frequency scan–based mitigation approach of …

Frequency Scan–Based Mitigation Approach of SubsynchronousControl Interaction in Type-3 Wind Turbines

Faris M. Alatar

Thesis submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science

in

Electrical Engineering

Ali Mehrizi-Sani, Chair

Chen-Ching Liu

Vassilis Kekatos

July 26, 2021

Blacksburg, Virginia

Keywords: Frequency Scan, Resonance, Subsynchronous Control Interaction, Type-3 Wind

Turbines, Series Compensation, Wind Farm

Copyright 2021, Faris M. Alatar


Faris M. Alatar

ABSTRACT

Subsynchronous oscillations (SSO) were an issue that occurred in the past with conven-

tional generators and were studied extensively throughout the years. However, with the rise

of inverter-based resources, a new form of SSO emerged under the name subsynchronous

control interaction (SSCI). More specifically, a resonance case occurs between Type-3 wind

turbines and series compensation that can damage equipment within the wind farm and

disrupt power generation. This work explores the types of SSCI and the various analy-

sis methods as well as mitigation of SSCI. The work expands on the concept of frequency

scan to be able to use it in an on-line setting with its output data used to mitigate SSCI

through the modification of wind turbine parameters. Multiple frequency scans are con-

ducted using PSCAD/EMTDC software to build a lookup table and harmonic injection is

used in a parallel configuration to obtain the impedance of the system. Once the impedance

of the system is obtained then the value of the parameters is adjusted using the look-up

table. Harmonic injection is optimized through phase shifts to ensure minimal disruption

of the steady-state operating point and is conducted using Python programming language

with PSCAD Automation Library. Simulation results demonstrate the effectiveness of this

approach by ensuring oscillations do not grow exponentially in comparison to the regular

operation of the wind farm.


Faris M. Alatar

GENERAL AUDIENCE ABSTRACT

Due to climate change concern and the depletion of fossil fuel resources, electrical power

generation is shifting towards renewables such as solar and wind energy. Wind energy can

be obtained using wind turbines that transform wind energy into electrical energy, these

wind turbines come in four different types. Type-3 wind turbines are the most commonly

used in the industry which use a special configuration of the classical induction generator.

These wind turbines are typically installed in a distant location which makes it more difficult

to transfer energy from its location to populated areas, hence, series capacitors can be used

to increase the amount of transferred energy. However, these series capacitors can create a

phenomenon called subsynchronous control interaction (SSCI) with Type-3 wind turbines.

In this phenomenon, energy is exchanged back and forth between the series capacitors and

the wind turbines causing the current to grow exponentially which leads to interruptions

in service and damage to major equipments within the wind turbine. This work explores

SSCI, the tools to study it, and the currently available mitigation methods. It also presents

a method to identify the cases where SSCI can happen and mitigates it using adjustable

parameters.

Dedication

To my dear wife, Raja’.

iv

Acknowledgments

I would like to first thank my supervisor, Dr. Ali Mehrizi-Sani, for the enormous amount of

support that he has provided throughout this period. Even though we never had the chance

to meet personally, this was never an obstacle to his continuous support. Thanks go out for

his support whenever I felt desperate, his guidance whenever I was lost, and his continuous

and meticulous attention to detail.

A special thanks goes to Dr. Chen-Ching Liu and Dr. Vassilis Kekatos for the courses they

taught me. I will forever be grateful for the knowledge I gained from those courses. I am

also grateful to Dr. Virgilio Centeno, working as a GTA with Dr. Centeno for two semesters

was an amazing experience. I am thankful for him offering me the chance to teach.

I am grateful for having the opportunity to intern in Hitachi ABB Power Grids for a year.

A special thanks goes to my former boss, John Daniel, and colleagues, Jason, Eden, and

Adam, I learned so much from each one. Sidhaarth and Rahul for the gatherings and walks.

Ardavan and Yousef for the occasional hangouts. Ethan for the insight into college life. My

Jordanian friends for the trips and hangouts. I am also proud to be a Fulbrighter, thank

you Fulbright for the scholarship.

Finally, no words can describe my gratitude to my wife and family. Raja’, thank you for

everything, literally everything. Mom and Dad, thank you for providing me with the oppor-

tunities that led me here. Zain, thank you for your texts. Laith, thank you for your calls.

And to my friends Tillawi, Ala’a, Tafeeli, Amer, Jaber, Bashar, and Ibrahim, thank you for

sticking around.

A thesis during a pandemic, it wouldn’t have been possible if it weren’t for all of you.

Thanks everyone.

v

Contents

List of Figures ix

List of Tables xvi

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Integration of Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Subsynchronous Oscillations (SSO) . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.1 Subsynchronous Resonance (SSR) . . . . . . . . . . . . . . . . . . . . 7

1.4.2 Subsynchronous Torsional Interaction (SSTI) . . . . . . . . . . . . . 10

1.4.3 Subsynchronous Control Interaction (SSCI) . . . . . . . . . . . . . . 10

1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Subsynchronous Control Interaction (SSCI) 12

2.1 History of SSCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Types of SSCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.1 Series Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.2 Weak Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

vi

2.3 SSCI Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 SSCI Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.1 Eigenvalue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.2 EMT Simulation Programs . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.3 Impedance Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.4 Frequency Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Mitigation of SSCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5.1 System Planning Stage . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5.2 Operation Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5.3 Active Damping Control . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.6 SSCI Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3 Frequency Scan for SSCI 27

3.1 Concept of Frequency Scans . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Studied System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Single Frequency Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4 Effect of Parameter Change on Impedance . . . . . . . . . . . . . . . . . . . 35

3.5 Effect of Online Turbines on Impedance . . . . . . . . . . . . . . . . . . . . 45

3.6 Effect of Power Order on Impedance . . . . . . . . . . . . . . . . . . . . . . 47

3.7 Multifrequency Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

vii

3.8 Verification of Multifrequency Injection Setup . . . . . . . . . . . . . . . . . 52

4 Frequency Scan Based Mitigation Approach of SSCI 56

4.1 Parallel Multifrequency Injection Scan . . . . . . . . . . . . . . . . . . . . . 56

4.2 Mitigation of SSCI Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3 Simulated Example of Mitigation Approach . . . . . . . . . . . . . . . . . . 62

4.3.1 Output Power Exceeds 1.050 pu . . . . . . . . . . . . . . . . . . . . . 62

4.3.2 Output Power Exceeds 1.025 pu . . . . . . . . . . . . . . . . . . . . . 63

4.3.3 Access to External Signal . . . . . . . . . . . . . . . . . . . . . . . . 64

4.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5 Contributions and Future Work 67

Bibliography 68

Appendices 79

Appendix A System Scan Results 80

A.1 Variation of q-axis Proportional Gain . . . . . . . . . . . . . . . . . . . . . . 80

A.2 Variation of d-axis Proportional Gain . . . . . . . . . . . . . . . . . . . . . . 91

A.3 Variation of dq-axis Proportional Gain . . . . . . . . . . . . . . . . . . . . . 101

A.4 Variation of Online Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

A.5 Variation of Power Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

viii

List of Figures

1.1 Total installed renewable energy from 2011–2020. . . . . . . . . . . . . . . . 2

1.2 Wind turbine types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Classification of SSO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Equivalent circuit of DFIG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1 Current waveforms recorded in the Minnesota incident - Figure from Refer-

ence [25]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Weak grid SSCI demonstration. . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Representation of load system and source system for impedance modeling. . 21

3.1 Illustration of frequency scan system split. . . . . . . . . . . . . . . . . . . . 28

3.2 Modified IEEE second benchmark model. . . . . . . . . . . . . . . . . . . . 29

3.3 Frequency scan setup for WF side - single frequency injection. . . . . . . . . 31

3.4 Frequency scan setup for grid side - single frequency injection. . . . . . . . . 31

3.5 Frequency scan of WF side at 100% power order and 100% of online turbines. 32

3.6 Frequency scan of grid side before and after outage of line 2. . . . . . . . . . 33

3.7 System scan results before and after outage of line 2. . . . . . . . . . . . . . 34

3.8 DFIG block diagram, two back-to-back converters connect the rotor to the

grid, and the stator is directly connected to the grid. . . . . . . . . . . . . . 35

ix

3.9 RSC control loops: stator real power (top loop), and stator reactive power

(bottom loop). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.10 GSC control loops: DC bus voltage (top loop), and grid-side reactive power

(bottom loop). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.11 Frequency scan results for q-axis proportional gain variations (KpQ value in

legend). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.12 Frequency scan results for d-axis proportional gain variations (Kpd value in

legend). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.13 Frequency scan results for dq-axis proportional gains variations (Kpdq value

in legend). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.14 Γ-model induction generator model. . . . . . . . . . . . . . . . . . . . . . . . 41

