Wind farms normally consists of tens to hundreds of wind turbines. The number of wind turbines

of the wind farm for which SSCI analyses are carried out, has an influence on the damping. This

poses the requirement of modelling every wind turbine (with associated controls) for the WNE

impedance scan. This in turn requires the use of a high performance cluster to reach acceptable

simulation times. Conducting the WNE impedance scan for 3 WTs takes approximately 900

seconds per simulation second.

─ To overcome the obstacle of simulation times, Parallel Network Interfaces (PNI) have been used.

With PNI each WT is modelled in a separate simulation case and transmission lines are used to

connect these cases. This reduces the simulation time to approximately 30 seconds per

simulation second. However, adding the transmission line (which in reality is not there) changes

the damping significantly. From qualitative point of view this is acceptable, as long as this is

done in a consequent manner.

EMS/SCADA

Matching topology?

Matching PWIND?

Monitor VW

NO

NO

STOP

PROCESS 3

YES

YES

REPORT

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The analysis are carried out using the processes defined in the previous chapter. The first step is to

conduct the grid side analysis (process 1). The results are given in Figure 4.78.

Figure 4.78 Grid Side Analysis.

From these results in can be concluded that the zero crossing of the reactance X happens at 22 Hz

(the impedance dip is also observed at this frequency). The damping of the system is a constant

value across the frequency and is approximately 40 ohms. The constant value results from

modelling the network as an equivalent impedance. In Figure 4.79 the zero crossing points are

given for 3 different cases. Case 1 represents a network with the highest series compensation,

whereas case 3 has the lowest.

Figure 4.79 Zero Crossing over for 3 Cases.

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For this specific network topology the results are summarised in Table 4.14.

Table 4.14 Grid Side Damping.

Case fR (Hz) RCASE (ohms)

1 22 40.53

2 26 32.53

3 36 18.53

In the second step process 2 is conducted. Using white noise excitation the damping of the wind

turbine at sub-synchronous frequencies is determined for several wind speeds and active power

references. The results are presented for wind speeds 7 m/s, 10.2 m/s (nominal wind speed), and

14 m/s and for active power references of 60%, 80%, and 100%.

For case 1 (fR = 22 Hz), Figure 4.80 illustrates the effect of different wind speeds on the damping

provided by the wind turbine. The general trend is that increasing wind speeds increase the

damping (the negative resistance decreases with increasing wind speeds) independent of the active

power setpoint (Pref).

Figure 4.80 Wind Speed Influence on Damping (fR = 22 Hz).

For the same case, Figure 4.81 illustrates the effect of different active power setpoints (Pref) on

the damping provided by wind turbines. For low wind speeds decreasing levels of active power

setpoints lead to decreased damping. For higher wind speeds the change in damping provided by

the wind turbine is relatively small. The results are tabulated to yield the damping provided by the

wind turbine for different wind speeds and active power setpoints for the frequencies of interest

(Table 4.15).

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Figure 4.81 Active Power Reference Influence on Damping (fR = 22 Hz).

Table 4.15 Wind Farm Side Damping.

fR = 22 Hz

Pref ↓ 7 m/s 10.2 m/s 14 m/s

100% -38.11 -31.97 -28.56

80% -55.95 -30.61 -30.05

60% -53.26 -32.49 -29.12

fR = 26 Hz

Pref ↓ 7 m/s 10.2 m/s 14 m/s

100% -47 -45.38 -42.21

80% -76.02 -43.30 -40.14

60% -65.82 -44.93 -41.19

fR = 36 Hz

Pref ↓ 7 m/s 10.2 m/s 14 m/s

100% -115 -96.16 -85.50

80% -232.40 -108.46 -77.86

60% -160.21 -111.06 -101.46

As last the impact of the wind farm size on the wind turbine side damping is qualitatively assessed

and illustrated in Figure 4.82. Two important conclusions from these analyses are:

─ The damping provided by the wind farm is proportional to the size of the wind farm.

REPORT

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─ The start of the negative resistance region (i.e. the zero crossing-over frequency) is

independent of the size of the wind farm.

These results are in line with the conclusions from [116].

Figure 4.82 Impact of Wind Farm Size on Damping.

The last step deals with online monitoring of the conditions under which SSCI could occur. Figure

4.83 illustrates which conditions require monitoring from SSCI occurrence perspective for case 1

(fR = 22 Hz). For this case active power set points of 60% and 80% can lead to SSCI when the

wind speed is 7 m/s.

Figure 4.83 Net Damping for fR = 22 Hz.

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Figure 4.84 shows a comparison between a case with and without SSCI occurrence. The case

without SSCI occurrence represents case 1 (highest compensation), with wind speed 10.2 m/s and

active power set point of 100%. The case with SSCI has the same compensation level as case 1,

but the grid damping is reduced significantly, such that the net damping is negative. The

parameters on the wind turbine side remain unchanged. The phase current increases to around 2.5

p.u. in the case of SSCI.

Figure 4.84 Comparison between Stable and SSCI Situation.

Based on the simulation results presented in this chapter, the occurrence of SSCI can be monitored

and forecasted with a certain probability provided that the recommended look-up tables are

developed and provided that the network topology, wind speed, and active power set points are

monitored.


The aim of this section was to develop an indicator for determining the distance to SSCI occurrence.

Because of the very short time needed for the SSCI based oscillations to grow, the prediction of the

SSCI is equivalent to the prediction of the instability. It has been shown that SSCI can be predicted

and monitored in terms of 3 independent parameters (i.e. the grid resonance frequency, the wind

speed, and the active power setpoint). Only specific combinations of these parameters could lead

to SSCI. Even though the grid resonance frequency might have a value that could cause SSCI, if

the net damping is large enough SSCI will not occur. In the same way, if the wind farm has a

negative resistance across a certain sub-synchronous frequency band (for a specific combination of

wind speed and active power set point), SSCI cannot occur if there is no grid resonance at sub-

synchronous frequencies.

