Wide Area Measurement Applications for Improvement of Power System Protection

Transcription

1 Wide Area Measurement Applications for Improvement 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

2 Wide Area Measurement Applications for Improvement of 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.

3 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.

4 Contents List of Figures viii List of Tables xiii 1 Motivation Power System Protection Wide Area Measurements Organization of the Dissertation Technical Background Power System Analysis Steady State Analysis Bus-Admittance Matrix Kron Network Reduction Sensitivity Factors Calculation of Susceptance Matrix Using DC Power Flow Derivation of Generator Shift Factor Derivation of Line Outage Distribution Factor Transient Analysis iv

5 Contents v 2.2 Power System Simulation Tools Protection Schemes Distance & Impedance Protection Loss-of-Field Protection Adaptive Protection Supervisory Control for Back-Up Zone Protection Introduction Distance Relay Back-up Protection Criteria Load-encroachment and Supervision of Back-up Protection Study Model Description WECC Full Loop Model California Model Selection of Appropriate Location for Back-up Protection Line Outage Distribution Factors Technique for Determining Line Outage Distribution Factor Implementation of LODF to California (Heavy Summer) Model Formation of LODF Matrix for CA System and Identification of Critical Lines Identification of Zone 3 Settings for Critical Lines after Single Contingency Relay Settings for Multi-Terminal Lines Multiple Contingency Studies

6 Contents vi Inertial Re-Dispatch of Generators Comparison between CA and Full-Loop Study System Load-Encroachment Examples in CA System Summary Adaptive Loss-of-Field Protection LOF Relaying Background Loss-of-Field Relay Protection Criteria Steady State Instability as a Consequence of LOF Condition Steady State Stability Limit Circle Development Adaptive LOF Relay Scheme LOF Group Settings Adaptive LOF Relay Application in CA System Summary Impact of Generation Re-distribution Immediately after Generation Loss Generation Re-distribution with Respect to Location Generator Location as a Function of Admittance from an Event Location Network Reduction to Determine Admittance between Generators IEEE 39 Bus System Examples IEEE 118 Bus System Examples WECC System Examples Linear Regression to Predict Power Injection Changes at Generators after Contingency IEEE 39 Bus System Examples

7 Contents vii Accuracy of Regression Model IEEE 118 Bus System Examples Potential Application in Protection Studies Summary Conclusion & Future Work Summary Future Work Bibliography 122 A Sample Study Systems 126 A.1 IEEE 39 Bus System Data A.2 IEEE 118 Bus System Data A.2.1 IEEE 118 Bus System with 54 Generators A.2.2 IEEE 118 Bus System with 19 Generators

8 List of Figures 1.1 Digital Relay Characteristics to Prevent Load Encroachment Loss-of-field Relay Characteristics Two-port π-model of a Transmission Line Distance Relay Protection Distance Relay Protection Zones Distance Relay Overlapping Zones Mho Relay Element Characteristics Generator Capability Curve Impedance Variance during LOF Conditions Three Zone Distance (Mho Relay) Characteristics Effect of Load Encroachment on Zone-3 Characteristics Supervision of Backup Protection Principle of LODF Effect of Infeeds on Zone Settings of Distance Relays Flow-Chart for Inertial Re-dispatch of Generators WECC Map, Relay at Captain Jack (500kV Bus) viii

9 List of Figures ix 3.8 R-X Characteristics of Relay at Captain Jack (500kv bus), Monitoring Line from Captain Jack to Olinda R-X Characteristics of Relay at Midway (500kV bus), Monitoring Line from Midway to Vincent, ck R-X Characteristics of Relay at Midway (500kV Bus), Monitoring Line from Midway to Vincent, ck R-X Characteristics of Relay at Midway (500kV Bus), Monitoring Line from Midway to Vincent, ck R-X Characteristics of Relay at Vincent (500kV Bus), Monitoring Line from Midway to Vincent, ck Phasor Diagram of Generator Voltage and Current during Reduced Excitation Loss-of-Field as an Instability Condition Simple System for Steady-State Stability Analysis Steady-State Stability Limit Circles Apparent Impedance Seen by an Impedance Relay Graphical Method for Steady State Stability Limit LOF Relay at Diablo Machine Terminal LOF Relay Settings Dibalo1- One Machine Infinite Bus LOF Relay Settings Network Diagram near Diablo Apparent Impedances Seen by Traditional Relay after LOF Conditions Apparent Impedances Seen by Relay after LOF Conditions - Relay at Diablo Apparent Impedances Seen by Relay after LOF Conditions - Relay at Diablo Apparent Impedances Seen by Relay after LOF Conditions - Relay at Diablo1 70

10 List of Figures x 5.1 Abstract Power System Distribution of Generation in an Abstract Power System Loss of Generator G 4 in an Abstract Power System Re-distribution of Generation in an Abstract Power System, Just after the Contingency One Line Diagram of IEEE 39 Bus System MW Outputs of Remaining Generators after Generator 3 at Bus 32 Outage Histogram of MW Outputs of Remaining Generator after Generator 3 at Bus 32 Outage MW Output at Remaining Generator after Generator 3 at Bus 32 Outage MW Output at Remaining Generator after Generator 7 at Bus 36 Outage Histogram of MW Outputs of Remaining Generator after Generator 7 at Bus 36 Outage MW Output at Remaining Generator after Generator 7 at Bus 36 Outage MW Output at Remaining Generator after Generator at Bus 10 Outage MW Output at Remaining Generator after Generator at Bus 80 Outage MW Output at Remaining Generator after Generator at Bus 66 Outage Generators Dibalo 1 & 2 Outage in WECC System Immediate Injection Changes at Generators Buses after Generator 1 Outage Immediate Injection Changes at Generators Buses after Generator 3 Outage Immediate Injection Changes at Generators Buses after Generator 10 Outage Immediate Injection Changes at Generators Buses after Each Generators Outage Immediate Injection Changes at Generators Buses after Each Generators Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 4 (543.5 MW) Outage

