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Wide Area Signals Based Damping Controllers forMultimachine Power SystemsKe TangClemson University, [email protected]

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WIDE AREA SIGNALS BASED DAMPING CONTROLLERS FOR MULTIMACHINE POWER SYSTEMS

A Dissertation Presented to

the Graduate School of Clemson University

In Partial Fulfillment of the Requirements for the Degree

Doctor of Philosophy Electrical Engineering

byKe Tang

May 2016

Accepted by: Dr. Ganesh Kumar Venayagamoorthy, Committee Chair

Dr. Keith Corzine Dr. Rajendra Singh

Dr. Amy Apon

ii

ABSTRACT

Nowadays, electric power systems are stressed and pushed toward their stability

margins due to increasing load demand and growing penetration levels of renewable energy

sources such as wind and solar power. Due to insufficient damping in power systems,

oscillations are likely to arise during transient and dynamic conditions. To avoid

undesirable power system states such as tripping of transmission lines, generation sources,

and loads, eventually leading to cascaded outages and blackouts, intelligent coordinated

control of a power system and its elements, from a global and local perspective, is needed.

The research performed in this dissertation is focused on intelligent analysis and

coordinated control of a power system to damp oscillations and improve its stability. Wide

area signals based coordinated control of power systems with and without a wind farm and

energy storage systems is investigated. A data-driven method for power system

identification is developed to obtain system matrices that can aid in the design of local and

wide area signals based power system stabilizers. Modal analysis is performed to

characterize oscillation modes using data-driven models. Data-driven models are used to

identify the most appropriate wide-area signals to utilize as inputs to damping controller(s)

and generator(s) to receive supplementary control.

Virtual Generators (VGs) are developed using the phenomena of generator coherency

to effectively and efficiently control power system oscillations. VG based Power System

Stabilizers (VG-PSSs) are proposed for optimal damping of power system oscillations.

Herein, speed deviation of VGs is used to generate a supplementary coordinated control

iii

signal for an identified generator(s) of maximum controllability. The parameters of a VG-

PSS(s) are heuristically tuned to provide maximum system damping.

To overcome ‘fallouts’ and ‘switching’ in coherent generator groups during

transients, an adaptive inter-area oscillation damping controller is developed using the

concept of artificial immune systems – innate and adaptive immunity.

With increasing levels of electric vehicles (EVs) on the road, the potential of

SmartParks (a large number of EVs in parking lots) for improving power system stability

is investigated. Intelligent multi-functional control of SmartParks using fuzzy logic based

controllers are investigated for damping power system oscillations, regulating transmission

line power flows and bus voltages.

In summary, a number of approaches and suggestions for improving modern power

system stability have been presented in this dissertation.

iv

DEDICATION

I would like to express my deepest gratitude to my parents for their continued support,

and my advisor and committee members for the wisdom from their expertise and

experience. Besides, I would like to express my gratitude to all the current students in my

laboratory for their generous help during the accomplishment of my Ph. D dissertation.

v

ACKNOWLEDGEMENT

Firstly, I would like to thank my advisor Dr. G. Kumar Venayagamoorthy for his

assistance to carry out the research and for his support to write this thesis. This work could

not have been accomplished without his abundant knowledge, his academic profession and

his generous support. I would also like to thank you for your patience and dedication of

time. Additionally, I would like to thank Dr. Keith Corzine, Dr. Rajendra Singh and Dr.

Amy Apon for serving on my committee.

Second, I would like to thank my parents. None of my achievements would have been

accomplished without your love and support.

Besides, I would like to thank all the members of Dr. G. Kumar Venayagamoorthy’s

research group member, for all the support and encouragement I have received from them

during the course of this project.

I would like to thank the Real-Time Power and Intelligent Systems (RTPIS)

Laboratory (http://rtpis.org/) for providing the world-class equipment and an excellent

working environment to facilitate my research work.

Last but not least, I would like to acknowledge the National Science Foundation and

Duke Energy for providing the financial support. This work is supported by the National

Science Foundation contract/grant number 1312260 and 1232070, as well as the Duke

Energy Distinguished Professor Endowment Fund. The views and conclusions herein are

those of the author and not the National Science Foundation or Duke Energy.

http://rtpis.org/

vi

TABLE OF CONTENTS

Page

TITLE PAGE ................................................................................................................ ii

ABSTRACT .................................................................................................................. ii

DEDICATION ............................................................................................................. iv

ACKNOWLEDGEMENT .............................................................................................v

LIST OF TABLES .........................................................................................................x

CHAPTERS

I. INTRODUCTION ..................................................................................................1

1.1 Overview .......................................................................................................1

1.1.1 Power System Stability .................................................................................... 2

1.1.2 Power System Oscillations .............................................................................. 4

1.1.3 Generator Coherency ....................................................................................... 5

1.2 Benchmark Power Systems ...........................................................................6

1.2.1 IEEE 12-Bus power system ............................................................................. 6

1.2.2 IEEE 68-Bus power system ............................................................................. 7

1.3 Approaches toward smart power systems .....................................................8

1.3.1 Data-driven modeling of power system ........................................................... 9

1.3.2 Generator coherency analysis ......................................................................... 9

1.3.3 Coherency based power system stabilizers .................................................... 10

1.3.4 Wide area signals based adaptive power system staiblizers .......................... 10

1.4 Objectives of this dissertation .....................................................................11

1.5 Contributions of this dissertation ................................................................11

vii

Table of Contents (Continued) Page

1.6 Summary .....................................................................................................12

II. POWER SYSTEM OSCILLATIONS .................................................................13

2.1 Introduction .................................................................................................13

2.2 Power system oscillations and damping torque ..........................................13

2.3 Active power transfer and power system oscillations .................................15

2.4 Summary .....................................................................................................18

III. MODAL ANALYSIS FOR OSCILLATIONS ...................................................19

3.1 Introduction .................................................................................................19

3.2 Stochastic subspace identification ...............................................................20

3.2.1 Input and output signal based SSI .................................................................. 22

3.2.2 Output based SSI ........................................................................................... 24

3.3 Decision of system order .............................................................................25

3.4 Observability factor of oscillation modes ...................................................26

3.5 Controllability factor of oscillation modes ..................................................27

3.6 Modal analysis results for IEEE-68Bus system .........................................28

3.7 Summary .....................................................................................................30

IV. ROBUST POWER SYSTEM STABILIZERS ...................................................31

4.1 Introduction .................................................................................................31

4.2 Power system stabilizer development using linear matrix inequality .........32

4.3 Performance verification .............................................................................36

4.4 Summary .....................................................................................................39

V. COHERENCY ANALYSIS ................................................................................40

5.1 Introduction .................................................................................................40

5.2 Coherency analysis using hierarchical clustering .......................................41

viii

Table of Contents (Continued) Page

5.3 Coherency analysis using K-harmonic means clustering ............................45

5.3.1 Mathematical formulation .............................................................................. 45

5.3.2 Online coherency grouping techniques .......................................................... 47

5.3.3 Number of groups .......................................................................................... 48

5.4 Summary .....................................................................................................55

VI. COHERENCY BASED DAMPING CONTROLLER .......................................56

6.1 Introduction .................................................................................................56

6.2 Development of VG-PSS ............................................................................59

6.2.1 Modal analysis based on system matrices ..................................................... 59

6.2.2 Inter-area oscillation analysis ........................................................................ 60

6.2.3 Structure of VG-PSS ...................................................................................... 60

6.2.4 Determination of virtual generators ............................................................... 62

6.2.5 PSO for VG-PSS tuning ................................................................................ 64

6.2.6 PSO versus other design techniques .............................................................. 67

6.2.7 Time delay compensation .............................................................................. 67

6.3 Simulation results ........................................................................................68

6.4 Summary .....................................................................................................77

VII. ADAPTIVE DAMPING CONTROLLER ........................................................78

7.1 Introduction .................................................................................................78

7.2 Problem formulation ....................................................................................79

7.3 Artificial immune system ............................................................................79

7.3.1 Innate immunity ............................................................................................. 80

7.3.2 Adaptive immunity ........................................................................................ 80

7.4 AIS based oscillation damping controller ...................................................83

7.4.1 Innate damping controller .............................................................................. 83

7.4.2 Adaptive damping controller ......................................................................... 85

7.5 Performance evaluation of AIS controller ...................................................87

7.6 Summary .....................................................................................................94

ix

Table of Contents (Continued)

Page

VIII WIDE-AREA MEASUREMENT BASED MULTI-OBJECTIVE SMARTPARK CONTROLLERS FOR A POWER SYSTEM WITH A WIND FARM .............95

8.1 Introduction .................................................................................................95

8.2 Problem formulation ...................................................................................95

8.3 Power system with a wind farm and SmartParks ......................................100

8.3.1 12-BUS FACTS benchmark test power system ......................................... 100

8.3.2 Wind farm model ........................................................................................ 101

8.3.3 SmartPark model ........................................................................................ 101

8.4 Development of an intelligent multi-functional controller (IMFC) for SmartParks ..............................................................................................104

8.4.1 Tagaki-Sugeno fuzzy network (TSFN) ...................................................... 105

8.4.2 MVO based TSFN parameter tuning .......................................................... 107

8.4.3 Development of IMFC for SmartPark installation at Bus 6 ....................... 108

8.4.4 Development of IMFC for SmartPark installation at Bus 4 ....................... 109

8.4.5 Development of IMFC for SmartPark installation at Bus 4 and 6 .............. 110

8.5 Simulation results......................................................................................111

8.6 Summary ...................................................................................................122

IX. CONCLUSION.................................................................................................123

9.1 Introduction ...............................................................................................123

9.2 Research summary ....................................................................................123

9.3 Main conclusions .......................................................................................124

9.4 Suggestions for future research .................................................................126

9.5 Summary ...................................................................................................127

REFERENCES ..........................................................................................................130

BIOGRAPHY ............................................................................................................139

x

LIST OF TABLES

Table Page

Table 2.1 Oscillation frequencies and Damping ratios under multiple cases. .........18

Table 4.1 Designed Controllers ................................................................................35

Table 5.1 Coherent generator groups for the general case ........................................44

Table 5.2 The Process of KHMC in Finding Group Centers ....................................46

Table 5.3 Group Merging and Splitting ...................................................................49

Table 5.4 Offline Clustering Result ..........................................................................51

Table 5.5 Coherency Grouping Result for Case I ....................................................53

Table 5.6 Coherency Grouping Result for Case II ...................................................55

Table 6.1 The optimized parameters of the VG-PSS ...............................................68

Table 6.2 Settling time of generator speed deviations for the three case studies (in

seconds)...................................................................................................76

Table 7.1 Tuned stimulation and inhibition factors .................................................87

Table 7.2 Damping ratio for different modes under Case I – III ..............................94

Table 8.1 Damping ratios of speed deviation responses ........................................114

Table A.1 The reference of generator active power for VG-PSS design ..............128

Table A.2 The reference of generator active power development of adaptive wide

area signal based PSS............................................................................129

xi

LIST OF FIGURES

Figure Page

Figure 1.1 The categories of power system stability ................................................2

Figure 1.2 IEEE 12-Bus power system with a wind farm ........................................7

Figure 1.3 IEEE 68-Bus power system .....................................................................8

Figure 2.1 IEEE 68-Bus 16-machine system ...........................................................16

Figure 2.2 Speed deviations plots of G15 for different values of P .....................17

Figure 2.3 Damping ratio change with respect to active power transfer from NE to

NY. .......................................................................................................17

Figure 3.1 PRBS injection location, PRBS signal and speed response of generator

G10. ......................................................................................................22

Figure 3.2 Impulses responses of systems with different orders. ..........................26

Figure 3.3 Identified system modes for P =680MW. ...........................................28

Figure 3.4 The phasor plot of observability factors of G1 ~ G16 obtained through

PRBS injection. ....................................................................................29

Figure 3.5 The controllability factors of G1 ~ G16 obtained through PRBS injection.

..............................................................................................................29

Figure 4.1 IEEE 68-Bus 16-machine system of thirteen-PSS installations with fault

locations shown. ...................................................................................32

Figure 4.2 Structure of PSS. ..................................................................................33

Figure 4.3 The diagram of PSS design. ..................................................................33

xii

List of Figures (Continued)

Page

Figure 4.4 The LMI design problem. .....................................................................34

Figure 4.5. Speed deviation of generators for Case I with and without PSSs. ......37


Figure 4.6 Speed deviation of generators for Case II with and without PSSs. .......38

Figure 5.1 IEEE 68-bus 16-machine power system. Coherent groups obtained using

offline clustering is shown as colored regions .....................................42

Figure 5.2 Dendrogram of generator coherency for Case A ...................................43

Figure 5.3 Dendrogram of generator coherency for Case B ...................................43

Figure 5.4 Dendrogram of generator coherency for Case C ..................................44

Figure 5.5 Speed responses of the sixteen generators in IEEE 68-Bus system .....51

Figure 5.6 Speed response of generators following fault at bus 1 ..........................52

Figure 5.7 Online coherent generator groups for a three phase short circuit fault at

bus 1 in Figure 5.1 ...............................................................................52

Figure 5.8 Speed response of generators following fault at bus 8 .........................54

Figure 5.9 Online coherent generator groups for a three phase short circuit fault 54

Figure 6.1 The diagram of the proposed control scheme with VG-PSS .................58

Figure 6.2 The overall flowchart of design approach ............................................59

Figure 6.3 The proposed structure of VG-PSS ......................................................61

Figure 6.4 PSO flowchart for VG-PSS parameters tuning algorithm. ...................66

xiii


Page

Figure 6.5 Case Study I -- The speed deviations plots of selected generators with

VG-PSS on G9. ....................................................................................69

Figure 6.6 Case Study I -- The speed deviations plots of selected generators for

different sites of VG-PSS installations. ...............................................70

Figure 6.7 Case Study II.A -- The speed deviations plots of selected generators with

VG-PSS on G9. ....................................................................................71

Figure 6.8 Case Study II.A -- The speed deviations plots of selected generators for


Figure 6.9 Case Study II.B -- The speed deviations plots of selected generators with

VG-PSS on G9 under a new load condition ........................................73

Figure 6.10 Case Study III -- The speed deviations plots of selected generators with

VG-PSS on G9. ....................................................................................74

Figure 6.11 Case Study III -- The speed deviations plots of selected generators for


Figure 6.12 Impact of time delay for the speed responses at G9. ..........................77

Figure 7.1 A biological immune system ................................................................81

Figure 7.2 The schematic of the proposed AIS based control for a dynamic

system. .................................................................................................82

Figure 7.3 Flowchart illustrating the development of an AIS based damping

controller. .............................................................................................84

xiv


Page

Figure 7.4 Diagram of the proposed innate controller scheme. .............................85

Figure 7.5 Schematic diagram of the AIS based controller. ..................................89

Figure 7.6 Speed responses of selected generators with local PSSs installation under

Case I. ..................................................................................................90


Case II. .................................................................................................91


Case III. ................................................................................................92

Figure 7.9 Deviation of parameters with time for all.............................................93

Figure 8.1 The overall diagram for the SmartPark control scheme .......................99

Figure 8.2 12-bus power system ..........................................................................100

Figure 8.3 Schematic circuit representation of a SmartPark ................................102

Figure 8.4 The inner control loop for SmartPark .................................................102

Figure 8.5 The structure of IMFCs .......................................................................106

Figure 8.6 The flowchart for development of IMFC ..........................................112

Figure 8.7 The speed deviations of G2 and G3 following a 100ms three phase fault

at Bus 6. .............................................................................................114

Figure 8.8 The active power flows on transmission lines following wind speed

changes. ..............................................................................................115

xv


Page

Figure 8.9 The active power output of the SmartPark 1 for Case 1. (Under wind

speed of 12 m/s) .................................................................................116

Figure 8.10 The voltage profile of selected buses. ..............................................117


changes. ..............................................................................................118

Figure 8.12 The active power and reactive output of the SmartPark for Case 2. .119

Figure 8.13 Power system measurements following a 100ms three phase fault at

Bus 6. .................................................................................................120


changes. ..............................................................................................121

1

CHAPTER 1

INTRODUCTION

1.1 Overview

During power system operations, oscillations can be frequently observed as a result of lack of

damping torques. Generally, these oscillations are easy to arise following contingencies while the

power system is under critical operating conditions. Without proper measures of control,

oscillations may lead to serious consequences such as tripping of generators and transmission lines.

The oscillation modes can be generally categorized into local modes, intra-area modes and inter-

area modes in terms of the frequencies and the size of areas involved in the oscillations. Rise of

inter-area modes are largely due to heavy loading of crucial transmission lines [1].

In previous research, various control schemes have been suggested for oscillation damping

control [2-4]. Power System Stabilizers (PSS) that make use of local measurement to provide

supplementary control signals were developed for damping control. Lead-lag compensation,

robust controller design, as well as other schemes have be adopted for PSS design. However, the

use of local measurements contain limited information, and may not be effective for damping of

inter-area oscillations [5]; instead, with the prevailing of Phasor Measurement Unit (PMU)

installation in the power system, wide area measurements become available and can be used for

oscillation damping [6-7].

The concept of generator coherency is suggested based on the phenomenon that generators

tend to oscillate in coherent groups following contingencies [1]. Each group of coherent generators

can be equivalent to a Virtual Generator (VG) as a mathematical simplification of power system.

In this dissertation, the notion of a virtual generator is used to assist the design of oscillation

controllers that maintains to power system rotor-angle stability.

2

1.1.1 Power System Stability

The issue of stability becomes an increasing concern in the inter-connected modern power

systems. This concern is partly due to the fact that more generators are required to maintain

synchronism in a more complicated power system topology. Meanwhile, the integration of

intermittent renewable energy brings about more uncertainty to the transient behavior of the power

system. Loss of power system stability has huge social and economic impacts, as can be illustrated

by the example of 1997 North American blackout.

As indicated in Figure 1.1 [8], three aspects of power system stability are broadly considered

in engineering practices: rotor angle stability, frequency stability and voltage stability. The first

two have a close relationship with the active power generation and transmission, while the latter

is more closely related to the voltage profile and the load dynamics of the power system. Each of

these three aspects of stability can be further classified into subcategories in terms of the intensity

of disturbances and the length of time.

Figure 1.1 The categories of power system stability

3

The study of phase-angle stability can be categorized into first-swing stability and oscillatory

stability, which are affected by synchronizing torque and damping torque respectively. The focus

of this study is on the maintenance of phase angle oscillatory stability through intelligent control

schemes that increases the damping torque. Nevertheless, the consideration for voltage stability,

frequency stability and phase angle first swing stability cannot be ignored during verification of

control effectiveness.

Traditional studies of power system stability have yielded various approaches for the design

of Power System Stabilizers (PSS). The measurements of generator speeds, phase angles and/or

output active power can be used to generate a supplementary control signal injected at Automatic

Voltage Regulator (AVR). This approach resulted in a supplementary torque on the generator

motor with a phase that is in exactly the opposite phase of the generator speed during oscillation.

However, the presence of effective traditional damping schemes cannot exclude further studies of

power system stability, due to the following considerations.

The advent of new analytic mathematical tools as exemplified by modern robust control

theorem and toolboxes, artificial intelligence based algorithms (such as neural

networks and fuzzy logics) can be applied for power system analysis and controller

design.

The usage of PMUs makes wide area measurement available, and can assist in stability

analysis and control. With the PMUs working at much higher sampling frequencies

than the traditional SCADA system, detailed power system dynamics can be captured.

The FACTS devices and SmartParks can be deployed to participate in the stability

control schemes. With the fast switching frequencies, FACTS can respond to control

signals instantaneously to regulate the power flows in the power systems.

4

The integration of wind and solar power into the power system leads to different levels

of transmission line power flows and reactive power output of generators. Thus, more

advanced control schemes are required to make the power system resistant to critical

operating conditions.

The application of energy storage devices (such as SmartParks) can impact the active

and reactive power flow in the power systems, and thus can serve for power system

control purposes.

The desired power system is able to maintain stability in spite of the increased complexity,

uncertainty and stochasticity. Thus, it is desired that improved control schemes be applied to the

power systems using more android analytic tools. The prevention of losses from the consequences

caused by power system oscillation is not the sole purpose of this research. If stability margin is

improved using novel state-of-art technologies, the power system will be able to operate under

more volatile conditions, leading to the potential for integration of more renewable energy.

1.1.2 Power System Oscillations

With the development of society, the increase of power system load requires improved delivery

capability. Unfortunately, this is limited by the rate of power system facility construction. As a

consequence, more power lines are gradually pushed toward the operation limits. Hereby, the

occurrence of oscillations becomes more frequent; reports of large area outages are thus becoming

common. This necessitates the need for more detailed analysis of oscillation phenomenon.

In a power system, active and reactive power are delivered through the transmission and

distribution networks that connects the generation units with the load. The balance of active power

generation and consumption are related to the steady state of system frequencies as well as the

phase angle of generator rotor. As for a generator, the increase in the active power output caused

5

an increase in the leading phase angles. Thus, while subject to a disturbance that causes a change

of active power flow, the fluctuations of the phase angle will occur under the influence of

synchronizing torque and damping torque during the electrical-mechanical dynamics. This

disturbance can be either a change of load, a change of power transmission in a line, or an outage

in a bus. Due to the nonlinear dynamic characteristic of generators and the interconnectivity of

power system, the process of phase angle fluctuation will involve multiple generators and

transmission lines, causing oscillations in the generator speed in all generators and active power

transmission in all major lines. In this sense, the oscillation is no longer a local phenomenal, but

engages the whole power system.