3.15 System scan comparison between 2 Kpdq values. . . . . . . . . . . . . . . . . 44

3.16 Frequency scan results for various online turbines. . . . . . . . . . . . . . . . 45

3.17 Frequency scan results for various power orders. . . . . . . . . . . . . . . . . 46

3.18 Typical IGBT characteristic curve - Figure from Reference [80]. . . . . . . . 48

3.19 Multifrequency injection signal from 1 Hz to 60 Hz with δ = [0]n×1. . . . . . 53

3.20 Multifrequency injection signal from 1 Hz to 60 Hz with quadratic phase shift. 53

3.21 Multifrequency injection signal from 1 Hz to 60 Hz with Schroeder equation. 54

3.22 Multifrequency injection signal from 1 Hz to 60 Hz with optimized phases. . 54

3.23 Comparison between single frequency and multifrequency injections. . . . . . 55

4.1 Parallel scan setup in PSCAD/EMTDC. . . . . . . . . . . . . . . . . . . . . 56

x

4.2 Components of parallel scan box. . . . . . . . . . . . . . . . . . . . . . . . . 57

4.3 System impedance using parallel scan. . . . . . . . . . . . . . . . . . . . . . 58

4.4 Parallel scan impact on steady-state operation. . . . . . . . . . . . . . . . . 59

4.5 Flowchart of SSCI mitigation approach. . . . . . . . . . . . . . . . . . . . . 61

4.6 RMS voltage, real power, and reactive power waveforms for when output

power exceeds 1.050 pu. (black-dashed line is when line #2 trips, yellow-

dashed line is when SSCI is detected, and yellow straight line is when a stable

operating point is found). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.7 RMS voltage, real power, and reactive power waveforms when output power

exceeds 1.025 pu. (black-dashed line is when line #2 trips, yellow-dashed line

is when SSCI is detected, and yellow straight line is when a stable operating

point is found). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.8 RMS voltage, real power, and reactive power waveforms with access to ex-

ternal signal. (black-dashed line is when line #2 trips, yellow-dashed line is

when SSCI is detected, and yellow straight line is when a stable operating

point is found). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.9 Comparison between no mitigation operation and the three mitigation ap-

proaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.1 System scan for Kpd = 2.00 and Kpq = 0.50. . . . . . . . . . . . . . . . . . . 81




xi





















xii












A.36 System scan for Kpd = 8.50 and Kpq = 2.00 . . . . . . . . . . . . . . . . . . 99









xiii














A.58 System scan for Kpd = 10.00 and Kpq = 10.00. . . . . . . . . . . . . . . . . . 111

A.59 System scan for 100% online turbines. . . . . . . . . . . . . . . . . . . . . . 112

A.60 System scan for 50% online turbines. . . . . . . . . . . . . . . . . . . . . . . 113



A.63 System scan for 100% power order. . . . . . . . . . . . . . . . . . . . . . . . 115

A.64 System scan for 50% power order. . . . . . . . . . . . . . . . . . . . . . . . . 116

xiv



xv

List of Tables

1.1 Frequencies of currents in stator and rotor of the DFIG . . . . . . . . . . . . 9

2.1 List of previous SSCI incidents . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 SSCI analysis methods summary . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1 Line parameters for modified IEEE second benchmark model . . . . . . . . . 29

3.2 Crossover frequency and resistance values for q-axis proportional gain variations 38

3.3 Crossover frequency and resistance values for d-axis proportional gain variations 40

3.4 Crossover frequency and resistance values for dq-axis proportional gains vari-

ations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.5 Crossover frequency and resistance values for various online turbines . . . . . 46

3.6 Crossover frequency and resistance values for various power orders . . . . . . 47

3.7 Peak values of multifrequency injection . . . . . . . . . . . . . . . . . . . . . 51

3.8 Crossover frequency and resistance values for single frequency and multifre-

quency injections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.1 Comparison between the three mitigation approaches . . . . . . . . . . . . . 66

xvi

List of Abbreviations

DFIG Doubly-Fed Induction Generator

DFR Digital Fault Recorder

FACTS Flexible AC Transmission System

GSC Grid Side Converter

HVDC High Voltage DC

IBR Inverter-Based Resource

IGE Induction Generator Effect

PSS Power System Stabilizer

RSC Rotor Side Converter

SSCI Subsynchronous Control Interaction

SSO Subsynchronous Oscillation

SSR Subsynchronous Resonance

SSTI Subsynchronous Torsional Interaction

SVC Static VAR Compensator

TA Torque Amplification

TI Torsional Interaction

xvii

VSC Voltage-Sourced Converter

WF Wind Farm

WPP Wind Power Plant

WT Wind Turbine

xviii

Chapter 1

Introduction

1.1 Background

Throughout history, power systems have been experiencing increased stress due to the in-

creased dependency on electricity in multiple sectors, global economic growth and increased

populations. As more and more sectors rely on electricity for their operation, such as trans-

portation, space heating, and some industrial processes, ensuring a continuous supply of

electrical power becomes a more challenging task and one of critical importance [1]. Several

events in history, such as the Northeast blackout of 2003, and the 2019 GB blackout, have

showed the enormous financial losses, and the disruption of services to customers that can

occur due to faults and errors in electrical power systems [2].

Power systems have long been operated in a traditional and conventional way, where the

dominating power generation was done by non-renewable energy sources such as coal, natural

gas, and oil. Driven by climate concerns, decreasing costs, and the depletion of fossil fuels,

power generation is shifting towards using renewable energy sources in an accelerating pace.

The usage of renewable energy has been increasing throughout the last decade as shown in

Figure 1.1 where the net addition of renewable energy in 2020 exceeded that in 2019 by 50%

[3].

As more and more sectors increasingly rely on electricity, this figure is only expected to

1

2 CHAPTER 1. INTRODUCTION

increase. According to the International Energy Agency (IEA), an additional 22,101 TWh

is expected to be generated from renewable sources by 2040 while non-renewable energy

production is expected to drop by a value of 9,664 TWh in the same period [4].

Figure 1.1: Total installed renewable energy from 2011–2020.

1.2 Wind Energy

One of the most prominent sources of renewable energy is wind energy. This is because of the

massive production potential that wind can offer. Wind energy has been used throughout

human civilization in mills, sailing, and pumping. Wind energy has proven to be one of the

most viable choices for clean energy production and has been utilized in power generation

through the use of wind turbine (WT), where the basic working principle is to convert wind

energy into mechanical energy and in turn into electrical energy that can be utilized.

WTs can assist in power generation without affecting the climate. This is due to not pro-

ducing greenhouse gas emissions, and using little land area in comparison to other renewable

1.2. WIND ENERGY 3

energy sources. In addition to this, the cost of WTs has been declining due to increasing

capacity factors where larger towers with bigger blades are being developed and installed [5].

WTs have developed throughout history, and the technology used in them has advanced.

They were first used to cover local energy demands but then started to get connected to the

electrical grid. WTs are mainly divided into fixed-speed turbines, and variable speed turbines

- where the variable speed operation is made possible due to the usage of power electronic

components. Variable speed operated WTs have several advantages over fixed-speed. Some

of which include a better utilization of wind energy, less mechanical stress, along with better

control capabilities.

WTs have drastically changed during the past 30 years and can now be categorized into four

main types according to the AC generator and converter types used in them, as shown in

Figure 1.2:

1. Type-1 WT - use squirrel cage induction generators (SCIG) operating at a fixed speed

that need complex considerations in the development of mechanical parts with limited

control capabilities. A capacitor bank is needed to compensate for the reactive power

demand from the SCIG [6].

2. Type-2 WT - use wound rotor induction generators (WRIG) with adjustable rotor

resistance control for better control capabilities. The main disadvantage of this type is

that the limited controllability comes at the expense of efficiency due to energy being

wasted in the rotor resistance along with the capacitor bank requirement for reactive

power compensation.

3. Type-3 WT - use doubly-fed induction generators (DFIG), this type can provide its

own reactive power. The power converters used in this type only need to handle 30%

of the rated turbine power.


4. Type-4 WT - use permanent magnet synchronous generators (PMSG) with full power

converters, this type can provide its own reactive power as well. An advantage of this

type is that the gearbox can be eliminated thus reducing the overall mechanical stress.

The disadvantage of this type is that the power converters need to be able to handle

the full rated turbine power.

The first two types of turbines were used in the first stages of wind turbine installations.

However, recently, most installed WTs are either Type-3 or Type-4 WTs [7]. According to

the Global Wind Energy Council (GWEC), the global wind energy market is expected to

grow on average by 4% each year in the next five years [8].

1.3 Integration of Wind Energy

WTs did not leave a serious impact on the power grid system at their early stages, where

wind fluctuations were directly transferred into the grid, and they lacked reactive and active

powers’ controllability. However, as more WTs got installed and wind penetration increased

in the grid, these previously neglected issues became more noticeable and needed to be

addressed. This has been made possible mostly due to the advancement in power electronics

that has allowed for WTs to become an active power generation unit instead of an unregulated

power source. Nevertheless, the integration of WTs into the electrical grid comes with issues

that can be mainly categorized into two main types; operational issues and dynamic issues

[9].

Operational issues are related to the fact that wind energy is not dispatchable, thus creating

the complexity of having to rely on an intermittent power source due to the nature of wind

energy. In [10], a two stage stochastic programming was proven to be effective to overcome

the uncertainty with real time decisions.

1.3. INTEGRATION OF WIND ENERGY 5

Gear

Box

Induction

Generator

PFC

Capacitors

Turbine

Transformers

Collector

Bus

Grid

Gear

Box

Induction

Generator

PFC

Capacitors

Turbine

Transformers

Collector

Bus

Grid

Gear

Box

DFIGTurbine

Transformers

Collector

Bus

Grid

PMSGTurbine

Transformers

Collector

Bus

Grid

(a) Type-1 Wind Turbine

(b) Type-2 Wind Turbine

(c) Type-3 Wind Turbine

(d) Type-4 Wind Turbine

Variable

Resistor

RSC GSC

PWM Converter

Figure 1.2: Wind turbine types.


Dynamic issues, however, are short in the nature of their time-scale. These issues are mostly

related to fault handling, inter-area oscillations, resonances (both electrical and electrome-

chanical) and interactions.

Typically, wind farms are installed in locations that are far away from load centers. There-

fore, the power generated must be transferred to load centers through either new or existing

transmission lines [11]. New transmission lines require a significant investment, therefore,

a better utilization of already existing transmission lines is almost always desired. Series

compensation allows for this enhanced utilization by reducing the total inductive reactance

of the line, and it also improves the stability and contrallibility in the grid, resulting in

increasing the total available transfer capability of the existing line [12]. That said, series

compensation does give rise to one type of dynamic issues called subsynchronous oscillations

(SSO).

