A New Special Protection Scheme for Power System

Controlled Separation

Sandeep Maram

Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science

in

Electrical Engineering

Dr. Lamine Mili, Chair

Dr. Yilu Liu

Dr. Virgilio A Centeno

January 11, 2007

Falls Church, Virginia

Keywords: Controlled separation, out-of-step blocking, transfer tripping, system

separation, apparent impedance.

A New Special Protection Scheme for Power System

Controlled Separation

Sandeep Maram

ABSTRACT

A new power system controlled separation scheme is proposed to prevent the propagation

of cascading failures across a transmission network should it undergoes a major

disturbance, thereby reducing the possibility of a large-scale blackout. This scheme is

developed based on a set of conjectures, which state the following: (i) the locations of

out-of-step operations are independent of the severity and the location of the initial faults;

(ii) these out-of-step operations occur sequentially over a sufficiently long duration so

that relay blocking and transfer tripping can take place to minimize the load-generation

imbalance in the formed islands. To verify these conjectures, extensive dynamic stability

simulations are executed on a 30-bus and a 517-bus system, which exhibit characteristics

suitable for this study. Furthermore, we verify that these out-of-step operations do depend

on the prevailing system topology and the operating conditions.

iii

ACKNOWLEDGEMENTS

I would like to express my sincere thanks to my advisor Dr. Lamine Mili for his

continuous support and encouragement during the course my research work. He is an

excellent teacher and mentor to me and always guided me in taking correct decisions for

my academic and career growth. I am very grateful to him for giving me an opportunity

to work under his able guidance. I would like to express my sincere thanks to Dr. Yilu

Liu and Dr. Virgilio Centeno for their valuable comments and for serving as my advisory

committee members. Special thanks go to Mike Adibi of IRD Corporation for initiating

this research work, for his continuous encouragement, and for his valuable inputs from

time to time.

iv

TABLE OF CONTENTS Chapter 1 Introduction 1 1-1 Power system structure 2

1-2 Power system reliability 3

1-3 Operating states of a power system 4

1-4 Literature review 7

1-5 Research Contribution 9

1-6 Thesis organization 11

Chapter 2 Protective Relays 12 2-1 Fault clearing and reclosing 13

2-2 Distance relays 14

2-2-1 Impedance relays 15

2-2-2 Mho relay 17

2-2-3 Representation of Mho and Impedance Relays 17

2-3 Out-of-step blocking and tripping 18

2-3-1 Out-of-step relays 20

2-3-2 Ohm unit relays 22

Chapter 3 System Modeling 23 3-1 Synchronous machine modeling 23

3-1-1 Parks transformation 26

3-2 Exciter models 30

3-3 Governor and turbine models 32

Chapter 4 Methodology and simulation set up 35

4-1 Power system separation conjectures 35

v

4-2 Description of the 30-bus system 36

4-3 Description of the 517-bus system 37

4-4 Description of the software programs used for conducting the simulations 39

4-5 Description of the Simulation set up 40

4-6 Data clustering for power system separation 41

4-6-1 Hierarchical clustering 41

4-6-2 Partitioning clustering 43

4-6-3 Clustering methods applied to power system separation 44

4-7 Relay and apparent impedance representations 44

Chapter 5 Simulation Results 48

5-1 Simulations performed on the 517-bus system 48

5-1-1 Checking the out-of-step cascading effect 49

5-1-2 Effect of the initial fault locations on out-of-step operations 52

5-1-3 Effect of the fault intensities on the out-of-step operations 53

5-1-4 Effect of out-of-step blocking on tie-lines 54

5-1-5 Impact of changes in the loading conditions 56

5-1-6 Impact of the changes in network configuration 57

5-1-7 Impact of out-of-step blocking and tripping operations 59

5-2 Simulations performed on the 30-bus system 66

5-3 Weak link identification of a Network using a clustering method 67

Chapter 6 Conclusions 69 References 71

vi

LIST OF FIGURES Figure 1-1: Basic structure of a power system 2

Figure 1-2: Operating States in Power System 5

Figure 2-0: Step distance relaying functions for a complete line protection 15

Figure 2-1: Impedance Relay Characteristics 16

Figure 2-2: Impedance relay characteristics with three zones 17

Figure 2-3: Mho distance relay characteristics with fault impedance loci 18

Figure 2-4: Stable and Unstable Swings 19

Figure 2-5: Out of Step relay with circular characteristics 20

Figure 2-6: Out of Step Relay with Blinders (Ohm Unit Relay) 21

Figure 2-7: Swing Blocking Relaying 22

Figure 3-1: Schematic representation of a three-phase synchronous machine 24

Figure 3-2: Rotor and stator windings 25

Figure 3-3: Block diagram of the IEEE Type-1-excitation system 31

Figure 3-4: Block diagram of the IEEE Type-4-excitation system 31

Figure 3-5: Block diagram of the solid-fed-static exciter 32

Figure 3-6: The IEEE-standard-turbine-governor model 32

Figure 3-7: The hydro-turbine-governor model 33

Figure 3-8: The cross-compound-turbine governor model 33

Figure 3-9: The steam turbine governor model 34

Figure 4-1: One line diagram of reduced 30-bus system 37

Figure 4-2: Structure of the 517-bus system with four sub-systems connected by

tie-lines 38

Figure 4-3: Agglomerative and divisive type clustering techniques 42

Figure 4-4: k-means partitioning of 22 elements into 4 clusters around four

centroids 43

Figure 4-5: Apparent impedance path of line 135-136 46

Figure 4-6: Apparent impedance path of line 135-136 47

vii

Figure 5-1: Simulation result that illustrates the cascading effect 51

Figure 5-2: Apparent impedance paths for tie-line g-h 53

Figure 5-3: Apparent impedance path of tie-line e-f for different fault intensities 54

Figure 5-4: Impact on tie-line g-h of blocking the out-of-step relay of tie-line e-f 55

Figure 5-5: Light Load and Peak load case results (38 generators in operation) 56

Figure 5-6: Apparent impedance path for the two network configurations 59

Figure 5-7: Apparent impedance locus of tie-line e-f (blocked) and tie-line g-h 60

Figure 5-8: The transfer tripping operation performed on tie-lines f-h and e-g 61

Figure 5-9: Transient stability curves obtained on the reduced 30-bus system 66

Figure 5-10: Eleven clusters identified on the 30-bus system using k-means

clustering with mean silhouette value of 0.82 68

viii

LIST OF TABLES Table 2-0: Relay time and interrupting time for different line voltages 13

Table 2-1: De-ionization times for different line voltages 14

Table 3-1: Definitions of the variables and parameters of a synchronous machine 30

Table 4-2: 517-Bus system dynamic models 39

Table 5-1: Parameters of line 64-132 49

Table 5-2: Initial operating conditions for checking the cascading case 50

Table 5-3: Parameters of line 47-33 52

Table 5-4: Initial operating conditions for the light-load case 57

Table 5-5: Initial operating conditions for the reduced network 58

Table 5-6: Initial operating conditions for the out-of-step blocking and transfer

tripping simulation case 62

Table 5-7: Simulations results obtained using different initial fault locations 63 Table 5-8: Simulations results obtained using different initial fault intensities 64

Table 5-9: Simulations results obtained using different load levels 65

1

Chapter 1 Introduction

Electric energy is produced by electric power systems, which are critical infrastructures

whose service is vital to the economy of a nation. Providing continuous supply of electric

energy to meet the load demand is a complex technical challenge. It involves real-time

estimation of the system state together with the control and coordination of generating

units aimed at delivering in a secure manner electric power to the load. Consequently,

power system network security is a major concern worldwide. However, due to

deregulation, power systems are being operated closer to their maximum loadability. In

addition, environmental constraints hinder the expansion of the electric transmission

networks from meeting future demand growth. As a result, power systems are more

vulnerable to severe disturbances like faults on major pieces of equipment. Such

contingencies may result in cascading failures leading to large-scale blackouts. Therefore,

there is a need for new control schemes aimed at reducing this risk. It turns out that

controlled system separation is one good solution to this problem.

