Wide Area Measurement Applications for Improvement … Area Measurement Applications for Improvement of Power System Protection Mutmainna Tania Abstract The increasing demand for …

Wide Area Measurement Applications forImprovement of Power System Protection

Mutmainna Tania

Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State

University in partial fulfilment of the requirements for the degree of

Doctor of Philosophy

in

Electrical Engineering

Arun G. Phadke (Co-Chair)

Jaime De La Reelopez (Co-Chair)

Virgilio A. Centeno

Richard W. Conners

Werner E. Kohler

December 7, 2012

Blacksburg, Virginia

Keywords: Back-up Distance Protection, Supervisory Control, Adaptive Loss-of-Field

Protection, Wide Area Measurement System, Generation Redistribution

c©Copyright 2012, Mutmainna Tania

Wide Area Measurement Applications for Improvementof Power System Protection

Mutmainna Tania

Abstract

The increasing demand for electricity over the last few decades has not been followed by

adequate growth in electric infrastructure. As a result, the reliability and safety of the electric

grids are facing tremendously growing pressure. Large blackouts in the recent past indicate

that sustaining system reliability and integrity turns out to be more and more difficult due

to reduced transmission capacity margins and increased stress on the system. Due to the

heavy loading conditions that occur when the system is under stress, the protection systems

are susceptible to mis-operation. It is under such severe situations that the network cannot

afford to lose its critical elements like the main generation units and transmission corridors.

In addition to the slow but steady variations in the network structure over a long term,

the grid also experiences drastic changes during the occurrence of a disturbance. One of

the main reasons why protection relays mis-operate is due to the inability of the relays to

adjust to the evolving network scenario. Such failures greatly compound the severity of

the disturbance, while diminishing network integrity leading to catastrophic system-wide

outages. With the advancement of Wide Area Measurement Systems (WAMS), it is now

possible to redesign network protection schemes to make them more adaptive and thus

improve the security of the system.

Often flagged for exacerbating the events leading to a blackout, the back-up distance

protection relay scheme for transmission line protection and the loss-of-field relay scheme for

generator unit protection can be greatly improved from an adaptability-oriented redesign.

Protection schemes in general would benefit from a power re-distribution technique that

helps predict generator outputs immediately after the occurrence of a contingency.

iii

Acknowledgements

I would like to express my sincere gratitude to my advisor, Dr. Jaime De La Ree, for his

patience and encouragement throughout my graduate career. He has been a great support for

me over the last several years and has provided vision and invaluable advice for completing

this dissertation, all while allowing me the freedom to pursue the work that interested me.

I am also heartily thankful to my research professor and mentor, Dr. Arun Phadke,

whose guidance from initial to final phase of my research work kept me inspired and enabled

me to develop a profound understanding of my field. It was a great privilege to receive

guidance from such a talented researcher, teacher and remarkable human being.

I would also like to extend thanks to Dr. Virgilio Centeno for his confidence in my

research ability to grant me research funding for pursuing a doctoral degree and for fostering

a continuous learning environment within our research group. I would like to thank the

rest of my committee members, Dr. Werner Kohler and Dr. Richard Conners, for their

encouragement, insightful comments, and relevant questions.

I wish to thank my parents, Khan Md. Abdur Rob and Shawkat Ara Begum, for their

love and blessings which served as one of my biggest driving forces. I owe everything to them

and would not be where I am without them. I also would like to extend my gratitude to

my sister, Zakia Farahna Shanta, my brother, Farzad Bari Auvi, and dearest friend, Santosh

Veda, for their love and constant support.

Finally, I would like to express my deepest appreciation to my beloved husband and best

friend, Kevin Jones, for his inspiration, friendship and love. I am indebted to him for his

patience, kindness and encouragement, which motivated me to finish my dissertation. I feel

extremely blessed to have such a wonderful partner who has helped make this journey such

an enjoyable one.

Contents

List of Figures viii

List of Tables xiii

1 Motivation 1

1.1 Power System Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Wide Area Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Technical Background 9

2.1 Power System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.1.1 Bus-Admittance Matrix . . . . . . . . . . . . . . . . . . . . 10

2.1.1.2 Kron Network Reduction . . . . . . . . . . . . . . . . . . . 11

2.1.1.3 Sensitivity Factors . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1.4 Calculation of Susceptance Matrix Using DC Power Flow . . 14

2.1.1.5 Derivation of Generator Shift Factor . . . . . . . . . . . . . 20

2.1.1.6 Derivation of Line Outage Distribution Factor . . . . . . . . 21

2.1.2 Transient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

iv

Contents v

2.2 Power System Simulation Tools . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Protection Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.1 Distance & Impedance Protection . . . . . . . . . . . . . . . . . . . . 26

2.3.2 Loss-of-Field Protection . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3.3 Adaptive Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Supervisory Control for Back-Up Zone Protection 33

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Distance Relay Back-up Protection Criteria . . . . . . . . . . . . . . . . . . 34

3.3 Load-encroachment and Supervision of Back-up

Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4 Study Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.1 WECC Full Loop Model . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.2 California Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.5 Selection of Appropriate Location for Back-up

Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.5.1 Line Outage Distribution Factors . . . . . . . . . . . . . . . . . . . . 39

3.5.1.1 Technique for Determining Line Outage Distribution Factor 40

3.6 Implementation of LODF to California

(Heavy Summer) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.6.1 Formation of LODF Matrix for CA System and

Identification of Critical Lines . . . . . . . . . . . . . . . . . . . . . . 41

3.6.2 Identification of Zone 3 Settings for Critical Lines after

Single Contingency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.6.2.1 Relay Settings for Multi-Terminal Lines . . . . . . . . . . . 42

3.7 Multiple Contingency Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Contents vi

3.7.1 Inertial Re-Dispatch of Generators . . . . . . . . . . . . . . . . . . . 44

3.7.2 Comparison between CA and Full-Loop Study System . . . . . . . . 46

3.8 Load-Encroachment Examples in CA System . . . . . . . . . . . . . . . . . . 46

3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4 Adaptive Loss-of-Field Protection 54

4.1 LOF Relaying Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 Loss-of-Field Relay Protection Criteria . . . . . . . . . . . . . . . . . . . . . 56

4.2.1 Steady State Instability as a Consequence of LOF Condition . . . . . 58

4.2.2 Steady State Stability Limit Circle . . . . . . . . . . . . . . . . . . . 61

4.3 Development Adaptive LOF Relay Scheme . . . . . . . . . . . . . . . . . . . 63

4.3.1 LOF Group Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.3.2 Adaptive LOF Relay Application in CA System . . . . . . . . . . . . 67

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5 Impact of Generation Re-distribution Immediately after Generation Loss 72

5.1 Generation Re-distribution with Respect to Location . . . . . . . . . . . . . 74

5.2 Generator Location as a Function of Admittance from an Event Location . . 78

5.2.1 Network Reduction to Determine Admittance between

Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.2.2 IEEE 39 Bus System Examples . . . . . . . . . . . . . . . . . . . . . 79


5.2.4 WECC System Examples . . . . . . . . . . . . . . . . . . . . . . . . 87

5.3 Linear Regression to Predict Power Injection

Changes at Generators after Contingency . . . . . . . . . . . . . . . . . . . . 88


Contents vii

5.3.2 Accuracy of Regression Model . . . . . . . . . . . . . . . . . . . . . . 101


5.4 Potential Application in Protection Studies . . . . . . . . . . . . . . . . . . . 114

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6 Conclusion & Future Work 118

6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Bibliography 122

A Sample Study Systems 126

A.1 IEEE 39 Bus System Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

A.2 IEEE 118 Bus System Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

A.2.1 IEEE 118 Bus System with 54 Generators . . . . . . . . . . . . . . . 131

A.2.2 IEEE 118 Bus System with 19 Generators . . . . . . . . . . . . . . . 132

List of Figures

1.1 Digital Relay Characteristics to Prevent Load Encroachment . . . . . . . . . 4

1.2 Loss-of-field Relay Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Two-port π-Model of a Transmission Line . . . . . . . . . . . . . . . . . . . 15

2.2 Distance Relay Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3 Distance Relay Protection Zones . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Distance Relay Overlapping Zones . . . . . . . . . . . . . . . . . . . . . . . . 28

2.5 Mho Relay Element Characteristics . . . . . . . . . . . . . . . . . . . . . . . 29

2.6 Generator Capability Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.7 Impedance Variance during LOF Conditions . . . . . . . . . . . . . . . . . . 31

3.1 Three Zone Distance (Mho Relay) Characteristics . . . . . . . . . . . . . . . 34

3.2 Effect of Load Encroachment on Zone-3 Characteristics . . . . . . . . . . . . 36

3.3 Supervision of Backup Protection . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Principle of LODF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.5 Effect of Infeeds on Zone Settings of Distance Relays . . . . . . . . . . . . . 42

3.6 Flow-Chart for Inertial Re-dispatch of Generators . . . . . . . . . . . . . . . 45

3.7 WECC Map, Relay at Captain Jack (500kV Bus) . . . . . . . . . . . . . . . 47

viii

List of Figures ix

3.8 R-X Characteristics of Relay at Captain Jack (500kv bus), Monitoring Line

from Captain Jack to Olinda . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.9 R-X Characteristics of Relay at Midway (500kV bus), Monitoring Line from

Midway to Vincent, ck 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.10 R-X Characteristics of Relay at Midway (500kV Bus), Monitoring Line from


3.11 R-X Characteristics of Relay at Midway (500kV Bus), Monitoring Line from


3.12 R-X Characteristics of Relay at Vincent (500kV Bus), Monitoring Line from


4.1 Phasor Diagram of Generator Voltage and Current during Reduced Excitation 56

4.2 Loss-of-Field as an Instability Condition . . . . . . . . . . . . . . . . . . . . 57

4.3 Simple System for Steady-State Stability Analysis . . . . . . . . . . . . . . . 58

4.4 Steady-State Stability Limit Circles . . . . . . . . . . . . . . . . . . . . . . . 59

4.5 Apparent Impedance Seen by an Impedance Relay . . . . . . . . . . . . . . . 60

4.6 Graphical Method for Steady State Stability Limit . . . . . . . . . . . . . . 62

4.7 LOF Relay at Diablo Machine Terminal . . . . . . . . . . . . . . . . . . . . 64

4.8 LOF Relay Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.9 Dibalo1- One Machine Infinite Bus . . . . . . . . . . . . . . . . . . . . . . . 66

4.10 LOF Relay Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.11 Network Diagram near Diablo . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.12 Apparent Impedances Seen by Traditional Relay after LOF Conditions . . . 68

4.13 Apparent Impedances Seen by Relay after LOF Conditions - Relay at Diablo1 69



List of Figures x

5.1 Abstract Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.2 Distribution of Generation in an Abstract Power System . . . . . . . . . . . 75

5.3 Loss of Generator G4 in an Abstract Power System . . . . . . . . . . . . . . 76

5.4 Re-distribution of Generation in an Abstract Power System, Just after the

Contingency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.5 One Line Diagram of IEEE 39 Bus System . . . . . . . . . . . . . . . . . . . 80

5.6 MW Outputs of Remaining Generators after Generator 3 at Bus 32 Outage . 81

5.7 Histogram of MW Outputs of Remaining Generator after Generator 3 at Bus

32 Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.8 MW Output at Remaining Generator after Generator 3 at Bus 32 Outage . . 83


5.10 Histogram of MW Outputs of Remaining Generator after Generator 7 at Bus

36 Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84


5.12 MW Output at Remaining Generator after Generator at Bus 10 Outage . . . 86



5.15 Generators Dibalo 1 & 2 Outage in WECC System . . . . . . . . . . . . . . 88

5.16 Immediate Injection Changes at Generators Buses after Generator 1 Outage 90



5.19 Immediate Injection Changes at Generators Buses after Each Generators Outage 93

5.20 Immediate Injection Changes at Generators Buses after Each Generators Outage 93

5.21 Actual and Predicted Changes in Injections at Generator Buses after Gener-

ator 4 (543.5 MW) Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

List of Figures xi


ator 5 (419.9 MW) Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99


ator 6 (561.7 MW) Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99


ator 7 (471.8 MW) Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100


ator 8 (451.8 MW) Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100


ator 9 (741.7 MW) Outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.27 Immediate Injection Changes at Generator Buses after Generator 1 Outage . 105

5.28 Immediate Injection Changes at Generator Buses after generator 9 Outage . 105

5.29 Immediate Injection Changes at Generator Buses after Generator 11 Outage 106

5.30 Immediate Injection Changes at Generator Buses after Generator 16 Outage 106


ator 1 (450 MW) at Bus 10 Outage . . . . . . . . . . . . . . . . . . . . . . . 111


ator 7 (204 MW) at Bus 49 Outage . . . . . . . . . . . . . . . . . . . . . . . 111


ator 10 (160 MW) at Bus 61 Outage . . . . . . . . . . . . . . . . . . . . . . 112


ator 14 (477 MW) at Bus 80 Outage . . . . . . . . . . . . . . . . . . . . . . 112

5.35 Impedance Trajectory Seen by Relay at Line between Bus 90 and 91 . . . . . 115

5.36 Impedance Trajectory Seen by Relay at Line between Bus 68 and 65 . . . . . 116

5.37 Generators at SONGS 1 & 2 in WECC System . . . . . . . . . . . . . . . . 116

5.38 Impedance Trajectory Seen by Relay at Line between Hassayampa to North

Gila in WECC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

List of Figures xii

A.1 One Line Diagram of IEEE 39 Bus System with 10 Generators . . . . . . . . 126



List of Tables

3.1 500 kV Links in CA System . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2 Midway-Vincent Line Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.1 Slopes & y-Intercepts of Best Fitted Lines alongside Transient MW Changes 94

5.2 Coefficient of Determinations of Regression Models to Predict Power Injection

Changes for IEEE 39 Bus Study . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.3 List of Contingency Cases Used for Prediction . . . . . . . . . . . . . . . . . 107

5.4 Coefficient of Determinations of Regression Models to Predict Power Injection

Changes for IEEE 118 Bus Study . . . . . . . . . . . . . . . . . . . . . . . . 113

A.1 IEEE 39 Bus System - Bus Data . . . . . . . . . . . . . . . . . . . . . . . . . 128

A.2 IEEE 39 Bus System - Branch Data . . . . . . . . . . . . . . . . . . . . . . . 130

A.3 IEEE 39 Bus System - Generator Data . . . . . . . . . . . . . . . . . . . . . 130

A.4 IEEE 118 Bus System - Original Bus Data . . . . . . . . . . . . . . . . . . . 137

A.5 IEEE 118 Bus System - Additional Bus Data . . . . . . . . . . . . . . . . . . 139

A.6 IEEE 118 Bus System - Branch Data . . . . . . . . . . . . . . . . . . . . . . 145

A.7 IEEE 118 Bus System - Additional Branch Data . . . . . . . . . . . . . . . . 146

A.8 IEEE 118 Bus System - Generator Data . . . . . . . . . . . . . . . . . . . . . 147

xiii

Chapter 1

Motivation

During northeast blackout of 2003, a series of line outages in northeastern Ohio caused heavy

loadings on parallel circuits that led to tripping and locking-out of the 345 kV Sammis-

Star line. As a result the high voltage paths into northern Ohio from southeast Ohio were

severely weakened. The Sammis-Star line tripped at Sammis Generating Station due to a

zone 3 impedance relay, the purpose of which is to serve as a back-up protection. A zone-3

relay can be defined as an impedance relay that is set to detect faults on the protected

transmission line and beyond. It operates through a timer to see faults beyond the next bus

up to and including the furthest remote element attached to the bus. It is used for equipment

protection beyond the line and it is also an alternative protection to equipment failure such

as breaker failure transfer trip. In the Sammis-Star trip, the zone-3 relay operated because

it was set to detect a remote fault on the 138-kV side of a Star substation transformer in

the event of a breaker failure. There were no system faults occurring at the time. The

relay tripped because excessive real and reactive power flow in the line caused the apparent

impedance to be within the impedance circle (trip zone) of the relay. Several 138-kV line

outages just prior to the tripping of Sammis-Star contributed to the over-load and ultimately

tripping of this line [1] [2].

This was the event that was mainly responsible for triggering a cascade of line outages

on the high voltage system, causing electrical fluctuations and generator trips such that

within seven minutes the blackout rippled from the Cleveland-Akron area through most of

the northeastern United States and Canada which left 10 million people in Ontario and 45

million people in eight U.S. states without electricity. This manifestation is an example

1

Chapter 1. Motivation 2

of improper or insufficient protection principles of the power system elements. A proper

supervision and adjustment to the back-up protection characteristics could have allowed

blocking of zone-3 impedance relay at that 345 kV line and as a result the cascade of line

trips might have been avoided.

Similar events were also responsible for initiating the recent Blackout in India in July,

2012. Pre-blackout the system was weakened by multiple scheduled outages of transmission

lines connecting the Western region (WR) with the Northern region (NR) boundary two

important part of the New Grid. As a result the 400 kV Bina-Gwalior-Agra (a single circuit)

was the only main AC inter-tie available between WR-NR boundaries prior to the distur-

bance. Many of the NR utilities drew excessive power from the grid, utilizing Unscheduled

Interchange (UI), a mechanism that is introduced in India to control frequency of the grid

more strictly, which severely contributed to high loading on 400 kV Bina-Gwalior-Agra link.

This tie line eventually tripped on zone-3 protection of distance relay. This happened due

to load encroachment (high loading of line resulting in high line current and low bus volt-

age). However, there was no fault observed in the system. Since the inter-regional tie was

already very weak, tripping of 400 kV Bina-Gwalior line caused the NR system to completely

separate from the WR which was the originator of the succeeding blackout [3].

These cases are just a few of many examples where mis-operation of protection schemes,

whether by design flaw, lack of maintenance, or simple mistakes, have played a part in

large events on the power grid. And because our society and others depends so heavily

on this critical energy infrastructure, large events on the power grid translate directly to

large events in our economies and our lives. This dissertation investigates several protection

schemes which aim to increase the reliability and security of the operation of the power grid

by providing a wide area perspective to relays that may the have the potential to mis-operate

due to certain system conditions. This includes a supervisory zone for back-up protection,

an adaptive loss-of-field relaying scheme, and a study of the potential effects of the transient

effects of the loss of a large generator on in appropriate operation of protection schemes.

These ideas are made possible by the advent of wide area measurement technology. As wide

area measurement technology proliferates, it can be applied to scenarios in power system

protection which would benefit from more information about a scenario before deciding to

block or trip. The next two sections in this chapter discuss the recent developments in power

system protection and wide area measurements to serve as an introductory discussion for

the topics covered in the later chapters of the dissertation.


1.1 Power System Protection

Distance or impedance relays are the main topics of this dissertation. The purpose of the

distance protection relays are to provide sufficient resistive reach, to ensure correct relay

operation when a fault is inside of the designed protective zone. Traditional relays with

dynamic Mho characteristics mostly satisfy these requirements. However stressed system

conditions, depressed voltages, and high line loading may cause the apparent impedance

to enter the relay characteristic and initiate incorrect tripping as described in the blackout

examples. Zone-3 distance elements provide remote backup if the primary zones fails to

operate, and act as alternate solution to remote breaker or other equipment failure as a result

this relay has over-reaching characteristics. These criteria also make the relay vulnerable

to load encroachment which relates to the influence of heavy load current on Mho relay

settings causing the impedance trajectory to move inside the trip zone especially if the load

is dynamically changing above the static rating of the transmission line. Several techniques

such as memory polarization, modified maximum torque angles (relay reach), alteration the

impedance relay characteristic from a circle to a lens are applied to increase load limits of

transmission lines or reduce susceptibility to loadability violations [4] [5].

Digital/ Numerical relays are able to incorporate logics that identify the appropriate

load limits and prevent three-phase distance units from mis-operating. These logics are

commonly referred as Load Encroachment Functions. An enhanced technique for distance

relay protection that improves load limits is a combination of a load blinder element with its

Mho characteristics to limit reach along the real axis (As in Figure 1.1(a)). Application of

the blinder separates the area of the impedance characteristic that may result in an operation

under excessive dynamic load conditions and the relay operation is blocked within this region

[6]. Another such option (in Figure 1.1(b)) can be the reduction of the protective area of

the zone-3 element and using the forward offset into the first quadrant to ensure appropriate

coverage of the outgoing lines at the remote end substation [4].


Figure 1.1: Digital Relay Characteristics to Prevent Load Encroachment

Loss-of-field (LOF) relay is another type of impedance relay (offset Mho relay specifically)

which is applied at the generator terminals to detect failure of the generator excitation

system. Such failure collapses the internal generator voltage and causes reactive power to

flow from the system into the generator beyond the generator rating. Literature review

demonstrates that LOF relays may pick up during stable power swings or trip if the relay is

not properly coordinated with excitation control and their limit settings. Some LOF relay

mis-operations occurred because the units were left on manual control and the excitation

output was set as frequency dependent (shaft driven exciters). V/Hz relays and overvoltage

relays also initiated inappropriate trips due to lack of coordination with excitation system

controls.

For conventional LOF protection, the impedance boundary criterion of steady state sta-

bility limit is widely used to identify loss-of-field conditions which is independent of system’s

operating point. Hence, a LOF relay can even fail to detect system instability as the sta-

bility limit may possibly shift due to system changes. During under- excitation condition,

generator operates on leading power factor as a result the generator operates as VAR sink, so

the relay must be coordinated with the excitation system minimum excitation limit (MEL)

settings to fully utilize the generator reactive power capability during disturbances.


Figure 1.2: Loss-of-field Relay Characteristics

To address continuing concern over LOF relay performance and verify the notion that

machine’s stability parameters have changed significantly since mid-nineties, a study was

initiated to review the application and the performance of the offset Mho LOF relay for a

variety of system conditions. This research specified an LOF protection consisted of two

independent Mho functions (as in Figure 1.2 ) and a built in timer which coordinates with

the larger of the two relay characteristics. One setting has a relay reach of 1.0 per unit

circular diameter and the other characteristic is set at a circle diameter equal to machine

synchronous reactance (xd) . The offset, in both cases, will be equal to one-half of the direct

axis transient reactance (x′d

2). The inner circle provides loss-of-excitation protection from

full load down to about 30% load. As a LOF condition in such loading range has the greatest

adverse effects on the generator and system, this zone is permitted to trip in high-speed.

The outer circle is able to detect a loss-of-excitation from full load down to no load. This

research shows that the larger setting of this relay was unable to differentiate between stable

and un-stable power swing, as a result this region may operate on stable swings. A time

delay of up to 3 seconds is suggested to prevent such undesired operations [7].

1.2 Wide Area Measurements

A wide area measurement systems (WAMS) can be defined as a monitoring device that takes

measurements in the power grid at a high granularity and in synchronized real time, across


traditional control boundaries and then utilize that information for safe operation, improved

learning and grid reliability through wide area situational awareness and advanced analysis.

This advanced measurement technology provides great informational tools and operational

infrastructure that facilitate the understanding and management of the increasingly complex

behavior exhibited by large power systems.

Measurements taken from different power systems cannot be fully integrated unless they

are captured at the same time. An important requirement of WAMS, therefore, is that the

measurements be synchronized. Measurements are precisely time synchronized against the

satellite based Global Positioning System (GPS), and are combined to form integrated and

high resolution views of power system operating conditions. The initial data source for this

system is the Phasor Measurement Unit (PMU), which provides high quality measurements

of bus angles and frequencies in addition to more conventional quantities. A high sampling

rate, typically, 30 or more samples per second, is particularly important for measuring system

dynamics and is another important requirement of WAMS technology [8].