11 List of Figures xi 5.22 Actual and Predicted Changes in Injections at Generator Buses after Generator 5 (419.9 MW) Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 6 (561.7 MW) Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 7 (471.8 MW) Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 8 (451.8 MW) Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 9 (741.7 MW) Outage Immediate Injection Changes at Generator Buses after Generator 1 Outage Immediate Injection Changes at Generator Buses after generator 9 Outage Immediate Injection Changes at Generator Buses after Generator 11 Outage Immediate Injection Changes at Generator Buses after Generator 16 Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 1 (450 MW) at Bus 10 Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 7 (204 MW) at Bus 49 Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 10 (160 MW) at Bus 61 Outage Actual and Predicted Changes in Injections at Generator Buses after Generator 14 (477 MW) at Bus 80 Outage Impedance Trajectory Seen by Relay at Line between Bus 90 and Impedance Trajectory Seen by Relay at Line between Bus 68 and Generators at SONGS 1 & 2 in WECC System Impedance Trajectory Seen by Relay at Line between Hassayampa to North Gila in WECC System

12 List of Figures xii A.1 One Line Diagram of IEEE 39 Bus System with 10 Generators A.2 One Line Diagram of IEEE 118 Bus System with 54 Generators A.3 One Line Diagram of IEEE 118 Bus System with 19 Generators

13 List of Tables kv Links in CA System Midway-Vincent Line Ratings Slopes & y-intercepts of Best Fitted Lines alongside Transient MW Changes Coefficient of Determinations of Regression Models to Predict Power Injection Changes for IEEE 39 Bus Study List of Contingency Cases Used for Prediction Coefficient of Determinations of Regression Models to Predict Power Injection Changes for IEEE 118 Bus Study A.1 IEEE 39 Bus System - Bus Data A.2 IEEE 39 Bus System - Branch Data A.3 IEEE 39 Bus System - Generator Data A.4 IEEE 118 Bus System - Original Bus Data A.5 IEEE 118 Bus System - Additional Bus Data A.6 IEEE 118 Bus System - Branch Data A.7 IEEE 118 Bus System - Additional Branch Data A.8 IEEE 118 Bus System - Generator Data xiii

14 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

15 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, 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 disturbance. 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 voltage). 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.

16 Chapter 1. Motivation 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].

17 Chapter 1. Motivation 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 stability 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 stability 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.

18 Chapter 1. Motivation 5 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 (x d ). 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

19 Chapter 1. Motivation 6 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, 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].

20 Chapter 1. Motivation 7 As the increasing demand for electricity over time was not followed by increases in transmission 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 reliably 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 throughout 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 presentation 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 backup zones of protection and the identification of locations which may benefit from the

21 Chapter 1. Motivation 8 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-offield 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 dissertation and presents future work for the field related to the work described in this dissertation 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 investigation of the communication infrastructure for proper implementation of the research of this dissertation.

22 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

23 Chapter 2. Technical Background 10 were used in the studies described in the later chapters of the dissertation 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 Bus-Admittance Matrix Bus-admittance matrix, [Y ], or [Y bus ] is an n x n matrix which is fundamental to steadystate 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,

24 Chapter 2. Technical Background 11 I 1 Y 11 Y Y 1n V 1 I [I] = 2. = Y 21 Y Y 2n V = [Y ] [V ] (2.1).. I n Y n1 Y n2... Y nn V n The [I] vector contains the current injection phasors, where I i is the current injection into bus i and the [V ] vector is the voltage phasors of each node, where V i represents the voltage at bus i with respect to ground. Each diagonal element of admittance matrix, Y ii, is known as self admittance of i th node in a power system and equals to the sum of the admittances connected to i th node, including the shunt admittances. Each off-diagonal term Y ij is known as mutual or transfer admittance between i th & j th nodes and equals to the negative of all admittances connected directly between these two nodes. Y ij 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 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)

25 Chapter 2. Technical Background 12 which can be also described as, [ I g I n ] = [ Y gg Y ng Y gn Y nn ] [ V g V n ] (2.3) Where I g and I n represent the complex current injections at the generator and non-generator buses. Also, V g and V n 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. ] [I n = 0 Then, the network equation can be represented as, [ I g 0 ] = [ Y gg Y ng Y gn Y nn ] [ V g V n ] (2.4) The matrix form of the network equations can then be separated into two separate equations: [I g ] = [Y gg ][V g ] + [Y gn ][V n ] (2.5) Solving for [V n ] in Equation 2.6 results in the following, [0] = [Y ng ][V g ] + [Y nn ][V n ] (2.6) [V n ] = [Y nn ] 1 [Y ng ][V g ] (2.7) Then, by substituting Equation 2.7 into Equation 2.5, [I g ] = ([Y gg ] + [Y gn ][Y nn ] 1 [Y ng ])[V n ] (2.8)

26 Chapter 2. Technical Background 13 which again can be represented as the following. [I g ] = [Y reduced ][V n ] (2.9) where, [Y reduced ] = [Y gg ] + [Y gn ][Y nn ] 1 [Y ng ] (2.10) This [Y reduced ] 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 Y 1m element signifies the equivalent admittance between 1 st and m th generator. Y 11 Y Y 1m Y [Y reduced ] = 21 Y Y 2m (2.11) Y m1 Y m2... Y mm In Chapter 5, loads in the system will be replaced with impedances making all nongenerator 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 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

27 Chapter 2. Technical Background 14 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, P k, 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 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

28 Chapter 2. Technical Background 15 power injections; real power, P neti and reactive power, Q neti, and the voltage phasor V i θ i. The bus admittance matrix is represented by the [Y] matrix. The bus admittance matrix of diagonal elements Y=[Y ij ] may be calculated using Equation Y = G + jb (2.12) The bus conductance matrix is defined here as G=[G ij ], and the bus susceptance matrix is defined as B=[B ij ]. The diagonal elements Y ii 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 Y ij of the bus admittance matrix are the negative sums of the complex admittances between buses i and j. The Y ij 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 y ci, y cj and the off-diagonal bus admittance matrix elements are determined given by, Y ij = y ij = g ij jb ij (2.13) In Equation 2.13, the conductance is G ij = g ij, and the susceptance is B ij = b ij. As the line impedance can be written as z = r + jx, the admittance term y ij may also be written as a function of the impedance, creating a relationship between the resistance, r, and the

29 Chapter 2. Technical Background 16 reactance, x. y ij = 1 z ij = 1 r ij + jx ij = r ij r 2 ij + jx2 ij x ij j rij 2 + jx2 ij (2.14) So, G ij = g ij = r ij r 2 ij + jx2 ij (2.15) B ij = b ij = x ij r 2 ij + 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 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. f p i = P i = G ii V i 2 + V i f q i = Q i = B ii V i 2 + V i k=buses connected to i k=buses connected to i V k [G ik cos(θ i θ k ) B ik sin(θ i θ k )] P neti = 0 (2.17) V k [G ik sin(θ i θ k ) + B ik cos(θ i θ k )] Q neti = 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 θ i and voltage magnitude V i with the small changes in real and reactive power P i and Q i. 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.