1.4 Subsynchronous Oscillations (SSO)

SSO are oscillations that have a frequency below the fundamental frequency [13], and can

damage components in the power system, as well as disrupting the operation of the power

system. SSO can be classified into three main types, as depicted in Figure 1.3:

1. Subsynchronous Resonance (SSR)

(a) Induction Generator Effect (IGE)

(b) Torsional Interaction (TI)

2. Subsynchronous Torsional Interactional (SSTI)

3. Subsynchronous Control Interaction (SSCI)

1.4. SUBSYNCHRONOUS OSCILLATIONS (SSO) 7

Sub-Synchronous Oscillations (SSO)

Sub-Synchronous Resonance (SSR)

Induction Generator Effect (IGE)

Torsional Interaction (TI)

Sub-Synchronous Torsional Interaction

(SSTI)

Sub-Synchronous Control Interaction

(SSCI)

Figure 1.3: Classification of SSO.

1.4.1 Subsynchronous Resonance (SSR)

SSR is ”an electric power system condition where the electric network exchanges energy with

a turbine generator at one or more of the natural frequencies of the combined system below

its synchronous frequency” as defined by IEEE [14]. This includes both natural modes of

oscillation due to inherent system characteristics, and forced modes of oscillation that are

driven by a particular device or control system.

The first paper to ever discuss the possibility of an interaction between turbine generators

and series compensation was published in 1937 [15]. However, it only got the full attention

of researchers when the first case of SSR occurred at the Mohave coal-fired power plant back

in 1970 and 1971 which resulted in fractures of the shafts of the turbine generator [16]. It


was initially reported to be a mechanical failure but it was later identified correctly after the

second incident to be a case of SSR and was addressed in a paper in 1973 [17].

Induction Generator Effect (IGE)

IGE is a purely electrical phenomenon that involves the interaction between the series-

compensated line and the negative damping in DFIG at the resonance frequency.

The resonance frequency of a series compensated line is

fssr = fs

√Xc

XL

= fs√k (1.1)

where

fs is the synchronous frequency of the system

Xc is the series capacitor reactance

XL is the transmission line inductive reactance

k is the percentage of series compensation for the transmission line.

At fssr, the slip will be:

sssr =fssr − frfssr

(1.2)

where

fr is the electrical frequency of the rotor.

At fssr, which is typically below fr, the slip will be negative. The steady-state equivalent

circuit of DFIG using a classical induction machine representation is shown in Figure 1.4.

Having a negative slip results in a negative Rr which can overcome the positive resistance in

the remainder of the system (transmission line and stator resistance), resulting in a negative

1.4. SUBSYNCHRONOUS OSCILLATIONS (SSO) 9

system damping at fssr [18].

Figure 1.4: Equivalent circuit of DFIG.

The frequencies of currents in the stator and rotor are listed in Table 1.1 [9].

Table 1.1: Frequencies of currents in stator and rotor of the DFIG

Stator Current Rotor Electrical Frequency Rotor Current

Is1 → fs fr Ir1 → fs − frIs2 → fssr fr Ir2 → fssr − fr

Torsional Interaction (TI)

TI is the interplay between the mechanical system and electrical system represented by

the turbine-generator and the series-compensated line, respectively [19]. In this case, the

generator rotor oscillations grow undamped when the induced subsynchronous frequency

matches one of the natural oscillatory modes of the turbine generator shaft [20]. TI is more

likely to take place in conventional plants with low inertia and is not a typical risk in WTs.


1.4.2 Subsynchronous Torsional Interaction (SSTI)

SSTI is another known problem where the mechanical mass of a synchronous generator

resonates with the negative damping of a nearby power electronic controller and can cause

damage to generators. It is a device-dependent interaction which requires the presence of

power electronic controllers such as those found in FACTS, SVC, PSS, and HVDC links that

typically respond quickly to power variations where these controllers can exhibit negative

damping at subsynchronous frequencies [21]. The first SSTI incident involved an HVDC line

in Square Butte that connects North Dakota and Minnesota [22].

1.4.3 Subsynchronous Control Interaction (SSCI)

SSCI is a device-dependent type of SSO that is caused by an interaction between inverter-

based resources (IBR), and either series compensation or weak grid conditions. Typically,

any SSO that involves Type-3 and Type-4 WTs is categorized as a SSCI case. SSCI will be

further explained and discussed in Chapter 2.

1.5 Thesis Outline

The thesis is outlined as the following:

• Chapter 1 provides a background for renewable energy, wind energy, the integration

of WTs, and an introduction to SSR.

• Chapter 2 describes the SSCI phenomenon, study approaches, and mitigation methods.

• Chapter 3 describes the frequency scan study approach, and presents a different ap-

proach to frequency scans.

1.5. THESIS OUTLINE 11

• Chapter 4 presents a mitigation approach to prevent SSCI using on-line frequency

scan, and parameter modification of DFIG or wind farms.

• Chapter 5 is the conclusion and future work related to this thesis.

Chapter 2

Subsynchronous Control Interaction

(SSCI)

2.1 History of SSCI

The first incident of subsynchronous oscillations (SSO) related to wind turbines (WTs) oc-

curred back in 2007 in Minnesota [23] following an installation of 60% series compensation

on a 34 kV transmission line. Prior to installing the series compensation, SSO susceptibil-

ity studies were conducted as usual to assess the risk of SSO with the nearby conventional

generators. Transfer trip schemes were installed as a cautionary measure despite the studies

showing no significant risk of SSO. It was assumed at that time that Type-3 WT will be

immune to these oscillations due to their partial isolation with the usage of power electronics

[24].

However, three days after the installation of the series compensation, and after a normal

scheduled system outage for nearby breakers, the wind farm (WF) was left in a radial con-

nection with the series capacitor resulting in undamped current oscillations which damaged

components within some of the WTs.

Through the analysis following the event using the waveform traces collected by the digi-

12

2.1. HISTORY OF SSCI 13

tal fault recorders (DFR)1, it was identified that one frequency component (9.44 Hz) had

negative damping and four other frequency components (38.85 Hz, 59.86 Hz, 60.32 Hz, and

62.83 Hz) had damping of less than 1% [25]. The magnitude of the phase current peak

increased ten folds within 0.3 s as shown in Figure 2.1.

Figure 2.1: Current waveforms recorded in the Minnesota incident - Figure from Reference[25].

The frequencies of the oscillations did not coincide with any of the modal frequencies of

the nearby combustion turbine generators shafts nor with the Eigen frequencies of the WTs

structures.

The first subsynchronous control interaction (SSCI) incident to cause severe damage was

witnessed within the Electric Reliability Council of Texas (ERCOT) grid in 2009 [26] that1Even though the radial connection remained for almost five minutes, only the first second was captured

by the DFRs.

14 CHAPTER 2. SUBSYNCHRONOUS CONTROL INTERACTION (SSCI)

involved Type-3 WTs, and resulted in 20-30 Hz oscillations [27]. In 2011, 4 Hz oscillations

were observed in Type-4 WTs in Texas following a transmission outage [28]. Another incident

in Texas that also involved Type-3 WTs occurred in 2017 in three different events with the

same frequency range of oscillations between 20-30 Hz [29].

Throughout the years 2012 to 2016, multiple SSCI incidents were also witnessed in Xinjiang

as well as in northern regions of China that included both Type-3 and Type-4 WTs. After

this incident, multiple incidents occurred within the ERCOT grid and China grid [30]. These

incidents occurred frequently; for example, 58 SSCI events were detected within a one-year

span in Northern China. As well as that, some of these incidents involved a significantly

lower percentage of series compensation in comparison to the Minnesota and Texas incidents.

The last incident related to SSCI up to date occurred in 2019 in Great Britain (GB) when

an undamped electric resonance between an off-shore WF that consists of Type-4 WTs along

with weak grid conditions resulted in a voltage drop that led to the disconnection of Hornsea

offshore WF that ended up in an enormous blackout in Great Britain grid [31]. Table 2.1

summarizes the list of incidents related to SSCI.

Table 2.1: List of previous SSCI incidents

Year(s) Location WT Type Interaction With

2007 Minnesota Type-3 Series compensation2009 Texas Type-3 Series compensation2011 Texas Type-4 Weak grid

2012-2016 Northern China Type-3 Series compensation2014-2015 Xinjiang, China Type-4 Weak grid

2017 Texas Type-3 Series compensation2019 UK Type-4 Weak grid

2.2. TYPES OF SSCI 15

2.2 Types of SSCI

SSCI can be divided into two main types [32] depending on the WT type:

1. SSCI with series capacitance

2. SSCI with weak grid

2.2.1 Series Capacitance

This type of SSCI occurs in Type-3 WT where an interaction occurs between the voltage-

sourced converters (VSCs) in the WT and the series capacitor. The mechanism of this

SSCI is nearly identical to IGE, which was previously explained in 1.4.1, where the overall

resistance is negative at the resonance frequency resulting in undamped oscillations. A radial

connection between a series-compensated line and a WF significantly increases the risk of

SSCI due to the reduction in system inductive impedance thus effectively increasing the

system capacitive impedance.

2.2.2 Weak Grid

This type of SSCI occurs in Type-4 WT which mainly happens in VSCs that are connected

to weak grid conditions. An instability loop is introduced due to the coupling between the

POI voltage and the WT power output. A simple system, for illustration purposes, is shown

in Figure 2.2. The connected WT is modeled in dq-frame aligned with the POI voltage


(d-axis voltage aligned to the POI voltage). Therefore,

∆V = ∆vd

= −X∆iq −X√(

V∞Xid

)2

− 1

∆id(2.1)

The output power is defined as

P = V id ∴ ∆P = id∆V + V∆id (2.2)

Figure 2.2: Weak grid SSCI demonstration.

The instability is introduced as whenever the power order increases, id increases. However,

that also reduces the value of the POI voltage which effectively reduces the power output of

the WT [33].

2.3 SSCI Features

According to the definition in [19], SSCI can be listed under the category of Device Depen-

dent Subsynchronous Oscillations (DDSO) where SSCI has distinctive features which makes

it different than other SSO cases. The first difference is that subsynchronous resonance (SSR)

does not include power electronic converters unlike SSCI and subsynchronous torsional inter-

action (SSTI) where power electronic converters actively participate in the oscillations. The

2.3. SSCI FEATURES 17

involvement of power electronic converters makes it difficult to use approaches previously

used in SSR in SSCI cases.