In its present form, WAMS may be used as a stand-alone infrastructure that complements

the grid’s conventional supervisory control and data acquisition (SCADA) system. As a

complementary system, WAMS is specifically designed to enhance the operator’s real-time

view of the system in the form of situational awareness along with data sharing between

devices to ensure safe and reliable grid operation. Certain elements of WAMS existed in

basic forms in the Western Interconnection since the early 1990s. A significant contribution of

WAMS technologies was demonstrated during the failure of Western Electricity Coordinating

Council (WECC), the Western power system on August 10, 1996.

During this blackout, WECC system was divided into four asynchronous islands with

heavy loss of load. The results of this breakup, when compared to the dynamic information

being provided by WAMS led to several strategic actions such as remedial action schemes

(RAS) by the electric utilities. The data supported that electric grid operation in WECC

significantly relies on the existing system models and that these models were inadequate in

predicting system responses. One of the greatest benefits realized was that the data contained

precursors of the impending grid failure, which if had been properly analyzed, could have

allowed preventive actions which could have either eliminated or drastically reduced the

impact of the disturbance [9]. The cascading outage of 1996 was one of the biggest driving

forces for further WAMS development and improvement [8].


As the increasing demand for electricity over time was not followed by increases in trans-

mission capacity, a tremendous growing pressure bestowed upon the reliability and safety

of the electric grid. Recent large blackouts and outages, such as the August 2003 blackout

in the Northeast and 2011 Southwest Blackout indicated that maintaining the system reli-

ably had become more difficult because of reduced transmission margins and growing system

stress. The report by the U.S.-Canada Power System Outage Task Force on the August 2003

blackout recommended the development and adoption of technologies, such as WAMS, that

could improve system reliability by providing better wide area situational awareness [10].

The continuous data availability through PMUs, as well as their wide distribution through-

out the power system, was also proved beneficial to the post-event inquiry depicting accurate

representation of the events and state of the system at particular points in time throughout

September 2011 WECC (Southwest) disturbance [11].

1.3 Organization of the Dissertation

The dissertation contains six chapters which have been outlined in this section.

Chapter 1: Introduction - The first chapter introduces the dissertation by describing

the role of the mis-operation of protection schemes in large scale blackouts in the

last decade and the importance of adaptivity and wide area situational awareness in

power system protection. The chapter continues on to discuss relevant technologies

that enable many of the topics in this dissertation. The chapter concludes with the

motivation & objective for the work in this dissertation and a outline of the topics

covered in each chapter.

Chapter 2: Technical Background - This chapter outlines technical information related

to discussions and calculations contained in this dissertation. This includes a presenta-

tion of many types of steady-state analysis that are used in the large protection studies

presented in later chapters, transient analysis, a description of the software packages

used in the studies, and a discussion of adaptive power system protection.

Chapter 3: Supervision of Back Up Zones of Protection - CIEE (California Institute

for Energy and Environment) Electric Grid Research Program supported a research

study on the California study system to develop techniques for the supervision of back-

up zones of protection and the identification of locations which may benefit from the


implementation of such algorithms. This chapter discusses the work associated with

this study and presents the methodology and the results of the protection study [12].

Chapter 4: Adaptive Loss-of-Field Protection - Another study directly related to the

aforementioned project is one which aimed to develop an adaptive scheme for loss-of-

field relaying [13]. Loss-of-field protection is presented as an introduction to the idea

of an adaptive scheme for loss-of-field conditions.. The chapter continues on to explain

the details of this study and describes the results of the simulations testing the scheme

on the full California study system.

Chapter 5: Impact of Re-distribution of Generation on Protection - This chapter

presents the idea of an approximate linear relationship between the electrical distance

between generators in a power system & the transient change in MW just slightly after

the loss of a generator in the network. The idea is discussed abstractly followed by

numerical examples in the IEEE 39 bus system and the IEEE 118 bus system that verify

the ideas discussed. It is shown that for a small subset of contingencies calculated using

a dynamic simulation that the transient MW output of a generator can be predicted

for the remaining contingencies in a set. The coefficients of determination are used to

measure the effectiveness of the linear regression used in the aforementioned analysis.

A case is made for application to protection studies on large networks and an example

is shown from the IEEE 118 bus system and the WECC system.

Chapter 6 - Conclusion & Future Work - The final chapter summarizes the disserta-

tion and presents future work for the field related to the work described in this disser-

tation including implementation of the discusses protection schemes to various other

study models, utilizing the advanced EMS (Energy Management System)/ SCADA

system to compute more accurate protection settings on-line, addressing the issues

related to loss of WAMS data and their impacts on the proposed schemes and investi-

gation of the communication infrastructure for proper implementation of the research

of this dissertation.

Chapter 2

Technical Background

This chapter aims to explain some of the power system concepts, mathematical models &

tools and protection basics that is relevant to the research topics of this dissertation. This

discussion is provided as prelude to the detailed description in the later chapters.

2.1 Power System Analysis

The behaviors of large power systems are very complex phenomena due to the scale and

interdependency of the different parts of the system; events in geographically distant parts

of the network may interact strongly and in unexpected ways. The analysis of power systems

is concerned with understanding the behaviors of the integrated system with the purpose of

guiding operations and aiding in long term infrastructure planning. Generally, the system is

studied either under steady-state operating conditions or under dynamic conditions during

disturbances and the tools and algorithms used for both types of analysis can vary greatly

from one another in complexity, computational burden, and end use.

Chapters 3, 4 & 5 all present work on power system protection studies in which the

understanding and wielding of the power system analysis toolkit is required. This is not

only because of the type of information desired for the protection studies but also because of

the scale of the systems being studied. Realistic power systems are very large and handling

such large amount of data can be very different than working with many of the systems used

in power system research literatures. This section formally presents the analysis tools that

9

Chapter 2. Technical Background 10

were used in the studies described in the later chapters of the dissertation.

2.1.1 Steady State Analysis

Steady state analysis of power system concerns with small and slow disturbances in the

network, any transients from such disturbances are assumed to be subsided where the system

state is unchanging. Specifically, system load and transmission system losses are precisely

matched with power generation so that the system frequency remains constant. The foremost

concern during steady-state is economic operation of the system. However, reliability is also

important as the system must operate to avoid instability should disturbances or outages

occur. The primary tool for steady-state operation is the so-called load flow analysis, where

the node voltages and power flow through the system is determined using the steady state

power flow equations of the network. The time constant for the steady state operation is

in the order of several seconds to minutes. So all the differential equations involved in the

network model are assumed to be constant. Hence the power flow equations become algebraic

equations that can be solved using a non-linear iterative method such as Newton-Raphson.

This analysis is used for both operation and planning studies and throughout the system at

both the high transmission voltages and the lower distribution system voltages.

This section describes the types of steady-state analysis that have been used in the studies

contained in this dissertation. The bus-admittance matrix is presented as key metric in

steady state analysis as well as a prequel to the Kron network reduction which is used heavily

in Chapter 5 as a tool for removing zero-injection buses from the network. Additionally, the

derivation of generator shift factors and line outage distribution factors are presented as they

were used in heavily in Chapter 3.

2.1.1.1 Bus-Admittance Matrix

Bus-admittance matrix, [Y ], or [Ybus] is an n x n matrix which is fundamental to steady-

state network analysis. It relates current injections at a node to the node voltages in a

power system with n buses. It can be formed from the parameters of system components

such as such as transmission line series and shunt impedances, transformer impedances,

shunt capacitors and reactors etc. The [Y ] matrix is a key building block in formulating a

power flow study and can be written as following,


[I] =

I1

I2

...

In

=

Y11 Y12 . . . Y1n

Y21 Y22 . . . Y2n

......

. . ....

Yn1 Yn2 . . . Ynn

V1

V2

...

Vn

= [Y ] ∗ [V ] (2.1)

The [I] vector contains the current injection phasors, where Ii is the current injection

into bus i and the [V ] vector is the voltage phasors of each node, where Vi represents the

voltage at bus i with respect to ground.

Each diagonal element of admittance matrix, Yii, is known as self admittance of ith

node in a power system and equals to the sum of the admittances connected to ith node,

including the shunt admittances. Each off-diagonal term Yij is known as mutual or transfer

admittance between ith & jth nodes and equals to the negative of all admittances connected

directly between these two nodes. Yij element is non-zero only when there exists a physical

connection between buses i and j. The admittance matrix can be formulated very quickly

from the network parameters through visual inspection. A real power system usually contains

with thousands of nodes, each node is rarely connected to more than two or three other nodes,

therefore most of the elements of the admittance matrix are zero and the [Y ] matrix is sparse.

2.1.1.2 Kron Network Reduction

In the steady-state analysis of an interconnected power system, the system is assumed to

be operating under balanced conditions and is represented by a single phase network. The

network contains all its nodes and branches with impedances specified in per unit on the

system MVA base. In the previous section, the formulation of the bus-admittance matrix

was presented as a key piece of information for many forms of steady-state power system

analysis. There are many situations where the matrix can be simplified by removing nodes

in the system which have zero-injection. This can be accomplished with a mathematical

algorithm called the Kron network reduction. Begin with the node voltage equations for the

power system.

[I] = [Y ][V ] (2.2)


which can be also described as,[Ig

In

]=

[Ygg Ygn

Yng Ynn

]∗

[Vg

Vn

](2.3)

Where Ig and In represent the complex current injections at the generator and non-generator

buses. Also, Vg and Vn represent the complex voltages at the buses with injections and

voltages at zero injection buses, respectively.

In a power system, generator and load buses are considered the injection buses but the

current injection is always zero at buses where there are no external loads or generators

connected. Such nodes may be eliminated. Therefore, all of the loads in the system are

represented as impedances and included in the admittance matrix, as a result all of the

non-generator buses will have zero injection.[In

]= 0

Then, the network equation can be represented as,

[Ig

0

]=

[Ygg Ygn

Yng Ynn

]∗

[Vg

Vn

](2.4)

The matrix form of the network equations can then be separated into two separate equations:

[Ig] = [Ygg][Vg] + [Ygn][Vn] (2.5)

[0] = [Yng][Vg] + [Ynn][Vn] (2.6)

Solving for [Vn] in Equation 2.6 results in the following,

[Vn] = [Ynn]−1[Yng][Vg] (2.7)

Then, by substituting Equation 2.7 into Equation 2.5,

[Ig] = ([Ygg] + [Ygn][Ynn]−1[Yng])[Vn] (2.8)


which again can be represented as the following.

[Ig] = [Yreduced][Vn] (2.9)

where,

[Yreduced] = [Ygg] + [Ygn][Ynn]−1[Yng] (2.10)

This [Yreduced] matrix is a m by m matrix for a system with m generators and each

off-diagonal elements of this matrix represents admittances between two generator buses i.e.

the Y1m element signifies the equivalent admittance between 1st and mth generator.

[Yreduced] =

Y11 Y12 . . . Y1m

Y21 Y22 . . . Y2m

......

. . ....

Ym1 Ym2 . . . Ymm

(2.11)

In Chapter 5, loads in the system will be replaced with impedances making all non-

generator buses zero-injection buses. The Kron network reduction will be used to remove all

of these buses from the bus admittance matrix to create a matrix which is a representation

of the admittance between any two generator buses in the network. The Kron network

reduction is a key steady state analysis tool for the work contained in Chapter 5.

2.1.1.3 Sensitivity Factors

Any practical power system contains very large number of elements. Contingency analysis

requires outages of all these elements one-by-one corresponding to any particular operating

condition. However, the operating point of the system changes quite frequently with change

in loading/generating conditions. For proper monitoring of system security, a large number

of outage cases need to be simulated repeatedly. Analysis of thousands of possible outage

cases with full AC power flow technique involves a significant amount of computation time.

Therefore, much faster techniques based on linear sensitivity factors are used to estimate

the post contingency values of different quantities of interest, instead of using full non-linear

AC power flow analysis. The basic purpose of the linear sensitivity factors is to quickly

approximate any possible violation of operating limits using the changes in line flows for


any particular outage condition without the need of full AC power flow solution. The linear

approximations are derived using the relationships in the DC power flow.

Two such sensitivity factors for checking line flow violations are:

• Generation shift factors(GSF), and

• Line outage distribution factors (LODF)

The GSFs are defined as the relative change in the power flow on a particular line from bus

i to bus j due to a change in injection, ∆Pk, and corresponding withdrawal at the system

swing or slack bus.

The GSFs are linear estimates of the changes in flow with a change in power at one bus.

The total change in flow on each transmission line in the system may be calculated for the

change in injection at one or more buses using superposition. In a real power system, due to

governor actions, the loss of generation at the bus k will be compensated by other generators

throughout the system. A frequently used method is to assume that the loss of generation

is distributed among participating generators in proportion to their machine base, which is

a measure of their size.

LODFs represent the percentage of flow on a contingent line k that will flow on the

monitored elements such as line l, if the contingent facility is disconnected from the system.

After a line outage occurs in a system, the power flowing on that line is redistributed on

to the remaining lines in the system. LODFs determine the contribution of each remaining

lines in the system to reallocate the flow on the line that was taken out-of-service.

In Chapter 3, a study for CIEE is presented which aims to develop algorithms for the

supervision of back-up protection. These sensitivity factors are used to help to identify

locations which could potentially benefit from an implementation of such an algorithm.

2.1.1.4 Calculation of Susceptance Matrix Using DC Power Flow

The linear sensitivity factors are derived under the DC power flow conditions. To discuss

the basis for the DC power flow, the formulation of the Newton power flow equations is

discussed in the following section.

Consider a power system with N buses. Each bus i may be characterized by the net


power injections; real power, Pneti and reactive power, Qneti , and the voltage phasor |Vi|∠θi.The bus admittance matrix is represented by the [Y] matrix. The bus admittance matrix of

diagonal elements Y=[Yij] may be calculated using Equation 2.12.

Y = G+ jB (2.12)

The bus conductance matrix is defined here as G=[Gij] , and the bus susceptance matrix is

defined as B=[Bij]. The diagonal elements Yii of the bus admittance matrix are the algebraic

sums of all of the complex admittances of the lines of the incident bus i. The off- diagonal

elements Yij of the bus admittance matrix are the negative sums of the complex admittances

between buses i and j. The Yij component of the matrix will be non-zero if and only if buses

i and j are connected by a transmission line or transformer. The system can be modelled

using the assumption that the transmission lines may be represented by the π-equivalent

model as shown in the following Figure 2.1.

Figure 2.1: Two-port π-Model of a Transmission Line

With this model, line charging admittances are yci, ycj and the off-diagonal bus admit-

tance matrix elements are determined given by,

Yij = −yij = −gij − jbij (2.13)

In Equation 2.13, the conductance is Gij= gij , and the susceptance is Bij = bij. As the

line impedance can be written as z = r + jx, the admittance term yij may also be written

as a function of the impedance, creating a relationship between the resistance, r, and the


reactance, x.

yij =1

zij=

1

rij + jxij=

rijr2ij + jx2

ij

− j xijr2ij + jx2

ij

(2.14)

So,

Gij = −gij =−rij

r2ij + jx2

ij

(2.15)

Bij = bij =xij

r2ij + jx2

ij

(2.16)

To form the basic power flow equations, bus 1 in the N-bus system is chosen as the slack

bus in which both the voltage, V, and angle, θ, are known and constant. The power flow

equations have the form f(x) = 0 , where x is called the system state containing the bus

angles, θ, and bus voltages V of all of the buses excluding the system slack bus. The power

flow equations are solved by Equation 2.17-2.18 for the buses of the system not including the

system slack bus. For an injection at bus i, the measurements can be expressed as functions

of the state vector and elements of the bus-admittance matrix.

fpi = Pi = Gii|Vi|2 + |Vi|∑

k=busesconnected

toi

|Vk|[Gikcos(θi − θk)−Biksin(θi − θk)]− Pneti = 0 (2.17)

f qi = Qi = Bii|Vi|2 + |Vi|∑

k=busesconnected

toi

|Vk|[Giksin(θi − θk) +Bikcos(θi − θk)]−Qneti = 0 (2.18)

The Newton power flow scheme is an iterative method obtained by the Taylor series

expansion about the initial estimate and neglecting all the higher order terms. Jacobian

matrix provides the linearized relationship between small changes in voltage angle ∆θi and

voltage magnitude ∆|Vi| with the small changes in real and reactive power ∆Pi and ∆Qi.

Using the Newton power flow scheme, a Jacobian matrix can be defined as the gradient of

the power flow equations ∇xg. The structure of the Jacobian matrix appears as shown in

Equation 2.19.


J(x) =∂f

∂x=

[∂fp

∂θ∂fp

∂|V |∂fq

∂θ∂fq

∂|V |

]=

[∂P∂θ

∂P∂|V |

∂Q∂θ

∂Q∂|V |

](2.19)

The equations used in the Newton power flow scheme are simplified to form the decoupled

power flow method by applying the following assumptions according to the terms in the

Jacobian matrix:

1. Power system transmission lines have a high X/R ratio. For such system real power

changes ∆Pi are less sensitive to changes in voltage magnitude and are most sensitive

to changes in phase angles ∆θi.

2. Similarly, reactive power changes ∆Qi are less sensitive to changes in phase angles and

are most sensitive to changes in voltage magnitude ∆Vi.

3. Bii is the sum of susceptances of all the elements incident to bus i. In a typical power

system, the self susceptance Bii � Qi and we may neglect Qi.

4. cos(θi - θk)=1, due to the usually small value of (θi - θk).

5. Also, Gik sin(θi - θk) � Bik

Using the assumptions listed above, the Jacobian equations and power flow equations

can be written as the following sets of equations, respectively.

∂Pi∂θk

= −|Vi||Vk|Bik (2.20)

∂Qi

∂|Vk||Vk|

= −|Vi||Vk|Bik (2.21)

∆Pi = (∂Pi∂θk

)∆θk (2.22)

∆Qi = (∂Qi

∂|Vk||Vk|

)∆|Vk||Vk|

(2.23)

By substituting Equation 2.20 and 2.21 in Equation 2.22-2.23 the following relationships

may be derived,

∆Pi = −|Vi||Vk|Bik∆θk (2.24)


∆Qi = −|Vi||Vk|Bik∆|Vk||Vk|

(2.25)

Dividing the Equation 2.24- 2.25 by |Vi| and assuming |Vk| ∼= 1, further simplification can

be made to the power flow equations,

∆Pi|Vi|

= −Bik∆θk (2.26)

∆Qi

|Vi|= −Bik∆|Vk| (2.27)

Now, these matrix equations for the N-bus system can be represented, respectively.∆P1

|V1|∆P2

|V2|...

∆PN

|VN |

=

−B11 −B12 . . . −B1N

−B21 −B22 . . . −B2N

......

. . ....

−BN1 −BN2 . . . −BNN

∆θ1

∆θ2

...

∆θN

(2.28)

∆Q1

|V1|∆Q2

|V2|...

∆QN

|VN |

=

−B11 −B12 . . . −B1N

−B21 −B22 . . . −B2N

......

. . ....

−BN1 −BN2 . . . −BNN

∆|V1|∆|V2|

...

∆|VN |

(2.29)

To simplify the ∆P −∆θ relationship more assumptions can be made.

• First, all shunt reactances to ground are ignored.

• Second, all shunts to ground from auto-transformers are ignored.

• Lastly, the line resistance can be neglected due to the value of the line resistance

being much smaller than the line reactance, rik � xik, as mentioned earlier, which also

simplifies the Bik calculation.

So,

−Bik =−1

xik(2.30)

The ∆Q−∆|V | relationship is simplified by eliminating the effects from all phase shift

transformers. The simplifications to both relationships create two different B matrices. The


B′ matrix is represented as the new simplified B matrix for the ∆P − ∆θ relationship by

ignoring the shunt susceptances. The off-diagonal elements B′ik are calculated using the

previous Equation 2.30 and the diagonal elements B′ii are also calculated using the sum of

susceptances of all the elements incident to bus i.

B′ik = −Bik =−1

xik(2.31)

B′ii =N∑k=1

1

xik(2.32)

The B′′ matrix is the new simplified B matrix for the ∆Q − ∆|V | relationship. The off-

diagonal elements B′′ik are calculated from Bik. The diagonal elements B′′ik can be calculated

using sum of negative susceptances of all the elements incident to bus i.

B′′ik = Bik =xik

r2ik + x2

ik

(2.33)

B′′ii =N∑k=1

−Bik (2.34)

The B′ik and B′′ik matrices are constant and only need to be calculated once, which is one

of the advantages of the decoupled power flow. The DC power flow is derived from the

decoupled power flow formulation by omitting the ∆Q − ∆|V | relationship and by setting

all |Vi|= 1.0 p.u. As a result, following the DC power flow equation is produced.

∆P = B′∆θ (2.35)

Equation 2.35 implies that the DC power flow only calculates the MW flows on transmission

lines and transformers without giving any information of MVAR flows or voltage magnitudes.

For the research, the information provided by the DC power flow is sufficient. From previous

equations, the power flowing on each line l connecting buses i and j can then be calculated

according to Equation 2.36.

fl = Pij =1

xij(θi − θj) (2.36)

The distribution factors use the standard matrices calculated in the DC power flow equations.

Given the linearity of the DC power flow model, the changes due to any set of system

conditions can be calculated. For this particular investigation, the generation, or power


injection into the bus, is changed at all generator buses. Thus, a relationship between the

resulting change in the bus voltage angles and the change in the bus power injections ∆P

is desired.

Manipulating ∆P −∆θ relationship to calculate the change in bus voltage angles given

a known change in the bus power injections results in Equation 2.37.

∆θ = [X]∆P (2.37)

Then the relationship between the X matrix and the B′ matrix is defined in the next equation.

X = (B′)−1|incremented with a row and column of zeros at swing bus

[X] =

0 . . . 0... B′−1

0

(2.38)

The power on the swing bus is equal to the sum of injections of the remaining buses in the

system. Similarly, the net perturbations of the swing bus, in Equation 2.37 is the sum of the

changes on all other buses. Therefore, the [X] matrix in Equation 2.38 includes an entry of

zeros in the row and column of the system swing bus, considering bus 1 as swing bus.

2.1.1.5 Derivation of Generator Shift Factor

Sensitivity factors can be calculated for a change in power injection at bus k, which is

compensated by an opposite change in power at the swing bus. If the perturbation of

generator on bus k is set to +1.0 per unit power and the perturbation on other buses are

zero, then the power change is re-allocated to the swing/reference bus with -1 per unit power.

The generation shift from bus k to reference bus causes the flow on line l to change. The

ratio of the change in power flow on line l and generation change that occurs at bus k is

defined as the generator shift sensitivity factor(GSF).

The GSF for a line l connecting bus i to bus j with respect to a change in injection at

bus k can be represented by Equation 2.39.

al,k =dfldPk

=d

dPk(

1

xl(θi − θj)) =

1

xl(dθidPk− dθjdPk

) =1

xl(Xik −Xjk) (2.39)


In the previous equation, xl represents the line reactance of line l connecting buses i and j,

and the values Xik and Xjk are the respective elements of the X matrix. The distribution

factors al,k are computed for each generator bus for the system. With M generator buses in

the system, the resulting change in the flow of real power on line l connecting buses i and j

is calculated as ∆Pij using the sensitivity factor from Equation 2.39.

∆Pij = ∆fl =∑k=1,M

al,kPk (2.40)

A generalized generator shift sensitivity factor (GGSF) can be derived when the change

in generation at bus k is compensated by the generation at bus s instead of reference bus.

In this case, the effect of re-allocating +1.0 per unit power from generator located at bus k

is observed as -1.0 per unit power change on a generator located at bus s. The generation

is shifted from bus k to bus s which results in a change of power flow on line l from bus i to

bus j.