30 Chapter 2. Technical Background 17 J(x) = f x = [ f p θ f q θ f p V f q V ] = [ P θ Q θ P V 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 P i are less sensitive to changes in voltage magnitude and are most sensitive to changes in phase angles θ i. 2. Similarly, reactive power changes Q i are less sensitive to changes in phase angles and are most sensitive to changes in voltage magnitude V i. 3. B ii is the sum of susceptances of all the elements incident to bus i. In a typical power system, the self susceptance B ii Q i and we may neglect Q i. 4. cos(θ i - θ k )=1, due to the usually small value of (θ i - θ k ). 5. Also, G ik sin(θ i - θ k ) B ik Using the assumptions listed above, the Jacobian equations and power flow equations can be written as the following sets of equations, respectively. P i θ k = V i V k B ik (2.20) Q i V k V k By substituting Equation 2.20 and 2.21 may be derived, = V i V k B ik (2.21) P i = ( P i θ k ) θ k (2.22) Q i = ( Q i V k V k ) V k V k (2.23) in Equation the following relationships P i = V i V k B ik θ k (2.24)

31 Chapter 2. Technical Background 18 Q i = V i V k B ik V k V k (2.25) Dividing the Equation by V i and assuming V k = 1, further simplification can be made to the power flow equations, P i V i = B ik θ k (2.26) Q i V i = B ik V k (2.27) Now, these matrix equations for the N-bus system can be represented, respectively. P 1 V 1 P 2 V 2. P N V N Q 1 V 1 Q 2 V 2. Q N V N B 11 B B 1N θ 1 = B 21 B B 2N θ B N1 B N2... B NN θ N B 11 B B 1N V 1 = B 21 B B 2N V B N1 B N2... B NN V N To simplify the P θ relationship more assumptions can be made. (2.28) (2.29) 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, r ik x ik, as mentioned earlier, which also simplifies the B ik calculation. So, B ik = 1 x ik (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

32 Chapter 2. Technical Background 19 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 = B ik = 1 x ik (2.31) B ii = N k=1 1 x ik (2.32) The B matrix is the new simplified B matrix for the Q V relationship. The offdiagonal elements B ik are calculated from B ik. The diagonal elements B ik can be calculated using sum of negative susceptances of all the elements incident to bus i. B ik = B ik = x ik r 2 ik + x2 ik (2.33) B ii = N B ik (2.34) k=1 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 V i = 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 f l = P ij = 1 x ij (θ i θ j ) (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

33 Chapter 2. Technical Background 20 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 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] =. B 1 (2.38) 0 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 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 a l,k = df l dp k = d dp k ( 1 x l (θ i θ j )) = 1 x l ( dθ i dp k dθ j dp k ) = 1 x l (X ik X jk ) (2.39)

34 Chapter 2. Technical Background 21 In the previous equation, x l represents the line reactance of line l connecting buses i and j, and the values X ik and X jk are the respective elements of the X matrix. The distribution factors a l,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 P ij using the sensitivity factor from Equation P ij = f l = a l,k P k (2.40) k=1,m 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]. g l,ks = (X ik X jk ) (X is X js ) x l = a l,k a l,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 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 P n and P m are added at each end of the line k where P n = P nm and p m =- P nm. Pnm is equal to the power flowing over the line. Due to the added injections, the

35 Chapter 2. Technical Background 22 line will have no power through it which implies that the line is disconnected with respect to the rest of the system [15], where, so that, As in Equation 2.37, θ = [X] P (2.42). P n P =. P m. (2.43) θ n = X nn P n + X nm P m (2.44) θ m = X mn P n + X mm P m (2.45) According to the outage model criteria, the incremental injections P n and P m is equal to the power flowing over the tripped line P nm after the injections are added. θ n and θ m are the bus voltage angles for bus n and m respectively, after the line outage. P nm = P n = P m (2.46) where, Then, P nm = 1 x k ( θ n θ m ) (2.47) θ n = (X nn X nm ) P n (2.48) θ m = (X mn X mm ) P n (2.49) x k is the reactance of line k. P nm is the flow on the line from bus n to bus m, before the line outage. Similarly, θ n and θ n are the pre-outage bus voltage angles for bus n and m. θ n = θ n + θ n (2.50) θ m = θ m + θ m (2.51)

36 Chapter 2. Technical Background 23 Replacing θ n and θ m in Equation 2.47, P nm = 1 x k (θ n θ m ) + 1 x k ( θ n θ m ) (2.52) Substitution of θ n and θ m in Equation 2.52 results in the following equation. P nm = P nm + 1 x k (X nn + X mm 2X nm ) P n (2.53) As, Pnm = P n, the Equation 2.53 is simplified. P n = x k (X nn + X mm 2X nm ) P nm (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 P n and P m are imposed at the two ends of line k. θ i = X in P n + X im P m = (X in X im ) P n (2.55) Again, the substitution of P n derives, θ i = (X in X im )x k x k (X nn + X mm 2X nm ) P nm (2.56) Assuming a line l from bus i to bus j, the LODF d l,k while monitoring line l can be defined after an outage on line k using Equation d l,k = f l P nm (2.57) where f l represents the change is flow on line l and P nm is the original flow on line k, before it was disconnected. Now, f l = P ij = 1 x l ( θ i θ j ), where x l is the reactance of line l. d l,k = 1 x l ( θ i P nm θ j P nm ) (2.58) If neither i nor j is a reference bus, LODF for line l (between bus i and bus j), due to outage

37 Chapter 2. Technical Background 24 of line k (between bus n and bus m) is derived as, d l,k = 1 ( (X in X im )x k (X jn X jm )x k ) = x k (X in X jn X im + X jm ) x l x k (X nn + X mm 2X nm ) x l x k (X nn + X mm 2X nm ) (2.59) 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 systems. 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

38 Chapter 2. Technical Background 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 dissertation. 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 industry. The scripts perform many different types of steady-state power system analysis including power flow, constrained power flows including optimal power flow and security constrained economic dispatch, and even energy market studies. GE s Positive Sequence Load Flow software (PSLF) - PSLF is an integrated, interactive 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, dynamic 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].