To prevent cascading failures from propagating further throughout a power

system, various controlled separation schemes have been proposed and installed by many

utilities. A good scheme reduces the impact of an outage on the customers and the

economy of the affected area while reducing the possibility of damage to equipment.

In this research work, we propose a new real-time controlled separation scheme

using current communication and protection systems. In the subsequent sections a brief

introduction to power systems structure, reliability and operating states are described;

then, the objectives and contribution of the thesis are presented and discussed.

2

1-1 Power System Structure

As depicted in Fig. 1.1, a typical power system consists of generation units, transmission

networks, distribution networks, and loads. The electric power is produced by

synchronous generators located at the power plants, which convert a primary source of

energy into electrical power [1], [2]. Typically, the voltage of the generated electric

power ranges from 10kV to 25kV. This voltage is then stepped up to higher voltage

levels ranging from 230kV to 765kV by means of step-up transformers. Next, the electric

power at these high voltages is transmitted through the transmission network. At the HV-

MV substations, voltages are stepped down to lower levels. There, the electric energy is

distributed to the load through primary and secondary distribution feeders depending

upon the customer energy needs. For instance, industrial customers that require large

amount of electric power are connected to the primary feeders while a host of domestic

users are connected to secondary feeders.

GeneratingStation /

Power Plant

GeneratorStep-Up

Transformer

Transmission Network(Transmission lines of

765, 500, 345, 230,138 kV)

SubstationStep-DownTransformer

SubtransmissionCustomer

26 kV and 69 kV

SecondaryCustomer

120 V and 240 V

PrimaryCustomer

13 kV and 4 kV

Figure 1-1: Basic structure of a power system.

3

1-2 Power System Reliability

A power system is said to be reliable when it is able to satisfy the power system load

requirements with an acceptable continuity of service at the contractual frequency and

voltage quality. Power system reliability can be sub-divided into two components,

namely, adequacy and security. Adequacy stands for the ability of the system to generate

sufficient power to meet the load demand at every instant of time. On the other hand,

security is defined as the ability of the system to cope with any abnormal disturbances,

which may be caused by short-circuits or unduly relay trippings that result in the loss of

major system components. For the sake of computational feasibility, security N-1 is the

only security level executed by both the power system planners and the control center

operators. Specifically, this function checks whether the system has enough reserve

margins in transmission and in generation to withstand the loss of a single piece of

equipment subject to both system equality and inequality constraints; the latter include

limits on the voltages and currents across the transmission network.

The North American Electric Reliability Council (NERC) and various Regional

Reliability Councils have developed system operating and planning standards. These

standards ensure reliable operation of a power system; they are based on the following

requirements [1]:

• A balance between the real power generation and the load demand should be

maintained continuously;

• An appropriate supply of reactive power should be provided so that the voltages

across the system are maintained within given stability and operational limits;

• The power flows across system transmission lines and transformers should be

monitored to ensure that thermal limits are not exceeded;

4

• The system should return to stability within a reasonable time following any

single contingency;

• A power system should be prepared for emergencies;

• A power system should be appropriately planned, designed and maintained so that

it meets the foregoing reliability criteria.

1-3 Operating States of a Power system

A reliable operation and control of a power system is a very complex technical challenge.

It involves the execution of functions such as real-time system monitoring and

contingency analysis. However, system responses to different disturbances are difficult to

predict accurately for all operating conditions. Therefore, major failures cannot be

prevented from occurring from time to time; hence, the need of corrective control

schemes to ensure system integrity under major contingencies.

In security analysis, system operating conditions can be classified into five

different states, namely normal, emergency, alert, in extremis, and restorative state [2]. In

this section, are presented and discussed all five states together with the associated

preventive and control actions that can be initiated under special conditions. Figure 1-2

depicts the five operating states along with the associated possible state transitions.

Normal and Secure State

During a normal operating state of a power system, both equality and inequality

constraints are satisfied. Equality constraints refer to the balance between system’s

generation and load while inequality constraints state that some system variables, such as

currents and voltages, remain within the normal operating range of the physical

5

equipment and satisfy system dynamic stability constraints [3]. However, while an

operating condition of a power system is normal with all the constraints being satisfied, it

may be secure or insecure. In the secure case, the system is capable to withstand a single

contingency without violating any of the operating constraints. The reserve margins for

the transmission and generation are sufficient to handle the loss of a single piece of

equipment. In the insecure case, the system is unable to cope with contingencies.

Figure 1-2: Operating States in Power System [2].

Alert State

In the alert state, a power system is considered to be insecure. System operators must be

alert and constantly keep monitoring equality and inequality constraints. However, in an

event of any contingency, the lack of reserve margins may result in the violation of some

inequality constraints, inducing a transition of the system into emergency state [3]. In that

instance, some equipment may be overloaded, that is, they may operate above their rated

capabilities. If the severity of the disturbance is very high, the system may change its

Normal

and Secure

Alert Restorative

Emergency In Extremis

6

state directly to the in extremis state when preventive actions are not taken in a timely

manner.

Emergency State

A power system enters an emergency state from an alert state when a contingency occurs

in the system. During emergency conditions, the voltage levels fall below the stability

limits at various buses and the emergency ratings of system components are exceeded

due to overloading, implying that the inequality constraints are violated. The system can

be restored back to the alert state by initiating effective control strategies such as fault

clearing, fast valving, exciter control, generation tripping, and load shedding [3].

In Extremis State

When effective control measures are not applied to a power system operating in an

emergency state, the system will enter in an in-extremis state. Here, both the equality and

inequality constraints are violated [3]. A system settling in an in-extremis state may

undergo cascading outages, which may result in the formation of disconnected islands

while inducing major disruption in service, that is, brownouts or blackouts [2]. Controlled

system separation and load shedding are few actions that may be taken to prevent the

occurrence of major failures and ensure least disruption in service.

Restorative State

This state indicates that control actions are being implemented, which aim at restoring the

integrity of the power system via the sequential connection of the disconnected parts,

including the system load. Depending on the existing operating conditions, the system

may transit from this state to the alert state or the normal state.