In addition to this, SSR is usually associated with conventional steam turbine generators

(STGs) unlike SSCI which is associated with wind turbine generators (WTGs). The differ-

ences between WTGs and STGs are vast, such as power generation capacity (WTGs range

in a few megawatts unlike STGs which can exceed hundreds of megawatts), and the number

of generators in a WF is significantly larger than the number of generators in a conventional

power plant. This makes it very difficult to model the entire WF for SSCI analysis, and thus

these generators in a WF must be aggregated [34].

The third difference is that SSR and SSTI typically involve mechanical shaft dynamics

whereas SSCI is an electrical phenomenon that does not include any torsional oscillations

[35]. The last and fourth difference is that oscillations due to SSR and SSTI happen at a

fixed frequency unlike SSCI where they vary with different parameters such as wind speed,

number of WTs in service, grid stiffness, and control parameters of the WTs.


2.4 SSCI Analysis Methods

Four main methods and tools can be used to study and investigate the risk of SSCI in wind

farms. Each provide their own advantages and come with their own disadvantages.

2.4.1 Eigenvalue Analysis

Eigenvalue analysis is a powerful method to study SSCI where the complete system must be

linearized at a steady-state operating point in the form of:

x = Ax+Bu (2.3)

where the eigenvalues of the system can be obtained by solving:

det[λI −A] = 0 (2.4)

The obtained eigenvalues contains all frequencies of oscillations along with their respective

damping values. Eigenvalue analysis can also be used to study participation factors for each

component, as well as residue analysis for controller design. MATLAB is one of the most

commonly used softwares to conduct this analysis.

However, eigenvalue analysis requires high-order mathematical models which can make the

modeling process complex, and it also requires significant computational time and effort to

use taking into account the physical non-linearities, and the presence of switching devices

[36]. As well as this, manufacturers of WTs typically provide black-box models for their WTs

due to intellectual property rights which makes the usage of eigenvalue analysis impossible

to conduct without gaining access to the WT internal system [34].

2.4. SSCI ANALYSIS METHODS 19

Eigenvalue analysis is used extensively in research work in order to investigate SSCI. Refer-

ences [9] and [37] say that eigenvalue analysis is used to study SSCI in Type-3 WTs connected

to series compensation, and the participation factors of different parameters including the

percentage of series compensation and wind speed. It also did a feasibility test of using

eigenvalue analysis to identify and select proper mitigation signals for SSCI.

Grid connected Type-3 WTs were modeled extensively, and their behavior was studied in

Reference [38]. The first IEEE benchmark model for subsynchronous resonance studies was

modified in Reference [39] to connect 100 MW of Type-3 WTs to study SSCI using eigenvalue

analysis.

2.4.2 EMT Simulation Programs

Electromagnetic transient (EMT) programs use models which include sufficient detail in

order to simulate the dynamics of the system including power electronic converters, and

their control systems in the time domain unlike traditional transient stability programs

which are based in the frequency domain using phasors that will not be able to simulate

subsynchronous frequencies’ dynamics.

EMT programs require detailed models of the system components including the WT and its

control. These models are typically provided by the wind manufacturer in a black-box. One

of the advantages of EMT programs is that once the system has been modeled, then the

system can be used for small signal and large signal analysis. It can also serve as a validation

check for results obtained using other methods.

The disadvantage of EMT programs is that they are computationally expensive due to the

small time-steps required for switching devices. As well as this, they do not indicate the

potential risks that can arise in the future.


EMT programs can be software-based or hardware-based. PSCAD/EMTDC and MAT-

LAB/Simulink are the most commonly used software-based EMT programs where multiple

papers studied SSCI using them [36, 40, 41, 42, 43], while RTDS and OPAL-RT are the

most commonly used hardware-based EMT programs, and have been used in research as

well [44, 45, 46]. The configuration for hardware-based simulations is controller hardware in

the loop (CHIL) in order to simulate SSCI using physical WT controllers. The work in this

thesis will use PSCAD as the software-based EMT program in addition to frequency scans.

2.4.3 Impedance Modeling

Impedance modeling is a small signal modeling method which describes the system with

an input-output relationship (voltage and current) in the frequency domain. Once the

impedance model has been calculated, the Nyquist stability criterion can be used to de-

termine the stability of the system. It was first introduced back in 1976 [47] and has been

used extensively in black-box systems [48].

Depending on the components in the system, the impedance can be obtained either through

the analytical method, or through the measurement method. In the analytical method, the

components and the parameters of the components must be known, where the impedance is

calculated by applying the linearization theory where if there is a current disturbance at the

terminal then the resulting voltage is measured in order to obtain the impedance value [49].

This can either be done in the dq rotating domain or the abc stationary domain is applied

and the voltage response is measured to obtain the impedance value.

The WT system is divided into two segments; the source system and the load system where

each have their own impedance as shown in Figure 2.3.

2.4. SSCI ANALYSIS METHODS 21

Zs

ZlVs

I

Source Load

Figure 2.3: Representation of load system and source system for impedance modeling.

The current can be found as :

I(s) =Vs(s)

Zs(s) + Zl(s)=Vs(s)

Zl(s).

1

1 + Zs(s)/Zl(s)(2.5)

According to the Nyquist stability criterion, the system is stable if and only if the number

of counterclockwise encirclement around (-1 + j0) of Zs/Zl is equal to the number of right

half-plane (RHP) poles of Zs/Zl [50]. If there is an encirclement, then it means that there

is a frequency ω0 which can make Zs(jω0)/Zl(jω0) purely real and less than -1. This means

that there is a resonance at ω0 with a negative resistance.

The disadvantage of impedance modeling is that it is only applicable for one operating

condition where the impedance might vary with different parameters such as wind speed,

power output, and the number of online turbines. Another disadvantage is that it only

indicates resonance frequencies without damping values.

Impedance modeling has been used in research to study SSCI [50]. Reference [51] proposes

an aggregated RLC circuit to investigate SSCI and Reference [52] uses impedance modeling

to show the effect of different parameters such as rotating speed, series compensation, and

control parameters on SSCI.


2.4.4 Frequency Scan

Frequency scan is one of the most commonly used tools to investigate SSCI, more specifically

it is widely used in dealing with black-box models. Ideally, a frequency scan works by mea-

suring the impedance of the system from the stator windings. However, the more common

approach is to scan the entire WF and the system separately to obtain their impedances.

Once these impedances are found, then they are lumped into one impedance Zsys(f) where

it is then divided into resistance (real part) Rsys(f), and reactance Xsys(f) (imaginary part)

[53].

The resistance Rsys(f) and reactance Xsys(f) are then plotted against frequency f , and

resonance frequencies are identified in the reactance plot, if the resistance is negative then

the system is unstable, otherwise, the system is considered stable.

The advantage of this method is the ability for it to be used with black-box models, since

it mainly works on measuring the output related to a certain input without having to know

the exact configuration, parameters or topology of the WTs.

The disadvantage of frequency scans is that they are only applicable for one operating con-

dition where the impedance values vary with wind speed, series compensation, and different

parameters of WT controllers. Another disadvantage is that they can only be used to identify

the resonance frequencies without damping values.

Reference [51] proposed a method for identifying the damping values using frequency scans

using aggregated RLC circuit. Reference [54] used the frequency scan method but based it

on the slope of resistance and reactance curves instead of looking for resonance frequencies

and negative resistances.

The work in this thesis will also use frequency scans and will be further explained in Chapter

2.5. MITIGATION OF SSCI 23

Table 2.2: SSCI analysis methods summary

Method Advantages Disadvantages

Eigenvalue AnalysisIdentifies oscillatory frequencies withdamping values

Requires high-order mathematicalmodels

Can be used for participation factorand residue analysis

Linearized at a certain operating point

EMT ProgramsUsed to perform small and large-signalstudies

Computationally expensive due tosmall time-steps

can validate results from other analysismethods

Does not reveal potential risks

Impedance ModelingCan be used for participation factorand sensitivity analysis

Only valid for one operating point

Oscillation path can be found Does not give damping values for os-cillatory frequencies

Frequency ScanCan be used to deal with black-boxmodels

Only valid for one operating point

Identifies oscillatory frequencies Does not give damping values for os-cillatory frequencies

3. Table 2.2 summarizes the SSCI analysis methods with their advantages and disadvantages.

2.5 Mitigation of SSCI

Multiple methods have been suggested in research to mitigate SSCI in WTs. These methods

vary depending on the stage of implementation where they can be implemented in the system

planning stage, operation stage, or in the active damping control stage [35].


2.5.1 System Planning Stage

Reference [55] shows that increasing the series compensation percentage increases the risk.

Therefore, reducing the series compensation percentage serves as a method to mitigate SSCI

risk. The downside for this method is that it reduces the power transfer capabilities of the

transmission line significantly which defies the purpose of installing series compensation from

the beginning.

SSCI can also occur in Type-4 WT with weak grids as discussed in subsection 2.2.2. Reference

[56] addresses the weak grid instability by improving the short circuit ratio of the grid through

the installation of VSC HVDC lines. Another method that can improve the stability of

the grid will be the deployment of FACTS controllers, where these controllers can provide

damping for SSCI, as well as increase the power transfer capabilities of the transmission

line [57]. Reference [58] proposes a damping control algorithm using static synchronous

compensators (STATCOM) and static synchronous series compensators (SSSC). Both of

those methods, however, are very expensive.

Reference [59] studied the SSCI event that occurred in Hami, China, and concluded that

Type-4 WTs provide damping when added in a Type-3 WF. However, this method is rather

impractical in the industry and further complicates the process of modeling the WF.