39 Chapter 2. Technical Background 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 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 3 lengths, it is 75 ohms and so on. The relay is located at 4 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.

40 Chapter 2. Technical Background 27 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

41 Chapter 2. Technical Background 28 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.

42 Chapter 2. Technical Background 29 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, Z M, and the angle of this diameter with respect to the R axis, θ M. 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 θ M. Normally, θ M is set close to the protected line impedance angle to ensure maximum relay sensitivity for faults and minimum sensitivity for load conditions [19] 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-offield 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

43 Chapter 2. Technical Background 30 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.

44 Chapter 2. Technical Background 31 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 significantly 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 Thévenin 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.

45 Chapter 2. Technical Background Adaptive Protection Adaptive relaying is a concept of power system protection that allows for change and modification to relay characteristics to adjust to existing network conditions. In general, protection systems react to system faults or disturbances based on fixed, predetermined settings dictated 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 considers 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 contingency 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 protection 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.

46 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

47 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

48 Chapter 3. Supervisory Control for Back-Up Zone Protection 35 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 % 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.

49 Chapter 3. Supervisory Control for Back-Up Zone Protection 36 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.

50 Chapter 3. Supervisory Control for Back-Up Zone Protection 37 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 WECC Full Loop Model The PSLF model of full WECC heavy summer system that was created in February This study system encompasses 15,700 buses with a wide range of interconnected transmission 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

51 Chapter 3. Supervisory Control for Back-Up Zone Protection 38 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 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 AZ Moenkopi Eldorado AZ Public Service Co. - Southern CA Edison AZ Hassyampa- N.Gila AZ Public Service Co. - San Diego Gas & Electric Co. AZ Paloverde- Devers AZ Public Service Co. - Southern CA Edison AZ Mead- Marketplace NV Power Company - L.A. Dept. of Water & Power NV Capt. Jack- Olinda Bonneville Power Admin. - Pacific Gas & Electric OR Malin- 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

52 Chapter 3. Supervisory Control for Back-Up Zone Protection 39 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 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 line 1 3, from bus 1 to 3 is out of service, part of the flow S 1 3 of line 1 3 (Figure 3.4(a)) is being carried by other lines; the percentage of S 1 3 is the distribution factor for that line 1 3.

53 Chapter 3. Supervisory Control for Back-Up Zone Protection 40 Figure 3.4: Principle of LODF (a) L 13 in service. (b)l 13 out of service (unknown source) 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 Distribution factor K rs,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. d rs,pq = x pq x rs (X rp X sp X rp + X sq ) x pq (X pp + X qq 2X pq ) (3.1) Where x pq is the impedance of the line p-q and X pq is the pq th 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 d rs,pq factors. f rs = f 0 rs + d rs,pq f 0 pq (3.2) Where f 0 rs and f 0 pq are the pre-outage flows on the lines r-s and p-q, respectively f rs is the flow on line r-s after line p-q out.

54 Chapter 3. Supervisory Control for Back-Up Zone Protection Implementation of LODF to California (Heavy Summer) Model To apply the distribution factor analysis to the full California power system model, understanding 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, [Y bus ] for the California network, with around 4000 buses and 4474 lines as described in Section 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, d rs,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 ( ), 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 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.

55 Chapter 3. Supervisory Control for Back-Up Zone Protection 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 protection 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, E 1 = Z 1 I 1 + Z f (I 1 + I 2 ) (3.3) and the apparent impedance seen by relay R 1 can be computed as, where the true impedance to the fault is, Z app = E 1 I 1 = Z 1 + Z f (1 + I 2 I 1 ) (3.4) Z true = Z 1 + Z f (3.5)

56 Chapter 3. Supervisory Control for Back-Up Zone Protection 43 The current I 2, the contribution to the fault from the line tap which is referred as the infeed current when it is approximately in phase with I 1, completely arbitrary phase relationships are also possible, but in most cases the phase relationship is such that the current I 2 is an infeed current. The apparent impedance seen by relay R 1 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 R 1 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 R 1 are set to reach beyond buses 2 and 3, respectively, 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, overloads 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 observed 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 generators 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 generators (in-service) according to their machine inertia. Inertial re-dispatch was performed for

57 Chapter 3. Supervisory Control for Back-Up Zone Protection 44 generator outage contingencies 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 = W k S B (3.6) where W K is the kinetic energy of the rotating mass(generator) and S B 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 S rated 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, S rated. In the post-contingency, change in real power output in generators using Equation 3.7, P x = S rated,x S rated,total P total (3.7)

58 Chapter 3. Supervisory Control for Back-Up Zone Protection 45 Where, P x is the change in MW in machine x, after re-dispatch, P total is the total generation loss in MW in the whole system, before re-dispatch, S rated,x is machine base of machine x, S rated,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

59 Chapter 3. Supervisory Control for Back-Up Zone Protection Comparison between CA and Full-Loop Study System To verify our generator inertial re-dispatch algorithm, the same generator outage contingencies 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 characteristic 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.

60 Chapter 3. Supervisory Control for Back-Up Zone Protection 47 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 Captain 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.

61 Chapter 3. Supervisory Control for Back-Up Zone Protection 48 Figure 3.8: R-X Characteristics of Relay at Captain Jack (500kv bus), Monitoring Line from Captain 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.

62 Chapter 3. Supervisory Control for Back-Up Zone Protection 49 Midway-Vincent Line Current Rating A Circuit No. (MVA) 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.

63 Chapter 3. Supervisory Control for Back-Up Zone Protection 50 Figure 3.9: R-X Characteristics of Relay at Midway (500kV bus), Monitoring Line from Midway 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.

64 Chapter 3. Supervisory Control for Back-Up Zone Protection 51 Figure 3.10: R-X Characteristics of Relay at Midway (500kV Bus), Monitoring Line from Midway 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 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.