REPORT

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The proposed methodology for monitoring SSCI consists of 2 phases. The first phase is done offline

and aims to identify which combinations of the parameters could lead to SSCI. For each defined

network topology and active power setpoint, the distance to SSCI occurrence can then be

expressed in terms of the wind speed. The result of the first phase is a set of look-up tables. The

second phase monitors online the 3 parameters and carries out a matching with the look-up tables.

However, unlike e.g. small-disturbance voltage stability where the distance to instability is

expressed in terms of system loading and which can be influenced by the control room operators,

the monitoring variable for SSCI (i.e. the wind speed) cannot be influenced by control room

operators. But, as the wind speed can be forecasted, the distance to SSCI occurrence (i.e.

instability) can be predicted as well, given that the grid resonance frequency and wind turbine

active power setpoint are known.

4.5.7 Control Room Implementation

As the majority of the steps are carried out offline and only the monitoring process is done online,

the proposed method could be implemented in the control room. However, as SSCI is an electrical

(and not an electro-mechanical) phenomenon, the building up of oscillations happens very rapidly.

Therefore it is strongly recommended that for new wind farms SSCI investigations are conducted

and, if SSCI is present, mitigated in the development phase of the project.

The proposed method consists of 3 processes: grid side analysis, wind farm side analysis, and SSCI

monitoring. The grid side analysis results in a look-up table containing the grid resonance

frequencies and associated damping for predefined grid topologies. These analyses are carried out

offline and can be conducted fast.

The wind farm side analysis results in another set of look-up tables containing for each defined grid

resonance frequency the damping of the wind farm for several active power set points. These

analyses are also carried out offline. It should be noted that the damping provided by the wind

farm is heavily dependent on its control algorithms and settings. The studies suggested in this

chapter to determine the wind farm damping should be carried out with detailed manufacturer’s

models instead of generic models, which means that results will be wind farm specific. This step is

very time consuming and cannot be carried out using normal computers. High performance clusters

might help in achieving acceptable simulation times.

In the last process the monitoring is carried out online. The EMS/SCADA can be used to determine

the grid topology. If this grid topology matches with one of the entries of the first look-up table,

the grid resonance frequency can be determined using the same look-up table. The active power

output of the wind farm can be observed from the EMS/SCADA as well. If there is a match with the

second set of look-up tables, the wind speed needs to be monitored.

In terms of implementing this in the control room, an accurate wind forecast is the only missing

component for facilitating the proposed method.

REPORT

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A Generic Test Cases

Generic Test Case 1: Frequency Stability

Power System Modelling in PowerFactory

Table A.1 Synchronous generators typical parameters (ElmSym) in generic test case 1.

Parameter Value

Parallel machines 2 – 9

Active power 210 – 240

Reactive power 17 – 100

Voltage 1

Active power limits 80 – 260

Table A.2 Synchronous generators typical parameters (TypSym) in generic test case 1.

Parameter Value

Nominal apparent power 220 – 259

Nominal voltage 15.75

Power factor 0.98

Connection Y

Reactive power limits -130 to 130

Reactance x2 0.2

Resistance r2 0

Inertia constant 6.99 to 10.5

Td’ 0.465

Tq’ 0.188

Td’’ 0.12

Tq’’ 0.188

Xd 1.58

Xq 0.94

Xd’ 0.43

Xq’ 0.54

Xd’’ 0.225

Xq’’ 0.27

REPORT

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Idf_lim

-

-

--

1

1 usT

eigK

iK

1

a

a

K

sT

1

e eK sT

1

f

f

sK

sT

tU

pssU

rresu

0

_tU ref

_tU ref

Limit

Figure A.1 Excitation system used in steam and hydro power units.

Table A.3 Excitation system typical parameters in generic test case 1.

Parameter Value Description

idf_lim [p.u] 3 maximum excitation current

Ke [s] 1 Exciter gain

Te [s] 0.2 Exciter delay

Ka [p.u] 200 Controller Gain

Ta [s] 0.03 Controller delay

Kg [p.u] 0.048 OEL Gain

Ki [p.u] 5 OEL Integral Gain

Tu [s] 0.02 Time delay

Kf [p.u] 0.05 Gain

Tf [s] 1.5 Time delay

L2 [p.u] 4 maximum exciter voltage

vt_ref [p.u] 1 Voltage reference

REPORT

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PN/Pturb

1

R 1

1

1 sT

3

2

1

1

sT

sT

tA

tD

psco

pstep

ref

sgn n

cos n

tP

turbP

Figure A.2 Block diagram for TGOV1 steam turbines.

-

÷ x x-

-

xPn/

Pturb

1

1 fsT

1

r

rs

T s

1

1 gsT

psco

pstep

ref

R

turbD

1

wsTtA

turbP

tP

sgn n

cos n

Figure A.3 Block diagram for HYGOV hydro turbines.

REPORT

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Table A.4 Steam turbine governor typical parameters in generic test case 1.

TGOV1

Parameters

Value Description

T3 [p.u] 4 Turbine Delay Time Constant

T2 [p.u] 1.25 Turbine Derivative Time Constant

At [p.u] 1 Turbine power coefficient

Dt [p.u] 0 Frictional Losses Factor

R [p.u] 0.04 Controller Droop

T1 [s] 0.1 Governor Time Constant

PN [MW] 0 Turbine Rated Power(=0->PN=Pgnn)

Vmin [p.u] 0.3 Minimum Gate Limit

Vmax [p.u] 1 Maximum Gate Limit

Table A.5 Hydro turbine governor typical parameters in generic test case 1.