2.5.2 Operation Stage

After the 2009 ERCOT incident, Reference [60] proposed a method to prevent SSCI by

bypassing the series capacitor once subsynchronous currents are detected. Reference [61]

developed an algorithm that detects oscillations once subsynchronous currents exceed certain

pre-defined reference values. This method is inexpensive but does require a communication

signal to the series capacitor.

2.5. MITIGATION OF SSCI 25

Another method is through the selective switching of WTs, since the number of online

turbines affects the risk of SSCI [30]. Reference [61] proposes a decision-making process

to determine which WTs should be disconnected, however, this proposed method requires

extensive communication and a metering system in order to be utilized.

2.5.3 Active Damping Control

Mitigation of SSCI using auxiliary controllers has been studied extensively in research. Using

FACTS controllers was presented in Reference [58]. Reference [62] studied the addition of an

auxiliary controller and determining which control signal should be used. It also studied the

optimal placement of the auxiliary controller and concluded that placing the controller in

the rotor-side converter (RSC) yields better results than placing it in the grid-side converter

(GSC).

Reference [63] proposed an adaptive supplementary controller based on the multiple-model

adaptive control (MMAC) to mitigate SSCI. The aim of the controller is to move the un-

stable modes to the left-hand plane, thus stabilizing the system by reducing the controller

gain values. Reference [42] proposes a linear-quadratic regulator (LQR) controller using a

full-state observer while Reference [64] proposes an observer-based controller using optimal

quadratic technique.

The main problem with auxiliary controllers is the choice of the control signal to be used.

Reference [65] proposes a simple proportional controller to mitigate SSCI. However, it uses

the speed of the turbine as an input signal which can be extremely difficult to obtain due to

the disparity in the location of WTs.


2.6 SSCI Protection

SSCI can have dire consequences if proper measures are not taken and these can range

between:

• Loss of power generation: due to the undamped oscillations, voltage values can rise

significantly in a short period of time as it has been observed in previous incidents

which can trigger the over-voltage protection in the WTs leading to the tripping of

these generation units. The loss of these generation units, depending on their capacity,

can lead to a complete blackout as was observed in the 2019 Great Britain blackout

[31].

• Equipment damage: high voltage values can be reached before the protection scheme

related to them will activate resulting in damage to connected equipment. This was

observed in the ERCOT case where several crowbar circuits were damaged as a result

of the undamped oscillations [66].

• Power quality issues: subsynchronous harmonics increase the total harmonic distortion

(THD) and degrade the power quality which can reduce the operating lifetime of the

equipment and impact its operation [67].

The protection against SSCI should always be installed on the generator side to prevent po-

tential damage from occurring due to SSCI [68]. Reference [69] proposes a subsynchronous

frequency detection as well as a tripping relay that can be used to protect generators. Pro-

tection schemes should also consider the potential damage to series capacitors and crowbar

circuits.

Chapter 3

Frequency Scan for SSCI

3.1 Concept of Frequency Scans

Frequency scan is the most prominent method for studying subsynchronous control inter-

action (SSCI) when it comes to dealing with black-box models due to them having an

input-output relationship. Black-box models are typically provided by wind turbine (WT)

manufacturers to protect their intellectual property. Frequency scan works on the concept

of harmonic injection where a current/voltage harmonic is superimposed as an input at a

certain frequency, and the output related to that input is measured to obtain the impedance

value.

The harmonic injection can either be at a single frequency or at a combination of multiple

frequencies, where injecting frequencies individually will yield the most accurate results due

to the possibility of harmonic injection distortion in a multi-frequency injection [70]. Using

the frequency scan method to study SSCI, the system will be split into two separate systems

i.e. grid side and wind farm (WF) side and the frequency scan will take place at the point

of interconnection (POI) as illustrated in Figure 3.1.

The frequency range in SSCI is less than in the fundamental frequency (60 Hz), so the

27

28 CHAPTER 3. FREQUENCY SCAN FOR SSCI

Grid Wind Farm

ZWF(f)Zgrid(f)

POI

Figure 3.1: Illustration of frequency scan system split.

frequency range will be from 1 Hz to 60 Hz. The impedances of both sides will be:

Zgrid(f) = Rgrid(f) + j ∗Xgrid(f) (3.1)

ZWF(f) = RWF(f) + j ∗XWF(f) (3.2)

Once those impedance values are calculated, then the entire system resistance and reactance

can be obtained using:

Rsystem(f) = Rgrid(f) +RWF(f) (3.3)

Xsystem(f) = Xgrid(f) +XWF(f) (3.4)

The frequency value where there might be a risk of SSCI (fSSCI) is defined as:

Xsystem(fSSCI) = 0 & d

dfXsystem(fSSCI) > 0 (3.5)

The risk is confirmed if the resistance at this frequency (fSSCI) is:

Rsystem(fSSCI) < 0 (3.6)

Frequency scan will be used as a method to study SSCI along with PSCAD/EMTDC program

in this work.

3.2. STUDIED SYSTEM 29

Figure 3.2: Modified IEEE second benchmark model.

3.2 Studied System

IEEE second benchmark model [71] has been modified to connect a WF with 100 aggregated

Type-3 WTs each rated at 2 MW as shown in Figure 3.2 where the Type-3 turbine model is

the generic model provided by PSCAD/EMTDC. The lines’ parameters are listed in Table

3.1 where line 1’s capacitive reactance can be varied between 10% to 90% of the inductive

reactance to represent the series compensation percentage. Line 2 will be tripped at a

certain time to simulate the radial connection between series compensation and Type-3 WF

to investigate SSCI.

Table 3.1: Line parameters for modified IEEE second benchmark model

Line # Positive Sequence Zero SequenceElement Value Element Value

Line #1Resistance 1.9573 Ω Resistance 5.8719 ΩInductance 0.0561 H Inductance 0.1683 HCapacitance 10%-90% Capacitance 10%-90%

Line #2 Resistance 1.77215 Ω Resistance 5.31645 ΩInductance 0.05185 H Inductance 0.1555 H

Ideally, wind farms should be modeled explicitly where each wind turbine is modeled sepa-

rately to better understand the dynamics of individual turbines [72]. However, this process

is complex and requires huge computational effort and time. Therefore, wind farms can be

modeled with a single equivalent wind-turbine to represent an aggregated model [73].


The process of aggregation is typically done through the equivalencing of the collector system,

a process similar to distribution system modeling [74]. Multiple wind turbines exist within a

single wind farm with an interconnection between them depending on the wind farm layout

and terrain, the equivalency can be through the equivalence of the complete circuit (EOCC)

or the equivalence of major lines (EOML) [75] where the equivalent X, R, and B values can

be calculated. This will include dividing the wind farm into smaller groups of wind turbines

with similar attributes. The equivalent values should match the load flow and impedance

losses results from the detailed model.

If wind farms were to be modeled in details to better understand the dynamics of an in-

dividual turbine [76] and how each turbine contributes to the wind farm dynamics, then a

deaggregation process needs to take place. Deaggregation is to model each turbine sepa-

rately by splitting each group of wind turbines into individual wind turbines, and then to

model the system connecting them, i.e., the collector system. The collector system consists

of wires between wind turbines and transformers that connect the wind turbines to the grid.

The deaggregation will depend on the actual layout of the wind farm where the length and

properties of the wires need to be modeled. Moreover, each transformer in the wind farm

needs to be modeled in accordance with the datasheet of that transformer.

3.3 Single Frequency Injection

The first approach that can be followed is to inject each frequency separately, the setup for

single frequency injection was done using PSCAD/EMTDC as shown in Figure 3.3 for the

WF side and in Figure 3.4 for the grid side.

The steps to conducting the frequency scan are as follows:

3.3. SINGLE FREQUENCY INJECTION 31

Figure 3.3: Frequency scan setup for WF side - single frequency injection.

1. Bring the scanned WF/grid to a steady-state condition.

2. Inject three-phase positive sequence voltage with a single frequency finj. The frequency

is calculated based on the run number. The voltage value should not be large enough

to disrupt the steady-state and not small enough not to cause a response.

3. Measure the current Imultimeter(t) and voltage Vmultimeter(t) at the terminal of the scanned

WF/grid.

4. Calculate the fast Fourier transform (FFT) of the measured current Imultimeter(t) and

voltage Vmultimeter(t) in time domain to obtain the current Imultimeter(f) and voltage

Vmultimeter(f) values in the frequency domain.

Figure 3.4: Frequency scan setup for grid side - single frequency injection.


5 10 15 20 25 30 35 40 45 50 55 60-400

-200

0

200

400

600

Res

ista

nce

[Ohm

s]

5 10 15 20 25 30 35 40 45 50 55 60Frequency [Hz]

-1000

-800

-600

-400

-200

0

Rea

ctan

ce [

Ohm

s]

Figure 3.5: Frequency scan of WF side at 100% power order and 100% of online turbines.

5. Calculate the impedance at the injected harmonic frequency Z(finj) using

Z(finj) =Vmultimeter(finj)

Imultimeter(finj)(3.7)

6. Repeat steps 1-5 for another frequency. The range of frequency to be scanned for SSCI

is from 1 Hz to 60 Hz.

Once the frequency scan for the WF side and the grid side has been done, the impedances

can be combined to identify the potential risks of SSCI. The results of the WF frequency

scans operating at 100% power while 100% of the turbines are online are shown in Figure

3.5 and the frequency scan of the grid side for the IEEE second benchmark model before

outage of the line is shown in Figure 3.6. The top plot shows the resistance values while the

3.3. SINGLE FREQUENCY INJECTION 33

5 10 15 20 25 30 35 40 45 50 55 60-2

0

2

4

6

8R

esis

tanc

e [O

hms] After Outage

Before Outage

5 10 15 20 25 30 35 40 45 50 55 60Frequency [Hz]

-150

-100

-50

0

50

Rea

ctan

ce [

Ohm

s]

After OutageBefore Outage

Figure 3.6: Frequency scan of grid side before and after outage of line 2.

bottom plot shows the reactance values.