1.1.3 Generator Coherency

An interesting phenomenon is the oscillation of generators in coherent groups. Taking all

generator speeds in a power system as the measurements and plotted in the same time-domain

graph, it can be seen that some groups of generators are swinging in the same cluster of curves

against other groups. In many cases, it can be observed that a dominant mode appears in the

generators speed deviations, while different groups generally oscillate in different phase in terms

of this mode. In the meanwhile, other oscillation modes may also exist; as a result, generators

oscillating in the same coherent group may also oscillate against each other (have different phase

angle) in the other oscillation modes. A brief description of the oscillation phenomenon can be

indicated as follows.

Oscillation is not a local phenomenon; instead, multiple machines are involved in the

power system oscillations that are linked electro-mechanically with the active power

flow in the network.

6

Generators tend to oscillate in coherent groups, while each group are generally

composed of generators that have small electrical distances with each other. In many

cases, the geological distribution of generators are closely related to generator

coherency.

Instead of swinging in a sinusoidal manner, the power system oscillations generally

includes multiple modes. Generators oscillating coherently with the same phase at one

frequency, may be swinging in an opposite phase at another frequency.

The types of contingencies that trigger the oscillations can largely impact the active

power flow in the power network, and in term, lead to variations in generator coherency.

1.2 Benchmark Power Systems

1.2.1 IEEE 12-Bus power system

As indicated in Figure 1.2, this test system includes four generators (G1 through G4).The

bus near G1 serves as slack bus. In this study, traditional synchronous generator model is applied0

for G1, G2 and G3; while a doubly fed induction generator (DFIG) is used for G4, which is

propelled by a wind farm. In this case, the fluctuation of wind speed has huge impacts toward the

power generation at Bus 6, and thus affects the active power flow in the power system. Bus 4 is

the load bus that has large consumption of active power [9].

7

Figure 1.2 IEEE 12-Bus power system with a wind farm

1.2.2 IEEE 68-Bus power system

As indicated in Figure 1.3, the IEEE 68-Bus power system is mainly composed of several

part: New England (NE), New York (NY), and three other smaller exterior power systems that can

be equivalent with three generators. Thus overall, this power system includes 16 generators that

produces active power at different levels. (i. e. G1 through G16). Three major transmission lines

serve as connection corridor from NE to NY. (i. e. Bus 1-2, Bus 8-9, Bus 1-27). G13 serves as the

slack bus that maintains the active power balance between generation and load.

8

Figure 1.3 IEEE 68-Bus power system

1.3 Approaches toward smart power systems

In order to address the issue of power system oscillation for stability maintenance, various

approaches are used in this research for damping control. Although previous approaches has shown

the effective of traditional damping control schemes, this study focuses on the newly emerged

challenges and tools that are encountered by the modern power systems.

In this study, the phenomenon of power system oscillations are graphically introduced and

explored. A modal analysis for oscillations is carried out to assist damping controller design.

Besides, the generator coherency is studied; and mathematical simplification of generator groups

as virtual generators are derived with analytic tools. Thereafter, coherency-based damping

controllers are proposed and tested; and they are further improved to adapt to various operation

Area 3

Area 5

G7

G6

G9

G4

G5

G3

G8 G1

G2G13

G12

G11

G10

G16

G15

G14

59

23

61

29

58

22

28

26

60

25

53

2

24

21

16

56

57

19

20

55

10

13

15

14

17

27

64

11

6

5459

5

4

18

3

8

1

47

48 40

62

30

9

37

65

64

36

34

38

35

33

6311

43

45

3950

51

52

68

67

49

46

42

41

31

66

Area 1 Area 2

Area 4

New England Test System New York Power System

44

32

Area 3

Area 5

G7

G6

G9

G4

G5

G3

G8 G1

G2G13

G12

G11

G10

G16

G15

G14

59

23

61

29

58

22

28

26

60

25

53

2

24

21

16

56

57

19

20

55

10

13

15

14

17

27

64

11

6

5459

5

4

18

3

8

1

47

48 40

62

30

9

37

65

64

36

34

38

35

33

6311

43

45

3950

51

52

68

67

49

46

42

41

31

66

Area 1 Area 2

Area 4

New England Test System New York Power System

44

32

12

7

9

conditions using intelligent algorithms. Finally, a scheme for maintaining stability is proposed for

a power system with renewable energy integration.

1.3.1 Data-driven modeling of power system

In traditional power system stability analysis, accurate models of generators and loads are

created in terms of differential equations. For instances, a 6-order model differential equation can

be set up for each generator; and the load can use either constant impedance model or dynamic

model of higher orders. Thereafter, the model of power system is based on a large set of differential

equations that consider the interaction of generators, loads and the network. However, this buildup

is subject to the parameter change of power system components. Besides, different power system

models need to be rebuilt with the change of system operating condition. The linearized model for

power system stationary stability analysis is generally expressed in the form of system matrices.

The order of matrices can generally be very high for the full model of power systems. However,

in engineering practices, it is not always necessary to have representation of all system states.

System reduction is frequently applied for the simplification of power system model. An

alternative approach is to model the power system with fully data driven approaches. In this study,

measurements are made in response to injection of disturbances at crucial power system

components, and mathematical tools are applied to deduce the system matrices from the inputs and

outputs, as detailed in later sections.

1.3.2 Generator coherency analysis

As introduced above, the generators coherency is subject to variation of operating conditions.

Thus, it is desired to classify generators into different groups in response to the measurements that

reflect power system operating conditions. In this study, the coherency of generators are analyzed

based on both online and offline clustering algorithms. Changes of operating conditions may take

10

place during power system operations, yet the clustering tools designed in this study will be able

to capture these changes. Therefore, each group is equivalent to a virtual generator. Despite of the

fact that details of local and intra-area dynamics are partly ignored in the formulation of the virtual

generators, the validity for this simplification is based on the control effectiveness that is shown

by the proposed controllers.

1.3.3 Coherency based power system stabilizers

On the basis of the power system coherency, this research suggests a wide area signal based

controller that makes use of virtual generator speeds for damping control. A Virtual Generator

based Power System Stabilizer (VG-PSS) is proposed. The introduction of virtual generator notion

avoids the necessity to deal with the dynamics of individual generators in a multi-machine power

system. Besides, the controller is able to perceive and handle all major modes of inter-area

oscillations in the power system.

1.3.4 Wide area signals based adaptive power system staiblizers

Adaptivity is introduced to the VG-PSS to address the impact of operating condition change

on its damping effectiveness. In this study, Artificial Immune System (AIS) is adopted to impose

a deviation to the VG-PSS parameters during power system transient responses to disturbances.

The presence of innate immunity and adaptive immunity of AIS [10] further improves the

effectiveness of VG-PSS.

1.3.5 SmartPark for multiple control functions

The commercial use of electrical vehicle leads to the prevailing construction of SmartParks.

The batteries of SmartParks can be utilized for temporary active power storage and thus serve as

a shock absorber for surging active power in the power systems; they can also be utilized as a

damping controller. Meanwhile, the SmartPark can also supply reactive power for voltage

11

regulations. Instead of focusing on each one of these three functionalities, this study realizes all of

them simultaneously and coordinately.

1.4 Objectives of this dissertation

The objectives of this dissertation research are as follows:

Carry out generator coherency analysis to obtain virtual generator models.

Develop new methods based on data-driven approaches to analysis power system

oscillations.

Identify appropriate wide signals to observe power system oscillations.

Identify generators where wide-area damping controllers have maximum

controllability.

Develop a wide area measurement based adaptive damping controller for better

damping effectiveness.

Apply SmartPark in a power system to realize the functionalities of damping

controller, active power regulator and voltage regulator concurrently.

1.5 Contributions of this dissertation

The following contributions have been made and reported this document.

Developed and implemented K-Harmonic Means Clustering algorithm for generator

coherency analysis [11].

Suggested a Stochastic Subspace Identification algorithm to obtain the system

matrices for power systems [12].

System matrices based modal analysis to select optimal signals to observe and control

power system oscillations [13].

12

Developed a Virtual Generator based Power System Stabilizer for optimal damping

effectiveness [13].

Used Artificial Immune System to implement a wide area measurement based

adaptive damping controller [14].

Applied Intelligent Multi-funtional Fuzzy Controller to realize the functionality of

SmartParks as damping controller, active power regulator and voltage regulator

concurrently. [15].

1.6 Summary

In modern power systems, the maintenance of stability is constantly becoming a challenge

due to increasing industry and customer load, as well as the renewable energy integrations.

Fortunately, the advancing technology provides various intelligent control schemes; and remote

measurements are becoming available with the installation of PMUs. Making advantage of many

analytic tools, this study uses various approaches to provide damping torque in order to mitigate

inter-area oscillations in the power systems. The conception of generator coherency is also used to

assist in the design of damping controllers.

13

CHAPTER 2

POWER SYSTEM OSCILLATIONS

2.1 Introduction

The rise of oscillations in the modern power systems are largely due to the contradiction of

increased power flows and the limited transmission capabilities that pushes the power system to

the stability margin. Besides, while the fast responding Automatic voltage regulator (AVR)

enhances first swing stability by increasing the synchronism torque, research has shown a negative

effect of AVR toward the damping torque.[16] These oscillations manifest themselves through

various measurements such as generator phase angle, speed deviations, bus voltages and tie line

power flow.[17] Without supplementary damping torque supply, the volatile active power

fluctuation may cause crucial transmission lines to be tripped, triggering more contingencies that

further worsen both first swing and oscillatory stability of the power system

Power system oscillations are largely impacted by the active power flow that links the

generators with the loads. Due to the nonlinearity of generator characteristics, as soon as a

contingency causes generators to deviate from previous steady state, the phase angle of some

generators may lose either first swing stability or oscillatory stability, depending on the

synchronizing or damping torque on the generator shaft.

2.2 Power system oscillations and damping torque

Let Te(s) denote the electrical torque on the generator shaft expressed in terms of frequency

domain, while δ(s) is the rotor angle of the generators. The relationship between Te(s) and δ(s)

expressed as (2.1) can be figured out with mathematical modeling of the generator and the control

systems.

14

Te(s) =H(s) δ(s) (2.1)

Under a fixed frequency, i.e. s = jω , we have:

Te(jωo) =H(jωo) δ(jωo) (2.2)

The three terms Te(jωo), H(jωo) and δ(jωo) can be regarded as three complex values. As a

consequence, Te(jωo) can be decomposed into two terms as expressed in (2.3).

Te(jωo) = Ts(jωo)+Td(jωo) (2.3)

in which Ts(jωo) is in phase with the phase angle δ(jωo), while Td(jωo) is in phase with the

generator speed 90 degree ahead of δ(jωo). The amplitude of Ts is closely related to the

synchronizing torque that maintains the first swing stability, while the amplitude of Td is

closely related to the damping torque that maintains the oscillatory stability. Several properties

of the power system oscillations are shown as follows:

When damping torque Td decreases, the generator tend to oscillate with smaller

damping ratio, thus it take longer time to reach steady state.

When the decrease of Td crosses zero, a component of electrical torque that is in

opposite phase with the generator speed is resulted. Thus, a negative damping torque

makes the oscillation unstable with the increasing amplitude through time.

The value of ωo is directly related to the oscillation frequency. For instance, significant

oscillation with angle frequency of ωo is always accompanied by a small value of Td(jωo)

at ωo.

The values of these two torques are under influence of the overall power system model

including generator model, active power transfer and control schemes applied to generators.

For instance, the change in the active power flow in the power system may lead to a change in

generator phase angle and the electrical torque simultaneously, causing the variation of

15

damping torque. The next section is an exploration of the relationship between the oscillations

and power system operating conditions.

2.3 Active power transfer and power system oscillations

The flow of active power transfer impacts phase-angle stability. Under the same loading

condition, increase of active power generation at some generators will cause reduction of generator

at other generators, especially the generator at the slack bus. Accordingly, power flow will change

in the power system networks leading to a different operating condition. The location of

generations and loads may have a large impact on the oscillations. Generally, oscillation becomes

obvious when the load center and generation center do not overlap, especially when some critical

transmission lines connecting two areas in the system become heavily loaded. The magnitude of

oscillation is impacted by the extent of imbalanced distribution of loads and generations.

Occasionally, active power generation in one area of power system may be unanimously increasing,

resulting in the increased power flow in critical transmission lines. Under such condition, it can be

observed that the system matrices also varies from the nominal operating condition, the

eigenvalues of certain modes may approach to the imaginary axis, causing the rise of oscillation.

A serious contingency such as three-phase fault may trigger power system to lose stability due to

amplifying oscillation amplitudes. Besides, the tripping of crucial transmission lines linking two

areas will also result in a weaker link between different power system parts. Since less passage

ways exist for the inter-area power flows, the two subsystems at the sides of transmission lines

will be less electromagnetically coherent; and not sufficient damping torque for inter-area

oscillation modes may be generated.

To study the relationship of power transfers and the oscillations, the IEEE 68-Bus 16-

Machine system (also referred to as the NE-NY system) is used as shown in Figure 2.1. NE and

16

NY are connected by three crucial transmission lines Bus 8-Bus 9, Bus 2-Bus 1, Bus 27-Bus 1,

thus inter-area oscillation between NE and NY can be observed.

Figure 2.1 IEEE 68-Bus 16-machine system

Under the base operating condition, the total power transfer from NE to NY (sum of power

flow on lines 8-9, lines 2-1 and line 27-1) is 560 MW. Increase in NE-NY power transfer, P, is

investigated for the emergence of inter-area oscillation(s). In case of an increased power transfer,

an increase of active power generation in amount of P is equally shared by generators G1~G9 in

NE system, while the same amount of reduction is equally shared by rest of the generators G10 ~

G16 in NE-NY system. Shown in Figure 2.2 is the plot of speed deviation responses of G15 under

different values of P post a six-cycle three-phase fault at Bus 31. Oscillation is prominent when

P reaches 600MW; it further increases as the value of P rises. By visual inspection of the curves

in Figure 2.2, it can be seen that the dominant oscillation is around 0.22 Hz, which is verified by

the plot of damping ratio change with respect to active power transfer from NE to NY shown in

Area 3

Area 5

G7

G6

G9

G4

G5

G3

G8 G1

G2G13

G12

G11

G10

G16

G15

G14

59

23

61

29

58

22

28

26

60

25

53

2

24

21

16

56

57

19

20

55

10

13

15

14

17

27

64

11

6

5459

5

4

18

3

8

1

47

48 40

62

30

9

37

65

64

36

34

38

35

33

6311

43

45

3950

51

52

68

67

49

46

42

41

31

66

Area 1 Area 2

Area 4New England Test System New York Power System

44

32

Area 3

Area 5

G7

G6

G9

G4

G5

G3

G8 G1

G2G13

G12

G11

G10

G16

G15

G14

59

23

61

29

58

22

28

26

60

25

53

2

24

21

16

56

57

19

20

55

10

13

15

14

17

27

64

11

6

5459

5

4

18

3

8

1

47

48 40

62

30

9

37

65

64

36

34

38

35

33

6311

43

45

3950

51

52

68

67

49

46

42

41

31

66

Area 1 Area 2

Area 4New England Test System New York Power System

44

32

12

7

Fault location Line disconnected

17

Figure 2.3, which is drawn using modal analysis elaborated in Chapter 3. As the value of P

changes, the damping ratio changes significantly as listed in Table 2.1.

Figure 2.2 Speed deviations plots of G15 for different values of P

Figure 2.3 Damping ratio change with respect to active power transfer from NE to NY.

0 5 10 15 20 25 30-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1x 10

-3

Times (seconds)

Speed d

evia

tions (

p.u

.)

0MW

600MW

630MW

650MW

680MW

-1000 -500 0 500-5

0

5

10

15

20

25

30

Power Transfer from NE to NY (MW)

Dam

pin

g R

atio (

%)

0.22 Hz

0.65 Hz

0.54 Hz

0.42 Hz

18

Table 2.1 Oscillation frequencies and Damping ratios under multiple cases.

(MW)P Mode frequency and corresponding damping ratio

600 0.2235Hz, 11.53%

630 0.225Hz, 9.16%

650 0.2233Hz, 7.63%

680 0.2173Hz, 4.74%

700 0.2239Hz, 2.04%

720 0.2112Hz, 1.05%

740 0.2034Hz, -0.70%

It can be seen through Figure 2.3 and Table 2.1 that the damping ratio of 0.22 Hz rapidly

decreases with the increase of active power transfer from NE to NY that pushes the transmission

lines linking these two areas to the limits. Chapter 3 will further show that this mode is the

oscillation of generators in NE oscillating against the generators in NY.

2.4 Summary

The power system oscillation arises due to lack of damping torque, which is largely affected

by different operating conditions. Typically in a power system where the transmission of a large

amount of active power between two large areas takes place, the decrease of damping torque tend

to result in a reduced damping ratio for oscillations. This can serve as a scenario of basic case for

the damping control design in later chapters.

19

CHAPTER 3

MODAL ANALYSIS FOR OSCILLATIONS

3.1 Introduction

As mentioned above, power system oscillations generally occur in multiple modes. Different

mode exhibit itself through a distinct oscillation frequency, damping ratio as well as a different set

of power system devices that are participated in oscillations. By implementation of modal analysis,

oscillation modes that lack sufficient damping torque can be identified.

Before the development of a damping controller, it is essential to study the oscillations

analytically. For instances, in order to select proper input and output signals for the controllers, it

is desired that the measurements that best reflects the oscillation in concern are used as the input,

while the output signal need to be applied to a power system device that most effectively impacts

the electromagnetic transients of that oscillation mode. In order to achieve this, modal analysis

serves as a powerful tool. Besides facilitating controller design, modal analysis also provides a

way to exam the efficacy of a controller.

Prior to analyze the modes engaged in oscillations, it is necessary to obtain a model for the

power system without detailed mathematical model of every component that captures the full

dynamics. Traditional modeling of the power system is through the combination of differential

equations for each the power system component. However, since the number of components is

exponentially increasing in the modern power system, the bottom-up modeling of every

component may not be practical for a large power system. Also, the power system matrices

obtained through this approach are be characterized with high orders, which includes large amount

of redundant information resulted from excessively delicate mathematical formulations. Besides,

the change operating conditions (including power flow, active power generation, network topology

20

as well as power system components in operation) also affect the power system model. Thus, it is

desired that the power system model is constructed with fully data-driven approaches. Hereby, the

concept of data-driven refers to the methodology to obtain the system model through analysis of

inputs and outputs data, without delving into details of the transient dynamics for each component.

Despite the nonlinearity of power systems, representation of power systems through linear

state space has been widely adopted for stability analysis and control based on two facts: first,

although individual generators can only be best modelled by nonlinear differential equations,

modal analysis based on the linearization of interconnected power system near a nominal operating

point can effectively uncover the characteristics of oscillation modes; second, although power

systems are subject to changes of operating conditions, these variations are comparatively small

comparing to the major systematic topology and generator parameters that remain unchanged; thus,

the modal analysis results can be well applied to a range of operating points. Studies presented in

references [18-22] include state-space representation of power systems.

In this chapter, a fully data-driven approach is used for power system identification and

modal analysis, which provides a guideline for damping controller design as well as for the

verification of damping effectiveness for later chapters.

3.2 Stochastic subspace identification

The general conceptions of system matrices are used to better describe the dynamics of

linearized model of power systems, as expressed in A,B,C,D in (3.1);

( 1) ( ) ( )( ) ( ) ( )

x k Ax k Bu ky k Cx k Du k

(3.1)

Where u(k),y(k) and x(k) represents the inputs, outputs and system states at the moment of k.

Stochastic Subspace Identification (SSI) is an effective mathematical tool to recognize a system

21

through the inputs and outputs. SSI algorithm regards the system matrices as the map from the past

data to future data. Generally, in order to design a PSS for stabilizing control, the supplementary

signal at the AVR of generators are regarded as the input and the speed deviation responses are

taken as the output. In this study, in order to identify the system dynamics, Pseudo-Random binary

signals are injected as the input signals to disturb the power system.

This is exemplified by an approach to identify generator G10 regarded as a Single Input

Single Output (SISO) system, as shown in Figure 3.1. In this approach, PRBS is injected at the

AVR of G10, while the speed deviation of G10 is measured as output. For other approaches,

multiple inputs and outputs can also be used. Figure 3.1(a) is the injection location of PRBS, vt

and vt_ref signify generator terminal voltage and its reference value. Figure 3.1(b) is the PRBS

waveform applied to generator G10, whose spectrum covers the frequency range of power system

oscillation (0.1Hz – 2 Hz). Figure 3.1(c) is the actual speed response of G10 plotted together with

expected speed response calculated through the linearized model of G1, indicating that the power

system fits to the linearized model with accuracy.

(a)

22

(b)

(c)

Figure 3.1 PRBS injection location, PRBS signal and speed response of generator G10.

(a) Structure block diagram of AVR showing PRBS injecting site; (b) PRBS signals;(c) speed responses and its estimated value at G10

Though previous research has used SSI for power system identification [23], it is not applied

for Multiple Input Multiple Output (MIMO) case; besides, the matrices B and C, were not

identified. In the following cases shown, SSI is applied to (a) an input/output based model and (b)

an output based model of the power system.

3.2.1 Input and output signal based SSI

In this case, the power system is modelled as a discrete system with the following expression:

1 1

1 1

( 1) ( ) ( )( ) ( ) ( )

x k A x k B u kk C x k D u k

(3.2)

0 10 20 30 40 50 60 70 80 90 100-0.02 -0.01

0 0.01

0.02

Time: (s)

Am

plit

ude

(p

. u.)