HYTGOV1

Parameters Value

Description

r [p.u] 0.1 Temporary Droop

Tr [s] 10 Governor Time Constant

Tf [s] 0.1 Filter Time Constant

Tg [s] 0.5 Servo Time Constant

Tw [s] 1 Water Starting Time

At [p.u] 1 Turbine Gain

Dturb [p.u] 0.01 Frictional Losses Factor pu

qnl [p.u] 0.01 No Load Flow

R [p.u] 0.04 Permanent Droop

PN [MW] 0 Turbine Rated Power(=0->PN=Pgnn)

Gmin [p.u] 0 Minimum Gate Limit

Velm [p.u] 0.15 Gate Velocity Limit

Gmax [p.u] 1 Maximum Gate Limit

-2

1

1

1

sT

sT

4

3

1

1

sT

sT

1

w

w

K

sT

ref

PSS

Limy

Limy

Limit

Figure A.4 Power System Stabiliser block diagram.

REPORT

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Table A.6 PSS typical parameters in generic test case 1.

Parameter Value Description

Kw [p.u] 93.57909 PSS gain

Tw [s] 10 Washout filter time constant

T2 [s] 0.012543 Time constant 2




ylim [p.u] 0.1 Voltage limit

Table A.7 SVSs typical values in generic test case 1.

Parameter Value

Q reactance 700

Max of capacitors 10

Table A.8 Two-winding transformer typical values in generic test case 1.

Parameter (TypTr2) Value

Rated power [MW] 200 - 1000

Nominal frequency [Hz] 50

Rated voltage HV [kV] 20 – 400

Rated voltage LV [kV] 15.75 - 150

Ratio X/R 7 – 50

Short circuit voltage [%] 0.22 – 0.88

Table A.9 General load typical values in generic test case 1.

Parameter Min Value Max value

Active power [MW] 10 800

Reactive power [MW] 20 120

Table A.10 Transmission lines typical values in generic test case 1.

Parameter Min Value

Length [km] 1-220

Parallel lines 1-2

Rated voltage [kV] 110 – 380

Rated current [kA] 1 – 4.08

Nominal frequency [Hz] 50

AC- Resistance [Ohm/km] 0.015 – 0.192

Reactance [Ohm/km] 0.13 – 0.4

Capacitance [uF/km] 0.0085 – 0.0275

REPORT

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Approach for Defining the Dispatch Scenarios and Operating Conditions

Figure A.5 shows a flow chart of the general approach. The figure shows that a pre-defined Excel

file with several dispatch settings, from 0% renewables up to 62%, is used to run simulations.

Each condition is used sequentially, one at a time, and the results of the RMS simulations are

exported into a database where they will be processed (the explanation of the frequency data is

contained in the following section, related to the indicators). In order to run contingency selection,

together with the different dispatch scenarios, a previous severity analysis was performed to select

the elements that cause the biggest impact on the system and this way reduce the number of

simulations. This was done because of the big volume of operating conditions.

Figure A.5 Flow chart of adopted approach to run simulations. OC_db stands for operating condition data base, whereas time_DB is the data base of time responses.

Figure A.6 shows the methodology applied for this purpose, where each existing line in the system

is selected (one by one) to be out of service. Then, two steady state indices will reveal which line

causes the biggest stress in the system when absent.

To be used in Data

Processing to

compute frequency

and transient

indicators.

Start

Read Excel file with

Dispatch information

OC_db

i=1

Get: OC_db case i

time_DB

i=size of OC_db?

i++

NO

Finish

Run RMS simulation

REPORT

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Figure A.6 Flow chart to get the elements that cause the biggest impact in steady state conditions. SS_DB stands for data base of steady-state results. PFI denotes power

flow indicator, a measure of the loading of each component.

Start

Lines = get all lines

i=1

Set out of service

Line (i)

i=length(Lines)?

i++

FinishNO

SS_DBRun load

flow

Load

SS_DB

Compute PFI

for all cases

Select highest

PFI and

associated line

REPORT

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B Transition Scenario Implementation

B.1 Implementation into the GB Test System

Table B.1 Foreseen Grid Reinforcements in GB Transmission System.

Reinforcement Gone

Green

No

Progression

Reinforced

Boundary

Improvements

in MW

Scotland and North of England

HVDC link Peterhead-

Hawthorn Pit 2023 2029

B2

B4

B5

B6

B7

B7a

300

1360

2000

2010

620

360

Western HVDC Link 2017 N/A

B6

B7

B7a

2200

2500

2830

Series reactors

Reactive compensations

East England

Rayleigh Main series

reactors 2027 N/A EC5 1750

South England

Dynamic reactive

compensation SCVC 2019 2021 SC1 840

West England and North Wales

Carrington series reactor 2023 2020 B8

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Figure B.1 Power flow in the Scottish transmission network ([46] - Figure 3.4, pp 31).

Figure B.2 Power Flow in the North England transmission network ([46] - Figure 3.5, pp 54).

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Table B.2 Mapping of NOA Boundaries and ETYS Regions to 29 Zone Network Model.

ETYS 2016

Region

ETYS 2016

System Boundary

GB 29 Zone

substation

Scotland

B0 1

B2 2

3

B5

4

5

6

B6 7

8

North England

B7 9

10

B7a 11

EC1 16

West England

NW3 12

B8

13

14

15

B17 17

18

East England EC3

EC5

19

20

South England

B14

21

22

25

SC1

23

24

28

SC2 26

27

B13 29

REPORT

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Table B.3 Installed capacity for the 29 zones for the Gone Green scenario.