Combining the results of both sides (WF and grid) can indicate the risk of SSCI. Figure 3.7

compares the frequency scan results before and after the outage. Frequencies that satisfy

Equation 3.5 are circled in the reactance plots and resistances that satisfy Equation 3.6 are

plotted in yellow in the resistance plots. As it can be seen, there is no risk in the case before

outage since no negative resistance coincides with a crossover frequency, unlike the case after

outage where there is a risk of SSCI at 14 Hz.

10 20 30 40 50 60-400

-200

0

200

400

600

Res

ista

nce

[Ohm

s]

Before Outage

10 20 30 40 50 60-400

-200

0

200

400

600

After Outage

10 20 30 40 50 60Frequency [Hz]

-1000

-800

-600

-400

-200

0

Rea

ctan

ce [

Ohm

s]

10 20 30 40 50 60Frequency [Hz]

-1000

-800

-600

-400

-200

0

Figure 3.7: System scan results before and after outage of line 2.

3.4. EFFECT OF PARAMETER CHANGE ON IMPEDANCE 35

3.4 Effect of Parameter Change on Impedance

DFIG

RSC GSC

Ps

Pr

PWTG

VDC

Figure 3.8: DFIG block diagram, two back-to-back converters connect the rotor to the grid,and the stator is directly connected to the grid.

Type-3 WTs are based on the doubly-fed induction generator configuration (DFIG) where

the stator is directly connected to the grid and the rotor is connected to the grid through

back-to-back voltage-sourced converters (VSCs) as shown in Figure 3.8. These converters can

supply the rotor with variable frequency and voltage three-phase voltages. This configuration

allows for complete control of real power and reactive power.

The grid-side converter (GSC) is responsible for maintaining the DC link voltage and the

voltage magnitude at the POI. The rotor-side converter (RSC) is responsible for both active

power and reactive power [77] through the control of the stator reactive power Qs and the

electromagnetic torque Tem provided by the DFIG. The RSC is composed of PI controllers

as shown in Figure 3.9 where the outer control loop regulates reactive power and torque by

setting the reference currents in the dq domain. The inner control loop controls the rotor

voltages through the reference and actual current values.

References [18, 43, 62, 78] show that the RSC controller has a higher impact on SSCI than


PI

Ps

Ps*

+

−Idr−

Idr*

+ VdrPI

PI

Qs

Qs*

+

−Iqr−

Iqr*

+ VqrPI

Figure 3.9: RSC control loops: stator real power (top loop), and stator reactive power(bottom loop).

PI

VDC

VDC*

+

−Idg−

Idg*

+ Vdg

PI

PI

Qg

Qg*

+

−Iqg−

Iqg*

+ Vqg

PI

Figure 3.10: GSC control loops: DC bus voltage (top loop), and grid-side reactive power(bottom loop).


5 10 15 20 25 30 35 40 45 50 55 60-400

-200

0

200

400

600

Res

ista

nce

[Ohm

s]

15 20 25 30-40

-20

0

5 10 15 20 25 30 35 40 45 50 55 60Frequency [Hz]

-1000

-800

-600

-400

-200

0

Rea

ctan

ce [

Ohm

s]

1.02.03.04.0

5.06.07.08.0

9.010.0

15 20 25-10

-5

0

5

Figure 3.11: Frequency scan results for q-axis proportional gain variations (KpQ value inlegend).

the GSC controller as well as that the proportional gain in the inner control loop has the

greater influence on impedance. Three different attempts to change the impedance have

been conducted, in the first attempt only the proportional gain of the q-axis has been varied

as shown in Figure 3.11.

Table 3.2 lists the crossover frequency and the magnitude of the resistance at that crossover

frequency while varying the q-axis proportional gain. As the gain increases, so does the

negative resistance, which increases the magnitude of the oscillations if SSCI was to occur

without any distinguishable difference in the crossover frequency. However, setting the q-axis

proportional gain to 0.5 introduced a new crossover frequency at 28.40 Hz which was not


observed in other values.

Table 3.2: Crossover frequency and resistance values for q-axis proportional gain variations

Kpq Crossover Frequency [Hz] Resistance at Crossover [Ω]

0.50 13.3/28.40 −0.5754/− 2.17211.00 14.0 −3.48171.50 14.3 −5.70902.00 14.4 −7.00722.50 14.3 −7.65403.00 14.2 −8.12453.50 14.2 −8.86674.00 14.1 −8.98764.50 14.0 −9.22215.00 14.1 −9.48155.50 14.1 −9.78456.00 14.0 −9.95936.50 13.8 −9.83997.00 13.8 −10.12837.50 13.8 −10.13598.00 13.7 −10.08128.50 13.6 −10.17999.00 13.6 −10.29539.50 13.6 −10.511610.00 13.5 −10.1654


5 10 15 20 25 30 35 40 45 50 55 60-400

-200

0

200

400

600

Res

ista

nce

[Ohm

s]

20 25 30

-40

-20

5 10 15 20 25 30 35 40 45 50 55 60Frequency [Hz]

-1500

-1000

-500

0

Rea

ctan

ce [

Ohm

s]

1.02.03.04.0

5.06.07.08.0

9.010.0

20 25 30-20

-10

0

10

Figure 3.12: Frequency scan results for d-axis proportional gain variations (Kpd value inlegend).

In the second attempt only the proportional gain of the d-axis has been varied as shown in

Figure 3.12 and the crossover frequency along with the magnitude of the resistance is listed

in Table 3.3. Similar to q-axis proportional gain, increasing the d-axis proportional gain

increases the magnitude of the negative resistance without any distinguishable difference in

the crossover frequency. The magnitude of the resistances in the d-axis variations is slightly

higher than the q-axis variations.


Table 3.3: Crossover frequency and resistance values for d-axis proportional gain variations

Kpd Crossover Frequency [Hz] Resistance at Crossover [Ω]

0.50 13.0 −3.64601.00 13.7 −4.99671.50 14.2 −6.38392.00 14.4 −7.00722.50 14.3 −7.29863.00 14.2 −7.50283.50 14.4 −7.75134.00 14.1 −7.68164.50 14.0 −7.71055.00 13.9 −7.80915.50 13.9 −7.61796.00 13.9 −7.89696.50 14.1 −8.09417.00 14.1 −8.11257.50 14.3 −8.39448.00 14.2 −8.45948.50 14.4 −8.54439.00 14.1 −8.62969.50 14.3 −8.697310.00 14.2 −8.7607

As for the third attempt, both proportional gains (dq-axis) have been varied as shown in

Figure 3.13 and the crossover frequency along with the magnitude of the resistance at the

crossover frequency are listed in Table 3.4. Similar to both d-axis and q-axis variations,

the magnitude of the resistance increases by increasing both proportional gains. However,

setting both gains at 0.5 eliminates the risk of SSCI as there is no negative resistance at any

negative-to-positive crossover frequency.


5 10 15 20 25 30 35 40 45 50 55 60-400

-200

0

200

400

600

Res

ista

nce

[Ohm

s]

15 20 25 30-60

-40

-20

0

5 10 15 20 25 30 35 40 45 50 55 60Frequency [Hz]

-1000

-800

-600

-400

-200

0

Rea

ctan

ce [

Ohm

s]

1.02.03.04.0

5.06.07.08.0

9.010.0

20 25 30-10

-5

0

5

Figure 3.13: Frequency scan results for dq-axis proportional gains variations (Kpdq value inlegend).

Combining the impedances of the WF and the system with proportional gains equal to 0.5

and 0.5 can mitigate the risk of SSCI as shown in Figure 3.15. The remaining system scans

for all variations of q-axis, d-axis and dq-axis proportional gains are listed in Appendix A.

Figure 3.14: Γ-model induction generator model.

The physical interpretation behind the increased magnitude of the resistance at crossover


Table 3.4: Crossover frequency and resistance values for dq-axis proportional gains variations

Kpdq Crossover Frequency [Hz] Resistance at Crossover [Ω]

0.50 —– —–1.00 13.7 −2.04101.50 14.2 −4.97092.00 14.4 −7.00722.50 14.4 −8.29883.00 14.2 −8.86723.50 14.1 −9.53854.00 14.2 −10.19774.50 14.1 −10.61775.00 14.0 −10.67355.50 13.9 −10.96396.00 14.0 −11.39606.50 14.1 −11.62037.00 13.9 −11.42177.50 13.9 −11.81368.00 14.1 −12.27168.50 13.9 −12.17859.00 14.0 −12.33179.50 14.0 −12.585810.00 13.9 −12.3194

frequencies can be explained using the Γ-model of the induction generator [79] as shown in

Figure 3.14 which means that the rotor voltage is equal to

VR = −RR¯IR − jωsrLRIR + ¯ψs + jωsrψs (3.8)

where V = Vd + jVq and ωsr = ωstator − ωrotor, after splitting into dq components and

accounting for cross-coupling effect,

LRIdR = −VdR −RRIdR

LRIqR = −VqR −RRIqR

(3.9)


which yields the following equation,

LRIR = −VR −RRIR (3.10)

Equation 3.10 gives the relationship between the rotor voltage and rotor current without

considering the inner current control loop as was previously depicted in Figure 3.9. Taking

the inner current control into consideration, the voltage equation becomes

VR(s) =

(KpD/Q +

KiD/Q

s

)IR(s)−

(KpD/Q +

KiD/Q

s

)I∗R(s) (3.11)

The first term in Equation 3.11 can be considered as the RSC impedance while the second

term is a voltage source and as it can be seen the proportional gain goes into the real part

(resistance). The equivalent impedance from the stator will be seen divided by the slip and

since SSCI is below synchronous frequencies then the slip will be negative.

This means that the negative internal resistance increases with the proportional gain which

can increase the risk of having an entirely negative resistance.