GGSFs are calculated from the entries of the bus impedance matrix or [X] of the system

in the base case. The shifts are calculated between pairs of generators, in this case between

generators at bus c and at bus s, taking one pair at a time. In practice, when considering

contingencies, not all possible pairs of generators need be accounted for. Only those pairs of

generators are calculated which have the capability for such a shift [14].

gl,ks =(Xik −Xjk)− (Xis −Xjs)

xl= al,k − al,s (2.41)

GGSFs for line l for a generation shift from bus k to bus s is also the difference between

individual generation shift sensitivity factor for line l to a change in injection at bus k and

the same for shift in generation on bus s.

2.1.1.6 Derivation of Line Outage Distribution Factor

A line outage can be modelled by adding two opposite directional power injections each end

of the line to be dropped. So that the line can be left in the system but the effect of this

line is dropped which is modelled here by injections. Consider a line k from bus n to bus

m. Two injections ∆Pn and ∆Pm are added at each end of the line k where ∆Pn=Pnm and

∆pm=-Pnm. Pnm is equal to the power flowing over the line. Due to the added injections, the


line will have no power through it which implies that the line is disconnected with respect

to the rest of the system [15],

As in Equation 2.37,

∆θ = [X]∆P (2.42)

where,

∆P =

...

∆Pn...

∆Pm...

(2.43)

so that,

∆θn = Xnn∆Pn +Xnm∆Pm (2.44)

∆θm = Xmn∆Pn +Xmm∆Pm (2.45)

According to the outage model criteria, the incremental injections ∆Pn and ∆Pm is equal

to the power flowing over the tripped line Pnm after the injections are added. θn and θm are

the bus voltage angles for bus n and m respectively, after the line outage.

Pnm = ∆Pn = −∆Pm (2.46)

where,

Pnm =1

xk(θn − θm) (2.47)

Then,

∆θn = (Xnn −Xnm)∆Pn (2.48)

∆θm = (Xmn −Xmm)∆Pn (2.49)

xk is the reactance of line k. Pnm is the flow on the line from bus n to bus m, before the line

outage. Similarly, θn and θn are the pre-outage bus voltage angles for bus n and m.

θn = θn + ∆θn (2.50)

θm = θm + ∆θm (2.51)


Replacing θn and θm in Equation 2.47,

Pnm =1

xk(θn − θm) +

1

xk(∆θn −∆θm) (2.52)

Substitution of ∆θn and ∆θm in Equation 2.52 results in the following equation.

Pnm = Pnm +1

xk(Xnn +Xmm − 2Xnm)∆Pn (2.53)

As, Pnm = ∆Pn, the Equation 2.53 is simplified.

∆Pn =1

1− 1xk

(Xnn +Xmm − 2Xnm)Pnm (2.54)

If neither n or m is reference bus in the system, the change in phase angle at a different bus i

can be deduced using the next equation when the two injections ∆Pn and ∆Pm are imposed

at the two ends of line k.

∆θi = Xin∆Pn +Xim∆Pm = (Xin −Xim)∆Pn (2.55)

Again, the substitution of ∆Pn derives,

∆θi =(Xin −Xim)xk

xk − (Xnn +Xmm − 2Xnm)Pnm (2.56)

Assuming a line l from bus i to bus j, the LODF dl,k while monitoring line l can be defined

after an outage on line k using Equation 2.57.

dl,k =∆flPnm

(2.57)

where ∆fl represents the change is flow on line l and Pnm is the original flow on line k, before

it was disconnected.

Now, ∆fl = ∆Pij = 1xl

(∆θi −∆θj), where xl is the reactance of line l.

dl,k =1

xl(

∆θiPnm

− ∆θjPnm

) (2.58)

If neither i nor j is a reference bus, LODF for line l (between bus i and bus j), due to outage


of line k (between bus n and bus m) is derived as,

dl,k =1

xl((Xin −Xim)xk − (Xjn −Xjm)xkxk − (Xnn +Xmm − 2Xnm)

) =xkxl∗ (Xin −Xjn −Xim +Xjm)

xk − (Xnn +Xmm − 2Xnm)(2.59)

2.1.2 Transient Analysis

In steady state, for a specified network configuration, a system supplies real power (P) and

reactive power (Q) at load nodes by adjusting generations. The system is in equilibrium if

the generation and demand in the system are balanced. As load or generation change or

network topology change, the equilibrium point changes. It cannot be determined whether

the transition was smooth or reasonably fast using steady-state analysis. It is possible that

the system loses stability if it is unable to reach the desired new equilibrium. In this case,

steady-state analysis most likely diverges. Dynamic analysis allows observation of how the

operating point of a system moves in the time domain. The path or trajectory of a system’s

operating point reaching a new equilibrium or steady-state may differ depending on its initial

condition, which can be identified with dynamic simulations.

In dynamic analysis, the power system components that are included are synchronous

generators along with their associated excitation systems, prime movers, and governor sys-

tems. Additionally, the interconnecting transmission network which include static loads,

induction and synchronous motor loads or dynamic loads. The controls for these devices

are complex and diverse such as voltage and frequency control, automatic voltage regulators

(AVRs), automatic excitation regulators (AERs). There are other special controls such as

power system stabilizers (PSS), HVDC and FACTS controllers in the system. All of these

control parameters are time varying where some are fast, some are slow. It is necessary

to ensure coordination between such parameters for stable system operation and enhanced

performance.

Dynamic analysis of power system deals with effect of large and sudden disturbances such

as the occurrence of faults, immediate outage of a line or sudden application or removal of

loads/ generations [16]. This study involves with electromechanical transients and neglects

the electromagnetic transients of the network. Hence, it considers only the fundamental

frequency components of voltage and current. The complexity of the component models is

reduced by neglecting differential equations that involve smaller time constant (less than

milliseconds) parameters. A typical time step used for power system dynamic simulation is


10 ms [17].

In Chapters 3, 4 & 5, much steady-state analysis is performed for developing relay

settings and especially searching the network for regions of vulnerability that may be prone

to relay mis-operation or that would benefit from a fundamental change to their relaying

schemes. After the locations have been identified, algorithms developed and the settings

identified, dynamic power system simulations are used in all cases to verify the findings from

the steady-state analysis and to test the efficacy of the new relaying algorithms and settings.

2.2 Power System Simulation Tools

The purpose of this section is to describe the software tools used for the work in this dis-

sertation. Several software packages were used. Beyond the basic software tools such as

spreadsheet tools and text editors, the software packages used includes Matlab and a freely

distributed power system steady-state analysis tool called MATPower that runs inside of

Matlab. Additionally, GE’s PSLF software was used for both steady-state and dynamic

power system simulations in all of the studies described in this dissertation. Below is a more

detailed description of the capabilities of each of the software packages.

MATPower - MATPower is a set of Matlab scripts which were developed at Cornell that

are freely distributed for use by students, faculty, research institutions, and even in-

dustry. The scripts perform many different types of steady-state power system analysis

including power flow, constrained power flows including optimal power flow and secu-

rity constrained economic dispatch, and even energy market studies.

GE’s Positive Sequence Load Flow software (PSLF) - PSLF is an integrated, inter-

active program for simulating, analyzing and optimizing power system performances.

It contains the capability of modeling comprehensive, accurate, and flexible power

system, running load flow with relational database and graphics, fault analysis, dy-

namic simulation, large-scale short-circuit calculations of power system. To implement

the network model of a given power system in PSLF, the physical components like

transmission lines, generators, loads and control systems (excitation and governor) are

included using relational database [18].


2.3 Protection Schemes

This section discusses several of the key protection schemes utilized in this dissertation

including distance & impedance protection schemes as well as loss-of-field relaying schemes

which can be implemented as a form of impedance protection. The section concludes with a

discussion of adaptive power system protection which describes the idea that a relay setting

or relaying scheme may benefit from the ability to adaptive to the current conditions of

the grid particularly with the information made available by wide area measurements and

situational awareness.

2.3.1 Distance & Impedance Protection

On high voltage transmission lines the preferred method of protection is usually through the

application of distance relays or impedance relays as they are often called. Distance relays

are faster, more selective as it uses information from both voltage and current, and easier

to coordinate as they are not affected as much by the changes in generation capacity and

system configuration. The actual point of tripping depends upon the comparison that is the

ratio of voltage to current; the relay is in fact measuring the impedance of the circuit being

protected including the load impedance. However if there is a fault on the line, such as

direct phase to phase fault, then the circuit impedance to the fault is that of the conductors

themselves which is relatively a small value. Indeed, this is the very reason that the current

increased to such a high magnitude.

The relay is set to operate when the measured impedance falls below a specific value. If

the impedance per mile of the line conductor is known, the impedance relay can be set to

trip for faults within any particular distance from the relay. For example, consider the line

in Figure 2.2. It is 150 mile long with a total impedance of 100 ohms. At the half way point,

the line impedance is 50 ohms, at 34

lengths, it is 75 ohms and so on. The relay is located at

substation where bus A is located and close to the breaker. But it can be adjusted to reach

out as far along the line as desired, typically it is set to protect up to 90% of the length of

the line i.e. an impedance of 90 ohms for this particular example. This is because relays

usually have 10% error margin. Such settings are selected to avoid over-reaching protection.


Figure 2.2: Distance Relay Protection

The relay uses secondary values from CTs and PTs and measures secondary impedance.

The relay continuously compares voltage and current, if the primary impedance falls below

90 ohms, it trips its associated breaker. However if a fault occurs beyond the 90% of this

line, the impedance is higher than 90 ohm for such fault and the relay does not operate. So

the relay provides desired selectivity.

Figure 2.3: Distance Relay Protection Zones

An important feature of distance relay is the provision of zone protection, generally with

three zones. It allows the relay to provide back-up protection to its primary zones. Usually

a second element is installed to cover the rest of the line and reach out into the second zone

with impedance setting of 120% of the length of the line (Figure 2.3 ). A third element is

added to reach even further and provide back-up protection for first and second zones. In


each case, a timer is included to delay operation of the second and third elements in order

to allow primary protection operate in those zones.

Generally, the first element of the relay protects the primary zone by opening the first

breaker, breaker A. The second element provides local back-up in case the first element fails

to operate, i.e. it will trip breaker A after a short time delay. The second element also

provides remote back-up in the case of a fault at B or out on line 2. This would only operate

and trip out breaker A, if the primary protection at bus B fails to operate. Similarly, zone 3

protection is provided as remote back-up for faults along the remainder of transmission line

2 and on into line 3.

Figure 2.4: Distance Relay Overlapping Zones

Also, for protection of line between bus A and B as in Figure 2.4, a set of distance

relays will be installed at bus B looking towards Bus A. The first zone elements overlap

and the fault occurring within this zone causes instantaneous operation of both relays and

opening of both breakers. But fault occurring at the last 10% of the line 1, breaker B trips

instantaneously, but it will wait for clearing of zone 2 element of relay at bus A.

A Mho relay is a common type of improved distance relay as it provides directional

protection. Figure 2.5 shows the operational equation and operating characteristic of a Mho

distance element. The characteristic is the locus of all apparent impedance values for which

the relay element is on the verge of operation. The operation zone is located inside the circle.


Figure 2.5: Mho Relay Element Characteristics

The Mho characteristic is a circle passing through the origin of the impedance plane

where the relay element operates for impedances inside the circle. The characteristic is

oriented towards the first quadrant as in Figure 2.5, which is in the direction of forward

faults. For reverse faults, the apparent impedance lies in the third quadrant and represents

a restraint condition. The fact that the circle passes through the origin is an indication of

the inherent directionality of the Mho elements. However, close-in bolted faults result in a

very small voltage at the relay that may result in a loss of the voltage polarizing signal. This

needs to be taken into consideration when selecting the appropriate Mho element polarizing

quantity.

There are typically two settings in a Mho element: the characteristic diameter, ZM , and

the angle of this diameter with respect to the R axis, θM . The angle is equivalent to the

maximum torque angle of a directional element. The relay element presents its longest reach

and greatest sensitivity when the apparent impedance angle θ overlaps with θM . Normally,

θM is set close to the protected line impedance angle to ensure maximum relay sensitivity

for faults and minimum sensitivity for load conditions [19].

2.3.2 Loss-of-Field Protection

When a generator loses excitation capability, it appears to the system as an inductive load,

and the machine begins to absorb a large amount of VARs from the system. Hence, a loss-of-

field condition may be detected by observing for excessive reactive power flow. This condition

can, to some extent, be detected within the excitation system by monitoring field voltage or


current. Small units can use even use power factor or reverse power relays. For generators

that are paralleled to a power system, the preferred method to identify loss-of-field at the

generator terminals using impedance type relays which observes apparent impedance.

Figure 2.6: Generator Capability Curve

The power diagram (P-Q plane) of Figure 2.6 shows a typical capability curve for a

generator which demonstrates various limits for over and under-excitation conditions. The

first quadrant of the diagram applies for lagging power factor operation which is typically

the normal operating state of a generator (generator supplies VARs). The trajectory starts

at point A and moves into the leading power factor zone (4th quadrant) and may readily

exceed the thermal capability of the unit reaching point B during loss-of-field condition. The

apparent impedance seen by a loss of relay also lies in 4th quadrant of the R-X diagram,

so the LOF relay characteristics set the protection boundary in this quadrant depending on

the steady-state stability margin.


Figure 2.7: Impedance Variance during LOF Conditions

The LOF operates when impedance moves from a normal excitation condition to an

under-excitation state which is inside the trip zone and is typically marked by a Mho

impedance circle centered about the X axis, offset from the R axis. With complete loss

of excitation, the generator will eventually act like an induction generator with a positive

slip as the machine speed above synchronous speed, excessive currents can flow in the rotor,

resulting in overheating of elements. When a generating unit is initially supplying reactive

power and then draws reactive power due to los-of-excitation, the reactive swings can sig-

nificantly depress the voltage. In addition, the voltage will oscillate and adversely impact

sensitive loads. Such excessive reactive sink and voltage sag can cause system instability.

It can be observed from the basis of loss-of-field protection that the setting which dictates

when a relay would trip from a loss-of-field condition is calculated by metrics which change

based on the operating condition of the system. Most notably, the Thevenin impedance

will change dramatically for discrete changes in the system such as topology changes which

are close to the generator in question. Chapter 4 investigates a protection scheme which

enables the loss-of-field relay to adapt to prevailing system conditions such as topology

change yielding a more reliable and secure operation of the power system. The next section

introduces the idea that a relaying parameter may benefit from changing based on the current

system conditions.


2.3.3 Adaptive Protection

Adaptive relaying is a concept of power system protection that allows for change and modifi-

cation to relay characteristics to adjust to existing network conditions. In general, protection

systems react to system faults or disturbances based on fixed, predetermined settings dic-

tated by previously observed system parameters. But it is difficult to anticipate all possible

power system scenarios or operating conditions (especially at the transmission level) as the

system is growing and changing so frequently. Even though a protective relay setting con-

siders many possible scenarios reflecting large sets of contingencies, one particular relaying

option may be the best protective solution. The adaptive relaying scheme provides multiple

protection options where individual settings may correspond to specific or a group of con-

tingency scenarios. Descriptions of such adaptive relaying are given in Chapter 3 & 4. An

approach to including a supervisory boundary for zone-3 back-up protection for transmission

lines and generator loss-of-excitation protection is also presented in this dissertation as an

adaptive protection technique to set alarm and indicate system stress so that preventive

actions can be taken to mitigate the emerging strain in the system. The adaptive protec-

tion requires input from various elements of the network to notify the relays about current

system state which is provided by WAMS with the help of phasor measurement units and

other devices (such as dual use line relays used for breaker statuses, or information about

outages) in current practice.

Chapter 3

Supervisory Control for Back-Up

Zone Protection

3.1 Introduction

A distance relay is a protective relay in which the response to the input quantities is primarily

a function of the electrical circuit distance between the relay location and the point of fault

[20]. As seen in Section 2.3.1, the protected zone-2 and -3 of this relay is used as back-up

for the primary protection. It is usually time delayed. In addition, the back-up zone usually

removes more of the system elements than required by the operation of the primary zone of

protection. This is especially true in the case of long transmission lines or zone-3 elements

that have to provide backup protection for lines outgoing from substations with significant

in-feed. This is quite dangerous during wide area disturbances and can result in cascading

failures as seen recently during India blackouts [21].

Due to similar major disturbances in the past during zone-3 relay operations, back-up

protection such as zone-3 was scrutinized and eventually was removed in many situations.

But back-up zone-3 protection is still required in certain scenarios. A solution may be to

monitor other relays in the vicinity to supervise zone-3 [22]. It means that if the protection

zone-3 of a distance relay sees impedance characteristics within its protection boundary but

an appropriate combination of zone-1 relays is not able to see a fault, this zone-3 should be

blocked. CIEE Electric Grid Research Program requested to perform a study on the full

33

Chapter 3. Supervisory Control for Back-Up Zone Protection 34

California study system in GE’s PSLF (Positive Sequence Load Flow Software) and develop

techniques for supervising the back-up zones [23] [12]. This chapter describes work related to

this project and aims to develop schemes for supervising back-up zones with remote phasor

measurements so that back-up protection is not allowed to operate when it is not appropriate.

An exhaustive testing of the developed protection schemes is performed through simulations

in the full California study system.

3.2 Distance Relay Back-up Protection Criteria

Distance relay identifies the impedance between the relay location and the fault from voltage

and current measurements at relay location. For a fault at the remote end of the line, the

voltage at the local relay equals the current multiplied by impedance of the line, i.e. IZ.

Therefore, the ratio of the voltage to the current measured at the relay is effectively the

impedance of the line, Z. As the ratio V/I is proportional to the line length between the

relay and the fault, the ratio V/I, therefore, determines the impedance to the fault. A

distance relay is designed to only operate for faults occurring between the relay location and

the selected reach point and remain unchanged for all faults outside its protection margin

or zone [24].

Figure 3.1: Three Zone Distance (Mho Relay) Characteristics


Even though transmission lines are fully protected with zone-1 and zone-2 relays, zone-3

(As in Figure 3.1 ) of a distance relay is used to provide the remote backup protection in

case of the failure of its primary protection and is typically set to cover about 120-180% of

the longest adjacent line. This zone is given a delay time twice that associated with zone-2

operating time to achieve time selectivity, and the time delay is typically set in the range

of 1-2 seconds. Sometimes it is necessary to coordinate the zone-3 relay with over-current

relays on tapped distribution load. The relay should detect any fault for which it is expected

to provide backup and not limit the load carrying capability of the line. The setting of the

zone-3 relay ideally will cover (with adequate margin and with consideration for in-feed, if

required) the protected line, plus all of the longest line leaving the remote station [20].

In this study, 100% of the line in question and 150% of the adjacent longest line are used

as the setting of the zone-3 of the distance relays.

3.3 Load-encroachment and Supervision of Back-up

Protection

Distance relays are usually designed on the basis of fixed impedance setting and this setting

is called a relay reach. In conventional distance relaying the impedance between the relay and

the location of the fault is measured, which indicates whether a fault is internal or external

to its protection zone. However, the disadvantage of using relays is that their settings have

to be reset for changes in the network configuration. The relay either overreaches or under

reaches depending on the operating conditions of the power system and the location of

the fault [25]. In case of long transmission lines the back-up protection relay reach can

be significantly large and the apparent impedance seen by this relays approaches the relay

protective boundary while the loading of the line increases as demonstrated in Figure 3.2.

Impedance characteristics may enter the tripping zone of the relay under very heavy loads

and lead to tripping. This condition where impedance characteristic observed by distance

relay enters the relay protective zone due to the power shift in the transmission lines is

referred to as load encroachment.


Figure 3.2: Effect of Load Encroachment on Zone-3 Characteristics

Remote back-up protection is only supposed to operate as a last resort in situations

where all other devices have failed as a measure against the loss of system integrity. Load

encroachments of back-up zones of protection are an unwanted side effect of these types

of protection schemes. WAMS data can give the additional perspective for determining if

there are truly needs to take preventive actions. Multiple views of the system allow relays

to differentiate between trip and block. In this example demonstrated in Figure 3.3, relay

A can identify a violation of loadability limit with respect to a system fault i.e. whether a

zone-3 pick up is appropriate using information from PMUs at neighboring buses B and C.


Figure 3.3: Supervision of Backup Protection

3.4 Study Model Description

The proposed protection scheme is developed and tested using full WECC and CA heavy

summer models prepared in GE’s PSLF software.

3.4.1 WECC Full Loop Model

The PSLF model of full WECC heavy summer system that was created in February 2008.

This study system encompasses 15,700 buses with a wide range of interconnected transmis-

sion system connecting over 3000 generators to their loads across almost 1.8 million square

miles of territory. Along with a steady-state load-flow model, the study-system includes

a dynamic representation of WECC system. Generators included in the model are mostly

represented as thermal units and all machines contain appropriate dynamic elements such as


governor models, excitation system, power system stabilizer, static VAR compensator, static

synchronous condenser and some protection models to accurately represent the real system

and also improve the dynamic stability of the study system. The total system demand is

over 150GW represented by mostly constant current loads & frequency-dependent loads and

some constant impedance & constant power loads distributed within 18 partners or utilities

in the Western Interconnect. The Pacific high voltage DC link and WECC-Eastern Interface

DC tie are also included in this model.

3.4.2 California Model

California study system is a reduced model created from the WECC full loop model. This

model consists of over 4000 buses that are spread around within 6 main electric utilities in

the CA region. Over thousand generators supporting almost 56 GW of load demands and

power injections from outside California are represented with two large equivalent generators

in the Northern and the South-eastern interfaces. Seven 500 kV tie-lines are also included

to interconnect California power system with the external buses of the remaining WECC

system. Table 3.1 contains the list of inter-ties for the CA system.

500 kV Lines Linking utilities Interfaces

Navajo - Crystal AZ Public Service Co. - L.A. Dept. of Water & Power AZMoenkopi Eldorado AZ Public Service Co. - Southern CA Edison AZHassyampa- N.Gila AZ Public Service Co. - San Diego Gas & Electric Co. AZPaloverde- Devers AZ Public Service Co. - Southern CA Edison AZ

Mead- Marketplace NV Power Company - L.A. Dept. of Water & Power NVCapt. Jack- Olinda Bonneville Power Admin. - Pacific Gas & Electric ORMalin- Round Mt. PacifiCorp - Pacific Gas & Electric OR

Table 3.1: 500 kV Links in CA System

3.5 Selection of Appropriate Location for Back-up

Protection

To implement the supervisory protection scheme, the critical locations are to be detected

where the back-up will be needed. This opts for a detailed understanding of the study system


and critical elements of the system. Critical elements are those that if lost or tripped the

stability of the power system will be on stake. Identifications of critical lines are crucial

because when a line trips in the system other lines try to make up for the power loss by

transmitting power to the load to be fed by the tripped line. If a line is tripped which has a

large portion of total power flow here referred as a critical line, this loss may not be quickly

restored by the others as over-loading may occur. As a result, the back-up zone-3 protection

of these overloaded lines may seen impedance characteristics within its protection boundary

which can be identified by the relay as an in-zone fault instead of load-encroachment. In

this case operation of the relay by tripping the line to clear zone-3 fault is a mistake. This

unnecessary outage of heavy loaded lines can initiate cascading failure in the system and

cause blackouts.

As a part of the load-encroachment study, the method of line outage distribution factor

(LODF) is applied here perform first screening of the critical lines. The goal is to find the

line with large LODF, for one or multiple contingencies which may cause over-loads at lines

near an outage.

3.5.1 Line Outage Distribution Factors

LODF gives the percent of flow from the outage line that ends up flowing on another line.

As discussed before for a line outage, loss of power flow on that line will be carried by

other lines. Figure 3.4(b) shows line1−3, from bus 1 to 3 is out of service, part of the flow

S1−3 of line1−3 (Figure 3.4(a)) is being carried by other lines; the percentage of S1−3 is the

distribution factor for that line1−3.