65 Chapter 3. Supervisory Control for Back-Up Zone Protection 52 Figure 3.11: R-X Characteristics of Relay at Midway (500kV Bus), Monitoring Line from Midway to Vincent, ck 2 Figure 3.12: R-X Characteristics of Relay at Vincent (500kV Bus), Monitoring Line from Midway to Vincent, ck 2

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

67 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

68 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 Thévenin impedance of the system as seen from the generator terminals. Clearly the generator impedance is constant, but the system Thévenin 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 Thévenin 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 Thévenin impedance will increase; this reflects the evolving weakness of the power system. As the Thévenin 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.

69 Chapter 4. Adaptive Loss-of-Field Protection 56 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 Thévenin 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 E 1, stator current I 1, and the internal voltage of the generator E s. Also shown is the field circuit with a field current I f. Figure 4.1: Phasor Diagram of Generator Voltage and Current during Reduced Excitation I f If the effects of generator saturation is neglected, the voltage E s and the field current are proportional to each other. As a result the phasor E s (magnitude) can be used to

70 Chapter 4. Adaptive Loss-of-Field Protection 57 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 I 1 on the axis of E 1 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 I f which causes the internal voltage of the generator E s to drop. In order to maintain the phasor relationship between E s, E 1 and I 1 under these conditions, as E s reduces in magnitude the vector must move along the dashed horizontal line and the current I 1 must move along the dashed vertical line. This relationship retains the output real power constant at P, while the stator current moves from I 1 position to I 1, 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 E 1 to I 1 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 quadrant. 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

71 Chapter 4. Adaptive Loss-of-Field Protection 58 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] 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 E s and the machine reactance is X s. The equivalent impedance (Thévenin) of the power system is X t and power system equivalent voltage is E 2. Since steady-state analysis is considered here, the voltage E s is the field voltage E f, and the reactance X s is the the synchronous reactance X d. The total reactance between the machine internal bus and E 2 is X = X s + X t. The electric power output at the machine terminals (at bus S or at bus 2) is given by Equation 4.1. P e = E se 2 X sin δ (4.1) where δ is the angle by which the machine internal voltage E s leads E 0. The mechanical power input to the machine is P m, and in steady state electrical power and mechanical power are in balance at a rotor angle δ 0 which is zero when the machine is operating in steady state at δ 0. The rate of change of the output power P e with respect to δ is given by Equation 4.2. P e δ = E se 2 cos δ (4.2) X 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

72 Chapter 4. Adaptive Loss-of-Field Protection 59 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 the R-X Plane [26] The real and reactive power outputs of the machine (as measured at the machine terminals) are given by Equation 4.3. P 1 + jq 1 = E 1 I 1 (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, P 1 and Q 1 satisfy Equation 4.4. P [ ( Q 1 E )] 2 [ ( E 2 = )] 2 (4.4) 2 X t X s 2 X t X s 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 (P 0, Q 0 ), and a radius of S 0. This is given in Equation 4.5. (P P 0 ) 2 + (Q Q 0 ) 2 = S 2 0 (4.5)

73 Chapter 4. Adaptive Loss-of-Field Protection 60 For example, in the case of the steady-state stability limit given in Equation 4.4, these values are given by Equation P 0 = 0 (4.6) ( Q 0 = E ) 2 X t X s (4.7) ( S 0 = E ) 2 X t X s (4.8) Figure 4.5: Apparent Impedance Seen by an Impedance Relay (a) Generator Connected to Power System (b) Generator Supplying the Same Power to Parallel Load (c) Generator Supplying 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 seriesconnected R and X, which are related to the terminal conditions by Equation P = Q = E2 R R 2 + X 2 (4.9) E2 X R 2 + X 2 (4.10) Substituting Equation 4.9 & 4.10 into Equation 4.8 results in Equation (R R 0 ) 2 + (X X 0 ) 2 = Z 2 0 (4.11) This is an equation of a circle in the R-X plane with its center at (R 0, X 0 ) and a radius of

74 Chapter 4. Adaptive Loss-of-Field Protection 61 Z 0 as in Figure 4.4(b) where these parameters are given by Equation R 0 = P 0 E 2 P Q 2 0 S 2 0 (4.12) X 0 = Q 0 E 2 P0 2 + Q 2 0 S0 2 (4.13) Z 0 = S 0 E 2 P0 2 + Q 2 0 S0 2 (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 P 0, Q 0 and S 0 from Equation using E for the machine terminal voltage, rather than E 1. The LOF relay settings are then given in Equation [26]. R 0 = 0 (4.15) X 0 = X t + X s 2 Z 0 = (X t X s ) 2 (4.16) (4.17) 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 (Thévenin 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 x t =x trans +x thev [31]:

75 Chapter 4. Adaptive Loss-of-Field Protection 62 Figure 4.6: Graphical Method for Steady State Stability Limit In traditional LOF protection, the size of the steady state stability limit circle is unchanged 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) ) and the radius is (Xt+Xs). From Figure 4.6, it can be seen that the center and 2 2 the radius of the steady state stability limit circle are actually dependent on the system s Thévenin 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.

76 Chapter 4. Adaptive Loss-of-Field Protection 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 X d and Thévenin reactance of the power system, X t at the generator terminal. Since any topology change close to that terminal will change the value of X t, 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.

77 Chapter 4. Adaptive Loss-of-Field Protection 64 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 With this scenario, the precontingency and post-contingency X t values need to be calculated. Additionally, it should be noted that the Thévenin 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 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

78 Chapter 4. Adaptive Loss-of-Field Protection 65 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 corresponds 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 Thévenin 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.

79 Chapter 4. Adaptive Loss-of-Field Protection 66 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 Thévenin 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 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

80 Chapter 4. Adaptive Loss-of-Field Protection 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 transformer and system s Thévenin 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 condition. 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 This setting is calculated considering a system Thévenin impedance for the normal operating scenario where all of the power system elements in Figure 4.11 remain in-service.

81 Chapter 4. Adaptive Loss-of-Field Protection 68 Figure 4.12: Apparent Impedances Seen by Traditional Relay after LOF Conditions As demonstrated in Section 4.3, system s Thévenin 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

82 Chapter 4. Adaptive Loss-of-Field Protection 69 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 Figure 4.13: Apparent Impedances Seen by Relay after LOF Conditions - Relay at Diablo1 Figure 4.14: Apparent Impedances Seen by Relay after LOF Conditions - Relay at Diablo1

83 Chapter 4. Adaptive Loss-of-Field Protection 70 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 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. Figure 4.15: Apparent Impedances Seen by Relay after LOF Conditions - Relay at Diablo1

84 Chapter 4. Adaptive Loss-of-Field Protection 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.

85 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

86 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 techniques 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 redispatch 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 evaluating 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.