0 10 20 30 40 50 60 70 80 90 100-4

-2

0

2

4 x 10 -5

Time: (s)

Spee

d d

evia

tion

: (p

. u.)

Actual speed deviation Speed dev. of linearized model

23

in which the column vectors x, ω, u are the system states, supplementary inputs and speed

deviations respectively. k refers to the time step; in this case 0.064s is taken to be the gap between

each time step. A Hankel matrix of the past data array{u(k) | k = 0,1,…i+j-2} is defined as,

0| 1

0| 1

(0) (1) ... ( 1)(1) (2) ... ( )... ... ... ...

( 1) ( ) ... ( 2)

(0) (1) ... ( 1)(1) (2) ... ( )... ... ... ...

( 1) ( ) ... ( 2)

past i

past i

u u u ju u u j

U U

u i u i u i j

jj

Y Y

i i i j

(3.3)

A Hankel matrix of the future input data array {u(k) | k = i,i+1,…, 2i+j-2} is also defined as,

|2 1

|2 1

( ) ( 1) ... ( 1)( 1) ( 2) ... ( )... ... ... ...

(2 1) (2 ) ... (2 2)

( ) ( 1) ... ( 1)( 1) ( 2) ... ( )... ... ... ...

(2 1) (2 ) ... (2 2)

future i i

future i i

u i u i u i ju i u i u i j

U U

u i u i u i j

i i i ji i i j

Y Y

i i i j

(3.4)

Now, a historical data set is defined as,

[ , ]T T Tpast past pastW U Y (3.5)

It is easy to know from linear system theory that the future output Yfuture is impacted not only

by historic data set Wpast, but also by future inputs Ufuture. Thus, in order to figure out the map from

Wpast to Yfuture with the absence of Ufuture, an oblique projection from Yfuture to Wpast along Ufuture is

considered and is defined as,

24

/futurei future U pastO Y W (3.6)

Then singular value decomposition is applied as follows,

1 11 2

2

00 0

TT

i i iT

S VO USV U U G X

V

(3.7)

pinv( )i i iX G O (3.8)

where 1/21 1iG U S ; “pinv()” stands for the Moore-Penrose pseudo-inverse. It can be seen that each

column of Xi has the same dimension as the state variable x; it actually represents the estimation

of system states at each specific time. Xi+1 can be figured out in a similar way as Xi using (3.5) ~

(3.8) but replacing Upast, Ypast, Ufuture, Yfuture with 0|past iU U , 0|past iY Y , 1|2 1future i iU U , 1|2 1future i iU U

defined in a similar way as (3.3) ~ (3.4). Since the estimation of state variables at every specific

moment should satisfy (3.2), the system matrices A,B,C,D can be estimated from formulae (3.9)

by taking another pseudo-inverse,

1

| |

i i

i i i i

X XA BY UC D

(3.9)

Through this approach, the system matrices can be identified in two steps: (i) injection of PRBS

as the system input, and measure the system output; (ii) using formulae (3.2) ~ (3.9) to compute

system matrices.

3.2.2 Output based SSI

There are also some cases when it is not practical to inject PRBS to the power system as

supplementary inputs; instead, accurate modal analysis is required to be implemented only

according to the measured speed deviations, especially when a contingency happens. Different

25

from the previous case, the power system is equivalent with a discrete model where the input is

absent:

1

1

( 1) ( )( ) ( )

x k A x kk C x k

(3.10)

The computation process for Xi and Xi+1 is similar as the previous case except for that there

is no need to compute any values related to the input Upast and Ufuture; besides, Wpast should be

replaced with Ypast. Then, the matrices A and C can be calculated based on (3.11).

1

|

ii

i i

X AX

Y C

(3.11)

Through this approach, the system matrices can be identified in two steps: (i) following a

contingency in a power system, collect speed response deviations of all generators for a certain

window of time after the fault is tripped; (ii) compute system matrices based on a similar set of

formulae.

3.3 Decision of system order

Once the systematic matrices are obtained, the transfer function from input to output can be

decided and impulse response can be plotted. When system order is properly specified, the impulse

response will have minimal change as the system order further increases. By comparison of

impulse responses under different system orders, a correct value can be determined.

This is exemplified in Figure 3.2 for G10. Through SSI, impulse responses of a 3rd-, 4th-, 5th-

and 6th-order model are plotted together in the same diagram for comparison. A third order system

fails to catch up with system dynamics; nevertheless, it is evident that a 4th-order model is able to

represent the system, since impulse responses from 4th- or higher models appear to overlap.

26

Figure 3.2 Impulses responses of systems with different orders.

The identified system matrices for G10 are:

10

0.4439 0.6057 3.1296 0.96690.0467 0.1160 7.3734 0.11233.5372 7.8953 0.4947 2.2057

0.2754 0.0976 2.0730 0.0327

A

10 0.1863 0.0564 0.6314 0.0659 TB

10

910

0.0066 0.0037 0.0059 0.0046

2.0 10 0

C

D

Besides this example, another approach is to consider all the generator speed deviations as

the outputs, while all the AVR supplementary signals serve as the inputs. For any specific case,

other inputs and outputs can be chosen accordingly. Once the system matrices are identified, it is

of interest to figure out the existing oscillation modes. For each generator, the observability factor

of each mode needs to be calculated. Also, for each control input channel, the controllability factor

to each mode needs to be figured out.

3.4 Observability factor of oscillation modes

With the system matrix A, use singular value decomposition:

TA V W (3.12)

Time: (s)

Am

plit

ude

(p

. u

.)

3rd order

4th order

5th order

6th order

0 15

27

where TVW I and 1 2{ , ,... }ndiag ;

Each angular value σi is a representation of an oscillation mode. The corresponding

frequency of this mode is σi /2π. When the system order is set to be higher than the number of

actual oscillating modes, some of the modes embroiled in Λ will exhibit low connectivity with the

inputs and outputs.

Corresponding to the ith singular value σi, the observability factor of the mth input is

calculated as:

mi m ic v (3.13)

where cm is the mth row of matrix C, while iv is the ith column of matrix V. Since both of the two SSI

approaches can yield the matrix C, the observability factors can be calculated under both cases.

A high value of observability factor for a generator signifies that the measurements from this

generator has high component of that oscillation mode; and thus the measurements from this

generator can be selected as an input of damping controller.

3.5 Controllability factor of oscillation modes

Corresponding to σi, the controllability factor of the nth output is calculated as:

in i nw b (3.14)

where wi is the ith row of matrix W while bn is the mth column of matrix B. Since only the first SSI

approach can yield the matrix B, the controllability factors can be calculated only under the first

case.

A high value of controllability factor for a generator signifies that the AVR supplementary

signal has large impact toward this oscillation mode; and is suitable to be selected as an output of

damping controller.

28

3.6 Modal analysis results for IEEE-68Bus system

Using the approaches elaborated above, the PRBS signals are injected at the AVR of all

generators in IEEE 68-Bus power system under the power transfer from NE to NY of P =680MW.

The speed deviations of all the generators are measured. With these inputs and outputs, power

system matrices are identified. Using SVD for matrix A, major oscillation modes are identified

and shown in Figure 3.3.

Figure 3.3 Identified system modes for P =680MW.

It can be seen that the oscillation at 0.22Hz is a prominent and poorly damped mode. The

observability factors calculated by (3.13) are complex numbers and can thus be regarded as phasors.

For a specific oscillation mode, the observability factor phasors of all generators can be calculated

and plotted. The directions of these phasors can partially reflect the coherency of generators

engaged in the oscillation mode. Shown in Figure 3.4 is the phasor plot of observability factor of

each generator at the mode of 0.22 Hz. This mode is roughly the oscillation of NE area against NY

area: G1~G9 are oscillating against G10~G16; this oscillation is especially prominent on G14,

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.9152Hz

4.31% 0.57747Hz

8.2627% 0.43732Hz

11.16%

0.2243Hz

4.87%

0.21478Hz

23.4358%

Frequency (Hz)

Resid

ue /

Dam

pin

g r

atio

Dominant Inter-area

weakly damped mode

29

G15, G16. Correspondingly, the controllability factors are shown in Figure 3.5. It can be seen that

G8 and G9 are the two generators with highest controllability factors.

Figure 3.4 The phasor plot of observability factors of G1 ~ G16 obtained through PRBS injection.

Figure 3.5 The controllability factors of G1 ~ G16 obtained through PRBS injection.

-6 -4 -2 0 2 4 6 8

x 10-3

-6

-4

-2

0

2

4

6x 10

-3

1 G2 G3

G4 G5 G6

G7

G8

G9 G10

G11

G12 G13

G14 G15

G16

Real Axis

Imagin

ary

Axis

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Conto

llabilt

y f

acto

r

Generator Index

30

It is noticed that the generators with highest observability factors are different from those

with highest controllability, which is very common in many cases of inter-area oscillations. In

another words, the speed deviation of the generator most effective to implement damping control

may not be identical with the generator that the concerned oscillation mode can be observed. This

leads to the conclusion that local damping control is not sufficient for inter-area oscillations.

3.7 Summary

This chapter focuses on the methodology for modal analysis of the power system. First, an

SSI algorithm is applied to obtain the power system matrices following PRBS injections on AVRs

of all the generators to trigger power system transients. These matrices serve as a linearized power

system model that includes all the oscillation modes. Based on singular value decomposition, all

the oscillation modes can be identified and analysed. Besides, the observability and controllability

factors for all the generators can be calculated, which serves as a guidance for input and output

signal selection for damping controller design.

31

CHAPTER 4

ROBUST POWER SYSTEM STABILIZERS

4.1 Introduction

As power systems are operated close to the stability margin, oscillation caused by lack of

damping torque is frequently observed. Power System Stabilizer (PSS) enhances generator

stability by providing a supplementary signal to the automatic voltage regulator which enhances

the damping torque. Traditionally, PSSs are tuned by phase compensation of selected modes using

lead-lag compensators: the damping torque brought by PSS signals are expected to be exactly in

opposite phase with speed responses at the oscillation frequency. From perspective of control

theory, corresponding eigenvalues are shifted to the left in the complex plane. Based on this idea,

PSSs are designed after oscillation modes are obtained through Prony analysis in [4]. In [3], the

PSSs are regarded as filters for single modes during the design. However, since oscillations usually

occur in multiple modes, it is not guaranteed that all modes show reduced oscillation by such

design.

There are also applications of robust control schemes for PSS design. An H∞ design approach

is introduced in [24] to satisfy stability margin and disturbance attenuation requirements.

Elaborated in [25] is a dual-input PSS-design scheme using Glover-McFalane’s loop-shaping. In

[26], a mixed H2 /H∞ PSS design for a double-fed induction generator which shows robustness to

large disturbances is presented. Besides, PSSs can be designed through robust pole placement [27],

as well as conic programming [28]. Though there are abundant LMI tools to solve those robust

control problems, accurate linearized model is hard to obtain for an interconnected power system,

calling for data-driven approaches. Fortunately, this study makes use of the modal analysis

elaborated in the previous chapter: Stochastic Subspace Identification (SSI) algorithm is applied

http://fsymbols.com/signs/infinity/



32

to obtain a linearized single-input-multiple-output model of a power system and the Linear Matrix

Inequality (LMI) approach is then used to design several PSSs.

4.2 Power system stabilizer development using linear matrix inequality

In this study, PSSs are tuned in order to stabilize a multi-machine power system during

different disturbances. IEEE 68-Bus power system is used as shown in Figure 4.1, with the PSS

installation locations clearly marked. According to previous chapters, oscillation occurs in multiple

modes. Despite that geographically remote generators may swing in totally different frequency

range, local PSSs should be tuned to reduce the oscillation magnitude as well as the settling time.

Figure 4.1 IEEE 68-Bus 16-machine system of thirteen-PSS installations with fault locations shown.

Traditional PSS structure is shown in the upper part of Figure 4.2. It comprises a washout

filter, an amplitude limiter and a lead-lag compensator composed of two first-order functions

connected in series. This compensator can also be written in a more generalized 2nd-order transfer

function form as shown in the lower part of Figure 4.2, which is the standard structure adopted for

PSS in the industry today. Same parameters are used for the washout filters and limiters for all

33

PSSs. Thus for each of them, only the parameters in the 2nd-order transfer function need to be

figured out. The two-step PSS design process is shown in Figure 4.3. The processes inside the loop

are repeated to a number of PSSs one by one, for all generators in the system.

Figure 4.2 Structure of PSS.

Figure 4.3 The diagram of PSS design.

LMI is a mathematical tool that is useful in pole-placement and H2/H∞ control [29]. Using

the controlled system matrices, linear controller can be easily designed. Traditionally, controller

may take either output or state variable of the controlled system as input. In this study, since the

state variables are not observable, output-feedback instead of state-feedback controller is adopted,

as indicated in Figure 4.4. Letter u represents the controller output that is added to AVR


34

supplementary signal v. Given the continuous model matrices , , ,Mi Mi Mi MiA B C D , the open-loop power

system can be described as:

2

Mi Mi Mi

Mi Mi Mi

x A x B u B vy C x D u D vz uz y

(4.1)

Figure 4.4 The LMI design problem.

The aim is to design a controller with state space realization , , ,Ci Ci Ci CiA B C D to make the closed

loop transfer functions fromv to 2z and z satisfy:

Min 2 2z vT (4.2)

Subject to z vT

(4.3)

under the pole-placement requirement that every closed-loop pole i satisfies:

min ( ) 0ireal (4.4)

The order of controller equals that of the controlled system. The purpose of (4.2) is to minimize

speed deviation y subjected to a disturbance in v, so that the power system can be stabilized

following a contingency. Meanwhile, since it is not expected to have excessively large control

effort u, another constraint is set by (4.3). (4.1) ~ (4.4) have defined a mixed H2/H∞ output-

feedback design scheme that can be straightforwardly solved using MATLAB LMI toolbox [26].

A solution not may necessarily exist for every mathematical problem of this type, especially when

the controlled system has complex dynamics. Fortunately in this case, the power system model

obtained is of moderate order, leading to feasible design scheme.


35

Theoretically, the designed output-feedback controller can be replaced by an equivalent

transfer function; putting together with a washout filter and a magnitude limiter, a PSS can be

formed. However, it is not desired to have a PSS of high orders. Thus, after the controller is

designed and its matrices are known, it is further reduced to a 2nd-order transfer function through

balanced truncation. This process can also be implemented with MATLAB. Shown in Table 4.1

are the PSS controllers designed for thirteen generators.

Table 4.1 Designed Controllers

GeneratorIndex

System order Controller

G1 10 2

2

5.32 1110 34702.805 792.4

s ss s

G2 6 2

2

3.8365 34.94 1095818 345.9

s ss s

G3 10 2

2

12.26 176.3 212403.096 1752

s ss s

G4 10 2

2

33.88 636.6 125.939.96 3.558

s ss s

G5 12 2

2

39 766 513805.079 1889

s ss s

G6 12 2

2

27.4 1446 203402.708 646.7

s ss s

G7 8 2

2

24 31485 224102.969 1356

s ss s

G8 6 2

2

4.182 210.7 73832.706 642.9

s ss s

G9 8 2

2

0.5 54.25 10.834.243 2.538

s ss s

G10 4 2

2

28.77 87.5 1384.56.402 58.31

s ss s

G12 12 2

2

3.591 745.2 14102.503 337

s ss s

G13 8 2

2

2.836 46.11 320.111.45 45.44

s ss s

G14 6 2

2

55.15 761.8 487.22.773 101.9

s ss s

36

4.3 Performance verification

After the installation of all designed PSSs based on LMI-SSI approach described above, their

efficacy is examined through real-time simulation results carried out on the real-time digital

simulator (RTDS). Two cases corresponding to different contingencies and loading conditions are

considered during the simulations.

Case I: 8-cycle fault at Bus 2. Shown in Figure 4.5 is the comparison of speed deviation

responses with and without PSSs of the 13 generators with PSS installation.

Case II: 8-cycle fault at Bus 27, then the line connecting Bus 27 and Bus 1 is tripped.

Simulation result is shown in Figure 4.6.

It can be seen from these figures that with PSS installation, the power system settles to steady

state with quicker; meanwhile, the oscillation amplitude is also reduced. Though totally different

oscillation frequency may be observed for each generator following various contingencies, it can

be seen that the designed PSSs are able to stabilize the power system in both cases.

37

Figure 4.5. Speed deviation of generators for Case I with and without PSSs.

0 2 4 6 8 10 12-0.01

-0.005

0

0.005

0.01

G1

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-6

-4

-2

0

2

4x 10

-3 G2

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-8

-6

-4

-2

0

2

4x 10

-3 G3

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-0.01

-0.005

0

0.005

0.01

G4

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-0.01

-0.005

0

0.005

0.01

G5

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-0.01

-0.005

0

0.005

0.01

G6

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-0.01

-0.005

0

0.005

0.01

G7

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-0.01

-0.005

0

0.005

0.01

G9

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-4

-2

0

2

4x 10

-3 G10

Time: (s)S

pe

ed

de

v: (p

.u.)

0 2 4 6 8 10 12-4

-2

0

2

4x 10

-3 G12

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-4

-2

0

2

4x 10

-3 G13

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12-3

-2

-1

0

1

2

3x 10

-3 G14

Time: (s)

Sp

ee

d d

ev: (p

.u.)

Without PSSs

With PSSsSp

eed

dev.

in p

. u.

G1

Time: (s)

G2

Time : (s) Time: (s) G3

Time: (s)

G4

Time: (s)

G5

Time: (s)

G6

G8

G7

G12

G10

G13

G14

Time: (s)

Time: (s)

Time: (s)

Time: (s)

Time: (s)

Time: (s)

Time: (s)

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

. u.

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

. u.

Spee

d de

v. in

p. u

.

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

. u.

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

. u.

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

. u.

38

Figure 4.6 Speed deviation of generators for Case II with and without PSSs.

Without PSSs With PSSs

0 2 4 6 8 10 12 14 16 18 20-4

-3

-2

-1

0

1

2x 10

-3 G1

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-3

-2

-1

0

1

2

3x 10

-3 G2

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-3

-2

-1

0

1

2

3x 10

-3 G3

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-4

-2

0

2

4x 10

-3 G4

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-4

-2

0

2

4x 10

-3 G5

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-4

-2

0

2

4x 10

-3 G6

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-6

-4

-2

0

2

4x 10

-3 G7

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-8

-6

-4

-2

0

2

4x 10

-3 G9

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-1.5

-1

-0.5

0

0.5

1

1.5x 10

-3 G10

Time: (s)S

pe

ed

de

v: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-2

-1

0

1

2x 10

-3 G12

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-2

-1

0

1

2

3x 10

-3 G13

Time: (s)

Sp

ee

d d

ev: (p

.u.)

0 2 4 6 8 10 12 14 16 18 20-1.5

-1

-0.5

0

0.5

1

1.5x 10

-3 G14

Time: (s)

Sp

ee

d d

ev: (p

.u.)

With PSS

Spee

d de

v. in

p. u

.

G1

Time: (s)

G2

Time: (s)

G3

Time: (s)

G4

Time: (s)

G5

Time: (s)

G6

G8

G7

G12

G10

G13

G14

Time: (s)

Time: (s)

Time: (s)

Time: (s)

Time: (s)

Time: (s)

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

. u.

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

.u.

Spee

d de

v. in

p. u

.

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

. u.

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

.u.

Spee

d de

v. in

p. u

.Sp

eed

dev.

in p

. u.

Time: (s)

39

4.4 Summary

A new approach to tune PSS for multi-machine power system based on SSI and LMI

approach has been presented. Through analysis of system input and output data, SSI is able to

identify a single-input-multiple-output linearized power system and obtain its system matrices.

Thereafter, a LMI approach is applied to design an output-feedback controller that minimizes the

speed deviation response with limited control efforts. With subsequent order-reduction, the

designed controller can be implemented with a washout filter and a magnitude limiter to form the

standard PSS structure, typical case studies have shown that the LMI-SSI based PSS design is

effective for damping various modes of oscillation that exhibit in an interconnected multi-machine

power system.

40

CHAPTER 5

COHERENCY ANALYSIS

5.1 Introduction

Two factors make coherency analysis essential. In modeling and simulation of a power system that

includes large number of synchronous generators, as the size of grid expands, detailed transient analysis

becomes inhibiting due to significant calculation burden, leading to the requirement for a simplified model

to be obtained by generator clustering. Besides, Wide Area Control (WAC) is an effective way for

oscillation-damping control in order to maintain transient stability. Correct formulation of coherent groups

can provide virtual generator speed that can be used as WAC measurement signals.

It was traditionally regarded that the power system can be divided into several coherent areas where

generators in a given area tend to remain “in phase” in most cases. However, different events or

disturbances can affect the grouping results. For instance, an event happening near a coherent group may

cause its member generators to lose coherency during oscillation, as indicated in [1]. Thus, for effective

damping control for online operation of power systems, it is essential to have an online adaptive coherency

grouping approach.

The study on coherency analysis has been carried on for a very long time. With the speed deviation

data in time series from each generator, coherency analysis can be carried out, using either deterministic

or heuristic approaches, based on either the time-domain or frequency domain characteristics of the data.

Short-time Fourier analysis [2], Hilbert transform [30], Prony analysis [31] all serve as good alternatives.