Figure 3.4: Principle of LODF (a) L13 in service. (b)L13 out of service (unknown source)

3.5.1.1 Technique for Determining Line Outage Distribution Factor

Before the line outage contingency occur, the impedance matrix, [Z] ans system susceptance

matrix [X] are computed considering the initial topology of the system as described in Section

2.1.3. Distribution factor Krs,pq represents the fraction of the power in the line p-q that goes

out which ends up in line r-s after the outage.

drs,pq =xpqxrs

(Xrp −Xsp −Xrp +Xsq)

xpq − (Xpp +Xqq − 2Xpq)(3.1)

Where xpq is the impedance of the line p-q and Xpq is the pqth element of susceptance

matrix, X [15]. If the power on line r-s and line p-q is known, the flow on the line r-s, due

to the outage of line p-q can be determined using the drs,pq factors.

frs = f 0rs + drs,pq ∗ f 0

pq (3.2)

Where f 0rs and f 0

pq are the pre-outage flows on the lines r-s and p-q, respectively frs is

the flow on line r-s after line p-q out.


3.6 Implementation of LODF to California

(Heavy Summer) Model

To apply the distribution factor analysis to the full California power system model, under-

standing of the system parameters and familiarization with PSLF (GE Positive Sequence

Load Flow Software)are necessary as the system is modelled using the software. As LODFs

are to be found in terms of bus suceptance matrix or [X] matrix which is computed from

bus admittance matrix, [Ybus] for the California network, with around 4000 buses and 4474

lines as described in Section 2.1.3.

3.6.1 Formation of LODF Matrix for CA System and

Identification of Critical Lines

Using Equation 3.1, distribution factors for each single line contingencies are calculated and

a 4474 x 4474 dimensional LODF matrix is formed. As LODF gives the percent of flow from

the outage line that ends up flowing on another line, distribution factor, drs,pq represents

the fraction of the power in the line p-q that goes out which ends up in line r-s after the

outage. Using the Equation 3.2, post-contingency power flows in the lines are calculated.

Considering a power factor (0.8 0.9), the thermal capacity of the lines are compared with

the post-contingency power flows in the lines and overloads are detected. Lines with 30% or

more overloads are considered as critical lines.

3.6.2 Identification of Zone 3 Settings for Critical Lines after

Single Contingency

(n − 1) contingencies are created and the corresponding critical lines are monitored. The

zone-3 setting of critical lines were identified considering Mho relays, i.e. the apparent

impedances is seen by the relays in normal condition. The apparent impedances seen by the

relays due to the pre-determined overloads are determined. As the load on a line increases,

the apparent impedance locus approaches the origin of the R-X diagram. For some value of

line loading, the apparent impedance may cross into the zone of protection of a relay, and

may cause the relay to trip, this is called an encroachment of protective zone.


3.6.2.1 Relay Settings for Multi-Terminal Lines

When the multi-terminal lines have sources of generation behind the tap points, or if there

are grounded neutral wye-delta power transformers at more than two terminals, the pro-

tection system design requires careful study of infeed currents. Consider a three-terminal

transmission line as shown in Figure 3.5 for this study.

Figure 3.5: Effect of Infeeds on Zone Settings of Distance Relays

For a fault at F , there is a contribution to the fault current from each of the three

terminals. (For simplicity, it is assumed that this is a single-phase system and the actual

distance evaluations for each type of fault must be considered. This aspect of multi-terminal

line protection is no different from the usual considerations of faults on a three-phase system.)

The voltage at bus 1 is related to the current at the same bus by Equation 3.3,

E1 = Z1I1 + Zf (I1 + I2) (3.3)

and the apparent impedance seen by relay R1 can be computed as,

Zapp =E1

I1

= Z1 + Zf (1 +I2

I1

) (3.4)

where the true impedance to the fault is,

Ztrue = Z1 + Zf (3.5)


The current I2, the contribution to the fault from the line tap which is referred as

the infeed current when it is approximately in phase with I1, completely arbitrary phase

relationships are also possible, but in most cases the phase relationship is such that the

current I2 is an infeed current.

The apparent impedance seen by relay R1 that is shown in Equation 3.4 demonstrates

that it results in being larger than the actual value if the tap current is an infeed. As the

setting of zone-1 of relay R1 is usually about 80 90% of the actual line length(impedance)

1-2, for many of the faults inside the zone of protection will appear to be outside the zone of

the relay, and the relay will not detect such faults. It would also be insecure to set zone-1 of

the relay to higher value, in order to retain the apparent impedances for all faults inside the

zone-1 setting. For, such a setting, if the tap source should be out of service for some reason,

faults beyond the 80 90% point may cause zone-1 operation of this relay. In this case, the

infeed current should not be considered for defining zone-1 settings /citePhadke1994.

Subsequently, zones-2 and -3 of relay R1 are set to reach beyond buses 2 and 3, respec-

tively, under all possible configurations of the tap. As a result, these over-reaching zone

settings must consider contributions of all the infeeds. Then, even if some of the infeeds

should be out of service, the apparent impedances seen by the relay will be smaller, and will

definitely reside inside the protective zones.

3.7 Multiple Contingency Studies

Since no encroachment of zone 3 protective zones was found with single contingencies, over-

loads for multiple contingencies were studied. The study was started with contingencies like

500 kV line outage which created heavy overloads (30% or more of line capacity, maximum

MVA rating) along with generator outages. Performing this contingency analysis, it was ob-

served that for all generator outages, PSLS load flow add the MW losses in the system with

the Swing Generators. In the CA Study system there are 2 swing generators, one located in

the Northern boundary and the other in the Eastern boundary of CA. These swing genera-

tors are also modelled as equivalent generators outside CA. As a result of normal load-flow

in PSLF, all generation mismatches were picked up by these two equivalent generators, but

in the real system, the outage generations are to be distributed to the rest of the genera-

tors (in-service) according to their machine inertia. Inertial re-dispatch was performed for


generator outage contingencies.

3.7.1 Inertial Re-Dispatch of Generators

Inertia of generators indicate the amount of reserved rotating energy in the system. Under

steady state conditions the mechanical and electrical energy must be balanced. When the

system has a generation loss, the electrical demand at each remaining generator terminal

lacks the mechanical energy supplied, as result the system frequency rises. The rate of change

of frequency increase dependant upon the initial power mismatch and system inertia. The

speed of each machines will continue to reduce until the total mechanical power supplied to

the whole system matches to the electrical demand. The stored kinetic energy of the rotating

machines are delivered to grid as MW power.

For a synchronous machine inertia constant H is frequently specified. It is defined as the

ratio of the stored kinetic energy at rated speed to the rated apparent power of the machine

(MVA rating). This yields,

H =stored kinetic energy at synchronous speed in mega-Joules

generator MVA rating=Wk

SB(3.6)

where WK is the kinetic energy of the rotating mass(generator) and SB is the rated MVA of

the machine which indicates the size of the machine.

Since most of the generators in the CA system is represented as thermal units, similarity

in machine inertia constants are observed. So, H can be defined as a constant in Equation 3.5.

Then the amount of energy stored in each rotating machines become directly proportional to

the size of that machine(generator base/rated MVA) and it can be inferred that the bigger

the generators are the larger contributions to make-up for a generation loss.

For steady state analysis, it is agreed that ∆P at a generator will be ∝ Srated to that

machine. So after a generator outage contingency, the MW mismatch is accounted for by

re-dispatching the other generators(in service) based on their machine base, Srated . In the

post-contingency, change in real power output in generators using Equation 3.7,

∆Px =Srated,xSrated,total

∆Ptotal (3.7)


Where, ∆Px is the change in MW in machine x, after re-dispatch, ∆Ptotal is the total gener-

ation loss in MW in the whole system, before re-dispatch, Srated,x is machine base of machine

x, Srated,total is the total of machine bases in whole system. A multiple contingency analysis

was performed based on this concept utilizing the following algorithm to find overloads and

encroachments of back up zone (zone-3).

Figure 3.6: Flow-Chart for Inertial Re-dispatch of Generators


3.7.2 Comparison between CA and Full-Loop Study System

To verify our generator inertial re-dispatch algorithm, the same generator outage contin-

gencies were performed in both the Full-loop study system, which is a complete model of

WECC power system, it has the actual generators outside CA included in it. But these

generators are modelled as equivalents in the CA study system. It was observed that in the

Full-loop model 66-70% of make-up generations come from generators outside CA and in

the CA model 70-73% of losses were picked up by the equivalents modelled as generators

outside CA. After validating the algorithm with the testing in both systems, the multiple

contingency studies were performed.

3.8 Load-Encroachment Examples in CA System

The apparent impedance entering the protective zone due to the shifting of power flows

as result of changes in transmission network structure. This is especially true in the case

of long transmission lines or zone-3 elements that have to provide backup protection for

lines outgoing from substations with significant in-feed as the back-up zone protection char-

acteristic circle reaches very far. Again, zone-3 protective circle of a relatively short line

encloses a large protection area which makes the back-up zone to over-reach and be prone

to load-ability violation. Such a line between Captain Jack (500kV) and Olinda (500kV) is

demonstrated in the WECC map in Figure 3.7 which follows by a long transmission line

from Olinda (500kV) to Tracy (500kV). Hence, the zone-3 setting of Mho relay located at

Captain Jack looking toward Olinda is significantly larger than its primary zones as shown

in Figure 3.8.


Figure 3.7: WECC Map, Relay at Captain Jack (500kV Bus) [23]

Captain Jack- Olinda is a segment of path 66 is an inter-tie between PG&E and Pacifi-

Corp 500 kV lines. This route technically starts at Captain Jack station close to Malin, very

close to California-Oregon border, near the Malin substation, where the other 500 kV lines

start another link between PacifiCorp & PG&E. These substations also link to Bonneville

Power Administration (BPA) grid in the Pacific Northwest and brings large amount of power

to CA system through the PG&E high voltage lines. Consider, the loss of one of these links

due to maintenance or faults which stresses and increase loading in Captain Jack-Olinda

line. Such heavy loads causes apparent impedance seen by the Mho relay located at Cap-

tain Jack enter the zone-3 margin of this relay as shown in Figure 3.8 and may lead to an

inappropriate relay tripping. Both 500 kV lines between Round Mt. and Table Mt. are

taken out-of-service to simulate the loss of the tie-line between California and the Pacific

Northwest.


Figure 3.8: R-X Characteristics of Relay at Captain Jack (500kv bus), Monitoring Line fromCaptain Jack to Olinda

In this section the area of focus is the Midway- Vincent 500 kV lines with three parallel

circuits which are high voltage corridors between PG&E and S. California two major utilities

in WECC system. Scenarios are considered where Mho distance relays are located both end

of the lines and observe the characteristics of the over-reaching back-up zone protection.

Using the California Study System, power flow is monitored through this important link.

Power flow congestion is created in these corridors to simulate the impedance trajectories

observed by the relays and identify scenarios where the impedance plots encroach the back-up

zones of protection.

Transient studies are performed which determined the R-X characteristics observed by

the Mho relays protecting Midway-Vincent lines. The MVA ratings for Midway-Vincent

lines are listed in Table 3.2 as gathered from PSLF system model.


Midway-Vincent Line Current Rating ACircuit No. (MVA)

1 1848.12 2309.73 1848.1

Table 3.2: Midway-Vincent Line Ratings

As mentioned in Table 3.2, the circuit 2 between Midway-Vincent line (500kV) has the

highest flow capability among all three circuits where circuit 1 and 3 has the same rating.

Either of the lower rated circuit 1 or 3 is able to sustain losses of both circuit 2 and one of

the lower rated circuits in the heavy summer model of the California Study System. So some

of the adjacent lines to Midway 500 kV bus is tripped to increase power flow in the single

in-service line between Midway and Vincent to simulated load encroachment scenarios and

impedance characteristics seen by relays are monitored. But impedance plot (Figure 3.9 )

still remains far away from the zone of protection. As a result, total loads in S.California

area are increased to create flow over-loads in the single in-service MidwayVincent line (500

kV). Some examples are presented below to portray the R-X behaviors to be observed by

the relays: (zone-1, -2 & -3 protections are shown with blue circles; the red circle around the

zone 3 represents the supervisory boundary which is set at 150% of zone-3 protection).

Multiple contingencies listed below are applied and impedance trajectory due to load

increase in Midway-Vincent line is monitored as shown in Figure 3.9 where distance relay is

located at Midway bus (500kV) looking toward Vincent (500kV).

• 500 kV Lines out-of-service from Midway to Vincent, circuit 1 & 3 for maintenance at

1.0 sec.

• 500 kV Line out-of-service between Midway & Losbanos to fault at 2.0 sec.

• 500 kV Lines out-of-service between Gates & Losbanos to fault both circuits at 2.5 sec.

• Transformer failure from Gates (500kV) to Gates(230kV) at 3.0 sec.


Figure 3.9: R-X Characteristics of Relay at Midway (500kV bus), Monitoring Line fromMidway to Vincent, ck 2

Another example of impedance trajectory during load increase in Midway-Vincent line is

monitored is illustrated in Figure 3.10 where distance relay is again located at Midway

bus(500kV) looking toward Vincent(500kV). In this scenario, a 40% increase of S. California

loads are simulated to further over-load the monitored line than the previous case so that

impedance characteristics observed by distance relay at Midway approaches the supervisory

boundary of the back-up protection margin of the relay. The Step by step contingencies

which are applied to simulated the R-X trajectory in Figure 3.10 are listed below.

• 500 kV Lines out-of-service from Midway to Vincent, circuit 1 & 3 for maintenance at

1.0 sec.

• 500 kV Line out-of-service between Midway & Losbanos to fault at 2.0 sec.

• 500 kV Lines out-of-service between Gates & Losbanos to fault both circuits at 2.5 sec.

• Transformer failure from Gates (500kV) to Gates(230kV) at 3.0 sec.

• 40% load increase in S. California area(24) at 3.5 sec.


Figure 3.10: R-X Characteristics of Relay at Midway (500kV Bus), Monitoring Line fromMidway to Vincent, ck 2

If the total loads in S. California Edison is increased up to 75% of the base case scenario along

with the other contingencies in the previous case, the Midway-Vincent line is furthermore

overloaded. The load-ability limit of this line imposed by the zone-3 of the distance relay

at Midway is violated as the impedance trajectory seen by this relay enters the back-up

protection boundary or tripping zone of the relay as demonstrated in Figure 3.11. But the

relay at Vincent Mho characteristic is oriented towards the first quadrant as in Figure 3.12,

which is in the direction of forward faults toward Midway and the apparent impedance lies

in the third quadrant during the flow overload so this relay protection is not violated.


Figure 3.11: R-X Characteristics of Relay at Midway (500kV Bus), Monitoring Line fromMidway to Vincent, ck 2

Figure 3.12: R-X Characteristics of Relay at Vincent (500kV Bus), Monitoring Line fromMidway to Vincent, ck 2


3.9 Summary

Zone-3 distance relays are key elements in power system protection that are implemented

to detect faults on the protected transmission line and beyond to cover remote elements.

Besides providing back-up protection to its primary zones, these relays are often utilized for

equipment protection further ahead of the line and also used as an alternative protection to

equipment failure communication systems. As these relays over-reach to protect transmission

lines against remote faults, these may become susceptible to loadability violations. As seen

in the simulation cases in CA system, back-up relays can see the apparent impedance to be

within the impedance circle or the zone-3 reach of these relays due to increased loading in the

lines. Inclusion of a supervisory boundary to the back-up protection improves the distance

protection scheme which allows notification of approaching line over-loads and provision of

adjustment to avoid cascading line failures.

Chapter 4

Adaptive Loss-of-Field Protection

In the field of power system protection there are a great variety of protection schemes which

act to prevent damage to critical parts of the electric infrastructure. And just as there are

many types of protection schemes, there are many types of relays which act to physically

implement the protection schemes created by protection engineers. This chapter focuses on a

specific type of relaying called loss-of-field (LOF) relaying. This type of relaying is important

for protecting generators from a particular instability condition where the generator loses its

rotor field. A generator may lose its excitation due to inadvertent field breaker tripping, a

field open circuit, a field short circuit, voltage regulator failure, or loss-of-excitation system

supply [27]. While a typical LOF condition is partial, a complete loss-of-excitation can occur

in rare instances.

When a synchronous generator incurs a LOF condition it draws reactive power from the

system which damages rotor. This is caused by heavy loading of the generator windings due

to the excessive reactive power consumption which dictates heating of the rotor windings

and potentially a loss of magnetic coupling between the rotor and the stator. Because this

condition creates an increasing reactive power demand on the neighbouring area it has the

potential to cause the bus voltages to decline near the generator experiencing the loss-of-field

condition. This condition at a large generator such as major fossil plants can quickly cause

voltage collapse at nearby system and can even endanger the voltage stability of the rest of

the power system [28]. Therefore, LOF condition on a generator is a critical state of the

power system which should be identified as fast as possible, and the effect of loss-of-field on

the power system stability has to be assumed and investigated in order to prevent voltage

54

Chapter 4. Adaptive Loss-of-Field Protection 55

collapse or cascading failure of the network [29].

4.1 LOF Relaying Background

Impedance type loss-of-field relays are applied at the generator terminals to detect failure

of the generator excitation in the form of DC voltage or short circuit. The LOF relay is

designed to recognize this condition and trip the generator within one second of the failure.

The LOF relay settings consists of two concentric circles; the inner circle is the impedance

boundary criterion of actual steady state stability limit, which if encroached, will lead to

loss of synchronization of the generator, pole slipping and its eventual tripping. The outer

circle is used to create an alarm for system operators if the apparent impedance seen by

the relay indicates an operating condition which requires immediate action to mitigate an

impending problem. As described in the following section, the steady state stability limit

circle is affected by the system operating conditions, which has the potential to result in a

mis-operation of the LOF relay. In this chapter, an approach for creating coherent groups

of generators and finding the LOF settings for the generator members of the group which

allows on-line identifying system conditions based on wide area measurements. Thus the

steady state stability limit circle can be adaptively fit for different operating conditions.

The limits of stability are expressed as settings in the R-X plane for distance relays.

The setting of the loss-of-field relays is based upon generator voltage, generator impedance,

and the Thevenin impedance of the system as seen from the generator terminals. Clearly

the generator impedance is constant, but the system Thevenin impedance changes as the

structure of the power system changes and the terminal voltage of the generator may also

vary. However, because the changes due to the generator voltage are minimal, it can be

assumed that the only varying quantity in the equation is the Thevenin impedance which

changes most dramatically when there is a discrete change in impedance due to a topology

change (example: line outage). Consider a scenario where the power system is in a vulnerable

state because of a particular line outage or multiple line outages. In this scenario, the system

Thevenin impedance will increase; this reflects the evolving weakness of the power system.

As the Thevenin impedance increases, the steady-state stability margin will shrink, and the

LOF relay settings in place on the generators are then inappropriate [26]. In certain cases

of cascading failures, this may lead to a generator trip without getting a warning, further

exacerbating the situation.


The goal of this research is to determine adaptive LOF relay settings for generator

protection with remote phasor measurements so that these generator protection schemes are

not allowed to operate when it is not appropriate [23] [13]. This chapter aims to develop

an adaptive LOF relaying criteria for generators using the system Thevenin impedance as a

varying element with respect to the current system operating mode. California study system

in PSLF is used for testing and simulations to identify adaptive LOF protection settings for

generators in the system and validate the adjustment of relay based on system changes due

to events or disturbances.

4.2 Loss-of-Field Relay Protection Criteria

This section explains the reason that a loss-of-field condition is considered as a steady-state

instability. Figure 4.1 demonstrates the phasor diagram of the terminal voltage E1, stator

current I1, and the internal voltage of the generator Es. Also shown is the field circuit with

a field current If .

Figure 4.1: Phasor Diagram of Generator Voltage and Current during Reduced Excitation

If the effects of generator saturation is neglected, the voltage Es and the field current

If are proportional to each other. As a result the phasor Es (magnitude) can be used to


represent the field current. If the field current of the generator decreases which causes the

loss-of-field condition, the output real power P is not affected. Since the power P is equal

to EI cos θ, where θ is the power factor angle and in normal operating condition, current

lags voltage. The projection of the stator current vector I1 on the axis of E1 is a constant

parameter even if the field current changes. This is represented by x in Figure 4.1.

Now consider a decrease of field current If which causes the internal voltage of the

generator Es to drop. In order to maintain the phasor relationship between Es, E1 and I1

under these conditions, as Es reduces in magnitude the vector must move along the dashed

horizontal line and the current I1 must move along the dashed vertical line. This relationship

retains the output real power constant at P , while the stator current moves from I1 position

to I1′, the power factor goes from a lagging to a leading angle. The machine absorbs reactive

power from the system when the field current reduces or generator loses excitation [30] [26].

Figure 4.2: Loss-of-Field as an Instability Condition

The ratio of E1 to I1 is the apparent impedance Z or (R + jX) seen by LOF relay (a

distance relay) connected at the terminals of the generator. If x is constant, the apparent

impedance travels along the circle, crossing over from the first quadrant to the fourth quad-

rant. The characteristics of the impedance relays which define the steady stability margin

and a supervisory boundary for alarm are also shown in Figure 4.2. It is clear that as the field


current of the generator drops, the generator goes from a lagging power factor to a leading

power factor, and the apparent impedance seen by a distance relay quickly approaches the

steady-state stability boundary which is discussed in the following sections [26].

4.2.1 Steady State Instability as a Consequence of LOF Condition

Consider a simple system consisting of one machine connected to a power system where the

rest of the system is condensed into a single machine and impedance as shown in Figure 4.3

Figure 4.3: Simple System for Steady-State Stability Analysis

The internal voltage of the machine is Es and the machine reactance isXs. The equivalent

impedance (Thevenin) of the power system is Xt and power system equivalent voltage is E2.

Since steady-state analysis is considered here, the voltage Es is the field voltage Ef , and the

reactance Xs is the the synchronous reactance Xd. The total reactance between the machine

internal bus and E2 is X = Xs + Xt. The electric power output at the machine terminals

(at bus S or at bus 2) is given by Equation 4.1.

Pe =EsE2

Xsin δ (4.1)

where δ is the angle by which the machine internal voltage Es leads E0. The mechanical

power input to the machine is Pm, and in steady state electrical power and mechanical power

are in balance at a rotor angle δ0 which is zero when the machine is operating in steady state

at δ0. The rate of change of the output power Pe with respect to δ is given by Equation 4.2.

∂Pe∂δ

=EsE2

Xcos δ (4.2)

which remains positive for −π/2 ≤ δ ≤ π/2. This is the range of steady-state stability for

the system. Because the generator must have a positive output, the steady-state stability


limit of interest is δ = π/2. This remains positive for −π/2 ≤ δ ≤ π/2. This is the range of

steady-state stability for the system.

Figure 4.4: Steady-State Stability Limit (a) A Circle in the P-Q Plane (b) A Circle in theR-X Plane [26]

The real and reactive power outputs of the machine (as measured at the machine termi-

nals) are given by Equation 4.3.

P1 + jQ1 = E1I1 (4.3)

At the steady-state stability limit of the machine, the rotor angle is π/2, and it can be shown

that, at the stability limit, P1 and Q1 satisfy Equation 4.4.

P 21 +

[Q1 −

E21

2

(1

Xt

− 1

Xs

)]2

=

[E2

1

2

(1

Xt

− 1

Xs

)]2

(4.4)

This is an equation of a circle in the P -Q plane, as shown in Figure 4.4(a). The response of

the distance relay is determined when the machine is operating at its steady-state limit. It

can be shown that a circle in the P -Q plane maps into a circle in the apparent R-X plane.

Whether or not a machine approaches a limit (such as a steady-state stability limit) defined

by a circle in the P -Q plane can then be detected by the corresponding circle in the R-X

plane, using a distance relay. Let us take a general circle in the P -Q plane, with its center

at (P0, Q0), and a radius of S0. This is given in Equation 4.5.