Region Zone Synchronous PEIG Synchronous PEIG Synchronous PEIG Synchronous PEIG Synchronous PEIG

1 1,08 0,856 1,08 0,85033 0,864 1,85033 0 1,85033 0 3,00033

2 1,08 0,8598 0 0,85 0 1,85 0 1,85 0 2,85

3 1,08 0 1,08 0,85 1,08 1,85 0,864 0,85 0,864 0

4 1,08 0,8413 0 0,85 0 1,85 0 0 0 0

5 1,08 0 1,08 0,85 1,08 1,85 1,08 1,85 1,296 1,85

6 1,08 0 0 0,85 0 2,218 0 2,218 0 2,7

7 1,08 0,8427 1,08 0,85 1,08 1,1141 1,08 0 1,08 1,85

8 1,08 0 1,08 0,65 1,08 2,018 1,08 2,291 1,08 2,45

9 3,78 0,725 1,512 1,558 0 2,658 0 2,658 0 4,4

10 3,78 0,725 3,78 1,558 3,024 2,56 1,512 3,35 0,756 4,3

11 3,78 0,725 3,78 1,558 3,78 2,56 3,78 2,56 3,78 3,7

16 3,78 0,725 3,78 0,725 3,78 0,725 3,78 2,332 3,78 2,3

12 3,77 0,2 0 0,2 0 1,9 0 1,9 0 3,4

13 3,77 0 2,639 0 2,268 0 2,18 1 0 1

14 3,77 0,2 0 0,2 0 0,2 0 1,2 0 1,9

15 3,77 0 3,77 0 3,77 0 4,158 0,95 2,268 1,75

17 3,77 0 0 0,2 0 0,2 0,2 0 0,2

18 3,77 0 3,77 0 3,77 0 4,536 0,95 4,158 1,05

19 1,95 0,5495 1,755 1,3495 1,85 2,4995 2,34 4,1 2,145 6,3995

20 1,95 0,55 1,95 1,35 2,145 2,5 3,12 6,4 3,15 6,4

21 1 0 0,756 0,3 0,648 0,4 0 0,4 0 0,4

22 1 0 1 0 1 0 0 0,53 0 0,53

23 1 0,497 1 0,497 1 0,497 1 0,497 1,296 0,497

24 1 0 1 0 1 0 1 0 1 0,53

25 1 0 1 0 1 0 1 0 1 0,53

26 1 0,504 1 0,504 1 0,504 1 0,504 1 0,504

27 1 0 1 0 1 0 1 0,53 0 0,60475

28 1 0 1 0 1 0 1 0,53 1 0,60475

29 1 0,4995 1 0,4995 1 0,4995 1 0,4995 1 0,4995

Scotland

North

England

West

England

East

England

South

England

Generation (all

values in GW)

GONE GREEN

2016 2020 2025 2030 2035

REPORT

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Table B.4 Installed capacity for the 29 zones for the No Progression scenario.

Region Zone Synchronous PEIG Synchronous PEIG Synchronous PEIG Synchronous PEIG Synchronous PEIG

1 1,08 0,856 0,86 0,85 0,9 0,85 0,96 0,85 0,84 0

2 1,08 0,8598 0,86 0,85 0,9 0,85 0,96 0,85 0,84 0,85

3 1,08 0 0,86 0 0,9 0 0,96 0,5 0,84 0,5

4 1,08 0,8413 0,86 0,85 0,9 0,85 0,96 0,85 0,84 0,7

5 1,08 0 0,86 0 0,9 0,85 0,96 0,85 0,84 0,85

6 1,08 0 0,86 0 0,9 0,7 0,96 0,7 0,84 0,7

7 1,08 0,8427 0,86 0,85 0,9 0,85 0,96 0,85 0,84 0,85

8 1,08 0 0,86 0,7 0,9 0,85 0,96 0,85 0,84 0,85

9 3,78 0,725 3,15 0,725 4,4 0,725 4,28 0,725 4,03 0

10 3,78 0,725 3,15 0,55825 4,4 0,89175 4,28 1,39275 4,03 1,39275

11 3,78 0,725 3,15 0,55825 4,4 0,89175 4,28 0,89175 4,03 0,89175

16 3,78 0,725 3,15 0,55825 4,4 0,89125 4,28 0,89125 4,03 0,62

12 3,77 0,2 2,93 0,2 1,92 0,2 1,83 0,4 1,83 0,4

13 3,77 0 2,93 0 1,92 0 1,83 0,1 1,83 0,1

14 3,77 0,2 2,93 0,2 1,92 0,2 1,83 0,2 1,83 0,2

15 3,77 0 2,93 0 1,92 0 1,83 0,2 1,83 0,2

17 3,77 0 2,93 0 1,92 0 1,83 0 1,83 0

18 3,77 0 2,93 0 1,92 0,1 1,83 0,1 1,83 0,1

19 1,95 0,5495 2,45 1,0495 2,4 1,0495 2,9 1,0495 2,65 1,0495

20 1,95 0,55 2,45 0,55 2,4 1,15 2,9 1,15 2,65 1,15

21 1 0 0,79 0 1,17 0,105 1,11 0,105 1,12 0,105

22 1 0 0,79 0 1,17 0 1,11 0 1,12 0

23 1 0,497 0,79 0,392 1,17 0,392 1,11 0,392 1,12 0,892

24 1 0 0,79 0 1,17 0 1,11 0 1,12 0

25 1 0 0,79 0 1,17 0 1,11 0 1,12 0

26 1 0,504 0,79 0,504 1,17 0,504 1,11 0 1,12 0

27 1 0 0,79 0 1,17 0 1,11 0 1,12 0,603

28 1 0 0,79 0 1,17 0 1,11 0 1,12 0,3

29 1 0,4995 0,79 0,4995 1,17 0,4995 1,11 0 1,12 0

South

England

Generation per node (all

values in GW) 2030 2035

Scotland

North

England

West

England

East

England

GONE GREEN No Progression

2016 2020 2025

REPORT

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B.2 Implementation into the Irish Test System

Table B.5 Ireland ”Slow Change” Scenario.