7

1-4 Literature Review

Typically, major power system blackouts have been initiated by local disturbances that

cascaded across the transmission networks. Significant studies were performed to

understand their causes. It can be inferred that major power system contingencies

typically comprise three phases depending on their duration: the initial phase where

temporary system faults occur, which is rapidly cleared in milliseconds; the intermediate

phase where the system separates in seconds into undesirable parts; and the final phase

where load and generation imbalance causes in minutes a blackout [5]. Incidents of major

blackouts that took place in various nations have been reported in the literature [6] – [11].

Since the late 1990’s, power systems have been pushed closer to their limits,

resulting in a growing risk for a local failure to cascade into a large-scale catastrophic

blackout. The most common triggering fault of such an event is a short-circuit that

occurs on high voltage or extra-high voltage transmission lines of the system. At the

inception of a disturbance, the relays located on faulty transmission lines operate to clear

the fault. This induces variations of the electrical power generator outputs while the

generator mechanical inputs remain almost constant. The resulting effect of this power

imbalance is the formation of groups of coherent generators operating at different speeds,

swinging one against the others. Eventually this may lead to a loss of synchronism and

the splitting of the network. However, the islands so formed may not have a balance in

generation and load, which makes the failure to propagate further until a complete

collapse of the system. To prevent such events to occur, utilities have installed special

protection schemes based on under-frequency and under-voltage relays that perform load

and generation shedding and line tripping.

After a thorough analysis of the blackouts that struck the North-West of the

United States in summer 1996, Taylor [6] revealed their causes and proposed remedial

actions to prevent them from occurring in the future. In France, Counan et al. [8] studied

8

the behavior of the French electric system under multiple contingencies. They

recommended the use of curative actions such as load shedding based on frequency

criteria together with system separation induced by local relays trigged by generator loss

of synchronism.

Currently, controlled separation schemes have been implemented mainly in

elongated and isolated power systems to split the system along pre-determined

boundaries, e.g., the East – West boundary in Bangladesh [9]. They have been planned

based on simulations executed under various forecasted load conditions and contingency

scenarios. A more general separation scheme was proposed by Vital et al. [10]; the

authors apply the normal form method to the Manitoba-Hydro power system to determine

groups of machines that swing coherently against each other following a small

perturbation. The boundaries separating coherent generator groups are identified and

tripped to form islands [10]. If these islands are deemed to be not stable, then various

techniques such as load shedding, generation curtailment, relay tripping, are implemented

[6]-[11].

You et al. [12]-[13] propose a power system separation scheme aimed at creating

islands subject to load-generation balance via load shedding based on the rate of

frequency decline. This approach consists in using a slow coherency method to detect

clusters of coherent generator groups, the boundaries of which provide desirable locations

of separation. It involves power system modeling followed by the execution of a

computationally efficient method based on graph theory and pattern recognition. The

method seeks to determine the locations and the timing of system separation. This

approach assumes the availability of real-time wide-area phasor measurements.

Sun et al. [14]-[15] introduce a new two-phase and three-phase system separation

method based on ordered binary decision diagrams (OBDD). Here, the primary focus is

to ensure that the equality and inequality constraints are satisfied in all the islands formed

9

under a single contingency. This approach involves the implementation of complex

search algorithms that require the knowledge of the system operating states to find the

desirable splitting locations.

In summary, we may say that the special protection schemes installed so far by

the utilities are costly and require the implementation of complex tools for the real-time

estimation and assessment of system operating conditions. Consequently, there is a need

for the development of simpler and more cost effective methods of system separation.

The aim of this research work is precisely to meet this need.

1-5 Research Contribution

The main outcome of this research work is the development of a new and simple power

system controlled separation scheme aimed at preventing cascading events from

propagating further across a transmission network, thereby reducing the possibility of

large-scale blackout. It is a simple procedure that makes use of existing protective and

communication systems to detect the appropriate locations of system separation and to

initiate controlled system islanding with minimal load-generation imbalance [4]. The

proposed method generalizes and broadens the industry’s practice on corrective action

implemented during a power system disturbance, which may result in the loss of large

generating units and/or the outages of major transmission lines.

In the proposed method, out-of-step relays are placed across the network and are

continuously monitored at the control center. After the initial fault has occurred, the

system state varies depending on the severity of the fault. Under major disturbances, out-

of-step relays may trip depending upon whether the prevailing swing impedance locus

passes through their respective tripping zones. However, this relay tripping may result in

the break up of the system into islands with an imbalance of generation and load. In that

10

event, a relay blocking and transfer tripping is performed so that islanding occurs with

minimal generation-load imbalance. Arming of these out-of-step relays are updated from

time to time or in response to significant changes that may occur in the system topology

and the loading conditions.

The proposed method assumes that the power system consists of clusters of

machines connected via few tie-lines. Furthermore, it relies on the validity of a set of

three conjectures that will be described in Chapter 4. Briefly, these conjectures state that

the locations of out-of-step operations depend on the network topology and loading

conditions but not on the fault location and intensity. Also, it states that there is a

sufficient time-lag between two successive out-of-step operations so that appropriate

corrective actions can take place. Specifically, during a normal operation, at any given

time, the system separation scheme proceeds as follows:

1. Select a collection of out-of-step relays strategically located across the

transmission network to perform the splitting of the power system at desirable

locations. This splitting is performed only when a disturbance causes the apparent

impedance loci to enter the out-of-step relay tripping zones;

2. Determine the probable locations where out-of-step operation may occur and

identify a large collection of transmission lines whose outages can split the system

into islands based on the current network topology and loading conditions;

3. From the identified collection of transmission lines, make an appropriate selection

of out-of-step relays that will separate the system into islands having minimal

load and generation imbalance via the execution of out-of-step relay blocking and

transfer tripping operations.

11

1-6 Thesis Organization

Chapter 2 is devoted to the description and operation of various protective relays such as

distance relays, impedance relays, out-of-step relays, to cite a few. Furthermore, it

explains the implementation of a relay-blocking-and-transfer-tripping scheme by means

of out-of-step relays. Chapter 3 deals with the modeling of a synchronous machine, its

exciter and governor and provides all the block diagrams of the associated models.

Chapter 4 provides the statement of the proposed three conjectures that constitute the

basis of the current research work and gives the complete description of the test systems

developed to verify them. Furthermore, it outlines various data clustering concepts and

methodologies and advocates their application to the Z-bus matrix of a power

transmission network to identify its weak links. Chapter 5 analyzes the simulation results

that are obtained by carrying out dynamic stability studies on a 30-bus and 517-bus test

system. Chapter 6 summarizes the conclusions drawn from this research study.