(P − P0)2 + (Q−Q0)2 = S20 (4.5)


For example, in the case of the steady-state stability limit given in Equation 4.4, these

values are given by Equation 4.6-4.8.

P0 = 0 (4.6)

Q0 =E2

1

2

(1

Xt

− 1

Xs

)(4.7)

S0 =E2

1

2

(1

Xt

− 1

Xs

)(4.8)

Figure 4.5: Apparent Impedance Seen by an Impedance Relay (a) Generator Connectedto Power System (b) Generator Supplying the Same Power to Parallel Load (c) GeneratorSupplying the Same Power to a Series-Connected Load [26]

Consider the three circuits shown in Figure 4.5 where Figure 4.5(a) shows a generator

with output P + jQ with a terminal voltage, E. Figure 4.5(b) shows the generator with

the same terminal conditions but now supplying an impedance load R and X connected in

parallel at the generator terminal. The parallel impedances are next converted to series-

connected R and X, which are related to the terminal conditions by Equation 4.9-4.10.

P =E2R

R2 +X2(4.9)

Q =E2X

R2 +X2(4.10)

Substituting Equation 4.9 & 4.10 into Equation 4.8 results in Equation. 4.11.

(R−R0)2 + (X −X0)2 = Z20 (4.11)

This is an equation of a circle in the R-X plane with its center at (R0, X0) and a radius of


Z0 as in Figure 4.4(b) where these parameters are given by Equation 4.12-4.14.

R0 =P0E

2

P 20 +Q2

0 − S20

(4.12)

X0 =Q0E

2

P 20 +Q2

0 − S20

(4.13)

Z0 =S0E

2

P 20 +Q2

0 − S20

(4.14)

The circle in the impedance R-X plane for the steady-state stability limit is shown in Figure

4.4(b). For this case, the values can be substituted for P0, Q0 and S0 from Equation 4.6-4.8

using E for the machine terminal voltage, rather than E1. The LOF relay settings are then

given in Equation 4.15-4.17 [26].

R0 = 0 (4.15)

X0 =Xt +Xs

2(4.16)

Z0 =−(Xt −Xs)

2(4.17)

4.2.2 Steady State Stability Limit Circle

The steady state stability limit, as explained in the previous section, reflects the ability of the

generator to adjust for gradual load changes. The steady state stability limit is a function of

the generator voltage and the impedances of the generator, step-up transformer and system

(Thevenin equivalent impedance). This method assumes field excitation remains constant

(no AVR) and is conservative. When calculating, all impedances is converted to the same

MVA base, as the generator base. The steady state stability limit is a circle defined by the

equations shown in Figure 4.6 below where xt=xtrans+xthev [31]:


Figure 4.6: Graphical Method for Steady State Stability Limit

In traditional LOF protection, the size of the steady state stability limit circle is un-

changed once the relay is commissioned. However, in a practical system, the size of the

steady state stability limit circle is related with the system operating modes and changes

from time to time as the loading of the system changes or due to an event [32].

As previously mentioned, the steady state stability limit boundary impedance locus is

a circle as shown in Figure 4.6. The center of the impedance circle is located at the point

(0, −j(Xt−Xs)2

) and the radius is (Xt+Xs)2

. From Figure 4.6, it can be seen that the center and

the radius of the steady state stability limit circle are actually dependent on the system’s

Thevenin equivalent impedance since the impedance of the generator and the transformer

remain constant. When the system impedance increases, the radius gets larger and the center

moves up. At the same time, the new steady static stability impedance circle becomes larger,

covering the previous area. When the system impedance decreases, the radius gets smaller

and the center moves down.


4.3 Development Adaptive LOF Relay Scheme

This section and the rest of the chapter describe the work related to a study to implement

an adaptive LOF relaying scheme for generator protection using wide area measurements to

prevent mis-operation of the LOF relays when the steady-state stability limit changes due

to a topology change. This includes exhaustive testing using the California study system

to develop the group settings for the LOF relays and to test the relaying schemes through

simulations. The scheme as explained in the previous section uses an impedance relay as

the measuring element for loss-of-field for a generator. The application for this project is

based on the behavior of the system impedance as seen from the generator terminals for

various under-excited conditions or contingencies in the system. The primary indicator that

a generator or a machine has lost its excitation is the high reactive flow into the machine

[26]. So the final impedance after an under-excitation condition lies in the fourth quadrant

of the R-X diagram. Any relay characteristic that will initiate an action in this quadrant is

applicable [33]. Once again, the question of whether to trip or to alarm for this condition

must be addressed. In almost every case, an alarm is provided early in the locus of the

impedance swing so the operator can take the appropriate corrective action.

In order to make the relay settings adaptive, different system conditions (line outages)

are identified and the corresponding settings are calculated for each discrete condition. The

LOF relay settings depend on the synchronous reactance Xd and Thevenin reactance of

the power system, Xt at the generator terminal. Since any topology change close to that

terminal will change the value of Xt, the relay will be trained to adapt to these topology

changes and create a LOF relay setting group for each generator or generator groups. Each

member of LOF relay setting group will be correspond to the LOF settings for a specific

operation condition. After identifying the current operation condition using the wide area

knowledge of the topology of the network, the relay will adapt to the system and change

its setting. In the California study system, generators are connected to the system through

their step-up transformers which are referred as the generator groups.


Figure 4.7: LOF Relay at Diablo Machine Terminal

Figure 4.7 shows an example of the relay settings at the terminal of generators at Diablo.

The radius increased showing that the LOF relay setting changed from its normal conditions

after a contingency. This contingency was created by taking a line out-of-service adjacent

to bus Diablo (This example is elaborated in Section 4.3.2. With this scenario, the pre-

contingency and post-contingency Xt values need to be calculated. Additionally, it should

be noted that the Thevenin reactance of the power system at the machine terminal changes

significantly. LOF relay setting are determined by simulations using GE’s PSLF on California

Study System.

4.3.1 LOF Group Settings

The proposed adaptive LOF relay setting consists of two concentric circles for a specific

system operating mode as seen in Figure 4.8. The inner circle is the impedance boundary

criterion of actual steady state stability limit. Encroachment of this limit circle leads to loss

of synchronization of the generator, pole slipping and its eventual tripping. The outer circle

is used to create an alarm for the system operator if the apparent impedance seen by the

relay creates operating condition which requires mitigation. If the power system can supply

reactive power to the generator without a significant drop in voltage, an alarm is set off for

possible corrective action, followed by a shut-down trip after a particular time delay. Typical


delays used vary with machine and system, but are 10 sec to 1 min.

Figure 4.8: LOF Relay Settings

Simulation results gathered from California study system demonstrate that the steady

state stability limit circle is affected by the system operating conditions, which may cause the

LOF relay to mis-operate. Hence, this research calls for LOF protection for each generator

which is provided by a group of settings instead of individual one where each setting corre-

sponds to a different operating mode. This setting group allows on-line identification and

selection correct LOF settings for each generator depending on the current system conditions.

Consider, the example of generator Dibalo1 in CA system as seen in the previous section.

From the analysis above, it can be seen that the LOF protection is not accurate if the

steady state stability limit circle cannot adapt to the change of the system impedance when

the system operating mode varies. So, the LOF settings for the generator Dibalo1 should

consider for all possible scenario which causes system the Thevenin reactance to change

as result generator’s stability will change. The system impedance is calculated considering

generator Dibalo1 connected to a power system where the rest of the system is condensed

into a single machine and impedance as shown in Figure 4.9.


Figure 4.9: Dibalo1- One Machine Infinite Bus

All contingency cases (one bus away) that may affect the system’s reactance for Dibalo1

is considered and each Thevenin reactance calculated using short circuit analysis in GE’s

PSLF per scenario. So, LOF protection for Dibalo1 generator is provided by multiple of

settings with respect to the system’s current condition instead of one fixed setting as seen

in Figure 4.10. If the current operating mode can be provided on-line, then it is possible for

the relay located at Dibalo1 to select and modify the appropriate settings according to the

change of the system which may allow reliability of protection and operating speed of the

LOF relay to be improved.

Figure 4.10: LOF Relay Settings


4.3.2 Adaptive LOF Relay Application in CA System

To demonstrate an implementation of these group settings that has just been discussed, an

example scenario is shown below where loss-of-field relay is located at Diablo1 generator. The

generator step up transformer is connected to the Diablo 500 kV bus. It has two adjacent

paths; one transmission line to Gates and parallel sub-transmission lines going to Midway.

Diablo2 generator is also connected to the 500 kV bus as in Figure 4.11 one-line diagram.

Figure 4.11: Network Diagram near Diablo

The steady state stability limit of a generator defines the LOF relay characteristics is

calculated based on the generator voltage, the impedances of the generator, step-up trans-

former and system’s Thevenin equivalent impedance. In traditional LOF protection, the

size of the steady state stability limit circle is a fixed value once the relay is commissioned

which is determined for a specific system impedance calculated from a base operating con-

dition. However, in a practical system, the size of the steady state stability limit boundary

changes with the system operating modes as the loading of the system changes or due to

disturbances. The traditional LOF relay setting for a relay located at Diablo1 generator

terminal is represented by the red circle as shown in Figure 4.12. This setting is calculated

considering a system Thevenin impedance for the normal operating scenario where all of the

power system elements in Figure 4.11 remain in-service.


Figure 4.12: Apparent Impedances Seen by Traditional Relay after LOF Conditions

As demonstrated in Section 4.3, system’s Thevenin reactance becomes larger when the

connection between the generator and the rest of the network is weaken due to outages of

adjacent transmission lines, as a result the steady state stability limit circle for the generator

gets bigger also. Figure 4.13 exhibits loss-of-field relay settings for two scenarios which

compares conventional LOF schemes with the proposed adaptive LOF protection. The red

circle here represents the traditional setting calculated based on the normal operating mode

and the blue circle corresponds to the adaptive relay setting which is dictated by the current

system condition where a contingency is created by tripping the 500 kV line between Diablo

and Gates. The apparent impedances seen by the relays during the generator’s loss-of-field

conditions are also compared in Figure 4.13 for these two operation modes. The impedance

trajectory is different during the contingency case (purple) than the normal condition(cyan).

The system reactance becomes larger for the contingency case, as a result the steady state

stability limit circle gets bigger for the adaptive relay condition. But the traditional method

still sets the protective device according to the smaller circle and does not identify the system

change which eventually results in false tripping of the generator. In this case, the impedance

locus enters the stability boundary 300 ms before the traditional could detect it. Hence the

generator trips due to instability sooner that its traditional LOF relay can even identify

loss-of-excitation scenario which is harmful to the security of system and the generator. In


addition, adaptive LOF scheme provides an supervisory boundary to the stability limit for

alarms which allows provision to take preventive measures as demonstrated in Figure 4.14.

Figure 4.13: Apparent Impedances Seen by Relay after LOF Conditions - Relay at Diablo1



Loss-of-field relay settings for conventional relays is again compared with the adaptive

LOF protection setting which determined based on the present system condition where both

of the 500 kV lines from Diablo to Midway are taken out-of-service, as seen in Figure 4.15.

The red circle represents the traditional setting calculated based on the normal operating

mode, similar to the previous example and the green circle corresponds to the adaptive relay

setting which is dictated by the contingency scenario. The system reactance becomes even

larger than previous example during line outage case due to the severity of the event, as a

result the steady state stability limit circle gets even bigger for the adaptive relay condition.

Again, the impedance locus is different, when the system’s operating condition changes due

to outage of both the lines between Diablo and Midway (purple trajectory). With traditional

LOF relay, the generator may lose synchronization well before it encroaches its stability limit

(which is not adjusted for system change) which may cause the generator to be tripped almost

700ms earlier than it is predicted.



4.4 Summary

A static impedance boundary criterion of steady state stability limit is widely used to identify

loss-of-field conditions in the conventional LOF protection. This boundary is truly dependent

on the system’s operating condition, specifically the local topology of the network. This static

boundary of steady-state stability is prone to mis-operation is it doesn’t have the capability

of adjustment based on the changes in the network. If an adaptive LOF approach is desired,

the system conditions can be identified on-line using wide area measurements provided by

PMU devices and adaptive relay settings can be realized. This improves the reliability and

the operating speed of the LOF protection, which is advantageous for the security of the

generator and the power system as a whole. The simulation results from the California

Study system demonstrate that the proposed ideas can improve the performance of these

protective relays.

Chapter 5

Impact of Generation Re-distribution

Immediately after Generation Loss

At any point in time, the total power output of all of the generators must balance with the

total system load including losses. This idea is clearly evident during steady-state conditions.

However, consider a scenario where some type of discrete change on the network such as a

loss of load, or (more specific to this chapter) a forced generator outage occurs abruptly. In

any of these scenarios, the balance of the network is disrupted instantaneously. However,

it follows that due to conservation of energy that the network must also instantaneously

compensate for the balance disruption by (in the case of a generator outage) increasing the

power out of the terminals of remaining generators and decreasing the power into loads

who’s value depends on system conditions such as frequency or current. The energy used

to instantaneously balance the network after a discrete disruption in the generation-load

equilibrium comes from the stored kinetic energy in the rotors of all of the generators that

are connected to the network. After a negative step change in generation in the network,

generators all across the network responds by increasing the power output at the terminals

by converting stored kinetic energy into electrical energy with the side effect of slowing

the rotation of the rotors thereby decreasing the system frequency. Following this reaction

generator control systems increases the mechanical input power to the rotor to bring the

system frequency back to nominal. The amount of compensation by each generator just

after a step change in the operating point is much different than the contributions once the

network has again reached a steady-state condition.

72

Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 73

The obvious question which follows this observation is how much kinetic energy in each

generator is converted to electrical energy and subsequently injected onto the network to

balance the load demand. Note that this is different than using several steady-state tech-

niques to find generator contributions after contingencies because these techniques dictate

that the system will have already reached steady-state. Power flows out of the terminals of

the generator directly after a discrete disruption in the power balance of the network is a

function of the condition of the network before the contingency (operating point & network

topology), the particular contingency that occurred (the network topology right after the

contingency). The control systems of generators do not have enough time to react for the

factors used in steady-state analysis to take effect.

A detailed dynamic analysis of the system is indeed the appropriate method here which

is obviously the multi-time-scale simulation of short- and long-term dynamics of system

parameters. Such simulations remain quite computationally demanding as well in terms of

computing time, data maintenance and output processing [34].

To ease the computational burden, approximations can be made using an inertial re-

dispatch to determine the re-distribution of power after a generation loss or load increase.

An inertial re-dispatch considers the current output of the generator when assigning changes

in generation output. While this approach is useful in its own right, in the context of

steady-state analysis. It does not serve the purpose of efficiently and simplistically evaluat-

ing the power re-distribution across the network on a time scale just slightly following the

change even before the system attains the next steady-state. Additionally, redistribution of

generation based on generator inertia may not consider the topology of the system.

In this chapter a non-computationally intensive method (an alternative to comprehensive

dynamic simulations) is discussed for finding the re-distribution of power in a network just

slightly after a contingency (before generators’ primary control systems can operate) and

to observe how the electrical distances from generators to the location of initial change or

contingency may affect this re-distribution. This study aims to investigate the effect of a

system change such as a generation loss just slightly after the change which uses a Kron

network reduction method to remove non-generator buses from the system and determine

relation of redistributed injections with electrical distance between the generator buses. To

visualize the role of the network impedances in the re-distribution of power in this scenario,

illustrative examples are presented which discusses the contributions of generators based on

their location in the system with respect to a contingency location.


To determine the generator injections just slightly after a contingency, dynamic simula-

tion is performed using GE’s PSLF on study systems. The goal is to demonstrate that the

redistribution of the MW output of the generation is affected by the electrical distance to

each of the remaining in-service generators which are responsible for loads being served in

the system. These new injections of the remaining generators cause changes in transmission

flows and may create threat to protection.

5.1 Generation Re-distribution with Respect to Loca-

tion

This section discusses the ideas surrounding what happens to the balance of power in a

network the instant after a discrete disruption to the power balance. The ideas herein are

discussed at a very high level for the presentation of the general concept. Later sections

present mathematical metrics for evaluating many of the ideas discussed in this section.

Consider the generic scenario of the network portrayed in Figure 5.1. There is a generator

in the Northern part (which is referred to as the northern generator G1 for this discussion)

which serves load in the northern part of the grid and is then connected via a long transmis-

sion corridor with the larger network in the south. In the southern network, there are four

generators (which is referred to as the north-western (G2) , north-eastern (G3), south-western

(G3), and south-eastern (G4) generators) which all serve loads in the southern network.

Figure 5.1: Abstract Power System


Using superposition of the flow of electrical power in a network it can be stated that

each generator actually serves each load in some amount. However, for the purposes of

this discussion, it is assumed that the distribution of each generators contribution to the

network favors those loads which are electrically closest to the source. The footprint of each

generator (the loads which are served heavily by the respective generator) are demonstrated

in Figure 5.2. Each generator serves loads which are electrically closest to it and some loads

are served by multiple generators when the electrical distance between the load and each of

the generators is close in value.

Figure 5.2: Distribution of Generation in an Abstract Power System

Such a perspective on the contributions of individual generators allows the proper vi-

sualization of the effect of a generator in a system. Consider the scenario shown in Figure

5.3 where the G5 is suddenly tripped out of service. The impact of the loss of the generator

can be thought of as depriving those loads which were served in majority by that particular

generator source. Thus it is left up to the remaining generators to supply this energy to

these loads.


Figure 5.3: Loss of Generator G4 in an Abstract Power System

It can be taken that the amount of power provided by each remaining generators for

each load left by the outage is inversely proportional to the electrical distance between

those generators and each of the loads which needs to be served. Generators which are

electrically closest to the power deficient loads provide a larger portion of that energy than

those generators which are farther from other loads. This is illustrated in Figure 5.4 by the

resizing of the circles which represent the footprints of each of the generators in the abstract

power system discussed in this section.

Figure 5.4: Re-distribution of Generation in an Abstract Power System, Just after theContingency

A parallel can be drawn between the generic system described in this section and a real


system such as WECC power system. Consider, generator at Diablo Canyon Nuclear Power

Station in California (Northwest of Los Angeles) and generation units in Moss Landing,

Morro Bay, Kern are nearby machines. If the outage of the generations at Diablo Canyon

is considered all the mentioned generations in the contingency vicinity mostly pick-up the

instantaneous changes in output power (Map included in Figure 5.15 ). Even though there

are large generation units located at southern part of Washington State such as generations

at Benton county, Tacoma etc, immediate impact of the generation loss at Diablo is trivial to

theese Northern machines due to their location i.e quite large electrical distance with respect

to the event location.

The discussion in this section concerning the abstract power system shown in Figures

5.1 - 5.4 can be summarized with the following two ideas.

1. A major portion of the output of each generator serves those loads which are electrically

closest to it in proportion to the electrical distance between the generator in question

and each of the loads in the network.

2. After the loss of a generator, those generators that are electrically closer to the loads

left un-served by the contingency provide more energy to the network than those which

are farther from the loads. The amount of MW contribution is inversely proportional

to the electrical distance between each of the generators and each of the loads.

The merging of these two ideas infers that after a discrete disruption in the power balance

of the network such as a generator outage, the generators which are electrically closer to the

contingency (the generator that tripped) contribute more to serve the energy deficit in the

network proportional to their electrical distance to the contingency. Despite this being an

obvious approximation, the reason that the above inference is significant is the electrical

distance between generators can be determined using knowledge of the network topology

and lines impedances. This is discussed in detail in the proceeding section.


5.2 Generator Location as a Function of Admittance

from an Event Location

As presented in the previous section, after a discrete change in the power balance of the

network, the system responds immediately depending on relative locations of sources and

demands. A generator which is close to the loads that were supported by the generator

lost due to the contingency feels the greatest impact. A metric for describing the electrical

distance between a generator and the outage location can be created using the impedance

or admittance between the generators. This process is demonstrated in this section using

the IEEE 39 bus system and the IEEE 118 bus system.

5.2.1 Network Reduction to Determine Admittance between

Generators

The bus-admittance matrix of a power network contains elements which are indicative of the

inter-connectivity of the network. A matrix element with zero value means that no direct

connection exists between two nodes in the system. However, the off-diagonal non-zero

elements represent the admittance (electrical distance) between two nodes in the network.

In order to determine the admittance between each of the generator nodes, the admittance

matrix must be reduced so that all off-diagonal elements contain some non-zero value which

represents a metric of electrical distance between generators nodes (despite the generator

nodes not sharing a direct connection).

Consider the network equations which can be formulated using the node-voltage method

for a power system[16] with m number of generator buses and n number of non-generator

buses. [Ig

In

]=

[Ygg Ygn

Yng Ynn

]∗

[Vg

Vn

](5.1)

Where Ig and In represent the complex current injections at the generator and non-generator

buses. Also, Vg and Vn represent the complex voltages at the generator/injection buses and

non-injection buses, respectively. The load buses can considered as non-injection as they are

represented as impedances and included in the admittance matrix so that these buses have

zero injections. The admittance matrix can reduced to only relate the buses with injections


i.e. the generator buses which is presented with Equation 5.1 ,

[Ig] = [Yreduced][Vn] (5.2)

Where

[Yreduced] = [Ygg] + [Ygn][Ynn]−1[Yng] (5.3)

[Yreduced] has the dimensions m x m, as the system has m number of generators. If the

loads are not considered to be constant impedances, the identity of the load buses must be

retained. For this study all loads are converted into constant impedances using the load bus

voltages and currents, also eliminated from the network equation. An elaborated description

of network reduction and derivation of this desired reduced matrix are provided in Chapter

2.

5.2.2 IEEE 39 Bus System Examples

This section presents a numerical example of the algorithm described in the previous section

implemented on the IEEE 39 Bus System. The IEEE 39 bus system has 10 generators and

will therefore yield a reduced matrix, [Yreduced] which has dimensions 10 x 10. Figure 5.5

shows the one-line diagram of the IEEE 39 bus system.


Figure 5.5: One Line Diagram of IEEE 39 Bus System

The equivalent system created using network reduction technique presents an exact re-

production of the self and transfer impedances of the reduced system as seen from its gener-

ator buses. So, each non-diagonal element represents the admittance between each generator

buses. The bus admittance matrix of the IEEE 39 bus system was reduced to only include

the generator nodes in the network and therefore all of the off-diagonal elements represents

the effective admittance between each of the generator nodes in the network. The numerical

value of [Yreduced] is shown below.


Yreduced =

32.517 2.250 2.542 1.842 0.813 1.949 1.070 11.432 3.123 7.248

2.250 26.119 10.221 1.429 0.630 1.512 0.830 1.269 0.763 5.569

2.542 10.221 27.393 2.022 0.892 2.140 1.174 1.467 0.955 4.401

1.842 1.429 2.022 33.631 16.209 4.745 2.604 1.309 1.374 1.060

0.813 0.630 0.892 16.209 24.759 2.093 1.149 0.578 0.606 0.468

1.949 1.512 2.140 4.745 2.093 31.311 13.867 1.386 1.454 1.122

1.070 0.830 1.174 2.604 1.149 13.867 23.464 0.761 0.798 0.616

11.432 1.269 1.467 1.309 0.578 1.386 0.761 26.251 3.975 3.647

3.123 0.763 0.955 1.374 0.606 1.454 0.798 3.975 14.596 1.154

7.248 5.569 4.401 1.060 0.468 1.122 0.616 3.647 1.154 24.243

In order to compare the power injections at generators and admittances between the

each of the generators and a particular generator which is abruptly taken out of service,

a dynamic simulation was conducted. Generator 3 located at bus 32 in the IEEE 39 bus

system was taken out of service 1 second into the dynamic simulation. The number which is

of importance here is the step change in the value of the power coming out of the terminals

of each of the other generators. The power output of each of the generators is shown in

Figure 5.6.