Since approaches that focus on frequency domain characteristics are extremely time-consuming, time

domain based clustering is used for this study. Hereby, hierarchical clustering is a good approach by

consecutively merging small groups. Meanwhile, it is required that a faster and accurate clustering

41

algorithm be developed; thus, K-harmonic means clustering (KHMC) approach is introduced for online

coherency analysis. KHMC is insensitive to initialization of group centers and is fast. Besides, a

mechanism is developed to automatically determine the optimal number of groups during the online

analysis for KHMC. In this study, two types of clustering algorithms (hierarchical clustering and KHMC)

are elaborated based on IEEE 68-bus system.

5.2 Coherency analysis using hierarchical clustering

Hierarchical clustering is an algorithm that starts by regarding each of the generator as a separate

group. Thereafter, group merging is implemented to reduce the group numbers, and a dendrogram is

formed. In each iteration, two groups combine to form a new group. The y axis of the dendrogram is an

α-value, which is an index that measures the tightness of the clustering results, as defined in (5.1).

Generally, larger value of WSSE corresponds to smaller group number.[30]

2( )

2

( )

( )

i i j ii

i i alli

w x c

w x c

(5.1)

where cj(i) is the corresponding group center of a member xi, while call is the center of all the members in

all group. Thus the α-value can vary between zero and one.

The following steps are used during hierarchical clustering.

ii. Start by classifying each generator as a separate group.

iii. Identify two groups that are closest to each other.

iv. Merge the two closest groups. The new α-value can be updated incrementally.

v. Repeat ii and iii until all the generators are included in one group; and draw the dendrogram.

In the offline clustering, the generator speed deviation data are collected prior to the implementation

of clustering algorithm. In this study, a MATLAB program has been devised to visualize the dendrogram

42

for generator coherency using hierarchical clustering, which is a reflection of the overall closeness of

generators during transient performances.

The IEEE 68-bus 16-machine power system illustrated in Figure 5.1 is used in this study and is

simulated using the real-time digital simulator (RTDS). The following three cases indicates the impact of

operating condition on generator clustering.

Figure 5.1 IEEE 68-bus 16-machine power system. Coherent groups obtained using offline clustering is shown as colored regions

Case A: Fault happens at Generator 4 (at Bus 56) under normal load condition

The nearest load connected to Bus 56 is the load on Bus 20 of 680MW. The dendrogram and online

clustering result is shown in Fig 5.2. Since G4 and G5 are near the fault location, they oscillate in different

groups with each other as well as with other generators.

43

Figure 5.2 Dendrogram of generator coherency for Case A

Case B: Fault happens at connection line between Bus 2 and Bus 3 under normal load condition. In this

case, it is noticed that the generators in NE is oscillating coherently against those in NY, as shown in

Figure 5.3.

Figure 5.3 Dendrogram of generator coherency for Case B

44

Case 3 (The general case) PRBS signals are injected in the AVRs of all generators. Generator speed

deviations are measured. Accordingly, the clustering results of the dendrogram is shown in Figure 5.4.

Based on this case, an alpha-cut is applied to cluster the 16 generators in the IEEE 68-Bus power system

into five groups as documented in Table 5.1.

Table 5.1 Coherent generator groups for the general case

Group Generators Group 1 Group 2 Group 3 Group 4 Group 5

G1, G8 G2, G3 G4, G5, G6, G7, G9 G10, G11, G12, G,13 G14, G15, G,16

Figure 5.4 Dendrogram of generator coherency for Case C

0.7

0.75

0.8

0.85

0.9

0.95

1 8 4 7 5 6 9 10 11 12 13 2 3 14 15 161 8 4 7 5 6 9 10 11 12 13 2 3 14 15 161 8 4 7 5 6 9 10 11 12 13 2 3 14 15 16

Jaccard

dis

tance b

etw

een g

enera

tor

speed w

avefo

rms

alpha - cut

Generator Index

45

5.3 Coherency analysis using K-harmonic means clustering

In this section, a K-harmonic means clustering (KHMC) approach is applied for online coherency

analysis of synchronous generator. KHMC is a global optimizing algorithm that bases the adaptation of

the group centers based on the entire groups/clusters that exist prior. Unlike ordinary k-means clustering,

KHMC is insensitive to initialization of group centers and thus provides more accurate results [32-33].

Besides, the updated group center of a current time step can also serve as the initialization for the next

one; in this way, clustering results can be obtained at each consecutive time step, making KHMC very

suitable for online clustering. In order to decide the number of clusters in KHMC, an Average Within-

Group Distance (AWGD) threshold is adopted; groups may be merged or split to satisfy this threshold,

group number is thus decided indirectly.

5.3.1 Mathematical formulation

Common signals, x, used for coherency grouping are speed and speed deviations responses over a

window of time of generators. The distance between a generator i and a group center mk can be defined

as:

22

( ( ) ( ))ik i k i kj

d x m x j m j (5.2)

where j refers to the element index in a vector (xi or mk). Suppose there are K groups in total for all

the generators, the harmonic mean distance of generator i w.r.t to all group centers is defined as:

2

11/ (1/ )

ik

K

ik

D d

(5.3)

46

The determination of the optimal group centers is needed to properly classify coherent generators

together. The cost function to carry this out is defined as the weighed sum of iD for all generators, as

indicated below:

2minii

iJ H D (5.4)

where iH is the inertia constant of generator i. Generators with large H will dominate the cost function.

In order to minimize (5.4), the condition in (5.5) needs to be satisfied and if so, the group centers are

updated to minimize the cost function using (5.6).

4

31

2 ( ) 0ik

Ni i i k

ik

H D x mJm d

(5.5)

4 4

3 31 1

/ik ik

N Nnew i i i i ik

i i

H D x H Dmd d

(5.6)

where N is the number of generators in a power system. The centers are updated for every window until

the metric in (5.7) is satisfied or a maximum number of iterations is met. The KHMC based coherency

grouping is illustrated in Table 5.2.

20.01new

k km m (5.7)

Table 5.2 The Process of KHMC in Finding Group Centers

Step 1 Receive all the generator data (H, xi ) and initialize group centers mk;

Step 2 Calculate the distance dik between each generator i and group centers, mk, using (5.2);

Step 3 Update group centers using (5.6);

Step 4 If group centers becomes stable, then go to Step 5, otherwise, go back to Step 2

Step 5 Record the group centers, and stop.

47

The difference of KHMC from k-means clustering is its global convergence. In k-means clustering,

each group center only moves toward its closest generator at every step; this is a local adaption. In contrast,

for KHMC, change of every group center is dependent on all generators; each generator also affects all

group centers. Ultimately, the overall distance between each generator and its corresponding group center

is minimized as explained above. Besides, the adaption rule of (5.5)~(5.6) is much faster than gradient

descent; it also avoids the issue of deciding a learning ratio. This adaption rule is only realizable for

KHMC, not for k-means clustering. The robustness of KHMC makes it suitable for online clustering.

5.3.2 Online coherency grouping techniques

Online coherency grouping requires a stream of data of some window size. A power system model

is sampled to provide speed deviation signals of the generators at 10Hz. Clustering is made based on

generator speed deviation data of 2 seconds, i.e. a window size of 20 data points. For online analysis, a

moving window at 10Hz is used in this study. The KHMC algorithm is implemented in this study on a

remote processor from the one that simulates the power system. The clustering data is acquired through a

data acquisition system. The coherent groups are displayed on a screen.

Whenever a new window (has a new data point added at the end of the vector array, x and the first

data point of the previous window dropped) is received, group centers are updated using (5.2) ~ (5.7).

Since the window shifts by only one data point at each step, the group centers are located close to the old

ones, thus few iterations will be needed. The KHMC algorithm converges fast.

Once the group centers are determined each generator is assigned to its nearest group center

according to (5.8):

arg mini k ikk d (5.8)

48

Then decision-making whether to merge or split groups is made on a threshold. When a suitable

group number is achieved, the results are saved and dispatched for display to the user. The process repeats

for every window of data and is a continuous one.

5.3.3 Number of groups

It is generally assumed that group number K is predefined in KHMC; however, the value of K should

be updated for online generator coherency analysis.

A several methods for deciding of number of groups such as Alkaike information criteria approach

[34] and Silhoutte approach [35] exist. These methods make the decision on an index r = f(K) maximum

or minimum value reached when the value of K is optimal (where f(.) is a single-summit function).

However, for generator coherency grouping, a clear boundary of coherent areas may be vague in some

cases, and such index may not exist.

A better way is to set a threshold *1d for the average within -group distance 1d defined as:

1 , ( )1

i k ii

d dN

(5.9)

where ( )k i refers to the correspondent group index of generator i.

AWGD shows the cluster tightness; less AWGD corresponds to more groups. AWGD is a better

discriminant than Maximum Within-Group Distance (MWGD) [36]. K is decided as follows:

*1 1max{ | }K K d d ; (5.10)

In this study, the threshold of AWGD is defined as follows:

2*1 2

1

10.5N

ii

d xN

(5.11)

where xi is the speed deviation data set of generator i.

Based on (5.10), groups are merged or split according to two cases.

49

5.3.3.1 Group splitting

Number of groups should be increased by splitting an existing group that satisfies the condition in

(5.12a). This is achieved by splitting the group that has largest MWGD. Suppose generator i has the largest

distance towards its group center, during splitting, generator i is taken as a new group center as shown in

(5.11b). All other group centers are preserved.

*1 1d d (5.12a)

new ic x (5.12b)

5.3.3.2 Group merging

It is necessary to decide whether there are more groups than required. Two nearest groups should be

tentatively merged to check (5.13a) still holds. If it does, these two groups should be merges; otherwise,

the present group number is correct.

For merging these two groups i and j, whose inter-group distance is the smallest (with ci and cj are

their group centers, respectively), the new group center is computed using (5.13b).

Table 5.3 Group Merging and Splitting

Case Action

d1 > d1* Continue splitting groups by calling (5.12) and updating group centers through (5.1) ~ (5.6) until d1 < d1*.

d1 < d1* Continue merging groups by calling (5.13) and updating group centers through (5.1) ~ (5.6).

With the merger, the old groups i and j are deleted. This newly obtained group center needs to be

updated using (5.1) to (5.6) again. A summary of the process to determine the suitable number of groups

is illustrated in Table 5.3.

*1 1d d (5.13a)

50

i total i j total jnew

i total j total

H c H cc

H H

; (5.13b)

5.3.4 Offline and online clustering result

5.3.4.1 Offline clustering result

In Figure 5.5 the speed responses of 16 generators after a 50ms three-phase fault at the middle of

transmission line between buses 1 and 2 is shown. The blue lines corresponds to G1 and G8, green lines

corresponds to G2 and G3, yellow lines corresponds to G4, G5, G6, G7, G9, black lines corresponds to

G10, G10, G12, G13, and red lines corresponds to G14, G15, G16, G17. Table 5.3 shows the clustering

results for three cases studies. These cases investigate the effect of initialization of group centers for the

k-means and the KHMC.

Case 1: Using k-means clustering with poor initialization of group centers. All the initial centers are

zeros.

Case 2: Using k-means clustering with good initialization of group centers. Average of all generators

is taken for initial group centers.

Case 3: Using KHMC with poor initialization of group centers.

By visual inspection of Table 5.4 and Figure 5.5, it can be seen that Cases 2 and 3 yield better

clustering results than Case 1. k-means clustering works well only with proper group center initialization

values. However KHMC is insensitive to group center initialization values.

51

Figure 5.5 Speed responses of the sixteen generators in IEEE 68-Bus system

Table 5.4 Offline Clustering Result

Group Case 1 Case 2 Case 3

1 G1,G2,G8 G1,G8 G1,G8

2 G3 G2,G3 G2,G3

3 G4,G5,G6,G7,G9,

G10,G11

G4,G5,G6,G7,G9 G4,G5,G6,G7,G9

4 G12,G13 G10,G11,G12,G13 G10,G11,G12,G13

5 G14,G15,G16 G14,G15,G16 G14,G15,G16

5.3.4.2 Online clustering result

In online clustering, there might be different clustering result for each window of data. Generators

that are in the same group might be clustered into different group with the next window of data; however,

most coherent generators still tend to oscillate coherently.

Case I. 100ms three phase short circuit fault at bus 1.

A 100ms three-phase fault occurs at bus 1 at t = 3s. Shown in Figures 5.6 and 5.7 are the speed

responses of all 16 generators and online coherent generator groups, respectively. Table 5.5 presents

offline (using 18 seconds of speed data) and online (snapshots at three instances: 8s, 10s and 15s) coherent

0 2 4 6 8 10 12 14 16 180.99

0.995

1

1.005

1.01

Time [s]

speed in p

.u

52

generator groups using KHMC. Note that in the online clustering G1 and G8 are clustered in different

groups since they are close to the faulted bus.

Figure 5.6 Speed response of generators following fault at bus 1

Figure 5.7 Online coherent generator groups for a three phase short circuit fault at bus 1 in Figure 5.1

0 2 4 6 8 10 12 14 16 180.994

0.996

0.998

1

1.002

1.004

1.006

Time [s]

speed in p

.u.

0

5

10

15

20

0

5

10

15

201

2

3

4

5

6

7

Time [s]Generator index

Gro

up index

53

Table 5.5 Coherency Grouping Result for Case I

Group Offline Clustering

during 0~18s

Online Clustering

at 8s

Online Clustering

at 10s

Online Clustering

at 15s

1 G1 G1 G1 G1

2 G2,G3 G2,G3 G2,G3 G2,G3

3 G4,G5,G6,G7,G9 G4,G5,G6,G7,G9

G4,G5,G6,G7,G9 G4,G5,G6,G7,G9

4 G8 G8 G8 G8

5 G10,G11 G10 G10 G10,G11

6 G12,G13 G12,G13 G11,G12,G13 G12,G13

7 G14,G15,G16 G11,G14,G15,G16

G14,G15,G16 G14,G15,G16

Case II. 100ms three phase fault at bus 8.

A 100ms three-phase fault occurs at bus 8 at t = 3.5s. . Shown in Figures 5.8 and 5.9 are the speed

responses of all 16 generators and online coherent generator groups, respectively. At steady state before

the event happens, there is no oscillation, so that all 16 generators are clustered into one group. Later on,

clustering result might change in respect to time, but coherent generators still tend to be classified in same

groups.

Table 5.6 presents offline (using 18 seconds of speed data) and online (snapshots at three instances:

8s, 10s and 15s) coherency groups using KHMC. At 8s, G9 lost coherency with {G4, G5, G6, G7} for a

short while. G9 is much farther from the faulted bus than {G4, G5, G6, G7}. At 10s, adjacent groups {G1,

G8}, {G2, G3} and {G10, G11, G12, G13} merge.

54

Figure 5.8 Speed response of generators following fault at bus 8

Figure 5.9 Online coherent generator groups for a three phase short circuit fault

at bus 8 in Figure 5.1

0 2 4 6 8 10 12 14 16 180.994

0.996

0.998

1

1.002

1.004

1.006

Time [s]

speed in p

.u.

05

1015

20

0

5

10

15

201

2

3

4

5

6

7

8

Time [s]Generator index

Gro

up index

55

Table 5.6 Coherency Grouping Result for Case II

Group

index

Offline

Clustering during

0~18s

Online

Clustering at 8s

Online

Clustering at 10s

Online

Clustering at 15s

1 G1 G1,G8 G1,G2,G3, G8,G10,G11,G12,G13

G1,G8

2 G2,G3 G2,G3 G4,G5,G6,G7,G9 G2,G3

3 G4,G5,G6,

G7,G9

G4,G5,G6,G7 G14,G15,G16 G4,G5,G6,

G7,G9

4 G8 G9 G10,G11, G12,G13

5 G10,G11 G10,G11 G14,G15, G16

6 G12,G13 G12,G13

7 G14,G15,G16 G14,G15,G16

5.4 Summary

This chapter elaborated the methodology of generator clustering under different operating conditions

using two approaches: hierarchical clustering and KHMC. The former is suitable for drawing a detailed

dendrogram during offline clustering, while the latter is suitable for both offline and online clustering. The

offline clustering results yielded by these two approaches agree with each other under the basic operation

condition. With the KHMC based clustering algorithm, change of generator coherency during power

system transient can be captured.

56

CHAPTER 6

COHERENCY BASED DAMPING CONTROLLER

6.1 Introduction

There are many methods for damping oscillations in a power system. Traditional PSSs are installed

to damp local and intra-area oscillations, as elaborated in Chapter 4. Generally, the PSSs use respective

generator speed deviation signals as input signals to generate supplementary control signals that are

provided to Automatic Voltage Regulators (AVRs). However, locally measured generator speed signal

may not contain sufficient information to uncover the characteristics of inter-area oscillation modes [5];

as a result, local PSSs are not effective to damp inter-area oscillations. Fortunately, with the deployment

of Phasor Measurement Units (PMUs) in the power system, speed signals from remote generators can be

made available as additional input signals for the design of advanced damping controllers.

As for damping controller design using remote measurements, an overview of a Wide Area Control

(WAC) system structure is suggested in [6]; the importance of WAC using PMU data to maintain power

system stability is elaborated. Though a fuzzy controller making use of PMU measurements of voltages

and reactive powers is able to maintain voltage stability, the control approach by capacitor/reactor bank

switching may not be swift and accurate enough to damp inter-area oscillations. A two-area system based

real-time implementation of a wide-area controller by AVR supplementary control considering

communication delays is presented in [37]. The design approach in [37] is completely data-driven, with

the control law implemented by a neural network providing supplementary control signals to all generators.

For large power systems, it may not be practical to provide supplementary control to all generators. In

[38], WAC is applied to a large power system based on a linearized mathematical model; effective

57

measurement and control signals to damp inter-area oscillations are selected using geometric approach.

However, the damping control signal is based on a single remote measurement; and an accurate model of

a large power system is difficult to obtain. An innovative damping control method is implemented without

designing any wide area controllers in [39]. The local PSSs’ outputs are combined a matrix gain to

generate modulated PSS signals to the AVRs in a 12 bus power system with three generators. The optimal

matrix for modulating the initial PSS signals was obtained using the particle swarm optimization algorithm.

However, this approach is not directly applicable for larger power systems due to increased matrix size;

besides, since the local controllers have been designed only to address the local and intra-area oscillations,

they may not work effectively at the frequency range of inter-area oscillations. A typical H∞ wide-area

PSS design is proposed in [40]. Despite of the robustness of designed controller to uncertain system

parameters, the design with pole-placement constraints may not have a solution; also, since general H∞

design achieves a controller with the same order with system states; it has to be further reduced to form a

PSS at the risk of reduced efficacy. In [1], the concept of Virtual Generator (VG) is applied in design of a

single-input multiple-output controller using adaptive critic designs; it is indicated that a VG is a

mathematical equivalent of a group of generators that tend to oscillate coherently in response to

disturbances. However, the damping controller uses only one VG speed; this may not provide sufficient

information to damp inter-area oscillations over a wide range of operating conditions.

In this study, power system conditions that give rise to inter-area oscillations using Stochastic

Subspace Identification (SSI) based modal analysis are studied; and a new approach to implement

supplementary PSS based on VGs (VG-PSS) to damp inter-area oscillations is presented, as shown in

Figure 6.1. Speed deviations from all the large generation units are remotely measured and sent to a control

center, which implements coherency analysis and uses the proposed VG-PSS to generate a supplementary

control signal. The generator choice for the supplementary control location is determined based on the

58

generator that has maximum controllability on dominant weakly damped inter-area mode(s) in a power

system. The overall flowchart of the suggested design approach is shown in Figure 6.2, which is further

elaborated in theoretical details in following sections.

Figure 6.1 The diagram of the proposed control scheme with VG-PSS

𝐺1 𝐺2 𝐺3 𝐺𝑅

Time delay

𝜏1 𝜏2 𝜏3 𝜏𝑁 𝜏R

Control Center

Coherency Analysis

PSS + Time-delay compensator

VG - PSS

𝑉′𝑉𝐺−𝑃𝑆𝑆

𝜔1 𝜔2 𝜔3 𝜔𝑟 𝜔N

𝜔𝑉𝐺2 𝜔𝑉𝐺−𝑀

Supplementary control signalPower System

Generators 𝐺𝑁

𝜏control

…

… …

Synchronization

𝜔′1 𝜔′2 𝜔′3 𝜔′𝑟 𝜔′N

(𝑡)

(𝑡) (𝑡) (𝑡) (𝑡) (𝑡)

𝜔VG1 (𝑡) (𝑡) (𝑡)

(𝑡) (𝑡) (𝑡) (𝑡) (𝑡)

𝑉𝑉𝐺−𝑃𝑆𝑆 (𝑡)

59

Figure 6.2 The overall flowchart of design approach

6.2 Development of VG-PSS

In this section, a VG-PSS that is heuristically tuned according to modal analysis results, is proposed

for supplementary damping control. The modal analysis presented is based on a data-driven system

identification approach. In addition, the determination of virtual generator(s) based on coherency analysis

is presented and the tuning of VG-PSS is elaborated in the following sub-sections.

6.2.1 Modal analysis based on system matrices

Besides facilitating controller design, modal analysis also provides a way to exam the efficacy of a

controller. Prior to performing modal analysis, it is necessary to obtain a model for the power system

without detailed mathematical model of every component that captures the full dynamics. Chapter 3 has

elaborated an approach to obtain system matrices and to carry out modal analysis. In this study, the AVRs

Start

SSI-based system identification

Modal analysis

Power system simulation under contingency

Cost function calculation

Update of VG-PSS parameters using PSO

Maximum iteration achieved ?