87 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 74 To determine the generator injections just slightly after a contingency, dynamic simulation 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 Location 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 G 1 for this discussion) which serves load in the northern part of the grid and is then connected via a long transmission corridor with the larger network in the south. In the southern network, there are four generators (which is referred to as the north-western (G 2 ), north-eastern (G 3 ), south-western (G 3 ), and south-eastern (G 4 ) generators) which all serve loads in the southern network. Figure 5.1: Abstract Power System

88 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 75 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 visualization of the effect of a generator in a system. Consider the scenario shown in Figure 5.3 where the G 5 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.

89 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 76 Figure 5.3: Loss of Generator G 4 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 the Contingency A parallel can be drawn between the generic system described in this section and a real

90 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 77 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 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.

91 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 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 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. [ I g I n ] = [ Y gg Y ng Y gn Y nn ] [ V g V n ] (5.1) Where I g and I n represent the complex current injections at the generator and non-generator buses. Also, V g and V n 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

92 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 79 i.e. the generator buses which is presented with Equation 5.1, [I g ] = [Y reduced ][V n ] (5.2) Where [Y reduced ] = [Y gg ] + [Y gn ][Y nn ] 1 [Y ng ] (5.3) [Y reduced ] 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 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, [Y reduced ] which has dimensions 10 x 10. Figure 5.5 shows the one-line diagram of the IEEE 39 bus system.

93 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 80 Figure 5.5: One Line Diagram of IEEE 39 Bus System The equivalent system created using network reduction technique presents an exact reproduction of the self and transfer impedances of the reduced system as seen from its generator 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 [Y reduced ] is shown below.

94 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 81 Y reduced = 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

95 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 82 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 postcontingency 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 32 Outage 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 [Y reduced ] 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 3 rd 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

96 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 83 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.

97 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 84 Figure 5.9: MW Output at Remaining Generator after Generator 7 at Bus 36 Outage 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 Bus 36 Outage

98 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 85 Similarly, column 7 of the [Y reduced ] 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. Figure 5.11: MW Output at Remaining Generator after Generator 7 at Bus 36 Outage IEEE 118 Bus System Examples 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 ) to avoid unnecessary redundancy.

99 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 86 Figure 5.12: MW Output at Remaining Generator after Generator at Bus 10 Outage Figure 5.13: MW Output at Remaining Generator after Generator at Bus 80 Outage

100 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 87 Figure 5.14: MW Output at Remaining Generator after Generator at Bus 66 Outage 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.

101 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 88 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 proportional 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, [Y reduced ], for the reduced network. The larger the admittance between two generator buses, the smaller the impedance or electrical distance between them. Therefore, the approximate linear proportionality of the admittances between generators and the contingency with the transient change in MW directly after the contingency verifies the assumptions 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.

102 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 89 If the i th generator trips in a system with N generators and the admittance between each of the remaining N-1 generator buses and the i th generator bus is represented by [y] i. The vector [y] i contains the off-diagonal elements of i th 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 i th generator is represented by the vector [ P dyn ] i. A simple linear regression illustrates the relation between the dependent variables of [ P dyn ] i and the independent variables of [y] i based on the regression equation, [ P dyn ] i = β 0 i + β 1 i [y] i + [r] i for i th = 1 st, 2 nd,...n th generator outage (5.4) Where, β 0 i and β 1 i are the regression coefficients and r i is the residual matrix. The linear regression can determine the values of the coefficients β 0 i and β 1 i 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 IEEE 39 Bus System Examples 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 1 st 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 [ P dyn ] 1. Both [y] 1 and [ P dyn ] 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, [ P dyn ] 1 = β β 1 1 [y] 1 + [r] 1

103 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 90 Where, = β β [r] Performing the regression yields β 0 1=0.045 and β 1 1=0.589 when generator 1 is out-of-service. Figure 5.16 demonstrates the linear relationship between [y] 1 and [ P dyn ] 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 3 rd 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

104 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 91 vector [ P dyn ] 3. Similar to the previous case, both [y] 3 and [ P dyn ] 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, [ P dyn ] 3 = β β 1 3 [y] 3 + [r] 3 In this case, β 0 3=0.044 and β 1 3=0.612 when generator 3 is out-of-service. The linear relationship between [y] 3 and [ P dyn ] 3 are shown in Figure 5.17, after generator 3 at bus 32 is taken out-of-service, where both vectors are again normalized. Figure 5.17: Immediate Injection Changes at Generators Buses after Generator 3 Outage 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, β 0 10=0.033 and β 1 10= Figure 5.18 demonstrates the linear relationship between [y] 10 and [ P dyn ] 10 after the outage of generator 10 at bus 39, where both vectors are normalized.

105 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 92 Figure 5.18: Immediate Injection Changes at Generators Buses after Generator 10 Outage 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 admittances 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).

106 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 93 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 knowledge 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-

107 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 94 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 proportional 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 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 MW is lost from the system, β 0 1=0.045 and β 1 1= Again, for generator 3 contingency case which supplies MW, β 0 3=0.044 and β 1 3= The regression coefficients are, β 0 10=0.033 and β 1 10=0.798 for generator 10 outage contingency case which generates MW power. So, it can be considered that β 0 and β 1 are two dependent variables where P loss, the MW loss of the contingency generator is the dependent variable. Two separate simple linear regression illustrates the relation between the dependent variable β 0 and the independent variable P loss, also the relation between the another dependent variable β 1 and the independent variable P loss based on the following two regression equations. [β 0 ] = κ 0 + κ 1 [P loss ] + [r 0 ] (5.5)

108 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 95 or, β 0 1. β 0 N = κ 0 + κ 1 P loss1. P lossn + r 01. r 0N [β 1 ] = γ 0 + γ 1 [P loss ] + [r 1 ] (5.6) or, β 1 1. β 1 N = γ 0 + γ 1 P loss1. P lossn + r 11. r 1N These two sets of regression coefficients, κ 0, κ 1 and γ 0, γ 1 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, Y reduced 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 [ P dyn ] i, is calculated from simulation. Using the [y] i - [ P dyn ] i relation from Equation 5.6 three sets of β 0 i, β 1 i 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, κ 0, κ 1 and γ 0, γ 1 are then calculated from β 0 i, β 1 i for the mentioned generator outage contingency case. Vector P loss, 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 MW β 0 1 β 0 3 = κ 0 + κ 1 P loss1 P loss3 + r 01 r 03 (5.7) β 0 10 P loss10 r 010 or numerically, = κ 0 + κ r 01 r 03 r 010