12

Chapter 2 Protective Relays

In power systems, relays are used to detect abnormal power system conditions that arise

due to faults in the system by a continuous monitoring of various system variables such

as voltages, power flows, power injections, and system frequency [2]. Most protective

relays are used to detect and disconnect an element of the power system that is

functioning outside its normal range. The aim of relays used for protecting various

elements in the system is to provide high dependability and security. A relay that operates

correctly for all the faults, for which it is designed to respond to, is said to have high

dependability. A relay that does not operate incorrectly for any fault is said to have high

security [16]. Relays that are used in transmission line protection are of primary interest

in this research work. These relays are used to clear the faults by controlling the opening

and closing of circuit breakers when a fault occurs in the system. It is very essential that

the relaying schemes employed is able to discriminate between normal loading

conditions, swing conditions, out-of-step conditions and fault conditions [17], [18].

Tripping during stable power swings and faults due to improper functioning of relays

may eventually lead to a total system collapse. Major disturbances that occurred in the

past such as the 1965 Northeast blackout, the blackouts that struck the Western part of the

USA during summer 1996, the North America blackout of August 2003 were the results

of undesirable relay tripping.

During transient conditions, relay actions play a critical role. It is very essential

that a strategy is followed to avoid the splitting of the system at undesirable locations,

which may result in the formation of islands having imbalanced load and generation. Out-

of-step relaying has been installed to perform tripping and blocking operations when out-

of-step conditions are detected in the system. In the current chapter we discuss various

distance relays, out-of-step relays and their usage in performing blocking and tripping

operations.

13

2-1 Fault Clearing and Reclosing

When a fault occurs on a piece of equipment of a system, it is essential that it is detected

by the associated protection relays and eliminated via the opening of the circuit breakers

under the relay supervision [2]. Following a fault, the electric power output of the

generators varies while the mechanical input to the generators remains practically

constant, inducing a change in the generator speed and thereby, a change in the frequency

of the system. The effect of this frequency change depends on the fault duration [17].

The fault clearing time is the sum of the relay time (also referred to as fault

detection time), the signal transmission time and the time required by the circuit breakers

to open. On the other hand, the relay time and the interrupting times depend on the

transmission line voltages [17]. Generally, higher the line voltage, shorter is the fault

duration since the relays used for high voltages are faster. Table 2.0 shows the relay time

and the interrupting time used for different line-voltage levels. Note that the time is

expressed in cycles of 60 Hz.

Table 2.0: Relay time and interrupting time for different line voltages [17].

The time elapsed from the instant the breaker initiates the trip until the time when the

breaker contacts re-close constitutes the reclosing time. The reclosing time is much

longer for high and extra-high voltage lines as the de-ionization time is longer. Table 2.1

shows the typical de-ionization time for different line voltages in cycles of 60 Hz.

Line Voltage Relay Time

in Cycles of 60 Hz

Interrupting Time

in Cycles of 60 Hz

≤ 69 kV 1 – 3 8

≥ 115 kV 1 – 3 5

230 kV ¼ - 1 3

345 kV ¼ - 1 2

14

Table 2.1: De-ionization times for different line voltages [17].

Line Voltage

in kV

Minimum De-ionization

Time( in Cycles)

69 6

115 8.5

138 10

230 18

345 20

2-2 Distance Relays

Distance relays are the main devices used for the transmission line protection. In current

use, popular distance relays are impedance relays, reactance relays, mho relays, modified

mho and modified impedance relays [2]. Distance relays trip when the impedance

between the relay location and the fault location, measured as the ratio of measured

voltage phasor to measured current phasor, is less than the relay setting [2]. Distance

relays, which utilize local information such as currents and voltages, employ time

intervals in order to discriminate between faults that occur internally and externally to the

protected zone. The characteristic of a distance relay is well understood from the R-X

plane diagrams (See Figure 2.1 and Figure 2.2). The relay operation takes place when the

measured impedance falls within the relay characteristics, which depend on the parameter

to which the distance relay is set to respond to. It is circular for impedance relays and

horizontal for reactance relays.

Distance relays basically protect three different zones for a given transmission

line. Zone 1 is typically set between 85% and 90% of the line length over which the relay

operates instantaneously. Zones 2 and 3 are adapted for back-up protection of the line. In

these two zones, a timer initiates coordination delays that allow the primary protection to

operate first. Specifically, the coordination delay for Zone 2 is usually of the order of 0.3

seconds. The reach of Zone 2 is generally set from 120% to 150% of the line length. Care

15

is taken that Zone 1 of the neighboring line is operated before Zone 2 for a line being

protected. Regarding Zone 3, it usually extends to 120% to 180% of the neighboring line

section. It is important that Zone 3 coordinates in time and distance with Zone 2 of the

neighboring circuit. Usually the operating time for Zone 3 is set at 1.0 second [16]. The

zones expressed in distance relaying for 100% line protection are displayed in Figure 2.0.

Figure 2-0: Step distance relaying functions for a complete line protection [16].

2-2-1 Impedance Relays

A relay that operates on the basis of a voltage to current ratio is called an impedance

relay [19]. This ratio is also known as the apparent impedance seen by the relay [17]. The

relay operates when the magnitude of the apparent impedance is less than the value for

which the relay is set to operate. This type of relay detects faults in all four quadrants of

the R-X plane. Therefore, directional elements are unutilized for this type of relays. A

typical impedance relay has a timer, a directional element, and three impedance elements.

In order to protect the three zones, all three impedance elements are set to operate for

16

different impedance values, each at different time interval, should a fault occur on the

transmission line under their supervision.

As displayed in Figure 2.1, the tripping characteristic of a simple impedance relay

with impedance elements and timer is a circle centered at the origin. Whenever the value

of the apparent impedance falls within the radius of the circle, the relay operates. On the

other hand, the characteristic of the directional element is a straight line passing through

the origin while being perpendicular to the line of maximum torque [17]. With the

presence of a directional element, the tripping area is defined as that falling within the

circle and above the straight line. The characteristic of an impedance relay with a

directional element and zones is shown in Figure 2.2.

Figure 2-1: Impedance relay characteristics [2].

R

jX

Z

17

Figure 2-2: Impedance relay characteristics with three zones [17].

2-2-2 Mho Relay

Mho relay detects faults only in one direction thanks to the availability of three zone

elements and a timer. Note that directional elements are not needed. The third zone

impedance element can be adjusted to induce an offset characteristic for back-up

protection purpose. Note that generally, mho relays are used for protection of long lines.

2-2-3 Representation of Mho and Impedance Relays

Let us consider a transmission line, termed for short Line A-B, of length L with voltages

EA and EB, current IAB, and impedance ZAB , all in per unit. The apparent impedance ZA is

given by [17]

ZA = EA / IAB, (2.1)

= EA / ((EA – EB) / ZAB), (2.2)

= RA + j XA, (2.3)

18

Figure 2-3: Mho distance relay characteristics with fault impedance loci [17].

Consider the three zones of an impedance relay, namely Zone 1, 2, and 3. For

Zone i, where i = 1,2, 3, let ri denotes the radius of the tripping characteristic of the ith

element and let Ri and Xi denote the coordinates of the center in the impedance plane of

this element. Then, the distance between the apparent impedance ZA and the center of the

ith zone is given by

di = ((RA – Ri )2 + ( XA – Xi )2)1/2 . (2.4)

When di – ri ≤ 0, the timer di starts counting. On the other hand, when dti ≥ ∆Ti, Relay i

operates and the associated circuit-breaker clears the fault at dti = ∆Ti + ∆T0. Here, ∆Ti

denotes the relay time for each element i according to the zone standards while ∆T0

denotes the breaker time at line end A.