Figure 5.6: MW Outputs of Remaining Generators after Generator 3 at Bus 32 Outage


Figure 5.7 shows the change in MW output of the generator after the contingency at two

different times. The red shows the change in MW output at the instant of the contingency.

This is a measure of the amount of the generators’ stored kinetic energy which is converted

to electrical energy to instantaneously balance the discrete change in generation. The blue

shows the change in MW output of the generator from the pre-contingency state to the post-

contingency steady-state condition. The purpose of this graph is to demonstrate that the

change in power output directly after the contingency is not the same as the power output

once the system has reached steady state. In fact, the two are not even proportional to each

other.

Figure 5.7: Histogram of MW Outputs of Remaining Generator after Generator 3 at Bus 32Outage

Previously, it has been stated that the distribution of the pick-up of each of the generators

directly after the loss of another generator is dictated by the electrical distance between

each of the generators which remain in service and the generator which is lost. From the

[Yreduced] matrix calculated above, the distance between all of the generators left in service

and generator 3 (the machine which was lost) can be evaluated. To do this, the 3rd column

of the matrix is used because it corresponds to generator 3. Now, a column vector, each

of the elements of the column are associate by their row number with a particular bus and

therefore a particular generator. When those values are mapped to the corresponding change

in MW (just after the contingency) calculated using the dynamic simulation it can be seen


that the two sets are approximately linearly proportional to each other. Figure 5.8 shows

this as a plot of the admittances between each of the generators and generator 3 has been

superimposed on a plot of the transient change in MW of each of the respective generators.

Figure 5.8: MW Output at Remaining Generator after Generator 3 at Bus 32 Outage

The same procedure was repeated by removing generator 7 instead of generator 3. The

results of the dynamic simulation are shown below in Figure 5.9.



As in the previous example, Figure 5.10 shows the transient change in MW output of

the generator in red. In blue, the difference between the pre-contingency MW output and

the post-contingency steady-state output is shown. Again, there is a dramatic difference

between the two and they are not proportional to each other.

Figure 5.10: Histogram of MW Outputs of Remaining Generator after Generator 7 at Bus36 Outage


Similarly, column 7 of the [Yreduced] matrix was used to determine the admittance between

each of the generators and generator 7 (the machine which was lost) and a plot of this was

superimposed on a plot of the transient change in MW output of the generator. Again, the

results in Figure 5.11 show that the two sets are approximately linearly proportional to each

other.



In order to demonstrate that this observation is ubiquitous among different networks and not

just a special property of the IEEE 39 bus system the above procedure have been repeated

here on three different examples in the IEEE 118 bus system. The IEEE 118 bus system

contains 118 buses, 186 branches, 91 loads, and 54 generators. The generators at bus 10,

80, and 66 were the subject of these three examples, respectively. As with the previous

demonstration on the IEEE 39 bus system, the results show that admittance between each

of the generators and the generator which tripped are approximately linearly proportional

to the transient changes in MW just after the loss of the generator. Only the results are

shown in this section (Figures 5.12 - 5.14 ) to avoid unnecessary redundancy.


Figure 5.12: MW Output at Remaining Generator after Generator at Bus 10 Outage




5.2.4 WECC System Examples

Again, dynamic simulation is performed on WECC system by tripping two generator units

at Diablo, in order to illustrate the linear proportionality of the transient changes in MW

at generators with the admittances of each of these generators from a particular generator

which is abruptly tripped. Figure 5.15 shows the change in MW output of the generator

after this contingency at two different time scales. The red shows generators that has the

most change in MW output at the instant of the contingency. The blue shows the generators

that has biggest changes in MW output of the generator from the pre-contingency state to

the post-contingency steady-state condition. This graph again demonstrates that the major

changes in power output directly after the contingency occurs in the contingency area even

though the next steady-state power re-distribution might not be the same.


Figure 5.15: Generators Dibalo 1 & 2 Outage in WECC System

5.3 Linear Regression to Predict Power Injection

Changes at Generators after Contingency

In the previous section, it was established that immediately after a generation loss, the real

power generation pick-up by the remaining generators are approximately linearly propor-

tional to the admittances between those generators and the out-of-service generator. All the

nodes in the system except for the internal generator nodes are eliminated to obtain the

admittance matrix, [Yreduced], for the reduced network. The larger the admittance between

two generator buses, the smaller the impedance or electrical distance between them. There-

fore, the approximate linear proportionality of the admittances between generators and the

contingency with the transient change in MW directly after the contingency verifies the as-

sumptions in the discussion in Section 5.1. It then follows that with the knowledge of the

network impedances & topology, the size in MW of the contingency, and most importantly

the knowledge of the aforementioned linear relationship, an educated guess can be made of

the transient response of the of the generators which remain in the network. The question

then becomes how to quantify the linear relationship. This can be done using a simple linear

regression on the admittances and the transient changes in MW.


If the ith generator trips in a system with N generators and the admittance between each

of the remaining N-1 generator buses and the ith generator bus is represented by [y]i. The

vector [y]i contains the off-diagonal elements of ith column of the reduced admittance matrix

therefore it has (N-1) number of rows. The corresponding real power injection changes at

each of these generators immediately after the loss of ith generator is represented by the

vector [∆Pdyn]i. A simple linear regression illustrates the relation between the dependent

variables of [∆Pdyn]i and the independent variables of [y]i based on the regression equation,

[∆Pdyn]i = β0i + β1i ∗ [y]i + [r]i for ith= 1st, 2nd,...N th generator outage (5.4)

Where, β0i and β1i are the regression coefficients and ri is the residual matrix. The linear

regression can determine the values of the coefficients β0i and β1i which are the y-intercept

and the slope, respectively, of the line which represents the best linear approximation of the

linear relationship between the two data sets.


Consider an example in the IEEE 39 bus system with 10 generator buses (System data and

one line diagram for this study model is shown in Appendix A.1 ). If the generator 1 is

taken out-of-service and the admittances between each of the remaining nine generators and

generator 1 are shown in [y]1. Vector [y]1 has all nine of the off-diagonal elements in 1st

column of the reduced admittance matrix. The corresponding real power injection changes

at each of these nine generators immediately after the loss of generator 1 is shown here by

the vector [∆Pdyn]1. Both [y]1 and [∆Pdyn]1 are normalized by dividing each element of these

vectors by the sum of all elements of the respective vector. Now the following relationship

can be derived using regression as in Equation 5.6,

[∆Pdyn]1 = β01 + β11 ∗ [y]1 + [r]1


Where,

0.103

0.090

0.079

0.061

0.075

0.054

0.250

0.107

0.181

= β01 + β11 ∗

0.070

0.079

0.057

0.025

0.060

0.033

0.354

0.097

0.225

+ [r]1

Performing the regression yields β01=0.045 and β11=0.589 when generator 1 is out-of-service.

Figure 5.16 demonstrates the linear relationship between [y]1 and [∆Pdyn]1, after generator

1 at bus 30 is taken out-of-service, where both vectors are normalized.

Figure 5.16: Immediate Injection Changes at Generators Buses after Generator 1 Outage

Consider another example in the IEEE 39 bus system. In this case, generator 3 is

tripped and the admittances between each of the remaining nine generators and generator

3 are similarly represented by [y]3 which contains all nine of the off-diagonal elements in 3rd

column of the reduced admittance matrix. The respective real power injection changes at

each of these nine generators immediately after the loss of generator 3 is represented by the


vector [∆Pdyn]3. Similar to the previous case, both [y]3 and [∆Pdyn]3 are also normalized by

dividing each element of these vectors by the sum of all elements of the respective vector.

So, the following relationship can be derived using the regression equation in Equation 5.6,

[∆Pdyn]3 = β03 + β13 ∗ [y]3 + [r]3

In this case, β03=0.044 and β13=0.612 when generator 3 is out-of-service. The linear rela-

tionship between [y]3 and [∆Pdyn]3 are shown in Figure 5.17, after generator 3 at bus 32 is

taken out-of-service, where both vectors are again normalized.


Similarly, immediately after generator 10 is lost from the IEEE 39 bus system a linear

relationship can be seen between the admittances of the generators that remain in-service

from the contingency location and the change in real power injection at those generators. For

generator 10 outage case, the regression coefficients are, β010=0.033 and β110=0.798. Figure

5.18 demonstrates the linear relationship between [y]10 and [∆Pdyn]10 after the outage of

generator 10 at bus 39, where both vectors are normalized.



In Figure 5.19, each of the 10 generators contingency is considered except for the swing

generator case. All of the nine cases demonstrates a linear relationship between the ad-

mittances of the remaining generators in-service from the tripped generator and the change

in real power injection at those generators, immediately after each respective generator is

lost from the IEEE 39 bus system. In Figure 5.19 the actual admittances and MW values

are shown for better visualization where each color shows results from individual generator

outage case. Figure 5.20 demonstrates the linear relationship between the admittances and

change in power injections where both vectors are normalized after each of the generators is

taken out-of-service individually (except for the swing generator).


Figure 5.19: Immediate Injection Changes at Generators Buses after Each Generators Outage

Figure 5.20: Immediate Injection Changes at Generators Buses after Each Generators Outage

If the linear relationship in Equation 5.6 can somehow be determined without the knowl-

edge of the transient change in MW then contribution of each of the generators (transient

change in MW) can be predicted right after a generator loss. This seems evident and of no

value. However, an observant individual should notice that while it is true that the rela-


tionship between the admittances and transient MW changes is approximately linear for all

contingencies, the quantitative linear relationship (slope and y-intercept of the best fit line)

is different for different contingencies. Table 5.1 shows the slopes and y-intercepts alongside

the MW size of the contingency. It can be observed that the size of the contingency is pro-

portional to the slope of the line. This observation makes sense in that a larger contingency

requires more stored kinetic energy to be injected into the network.

Gen No. MW Slope y-intercept

1 205.9 0.589 0.0453 561.8 0.612 0.04410 824.2 0.798 0.033

Table 5.1: Slopes & y-Intercepts of Best Fitted Lines alongside Transient MW Changes

With this knowledge, only a sample of simulations should be done and the slopes and y-

intercepts of the best fits lines of those contingencies should be calculated as described in the

previous section. Then, another linear regression can be performed where the independent

variable is the MW size of the aforementioned sample of contingencies and the dependent

variable is the slope of the best fit lines of each of the respective contingencies. This process

should also be repeated using the y-intercepts as the dependent variable.

For example, from Table 5.1, when generator 1 supplying 205.9 MW is lost from the sys-

tem, β01=0.045 and β11=0.589. Again, for generator 3 contingency case which supplies 561.8

MW, β03=0.044 and β13=0.612. The regression coefficients are, β010=0.033 and β110=0.798

for generator 10 outage contingency case which generates 824.2 MW power. So, it can be

considered that β0 and β1 are two dependent variables where Ploss, the MW loss of the

contingency generator is the dependent variable. Two separate simple linear regression il-

lustrates the relation between the dependent variable β0 and the independent variable Ploss,

also the relation between the another dependent variable β1 and the independent variable

Ploss based on the following two regression equations.

[β0] = κ0 + κ1 ∗ [Ploss] + [r0] (5.5)


or, β01...

β0N

= κ0 + κ1 ∗

Ploss1

...

PlossN

+

r01

...

r0N

[β1] = γ0 + γ1 ∗ [Ploss] + [r1] (5.6)

or, β11...

β1N

= γ0 + γ1 ∗

Ploss1

...

PlossN

+

r11

...

r1N

These two sets of regression coefficients, κ0, κ1 and γ0, γ1 can be derived using data from three

individual generator outage contingency cases for IEEE 39 bus system using the previous

two equations and predict the effect of individual outage of the rest of the six generators in

the system. As the contingency cases are considered, reduced admittance matrix, Yreduced is

calculated using network reduction, which allows the admittance of each generator from the

contingency generator i, [y]i, to be known. Then respective changes in real power injection

at each of the nine generators immediately after the loss of a generator, vector [∆Pdyn]i,

is calculated from simulation. Using the [y]i - [∆Pdyn]i relation from Equation 5.6 three

sets of β0i, β1i are calculated considering outage of generator 1, 3 and 10. The real power

output data for all of the ten generators in IEEE 39 bus system are attached in Appendix A.1

which demonstrates that these three generators are chosen from different ranges of power

output. The two sets of regression coefficients, κ0, κ1 and γ0, γ1 are then calculated from

β0i, β1i for the mentioned generator outage contingency case. Vector Ploss, the MW loss of

the contingency generator is normalized by diving each elements of this vector by the total

generation of the system which is 5081.76 MW β01

β03

β010

= κ0 + κ1 ∗

Ploss1

Ploss3

Ploss10

+

r01

r03

r010

(5.7)

or numerically, 0.045

0.044

0.033

= κ0 + κ1 ∗

0.041

0.111

0.162

+

r01

r03

r010


β11

β13

β110

= γ0 + γ1 ∗

Ploss1

Ploss3

Ploss10

+

r11

r13

r110

(5.8)

or numerically, 0.589

0.612

0.798

= γ0 + γ1 ∗

0.041

0.111

0.162

+

r11

r13

r110

The regression coefficients, κ0=0.051, κ1=-0.097 and γ0=0.495, γ1=1.643 are calculated from

β0i, β1i for individual outage contingency case of generator 1, 3 and 10. Using κ0, κ1 and

γ0, γ1 coefficients, β0i and β1i are predicted for contingency case for generator 4, 5, 6, 7,

8, 9 (generator 2, swing generator is not included). The predicted values of β0i, β1i are

represented as β0i, β1i in the following equation.

β04

β05

β06

β07

β08

β09

= κ0 + κ1 ∗

Ploss4

Ploss5

Ploss6

Ploss7

Ploss8

Ploss9

(5.9)

Therefore,

β04

β05

β06

β07

β08

β09

= 0.051 + (−0.097) ∗

0.107

0.083

0.111

0.093

0.089

0.146

=

0.041

0.043

0.040

0.042

0.042

0.037

Again,

β14

β15

β16

β17

β18

β19

= γ0 + γ1 ∗

Ploss4

Ploss5

Ploss6

Ploss7

Ploss8

Ploss9

(5.10)


and therefore,

β14

β15

β16

β17

β18

β19

= 0.495 + 1.643 ∗

0.107

0.083

0.111

0.093

0.089

0.146

=

0.671

0.631

0.676

0.647

0.641

0.735

Where, predicted β0i, β1i values less (minus) some residuals r0i, r1i, the actual coefficients

β0i, β1i of the regression Equation 5.6, can be calculated.

β04

β05

β06

β07

β08

β09

=

β04

β05

β06

β07

β08

β09

−

r04

r05

r06

r07

r08

r09

and,

β14

β15

β16

β17

β18

β19

=

β14

β15

β16

β17

β18

β19

−

r14

r15

r16

r17

r18

r19

Here, β0i, β1i values are used in linear regression Equation 5.6 to predict the vector [∆Pdyn]i,

respective change in real power injections at each of the nine remaining generators in IEEE

39 bus system immediately after the loss of ith generator where i= 4, 5, 6, 7, 8 and 9. For

example, the linear regression equation to predict power injection changes at all generators

except generator 4, right after generator 4 is lost can be written as following,

[ ˆ∆Pdyn]4 = β04 + β14 ∗ [y]4


ˆ∆Pdyn at gen1

ˆ∆Pdyn at gen2

ˆ∆Pdyn at gen3

ˆ∆Pdyn at gen5

ˆ∆Pdyn at gen6

ˆ∆Pdyn at gen7

ˆ∆Pdyn at gen8

ˆ∆Pdyn at gen9

ˆ∆Pdyn at gen10

for gen4 outage

= 0.041 + 0.671 ∗

0.057

0.044

0.062

0.497

0.146

0.080

0.040

0.042

0.033

=

0.078

0.070

0.082

0.374

0.138

0.094

0.068

0.069

0.062

The Figure 5.21 demonstrates the actual and predicted change in injections at all in-service

generators, right after the loss of generator 4 of 543.5 MW. The magenta star represents the

MW value from the dynamic simulation (assumed actual value) and the blue star represents

the MW value predicted by the regression. Figures 5.22, 5.23, 5.24, 5.25 & 5.26 show

similar results for a contingency at generators 5 (419.9 MW), 6 (561.7 MW), 7 (471.8 MW),

8 (451.8 MW) & 9 (741.7 MW), respectively.

Figure 5.21: Actual and Predicted Changes in Injections at Generator Buses after Generator4 (543.5 MW) Outage









5.3.2 Accuracy of Regression Model

The coefficient of determination, R2, is a measure used in regression model analysis to assess

how well a model explains and predicts future outcomes. it is useful because it indicates the

level of the variance (fluctuation) of one variable that is predictable from the other variable.

It is a gauge that allows determination of how accurate predictions can be achieved from a

certain model/graph. The coefficient of determination is the ratio of the explained variation

to the total variation.

The coefficient of determination is such that 0 < R2 < 1, and denotes the strength of the

linear association between the outcomes and the values of the single regressor being used for

prediction (the dependent and the independent variables). The coefficient of determination

represents the percent of the data that is the closest to the line of best fit. It is a measure

of how well the regression line represents the data i.e. how well the linear regression acts as

a predictor of the independent variable. If the regression line passes exactly through every

point on the scatter plot, it would be able to explain all of the variation. The further the

line is away from the points, the less it is able to explain.

For this study, the linear regression equation acts as a predictor of actual ∆Pdyn for a


generator outage case which can be written as the following,

[ ˆ∆Pdyn] = β0 + β1 ∗ [y] (5.11)

The coefficient of determination for this regression model computes as,

R2 = 1− SSerrSStot

(5.12)

SStot represents total sum of squares, the deviations of the observations from their mean:

SStot =n∑k=1

(∆Pdynk − ¯∆Pdyn)2 (5.13)

Where k, n, ∆Pdynk,¯∆Pdyn represent sample observation data, the total number of sample,

kth observation and mean of observations. If we were to use ¯∆Pdyn to predict ∆Pdyn, then

SStot measures the variability of the ∆Pdyn around their predicted value. SSerr measures

the deviations of observations from their predicted values:

SSerr =n∑k=1

(∆Pdynk − ˆ∆Pdyn)2 (5.14)

Table 5.2 shows this calculation of coefficient of determinations of regression models to pre-

dict changes in power injection performed on one of the contingencies previously shown from

the IEEE 39 bus system. The admittance between each generator & the contingency and

Contingency Case MW Loss from Outage R2

Gen 4 at bus 33 Outage 543.55 0.99Gen 5 at bus 34 Outage 419.84 0.97Gen 6 at bus 35 Outage 561.86 0.94Gen 7 at bus 36 Outage 471.85 0.98Gen 8 at bus 37 Outage 451.84 0.45Gen 9 at bus 38 Outage 741.73 0.40

Table 5.2: Coefficient of Determinations of Regression Models to Predict Power InjectionChanges for IEEE 39 Bus Study

the transient MW change following the contingency is approximately a linear relationship.


This section has illustrated this linear relationship as a method to use a small sample set

of all of the possible generator contingencies to predict the response of the remainder of the

generators. The right-most column of Table 5.2 shows the coefficients of determination for

the generator contingencies where a prediction of real power output was attempted. The

majority of the coefficients are in the 90% range while there are two as low as 40%.

It indicates that almost 90% of the variability observed in sudden MW changes at gener-

ators can be explained by the admittances between each generator & the contingency. Thus,

the location of the remainder generators of the system contributes a lot of information how

power is re-distributed to them, immediately after a generation loss. It is further discussed

at the end of the next section.


IEEE 118 bus system is used as another sample study system to predict changes in real power

injection at generator buses after a single generation loss where linear relationship between

injection changes at generators and the admittances of these generators from the out-of-

service generator for some sample generator outage cases act as predictors. The original

IEEE 118 bus has 54 generators and only 19 out of them are injecting power to the system

during normal operating condition. For simplicity, statuses of all generators with zero power

injections are set to zero. As a result, this modified IEEE 118 bus system has 19 generators

in operation. System data and one line diagram for this study model is shown in Appendix

A.2.2.

Consider the example in the IEEE 118 bus system (modified) with 19 generator buses.

The network reduction is performed again to find admittance between each of these 19 gener-

ators. So [Yreduced] for this system is a 19 x 19 dimensional matrix. This reduced admittance

matrix determines the admittance of each generator from the contingency generator i, vector

[y]i. Generator contingency cases are considered individually and the respective changes in

real power injection at each of the nine generators immediately after the loss of a generator,

vector [∆Pdyn]i, is calculated from simulation.

For the generator 1 outage contingency case, the admittances between each of the re-

maining 18 generators and generator 1 are shown in [y]1. Vector [y]1 has all eighteen of the

off-diagonal elements in 1st column of the reduced admittance matrix. The corresponding


real power injection changes at each of these 18 generators immediately after the loss of

generator 1 is demonstrated here by the vector [∆Pdyn]1. Both [y]1 and [∆Pdyn]1 are normal-

ized by dividing each element of these vectors by the sum of all elements of the respective

vector as in previous section. Now the following relationship can be derived using the linear

regression Equation 5.6,

[∆Pdyn]1 = β01 + β11 ∗ [y]1 + [r]1

Where,

0.4123

0.1024

0.1652

0.1079

0.0179

0.0308

0.0101

0.0124

0.0184

0.0416

0.0281

0.0271

0.0163

0.0008

0.0027

0.0037

0.0019

0.0004

= β01 + β11 ∗

0.5117

0.0627

0.1786

0.1064

0.0103

0.0162

0.0026

0.0066

0.0129

0.0477

0.0173

0.0182

0.0076

0.0001

0.0003

0.0008

0.0003

0.00002

+ [r]1

β01=0.0061 and β11=0.908 when generator 1 at bus 10 is out-of-service. The Figure 5.27

demonstrates the linear relationship between [y]1 and [∆Pdyn]1, after generator 1 at bus 10

is taken out-of-service , where both vectors are normalized.


Figure 5.27: Immediate Injection Changes at Generator Buses after Generator 1 Outage

Similarly, individual outage contingency cases are considered for Generator 9 (at bus

59), 11 (at bus 65),& 16 (at bus 89) which demonstrates the approximate linear relationship

between power injections at all generators and their location in terms of admittance from

the tripped generator which are shown in Figure 5.28, 5.29 & 5.30.

Figure 5.28: Immediate Injection Changes at Generator Buses after generator 9 Outage




It is seen that β0 and β1 are two dependent variables of Ploss, which are dependent

on the MW loss of the contingency generator. Two separate linear regressions represent

the relation between the dependent variable β0 and the independent variable Ploss, also the

relation between the another dependent variable β1 and the independent variable Ploss based


on the following two regression equations.

[β0] = κ0 + κ1 ∗ [Ploss] + [r0] (5.15)

and,

[β1] = γ0 + γ1 ∗ [Ploss] + [r1] (5.16)

This two sets of regression coefficient, κ0, κ1 and γ0, γ1 are derived using data from 5

individual generator outage contingency cases (Table 5.3 ) for IEEE 118 bus system from

these equations. The effect of individual outage of the rest of the 14 generators in the

system are predicted using the predictor data. Using [y]i - [∆Pdyn]i relation from Equation

Contingency Case MW Loss from Outage

Gen 2 at bus 12 outage 85Gen 5 at bus 31 outage 7Gen 9 at bus 59 outage 155Gen 11 at bus 65 outage 391Gen 16 at bus 89 outage 607

Table 5.3: List of Contingency Cases Used for Prediction

5.6, 5 sets of β0i, β1i are calculated considering outage of generators listed in Table 5.3. The

real power output data for these predictor cases demonstrates that these five generators are

chosen from different ranges of power output. The two sets of regression coefficients, κ0, κ1

and γ0, γ1 are then calculated from β0i, β1i for the mentioned generators’ contingency cases.