109 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 96 β 1 1 β 1 3 = γ 0 + γ 1 P loss1 P loss3 + r 11 r 13 (5.8) β 1 10 P loss10 r 110 or numerically, = γ 0 + γ The regression coefficients, κ 0 =0.051, κ 1 = and γ 0 =0.495, γ 1 =1.643 are calculated from β 0 i, β 1 i for individual outage contingency case of generator 1, 3 and 10. Using κ 0, κ 1 and γ 0, γ 1 coefficients, β 0 i and β 1 i are predicted for contingency case for generator 4, 5, 6, 7, 8, 9 (generator 2, swing generator is not included). The predicted values of β 0 i, β 1 i are represented as ˆβ 0 i, ˆβ1 i in the following equation. ˆβ 0 4 ˆβ 0 5 ˆβ 0 6 ˆβ 0 7 ˆβ 0 8 = κ 0 + κ 1 P loss4 P loss5 P loss6 P loss7 P loss8 r 11 r 13 r 110 (5.9) ˆβ 0 9 P loss9 Therefore, Again, ˆβ 0 4 ˆβ 0 5 ˆβ 0 6 ˆβ 0 7 ˆβ 0 8 ˆβ = ( 0.097) = ˆβ 1 4 ˆβ 1 5 ˆβ 1 6 ˆβ 1 7 ˆβ 1 8 = γ 0 + γ 1 P loss4 P loss5 P loss6 P loss7 P loss8 (5.10) ˆβ 1 9 P loss9

110 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 97 and therefore, ˆβ 1 4 ˆβ 1 5 ˆβ 1 6 ˆβ 1 7 ˆβ 1 8 ˆβ = = Where, predicted ˆβ 0 i, ˆβ1 i values less (minus) some residuals r 0i, r 1i, the actual coefficients β 0 i, β 1 i of the regression Equation 5.6, can be calculated. β 0 4 β 0 5 β 0 6 β 0 7 β 0 8 = ˆβ 0 4 ˆβ 0 5 ˆβ 0 6 ˆβ 0 7 ˆβ 0 8 r 04 r 05 r 06 r 07 r 08 β 0 9 ˆβ 0 9 r 09 and, β 1 4 β 1 5 β 1 6 β 1 7 β 1 8 = ˆβ 1 4 ˆβ 1 5 ˆβ 1 6 ˆβ 1 7 ˆβ 1 8 r 14 r 15 r 16 r 17 r 18 β 1 9 ˆβ 1 9 r 19 Here, ˆβ 0 i, ˆβ 1 i values are used in linear regression Equation 5.6 to predict the vector [ P dyn ] i, respective change in real power injections at each of the nine remaining generators in IEEE 39 bus system immediately after the loss of i th 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, [ Pˆ dyn ] 4 = ˆβ ˆβ 1 4 [y] 4

111 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 98 Pˆ dyn at gen1 ˆ P dyn at gen2 ˆ P dyn at gen3 ˆ P dyn at gen5 ˆ P dyn at gen6 ˆ P dyn at gen7 ˆ P dyn at gen8 ˆ P dyn at gen9 ˆ P dyn at gen10 for gen4 outage = = 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 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 Generator 4 (543.5 MW) Outage

112 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 99 Figure 5.22: Actual and Predicted Changes in Injections at Generator Buses after Generator 5 (419.9 MW) Outage Figure 5.23: Actual and Predicted Changes in Injections at Generator Buses after Generator 6 (561.7 MW) Outage

113 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 100 Figure 5.24: Actual and Predicted Changes in Injections at Generator Buses after Generator 7 (471.8 MW) Outage Figure 5.25: Actual and Predicted Changes in Injections at Generator Buses after Generator 8 (451.8 MW) Outage

114 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 101 Figure 5.26: Actual and Predicted Changes in Injections at Generator Buses after Generator 9 (741.7 MW) Outage Accuracy of Regression Model The coefficient of determination, R 2, 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 < R 2 < 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 P dyn for a

115 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 102 generator outage case which can be written as the following, [ Pˆ dyn ] = β 0 + β 1 [y] (5.11) The coefficient of determination for this regression model computes as, R 2 = 1 SS err SS tot (5.12) SS tot represents total sum of squares, the deviations of the observations from their mean: SS tot = n ( P dynk P dyn ) 2 (5.13) k=1 Where k, n, P dynk, P dyn represent sample observation data, the total number of sample, k th observation and mean of observations. If we were to use P dyn to predict P dyn, then SS tot measures the variability of the P dyn around their predicted value. SS err measures the deviations of observations from their predicted values: SS err = n ( P dynk P ˆ dyn ) 2 (5.14) k=1 Table 5.2 shows this calculation of coefficient of determinations of regression models to predict 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 R 2 Gen 4 at bus 33 Outage Gen 5 at bus 34 Outage Gen 6 at bus 35 Outage Gen 7 at bus 36 Outage Gen 8 at bus 37 Outage Gen 9 at bus 38 Outage Table 5.2: Coefficient of Determinations of Regression Models to Predict Power Injection Changes for IEEE 39 Bus Study the transient MW change following the contingency is approximately a linear relationship.

116 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 103 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 generators 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 Examples 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-ofservice 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 generators. So [Y reduced ] 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 [ P dyn ] i, is calculated from simulation. For the generator 1 outage contingency case, the admittances between each of the remaining 18 generators and generator 1 are shown in [y] 1. Vector [y] 1 has all eighteen of the off-diagonal elements in 1 st column of the reduced admittance matrix. The corresponding

117 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 104 real power injection changes at each of these 18 generators immediately after the loss of generator 1 is demonstrated here by the vector [ P dyn ] 1. Both [y] 1 and [ P dyn ] 1 are normalized 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, [ P dyn ] 1 = β β 1 1 [y] 1 + [r] 1 Where, = β β [r] β 0 1= and β 1 1=0.908 when generator 1 at bus 10 is out-of-service. The Figure 5.27 demonstrates the linear relationship between [y] 1 and [ P dyn ] 1, after generator 1 at bus 10 is taken out-of-service, where both vectors are normalized.