2-3 Out-of-step Blocking and Tripping When the steady state equilibrium of a power system is disturbed due to a fault,

generators start swinging with respect to one another, which may result in the operation

of distance relays. Improper detection of unstable swings by protection relays may result

19

in the opening of transmission lines. The unstable and stable power swings are shown in

Figure 2.4. Control actions are typically initiated to bring the system back into stable

equilibrium using protective measures. For instance, when unstable swings occur due to

the loss of synchronism (out-of-step) between two groups of generators, these

fluctuations may be dampened by separating the coherent machines into different groups,

also called coherent areas [17]. The separation should be so that: (1) there is a minimal

load and generation imbalance in each separated area; (2) critical load is protected; (3)

power system is brought back to secure state as soon as possible.

Figure 2-4: Stable and unstable swings [18].

During out-of-step conditions, it is essential that the relays do not trip during

stable swings while allowing the tripping to occur during unstable conditions.

Furthermore, it may be necessary to block some of the relays from tripping where

splitting is not desirable and to initiate relay tripping where separation is desirable.

Therefore, it is required to identify strategic locations where the splitting of the system

should occur. To meet these requirements, it is important for the relaying schemes to

distinguish between normal loading conditions, swing conditions, out-of-step conditions

and fault conditions. It turns out that the above requirements can be met by out-of-step

relays strategically located across the transmission.

Unstable

Stable

Time

Angle

δo

20

2-3-1 Out-of-Step Relays

Out-of-step relays have multiple characteristics. First, they effectively identify out-of-

step conditions due to an incipient loss of synchronism. Second, they perform out-of-step

blocking or tripping depending upon whether the swing is stable or unstable. The

decision is made based on the rate-of-change of the locus of the apparent impedance

during system instability. For a stable swing, this rate-of-change is slow whereas for an

instable swing, it is quick. To do this detection, out-of-step relays comprise two relays

having circular or vertical characteristics in the R-X plane [2]. The relay characteristics

are circular when impedance relays are used and vertical when mho relays are used. As

depicted in Figure 2.5 and Figure 2.6, if the time required by the apparent impedance

locus to cross the two characteristics (buffer area) exceeds a specified value, then the out

of step function is initiated.

Figure 2-5: Out-of-step relay with circular characteristics [16].

21

Figure 2-6: Out-of-step relay with blinders (Ohm unit relay) [4].

Obviously, an out-of-step blocking scheme is needed to control the tripping of

distance relays in order to avoid improper system splitting during out-of-step conditions

that exhibit heavy swings. The relays that may trip at undesirable locations are blocked

whereas the other out-of-step relays are allowed to trip [17]. As displayed in Figures 2.5

and 2.6, the blocking action can be achieved by surrounding the tripping area with

concentric impedance relays or mho relays forming a buffer area. Under fault condition,

the apparent impedance passes gradually through the buffer area into the tripping area

[17]. If the time taken by the apparent impedance to cross the buffer area is equal or

greater than the pick-up time, ∆T, of the auxiliary relay associated with the out-of-step

relay, then the auxiliary relay operates to block the tripping of the relay. The pick up time

of the blocking relay is about ¼ to 1 cycle. The signal transmission time for the transfer,

which is generally the transmission of ‘yes’ or ‘no’ signal to the desirable location, is also

¼ to 1 cycle while the circuit-breaker’s opening time is about 1½ to 2 cycles. Therefore,

as the apparent impedance crosses the buffer area between the blinders, there are about 2

to 4 cycles available to block the out-of-step tripping action and to transfer the tripping to

other locations [4].

22

2-3-2 Ohm Unit Relays

Also known as angle impedance relays, ohm unit relays have linear characteristics, which

make these relays suitable for the protection of long transmission lines where early

tripping need to be prevented to allow larger swings to occur. Indeed, these relays are

equipped with blinders to control the tripping actions during out-of-step or swing

conditions. As shown in Figure 2.7, the angular range of distance relays can be controlled

and narrowed to any desired lower angles. The fault impedance locus is the shaded area

between the two lines at angles 600 and 750. The apparent impedance path or swing-

impedance locus is drawn intersecting the line impedance at various swing angles. The

distance relays normally used without blinders will trip for swing angles ranging from

900 to 2400, whereas the distance relays when used with blinders will trip for swing

angles ranging from 1350 to 1950 [4]. The circular characteristic characterizes the tripping

area boundary while the blinders define the angular range.

3000

1950

600

1350

180"

2400

900

OPE

N

BLINDER

CLOS

EOP

ENCLO

SE

BLIN

DER

CLOSE

OPEN

750

600

FAULT

LOCUS

SWIN

G

LOCUS

jX

R

δ

i

j

Figure 2-7: Swing blocking relaying [4].

23

Chapter 3 System Modeling 3-1 Synchronous Machine Modeling In a power plant, a synchronous generator is used to convert the mechanical energy

provided by the turbine on the shaft to electrical energy that is injected into the power

system. A synchronous machine mainly consists of two elements, the stator and the rotor.

Armature windings are placed on the stator and operate at high voltages while the field

windings are mounted on the rotor and are energized by DC-current. The three-phase

windings of the armature are distributed symmetrically around the air gap with 120

electrical degrees apart in space [2]. A synchronous machine may have several damper

windings mounted on the rotor. The rotor may be either cylindrical or have salient poles

depending upon the speed at which the machine has to be operated. Figure 3.1 shows the

schematic representation of a three-phase synchronous machine with one pair of field

poles [2].

The dynamic equations that govern a synchronous machine rotation are developed

under several assumptions, which are as follows [2] [19]:

• stator windings have equivalent sinusoidal distribution along the air gap;

• magnetic hysteresis and magnetic saturation effects are negligible;

• the relationship between the flux linkages and currents must reflect a conservative

coupling field;

• the relationships between the flux linkages and the current are independent of the

shaft angle, shaftθ when expressed in dqo -coordinate system.

24

Figure 3-1: Schematic representation of a three-phase synchronous machine [2].

A p-pole three-phase synchronous generator with three armature windings and

one field winding is described next. The circuit shown in Figure 3.2 is used to derive the

equations of the generator. In this particular case, the machine is assumed to be provided

with one damper winding along the d-axis and two damper windings along the q-axis.

The relation between the mechanical angle, shaftθ , and the electrical angle, eθ , is given by

2e shaftpθ θ= , (3.1)

where subscripts notation being used denote the following: a, b, c represent stator phase

windings, fd denotes field windings, 1d denotes d-axis damper winding, 1q and 2q

represent the q-axis damper windings.

25

Figure 3-2: Rotor and stator windings.