10 20 30 40 50 60-500

0

500

1000

Res

ista

nce

[Ohm

s]

KpDQ = 2.00

10 20 30 40 50 60-500

0

500

1000KpDQ = 0.50

10 20 30 40 50 60Frequency [Hz]

-1000

-800

-600

-400

-200

0

Rea

ctan

ce [

Ohm

s]

10 20 30 40 50 60Frequency [Hz]

-1000

-800

-600

-400

-200

0

Figure 3.15: System scan comparison between 2 Kpdq values.

3.5. EFFECT OF ONLINE TURBINES ON IMPEDANCE 45

5 10 15 20 25 30 35 40 45 50 55 60-15000

-10000

-5000

0

5000

Res

ista

nce

[Ohm

s]

T100T50

T25T10

20 25 30

-500

0

500

5 10 15 20 25 30 35 40 45 50 55 60Frequency [Hz]

-15000

-10000

-5000

0

5000

Rea

ctan

ce [

Ohm

s]

T100T50

T25T10

20 25 30

-200

0

200

Figure 3.16: Frequency scan results for various online turbines.

3.5 Effect of Online Turbines on Impedance

Another frequency scan was conducted while varying the number of online turbines to observe

the effect on the impedance. Due to the typical nature of black-box models in WTs, the

operator might only have the option to modify the number of online turbines. In this setup,

the number of turbines are varied between 100%, 50%, 25%, and 10%. The difference in the

impedance is shown in Figure 3.16.

Table 3.5 lists the crossover frequency and the magnitude of the resistance at that crossover

frequency. As it can be seen, reducing the number of online turbines significantly reduces

the crossover frequency and increases the magnitude of negative resistance more significantly


Table 3.5: Crossover frequency and resistance values for various online turbines

Online Turbines Crossover Frequency [Hz] Resistance at Crossover [Ω]

100% 14.4 −7.007250% 11.8/43.8 −10.3954/− 402.612025% 9.5 −14.712210% 6.4 −16.2921

at higher frequencies thus increasing the risk of SSCI. The complete system scan results for

the various number of online turbines are listed in Appendix A.

5 10 15 20 25 30 35 40 45 50 55 60-1

0

1

2

3

Res

ista

nce

[Ohm

s]

104

P100P50

P25P10

20 25 30

-30

-20

-10

5 10 15 20 25 30 35 40 45 50 55 60Frequency [Hz]

-20000

-15000

-10000

-5000

0

Rea

ctan

ce [

Ohm

s]

P100P50

P25P10

20 25 30-10

0

10

Figure 3.17: Frequency scan results for various power orders.

3.6. EFFECT OF POWER ORDER ON IMPEDANCE 47

3.6 Effect of Power Order on Impedance

Frequency scan was also conducted while varying the power order of the WF in order to

observe the effect on the impedance. This was done by multiplying the power reference

order with 100%, 50%, 25%, and 10%, where this power reference was sent to the RSC since

the RSC controller is responsible for the real power output of the WT. The difference in

the impedance is shown in Figure 3.17. The difference in the impedance is almost negligible

compared to the variations in number of online turbines in the lower frequency range and

becomes significant as frequency increases.

Table 3.6: Crossover frequency and resistance values for various power orders

Power Order Crossover Frequency [Hz] Resistance at Crossover [Ω]

100% 14.4 −7.007250% 14.3 −6.962925% 14.3 −7.081010% 14.3 −7.1230

Table 3.6 lists the crossover frequency with the magnitude of the resistance at that crossover

frequency. As it can be seen, changing the power order has no effect on the crossover

frequency.


3.7 Multifrequency Injection

A linear system must satisfy two conditions: homogeneity and additivity, i.e., if a linear

system T gets an input f(t) that produces an output g(t), then it must satisfy:

T (αf1(t) + βf2(t)) = αg1(t) + βg2(t) (3.12)

These conditions allow for the use of superposition where the response caused by multiple

inputs is the sum of responses caused by each input individually.

Frequency scans are ideally conducted in a single frequency injection setup to avoid any

harmonic injection distortion especially with nonlinear components [70]. The main reason

why harmonic injection distortion is a major issue with nonlinear components is the disrup-

tion of its operating region. Figure 3.18 shows a typical characteristic curve for an IGBT, a

component commonly used in voltage-sourced converter (VSC) [80].

Figure 3.18: Typical IGBT characteristic curve - Figure from Reference [80].

3.7. MULTIFREQUENCY INJECTION 49

Once the voltage value exceeds a certain limit, then either the IGBT goes into breakdown

region or the response becomes nonlinear which is undesired. Therefore, when subjecting the

WF to harmonic injection, the amplitude must not be large enough to disrupt the operating

region of the IGBTs, hence why the ideal setup for frequency scans is a single frequency

injection where the amplitude is not too high that the ratio between voltage and current

remains intact and the impedance value can be obtained for that frequency.

However, single frequency injection is significantly time consuming and is not applicable as

an on-line tool since it only handles one frequency at a time. If multifrequency injection is

to be used, then the injected voltage will be:

Vinjected(δ) = Anmax∑

n=nmin

sin(2πfnt+ δn) (3.13)

where A is the amplitude of the injected harmonic

fn is the injected harmonic frequency

δn is the phase shift of the injected harmonic at fn

nmin, nmax is the lowest/highest frequency of interest.

Using the multifrequency injection for a frequency range from 1 Hz to 60 Hz with δ = [0]n×1

and A = 0.7 kV yields the voltage signal shown in Figure 3.19.

Even though the amplitude was set at 0.7 kV, the peak value exceeded 30 kV resulting in a

large spike that can disrupt the operating region. Changing the phase angle of each frequency

results in lower spikes thus less disruption of the steady-state operation. Reference [70] uses


a quadratic phase shift where the multifrequency injected voltage becomes:

Vinjected(δ) = A

nmax∑n=nmin


where

δn =π

180n2 (3.15)

Using eqns 3.14 and 3.15, the resulting voltage signal is shown in Figure 3.20 where the peak

has been reduced to around 11 kV.

References [81, 82] propose the usage of Schroeder equation as a way of minimizing the peak

value in the injected signal where it becomes:

Vinjected(δ) = Anmax∑

n=nmin


where

δn =(n− nmin)× (n− nmin + 1)

nmax − nmin + 1× 360 (3.17)

Using eqns 3.16 and 3.17, the resulting voltage signal is shown in Figure 3.21, where the

peak has been reduced to around 8 kV.

3.7. MULTIFREQUENCY INJECTION 51

An optimization problem can be defined to reduce the peak of the injected signal by optimiz-

ing the phase angles of each frequency where the formulation for the optimization problem

will be:minimize

δmax |Vinjected(δ)|

subject to f1n = −δn ≤ 0

f2n = δn − 360 ≤ 0

(3.18)

The constraints are there to ensure that only positive phase shifts that are less than or

equal to 360 due to PSCAD/EMTDC requirements. These constraints can be relaxed since

the sinusoidal function is a periodic function. Reference [83] approached the optimization

problem using the crest factor as a parameter that yields the same results since the RMS

value is fixed for the combination of the sinusoidal function.

Using the results of optimization in eqn 3.18, the resulting voltage signal is shown in Figure

3.22, where the peak is around 8 kV.

Table 3.7 lists the peak values of each method of the four methods.

Table 3.7: Peak values of multifrequency injection

Method Peak Value [kV]

[δ]n×1 = 0 30.6848Quadratic Phase Shift 11.1948Schroeder Equation 8.1726Optimization Problem 7.6655


3.8 Verification of Multifrequency Injection Setup

Multifrequency injection frequency scan was conducted and the results of the multifrequency

were compared to the single frequency injection frequency scan. In this verification case, the

comparison was done on the default case for the WF where the power order is set at 100%

and the number of online turbines is also at 100%. The WF frequency scan comparison is

shown in Figure 3.23.

The multifrequency injection results seem to differ from single frequency injection results as

the frequency increases. However, for the lower frequencies, which are the typical frequencies

of a SSCI, the results are almost identical. Table 3.8 compares the crossover frequency and

magnitude of resistance at the crossover frequency between multifrequency injection, and

single frequency injection.

Table 3.8: Crossover frequency and resistance values for single frequency and multifrequencyinjections

Method Crossover Frequency [Hz] Resistance at Crossover [Ω]

Single Frequency Injection 14.4 −7.0072Multifrequency Injection 14.3 −6.8447

The comparison shows that the multifrequency injection is capable of identifying the crossover

frequency with high accuracy while saving time. The multifrequency injection can also be

used as an on-line method to identify SSCI risks and mitigate them if applicable which will

be discussed and demonstrated in Chapter 4.

3.8. VERIFICATION OF MULTIFREQUENCY INJECTION SETUP 53

Figure 3.19: Multifrequency injection signal from 1 Hz to 60 Hz with δ = [0]n×1.

Figure 3.20: Multifrequency injection signal from 1 Hz to 60 Hz with quadratic phase shift.


Figure 3.21: Multifrequency injection signal from 1 Hz to 60 Hz with Schroeder equation.

Figure 3.22: Multifrequency injection signal from 1 Hz to 60 Hz with optimized phases.

3.8. VERIFICATION OF MULTIFREQUENCY INJECTION SETUP 55

Figure 3.23: Comparison between single frequency and multifrequency injections.

Chapter 4

Frequency Scan Based Mitigation

Approach of SSCI

4.1 Parallel Multifrequency Injection Scan

Using the multifrequency injection method described in Section 3.7, the studied system has

been modified to adjust for a parallel scan configuration, as shown in Figure 4.1.

Figure 4.1: Parallel scan setup in PSCAD/EMTDC.

Where the parallel scan box consists of three main parts, the first being the harmonic

generation part which has three harmonic injection blocks, each for a single phase, the

harmonic injection part with three single phase current sources that take their output from

their respective harmonic injection block and the parallel scan enabler that scans the entire

system as shown in Figure 4.2. The harmonic generation blocks takes the magnitudes and

phase angles from a .txt file that is generated using Python to match the optimized injection

56

4.1. PARALLEL MULTIFREQUENCY INJECTION SCAN 57

Figure 4.2: Components of parallel scan box.

signal.