Vector Ploss, the MW losses of the tripped generator are normalized by diving each elements

of this vector by the total generation of the system which is 4345.14 MW.β02

β05

β09

β011

β016

= κ0 + κ1 ∗

Ploss2

Ploss5

Ploss8

Ploss11

Ploss16

+

r02

r05

r09

r011

r016

(5.17)


β12

β15

β19

β111

β116

= γ0 + γ1 ∗

Ploss2

Ploss5

Ploss8

Ploss11

Ploss16

+

r12

r15

r19

r111

r116

(5.18)

The regression coefficients, κ0=0.017, κ1=-0.061 and γ0=0.57, γ1=2.29 are calculated from

β0i, β1i for individual outage contingency case of generators listed in Table 5.2. Using κ0,

κ1 and γ0, γ1 coefficients, β0i and β1i are predicted for contingency case for generator rest of

the 14 generators (generator 13, swing generator is not included). The predicted values of

β0i, β1i are represented as β0i, β1i in the following equations.

β01

β03

β04

β06

β07

β08

β010

β012

β014

β015

β017

β018

β019

= κ0 + κ1 ∗

Ploss1

Ploss3

Ploss4

Ploss6

Ploss7

Ploss8

Ploss10

Ploss12

Ploss14

Ploss15

Ploss17

Ploss18

Ploss19

(5.19)


β11

β13

β14

β16

β17

β18

β110

β112

β114

β115

β117

β118

β119

= γ0 + γ1 ∗

Ploss1

Ploss3

Ploss4

Ploss6

Ploss7

Ploss8

Ploss10

Ploss12

Ploss14

Ploss15

Ploss17

Ploss18

Ploss19

(5.20)

β0i, β1i values are used in linear regression Equation 5.6 to predict the vector [∆Pdyn]i,

respective change in real power injections at each of the remaining generators in IEEE 118

bus system right after the loss of ith generator where i= 1, 3, 4, 6, 7, 8, 10, 12, 14, 15, 17,

18 and 19. For example, the linear regression equation to predict power injection changes

at all generators except generator 13 (swing bus), after generator 1 is lost can be written as

following,

[ ˆ∆Pdyn]1 = β01 + β11 ∗ [y]1


ˆ∆Pdyn at gen1

ˆ∆Pdyn at gen2

ˆ∆Pdyn at gen3

ˆ∆Pdyn at gen5

ˆ∆Pdyn at gen6

ˆ∆Pdyn at gen7

ˆ∆Pdyn at gen8

ˆ∆Pdyn at gen9

ˆ∆Pdyn at gen10

ˆ∆Pdyn at gen11

ˆ∆Pdyn at gen12

ˆ∆Pdyn at gen14

ˆ∆Pdyn at gen15

ˆ∆Pdyn at gen16

ˆ∆Pdyn at gen17

ˆ∆Pdyn at gen18

ˆ∆Pdyn at gen19

hat∆Pdyn at gen1

for gen4 outage

= 0.0104 + 0.8064 ∗

0.51170

0.06268

0.17857

0.10637

0.01026

0.01616

0.00260

0.00660

0.01285

0.04771

0.01725

0.01823

0.00756

0.00009

0.00026

0.00081

0.00026

0.00002

=

0.4230

0.0609

0.1544

0.0962

0.0187

0.0234

0.0125

0.0157

0.0207

0.0489

0.0243

0.0251

0.0165

0.0104

0.0106

0.0110

0.0106

0.0104

Figure 5.31, 5.32, 5.33 & 5.34 demonstrate the actual and predicted change in injections at

all in-service generators, right after the loss of generator 1 (450 MW at bus 10), 7 (204 MW

at bus 49), 10 (160 MW at bus 61) & 14 (477 MW at bus 80), respectively.


Figure 5.31: Actual and Predicted Changes in Injections at Generator Buses after Generator1 (450 MW) at Bus 10 Outage





It has been said that the relationship between the admittance between each generator &

the contingency and the transient MW change following the contingency is approximately


linear. This section has demonstrated this as well as the ability to use this knowledge and a

small sample of all of the possible generator contingencies to predict the response of the rest

of the generators. The right-most column of Table 5.4 shows the coefficients of determination

for the generator contingencies where a prediction of real power output was attempted. The

majority of the coefficients are in the 90% range while there is one in the high 80% range

and one as low as 39%.

Contingency Case MW Loss from Outage R2

Gen 1 at bus 10 outage 450 0.99Gen 3 at bus 25 outage 220 0.97Gen 4 at bus 26 outage 314 0.98Gen 6 at bus 46 outage 19 0.92Gen 7 at bus 49 outage 204 0.95Gen 8 at bus 54 outage 48 0.93Gen 10 at bus 61 outage 160 0.96Gen 12 at bus 66 outage 392 0.87Gen 14 at bus 80 outage 477 0.93Gen 15 at bus 87 outage 4 0.39Gen 17 at bus 100 outage 252 0.94Gen 18 at bus 103 outage 40 0.90Gen 19 at bus 111 outage 36 0.94

Table 5.4: Coefficient of Determinations of Regression Models to Predict Power InjectionChanges for IEEE 118 Bus Study

It is believed that divergences from the linear model are due to ideas presented in Section

5.1 where an abstract power system was presented. Consider two scenarios, both where the

same generator in the network trips out abruptly causing a discrete change in the power

balance of the system. In the first scenario, imagine a load profile in which the majority

of the load served by the generator in question is electrically close. This means that the

electrical distance between this generator and every other generator in the network is a good

approximation of the electrical distance between each generator and the loads in need of

energy after the contingency. The second scenario places the loads served by the generator

in question farther away. Then, the electrical distance between each generator and the

generator in question is no longer a good approximation of the electrical distance between

each generator and the loads in need of energy after the contingency.


5.4 Potential Application in Protection Studies

Chapters 3 & 4 presented the summary of computationally intense protection studies per-

formed on the WECC and CA systems. One of the biggest challenges in performing studies

such as this is to try to identify the weak points in the system so that they can be scrutinized

and evaluated to ensure if appropriate protection scheme is implemented. Consider the po-

tential scenario where the loss of a generator in a large network. As discussed previously in

this chapter, the response of the system will be to convert stored kinetic energy from the

rotors of the machines into electrical energy which will be subsequently injected into the

network. There may exist a scenario in which the amount of transient MW change in the

output of a generator could be misinterpreted as a fault by a distance relay. It is desirable

to identify these scenarios in order to prevent mis-operation of a relay in the field.

One way to study this would be to take each generator out one by one and run a dynamic

simulation for each. For a sufficiently large system this could be time consuming. It makes

sense that most contingencies would not even come close to causing a relay mis-operation.

Therefore, an ideal scenario would be one in which the contingencies that could potentially

cause an inappropriate relay operation (depending on the relative size of the transient MW

output) could be quickly identified in a first pass. Once potential candidate scenarios are

identified, a comprehensive dynamic study can be performed for those scenarios to check for

violations.

This chapter has demonstrated that the transient MW output of the generators after a

loss of a generator can be reasonably predicted using network admittances, a small subset of

contingencies run as dynamic simulations, and knowledge of the linear relationship between

admittances and transient MW output. This procedure can be used as screening technique

for a protection study of a large network where it is impractical to perform all of the dynamic

simulations or to manually search for weakness in the grid. Shown in the next few sub-

sections are examples of the above hypothesis demonstrated on the IEEE 118 bus system

and the WECC system.

IEEE 118 Bus System Examples

As discussed earlier potential load encroachment scenarios for back-up protection relays are

evaluated in this section for generator outage contingencies in IEEE 118 bus system. Figure


5.35 demonstrates impedance trajectory (on R-X plane) seen by the Mho relay located at

bus 90 monitoring 138 kV line between bus 90 & 91. Generator supplying 607 MW at bus

89 is tripped which followed by outages of two adjacent 138 kV lines from bus 89 to 90

and 150% Load increase at bus 90. This condition does not create load encroachment for

the monitored line but the impedance trajectory of the relay approaches very close to the

supervisory boundary of the back-up protection within 4 seconds of the event occurrence.

Figure 5.35: Impedance Trajectory Seen by Relay at Line between Bus 90 and 91

Another example is shown here in Figure 5.36 which illustrates the impedance trajectory

seen by relay at bus 68 that monitors 345 kV line between bus 68 and 65. In this case a 392

MW generator is taken-of-service at bus 66 and another 391 MW generator at bus 65 trips,

a second later the previous outage which brings the impedance trajectory seen by this relay

close to the boundary of the back-up protection within 5 seconds of the first contingency.

This sudden and drastic movement of R-X point toward the protection boundary occurs as

a result of high flow in that line due to sudden MW injection changes of generators in the

area of contingency(such as generator at bus 49).


Figure 5.36: Impedance Trajectory Seen by Relay at Line between Bus 68 and 65

WECC System Examples

In this section, a back-up protection example is shown for 500 kV line from Hassayampa

to North Gila as seen in the map of southern WECC system in Figure 5.37. This line is

owned by Arizona Public Service (APS) and it is a segment of the South-West power link

(SWPL), a major transmission corridor that transports power in an east-west direction, from

generators in Arizona, through the service territory of Imperial Irrigation District (IID), into

the San Diego area. This is a major inter-tie for supplying loads in San Diego. The loss of

this 500 kV transmission line initiated widespread outage during the San Diego Blackout in

2011.

Figure 5.37: Generators at SONGS 1 & 2 in WECC System [23]

Figure 5.38 illustrates impedance presented to the distance relay at Hassayampa to

North Gila when two units (2350 MW generators) of San Onofre Nuclear Generating Station

(SONGS) in southern California trip and cause sudden increase of tie flow in the 500 kV


SWPL. Such heavy loading causes the impedance trajectory of distance relay to move away

from the normal load area and approach close to relay characteristic.

Figure 5.38: Impedance Trajectory Seen by Relay at Line between Hassayampa to NorthGila in WECC System

5.5 Summary

This chapter presents the concept of an approximately linear relationship between the elec-

trical distances between generator nodes in a network and the transient changes in MW

output of each respective generator directly after the loss of a generator. The approxima-

tion is due to the fact that it is not exactly the electrical distance between the generator

nodes but rather the electrical distance between the loads that are served in majority by the

generator lost during the contingency. When those loads are electrically farther from the

generator, then the linear approximation will not be as good. These ideas are demonstrated

on the IEEE 39 bus system as well as the IEEE 118 bus system yielding similar results which

indicates that the linear relationship is not a special property of one network but rather an

idea that can be applied to any network. Additionally, the efficacy of the linear regression is

evaluated by calculating the coefficients of determination for each contingencies. A discus-

sion of the application of such concept is presented for power system protection and a few

examples are shown from the IEEE 118 bus system and the WECC system.

Chapter 6

Conclusion & Future Work

Some of the recent blackouts in power system have shown that losing important system ele-

ments like critical transmission lines during stressed system conditions due to over-reaching

or inappropriate protection schemes can be detrimental to the system integrity and can cause

potentially cascading failures. When the system is operating in a stressed condition, it is

crucial to operate in a secure and reliable manner and retain all functioning and contributing

elements in the network (especially key generation units and transmission corridors) without

jeopardizing the overall security of the network. Every power system contains many pro-

tective relays identify abnormal system conditions and disturbances and initiate corrective

actions in order to recover the normal operating state of the system. Most of the protective

schemes in the systems are set to be very dependable so that system faults are always de-

tected and cleared by some relay. As a result, protection zones of some relays extend beyond

its necessary protective zone providing back-ups to a remote element and may eliminate

system elements unnecessarily. In other cases, relays are designed to operate on a specific

system condition fail to evolve with the system changes and result in tripping of important

network components inappropriately. The goal of this dissertation is to demonstrate avenues

to improve such power system protection schemes utilizing WAMS technology.

6.1 Summary

Chapter 3 discussed incorporation of a supervisory boundary the back-up distance protection

scheme to alert system stress and avoid possible false tripping of zone-3 due to violations of

118

Chapter 6. Conclusion & Future Work 119

load limits in transmission lines referred as load encroachment. WECC full loop model and

California study system is used as a bench-mark for this protection scheme. Line outage

distribution factor sensitivity analysis is utilized to determine the initial impact of N-1 line

outage contingencies in the sample systems. An inertial dispatch algorithm for generators

is developed to re-distribute power after generator losses to identify possible transmission

congestion and over-loads. Contingency analyses of multiple critical elements are performed

to obtain results that demonstrate the utilization of supervisory control to aid back-up zone

protection schemes. The research shows that the inter-ties between utilities in WECC are

prime locations of possible load encroachment.

The steady state stability limit of a generator and its significance during reduced field

excitation scenarios is explained in Chapter 4. The insufficient field excitation of a generator

is referred as loss-of-field condition which can be identified with impedance type relay. The

critical LOF conditions of the generator characteristics lie in the fourth quadrant of P-

Q of the generator capability curve that is represented with R-X impedance plane of the

monitoring LOF relay. The purpose of the LOF protection is to provide safety against the

generators steady-state limit which is a function of generator voltage, impedances of the

machine and step-up-transformer and most importantly the system’s Thevenin equivalent

impedance. But the system impedance is a variable quantity that changes with the system,

as seen from WECC simulation results. When the power system becomes weaker due to line

outages the system’s impedance increases and causes the generator load limit to drop; as a

result generator becomes susceptible to tripping. Hence an adaptive LOF protection scheme

is suggested to adjust the relay setting with prevailing system conditions and also provides

additional security with a regulatory margin to allow preventive measures by creating alarms.

In Chapter 5, a screening technique is introduced which aims to predict possible power

contribution of the generators remaining in the system after an immediate outage of a gener-

ator. An approximate linear relationship is derived between the changes in generators’ power

injections and their electrical distance from the event location i.e. the nearby a generator

to a tripped generator in terms of admittance between them, the more power is injected by

that generator to satisfy system demands and alleviate the MW mismatch in the system

that is imposed by the generator loss. Kron network reduction is used to reduce the system

admittance matrix to determine the direct admittance between each of the generators in the

system. This method of generator outage contingency analysis method helps determine pos-

sible overloads in transmission lines that are adjacent to a generator that is expected to inject


large amount of power right after a generator outage. This procedure can be incorporated

with system remedial action schemes (a corrective method for N-2 or worse contingencies)

to flag areas which can potentially suffer heavy loading when the system is operating under

stressed conditions to avoid inappropriate tripping of key system elements.

6.2 Future Work

As technologies such as phasor measurement units, smart-grid communication infrastruc-

tures, sub-station automation system proliferate, more applications of the wide-area mea-

surement systems are worthy of further investigation in the areas addressed in this disser-

tation. This final section outlines some of the potential avenues for further research in the

area of wide-area protection and automation.

• The analysis of protection improvement techniques applied in WECC system can be

continued to study Eastern Interconnections, ERCOT and Quebec systems as more

PMUs are being employed in these systems to enable wide area control. The 2008

study model demonstrates sufficient capacity of transmission corridors to deliver power

demand. But the rapid growth of system demands in the CA region in the last few years

could result in less capacity in the WECC lines and susceptible to load encroachment.

Further inquiry of back-up protection scheme can be performed on a new system model

of WECC.

• Development of method for on-line computation of system impedance accurately will

allow adjustment of LOF relay settings to adapt with prevailing power system con-

ditions. As discussed in this dissertation, the LOF relay settings can be identified

from off-line studies and the steady state stability can grow or shrink to adapt with

system changes such as variation in topology, change in loading/generation. However,

this technique can be utilized to identify relay settings for LOF conditions which is a

function of system’s Thevenin equivalent impedance by performing short-circuit anal-

ysis to identify the current system impedance at specific time intervals based on the

updated snapshots of the system extracted from the EMS (Energy Management Sys-

tem)/ SCADA system. Then the derived LOF settings will be even more precise and

appropriate for an evolving power system.


• This dissertation assumed continuous data availability for on-line analysis of protec-

tion schemes from all PMU units installed in the field. The impact of loss of wide

area measurements required for supervision of back-up protection and LOF protection

schemes can be investigated. Any default settings or alternate solutions to adjust to

the prevalent system criteria should any supporting devices such as PMU elements,

communication network parameters fail or mis-operate.

• The generation re-distribution technique post generator outage, described in Chapter

5, can be applied to existing protection schemes which will provide wide area knowledge

of impending generation imbalance in the system. In the case of a generator trip, the

trip signal can be made available as a flag to relays who’s zones of protection may

be violated due to over-loading of transmission lines by the immediate redistribution

of power amongst the remaining generators. The relays may then subsequently block

their trip signal or obtain information from other relays to determine if what is seen is

actually a fault, or a transient redistribution of power amongst the remaining generators

that resulted in load encroachment scenarios and being interpreted as a system fault.

• A study of communication structures and requirements to deploy WAMS for adaptive

relaying can be advised. As efficient information gathering from various devices in

system and prompt distribution of these data are essential for WAMS technology,

appropriate investigation is required to identify how the communication conventions

behave and comply with power system protection protocols. This calls for analysis of

various system architecture to determine whether to provide centralized or distributed

control to avoid latency and allow reliable & optimal operation of system protection

schemes.

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Appendix A

Sample Study Systems

A.1 IEEE 39 Bus System Data

Figure A.1: One Line Diagram of IEEE 39 Bus System with 10 Generators

126

Appendix 127

Bus Data

Bus Bus Pd Qd Vm Va Vmax Vmin

No. Type (MW) (MVAR) (pu) (degrees) (pu) (pu)

1 1 0 0 1 0 1.06 0.94

2 1 0 0 1 0 1.06 0.94

3 1 322 2.4 1.0341 -9.73 1.06 0.94

4 1 500 184 1.0116 -10.53 1.06 0.94

5 1 0 0 1.0165 -9.38 1.06 0.94

6 1 0 0 1.0172 -8.68 1.06 0.94

7 1 233.8 84 1.0067 -10.84 1.06 0.94

8 1 1022 276.6 1.0057 -11.34 1.06 0.94

9 1 0 0 1.0322 -11.15 1.06 0.94

10 1 0 0 1.0235 -6.31 1.06 0.94

11 1 0 0 1.0201 -7.12 1.06 0.94

12 1 8.5 88 1.0072 -7.14 1.06 0.94

13 1 0 0 1.0207 -7.02 1.06 0.94

14 1 0 0 1.0181 -8.66 1.06 0.94

15 1 320 153 1.0194 -9.06 1.06 0.94

16 1 329.4 32.3 1.0346 -7.66 1.06 0.94

17 1 0 0 1.0365 -8.65 1.06 0.94

18 1 158 30 1.0343 -9.49 1.06 0.94

19 1 0 0 1.0509 -3.04 1.06 0.94

20 1 680 103 0.9914 -4.45 1.06 0.94

21 1 274 115 1.0337 -5.26 1.06 0.94

22 1 0 0 1.0509 -0.82 1.06 0.94

23 1 247.5 84.6 1.0459 -1.02 1.06 0.94

24 1 308.6 -92.2 1.0399 -7.54 1.06 0.94

25 1 824 147.2 1.0587 -5.51 1.06 0.94

26 1 139 17 1.0536 -6.77 1.06 0.94

27 1 281 75.5 1.0399 -8.78 1.06 0.94

28 1 206 27.6 1.0509 -3.27 1.06 0.94

29 1 283.5 26.9 1.0505 -0.51 1.06 0.94

Continued on next page

Appendix 128

Table continued from previous page

Bus Bus Pd Qd Vm Va Vmax Vmin

No. Type (MW) (MVAR) (pu) (degrees) (pu) (pu)

30 2 200 0 1.0475 0 1.06 0.94

31 3 9.2 4.6 0.982 0 1.06 0.94

32 2 0 0 0.9831 1.63 1.06 0.94

33 2 0 0 0.9972 2.18 1.06 0.94

34 2 0 0 1.0123 0.74 1.06 0.94

35 2 0 0 1.0493 4.14 1.06 0.94

36 2 0 0 1.0635 6.83 1.06 0.94

37 2 0 0 1.0278 1.27 1.06 0.94

38 2 0 0 1.0265 6.55 1.06 0.94

39 2 100 0 1.03 -10.96 1.06 0.94

Table A.1: IEEE 39 Bus System - Bus Data

Branch Data

Branch From To R R B

No. Bus Bus (pu) (pu) (pu)

c 1 2 0.0035 0.0411 0.6987

2 1 39 0.001 0.025 0.75

3 2 3 0.0013 0.0151 0.2572

4 2 25 0.007 0.0086 0.146

5 3 4 0.0013 0.0213 0.2214

6 3 18 0.0011 0.0133 0.2138

7 4 5 0.0008 0.0128 0.1342

8 4 14 0.0008 0.0129 0.1382

9 5 6 0.0002 0.0026 0.0434

10 5 8 0.0008 0.0112 0.1476


Appendix 129




11 6 7 0.0006 0.0092 0.113

12 6 11 0.0007 0.0082 0.1389

13 7 8 0.0004 0.0046 0.078

14 8 9 0.0023 0.0363 0.3804

15 9 39 0.001 0.025 1.2

16 10 11 0.0004 0.0043 0.0729

17 10 13 0.0004 0.0043 0.0729

18 13 14 0.0009 0.0101 0.1723

19 14 15 0.0018 0.0217 0.366

20 15 16 0.0009 0.0094 0.171

21 16 17 0.0007 0.0089 0.1342

22 16 19 0.0016 0.0195 0.304

23 16 21 0.0008 0.0135 0.2548

24 16 24 0.0003 0.0059 0.068

25 17 18 0.0007 0.0082 0.1319

26 17 27 0.0013 0.0173 0.3216

27 21 22 0.0008 0.014 0.2565

28 22 23 0.0006 0.0096 0.1846

29 23 24 0.0022 0.035 0.361

30 25 26 0.0032 0.0323 0.513

31 26 27 0.0014 0.0147 0.2396

32 26 28 0.0043 0.0474 0.7802

33 26 29 0.0057 0.0625 1.029

34 28 29 0.0014 0.0151 0.249

35 12 11 0.0016 0.0435 0

36 12 13 0.0016 0.0435 0

37 6 31 0 0.025 0

38 10 32 0 0.02 0

39 19 33 0.0007 0.0142 0


Appendix 130




40 20 34 0.0009 0.018 0

41 22 35 0 0.0143 0

42 23 36 0.0005 0.0272 0

43 25 37 0.0006 0.0232 0

44 2 30 0 0.0181 0

45 29 38 0.0008 0.0156 0

46 19 20 0.0007 0.0138 0

Table A.2: IEEE 39 Bus System - Branch Data

Generator Data

Generator Pg Qg Qmax Qmin Vg mBase Pmax Pmin

Bus (MW) (MVAR) (MVAR) (MVAR) (pu) (MVA) (MW) (MW)

30 0 103.3 9999 -9999 1.0475 100 350 031 572.9 170.3 9999 -9999 0.982 100 1145.55 032 900 175.9 9999 -9999 0.9831 100 750 033 632 103.3 9999 -9999 0.9972 100 732 034 508 164.4 9999 -9999 1.0123 100 608 035 650 204.8 9999 -9999 1.0493 100 750 036 560 96.9 9999 -9999 1.0635 100 660 037 540 -4.4 9999 -9999 1.0278 100 640 038 830 19.4 9999 -9999 1.0265 100 930 039 1000 68.5 9999 -9999 1.03 100 1100 0

Table A.3: IEEE 39 Bus System - Generator Data

Appendix 131

A.2 IEEE 118 Bus System Data

A.2.1 IEEE 118 Bus System Data with 54 Generators

Figure A.2: One Line Diagram of IEEE 118 Bus System with 54 Generators

Appendix 132

A.2.2 IEEE 118 Bus System with 19 Generators

Figure A.3: One Line Diagram of IEEE 118 Bus System with 19 Generator

Appendix 133

Bus Data

Bus Bus Pd Qd Vm Va Base Vmax Vmin

No. Type (MW) (MVAR) (pu) (degrees) KV (pu) (pu)