Demand 2020 2025 2030 2040

Total Data Centre Capacity (MVA) 400 550 850 850

Total number of Electric Vehicles 8000 43000 90000 309000

Total % of Vehicles which are Electric 0% 2% 4% 13%

Total number of Heat Pumps 38000 48000 100000 212000

Total % of Households with Heat Pumps 2% 3% 5% 10%

Total Demand (TWh) 21.2 32.3 35.1 36.6

Generation 2020 2025 2030 2040

Coal 860 860 0 0

Gas 4120 3760 4660 5430

Peat 310 310 0 0

Distillate Oil 410 320 320 0

Heavy Fuel Oil 590 0 0 0

Waste (assume 50% renewable) 80 80 80 100

Fossil fuel generation Total [MW] 6330 5290 5020 5480

Wind (onshore) 3930 4540 4640 4860

Wind (offshore) 30 30 250 500

Wind generation total 3960 4570 4890 5360

Hydro 240 240 240 240

Biomass/Landfill Gas (including Biomass SHP) 240 240 270 410

Solar PV 70 90 200 400

Ocean (Wave/Tidal) 0 0 20 40

Renewable generation Total [MW] 4550 5180 5660 6500

Pumped Storage 290 290 290 290

Small Scale Battery Storage 0 0 50 150

Large Battery Storage 0 0 50 150

Demand Side Management 300 330 400 500

DC Interconnection 500 500 500 1200

Conventional Combined Heat & Power 150 150 150 150

Total Capacity [MW] 12120 11740 12120 14420

REPORT

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Table B.6 Ireland ”Low Carbon Living” Scenario.

Demand 2020 2025 2030 2040

Total Data Centre Capacity (MVA) 700 1400 1950 1950

Total number of Electric Vehicles 20000 163000 426000 785000

Total % of Vehicles which are Electric 1% 8% 19% 33%

Total number of Heat Pumps 56000 194000 279000 529000

Total % of Households with Heat Pumps 3% 10% 14% 25%

Total Demand (TWh) 32.6 38.8 43.8 45.8

Generation 2020 2025 2030 2040

Coal 860 0 0 0

Gas 4120 4210 4210 4760

Peat 310 0 0 0

Distillate Oil 410 210 100 0

Heavy Fuel Oil 590 0 0 0

Waste (assume 50% renewable) 80 100 100 100

Fossil fuel generation Total [MW] 6330 4470 4360 4810

Wind (onshore) 4120 5010 5500 6300

Wind (offshore) 30 800 3000 3500

Wind generation total 4150 5810 8500 9800

Hydro 240 240 240 240

Biomass/Landfill Gas (including Biomass SHP) 240 320 750 800

Solar PV 150 700 2500 3500

Ocean (Wave/Tidal) 0 20 100 250

Renewable generation Total [MW] 4820 7140 12140 14640

Pumped Storage 290 290 650 650

Small Scale Battery Storage 0 50 500 800

Large Battery Storage 0 80 1200 1750

Demand Side Management 350 500 750 1250

DC Interconnection 500 1200 1950 1950

Conventional Combined Heat & Power 150 170 180 220

Total Capacity [MW] 12440 13900 21730 26070

REPORT

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Table B.7 IEEEX1 AVR model: typical parameters.

Parameter Value Unit Description

Tr 0 [s] Measurement Delay

Ka 50 [pu] Controller Gain

Ta 0.1 [s] Controller Time Constant

Tb 0 [s] Filter Delay Time

Tc 0 [s] Filter Derivative Time Constant

Te 0.5 [s] Exciter Time Constant

Kf 0.04 [pu] Stabilisation Path Gain

Tf1 1 [s] Stabilisation Path Delay Time

E1 1 [pu] Saturation Factor 1

Se1 0 [pu] Saturation Factor 2

E2 1.2 [pu] Saturation Factor 3

Se2 0.1 [pu] Saturation Factor 4

Ke 0 [pu] Exciter Constant

Vrmin -5.4 [pu] Controller Minimum Output

Vrmax 5.4 [pu] Controller Maximum Output

Table B.8 HYGOV governor model: typical parameters.


r 0.5 [pu] Temporary Droop

Tr 10 [s] Governor Time Constant

Tf 0.05 [s] Filter Time Constant

Tg 0.5 [s] Servo Time Constant

Tw 1.3 [s] Water Starting Time

At 1.1 [pu] Turbine Gain

Dturb 0.5 [pu] frictional losses factor pu

qnl 0 [pu] No Load Flow

R 0.04 [pu] Permanent Droop

PN 0 [Mw] Turbine Rated Power(=0->PN=Pgnn)

Gmin 0 [pu] Minimum Gate Limit

Velm 0.2 [pu] Gate Velocity Limit

Gmax 0.76 [pu] Maximum Gate Limit

REPORT

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Table B.9 IEEEG2 governor model: typical parameters.


K 22.22 [pu] Controller Gain

T1 0.5 [s] Governor Time Constant

T3 0.35 [s] Servo Time Constant

T2 0.05 [s] Governor Derivative Time Constant

T4 0.1 [s] Water Starting Time

PN 0 [MW] Turbine Rated Power(=0->PN=Pgnn)

Pmin 0.3 [pu] Minimum Gate Limit

Pmax 1 [pu] Maximum Gate Limit

Table B.10 WP controller – WP Q control module.