The electrical equations of the windings present in the synchronous machine as shown in

Figure 3.2 can be obtained using Kirchhoff’s voltage law. The voltage equations of the

armature, field and damper windings are expressed as follows 19]:

aa a s

dv i rdtλ

= + , (3.2)

bb b s

dv i rdtλ

= + , (3.3)

c

c c sdv i rdtλ

= + , (3.4)

fd

fd fd fd

dv i r

dtλ

= + , (3.5)

1

1 1 1d

d d ddv i rdtλ

= + , (3.6)

1

1 1 1q

q q q

dv i r

dtλ

= + , (3.7)

26

2

2 2 2q

q q q

dv i r

dtλ

= + . (3.8)

The torque equation can be written as

2m e f

dJ T T Tp dt ω

ω= − − . (3.9)

where, J is the inertia constant, Tm is the mechanical torque applied to the shaft in the

direction of rotation, Te is the electrical torque which is opposing the mechanical torque ,

ω is the rotor angular velocity, and Tfw is the friction windage torque.

3-1-1 Park’s Transformation

We have represented the electrical and mechanical equations of a synchronous machine

in which the different variables and parameters have been expressed in the stator a-b-c

reference frame. In this reference frame, Eqs. (3.2) – (3.9) contain inductances terms that

are time variant and are dependent on the electrical angle θe. This time dependence

introduces difficulties in the modeling of a synchronous machine [2].

In order to make the inductances time independent with constant values

irrespective of the electrical angles, a synchronously rotating d-q-o reference frame is

used instead. At synchronous speed, this d-q-o reference frame is fixed with respect to the

rotor. The transformation from the stator to the d-q-o reference frame is called Park’s

transformation, which is given by

27

2 23 3

2 2 23 3 3

1 1 12 2 2

dqo

sin sin( ) sin( )

T cos cos( ) cos( )

π πθ θ θ

π πθ θ θ

⎛ ⎞− +⎜ ⎟⎜ ⎟⎜ ⎟= − +⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

. (3.10)

The new variables are obtained by projecting the actual variables on three axes,

namely, the direct axis (or axis d), which is along the main axis of the field winding, the

quadrature axis (or axis q), which is along the neutral axis of field winding, and lastly the

stationary axis (or axis o). The inverse transformation is given by

1

12 2 13 3

2 2 13 3

dqo

sin cos

T sin( ) cos( )

sin( ) cos( )

θ θπ πθ θ

π πθ θ

−

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟= − −⎜ ⎟⎜ ⎟

+ +⎜ ⎟⎝ ⎠

. (3.11)

Therefore, we can write the equations of the synchronous machine in the d-q-o reference

frame as follows [19]:

d

d s d qdv r idtλωλ= − + , (3.12)

q

q s q d

dv r i

dtλ

ωλ= + + , (3.13)

o

o s odv r idtλ

= + , (3.14)

fd

fd fd fd

dv r i

dtλ

= + , (3.15)

28

11 1 1

dd d d

dv r idtλ

= + , (3.16)

1

1 1 1q

q q q

dv r i

dtλ

= + , (3.17)

2

2 2 2q

q q q

dv r i

dtλ

= + , (3.18)

where the flux linkages are expressed as

1 1d ls md d sfd fd s d d( L L )i L i L iλ = + + + , (3.19)

1 132fd sfd d fdfd fd fd d dL i L i L iλ = + + , (3.20)

1 1 1 1 1 132d s d d fd d fd d d dL i L i L iλ = + + , (3.21)

1 1 2 2q ls mq q s q q s q q( L L )i L i L iλ = + + + , (3.22)

1 1 1 1 1 1 2 232q s q q q q q q q qL i L i L iλ = + + , (3.23)

2 2 1 2 1 2 2 232q s q q q q q q q qL i L i L iλ = + + , (3.24)

o ls oL iλ = . (3.25)

The torque equation in the d-q-o reference frame is written as

( )2 32 2m d q q d fw

dw PJ T i i Tp dt

λ λ⎛ ⎞⎛ ⎞= + − −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

. (3.26)

All the variables involved in the equations given by (3.1) to (3.25) are expressed in actual

units. They must be converted to per units when they are encoded in a software program.

29

The scaled transient reactance, sub-transient reactance, and time constants are given by

[19]

11 1d ls

md lfd

X ' X

X X

= ++

, (3.27)

11 1q ls

mq lfd

X ' X

X X

= ++

, (3.28)

1

11 1 1d ls

md lfd l d

X " X

X X X

= ++ +

, (3.29)

1 2

11 1 1q ls

mq l q l q

X " X

X X X

= ++ +

, (3.30)

fddo

s fd

XT '

Rω= , (3.31)

1

1

qqo

s q

XT '

Rω= , (3.32)

11

1 11 1do l d

s d

md lfd

T " XR

X Xω

⎛ ⎞⎜ ⎟⎜ ⎟= +⎜ ⎟+⎜ ⎟⎝ ⎠

, (3.33)

22

1

1 11 1qo l q

s q

mq l q

T " XR

X Xω

⎛ ⎞⎜ ⎟⎜ ⎟= +⎜ ⎟+⎜ ⎟⎝ ⎠

. (3.34)

Table 3.1 provides the definitions of the various parameters and variables involved in

Eqs. (3.12) to (3.34).

30

Table 3-1: Definitions of the variables and parameters of a synchronous machine. Parameter/Variable Definitions

dv , qv armature d-axis, q-axis terminal voltages

vfd , v1d ,v1q ,v2q d-axis, q-axis field and damper winding voltages

rs armature phase resistance

rfd , r1d , r1q , r2q d-axis, q-axis field and damper winding resistances

dλ , qλ armature flux in d-axis, q-axis

1 1 2fd d q q, , ,λ λ λ λ d-axis, q-axis field and damper winding fluxes

id , iq armature d-axis, q-axis terminal currents

ifd , i1d , i1q, i2q d-axis, q-axis field and damper winding currents

Lls armature phase leakage inductance

Lmd , Lmq d-axis, q-axis magnetizing inductances

Xd , Xq d-axis, q-axis synchronous reactances

X’d , X’q d-axis, q-axis transient reactances

X”d , X”q d-axis, q-axis sub-transient reactances

T’do , T’qo d-axis, q-axis transient open circuit time constants

T”do , T”qo d-axis, q-axis sub transient open circuit time constants

3-2 Exciter Models

Exciters are used to provide direct current to the synchronous machine field winding. In

addition, they allow the operator to control the reactive power injected in the power

system by controlling the field current [2]. Exciters can be classified into three types,

namely DC excitation systems, AC excitation systems, and static excitation systems.

In order to ensure proper controlling and protective measures, exciters are

equipped with power system stabilizers, voltage regulators, limiters, and protection

relays. Figures 3.4, 3.5 and 3.6 depict the various exciter models of the generators that are

connected to the 30-bus system and the 517-bus test system, which are the test systems

on which the simulations are carried out.

31

Figure 3-3: Block diagram of the IEEE Type-1-excitation system [21].

Figure 3-4: Block diagram of the IEEE Type-4-excitation system [21].

32

Figure 3-5: Block diagram of the solid-fed-static exciter [21].