118 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 105 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 & Figure 5.28: Immediate Injection Changes at Generator Buses after generator 9 Outage

119 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 106 Figure 5.29: Immediate Injection Changes at Generator Buses after Generator 11 Outage Figure 5.30: Immediate Injection Changes at Generator Buses after Generator 16 Outage It is seen that β 0 and β 1 are two dependent variables of P loss, which are dependent on the MW loss of the contingency generator. Two separate linear regressions represent the relation between the dependent variable β 0 and the independent variable P loss, also the relation between the another dependent variable β 1 and the independent variable P loss based

120 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 107 on the following two regression equations. [β 0 ] = κ 0 + κ 1 [P loss ] + [r 0 ] (5.15) and, [β 1 ] = γ 0 + γ 1 [P loss ] + [r 1 ] (5.16) This two sets of regression coefficient, κ 0, κ 1 and γ 0, γ 1 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 - [ P dyn ] i relation from Equation Contingency Case MW Loss from Outage Gen 2 at bus 12 outage 85 Gen 5 at bus 31 outage 7 Gen 9 at bus 59 outage 155 Gen 11 at bus 65 outage 391 Gen 16 at bus 89 outage 607 Table 5.3: List of Contingency Cases Used for Prediction 5.6, 5 sets of β 0 i, β 1 i 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, κ 0, κ 1 and γ 0, γ 1 are then calculated from β 0 i, β 1 i for the mentioned generators contingency cases. Vector P loss, 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 MW. β 0 2 β 0 5 β 0 9 β 0 11 = κ 0 + κ 1 P loss2 P loss5 P loss8 P loss11 + r 02 r 05 r 09 r 011 (5.17) β 0 16 P loss16 r 016

121 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 108 β 1 2 β 1 5 β 1 9 β 1 11 = γ 0 + γ 1 P loss2 P loss5 P loss8 P loss11 + r 12 r 15 r 19 r 111 (5.18) β 1 16 P loss16 r 116 The regression coefficients, κ 0 =0.017, κ 1 = and γ 0 =0.57, γ 1 =2.29 are calculated from β 0 i, β 1 i for individual outage contingency case of generators listed in Table 5.2. Using κ 0, κ 1 and γ 0, γ 1 coefficients, β 0 i and β 1 i are predicted for contingency case for generator rest of the 14 generators (generator 13, swing generator is not included). The predicted values of β 0 i, β 1 i are represented as ˆβ 0 i, ˆβ1 i in the following equations. ˆβ 0 1 ˆβ 0 3 ˆβ 0 4 ˆβ 0 6 ˆβ 0 7 ˆβ 0 8 ˆβ 0 10 ˆβ 0 12 ˆβ 0 14 ˆβ 0 15 ˆβ 0 17 ˆβ 0 18 = κ 0 + κ 1 P loss1 P loss3 P loss4 P loss6 P loss7 P loss8 P loss10 P loss12 P loss14 P loss15 P loss17 P loss18 (5.19) ˆβ 0 19 P loss19

122 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 109 ˆβ 1 1 ˆβ 1 3 ˆβ 1 4 ˆβ 1 6 ˆβ 1 7 ˆβ 1 8 ˆβ 1 10 ˆβ 1 12 ˆβ 1 14 ˆβ 1 15 ˆβ 1 17 ˆβ 1 18 = γ 0 + γ 1 P loss1 P loss3 P loss4 P loss6 P loss7 P loss8 P loss10 P loss12 P loss14 P loss15 P loss17 P loss18 (5.20) ˆβ 1 19 P loss19 ˆβ 0 i, ˆβ1 i values are used in linear regression Equation 5.6 to predict the vector [ P dyn ] i, respective change in real power injections at each of the remaining generators in IEEE 118 bus system right after the loss of i th 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, [ Pˆ dyn ] 1 = ˆβ ˆβ 1 1 [y] 1

123 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 110 ˆ P dyn at gen1 ˆ P dyn at gen2 ˆ P dyn at gen3 ˆ P dyn at gen5 ˆ P dyn at gen6 ˆ P dyn at gen7 ˆ P dyn at gen8 ˆ P dyn at gen9 ˆ P dyn at gen10 ˆ P dyn at gen11 ˆ P dyn at gen12 ˆ P dyn at gen14 ˆ P dyn at gen15 ˆ P dyn at gen16 ˆ P dyn at gen17 ˆ P dyn at gen18 ˆ P dyn at gen19 hat P dyn at gen1 for gen4 outage = = 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.

124 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 111 Figure 5.31: Actual and Predicted Changes in Injections at Generator Buses after Generator 1 (450 MW) at Bus 10 Outage Figure 5.32: Actual and Predicted Changes in Injections at Generator Buses after Generator 7 (204 MW) at Bus 49 Outage

125 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 112 Figure 5.33: Actual and Predicted Changes in Injections at Generator Buses after Generator 10 (160 MW) at Bus 61 Outage Figure 5.34: Actual and Predicted Changes in Injections at Generator Buses after Generator 14 (477 MW) at Bus 80 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

126 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 113 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 R 2 Gen 1 at bus 10 outage Gen 3 at bus 25 outage Gen 4 at bus 26 outage Gen 6 at bus 46 outage Gen 7 at bus 49 outage Gen 8 at bus 54 outage Gen 10 at bus 61 outage Gen 12 at bus 66 outage Gen 14 at bus 80 outage Gen 15 at bus 87 outage Gen 17 at bus 100 outage Gen 18 at bus 103 outage Gen 19 at bus 111 outage Table 5.4: Coefficient of Determinations of Regression Models to Predict Power Injection Changes 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.

127 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss Potential Application in Protection Studies Chapters 3 & 4 presented the summary of computationally intense protection studies performed 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 potential 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 subsections 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

128 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 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).

129 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 116 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 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 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

130 Chapter 5. Impact of Generation Re-distribution Immediately after Generation Loss 117 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 North Gila in WECC System 5.5 Summary This chapter presents the concept of an approximately linear relationship between the electrical 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 approximation 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 discussion 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.