Name Value Unit Description

rWPdroop 0 [ZWPbase] Resistive component of WP voltage drop impedance

xWPdroop 0 [ZWPbase] Inductive component of WP voltage drop impedance

qinitoffset -1 [PWTN]

Difference between initial p.u. WT output reactive power

and initial p.u. WP output reactive power to compensate

for the losses inside the WP

uWPqdip 0.8 [Un] Voltage threshold for UVRT detection

KWPqu 0 [-] Voltage controller cross coupling gain

Tuqfilt 0.01 [s] Time constant for the UQ static mode

MWPqmode 3 [-]

Reactive power/voltage controller mode (0- reactive

power reference, 1- power factor reference, 2- UQ

static, 3- voltage control)

KPWPx 10 [PWPN/PWTN] Reactive power/voltage PI controller proportional gain

KIWPx 10 [PWP/PWT/s] Reactive power/voltage PI controller integral gain

KWPqref 0 [PWPN/PWTN] Reactive power reference gain

xerrmin -0.4 [PWPN or UN] Minimum reactive power error (or voltage error if

MWPqmode = 2) input to PI controller

KIWPxmin -1 [PWP/PWT/s] Minimum reactive Power/voltage reference from

integration

xrefmin -1 [PWTN] Minimum WT reactive power/voltage reference

xerrmax 0.4 [PWPN or UN] Maximum reactive power error (or voltage error if

MWPqmode = 2) input to PI controller

KIWPxmax 1 [PWP/PWT/s] Maximum reactive Power/voltage reference from

integration

xrefmax 1 [PWTN] Maximum WT reactive power/voltage reference

REPORT

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Table B.11 Type 3 and 4 WT controller – Q control module.

Name Value Unit Description

KIq 0 [Un/Pn/s] Reactive power PI controller integrational gain

Tqfiltq 0.01 [s] Reactive power measurement filter time constant

KPq 0 [Un/Pn] Reactive power PI controller proportional gain

MqG 2 [-]

General Q control mode: 0 = voltage, 1 = reacitve

power, 2 = open loop reactive power, 3 = power

factor, 4 = open loop power factor

Tpfiltq 0.005 [s] Power measurement filter time constant

Tqord 10 [s] Time constant in reactive power order lag

uref0 0 [Un] User defined bias in voltage reference uWTref =

uref0+DeltauWTref (used when MqG = MqGu)

KIu 5 [In/Un/s] Voltage PI controller integational gain

KPu 5 [In/Un] Voltage PI controller proportional gain

iqpost 0 [In] Post fault reactive current injection

MqUVRT 1 [-]

UVRT Q control mode: 0 = voltage dependent

reactive current injection, 1 = reactive current as pre-

fault + voltage dependent value, 2 = like 1 but

extended to post-fault

Tufiltq 0.005 [s] Voltage measurement filter time constant

uqdip 0.8 [Un] Voltage threshold for UVRT detection in q control

Tpost 0 [s] Length of time period where post fault reactive power

is injected

udb1 0.9 [Un] Voltage dead band lower limit

udb2 1.1 [Un] Voltage dead band upper limit

Kqv 2 [In/Un] Voltage scaling factor for UVRT current

rdroop 0 [Zbase] Resistive component of voltage drop impedance

xdroop 0 [Zbase] Inductive component of voltage drop impedance

Mcos 0 [-] 0 = cosphi const. or on ext. setpoint, 1 = cosphi

dependent on P, Mcos is only effective if MqG = 3 or 4

u_min 0 [Un] Minimum voltage in voltage PI controller integral term

iq_min -1.05 [In] Minimum reactive current injection

u_max 2 [Un] Maximum voltage in voltage PI controller integral

term

iq_max 1.05 [In] Maximum reactive current injection

iqh1 1.05 [In] Maximum reactive current injection during dip

REPORT

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Figure B.3 Dynamic representation of general load.

REPORT

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C Assessment of KPIs in the Irish System –

Supplementary Information

C.1 Generation Dispatches – WINTER PEAK

Unit name

Aghada AD1.ElmSym 250 200 150 100 100 X X X X X X X

Aghada AT1.ElmSym X X X X X X X X X X X X



Ardnacrusha AA1.ElmSym 20 20 20 20 20 20 20 20 20 15 X X

Ardnacrusha AA2.ElmSym 20 20 20 20 20 20 20 20 20 15 15 X



Carrigadrohid LE3.ElmSym X X X X X X X X X X X X

Cathaleens Fall ER1.ElmSym X X X X X X X X X X X X


Cathaleens Fall ER3.ElmSym 20 20 20 20 20 20 20 20 20 15 15 15


Cushaling ED1.ElmSym 120 120 120 120 120 120 120 120 110 90 X X

Cushaling ED3.ElmSym X X X X X X X X X X X X


Derryiron RP1.ElmSym X X X X X X X X X X X X


Glanagow WG1.ElmSym 400 400 400 400 400 400 400 400 400 380 350 350

Great Island GI4.ElmSym 400 400 400 400 400 400 400 400 400 380 350 350

Huntstown GT HNC.ElmSym 230 230 210 165 X X X X X X X X

Huntstown HN2.ElmSym 380 380 380 380 390 390 390 390 390 380 350 350

Huntstown ST HNC.ElmSym 100 100 80 70 X X X X X X X X

Inniscarra LE1.ElmSym X X X X X X X X X X X X


Irishtown DB1.ElmSym 400 400 400 400 400 400 400 400 400 380 350 350

Lanesboro LR4.ElmSym 90 90 90 90 90 90 90 90 85 85 85 X

Longpoint AD2.ElmSym 425 425 425 425 425 425 425 425 425 425 425 425

Marina MRT.ElmSym X X X X X X X X X X X X

Moneypoint MP1.ElmSym 275 225 150 150 150 150 160 200 X X X X

Moneypoint MP2.ElmSym 275 225 200 150 150 150 X X X X X X

Moneypoint MP3.ElmSym 275 225 200 150 150 150 160 X X X X X

North Wall NW5.ElmSym X X X X X X X X X X X X

Pollaphuca LI1.ElmSym 14 14 14 14 14 14 14 14 14 10 10 10


Pollaphuca LI4.ElmSym 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5


Seal Rock SK3.ElmSym 65 65 65 65 65 65 65 65 60 X X X

Seal Rock SK4.ElmSym 65 65 65 65 65 65 65 65 60 50 50 50

Shannonbridge WO4.ElmSym 140 140 140 140 140 140 140 140 120 87 87 X

Shellybanks PB4.ElmSym X X X X X X X X X X X X

Shellybanks PB5.ElmSym 140 115 115 115 115 115 X X X X X X

Shellybanks PB6.ElmSym 150 115 115 115 115 115 115 X X X X X

Tarbert TB1.ElmSym X X X X X X X X X X X X




Tawnaghmore TP1.ElmSym X X X X X X X X X X X X


Turlough Hill TH1.ElmSym 59.46 59.42 60.54 57.84 59.75 58.20 63.32 59.28 59.50 60.34 56.05 56.00