Y

N

End

Verification of results

60

of all the generators are regarded as the system inputs where PRBSs are injected as disturbances to trigger

power system transients, while the speed deviations of all the generators are measured as outputs. With

the application of SSI algorithm, the system matrices A,B,C,D are identified. Thereafter, the observability

and controllability factors for each generators can be calculated. It can be seen from Figure 3.5 that the

generator G8 and G9 are with the highest controllability factor; thus, damping controller output can be

applied on G8 and G9.

6.2.2 Inter-area oscillation analysis

Inter-area oscillation refers to the phenomenon where two areas in a power system oscillate against

each other generally at a low frequency. These areas may contain one or more synchronous generators.

When the operating condition is pushed toward stability limit in a power system, oscillations may occur

due to lack of damping torque as can be identified using techniques elaborated in Chapter 3. The modes

of oscillations are largely determined by the power system topology, as well as the parameters of

generators and transmission lines. In Chapter 2, it has been verified that as the active power transfer from

NE to NY increases, the power flow in the transmission lines rises, and the damping torque for the 0.22

Hz oscillation between NE and NY decreases. The operating condition with high active power transfer

from NE to NY serves as benchmark to verify the effectiveness of damping controller designed in this

study.

6.2.3 Structure of VG-PSS

The traditional structures of local PSSs are composed of a washout component, a lead-lag

compensator and a magnitude limiter. Through compensation of phase angle at a specific oscillation mode,

a torque is made exactly in opposite phase of speed deviation, leading to increased damping ratio.

However, according to the analysis, local PSSs may not effectively deal with inter-area oscillation modes,

for the generators of maximum controllability are not necessarily with maximum observability. In

61

contrast, a PSS using remote measurement is more capable to provide damping torque for inter-area

oscillations. In previous research of Wide Area Control (WAC), the input signal to the controller uses

either the speed deviation of one generator of maximum observability or the difference of average speed

between two the groups of generators that are oscillating against each other. In this research, on basis of

the local PSS structure, a proposed VG- PSS is shown in Figure 6.3.

Figure 6.3 The proposed structure of VG-PSS

Taken as the inputs are the virtual generator speeds that are mathematical simplification for groups

of coherent generators, as explained in detail in the coming sections. AVR supplementary signal at

generator of maximum controllability is taken as the output. This PSS is expected to make use of wide

area information to stabilize the power system. Ten parameters are to be decided. The value of K1~KM

reflect the impact of each virtual generator speed on the control efficacy; larger values of Ki signifies that

the ith virtual generator has larger engagement in this oscillation. T1~T4 reflect the oscillation frequency

as well as the compensation angle. Although the concerned frequency range of the proposed PSS differs

from that of local PSSs, its parameters will be configured in an intelligent way as in the analysis of

following sections.

In this approach, a heuristic algorithm Particle Swarm Optimization (PSO) is deployed to tune the

parameters. The optimal parameters will be reached by repetitively testing the efficacy of each set of

𝐾1

𝐾2

𝐾3

……

……

𝐾𝑀

Σ 10𝑠

1 + 10𝑠𝐾0

𝑇1𝑠 + 1

𝑇2𝑠 + 1

𝑇3𝑠 + 1

𝑇4𝑠 + 1𝐾𝐶

1 + 𝑠𝑇𝐶11 + 𝑠𝑇𝐶2

2

Δ 𝜔𝑉𝐺1

Δ 𝜔𝑉𝐺2

Δ 𝜔𝑉𝐺3

Δ 𝜔𝑉𝐺−𝑀

𝑉𝑜

0.1

−0.1 Washout Time-delay compensator Limiter

62

WAPSS parameters using 20 particles. During the tuning process, the cost function for each set of

parameters is figured out through real-time simulation on Real-Time Digital Simulator (RTDS) with the

full model of every component in the power system.

6.2.4 Determination of virtual generators

Though damping control is applied using remotely measured signals, the large scale of power system

makes it prohibitive to take all generator speed responses as the controller input. Fortunately, it has been

shown in Chapter 4 that generators generally oscillate in coherent groups. Generally, generators with small

electrical distance show similarity in speed responses following a contingency. A Virtual Generator (VG)

is a mathematical equivalent of a group of coherent generators. A complicated multi-machine power

system can be significantly simplified with the concept of virtual generators. To achieve this, hierarchical

clustering algorithm can be applied based on the speed response data of all generators; a dendrogram is

yielded so that the generators are classified into several groups under certain threshold.

In this approach, four steps are introduced to obtain the virtual generators in a power system,

i. The power system is disturbed with PRBS injection [41] at the supplementary input site of

each generator; and speed responses of all generators are collected.

ii. A hierarchical clustering algorithm is implemented and the diagram is formed showing the

coherency of generators.

iii. Through visual inspection, an α-cut threshold is decided and the groupings of generators

are formed [23].

iv. The virtual generator speed for each group can be calculated using the formula,

1 1 2 2

1 2

......

n n

i

n

i i i i i iVG

i i i

H H HH H H

(6.1)

It can be seen from (6.1) that two conditions must be satisfied in order to calculate the VG speeds:

first, all the local generator speeds need to be observable by a control center (Figure 6.1) that executes the

63

calculation. With the advent of Phasor Measurement Units (PMUs), the real-time variation of frequency

at each generator bus can be measured, which is directly linked with the generator speed deviations. For

a larger system that covers large geographic domain with large number of generators, PMUs are installed

on a limited selection of generators that best represents system dynamics and helps deriving the virtual

generator model in each coherent group. Second, the measured frequencies from all generator buses are

real-time data flows and thus need to be synchronized. Fortunately, PMU is able to give each measured

data with a time stamp with the aid of a Global Positioning System (GPS) radio clock, as a result, the

synchronization of real-time measurement at all the generators can be realized. A time-delay is resulted

during the synchronization and communication of remote PMU data to the control center.

It is computationally and practically challenging to design a supplementary controller making use of

all generator speeds especially for a large power system nor is it necessary. A VG is a good representation

of a group of generators that behave in a similar manner. Although the concept of VG is originally

suggested as mathematical simplification of multiple generators, the determination of VGs is data-based.

The clustering/grouping approach uses the measured speed responses of generators following PRBS

disturbances at the AVRs of all generators, which represents the coherency of generators in a general

sense, and is a better approach rather than a clustering approach following a fault or an increase of

generation, as has been observed in [11] that the site and type of fault can largely impact the coherency of

generators. Considering that the generator coherency is subjected to change of operating conditions and

contingencies, variation in generator coherency occurs. However, based on the fact that geologically

adjacent generators tend to oscillate coherently, and that contingencies only lead to very slight change of

the overall power system topology, the proposed virtual generator modelling based on fixed coherent

groups is assumed in this study. Though efficacy of this design is demonstrated in the simulation results,

64

future research will use artificial immune system based adaptive controller to handle the variation of

generator coherency, leading to improved damping effectiveness.

6.2.5 PSO for VG-PSS tuning

Particle Swarm Optimization (PSO) is an adaptive algorithm that heuristically searches best

solutions with swarm intelligence; it is widely used for parameter tuning [42]. The parameters to be

determined are mirrored to the positions of particles; and a fitness function to be minimized is defined as

a satisfactoriness measurement for a set of parameters. To search for a minimal value of fitness function,

each particle keeps updating its position by actively moving toward the local and global optimum point,

respectively defined as the historical position of its own and of all particles that correspond to the smallest

fitness function value. During the optimization, the fitness function is monotonically decreasing until all

particles coherently converge to a global optimal position in a final stage. Due to its robustness to nonlinear

non-convex problems, PSO is adopted in this study to optimize the parameters of VG-PSS. The following

part of this section elaborates technical details for implementation, including the determination of fitness

function and the algorithm of parameter updating.

In this study, the position of a particle pi represents the set of all parameters corresponding to Figure

6.3, thus ,1 ,2 , ,1 ,2 ,3 ,4[ , ,..., , , , , ]i i i i M i i i ip K K K T T T T . Under this set of parameters, speed responses following a fault

are obtained through simulation; and a fitness function is required to analyse the speed responses. There

are generally two ways to determine the fitness function: through either frequency domain or time domain.

Since it is expected that a decreased oscillation be observed from the speed responses with the effect of

controller, the damping ratio under the concerned frequency can be taken as the cost function, which is

obtained by modal analysis of speed deviation simulation results. Experiments using this frequency-

domain based cost function shows ability to reject unexpected oscillation modes brought by the new set

of parameters obtained in the optimizing process. Alternatively, a cost function can be straightforwardly

65

defined by analysing the time series of speed response curves; for example, the H2-norm (i.e. squared

mean average through time) of speed responses can be taking as the cost function. Time-domain based

cost function leads to a better final-stage performance despite of slow convergence. It is desired to

combine the merits of both these two options: a frequency-domain part of the cost function is expected to

play a more important role at the first stage so that the particles approaches an appropriate solution with a

fast speed, while a time-domain part of cost function improves the efficacy of controller at the final stage.

Thus, the following cost function is adopted:

20

1 1min{ , } ( ( ))

GN N

f ii j

J j

(6.2)

in which ξf denotes the damping ratio near the frequency f; ( )i j denotes the speed deviation the i’th

generator at the time step j; α is a large real value; and ξ0 denotes a threshold of damping ratio; NG is the

generator number, while N is the length of data points. At the beginning of tuning process, since the

damping ratio under parameters of most particles may be very low, the judgement of performance is

mainly decided first term in (6.2). However, as the performance of each particle improves so that the

damping ratio ξf is larger than the threshold ξ0, the performance is only dependent on the second term that

reflects the speed deviation profiles of all generators. The parameters are further adjusted to minimize the

second term so that performance is further improved.

Define pi,lbest and pgbest as the local and global optimum point of particle pi respectively. At each

iteration, all particles are updated through (6.3) ~ (6.4). For all i’s.

, 0 , 1 1 , , 1 2 , 1( ) ( )i k i k i lbest i k gbest i kv v p p p p (6.3)

, 1 , ,i k i k i kp p v (6.4)

Meanwhile, whenever the cost fitness function is calculated with the updated particle position, ,i lbestp

and gbestp are also updated through (6.5) and (6.6).

66

, ,min{ , }new oldi lbest i lbest ip p p ; (6.5)

min{ , }new oldg g ip p p ; (6.6)

In the final stage, all the particles ultimately converge to a solution, and is taken as the solutions.

Shown in Figure 6.4 is flowchart of PSO parameter-tuning algorithm based on the speed deviation data

following PRBS injection at all the AVRs.

Figure 6.4 PSO flowchart for VG-PSS parameters tuning algorithm.

Update of local and global optimum using (6.5)~(6.6)

Start

Initialization of VG-PSS parameters

Go to the next particle, determination of fitness function using (6.2)

Iterations >= Reference?

Update of Parameters using (6.3) ~ (6.4)

Y

N

End

All particles iterated?

Y

N

67

6.2.6 PSO versus other design techniques

Numerous techniques exist for the design of supplementary damping controllers. Traditional pole-

placement is effectively applied for design of single-input single-output controller [29], yet it is not the

only way; other approaches such as bacterial foraging algorithm (BFA) and adaptive critic designs (ACDs)

have also been used for wide area controller designs, as shown in [43] and [44]. For this study, since the

proposed VG-PSS uses speed deviations of multiple VGs, and the contribution of each VG for the control

signal is unknown, it is preferred to use the PSO-based heuristic approach in this study. Also, despite its

robustness, H∞-based approach yields several high-order separate controllers linking each VG speed

deviation input to the controller output; in contrast, there are limited amount of parameters in the proposed

VG-PSS that can be realized with a traditional lead-lag structure. With a simple mathematical form, the

VG-PSS establishes a standard schematic for the supplementary damping control, with the parameters

best tuned by PSO. The effectiveness of VG-PSS controller is presented in Section 6.3.

6.2.7 Time delay compensation

In the proposed VG-PSS, time delay is incurred about in two processes: (i) τPMU: the communication

between the control center and the PMUs; (ii) τcontrol: the communication between the control center and

the generator that the supplementary control is applied too. In this study, these two time delays are merged

as τ = τPMU + τcontrol, and is compensator inside the VG-PSS by the transfer function given in (6.7).

2

1

2

1( )1

CC C

C

T sG s KT s

(6.7)

where 11 1 sin( / 2)

1 sin( / 2)CT

and 2

1 1 sin( / 2)1 sin( / 2)CT

. ω is the oscillation frequency of concern. KC is

normalized so that ( ) 1CG j . This compensator is able to effectively provide a phase angle

compensation at the oscillation frequency of concern ω [45]. For a wide area control system, time delay

68

τ can be determined with the aid of GPS clock labels included in the PMU data. In this study, τ is assumed

to be time-invariant.

6.3 Simulation results

The contingency used for PSO tuning is a 50ms fault on Bus 27. Corresponding to different

contingencies, three case studies are shown to indicate the efficacy of VG-PSS damping controller. For

each of them, the VG-PSS is installed either on G8 or on G9. With VG-PSS on G8 or G9; and the

optimized parameters are shown in Table 6.1. In case studies I to III, a time delay of 100ms is considered.

Table 6.1 The optimized parameters of the VG-PSS

Parameters Case I

With VG-PSS on G8

Case II

With VG-PSS on G9

1K 0.9587 -0.2318

2K 0.363 -0.0524

3K -1.00 0.8703

4K -0.7126 0.5533

5K 1.00 0.9963

0K 25 19.2026

1T 1.5416 0.4680

2T 0.4024 0.7744

3T 5.2393 6.8278

4T 4.1175 2.7501

Case Study I: The system is originally at operating condition II presented in the appendix Table A.1.

A 50ms three-phase fault takes place at Bus 2, causing the tripping of transmission lines between Bus 1

and Bus 2. Shown in Figure 6.5 are the speed deviation responses of selected generators, the VG-PSS is

installed on G9.

69

Figure 6.5 Case Study I -- The speed deviations plots of selected generators with VG-PSS on G9.

Through modal analysis, with no PSSs, the damping ratio is 0.4%, and the power system is

marginally stable; with only the local PSSs, the damping ratio is 6.1%, while with only the VG-PSS

installation on G9, the damping ratio is 11.6%, with the cooperation of VG-PSS with local PSSs, the

damping ratio improved to 28.9%.

The VG-PSS installed on G8 shows similar effectiveness as shown in Figure 6.6. In order to verify

that the two VG-PSSs can be working cooperatively, Figure 6.6 compares the control effect with both

0 5 10 15 20 25-4

-2

0

2

4

x 10-3 G1

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-4

-2

0

2

4x 10

-3 G4

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-4

-2

0

2

4

x 10-3 G8

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-4

-2

0

2

4x 10

-3 G9

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-1

0

1x 10

-3 G13

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G14

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G15

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G16

Time : s

Speed d

ev :

p.u

.

No PSSs

With local PSSs

With VG-PSS

Local PSSs & VG-PSS

70

VG-PSSs and with only one VG-PSS installed on G8 or G9. It can be concluded that, when VG-PSSs are

installed on both G8 and G9, better damping effectiveness is achieved than VG-PSS installed on each

individual generator. Even without installation of local PSSs, the cooperating VG-PSSs are able to provide

significant damping torque.

Figure 6.6 Case Study I -- The speed deviations plots of selected generators for different sites of

VG-PSS installations.

0 5 10 15 20

-2

0

2

4

x 10-3 G1

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20

-2

0

2

4

x 10-3 G4

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-4

-2

0

2

4

x 10-3 G8

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20

-2

0

2

4

x 10-3 G9

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-1

0

1x 10

-3 G13

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G14

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G15

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G16

Time : s

Speed d

ev :

p.u

.

VG-PSS on G9

VG-PSS on G8

VG-PSS on G8 and G9

Local PSSs & VG-PSS on G8 and G9

71

Case Study II.A: With the transmission line Bus1–Bus2 already tripped, the system changes to

operating condition III.A in the appendix Table A.1. A 50ms three-phase fault happened at Bus 8. Shown

in Figure 6.7 are the speed deviation responses of selected generators.

Figure 6.7 Case Study II.A -- The speed deviations plots of selected generators with VG-PSS on

G9.

0 5 10 15 20 25

-2

0

2

x 10-3 G1

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25

-2

0

2

x 10-3 G4

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25

-2

0

2

x 10-3 G8

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25

-2

0

2

x 10-3 G9

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-1

0

1x 10

-3 G13

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G14

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G15

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G16

Time : s

Speed d

ev :

p.u

.

No PSSs

With local PSSs

With VG-PSS

Local PSSs & VG-PSS

72

Without local PSSs and VG-PSS, the power system becomes unstable following the contingency.

Through modal analysis, with only the local PSSs, the damping ratio is only 0.5% which is close to the

stability margin; with only the VG-PSS on G9, the damping ratio improves to 7.5%; and with both local

PSSs and the VG-PSS on G9, the damping ratio improves to 16.87%. Figure 6.8 compares the control

effect with both VG-PSSs and with only one VG-PSS installed on G8 or G9 showing the ability of

cooperating VG-PSSs to improve the damping effectiveness.

Figure 6.8 Case Study II.A -- The speed deviations plots of selected generators for different sites of VG-PSS installations.

VG-PSS on G9

VG-PSS on G8

VG-PSS on G8 and G9


0 5 10 15 20

-2

0

2

4x 10

-3 G1

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20

-2

0

2

4x 10

-3 G4

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-4

-2

0

2

4x 10

-3 G8

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20

-2

0

2

4x 10

-3 G9

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-1

0

1x 10

-3 G13

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G14

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G15

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G16

Time : s

Speed d

ev :

p.u

.

73

Case Study II.B: The system changes to operating condition III.B listed in Table A.1 in the appendix.

Comparing to Case Study II.A, the load on Bus 1 has increased by 100%, from 256 MVA to 512 MVA.

The increased active power is supplied by G13. The same contingency as in Case Study II.A is applied

and the speed deviation responses of selected generators are shown in Figure 6.9.

Figure 6.9 Case Study II.B -- The speed deviations plots of selected generators with VG-PSS on G9 under a new load condition

Without local PSSs and VG-PSS, the power system becomes unstable following the contingency.

Through modal analysis, with only the local PSSs, the damping ratio is only 1.5% which is close to the

0 5 10 15 20

-2

0

2

x 10-3 G1

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-4

-2

0

2

4x 10

-3 G4

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20

-2

0

2

x 10-3 G8

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-4

-2

0

2

4x 10

-3 G9

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-1

0

1x 10

-3 G13

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G14

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G15

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G16

Time : s

Speed d

ev :

p.u

.

No PSSs

With local PSSs

With VG-PSS

Local PSSs & VG-PSS

74

stability margin; with only the VG-PSS on G9, the damping ratio improves to 7.9%; and with both local

PSSs and the VG-PSS on G9, the damping ratio improves to 17.54%.

Case Study III: The system operation is changed to operating condition IV as shown in Table A.1 in

the appendix. A 50ms three-phase fault is applied at Bus 27. Shown in Figure 6.9 are the speed deviation

responses of selected generators.

Figure 6.10 Case Study III -- The speed deviations plots of selected generators with VG-PSS on G9.

In this case, whether local PSSs are installed or not, if VG-PSS is not installed, the system becomes

unstable following the contingency. With the VG-PSS installed, damping ratio is 6.2% without local PSSs,

and is 11.2% when local PSSs are installed. Figure 6.10 compares the control effect with both VG-PSSs

0 5 10 15 20 25

-2

0

2

4x 10

-3 G1

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25

-2

0

2

x 10-3 G4

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25

-2

0

2

4x 10

-3 G8

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25

-2

0

2

4

x 10-3 G9

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-1

0

1x 10

-3 G13

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G14

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G15

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20 25-2

0

2x 10

-3 G16

Time : s

Speed d

ev :

p.u

.

With local PSSs

With VG-PSS

Local PSSs & VG-PSS

and with only one VG-PSS installed on G8 or G9, and same conclusions can be drawn as for Case Studies

I and II.

Figure 6.11 Case Study III -- The speed deviations plots of selected generators for different sites of VG-PSS installations.

It can be seen from Figures 5 ~ 10 that with the VG- PSS implementation, the power system settles

to steady state much faster. Also, the damping ratios are improved. Thus, the designed VG-PSS(s) is able

to stabilize the power system for all these three cases. The settling time of the generator speed deviations

(shown in Figures 6.5, 6.7, 6.9 and 6.10) for case studies I, II and III are given in Table 6.2. Herein, the

settling time is defined as the time it takes for the oscillations to settle within ±5% of the maximum speed

75

0 5 10 15 20

-2

0

2

4x 10

-3 G1

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20

-2

0

2

4x 10

-3 G4

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-4

-2

0

2

4x 10

-3 G8

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-4

-2

0

2

4

x 10-3 G9

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G13

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G14

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G15

Time : s

Speed d

ev :

p.u

.

0 5 10 15 20-2

0

2x 10

-3 G16

Time : s

Speed d

ev :

p.u

.

VG-PSS on G9

VG-PSS on G8

VG-PSS on G8 and G9


76

deviation. Again, it can be observed that VG-PSSs in combination with local PSSs provides the minimal

settling time in all three case studies.

Table 6.2 Settling time of generator speed deviations for the three case studies (in seconds)

Cases With no PSSs

(s)

With only local PSSs

(s)

With only VG-PSSs on G8

(s)

With only VG-PSSs on G9

(s)

With both VG-PSSs

and local PSSs

(s)

Case Study I >50 28.2 14.6 16.4 6.1

Case Study II.A Unstable >50 26.6 27.6 7.2

Case Study II.B Unstable >50 24.6 26.5 7.0

Case Study III Unstable Unstable 36.2 40.8 8.8

The effectiveness of time-delay compensators is shown in Figure 6.12. The comparison of speed

responses with and without the time-delay compensators for G9 are plotted for different time delays under

Case Study II. It can be seen that without compensation, the control effect worsens as the time-delay

increases (Figure 6.12(c)). However, the proposed compensator is able to counteract the time delay and

improve the damping effectiveness.