Using the scan multimeter that is highlighted in red in Figure 4.1, and by having all of the

WF impedances obtained in Chapter 3 in a look-up table, the system impedance can be

calculated as follows:

Zscan =ZWF × Zgrid

ZWF + Zgrid(4.1)

∴ Zgrid =Zscan × ZWF

ZWF − Zscan(4.2)

The results of using eqn 4.2 is shown in Figure 4.3 which was done using MATLAB post

processing of the scan current and voltage and also by using PSCAD/EMTDC FFT blocks in

comparison to the theoretical values. PSCAD values are the closest to match the theoretical

values.

58 CHAPTER 4. FREQUENCY SCAN BASED MITIGATION APPROACH OF SSCI

0 10 20 30 40 50 60-5

0

5

10

Res

ista

nce

[Ohm

s]

0 10 20 30 40 50 60Frequency [Hz]

-5

0

5

10

Rea

ctan

ce [

Ohm

s]

MATLABPSCADTheoretical

Figure 4.3: System impedance using parallel scan.

The amplitude of the current injection must be low enough to ensure that the parallel scan

does not interfere with the steady state operating point, therefore the amplitude was chosen

to be 1% of the steady state current value which amounts to 0.002 kA in this case. The

disruption caused due to this injection is minimal and is shown in Figure 4.4.

4.1. PARALLEL MULTIFREQUENCY INJECTION SCAN 59

Figure 4.4: Parallel scan impact on steady-state operation.

The parallel scan was enabled at time = 4 s, depicted with the black dashed line in Figure

4.4. The disruption in the output power is less than 1% with almost negligible effect on the

RMS voltage.


4.2 Mitigation of SSCI Approach

The approach to mitigate SSCI using the on-line frequency scan goes as the following:

1. Once SSCI is detected, the proportional gains of the dq-axis is reduced to very low

values to prevent oscillations from growing exponentially.

2. Parallel scan is enabled to identify grid impedance.

3. Grid impedance is combined with WF impedance to obtain the overall system impedance.

4. External or internal parameters are changed to mitigate the risk of SSCI.

In the simulated system in PSCAD, the following takes place:

1. The system is started with Line #2 in service.

2. It takes 3 seconds for the WF to stabilize and reach steady-state.

3. At time = 5 s, Line #2 trips.

4. Proportional gains are reduced.

5. Parallel scan is enabled.

6. Parallel scan results are processed.

7. Parameters are changed to mitigate SSCI.

The following flowchart depicts the methodology.

4.2. MITIGATION OF SSCI APPROACH 61

Steady-State

Detection of SSCI

Immediate Change of Parameters

Parallel Scan

Change of Parameters

Mitigation of SSCI Turn off WF

Steady-State

yes

no

Figure 4.5: Flowchart of SSCI mitigation approach.


4.3 Simulated Example of Mitigation Approach

Three different approaches in the mitigation are done, the difference between them is how

SSCI is detected. The base values for per-unit measurements and calculations are 200 MVA

and 230 kV.

4.3.1 Output Power Exceeds 1.050 pu

In the first approach, SSCI is detected once the output power of the WF exceeds 1.050

the steady-state power output. Figure 4.6 shows the RMS voltage, real power, and reactive

power waveforms. The line trips at t = 1.00 s leaving the WF in a radial connection with the

series-compensated line, at t = 1.10 s SSCI is detected when the power output is 1.050 pu

at which the parameters are decreased, and parallel scan is enabled. At t = 2.10 s, parallel

scan is disabled, and a stable operating point is obtained. The maximum real power during

the oscillations is 1.0554 pu, and the minimum is 0.9150 pu with the reactive power ranging

between −0.1258 and 0.0443 pu.

4.3. SIMULATED EXAMPLE OF MITIGATION APPROACH 63

Figure 4.6: RMS voltage, real power, and reactive power waveforms for when output powerexceeds 1.050 pu. (black-dashed line is when line #2 trips, yellow-dashed line is when SSCIis detected, and yellow straight line is when a stable operating point is found).

4.3.2 Output Power Exceeds 1.025 pu

In the second approach, SSCI is detected once the output power of the WF exceeds 1.025

the steady-state power output. Figure 4.7 shows the RMS voltage, real power, and reactive

power waveforms. The line trips at t = 1.00 s, leaving the WF in a radial connection with

the series-compensated line, at t = 1.06 s SSCI is detected when the power output is 1.025 pu

at which the parameters are decreased, and parallel scan is enabled. At t = 2.06 s, parallel

scan is disabled, and a stable operating point is obtained. The maximum real power during

the oscillations is 1.0487 pu, and the minimum is 0.9467 pu with the reactive power ranging

between −0.0798 and 0.0191 pu.


Figure 4.7: RMS voltage, real power, and reactive power waveforms when output powerexceeds 1.025 pu. (black-dashed line is when line #2 trips, yellow-dashed line is when SSCIis detected, and yellow straight line is when a stable operating point is found).

4.3.3 Access to External Signal

In the third approach, it is assumed that the WF has access to the tripping signal of the

CB associated with Line #2. Figure 4.8 shows the RMS voltage, real power, and reactive

power waveforms. The line trips at t = 1.00 s, leaving the WF in a radial connection with

the series-compensated line, at t = 1.00 s, SSCI is detected when the CB is open at which

the parameters are decreased, and parallel scan is enabled. At t = 2.00 s, parallel scan is

disabled, and a stable operating point is obtained. The maximum real power during the

oscillations is 1.0464 pu and the minimum is 0.9536 pu with the reactive power ranging

between −0.0447 and −0.0126 pu.

The normal operation without any mitigation approach yields an undamped oscillation that

4.3. SIMULATED EXAMPLE OF MITIGATION APPROACH 65

Figure 4.8: RMS voltage, real power, and reactive power waveforms with access to externalsignal. (black-dashed line is when line #2 trips, yellow-dashed line is when SSCI is detected,and yellow straight line is when a stable operating point is found).

grows to 4.29 pu before the rotor stops spinning due to growing subsynchronous currents.

Figure 4.9 shows the real power output in the normal operation without any migitation in

comparison to three mitigation approaches. Oscillations grow to 2.5 pu in 0.5 s without any

mitigation.

4.3.4 Discussion

SSCI is mitigated in all of the three approaches; (i) output power exceeds 1.050 pu, (ii)

output power exceeds 1.025 pu, and (iii) access to external signal. Real power oscillation

is the most significant in the first approach (output power exceeds 1.050 pu), and the least

significant in the third approach (access to external signal). Once a stable operating point

is obtained, in all of the previously mentioned approaches, the real power oscillation is less


Figure 4.9: Comparison between no mitigation operation and the three mitigation ap-proaches.

than 0.70%. Reactive power oscillations are minimized and the RMS voltage ranges between

0.998 pu and 1.002 pu. In the normal operation without any mitigation approach, the output

power grows to 2 pu in less than 0.30 s. This can either lead to excessive damage in WTs or

to the disconnection of the WF, both of these scenarios lead to an undesired disruption of

service.

Table 4.1: Comparison between the three mitigation approaches

Approach Real Power Range [pu] Reactive Power Range[pu]

Output power exceeds 1.050 pu 0.9150 to 1.0554 −0.1258 to 0.0443Output power exceeds 1.025 pu 0.9467 to 1.0487 −0.0798 to 0.0191Access to external signal 0.9536 to 1.0464 −0.0447 to −0.0126

Chapter 5

Contributions and Future Work

The contributions of this thesis are as follows:

• Discussing the various types of SSOs including SSR, SSTI, TI, and IGE.

• Explaining SSCI and the mechanism of interaction between series compensation and

Type-3 wind turbines.

• Comparing different methods of frequency scans and proposing an optimization prob-

lem to reduce peak voltage.

• Usage of on-line parallel harmonic injection, along with frequency scan to mitigate

SSCI.

Whereas in the future, this work can be built on in any one of the following ways:

• Investigating the effect of other parameters and their influence on the impedance of

the WF.

• Modifying the GSC controller to inject harmonics instead of using a parallel scan

approach.

• Obtaining the impedance of the WF without having to use a look-up table through

parametric equations.

67

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Appendices

79

Appendix A

System Scan Results

The full results for the system scan will be listed in this appendix.

A.1 Variation of q-axis Proportional Gain

In this section, system scan results under various proportional gains for the q-axis inner

control loop will be listed in Figures A.1 - A.20.

80

A.1. VARIATION OF Q-AXIS PROPORTIONAL GAIN 81

Figure A.1: System scan for Kpd = 2.00 and Kpq = 0.50.


82 APPENDIX A. SYSTEM SCAN RESULTS



A.2. VARIATION OF D-AXIS PROPORTIONAL GAIN 91


A.2 Variation of d-axis Proportional Gain

In this section, system scan results under various proportional gains for the d-axis inner

control loop will be listed in Figures A.21 - A.39.


Figure A.36: System scan for Kpd = 8.50 and Kpq = 2.00


A.3. VARIATION OF dq-AXIS PROPORTIONAL GAIN 101

A.3 Variation of dq-axis Proportional Gain

In this section, system scan results under various proportional gains for the dq-axis inner

control loops will be listed in Figures A.40 - A.58.


A.4 Variation of Online Turbines

In this section, system scan results under various number of online turbines will be listed in

Figures A.59 - A.62.

Figure A.59: System scan for 100% online turbines.

A.4. VARIATION OF ONLINE TURBINES 113



A.5. VARIATION OF POWER ORDER 115

A.5 Variation of Power Order

In this section, system scan results under various number of power orders will be listed in

Figures A.63 - A.66.

Figure A.63: System scan for 100% power order.

A.5. VARIATION OF POWER ORDER 117


frequency scan–based mitigation approach of …

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