3-3 Governor and Turbine Models Prime-mover-governing systems control the synchronous machine speed and thereby,

modulate the generated real power of the machine [2]. Prime mover provides the

mechanical energy required to drive the shaft of a synchronous machine while the

governors are used to control the speed of the shaft via the change in the gate/valve

position. A speed error signal, which is calculated by comparing the recorded speed at the

shaft to a desired value, is used to determine the new gate/valve position.

The 30-bus and the 517-bus test systems use steam-turbine-governor models and

hydro-turbine-governor models as depicted in Figures 3.6, 3.7, 3.8 and 3.9.

Figure 3-6: The IEEE-standard-turbine-governor model [21].

33

1

1 + T fs1 + T rs

rT rsc 1

1 + T gs

VAR(L)

nref

speedSPEED

+

-

+

+

R

∑

∑

g

q

X

h

q x At

x

Dturb

SPEED

+-

qNL

∑∑ ∑+ -

+

1

Velocity and position limits

g

PMECH+_

1T ws

Figure 3-7: The hydro-turbine-governor model [21].

1/R1 + sT1

∑

ReferenceVAR(L)

+

_

PMAX

PMIN = 0

1 + sFT5

(1+sT3)(1+sT4)(1+sT5)∑

High Pressure Unit(DH)(ET-HP)2

+

-

1/R1 + sT1

∑-

PMAX

PMIN=0

1 + sFT5

(1+sT3)(1+sT4)(1+sT5)

(-DH)(ET-HP)2

+_

∑PMECHLP

PMECHHP

∑

Low Pressure Unit

SPEEDLP

SPEEDHP

ReferenceVAR(L+1)

++

-

Figure 3-8: The cross-compound-turbine governor model [21].

34

Figure 3-9: The steam turbine governor model [21].

35

Chapter 4

Methodology and simulation set-up

4-1 Power System Separation Conjectures

The proposed system separation approach that is described in Chapter 1 is based on the

validity of the following three conjectures, which assume that the topology of the power

system consists of clusters of machines connected by few tie-lines [4]:

Conjecture # 1:

• The location of loss-of-synchronism (i.e. out-of-step operation) depends on the

current system topology and the prevailing power system network operating

conditions and does not depend on the location and the intensity of the initial

faults. Furthermore, under a prevailing network configuration and loading

condition, only limited out-of-step operations may take place in the system, which

may require the initiation of blocking and transfer tripping operations.

Conjecture # 2:

• The out-of-step operations take place sequentially. This means that an out-of-step

operation does not occur at multiple locations simultaneously. Furthermore, the

time interval between successive occurrences is sufficient to allow the initiation

of appropriate out-of-step blocking and transfer tripping operations.

Conjecture # 3:

• During normal operating conditions, at any given time, there are several locations

that can split the power system into separate parts connected by tie-lines with

light power flows which are the weak links of the system. Transfer tripping

36

operation can be made to these weak links in order to create islands with a

minimal load and generation imbalance, resulting in least disruption of service.

In order to verify the above conjectures, we perform simulations on two test

systems that are suitable for transient stability simulations. Furthermore, they have been

developed so that they experience transient and dynamic stability problems under a single

contingency. They will be described in the subsequent sections.

4-2 Description of the 30-bus test system

The 30-bus system includes three steam-electric plants, six hydro-electric plants and one

synchronous condenser. It is obtained after a dynamic reduction of an actual 50-bus

system [4]. The one-line diagram of this system is shown in Figure 4.1. It consists of the

interconnection of two systems operating at two voltage levels. Buses 109 and 135

through 142 operate at the 230-kV voltage level while the other buses operate at the 110-

kV voltage level. A two-winding transformer located between Buses 108 and 109 and a

three-winding transformer located between Buses 135 and 127 are interconnecting the

two sub-systems. The central transmission loop constitutes a metropolitan area where

most of the system load is concentrated. Two steam units are present near this load

center. This system serves a total load power of 650 MW.

The 30-bus system is loosely connected, which makes it more prone to stability

and uncontrolled separation problems when a severe disturbance occurs. This

characteristic makes this system suitable for the various simulations required to verify the

three conjectures stated in Section 4.1. The initial locations of out-of-step relays are

pinpointed by performing numerous simulations and by identifying the weak links in the

system using a clustering technique. The locations of the initial contingencies are

represented by cross-marks in the one-line diagram depicted in Fig. 4.1. The suspected

and monitored sites for out-of-step operation are indicated by M1, M2, M3 and M4. The

37

dynamic models used in developing the reduced 30-bus system are the round rotor

generator model (GENROU), the IEEE type-1 excitation system model (IEEEX1), the

IEEE standard governor model (IEEESGO), the steam turbine governor model (TGOV1)

and the hydro-governor model (HYGOV). Ten generators, ten exciters and ten governors

were modeled using these representations.

Figure 4.1: One line diagram of the reduced 30-bus system.

4-3 Description of the 517-bus test system

The 517-bus system consists of the interconnection of four tightly connected sub-systems

via short 500-kV and 345-kV transmission lines. It is obtained after reducing a 640-bus

system [4]. It includes 38 generators of cross-compound, tandem and combustion turbine

types. The 640-bus system serves a 22,000-MW load by means of 92 generating units

spread across 24 power plants. The latter consist of thermal stations connected to the

system via relatively short inter-tie lines.

38

Due to its inherent structure, the 517-bus system is fairly stable as compared to

the 30-bus system. It has been observed that for many major blackouts in the past such as

the 1965 Northeast Blackout, the 1997 New York Blackout, and the 2003 US-Canada

Blackout, the network separation occurred at tie lines present within the system or

between the interconnections [1], [5], and [21]. Therefore, this 517-bus system turns out

to be suitable for conducting various transient stability simulations aimed at studying the

validity of the three foregoing conjectures. It is observed that the power flows over the

tie-lines take very different magnitudes for various operating conditions of the system.

Note that the four sub-systems constituting the 517-bus are either generation rich or load

rich under different operating conditions. The turbine-generator dynamic models used for

this system are given in Table 4.2

Figure 4.2: Structure of the 517-bus system with four sub-systems connected by tie-lines.

39

Table 4.2: The 517-bus system dynamic models.

92 Generators - Round Rotor Generator Model (GENROU)

64 Exciters - IEEE Type 1 Excitation System (IEEEX1)

20 Exciters - IEEE Type 4 Excitation System (IEEEX4)

8 Exciters – Solid Fed Static Exciter (SCRX)

36 IEEE Standard Governor (IEEESGO)

36 Combustion Turbines: Governor (TGOV1)

20 Cross Compound Turbines : Governor (CRCMGV)

4-4 Description of the software programs used for conducting

the simulations

In this research work, the following software programs were used to conduct various

dynamic stability and power flow simulations: (i) the Extended Transient-Midterm

Stability Program (ETMSP), (ii) the Interactive Power Flow (IPFLOW), and (iii) the

Interactive Output Analysis Program (OAP) simulation package, all three sold by Electric

Power Research Institute (EPRI).