77

Figure 6.12 Impact of time delay for the speed responses at G9.

(a) 50ms time delay (b) 100ms time delay (c)200ms time delay

6.4 Summary

In this study, SSI-based modal analysis is used first to identify the operating conditions that give rise

to inter-area oscillation. It is shown that oscillation occurs when the center of generation does not overlap

with the load center. The concept of virtual generators is used to cluster the synchronous generators into

several coherent groups in an offline manner. Based on the VGs determined, supplementary wide area

controller using virtual generator speeds is developed. The particle swarm optimization algorithm is

applied to determine the optimized parameters of VG-PSS. Real-time simulation of the IEEE 68-bus

system with VG-PSS(s) have illustrated the enhanced damping of the proposed approach for damping

inter-area oscillations and maintaining the stability of a power system.

0 5 10 15 20-2

0

2

x 10-3

Time : s

(a)

Spee

d de

viat

ion

: p.u

.

0 5 10 15 20-2

0

2

x 10-3

Time : s

(b)

Spee

d de

viat

ion

: p.u

.

0 5 10 15 20-2

0

2

x 10-3

Time : s

(c)

Spee

d de

viat

ion

: p.u

.

With only local PSSs

Local PSSs and VG-PSS

without compensation for time delay

Local PSSs and VG-PSS

with compensation for time delay

78

CHAPTER 7

ADAPTIVE DAMPING CONTROLLER

7.1 Introduction

Traditionally, remote measurements based damping controllers have fixed parameters. In [38], inter-

area oscillations are damped by static VAR compensator based on optimal measurement signal selection.

In [46], WAC is implemented through phase compensation. An earlier study that shows a virtual generator

based power system stabilizer (VG-PSS) for damping of inter-area oscillation modes is reported in [13].

This VG-PSS uses remotely measured virtual generator speeds for supplementary damping control at the

generator of maximum controllability. These above-mentioned controllers have fixed parameters.

However, it is desired that the parameters self-tune online so that the controllers are adaptive to various

changing conditions that affect control effectiveness and system performance.

In [47], a conventional multiple-model adaptive control scheme is applied to form a control signal

from a bank of controllers; yet the number of operating conditions corresponding to each pre-designed

controller is limited. A neural-network based adaptive critic control scheme for WAC is suggested in [1];

however, the update of neural networks parameters is offline, thus the parameters of this controller remain

unchanged during the real-time operation of the power system. In [48], artificial immune system (AIS) is

introduced for adaptive excitation control of generators in an electric ship to handle high energy demand

loads such as pulsed loads. The conception of AIS provides a good methodology for development of an

adaptive controller. Since the parameters of controllers can be automatically changed in response to

different states, the controllers are able to operate under more critical operating conditions.

79

7.2 Problem formulation

In this study, the concept of AIS is applied for the development of a wide area signals based adaptive

damping controller for inter-area oscillations. Based on an optimal (innate) controller with best tuned

parameters developed in [13], the AIS further modifies the control policy by temporarily adjusting

controller parameters for unseen and abnormal disturbances. This is the second aspect of the AIS concept:

an adaptive immune controller. The wide area signals are derived from virtual generators formed by

coherency grouping. Each coherent group is modeled by a virtual generator. Comparing to a damping

controller with fixed parameters, the AIS-based control is more agile and can stabilize a power system

under various operating conditions and disturbances due to its innate and adaptive immune properties. By

modeling biological immune systems, AIS adaptively and interactively generates feedback control signals

to restore a system to its steady state. During the development of the optimal controller, generators in the

power system are assumed to be oscillating in fixed coherent groups. However, it is known that a variation

of operating conditions could lead to different coherent groups. For instance, generators near the fault site

tend to lose oscillatory coherency [1]. Thus, the performance of the innate controller is degraded. Besides,

since the oscillations occur in multiple frequencies during transients, a control with fixed parameters may

not be robust enough to handle with the complicated power system dynamics. Fortunately, the impact of

new coherent groups and multiple modes can be minimized by adaptive nature of the AIS.

7.3 Artificial immune system

The defensiveness of a biological immune system relies on the presence of innate and adaptive

immunity. As an analogy to a biological immune system that is resistant to antigen incursion, AIS can

provide enhanced power system stability by improving controller adaptiveness to disturbances and

contingencies. To maximize control effectiveness, an AIS based adaptive controller is introduced in this

study. In the application of AIS, the innate immunity is realized through optimal parameter configuration,

80

and the adaptive immunity is realized through adaptive change of controller parameters, as elaborated in

the following subsections.

7.3.1 Innate immunity

In the biological immune system, innate immunity refers to the ability of living body (such as human)

to provide the primary defense reactions against incurring antigens by generating neutrophils (such as

blood cells) to identify and destroy the antigens. The antigens are bound and engulfed by macrophages

before being further demolished by neutrophils like white blood cells. The control mechanism in innate

immunity is the ability to generate a control signal to maintain stability in response to the measured

perturbation from equilibrium. This response behavior can be achieved by an optimal action and can be

compared to a control system with fixed parameters.

7.3.2 Adaptive immunity

In the biological immune system, the dendritic cells that bind antigens can be further evolved into

antigen presenting cells (APCs), B cells and T cells. Based on this, a more sophisticated feedback law

mechanism to provide adaptive immunity is present. When an antigen is detected in a living body, APC

is generated that leads to the production of helper T cells. The helper T cells further activate B cells and

killer T cells that swallow and annihilate the antigen. The suppressor T cells function to hinder the activity

of all other cells activated by helper T cells as illustrated in Figure 7.1 [12].

A feedback mechanism adaptively regulates the activity of cells. The presence of invading antigens

leads to more activated helper T cells that significantly increase the amount of killer T cells and B cells.

Over time when the antigens diminish and helper T cells decrease in activity, both killer T cells and B

cells are inhibited by suppressor T cells that have been already generated. Ultimately, the antigens are

completely diminished, and killer T cells and B cells are deactivated.

81

Figure 7.1 A biological immune system

In an AIS-based controlled system, as soon as the system moves away from its steady state, the

controller parameters are regulated over time to restore the system to its steady state as quickly as possible.

The deviation of the controlled system from its steady state is analogous to the antigen, while the amount

of T cells and B cells is analogous to the regulation of controller parameters. When steady state has been

achieved, the controller parameters return to their innate values.

The nominal value for each of the N controller parameters is denoted as pi,standard (i = 1,2, … N). The

deviation of parameter at the moment of k is denoted as Δpi(k) as indicated in (7.1). The mechanism of

parameter updating process using AIS is shown in Figure 7.2.

,standard( ) ( )i i ip k p p k (7.1)

where

( ) ( ) ( )i i ip k TH k TS k (7.2)

Antigen

APC

Helper T Cell

Suppressor T Cell

B Cell Killer T Cell

- - -

+

+

+ +

+

--

82

Figure 7.2 The schematic of the proposed AIS based control for a dynamic system.

It is comprised of two competing terms. The first term is analogous to helper T cells that activates

the control effect; and is directly proportional to Δz as expressed in (7.3), where mi1 is a stimulation factor

to the gain of helper T cells.

1( ) ( )i iTH k m z k (7.3)

The second term in (7.2) corresponds to suppressor T cells that diminish the control effect. It is

inversely related to the amplitude of the changing rate at Δz. TSi (k) can be expressed as (7.4), in which

mi2 is an inhibition factor related to the gain of suppressor T cells. According to (7.4), the faster declining

rate of Δz leads to the larger value of TSi(k), which counteracts the parameter change brought by THi (k).

The output of division block in Figure 7.2 is reset to zero when steady state is reached.

2

2( )( ) exp

( 1)i iz kTS k m z

z k

(7.4)

÷ ÷

×

×

Σ −

+

Optimal controller with parameters pi(k)

Controller output, Δy(k)

System output, Δz(k)

Change of parameters, Δpi(k)

mi1(k)

mi2(k)

THi(k)

TSi(k) exp(－x2) z-1

Δzi (k－1)

Controlled System

System reference input, X ref (k) Disturbance, d(k)

Δz(k)

83

Equations (7.1)-(7.4) can also be applied for the update of any other controller parameters, so that

all of them will be regulated dynamically by AIS. Since two extra AIS parameters (mi1, mi2) are required

for the update of one controller parameter pi, totally 2N AIS parameters are introduced in addition to the

ten parameters in the innate controller (described later).

The adaptive immunity brings about robustness against changes of operating conditions, leading to

enhanced system stability. This is achieved by optimal tuning of innate and adaptive controller parameters,

as elaborated in the following section.

7.4 AIS based oscillation damping controller

In this section, the development of an AIS-based adaptive controller for damping inter-area

oscillation in an interconnected power system is described. The flowchart for the development is given in

Figure 7.3 with details elaborated in the following subsections.

The following subsections describe the test power system used in this study, as well as the innate

and adaptive damping controller.

7.4.1 Innate damping controller

Traditional local PSS makes use of local generator speed deviations to generate a supplementary

control signal, which is superimposed on the voltage reference at the AVR of local generator. In this study,

local PSSs are designed based on H∞ based robust control approaches [12] (as detailed in Chapter 4) to

maintain power system stability. However, since poorly damped oscillations occur under critical operating

conditions, robust wide-area damping controllers are required.

84

Figure 7.3 Flowchart illustrating the development of an AIS based damping controller.

The innate damping controller is based on a VG-PSS introduced in Chapter 6 that makes use of

virtual generator speeds to generate a supplementary control signal at a generator of maximum

controllability, as shown in Figure 7.4. The methodology for tuning the VG-PSS parameters has been

elaborated in Chapter 6.

Start

Stop

Verification of damping effect for innate controller

Satisfactory?

Initialization of innate controller Parameters T0~T

5, K

1~K

4

PSO tuning of T0~T

5, K

1~K

4 with cost function

Verification of damping effect for AIS parameters

Initialization of AIS Parameters m1~m

20

PSO tuning of m1~m

20with cost function

Satisfactory?

Y

Y

N

N

85

Figure 7.4 Diagram of the proposed innate controller scheme.

In this approach, unlike H∞ based controller design that yields five high-order transfer functions

linking the five inputs and the output, the proposed innate controller has a simple mathematical expression

with only ten parameters, facilitating further approaches for adaptive parameter adjustments. The tuned

parameters are shown in Table I of Chapter 6. In the practice, this innate controller is installed at G9. The

method to compensate the time delay induced by data communication was successfully implemented in

earlier study in [13]. Recent researches also see the practice of using neural network based predictions to

overcome the time delay [49].

7.4.2 Adaptive damping controller

Based on the innate controller proposed, an AIS-based adaptive damping controller is developed as

shown in Figure 7.5. For each of the ten innate controller parameters, two extra AIS-parameters are

required. Thus, there are totally 20 AIS-parameters (m1 ~ m20) to be determined. The local speed deviation

Δω9 is used as the input for the AIS, thus the time delay is not considered by the adaptive damping

controller.

The stimulation and inhibition factors are determined through PSO approach, with the cost function

expressed in (7.5),

𝐾1

𝐾2

𝐾3

𝐾4

𝐾5

Σ 10𝑠

1 + 10𝑠𝐾0

𝑇1𝑠 + 1

𝑇2𝑠 + 1

𝑇3𝑠 + 1

𝑇4𝑠 + 1 𝐾𝐶 1 + 𝑠𝑇𝐶11 + 𝑠𝑇𝐶2

2

Δ 𝜔𝑉𝐺1

Δ 𝜔𝑉𝐺2

Δ 𝜔𝑉𝐺3

Δ 𝜔𝑉𝐺4

Δ 𝜔𝑉𝐺5

𝑉𝑜 0.1

−0.1 Washout Time-delay

compensator Limiter Lead-lag compensator

Generator Excitation

System

https://en.wiktionary.org/wiki/%CE%94

86

162

1 1( ( ))

N

ii j

J j

(7.5)

Where Δωi(j) is the speed deviation response of generator j at the moment of j. During the tuning of PSO,

each set of system parameters is represented as a particle. The ith particle is updated in terms of (7.6) and

(7.7),

, 0 , 1 1 , , 1 2 , 1( ) ( )i k i k i lbest i k gbest i kv v p p p p (7.6)

, 1 , ,i k i k i kp p v (7.7)

The cost function (7.5) only considers the time domain speed deviation responses. According to

Parseval’s theorem [50], the presence of any oscillation mode adds a positive value to J. Thus, the

optimization will enhance the damping for various oscillation modes.

The tuning process is carried out under simulation of 50ms three-phase faults at Bus 31. The power

system as well as the control circuit is simulated using RTDS; the delay block z-1 is realized via a first-

order holder with 10Hz sampling frequency. The PSO algorithm is implemented through MATLAB

programs, which interface RTDS with an RSCAD script. The tuned stimulation and inhibition factors are

indicated in Table 7.1.

The coordination of these two controllers is achieved by the consecutive tuning of innate and

adaptive controller. In response to oscillations following disturbances, with parameters adjusted by the

adaptive controller in the real time, the innate controller is able to provide a near-optimal supplementary

control signal at any moment, making the power system survivable under more critical operation

conditions.

87

7.5 Performance evaluation of AIS controller

The effectiveness of this adaptive controller with optimized parameters is verified through

simulation carried out on the RTDS. Three cases are studied corresponding to three different operating

conditions as well as contingencies, with different fault site, power generation and loading conditions. The

active power of each generator under these operating conditions are documented in the Table. A.2 in the

appendix. Compared with the study cases in [13], the active power transfer from NE to NY is higher, thus

the transmission lines linking these two subsystems are subject to heavier power flows, leading to easier

loss of oscillatory instability.

Table 7.1 Tuned stimulation and inhibition factors

m1 m2 m3 m4 m5 m6 m7

0.4495 -0.3506 -0.3514 0.0081 0.2286 0.4323 -0.0846

m8 m9 m10 m11 m12 m13 m14

-0.2564 -0.4868 0.3535 0.0894 -0.5 -0.2395 -0.4265

m15 m16 m17 m18 m19 m20

0.5 -0.0305 0.2578 -0.1623 0.2424 0.3076

Case I: The power system is operating under Operating Condition 1 (OC1), then a 50ms three-phase

fault happened at Bus 2, causing the transmission line connecting Bus 1 and Bus 2 to be tripped. The speed

responses of some selected generators are shown in Figure 7.6 when local PSSs are installed in G1-G12.

Without installation of innate controller, the oscillation amplitude increases with the time until loss of

synchronism. The innate controller is effective to maintain stability, while AIS-based adaptive controller

improves the damping effectiveness. A comparison of the damping ratio for each oscillation mode with

88

and without the designed controller is shown in Table 7.2. These damping ratios are calculated using

Prony Analysis [51].

Case II: With the transmission line from Bus 1 to Bus 2 already tripped, the system operating

condition change to OC2, then a 100ms three-phase fault happened at Bus 8. The speed responses of some

selected generators are shown in Figure 7.7 when local PSSs are installed in G1-G12. With only the local

PSSs, the power system quickly loses synchronism. With the installation of innate controller, the system

is marginally stable. With both the innate and adaptive controller, the system quickly recovers to steady

state. The comparison of the damping ratio for each oscillation mode with and without the designed

controller is shown in Table 7.2.

89

Figure 7.5 Schematic diagram of the AIS based controller.

𝛥𝜔9(𝑘)

𝛥𝜔9(𝑘 − 1)

×

×

𝐾0−𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑



𝑇𝐻𝑇1(𝑘)

𝑇𝑆𝑇1(𝑘)

𝑇1 𝑇1−𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑

𝐾2 𝐾3

𝐾4

𝐾5

Washout Time-delaycompensator Limiter

Lead-lagcompensator

Parameters

… …

… …

𝑧−1 ÷÷

exp(−𝑥2)

Σ

𝑚1 𝑇𝐻𝐾0(𝑘)

𝑚2 𝑇𝑆𝐾0(𝑘)

𝐾0 ++

-

++

-

++

-

++

-

++-

Σ

Σ

Σ



𝐾1



𝐾5

𝑚13 𝑚14

𝐾1

Σ10𝑠

1 + 10𝑠𝐾𝐶

1 + 𝑠𝑇𝐶11 + 𝑠𝑇𝐶2

2

Δ 𝜔𝑉𝐺1

Δ 𝜔𝑉𝐺2

Δ 𝜔𝑉𝐺3

Δ 𝜔𝑉𝐺4

Δ 𝜔𝑉𝐺5

𝑉𝑜0.1

−0.1

𝐾0

𝑇1𝑠 + 1

𝑇2𝑠 + 1

𝑇3𝑠 + 1

𝑇4𝑠 + 1

𝑚19 𝑇𝐻𝑇4(𝑘)

𝑚20 𝑇𝑆𝑇4(𝑘)

𝑇4 𝑇4−𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑

90

Figure 7.6 Speed responses of selected generators with local PSSs installation under Case I.

Local PSSs

Optimal Controller

Adaptive Controller

0 5 10 15 20-2

0

2

x 10-3

G1

0 5 10 15 20-202

x 10-3 G

5

0 5 10 15 20-2

0

2x 10

-3

speed d

evi

atio

n (

p.u

.)

G8

0 5 10 15 20-1

0

1x 10

-3 G10

0 5 10 15 20-1

0

1x 10

-3 G13

0 5 10 15 20-2

0

2x 10

-3

time (s)

G16

91

Figure 7.7 Speed responses of selected generators with local PSSs installation under Case II.

Local PSSs

Optimal Controller

Adaptive Controller

0 5 10 15 20

-2

02

x 10-3 G1

0 5 10 15 20

-2

02

x 10-3 G5

0 5 10 15 20

-2

02

x 10-3 G8

speed d

evia

tion (

p.u

.)

0 5 10 15 20-2

0

2x 10

-3 G10

0 5 10 15 20-2

0

2x 10

-3 G13

0 5 10 15 20-2

0

2x 10

-3 G16

time (s)

92

Figure 7.8 Speed responses of selected generators with local PSSs installation under Case III.

Case III: System operating conditions change to OC3, then a 100ms three-phase fault happened at

Bus 27. Compared with OC2, there is an increase of active power transfer from New England to New

York, and the load at Bus 1 has increased by 100%. The speed responses of some selected generators are

shown in Figure 7.8 with local PSSs installation on G1-G12. With only the innate controller, power system

loses stability following the disturbances. However, the power system is stabilized with the installation of

0 5 10 15 20

-202

x 10-3 G1

0 5 10 15 20-2

0

2

x 10-3 G5

0 5 10 15 20-2

0

2

x 10-3 G8

speed d

evia

tion (

p.u

.)

0 5 10 15 20-2

0

2x 10

-3 G10

0 5 10 15 20-2

0

2x 10

-3 G13

0 5 10 15 20-2

0

2x 10

-3 G16

time (s)

Innate Controller

Adaptive Controller

93

both innate and adaptive controller. The comparison of the damping ratio for each oscillation mode with

and without the designed controller is shown in Table 7.2.

Figure 7.9 Deviation of parameters with time for all three case studies (Case I, II & III).

The deviation of the innate controller parameters with respect to time under the three cases described

above are shown in Figure 7.9.

Case I

Case II

Case III

0 5 10 15

-0.4-0.2

00.2

K1

0 5 10 15-0.4-0.2

00.20.4

K2

0 5 10 15

-0.5

0

0.5

K3

0 5 10 15-0.2

0

0.2

K4

0 5 10 15-0.4-0.2

00.20.4

K5

Change o

f P

ara

mete

rs

0 5 10 15-1

0

1

K0

0 5 10 15

-0.2

0

0.2

0.4

T1

0 5 10 15

-0.5

0

0.5

T2

0 5 10 15

-0.2

0

0.2

Time (s)

T3

0 5 10 15-0.5

0

0.5

Time (s)

T4

94

Table 7.2 Damping ratio for different modes under Case I – III

Cases Cases 0.22 Hz 0.42 Hz 0.54 Hz 0.65 Hz

Only with local PSSs

Case I -2 % 12.6% 7.3% 6.9%

Case II Unstable

Case III Unstable

With innate controller

Case I 9.1 % 15.2% 11.2% 12.4%

Case II 3 % 14.1% 10.2% 11.9%

Case III Unstable

With adaptive controller

Case I 14.6 % 17.1% 13.5% 13.1%

Case II 15.6 % 16.1% 14.5% 13.6%

Case III 14.7 % 16.3% 13.9% 14.4%

7.6 Summary

This study has proposed an AIS-based wide area adaptive damping controller that uses virtual

generator speeds for supplementary control signal to mitigate inter-area oscillations in a power system.

The control is carried out at the generator of maximum controllability identified through modal analysis.

The optimal tuning of controller parameters provides innate immunity, while adaptive immunity is

available by a mechanism to adjust controller response policy according to the measured disturbance. The

parameters of innate and adaptive controllers are tuned by particle swarm optimization. As verified by

simulations on RTDS, the proposed AIS based controller is able to stabilize the power system under

different disturbances, and achieve better performance under various operating conditions.

95

CHAPTER 8

WIDE-AREA MEASUREMENT BASED MULTI-OBJECTIVE SMARTPARK

CONTROLLERS FOR A POWER SYSTEM WITH A WIND FARM

8.1 Introduction

The integration of variable generation such as wind and solar power has brought about

significant challenges and uncertainty in power system operation, making it essential to take

measures for advanced coordinated control. With the batteries of plug-in electrical vehicles (PEVs),

active and reactive power support functions can be provided at certain buses in a power system.