1 1 51 27 0.955 10.67 138 1.06 0.94

2 1 20 9 0.971 11.22 138 1.06 0.94

3 1 39 10 0.968 11.56 138 1.06 0.94

4 1 39 12 0.998 15.28 138 1.06 0.94

5 1 0 0 1.002 15.73 138 1.06 0.94

6 1 52 22 0.99 13 138 1.06 0.94

7 1 19 2 0.989 12.56 138 1.06 0.94

8 1 28 0 1.015 20.77 345 1.06 0.94

9 1 0 0 1.043 28.02 345 1.06 0.94

10 2 0 0 1.05 35.61 345 1.06 0.94

11 1 70 23 0.985 12.72 138 1.06 0.94

12 2 47 10 0.99 12.2 138 1.06 0.94

13 1 34 16 0.968 11.35 138 1.06 0.94

14 1 14 1 0.984 11.5 138 1.06 0.94

15 1 90 30 0.97 11.23 138 1.06 0.94

16 1 25 10 0.984 11.91 138 1.06 0.94

17 1 11 3 0.995 13.74 138 1.06 0.94

18 1 60 34 0.973 11.53 138 1.06 0.94

19 1 45 25 0.963 11.05 138 1.06 0.94

20 1 18 3 0.958 11.93 138 1.06 0.94

21 1 14 8 0.959 13.52 138 1.06 0.94

22 1 10 5 0.97 16.08 138 1.06 0.94

23 1 7 3 1 21 138 1.06 0.94

24 1 13 0 0.992 20.89 138 1.06 0.94

25 2 0 0 1.05 27.93 138 1.06 0.94

26 2 0 0 1.015 29.71 345 1.06 0.94

27 1 71 13 0.968 15.35 138 1.06 0.94

28 1 17 7 0.962 13.62 138 1.06 0.94

29 1 24 4 0.963 12.63 138 1.06 0.94


Appendix 134




30 1 0 0 0.968 18.79 345 1.06 0.94

31 2 43 27 0.967 12.75 138 1.06 0.94

32 1 59 23 0.964 14.8 138 1.06 0.94

33 1 23 9 0.972 10.63 138 1.06 0.94

34 1 59 26 0.986 11.3 138 1.06 0.94

35 1 33 9 0.981 10.87 138 1.06 0.94

36 1 31 17 0.98 10.87 138 1.06 0.94

37 1 0 0 0.992 11.77 138 1.06 0.94

38 1 0 0 0.962 16.91 345 1.06 0.94

39 1 27 11 0.97 8.41 138 1.06 0.94

40 1 66 23 0.97 7.35 138 1.06 0.94

41 1 37 10 0.967 6.92 138 1.06 0.94

42 1 96 23 0.985 8.53 138 1.06 0.94

43 1 18 7 0.978 11.28 138 1.06 0.94

44 1 16 8 0.985 13.82 138 1.06 0.94

45 1 53 22 0.987 15.67 138 1.06 0.94

46 2 28 10 1.005 18.49 138 1.06 0.94

47 1 34 0 1.017 20.73 138 1.06 0.94

48 1 20 11 1.021 19.93 138 1.06 0.94

49 2 87 30 1.025 20.94 138 1.06 0.94

50 1 17 4 1.001 18.9 138 1.06 0.94

51 1 17 8 0.967 16.28 138 1.06 0.94

52 1 18 5 0.957 15.32 138 1.06 0.94

53 1 23 11 0.946 14.35 138 1.06 0.94

54 2 113 32 0.955 15.26 138 1.06 0.94

55 1 63 22 0.952 14.97 138 1.06 0.94

56 1 84 18 0.954 15.16 138 1.06 0.94

57 1 12 3 0.971 16.36 138 1.06 0.94

58 1 12 3 0.959 15.51 138 1.06 0.94


Appendix 135




59 2 277 113 0.985 19.37 138 1.06 0.94

60 1 78 3 0.993 23.15 138 1.06 0.94

61 2 0 0 0.995 24.04 138 1.06 0.94

62 1 77 14 0.998 23.43 138 1.06 0.94

63 1 0 0 0.969 22.75 345 1.06 0.94

64 1 0 0 0.984 24.52 345 1.06 0.94

65 2 0 0 1.005 27.65 345 1.06 0.94

66 2 39 18 1.05 27.48 138 1.06 0.94

67 1 28 7 1.02 24.84 138 1.06 0.94

68 1 0 0 1.003 27.55 345 1.06 0.94

69 3 0 0 1.035 30 138 1.06 0.94

70 1 66 20 0.984 22.58 138 1.06 0.94

71 1 0 0 0.987 22.15 138 1.06 0.94

72 1 12 0 0.98 20.98 138 1.06 0.94

73 1 6 0 0.991 21.94 138 1.06 0.94

74 1 68 27 0.958 21.64 138 1.06 0.94

75 1 47 11 0.967 22.91 138 1.06 0.94

76 1 68 36 0.943 21.77 138 1.06 0.94

77 1 61 28 1.006 26.72 138 1.06 0.94

78 1 71 26 1.003 26.42 138 1.06 0.94

79 1 39 32 1.009 26.72 138 1.06 0.94

80 2 130 26 1.04 28.96 138 1.06 0.94

81 1 0 0 0.997 28.1 345 1.06 0.94

82 1 54 27 0.989 27.24 138 1.06 0.94

83 1 20 10 0.985 28.42 138 1.06 0.94

84 1 11 7 0.98 30.95 138 1.06 0.94

85 1 24 15 0.985 32.51 138 1.06 0.94

86 1 21 10 0.987 31.14 138 1.06 0.94

87 2 0 0 1.015 31.4 161 1.06 0.94


Appendix 136




88 1 48 10 0.987 35.64 138 1.06 0.94

89 2 0 0 1.005 39.69 138 1.06 0.94

90 1 163 42 0.985 33.29 138 1.06 0.94

91 1 10 0 0.98 33.31 138 1.06 0.94

92 1 65 10 0.993 33.8 138 1.06 0.94

93 1 12 7 0.987 30.79 138 1.06 0.94

94 1 30 16 0.991 28.64 138 1.06 0.94

95 1 42 31 0.981 27.67 138 1.06 0.94

96 1 38 15 0.993 27.51 138 1.06 0.94

97 1 15 9 1.011 27.88 138 1.06 0.94

98 1 34 8 1.024 27.4 138 1.06 0.94

99 1 42 0 1.01 27.04 138 1.06 0.94

100 2 37 18 1.017 28.03 138 1.06 0.94

101 1 22 15 0.993 29.61 138 1.06 0.94

102 1 5 3 0.991 32.3 138 1.06 0.94

103 2 23 16 1.001 24.44 138 1.06 0.94

104 1 38 25 0.971 21.69 138 1.06 0.94

105 1 31 26 0.965 20.57 138 1.06 0.94

106 1 43 16 0.962 20.32 138 1.06 0.94

107 1 50 12 0.952 17.53 138 1.06 0.94

108 1 2 1 0.967 19.38 138 1.06 0.94

109 1 8 3 0.967 18.93 138 1.06 0.94

110 1 39 30 0.973 18.09 138 1.06 0.94

111 2 0 0 0.98 19.74 138 1.06 0.94

112 1 68 13 0.975 14.99 138 1.06 0.94

113 1 6 0 0.993 13.74 138 1.06 0.94

114 1 8 3 0.96 14.46 138 1.06 0.94

115 1 22 7 0.96 14.46 138 1.06 0.94

116 1 184 0 1.005 27.12 138 1.06 0.94


Appendix 137




117 1 20 8 0.974 10.67 138 1.06 0.94

118 1 33 15 0.949 21.92 138 1.06 0.94

Table A.4: IEEE 118 Bus System - Original Bus Data

Additional Bus Data



119 1 0 0 0.966 10.98 138 1.06 0.94

120 1 0 0 1.02 15.58 138 1.06 0.94

121 1 0 0 1.03 13.29 138 1.06 0.94

122 1 0 0 1.03 21.06 138 1.06 0.94

123 1 0 0 1.0605 35.88 138 1.06 0.94

124 1 0 0 1.01 12.49 138 1.06 0.94

125 1 0 0 0.99 11.48 138 1.06 0.94

126 1 0 0 1 11.79 138 1.06 0.94

127 1 0 0 0.98 11.3 138 1.06 0.94

128 1 0 0 1 21.11 138 1.06 0.94

129 1 0 0 1.06 28.18 138 1.06 0.94

130 1 0 0 1.03 29.96 138 1.06 0.94

131 1 0 0 0.99 15.61 138 1.06 0.94

132 1 0 0 0.99 13.01 138 1.06 0.94

133 1 0 0 0.98 15.06 138 1.06 0.94

134 1 0 0 1.01 11.51 138 1.06 0.94

135 1 0 0 1 11.08 138 1.06 0.94

136 1 0 0 0.99 7.52 138 1.06 0.94


Appendix 138




137 1 0 0 1.01 8.67 138 1.06 0.94

138 1 0 0 1.01 18.58 138 1.06 0.94

139 1 0 0 1.04 21.03 138 1.06 0.94

140 1 0 0 0.97 15.35 138 1.06 0.94

141 1 0 0 0.965 15.06 138 1.06 0.94

142 1 0 0 0.97 15.24 138 1.06 0.94

143 1 0 0 1.01 19.45 138 1.06 0.94

144 1 0 0 1.01 24.12 138 1.06 0.94

145 1 0 0 1 23.51 138 1.06 0.94

146 1 0 0 1.01 27.72 138 1.06 0.94

147 1 0 0 1.01 27.56 138 1.06 0.94

148 1 0 0 1.04 29.99 138 1.06 0.94

149 1 0 0 0.995 22.62 138 1.06 0.94

150 1 0 0 0.99 21.11 138 1.06 0.94

151 1 0 0 1.01 21.99 138 1.06 0.94

152 1 0 0 0.968 21.67 138 1.06 0.94

153 1 0 0 0.963 21.8 138 1.06 0.94

154 1 0 0 1.015 26.75 138 1.06 0.94

155 1 0 0 1.05 28.99 138 1.06 0.94

156 1 0 0 0.996 32.55 138 1.06 0.94

157 1 0 0 1.025 31.44 138 1.06 0.94

158 1 0 0 1.01 39.73 138 1.06 0.94

159 1 0 0 0.996 33.33 138 1.06 0.94

160 1 0 0 0.98 33.35 138 1.06 0.94

161 1 0 0 1 33.85 138 1.06 0.94

162 1 0 0 1.02 27.08 138 1.06 0.94

163 1 0 0 1.027 28.07 138 1.06 0.94

164 1 0 0 1.01 24.48 138 1.06 0.94

165 1 0 0 0.982 21.74 138 1.06 0.94


Appendix 139




166 1 0 0 0.976 20.62 138 1.06 0.94

167 1 0 0 0.962 17.58 138 1.06 0.94

168 1 0 0 0.983 18.14 138 1.06 0.94

169 1 0 0 0.99 19.78 138 1.06 0.94

170 1 0 0 0.985 15.04 138 1.06 0.94

171 1 0 0 1.03 14 138 1.06 0.94

172 1 0 0 1.015 27.16 138 1.06 0.94

Table A.5: IEEE 118 Bus System - Additional Bus Data

Branch Data



1 119 2 0.0303 0.0999 0.0254

2 119 3 0.0129 0.0424 0.01082

3 120 5 0.00176 0.00798 0.0021

4 3 5 0.0241 0.108 0.0284

5 5 121 0.0119 0.054 0.01426

6 121 7 0.00459 0.0208 0.0055

7 122 9 0.00244 0.0305 1.162

8 122 5 0 0.0267 0

9 9 123 0.00258 0.0322 1.23

10 4 11 0.0209 0.0688 0.01748

11 5 11 0.0203 0.0682 0.01738

12 11 124 0.00595 0.0196 0.00502

13 2 124 0.0187 0.0616 0.01572


Appendix 140




14 3 124 0.0484 0.16 0.0406

15 7 124 0.00862 0.034 0.00874

16 11 13 0.02225 0.0731 0.01876

17 124 14 0.0215 0.0707 0.01816

18 13 125 0.0744 0.2444 0.06268

19 14 125 0.0595 0.195 0.0502

20 124 16 0.0212 0.0834 0.0214

21 125 17 0.0132 0.0437 0.0444

22 16 17 0.0454 0.1801 0.0466

23 17 126 0.0123 0.0505 0.01298

24 126 127 0.01119 0.0493 0.01142

25 127 20 0.0252 0.117 0.0298

26 125 127 0.012 0.0394 0.0101

27 20 21 0.0183 0.0849 0.0216

28 21 22 0.0209 0.097 0.0246

29 22 23 0.0342 0.159 0.0404

30 23 128 0.0135 0.0492 0.0498

31 23 129 0.0156 0.08 0.0864

32 130 129 0 0.0382 0

33 129 131 0.0318 0.163 0.1764

34 131 28 0.01913 0.0855 0.0216

35 28 29 0.0237 0.0943 0.0238

36 30 17 0 0.0388 0

37 122 30 0.00431 0.0504 0.514

38 130 30 0.00799 0.086 0.908

39 17 132 0.0474 0.1563 0.0399

40 29 132 0.0108 0.0331 0.0083

41 23 133 0.0317 0.1153 0.1173

42 132 133 0.0298 0.0985 0.0251


Appendix 141




43 131 133 0.0229 0.0755 0.01926

44 125 33 0.038 0.1244 0.03194

45 127 134 0.0752 0.247 0.0632

46 35 135 0.00224 0.0102 0.00268

47 35 37 0.011 0.0497 0.01318

48 33 37 0.0415 0.142 0.0366

49 134 135 0.00871 0.0268 0.00568

50 134 37 0.00256 0.0094 0.00984

51 38 37 0 0.0375 0

52 37 39 0.0321 0.106 0.027

53 37 136 0.0593 0.168 0.042

54 30 38 0.00464 0.054 0.422

55 39 136 0.0184 0.0605 0.01552

56 136 41 0.0145 0.0487 0.01222

57 136 137 0.0555 0.183 0.0466

58 41 137 0.041 0.135 0.0344

59 43 44 0.0608 0.2454 0.06068

60 134 43 0.0413 0.1681 0.04226

61 44 45 0.0224 0.0901 0.0224

62 45 138 0.04 0.1356 0.0332

63 138 47 0.038 0.127 0.0316

64 138 48 0.0601 0.189 0.0472

65 47 139 0.0191 0.0625 0.01604

66 137 139 0.0715 0.323 0.086

67 137 139 0.0715 0.323 0.086

68 45 139 0.0684 0.186 0.0444

69 48 139 0.0179 0.0505 0.01258

70 139 50 0.0267 0.0752 0.01874

71 139 51 0.0486 0.137 0.0342


Appendix 142




72 51 52 0.0203 0.0588 0.01396

73 52 53 0.0405 0.1635 0.04058

74 53 140 0.0263 0.122 0.031

75 139 140 0.073 0.289 0.0738

76 139 140 0.0869 0.291 0.073

77 140 141 0.0169 0.0707 0.0202

78 140 142 0.00275 0.00955 0.00732

79 141 142 0.00488 0.0151 0.00374

80 142 57 0.0343 0.0966 0.0242

81 50 57 0.0474 0.134 0.0332

82 142 58 0.0343 0.0966 0.0242

83 51 58 0.0255 0.0719 0.01788

84 140 143 0.0503 0.2293 0.0598

85 142 143 0.0825 0.251 0.0569

86 142 143 0.0803 0.239 0.0536

87 141 143 0.04739 0.2158 0.05646

88 143 60 0.0317 0.145 0.0376

89 143 144 0.0328 0.15 0.0388

90 60 144 0.00264 0.0135 0.01456

91 60 145 0.0123 0.0561 0.01468

92 144 145 0.00824 0.0376 0.0098

93 63 143 0 0.0386 0

94 63 64 0.00172 0.02 0.216

95 64 144 0 0.0268 0

96 38 146 0.00901 0.0986 1.046

97 64 146 0.00269 0.0302 0.38

98 139 147 0.018 0.0919 0.0248

99 139 147 0.018 0.0919 0.0248

100 145 147 0.0482 0.218 0.0578


Appendix 143




101 145 67 0.0258 0.117 0.031

102 146 147 0 0.037 0

103 147 67 0.0224 0.1015 0.02682

104 146 68 0.00138 0.016 0.638

105 47 148 0.0844 0.2778 0.07092

106 139 148 0.0985 0.324 0.0828

107 68 148 0 0.037 0

108 148 149 0.03 0.127 0.122

109 128 149 0.00221 0.4115 0.10198

110 149 71 0.00882 0.0355 0.00878

111 128 150 0.0488 0.196 0.0488

112 71 150 0.0446 0.18 0.04444

113 71 151 0.00866 0.0454 0.01178

114 149 152 0.0401 0.1323 0.03368

115 149 75 0.0428 0.141 0.036

116 148 75 0.0405 0.122 0.124

117 152 75 0.0123 0.0406 0.01034

118 153 154 0.0444 0.148 0.0368

119 148 154 0.0309 0.101 0.1038

120 75 154 0.0601 0.1999 0.04978

121 154 78 0.00376 0.0124 0.01264

122 78 79 0.00546 0.0244 0.00648

123 154 155 0.017 0.0485 0.0472

124 154 155 0.0294 0.105 0.0228

125 79 155 0.0156 0.0704 0.0187

126 68 81 0.00175 0.0202 0.808

127 81 155 0 0.037 0

128 154 82 0.0298 0.0853 0.08174

129 82 83 0.0112 0.03665 0.03796


Appendix 144




130 83 84 0.0625 0.132 0.0258

131 83 156 0.043 0.148 0.0348

132 84 156 0.0302 0.0641 0.01234

133 156 86 0.035 0.123 0.0276

134 86 157 0.02828 0.2074 0.0445

135 156 88 0.02 0.102 0.0276

136 156 158 0.0239 0.173 0.047

137 88 158 0.0139 0.0712 0.01934

138 158 159 0.0518 0.188 0.0528

139 158 159 0.0238 0.0997 0.106

140 159 160 0.0254 0.0836 0.0214

141 158 161 0.0099 0.0505 0.0548

142 158 161 0.0393 0.1581 0.0414

143 160 161 0.0387 0.1272 0.03268

144 161 93 0.0258 0.0848 0.0218

145 161 94 0.0481 0.158 0.0406

146 93 94 0.0223 0.0732 0.01876

147 94 95 0.0132 0.0434 0.0111

148 155 96 0.0356 0.182 0.0494

149 82 96 0.0162 0.053 0.0544

150 94 96 0.0269 0.0869 0.023

151 155 97 0.0183 0.0934 0.0254

152 155 98 0.0238 0.108 0.0286

153 155 162 0.0454 0.206 0.0546

154 161 163 0.0648 0.295 0.0472

155 94 163 0.0178 0.058 0.0604

156 95 96 0.0171 0.0547 0.01474

157 96 97 0.0173 0.0885 0.024

158 98 163 0.0397 0.179 0.0476


Appendix 145




159 162 163 0.018 0.0813 0.0216

160 163 101 0.0277 0.1262 0.0328

161 161 102 0.0123 0.0559 0.01464

162 101 102 0.0246 0.112 0.0294

163 163 164 0.016 0.0525 0.0536

164 163 165 0.0451 0.204 0.0541

165 164 165 0.0466 0.1584 0.0407

166 164 166 0.0535 0.1625 0.0408

167 163 106 0.0605 0.229 0.062

168 164 166 0.00994 0.0378 0.00986

169 166 106 0.014 0.0547 0.01434

170 166 167 0.053 0.183 0.0472

171 166 108 0.0261 0.0703 0.01844

172 106 167 0.053 0.183 0.0472

173 108 109 0.0105 0.0288 0.0076

174 164 168 0.03906 0.1813 0.0461

175 109 168 0.0278 0.0762 0.0202

176 168 169 0.022 0.0755 0.02

177 168 170 0.0247 0.064 0.062

178 17 171 0.00913 0.0301 0.00768

179 133 171 0.0615 0.203 0.0518

180 133 114 0.0135 0.0612 0.01628

181 131 115 0.0164 0.0741 0.01972

182 114 115 0.0023 0.0104 0.00276

183 68 172 0.00034 0.00405 0.164

184 124 117 0.0329 0.14 0.0358

185 75 118 0.0145 0.0481 0.01198

186 153 118 0.0164 0.0544 0.01356

Table A.6: IEEE 118 Bus System - Branch Data

Appendix 146

Additional Branch Data

Branch From To R X Branch From To R XNo. Bus Bus (pu) (pu) No. Bus Bus (pu) (pu)

1 119 1 0 0.025 28 146 65 0 0.0252 120 4 0 0.02 29 147 66 0 0.023 121 6 0.0007 0.0142 30 148 69 0.0007 0.01424 122 8 0.0009 0.018 31 149 70 0.0009 0.0185 123 10 0 0.0143 32 150 72 0 0.01436 124 12 0.0005 0.0272 33 151 73 0.0005 0.02727 125 15 0.0006 0.0232 34 152 74 0.0006 0.02328 126 18 0 0.0181 35 153 76 0 0.01819 127 19 0.0008 0.0156 36 154 77 0.0008 0.015610 128 24 0 0.025 37 155 80 0 0.018111 129 25 0 0.02 38 156 85 0.0008 0.015612 130 26 0.0007 0.0142 39 157 87 0 0.02513 131 27 0.0009 0.018 40 158 89 0 0.0214 132 31 0 0.0143 41 159 90 0.0007 0.014215 133 32 0.0005 0.0272 42 160 91 0.0009 0.01816 134 34 0.0006 0.0232 43 161 92 0 0.014317 135 36 0 0.0181 44 162 99 0.0005 0.027218 136 40 0.0008 0.0156 45 163 100 0.0006 0.023219 137 42 0 0.025 46 164 103 0 0.018120 138 46 0 0.02 47 165 104 0.0008 0.015621 139 49 0.0007 0.0142 48 166 105 0 0.02522 140 54 0.0009 0.018 49 167 107 0 0.0223 141 55 0 0.0143 50 168 110 0.0007 0.014224 142 56 0.0005 0.0272 51 169 111 0.0009 0.01825 143 59 0.0006 0.0232 52 170 112 0 0.014326 144 61 0 0.0181 53 171 113 0.0005 0.027227 145 62 0.0008 0.0156 54 172 116 0.0006 0.0232

Table A.7: IEEE 118 Bus System - Additional Branch Data

Appendix 147

Generator Data

Generator Pg Qg Qmax Qmin Vg mBase Pmax Pmin

Bus (MW) (MVAR) (MVAR) (MVAR) (pu) (MVA) (MW) (MW)

10 450 0 200 -147 1.05 100 550 012 85 0 120 -35 0.99 100 185 025 220 0 140 -47 1.05 100 320 026 314 0 1000 -1000 1.015 100 414 031 7 0 300 -300 0.967 100 107 046 19 0 100 -100 1.005 100 119 049 204 0 210 -85 1.025 100 304 054 48 0 300 -300 0.955 100 148 059 155 0 180 -60 0.985 100 255 061 160 0 300 -100 0.995 100 260 065 391 0 200 -67 1.005 100 491 066 392 0 200 -67 1.05 100 492 069 516.4 0 300 -300 1.035 100 805.2 080 477 0 280 -165 1.04 100 577 087 4 0 1000 -100 1.015 100 104 089 607 0 300 -210 1.005 100 707 0100 252 0 155 -50 1.017 100 352 0103 40 0 40 -15 1.01 100 140 0111 36 0 1000 -100 0.98 100 136 0

Table A.8: IEEE 118 Bus System - Generator Data

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