Turlough Hill TH2.ElmSym 60 60 60 60 60 60 60 60 60 60 60 60



Tynagh CT TYC.ElmSym 250 250 210 160 150 X X X X X X X

Tynagh ST TYC.ElmSym X X X X X X X X X X X X

Synchronous Generator Output [MW]

REPORT

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Wind Farm name

ATHEA_DROMADA WP CONTROL.ElmComp 0 12 27 39 54 69 81 93 108 120 135 147

BALLYWATER WP CONTROL.ElmComp 0 6 9 12 15 18 24 27 30 36 39 42

BARNADIVINE WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

BOGGERAGH WP CONTROL.ElmComp 0 9 18 27 39 48 57 66 75 87 96 105

BOOLTIAGH WP CONTROL.ElmComp 0 3 6 9 12 15 18 21 24 27 30 33

CASTLEDOCKEREL WP CONTROL.ElmComp 0 6 9 12 15 18 24 27 30 36 39 42

CASTLETOWNMOOR WP CONTROL.ElmComp 0 9 21 33 45 54 66 78 87 99 108 120

CAUTEEN DSO WP CONTROL.ElmComp 0 15 33 45 63 81 96 114 129 144 162 177

CLAHANE WP CONTROL.ElmComp 0 6 9 15 21 24 30 33 39 45 48 54

CLOGHBOOLA DSO WP CONTROL.ElmComp 0 3 6 9 12 15 18 21 24 27 30 33

CLOGHBOOLA WP CONTROL.ElmComp 0 6 9 15 21 27 30 36 42 48 51 57

COOMACHEO WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

COOMAGEARLAHY/GLANLEE WP CONTROL.ElmComp 0 9 21 33 45 54 66 78 87 99 108 120

COOMATAGART DSO WP CONTROL.ElmComp 0 6 12 18 24 30 36 42 48 54 60 66

COOMATAGART WP CONTROL.ElmComp 0 9 21 30 42 51 63 72 84 93 105 114

CORDAL DSO WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

CORDAL WP CONTROL.ElmComp 0 9 18 27 36 48 54 66 75 84 93 102

CUNGHILL WP CONTROL.ElmComp 0 3 6 12 12 18 18 24 27 30 33 36

DERRYBRIAN WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

DONEGAL WP CONTROL.ElmComp 0 15 36 51 72 90 105 123 141 159 177 195

GARVAGH WP CONTROL.ElmComp 0 6 9 15 18 21 27 30 36 39 45 48

IKERRIN DSO WP CONTROL.ElmComp 0 3 6 12 12 18 18 24 27 30 33 36

KILL HILL WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

KNOCKACUMMER WP CONTROL.ElmComp 0 9 18 27 39 48 57 66 75 87 96 105

LISHEEN WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

MOUNT LUCAS WP CONTROL.ElmComp 0 9 15 21 30 36 45 51 60 66 75 81

RATRUSSAN WP CONTROL.ElmComp 0 9 15 21 30 36 45 51 60 66 75 81

REANMORE DSO WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

SLIABH BAWN WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

SLIEVE CALLAN WP CONTROL.ElmComp 0 6 12 21 27 36 42 48 54 63 69 75

TRIEN DSO WP CONTROL.ElmComp 0 6 12 18 24 30 36 42 48 54 60 66

WEST GALWAY B WP CONTROL.ElmComp 0 15 30 45 63 78 93 108 123 141 156 171

WEST GALWAY-A WP CONTROL.ElmComp 0 9 18 27 36 45 54 63 72 81 90 99

WEXFORD DSO WP CONTROL.ElmComp 0 3 6 12 15 18 21 24 27 33 36 39

WOODHOUSE WP CONTROL.ElmComp 0 3 3 6 9 9 12 12 15 18 18 21

Combined MW output ==> 0 252 501 756 999 1251 1500 1752 2007 2250 2499 2745

Wind Farm Output [MW]

REPORT

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C.2 Generation Dispatches – SUMMER PEAK

Unit name

Aghada AD1.ElmSym X X X X X X X X X X X X




Ardnacrusha AA1.ElmSym 20 20 20 20 20 20 20 20 20 15 X X




Carrigadrohid LE3.ElmSym X X X X X X X X X X X X





Cushaling ED1.ElmSym 120 120 120 120 120 120 120 120 110 50 X X





Glanagow WG1.ElmSym 400 400 400 400 400 400 400 400 400 380 350 275

Great Island GI4.ElmSym 400 400 400 400 400 400 400 400 345 345 300 275

Huntstown GT HNC.ElmSym 230 200 210 165 X X X X X X X X

Huntstown HN2.ElmSym 390 380 380 280 310 330 390 370 345 300 250 250

Huntstown ST HNC.ElmSym X X X X X X X X X X X X



Irishtown DB1.ElmSym 400 400 400 400 400 400 360 300 300 300 250 250

Lanesboro LR4.ElmSym 90 90 90 90 90 90 90 90 85 85 85 X

Longpoint AD2.ElmSym 425 425 425 425 425 425 425 425 425 425 425 425

Marina MRT.ElmSym X X X X X X X X X X X X

Moneypoint MP1.ElmSym 275 225 150 150 150 150 160 X X X X X

Moneypoint MP2.ElmSym 275 225 150 150 150 150 X X X X X X

Moneypoint MP3.ElmSym 275 225 150 150 X X X X X X X X

North Wall NW5.ElmSym X X X X X X X X X X X X





Seal Rock SK3.ElmSym 65 65 65 65 65 65 65 65 60 X X X

Seal Rock SK4.ElmSym 65 65 65 65 65 65 65 65 60 50 50 50

Shannonbridge WO4.ElmSym 140 140 140 140 140 140 140 140 X X X X

Shellybanks PB4.ElmSym X X X X X X X X X X X X

Shellybanks PB5.ElmSym 140 115 115 90 115 115 X X X X X X

Shellybanks PB6.ElmSym 150 115 115 115 115 X X X X X X X







Turlough Hill TH1.ElmSym 57.3 51.6 53.8 53.7 56.2 59.7 54.4 53.9 53.7 54.1 61.7 56.7