Parking lots with a large number of PEVs, referred to as SmartParks, can provide these functions

at bulk level. Thus, by appropriate control of SmartParks, active and reactive power flows in a

power system can be regulated to achieve the functionalities of oscillation damping control,

transmission line power flow regulation and bus voltage control. In this paper, in order to realize

these three functionalities concurrently by using SmartParks, fuzzy-logic based controllers are

proposed. Wide area measurements from a power system can be used to generate the active and

reactive power output dispatch command signals for SmartParks. The parameters of the fuzzy logic

controllers are heuristically determined to provide optimal system-wide performances for

oscillation damping, transmission line power flow regulation and bus voltage control. Typical

results are provided on a 12-bus power system with 400 MW wind farm implemented on a real-

time simulation platform.

8.2 Problem formulation

Nowadays, as Plug-in-Vehicles (PEVs) are increasingly being applied in power systems, the

battery of PEVs can participate in power system control [52]-[54]. A SmartPark is a PEV parking

96

lot capable of vehicle-to-grid (V2G) and grid-to-vehicle (G2V) transactions. The cumulative

battery energy storage of the PEVs has the capability to provide active and reactive power

injections into a power system [55]. It can be assumed that a predictable amount of PEVs are

present in the SmartPark connected to the power grid during day and night such as university

parking lots and airport parking lots. Meanwhile, due to the variable nature of renewable sources

of energy such as wind and solar power, increasing levels of penetration can cause fluctuation of

bus voltages and power flows in the transmission system. In the predictable future, the batteries of

PEVs can be used to mitigate the fluctuations caused by large integration of wind and solar power

sources.

Previous research has explored various applications of SmartParks in power system control. In

[56], SmartPark is deployed as a shock absorber to maintain constant active power flows in

transmission lines connected to a wind farm. Active power is absorbed or injected by a SmartPark

to compensate for a change in a wind farm output. However, this functionality can be effective

only if a SmartPark is in proximity to a wind farm. Coordinated control based on remote

measurements is needed when SmartParks are distant from wind farms. In [57], to provide bus

voltage regulation, a SmartPark has been utilized as a virtual STATCOM to provide reactive power

compensation. Herein, local bus voltage measurements are used to control the SmartPark’s

reactive power dispatch. However, voltage support of adjacent buses have not been explored. The

impact of SmartPark on adjacent buses has not been shown. The application of SmartPark for

oscillation damping controller has been studied in [58]. The difference of the generator speeds and

the state of charge of the SmartPark are used as inputs to a fuzzy logic based controller. The fuzzy

controller determines the amount of SmartPark active power to be dispatched in order to enhance

the damping torque. The above mentioned studies have focused on individual applications of

97

SmartPark capabilities. However, for maximum utilization of SmartPark resources for control of

power systems, it is desired that all these capabilities be tapped concurrently. Furthermore,

SmartParks installed at different locations/buses need to be coordinated for enhanced system-wide

performance. This requires wide-area power system measurements and intelligent coordinated

control.

In this paper, the multi-functionality of SmartParks through a coordinated approach to achieve

three objectives, namely, i) power oscillation damping control, ii) transmission line power flow

control and iii) voltage regulation, is investigated. This multi-functionality is studied on a power

system with wind power fluctuations. In order to realize these objectives, an intelligent coordinated

control is needed to dispatch active and reactive power from the SmartPark(s) in real time. The

intelligent control of SmartPark inverters is based on wide-area power system measurements such

as generator speed deviations, transmission line power flows and bus voltages.

The overall diagram to implement the above mentioned multi-functional control of SmartParks

is shown in Figure 8.1. Two control loops are implemented. Using the decoupled d-q axis current

control, the inner control loop provides a reference tracking control for the active and reactive

power dispatches and this is fast-responding control action. The outer loop makes use of wide-area

system measurements to generate the active/reactive power reference signals to the inner control

loop. This is slower in response compared to the inner control loop. The inner control loops

developed in [57] can achieve satisfactory active/reactive power reference tracking. Therefore, this

study is focused on the development of outer loop control to achieve the three objectives mentioned

above. Due to the nonlinearity of power system and the unknown relationship between the

controller’s multiple inputs and multiple outputs, a Tagaki-Sugeno type fuzzy logic controller is

proposed instead of traditional controllers such as PI controllers and lead-lag compensators. To

98

develop an optimal fuzzy controller, a system-wide fitness function that reflects the three

objectives is used to determine the parameters of the controller. With optimal controller parameters

determined offline, an overall satisfactory power system performance can be realized under

disturbances for various operating conditions including different wind speeds.

99

Figure 8.1 The overall diagram for the SmartPark control scheme

PSP2, QSP2PSP1

Pulses Pulses

𝛥 Pref

𝛥𝑃16 − 𝛥𝑃64 𝛥𝑉4

𝛥 Qref

Inner control loop Inner control loop

IMFC_1 / IMFC_1' IMFC_2 / IMFC_2'

SmartPark 1 SmartPark 2

12 Bus Power System Bus 6 Bus 4

Switch 1 Switch 2

𝛥𝑃64 Σ

𝑉4

𝑉4,ref

+

𝛥𝜔2 − 𝛥𝜔3

Σ 𝛥𝜔2

𝛥𝜔3

+

− −

𝛥𝑃16 − 𝛥𝑃64

Σ 𝑃16

𝑃16,ref

Σ

𝛥𝑃16

Σ 𝑃64 𝑃64,ref

+

+ +

+

−

−

PMUs

Mea

sure

men

ts

𝑃wind, 𝑛𝑜𝑟𝑚𝑖𝑛𝑎𝑙

𝛥 Pref

Σ Σ

+

+ 𝑃wind

Σ +

− Pref

Ptotal

SP-DC

100

8.3 Power system with a wind farm and SmartParks

8.3.1 12-BUS FACTS benchmark test power system

Shown in Figure 8.2 is the 12-bus FACTS benchmark test power system used in this study, it

consists of three voltage levels (as labeled in Figure 2) and is divided into three areas [59]. G1 is

a representation of an infinite power system, thus the voltage amplitude and angle at Bus 9 is

regarded to be constant. G2 and G3 are synchronous generators; thus, during power system

transients, the rotation speed of G2 and G3 are subject to fluctuations. G4 at Bus 6 is a

representation of a wind farm with a DFIG model, which is further connected with Bus 1 and Bus

4 through two transmission lines. Bus 4 is the major load bus with the lowest voltage profile, and

is subject to large fluctuation following disturbances.

As the output of wind farm changes, the active power flow in the power system is subject to

variations, leading to possible exceeding of power flow constraints in transmission lines.

Following contingencies, oscillations are exhibited through speed deviations of G2 and G3,

leading to possible loss of synchronism.

Figure 8.2 12-bus power system

101

8.3.2 Wind farm model

As a variable generation source, a Doubly Fed Induction Generator (DFIG) based wind farm

is used in this study. The stator side and rotor side of the DFIG are connected to a DC-link capacitor

through a Grid Side Converter (GSC) and a Rotor Side Converter (RSC) respectively. In the wind

farm, with a d-q decoupled control method, the active power output of the DFIG can be regulated

to realize maximum power point tracking through control of RSC; while the DC voltages as well

as the DFIG reactive power output can be regulated through control of GSC. Detailed modeling

of a DFIG is given in [60]. In this study, the output of the wind farm varies as the wind speed

changes, and thus leads to variation of transmission lines power flows. Variation of wind speeds

causes the change of the active power output of G4, therefore it impacts the power flow of the

whole power system. Control actions are required to maintain the transmission line flows.

8.3.3 SmartPark model

A graphical representation of a SmartPark model is shown in Figure 8.3. The battery of the

PEV can be modeled as a DC voltage source connected with a three phase inverter, and ultimately

linked with the power system through an inductance. The DC voltage is 307V at 50% state of

charge; the inductance in series is 0.005Ω, while the rms line-to-line voltage of inverter output is

208V [57]. Assuming a constant grid voltage, the amplitude and phase of the inverter side voltage

is regulated through pulses for the six fast switches to regulate, and thus the active and reactive

power injected to the power grid can be impacted. In operations, it is generally required that the

active and reactive power output of the SmartPark tracks a reference value. To realize this, as

indicated in Figure 8.4, is the inner control loop for generation of pulses. For the convenience of

analysis, the current in the rotating a,b,c phases are transformed to a stationary d-q-axis system.

The equivalent current iqs is in phase with the grid voltage and is closely related to the active power

102

output of the SmartPark, while the equivalent current ids is 90 degrees lagging the grid voltage and

is closely related to the reactive power output [61]. Thus, the output voltage can be expressed in a

phasor form as C CV V . Large amount of active power delivery by the batteries corresponds

to a higher phase angle α; while large amount of reactive power delivery corresponds to higher

voltage level |V|.

Figure 8.3 Schematic circuit representation of a SmartPark

Figure 8.4 The inner control loop for SmartPark

In this control scheme, the references for iqs and ids are given by (8.1) and (8.2) in terms of

active and reactive power references (namely P* and Q*) respectively. The integrators in Figure

4 guarantee that P and Q reach their reference values in steady states.

*

* *2 d3qs

peak

Pi K P P tv

(8.1)

103

*

* *2 d3ds

peak

Qi K Q Q tv

(8.2)

The total actual active and reactive power output can be expressed in (8.3) and (8.4), and can

be directly measured.

3 ( )2 qs qs ds dsP v i v i (8.3)

3 ( )2 qs ds ds qsQ v i v i (8.4)

For each phase, the current reference value is compared with the actual values; their differences

are modulated to generate inverter pulses corresponding to each specific case. According to

previous research, due to the fast switching characteristics of the IGBTs that comprises the

SmartPark circuit, it can be seen that the actual active/reactive power generation by SmartParks

almost overlaps with the reference values [56].

The state of charge (SOC) is a reflection of fuel gauge for PEV batteries. The SmartPark

functionalities cannot be realized under excessively high or low value of SOC. Generally, the

charging or discharging of batteries corresponds to a positive or negative active power generated

by the SmartPark, leading to the change of SOC. Fortunately, the functionality of SmartPark as

damping controller only involves the SmartPark active power output in a short transient process,

and has little impact on the SOC. Since the wind speed is generally changing around the nominal

value, there is both positive and negative amount of active power output of SmartPark as a

transmission line active power regulator, the net effect of charging and discharging is to maintain

the SOC value to a proper range. SmartPark as a voltage regulator mainly involves the reactive

power output, and has negligible impact on the SOC.

All these issues related damping oscillations, voltage regulation and power flow regulation

require a coordinated intelligent multi-functional control which is addressed in the next section.

104

8.4 Development of an intelligent multi-functional controller (IMFC) for SmartParks

So far, with the main circuit and the inner loop controller elaborated above, a SmartPark is able

to track its active and reactive power references during operation. An outer-loop controller is

required to generate these references from the power system measurements. There are many

traditional methods for development of controllers. Such as H∞-based approaches [62], [63].

However, in an interconnected power system, relationships between measurements (including

speed deviations of generators, transmission line power flows, and voltage deviations at buses)

and active/reactive power references of a SmartPark are unknown. Besides, conventional power

system models are subject to a lot of constraints including nonlinearity, time-dependence and

stochastic nature of power systems. In this study, instead of using traditional control approaches,

a Takagi-Sugeno type fuzzy network based IMFC is developed to generate the reference signals

to a SmartPark. The structure of a Takagi-Sugeno type fuzzy network provides a nonlinear

mathematical relationship between the input and output signals. The parameters of the fuzzy

network can be heuristically determined to provide optimal SmartPark and power system

performance. During the development of this controller, power system measurements that provide

the most observability to achieve the objectives are used as the inputs to the SmartPark. The

oscillatory stability can be best observed from the speed deviations of the generators as well the

voltage profiles at selected buses. The power flow regulation can be observed directly from

transmission line power flow measurements. The voltage regulation can be observed directly from

the voltage profiles measured at the respective buses.

The following three objectives of the multi-functional control can be realized as follows:

i. An improved oscillation damping performance can be achieved by an increased

damping ratio in the speed deviation responses of generators and transmission line

105

power flows. As a result the generator speed deviation responses and/or transmission

line power flows can be used as inputs of an IMFC which in turn can generate changes

to the active power reference command to a SmartPark.

ii. The transmission line power flows deviations from their nominal values can be used to

generate an active power reference command to a SmartPark to regulate transmission

line power flows.

iii. The voltage profile at crucial buses can be directly measured to generate a reactive

power reference command to a SmartPark to regulate voltage levels at respective buses.

The above mentioned objectives to enhance power system operational performance are

illustrated with two SmartParks having secondary controllers (IMFC_1 and IMFC_2) as shown in

Figures 8.1 and 8.2. SmartPark 1 realizes the first two of three functionalities concurrently.

SmartPark 2 realizes the last two of three functionalities concurrently.

8.4.1 Tagaki-Sugeno fuzzy network (TSFN)

Indicated in Figure 5 is a schematic diagram of a Tagaki-Sugeno Type fuzzy network. It is

composed of several layers [64], [65]. In Layer 1, each of the input channels is propagated through

nonlinear functions to form the inputs of Layer 2. Suppose there are M inputs, and each input has

connections with N nonlinear membership (Gaussian) functions; thus, Layer 2 has totally MN

inputs. Each element of Layer 3 is the product of several Layer 2 members connected to different

elements of Layer 1. Thus, there are R=NM product functions in Layer 3. Each element of Layer 4

(output layer) is a linear weighed sum of Layer 3 outputs. It is worth noting that an offset is added

to each output node in order to guarantee that zero inputs lead to zero outputs for initialization.

The formulae of this mathematical formulation is shown in (8.5).

106

1

2, 2, 1,

3, 2,

'4, 3,

1'4, 4,

(

);

;

.

; 1,2...

N

i i j

p

k pp p

R

m k kk

m m m

l f l

l l

l c l

l l d m K

(8.5)

in which K is the number of outputs, md is the offset that corresponds to the value of l’4,m under

zero-inputs. The function of this deviation is to guarantee that control signals decay to zero

whenever the power system restores to its original steady state. The nonlinear membership

functions f2,i() can be realized through various analytic mathematical forms. In this study, Gaussian

functions with the expressions in (8.6) are adopted.

2 2( ) /(2 )( ) x b cf x ae (8.6)

(a) (b)

Figure 8.5 The structure of IMFCs

(a) TKFN for IMFC_1 and (b) TKFN for IMFC_2.

There are two parameters in each of the MN Gaussian membership functions; meanwhile,

there are NM parameters of ck ’s in the output layer. Thus, (2MN + KNM) parameters are present in

TSFN controller. To guarantee that the controller generates correct signals for better control

107

effectiveness, it is essential to optimally configure these parameters. Herein, a heuristic

optimization method, namely, Mean Variance Optimization (MVO) is applied [68]. MVO

iteratively determines the system parameters for minimization of an objective function, as

elaborated in the following subsection.

8.4.2 MVO based TSFN parameter tuning

The TSFN parameters can be heuristically configured to achieve the objectives of IMFCs.

Traditionally, heuristic algorithms like particle swarm optimization, MVO and genetic algorithm

are used for tuning of controller parameters [66]-[69]. In this study, MVO is used to tune the TSFN

parameters for minimization of an objective function that is obtained through simulations. In each

iteration, the MVO assigns new values to a chosen number of parameters in the best individual

according to the distribution characteristics of the parameters such as the mean and the variance

value, which are calculated through a list of the best N individuals that are evaluated. The

relationship of old and new value of the parameter can be expressed in (8.7),

(1 )(1 ) (1 ) ( 1 )old oldx s x s snew oldx x e x e e x x (8.7)

where ln( ) ss v f ; x and v are the mean and variance of that parameter respectively; fs is a shaping

scaling factor.

The list of best N individuals is constantly being updated whenever a better solution is found.

In the next iteration, a different set of parameters are subject to mutation.

The objective function serves as an evaluation of the system performance, and is calculated

through simulated measurements such as speed deviation, voltage as well as transmission line

active power flows. As elaborated in the following subsections, in order to achieve an IMFC, the

overall objective function can be expressed as the weighted sum of the three individual objectives.

The selection of weights needs to consider the importance for each objective, as well as the

108

calibration for different numerical scales. In case more than one TSFN controller is installed in a

power system, the parameters of all the TSFN controllers can be concurrently optimized. The

development of IMFCs for two SmartPark installations is investigated in this study via three case

studies.

8.4.3 Development of IMFC for SmartPark installation at Bus 6

An IMFC is developed for SmartPark installation Bus 6 to damp generator oscillations and

mitigate active power fluctuations caused by wind speed changes. This controller, referred to as

‘IMFC_1’ is shown in Figures 1 and 5a. Switch 1 turned on connects SmartPark 1 to Bus 6.

Without the SmartPark, significant difference of speed deviation of generators G2 and G3

(Δω2−Δω3) can be observed. Besides, the variation of active power output of the wind farm

(ΔPwind), is accompanied by the difference of the active power flow deviation, (ΔP16−ΔP64), of the

two transmission lines, namely, lines 1-6 and 6-4, as expressed in (8.8),

ΔPwind = −(ΔP16−ΔP64) (8.8)

Thus, two inputs are selected for IMFC_1, namely, i) the difference between speed deviations

of generators G2 and G3, (Δω2−Δω3) and ii) the difference of the active power flow deviation, −

(ΔP16−ΔP64). The output of the IMFC_1 is the active power output reference command to the

SmartPark 1, PSP1. Each input is connected to five Gaussian membership functions, thus totally

there are 45 (2MN + KNM =2×5×2+52 ) parameters. The ability of the SmartPark as an active power

source is based on the battery energy storage. Under this control, the increase of the wind power

output is accompanied by the charging of the battery; while the decrease of the wind power output

is accompanied by the discharging of the battery. Thus, the variation of wind speed brings about

alternating battery charging and discharging process, and maintains the SOC between some

minimum and maximum levels.

109

In each iteration of MVO based parameter configuration, three events were taken for the

verification of the control effectiveness: (i) three phase faults at Bus 6 is applied, the speed

deviations of G2 and G3 are measured; (ii) increase in wind speed, active power flow on

transmission line Bus 1-Bus 6 and Bus 6-Bus 4 are measured. (iii) decrease in wind speed, active

power flow on transmission line Bus 1-Bus 6 and Bus 6-Bus 4 are measured. The cost function

used by MVO for determining the TSFN parameters is given in (8.9),

1 2 3

2 2 2 2 2 21 2 1 3 1 1 16 2 64 2 16 3 64 3( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( ))

t t tJ t t P t P t P t P t

(8.9)

where t1 corresponds to a time window after the fault; t2 corresponds to a time window following

the wind speed increase; while t3 corresponds to a time window following the wind speed decrease.

8.4.4 Development of IMFC for SmartPark installation at Bus 4

In this case, an IMFC is developed for SmartPark installation Bus 4 for voltage regulation and

to mitigate active power fluctuations caused by wind speed changes. The structure of this controller,

referred to as ‘IMFC_2’ has been shown in Figure 1 and Figure 5b. Switch 2 turned on connects

SmartPark 2 to Bus 4. Since the voltage of Bus 4 can be directly measured, the voltage deviation

(ΔV4=V4−Vstandard) is taken as the one of the input for the IMFC_2. Like the previous subsection,

the difference of the active power flow deviation of the two transmission lines (ΔP16−ΔP64) is

taken as the other output, since it is a reflection of the wind farm output impact on the transmission

line active power flow. The outputs of this controller are the active and reactive power output

reference commands to SmartPark 2. This controller has a total of 48 parameters. Each input is

connected to four Gaussian membership functions, thus totally there are 48 (2MN + KNM

=2×4×2+2×24) parameters.

110

In each iteration of the MVO based parameter search, three events were taken for the

verification of the control effectiveness: (i) three phase faults at Bus 4 is applied, the speed

deviations of G2 and G3 are measured; (ii) increase in wind speed, active power flow on

transmission line Bus 4-Bus 5 and Bus 4-Bus 3 are measured; (iii) decrease in wind speed, active

power flow on transmission line Bus 4-Bus 5 and Bus 4-Bus 3 are measured. The cost function

used by MVO is expressed in (8.10),

1 2 3

2 2 2 2 22 4 1 2 45 2 43 2 45 3 43 3( ( )) ( ( )) ( ( )) ( ( )) ( ( ))

t t tJ V t P t P t P t P t

(8.10)



It is illustrated in Section 4 that the increase and decrease of the wind power output is accompanied

by reverse effects of battery charging and discharging. Thus, the alternating increase and decrease

of wind speed leads to the maintenance of SOC between some minimum and maximum levels..

8.4.5 Development of IMFC for SmartPark installation at Bus 4 and 6

In this case, it is desired that a constant power flow is maintained at the four transmission lines

(Bus 1-Bus 6, Bus 6-Bus 4, Bus 4-Bus 3, Bus 4-Bus 5), the voltage profile near load buses be

maintained, and damping torque is provided to better maintain phase angle stability of G2 and G3.

Thus, two IMFCs are concurrently installed at Buses 4 and 6. These implies switches 1 and 2 in

Figure 1 are turned on connecting SmartPark 1 and 2 to Buses 6 and 4, respectively. The

parameters of the two IMFCs designed in Section 3.3 and 3.4 are taken as the initial parameters, a

total of 93 parameters. Thereafter, these 93 parameters are further tuned with MVO according to

the cost function as expressed in (8.11),

111

1

1

2 3

2 21 2 1 3 1

22 4 1

2 2 2 2 2 2 2 23 16 2 64 2 45 2 43 2 16 3 64 3 45 3 43 3

3 1 3 2 3 3

( ( )) ( ( ))

( ( ))

( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( ))

t

t

t t

J t t

J V t

J P t P t P t P t P t P t P t P t

J J J J

(8.11)



The concurrently tuned IMFC controllers at Buses 4 and 6 are referred to as ‘IMFC_1' ’ and

‘IMFC_2' ’ respectively.

8.5 Simulation results

Shown in Figure 8.6 is controller flowchart for the developing the IMFCs using MVO.

112

Figure 8.6 The flowchart for development of IMFC

To verify the effectiveness of the proposed controllers, (IMFC_1, IMFC_2, IMFC_1' and

IMFC_2'), simulations are carried out on a 12-bus power three-area system [59]. Several different

simulation cases are presented in the following subsections. The fuzzy logic controller

implementation is realized through a C code based block that is embedded as an RTDS component.

The calculation of the objective function for each MVO iteration is via a simulation on a Real

Time Digital Simulator (RTDS). The MVO algorithm is implemented using MATLAB, which

interacts with RTDS platform using the RSCAD script files. Once the fuzzy controller parameters

are configured through MVO, the controller development is accomplished.

Case 1: SmartPark installation at Bus 6

Start

MVO tuning of TKFN parameters for SmartPark installation at Bus 6

Design of inner loop controller of SmartPark

MVO tuning of TKFN parameters for SmartPark installation at Bus 4

Secondary MVO tuning of TKFN for SmartPark installation at Bus 4 and Bus 6

End

Performance verification

Satisfactory ?

Y N

Development of TKFN structure

113

In this case, the parameter tuning algorithm takes approximately 400 MVO iterations to

converge. With the optimally configured parameters, the damping effectiveness of this control

method is presented by post-fault generator speed deviations. The simulation result is compared

with a prior study where a SmartPark with a Difference Controller (SP-DC) is used. The SP-DC

controller calculates the active power output reference of the SmartPark as the difference between

the wind farm active power output under nominal wind speed (12 m/s) and the actual wind farm

active power output [56].

Indicated in Figure 8.7 are the speed deviations of G2 and G3 following a 100ms three phase

fault at Bus 6 for wind speed of 12 m/s, 15 m/s and 10 m/s. It can be seen that IMFC_1 enables

the SmartPark 1 to inject active power into Bus 6 to damp generator speed oscillations more

effectively compared with the previously developed SP-DC controller. This is seen from the

damping ratios shown in as Table I.

114

Figure 8.7 The speed deviations of G2 and G3 following a 100ms three phase fault at Bus 6.

(a) Speed deviation at G2 with wind speed of 12 m/s; (b) Speed deviation at G2 with wind speed of 15 m/s;(c) Speed deviation at G2 with wind speed of 10 m/s; (d) Speed deviation at G3 with wind speed of 12 m/s;(e) Speed deviation at G3 with wind speed of 15 m/s; (f) Speed deviation at G3 with wind speed of 10 m/s.

Table 8.1 Damping ratios of speed deviation responses

Condition Damping Ratio

Wind speed of 12 m/s Wind speed of 15 m/s Wind speed of 10 m/s

No SmartPark 7.1% 5.5% 3.5%

SP_DC 9.2% 8.2% 8.1%

IMFC_1 16.0% 13.5% 16.5%

Illustrated in Figure 8.8 are the active power flows on transmission lines Bus 1-Bus 6 and Bus

6-Bus 4 following a change in wind speed. It can be seen that the proposed controller achieves

4 6 8 10 12

-1

0

1

x 10-3

Speed d

ev (

p.u

.)

(a)

Time (s)

No SmartPark

SmartPark with SP-DC

SmartPark with IMFC_1

4 6 8 10 12

-1

0

1

x 10-3

Speed d

ev (

p.u

.)

(b)

Time (s)

4 6 8 10 12

-5

0

5

x 10-4

Speed d

ev (

p.u

.)

(c)

Time (s)

4 6 8 10 12-5

0

5x 10

-3

Time (s)

Speed d

ev (

p.u

.)

(d)

4 6 8 10 12-6

-4

-2

0

2

4

6x 10

-3

Time (s)

Speed d

ev (

p.u

.)

(e)

4 6 8 10 12-1.5

-1

-0.5

0

0.5

1

1.5x 10

-3

Time (s)

Speed d

ev (

p.u

.)

(f)

115

comparable effectiveness for regulating transmission line power flows, with some improvements.

The active power output of the SmartPark 1 is shown in Figure 8.9. It can be seen that, the increase

and decrease of wind speed can lead to opposite trends of battery charging or discharging.

Figure 8.8 The active power flows on transmission lines following wind speed changes.

(a) Active power from Bus 1 to Bus 6 with wind speed change from 12 m/s to 15 m/s;(b) Active power from Bus 1 to Bus 6 with wind speed change from 12 m/s to 10 m/s.(c) Active power from Bus 6 to Bus 4 with wind speed change from 12 m/s to 15 m/s;(d) Active power from Bus 6 to Bus 4 with wind speed change from 12 m/s to 10 m/s;

0

100

200

(a)

No SmartPark



100

200

300

(b)

0 5 10 15 20175

180

185

Active

Pow

er(

MW

)

Time (s)0 5 10 15 20

175

180

185

Active P

ow

er

(MW

) Time (s)

50

100

150

Active P

ow

er

(MW

)

(c)

0

50

100

Active P

ow

er

(MW

)

(d)

0 5 10 15 2076

77

78

Time (s)

0 5 10 15 2076

77

78

Time (s)

116

Figure 8.9 The active power output of the SmartPark 1 for Case 1. (Under wind speed of 12

m/s)

Case 2: SmartPark installation at Bus 4

In this case, the parameter tuning algorithm takes approximately 300 MVO iterations to

converge. With the optimally configured parameters, the damping effectiveness of this control

scheme is presented by the post-fault generator speed deviations. Shown in Figure 8.10 are the

voltage profile of selected buses that are close to a major load. It can be seen that the voltage profile

is improved, and quickly settles to steady state with the proposed IMFC_2.

0 5 10 15 20-200

-150

-100

-50

0

50

Time (s)

Active P

ow

er

(MW

)

0 5 10 15 20-50

0

50

100

150

200

Time (s)

Active P

ow

er

(MW

)

0 5 10 15 20-150

-100

-50

0

50

100

Time (s)

Active P

ow

er

(MW

)

117

Figure 8.10 The voltage profile of selected buses.

(a) Voltage at Bus 4 with wind speed of 12 m/s; (b) Voltage at Bus 4 with wind speed of 15 m/s;(c) Voltage at Bus 4 with wind speed of 10 m/s; (d) Voltage at Bus 5 with wind speed of 12 m/s.(e) Voltage at Bus 5 with wind speed of 15 m/s; (f) Voltage at Bus 5 with wind speed of 10 m/s.

Shown in Figure 8.11 are the active power flows on transmission lines Bus 4-Bus 5 and Bus

4-Bus 3 following a change in wind speed. It can be seen that the proposed IMFC_2 is effective in

regulating the transmission line power flows. The active and reactive power output of the

SmartPark 2 is shown in Figure 8.12. Likewise, it can be seen that, the increase and decrease of

wind speed can lead to opposite trends of battery charging or discharging.

0.8

0.9

1

Vol

tage

(p.

u.)

(a)

Time (s)

No SmartPark


0.8

0.9

1

Vol

tage

(p.

u.)

(b)

Time (s)

0.8

0.9

1

Vol

tage

(p.

u.)

(c)

Time (s)

4 6 8 10 120.9

0.95

1

1.05

1.1

Time (s)

Vol

tage

(p.

u.)

(d)

4 6 8 10 120.9

0.95

1

1.05

1.1

Time (s)

Vol

tage

(p.

u.)

(e)

4 6 8 10 120.9

0.95

1

1.05

1.1

Time (s)

Vol

tage

(p.

u.)

(f)

118


(a) Active power from Bus 3 to Bus 4 with wind speed change from 12 m/s to 15 m/s;(b) Active power from Bus 3 to Bus 4 with wind speed change from 12 m/s to 10 m/s.(c) Active power from Bus 5 to Bus 4 with wind speed change from 12 m/s to 15 m/s;(d) Active power from Bus 5 to Bus 4 with wind speed change from 12 m/s to 10 m/s;

0 5 10 15 20140

160

180

200

Active p

ow

er

(MW

)

(a)

Time (s)

No SmartPark


0 5 10 15 20

160

180

200

220

Active p

ow

er

(MW

)

(b)

Time (s)

0 5 10 15 2010

20

30

40

Time (s)

Active p

ow

er

(MW

)

(c)

0 5 10 15 2020

30

40

50

Time (s)

Active p

ow

er

(MW

)

(d)

119

Figure 8.12 The active power and reactive output of the SmartPark for Case 2.

(a)Active Power output for wind speed increase; (b) Reactive Power output for wind speed increase(c)Active Power output for wind speed decrease; (d)Reactive Power output for wind speed decrease

(e)Active Power output following a fault; (f) Reactive Power output following a fault

Case 3: SmartPark installations at Bus 4 and Bus 6

In this case, the parameter tuning algorithm takes approximately 300 iterations to converge.

With the optimally configured parameters, the damping effectiveness of this control method is

presented by the post-fault generator speed deviations. The effectiveness of the proposed

controllers (IMFC_1' and IMFC_2') is compared with that of previously developed controller in

[56], as well as with the case of no controller. Shown in Figure 8.13 are the speed deviations of

G2 and G3 and the voltage profile at Bus 4 and Bus 5 following a 100ms three phase fault at Bus

6 under nominal wind speed of 12 m/s. It can be seen that, with the proposed IMFC controllers,

the damping effectiveness and the voltage profile are with the best performances.

-100

-50

0

50

Active p

ow

er

(M

W)

(a)

Time (s)-50

0

50

Rective p

ow

er

(M

VA

R)

(b)

Time (s)

0

50

100

Active p

ow

er

(M

W)

(c)

Time (s)-20

-10

0

10

Rective p

ow

er

(M

VA

R)

(d)

Time (s)

0 5 10 15 20-100

0

100

200

Time (s)

Active p

ow

er

(M

W)

(e)

0 5 10 15 20-50

0

50

100

Time (s)

Rective p

ow

er

(M

VA

R)

(f)

120

Figure 8.13 Power system measurements following a 100ms three phase fault at Bus 6.

(a)Speed deviation at G2; (b) Speed deviation at G3; (c) Voltage at Bus 4; (d) Voltage at Bus 5.

Shown in Figure 8.14 are the active power flows on the four transmission lines following

change in wind speeds. It can be seen that the proposed controllers achieve comparable

effectiveness for regulating transmission power flows, with some improvements.

4 6 8 10 12

-1

-0.5

0

0.5

1

x 10-3

Spe

ed d

ev. a

t G2

(p.u

.)

(a)

Time (s)

No SmartPark


SmartPark with SmartPark with IMFC_1' and IMFC_2'

4 6 8 10 12-5

0

5x 10

-3

Spe

ed d

ev. a

t G3

(p.u

.)

(b)

Time (s)

4 6 8 10 120.96

0.98

1

1.02

Vol

tage

at B

us 4

(p.u

.)

(c)

Time (s)

4 6 8 10 121

1.02

1.04

1.06

1.08

Time (s)

Vol

tage

at B

us 5

(p.u

.)(d)

121


(a) Active power transfer from Bus 1 to Bus 6 subjected to wind speed change from 12 m/s to 15 m/s(b) Active power transfer from Bus 1 to Bus 6 subjected to wind speed change from 12 m/s to 10 m/s(c) Active power transfer from Bus 6 to Bus 4 subjected to wind speed change from 12 m/s to 15 m/s(d) Active power transfer from Bus 6 to Bus 4 subjected to wind speed change from 12 m/s to 10 m/s(e) Active power transfer from Bus 3 to Bus 4 subjected to wind speed change from 12 m/s to 15 m/s(f) Active power transfer from Bus 3 to Bus 4 subjected to wind speed change from 12 m/s to 10 m/s(g) Active power transfer from Bus 5 to Bus 4 subjected to wind speed change from 12 m/s to 15 m/s(h) Active power transfer from Bus 5 to Bus 4 subjected to wind speed change from 12 m/s to 10 m/s

50

100

150

200

(a)

No SmartParks


SmartPark with SmartPark with IMFC_1' and IMFC_2'

176

178

180

182

150

200

250

300

(b)

178

179

180

181

50

100

150

Active p

ow

er(

MW

)

(c)

76

77

78

79

0

50

100

(d)

76

77

78

79

140

160

180

200

(e)

181

182

183

184

180

200

220

240

(f)

182

182.5

183

183.5

0 10 2010

20

30

40

(g)

0 10 2029

29.5

30

30.5

Time (s)

0 10 2020

40

60

(h)

0 10 2029.5

30

30.5

122

8.6 Summary

With the increased use of PEVs in power systems, the SmartPark can be applied for power

system control through charging and discharging of the PEV batteries. By injection of active and

reactive power at certain buses, SmartPark is able to impact the power flow in the power system,

leading to different operating conditions. With the application of PMUs, remote measurements in

power systems can be used for control purposes. To realize functionalities of SmartPark as

damping controller, voltage regulator, and active power transmission regulator simultaneously, the

proposed controller in this study is with two control loops: the inner control loop traces a reference

of active and reactive power references through current control of power electronic devices, while

Tagaki-Sugeno type fuzzy logic based IMFCs controllers generate the SmartPark active and

reactive power references using remote measurements. The parameters of IMFCs are heuristically

tuned using MVO. Simulation results have verified that the proposed controller is able to realize

the multiple functionalities of SmartParks.

As part of future work, concurrent realization of multiple functionalities of SmartPark in power

system control will be further tested and illustrated in multi-area power systems. In those cases,

the local, intra-area and inter-area oscillations appear in multiple modes [70]. Thus, more delicate

choices of input- , output-signals and objective functions will be essential. Due to the large

geographical size of power systems, a novel approach to optimally choose the site of SmartPark

installations will also be devised.

123

CHAPTER 9

CONCLUSION

9.1 Introduction

The previous chapters in this dissertation include: power system modeling and modal

analysis, development of local power system stabilizers and wide area signal based damping

controllers, application of SmartPark in power system stability control. This chapter serves as a

summary of the accomplishments in this dissertation.

9.2 Research summary

The research work presented in each chapter is summarized as follows:

Chapter 1: The concept of power stability is introduced. The Benchmark power

systems are presented. Main objectives and contributions of this dissertation are

enumerated.

Chapter 2: The phenomenon of power system oscillation is reviewed. The cause of

oscillation elaborated. The relationship between active power transfer and power

system oscillation is presented.

Chapter 3: Power system model is obtained through stochastic subspace

identification. Based on the system matrices, modal analysis is carried out for power

system oscillation

Chapter 4: Robust local power system stabilizers are developed using linear matrix

inequality based on power system matrices.

124

Chapter 5: Coherency analysis of generators is carried out using hierarchical

clustering and k-harmonic harmonic means clustering algorithms. The concept of

virtual generator is introduced.

Chapter 6: Virtual generator based power system stabilizer is developed to damp the

inter-area oscillations in multi-machine power systems.

Chapter 7: Artificial immune system is applied to realize adaptive wide area

measurement based power system stabilizers for better damping effectiveness under

various operating conditions.

Chapter 8: SmartParks are applied in power system with wind power integration to

realize the functionalities of damping controller, active power flow regulator and

voltage regulator concurrently.

9.3 Main conclusions

With the increase of load and the integration of renewable energy, power system is constantly

pushed toward stability margin, characterized by oscillations resulted from lack of damping torque.

The oscillation involves generators and transmission lines in the whole power system, as reflected

by fluctuating generator speeds, phase angles, power flows, and bus voltages. There are multiple

modes of oscillations characterized by different frequencies and damping ratios. They can be

categorized into local modes, intra-area modes, and inter area modes. For analysis of oscillation

modes, modal analysis can be carried out based on the system matrices identified using Stochastic

Subspace Identification (SSI). Through modal analysis, the oscillation modes in a power system

can be identified; moreover, the observability factor and controllability factor can be calculated as

a reflection of the relationship between the modes and generators.

125

The local modes and intra-area modes of oscillations can be damped by local Power System

Stabilizers developed using Linear Matrix Inequality (LMI) approach. For the inter-area modes,

since local measurements may lack observability for the oscillations in concern, wide-area

measurement based damping controllers can be used. During power system transients, generators

with small electrical distance generally oscillate coherently; thus, generators in a power system

can be classified into coherent groups using Hierarchical Clustering (HC) or K-Harmonic Means

Clustering (KHMC) algorithms. Each group of generators can be equivalent to a Virtual Generator

(VG). Based on this, a Virtual Generator based Power System Stabilizer (VG-PSS) is proposed

that makes use of VG speed deviation to generate a control signal on the generator of maximum

controllability. The parameters of the VG is automatically tuned through Particle Swarm

Optimization (PSO).

With the change of power system operating conditions, the generator coherency is subjected

to variation. In order to alleviate the impact of coherency variation on the effectiveness of VG-

PSS, an Artificial Immune System (AIS) is adopted to impose a deviation of parameter change to

the VG-PSS during power system transients, leading to improved efficacy of damping control. The

parameters of the AIS are also configured using PSO.

Besides damping control schemes via supplementary signal of generator Automatic Voltage

Regulators (AVRs), the batteries of electrical vehicles can also be utilized for maintenance of

power system stability. As part of future studies, fuzzy logic based controllers will be utilized to

regulate the active and reactive power references for SmartParks, to achieve the functionality of

shock absorber, voltage regulator and damping controller concurrently and coordinately, making

the power system more resistant to changes of operating conditions such as wind speed variations.

126

As a summary, despite the fact that power systems are facing more challenges with the

development of society, power system stability can be improved with the application of modern

control technologies and artificial intelligences.

9.4 Suggestions for future research

Despite of the effectiveness shown by the proposed schemes of stability control, the

following improvements can be made as a continuation of the research in this dissertation.

The development of local power system stabilizers for different generators can be

coordinated to improve damping effectiveness.

The online synchronous generator coherency grouping can be applied to adaptively

select wide area signals to VG-PSSs.

Multiple VG-PSSs can be applied in a large power system for better damping

effectiveness. The scheme to coordinate the VG-PSSs can be studied, for example,

using fuzzy logic

Concurrent realization of multiple functionalities of SmartParks in power system

control needs to studied further for multi-area large power systems.

The optimal placement of large SmartParks in a multi-area power system can be

investigated.

Adaptive VG-PSSs can be coordinated with SmartParks to enhance power system

stability.

127

9.5 Summary

A summary of the research work in this dissertation has been presented in this chapter. The

main conclusions have been presented. Suggestions for further research along the lines of

objectives of this dissertation have been highlighted.

128

APPENDIX A

IEEE 68-BUS SYSTEM GENERATION DATA

Table A.1 The reference of generator active power for VG-PSS design

Generator Active Power Generation for Base Condition

(MW)

Active Power Generation for

Operating Condition II

(MW)


Operating Condition III.A

(MW)


Operating Condition III.B

(MW)


Operating Condition IV(MW)

G1 250 272.2 276.7 276.7 279.4

G2 545 567.2 571.7 571.7 574.4

G3 650 672.2 676.7 676.7 679.4

G4 632 654.2 658.7 658.7 661.4

G5 505.2 527.4 531.9 531.9 534.6

G6 700 722.2 726.7 726.7 729.4

G7 560 582.2 586.7 586.7 589.4

G8 540 562.2 566.7 566.7 569.4

G9 800 822.2 826.7 826.7 829.4

G10 500 500 500 500 500

G11 1150 1150 1150 1150 1150

129

Table A.2 The reference of generator active power development of adaptive wide area signal based PSS

Generator Base Case (MW) OC 1 (MW) OC 2 (MW) OC 3 (MW)

G1 250 279.4 281.1 283.3

G2 545 574.4 576.1 578.3

G3 650 679.4 681.1 683.3

G4 632 661.4 663.1 665.3

G5 505.2 534.6 536.3 538.5

G6 700 729.4 731.1 733.3

G7 560 589.4 591.1 593.3

G8 540 569.4 571.1 573.3

G9 800 829.4 831.1 833.3

G10 500 500 500 500

G11 1150 1150 1150 1150

G12 1350 1350 1350 1350

G13 3445 3180 3165 3595

G14 1785 1785 1785 1785

G15 1000 1000 1000 1000

G16 4000 4000 4000 4000

130

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[3] J. Zhang, C. Y. Chung, Y. Han, “A Novel Modal Decomposition Control and Its Application

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[4] D. J. Trudaowski, J. R. Smith, T.A. Short, D. A. Pierre, “An Application of Prony Methods in

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139

BIOGRAPHY

Ke Tang, Clemson University

He received his MS degree from Chinese Academy of Sciences at 2012. He received his

Bachelor degree from Huazhong University of Science and Technology, Wuhan, China, in 2009.

His research emphasis is on modern power system stability and control including generator

coherency analysis, wide area signals based damping control, and stability issues with increasing

levels of renewable energy sources, and energy storage systems. He has been a Graduate Research

Asisstant with the Real-Time Power and Intelligent Systems Laboratory for the period August

2012 to April 2016. Ke received the third best student paper award at the 2016 IEEE Clemson

University Power System Conference for his paper entitled “Virtual Generators based Damping

Controller for a Multimachine Power System Using µ-Synthesis”.

mailto:[email protected]

wide area signals based damping controllers for

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