Tynagh CT TYC.ElmSym 250 250 210 130 150 X X X X X X X

Tynagh ST TYC.ElmSym X X X X X X X X X X X X

Synchronous Generator Output [MW]

REPORT

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Wind Farm name

ATHEA_DROMADA WP CONTROL.ElmComp 0 12 27 39 54 69 81 93 108 120 135 147

BALLYWATER WP CONTROL.ElmComp 0 6 9 12 15 18 24 27 30 36 39 42

BARNADIVINE WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

BOGGERAGH WP CONTROL.ElmComp 0 9 18 27 39 48 57 66 75 87 96 105

BOOLTIAGH WP CONTROL.ElmComp 0 3 6 9 12 15 18 21 24 27 30 33

CASTLEDOCKEREL WP CONTROL.ElmComp 0 6 9 12 15 18 24 27 30 36 39 42

CASTLETOWNMOOR WP CONTROL.ElmComp 0 9 21 33 45 54 66 78 87 99 108 120

CAUTEEN DSO WP CONTROL.ElmComp 0 15 33 45 63 81 96 114 129 144 162 177

CLAHANE WP CONTROL.ElmComp 0 6 9 15 21 24 30 33 39 45 48 54

CLOGHBOOLA DSO WP CONTROL.ElmComp 0 3 6 9 12 15 18 21 24 27 30 33

CLOGHBOOLA WP CONTROL.ElmComp 0 6 9 15 21 27 30 36 42 48 51 57

COOMACHEO WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

COOMAGEARLAHY/GLANLEE WP CONTROL.ElmComp 0 9 21 33 45 54 66 78 87 99 108 120

COOMATAGART DSO WP CONTROL.ElmComp 0 6 12 18 24 30 36 42 48 54 60 66

COOMATAGART WP CONTROL.ElmComp 0 9 21 30 42 51 63 72 84 93 105 114

CORDAL DSO WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

CORDAL WP CONTROL.ElmComp 0 9 18 27 36 48 54 66 75 84 93 102

CUNGHILL WP CONTROL.ElmComp 0 3 6 12 12 18 18 24 27 30 33 36

DERRYBRIAN WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

DONEGAL WP CONTROL.ElmComp 0 15 36 51 72 90 105 123 141 159 177 195

GARVAGH WP CONTROL.ElmComp 0 6 9 15 18 21 27 30 36 39 45 48

IKERRIN DSO WP CONTROL.ElmComp 0 3 6 12 12 18 18 24 27 30 33 36

KILL HILL WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

KNOCKACUMMER WP CONTROL.ElmComp 0 9 18 27 39 48 57 66 75 87 96 105

LISHEEN WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

MOUNT LUCAS WP CONTROL.ElmComp 0 9 15 21 30 36 45 51 60 66 75 81

RATRUSSAN WP CONTROL.ElmComp 0 9 15 21 30 36 45 51 60 66 75 81

REANMORE DSO WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

SLIABH BAWN WP CONTROL.ElmComp 0 6 12 18 21 27 33 39 45 48 54 60

SLIEVE CALLAN WP CONTROL.ElmComp 0 6 12 21 27 36 42 48 54 63 69 75

TRIEN DSO WP CONTROL.ElmComp 0 6 12 18 24 30 36 42 48 54 60 66

WEST GALWAY B WP CONTROL.ElmComp 0 15 30 45 63 78 93 108 123 141 156 171

WEST GALWAY-A WP CONTROL.ElmComp 0 9 18 27 36 45 54 63 72 81 90 99

WEXFORD DSO WP CONTROL.ElmComp 0 3 6 12 15 18 21 24 27 33 36 39

WOODHOUSE WP CONTROL.ElmComp 0 3 3 6 9 9 12 12 15 18 18 21

Combined MW output ==> 0 252 501 756 999 1251 1500 1752 2007 2250 2499 2745

Wind Farm Output [MW]

REPORT

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D Use of Inertia for Frequency Stability KPI As it was explained in Section 4.2.1, i.e. equation (4.3), the inertia H [s] is proportionally related to

the Kinetic Energy [MW.s]. Figure D.1 and Figure D.2 below constitute an alternative

representation to Figure 4.13 and Figure 4.14 for Generic Test Case 1 (cf. Section 4.2.2). By

comparing Figure D.1 and Figure D.2 with Figure 4.13 and Figure 4.14, it can be seen that similar

patterns are found when analysing ROCOF/Nadir with respect to different values of system Kinetic

Energy or System Inertia (Hsys). The system inertia is computed by summing up all the inertia

constants of the generators in service in each operational scenario (cf. Section 4.2.2).

Figure D.1 ROCOF vs Inertia, generic test case 1.

Figure D.2 NADIR vs Inertia, generic test case 1.

0

0,05

0,1

0,15

0,2

0,25

0,3

0 100 200 300 400 500 600 700

RO

CO

F [H

z/s]

Hsys [s]

Winter

Spring

Summer

49,78

49,8

49,82

49,84

49,86

49,88

49,9

49,92

0 100 200 300 400 500 600 700

NA

DIR

[H

z]

Hsys [S]

Winter

Spring

Summer

REPORT

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