IPFLOW is a comprehensive power flow program that allows us to perform

steady-state calculation of a power system. This program uses the static power flow

model of a system to determine the power flows on each transmission line, the power

injection and the voltage magnitude and phase angle at every network node [22]. The

program also has a graphical user interface, making it very user friendly.

ETMSP is a state-of-the-art dynamic stability program that allows us to analyze

power system dynamics following contingencies placed in the system. Various power

system parameters can be monitored during the entire duration of the simulations. The

40

software program includes numerous models of power system devices. The program

utilizes the IPFLOW output as the base case for the calculations it performs [22].

4-5 Description of the Simulation Set-up

The simulations are carried out as follows. First, we prepare the input data files of the

30-bus and the 517-bus systems for the ETMSP and IPFLOW programs. Then, we run

various dynamic stability simulations on these two test systems by placing on each of

them three-phase faults (initial faults) with different fault clearing durations. In each

case, we sequentially execute the following three steps:

Step 1: Identify possible out-of-step operation locations by continuously monitoring the

path taken by the apparent impedance of the transmission lines;

Step 2: Identify possible out-of-step locations by monitoring the frequency response of

the generators (swing curves). These locations may be the tie-lines connecting

coherent groups of generators that swing against each others.

Step 3: Verify the independence of the out-of-step operations with respect to the location

and severity of the initial fault.

To verify the dependence of out-of-step operations on system topology and load

conditions, we modify the topology and the load levels of both the 30-bus and the 517-

bus system and repeat the above three steps. From the results obtained in Step 2, we

check whether there is any time interval between the various out-of-step operations that

occur in the system after the placements of three phase faults in the system. Then, we

verify the second conjecture, which states that out-of-step operations occur sequentially

with adequate time interval to allow transfer tripping operations. Finally, we determine

all the possible locations that can split the power system into islands that are

approximately balanced in load and generation.

41

In the subsequent sections, we will describe the clustering techniques that are

used to identify the initial out-of-step relay operations. Furthermore, we will describe the

relay and apparent impedance representations that are being used.

4-6 Data Clustering for Power System Separation

Data clustering is the process of grouping data that exhibit a certain degree of similarities.

It is a collection of techniques of statistical data analysis that can be applied in different

fields such as bioinformatics, image processing, pattern recognition, data mining, and

machine learning, to cite a few. Clustering can be grouped into two broad classes of

methods, namely, un-supervised and supervised clustering methods [23]. In Un-

Supervised clustering the clustering is done on the un-labeled samples while in the

supervised clustering the data samples are distinct. Un-supervised clustering can be

broadly classified into: (1) Hierarchical Clustering; and (2) Partitioning Clustering.

4-6-1 Hierarchical clustering

A popular class of clustering techniques that achieve un-supervised clustering consists of

hierarchical methods. These methods can be of two types, namely agglomerative or

divisive type. Figure 4.3 illustrates the principles that underline each clustering type. The

procedures of the agglomerative type start by assuming that each element in the dataset

forms a separate cluster. In the subsequent steps, the two closest (most similar) clusters

are merged when the distance (similarity) that separates them is smaller than a given

threshold [24]. The cluster merging process continues until all the elements are

encapsulated into one single cluster.

42

Figure 4.3: Agglomerative and divisive type clustering techniques

What distinguishes an agglomerative algorithm from another one is the different

distance (similarity) that each of them uses. Indeed, a distance may be defined in many

different ways; for instance, it may be defined as the shortest distance, or the farthest

distance, or the average of all the distances among every possible pair of elements

belonging to two distinct clusters, yielding different methods termed single linkage, or

complete linkage, or average linkage agglomerative clustering methods, respectively

[24]. In all cases, groups of clusters with minimum dissimilarities are merged together at

different stages of the algorithm.

A very different approach is being used by the divisive hierarchical methods.

Here, all the elements are first considered to belong to one single cluster. Then, this mega

cluster is broken down successively into smaller and smaller clusters until there is only

one element left over in each cluster.

1

2

3

4

1, 2

3, 4

1, 2, 3, 4

Agglomerative clustering

Divisive clustering

43

4-6-2 Partitioning Clustering

A popular partitioning clustering method is the k-means clustering. This method

classifies a given set of elements into a fixed number of mutually exclusive clusters, say k

clusters [24]. One of the requirements is that the clusters so formed should have at least

one element. To this end, the algorithm proceeds as follows. First, it randomly chooses k

centroids, one for each of the k clusters. Then, the remaining data elements are assigned

to their nearest centroid [23]. When no element is left over, the initial grouping of

elements is completed. Next begins an iterative process where the centroids of the

clusters are sequentially recalculated and all the clustering procedure re-executed until

the centroid locations do not change anymore.

It is clear that a good partitioning technique should form clusters that contain

elements that are very dissimilar from those belonging to the other clusters. This is done

through the execution of silhouette plots. A cluster having larger silhouette value is

considered to be well separated from the elements in the neighboring clusters.

Figure 4-4: k-means partitioning of 22 elements into 4 clusters around four centroids.

centroids centroids

44

4-5-3 Clustering Methods Applied to Power System Separation

For a given large-scale power system containing thousands of buses, a huge dataset can

be generated and grouped into different clusters of highly connected buses, which are

related to each other via few tie-lines, termed weak links of the network. From a graph-

theoretic viewpoint, these weak links are the minimal cut-sets of the network. Recall that

a minimal cut-set is defined as the minimal collection of links which, when cut, split the

graph into two disconnected sub-graphs [25]. Unfortunately, a graph-theoretic approach

suffers from two major drawbacks; it does not carry information about either the

parameters or the loading conditions of the branches of the transmission network. To

overcome these weaknesses, we may use instead the elements of the Jacobian matrix of

the system power flow model as measures of the electrical distances between buses.

In this research work, we carry out a preliminary study by using the elements of

the Z-bus matrix instead. The latter provides information about the branch parameters,

but not of the branch loading conditions. By applying clustering techniques to the Z-bus

matrix, the weak links of the network may be identified as those branches that have their

ending buses in two different clusters. These identified weak links are expected to be the

locations where out-of-step operation may occur when a disturbance affects the power

system.

4-7 Relay and Apparent Impedance Representations

In order to detect the possible out-of-step operations when a disturbance occurs in the

system, it is required to track the path taken by the apparent impedance at various bus

locations. An out-of-step operation is considered to occur when the apparent impedance

locus enters the tripping area of the relay present on the monitored transmission line. In

this thesis, the apparent impedance and relay characteristics representation have been

simplified by expressing relay tripping area and apparent impedance in per unit on the

45

basis of individual line impedance [4]. Specifically, the new apparent impedance Z0 is

expressed as

Z0 = Zi / Zij ,

where, Zi is the apparent impedance at the ith bus and Zij is the line impedance connecting

the ith bus to the jth bus. Z0 represents a position in the R0 + jX0 plane. The relay-tripping-

area boundary is formed by the line impedance, Zij, being approximately equals to Zi.

When the path taken by the apparent impedance Z0 falls below the line impedance value

of 1.0 p.u., then the relay operates and trips the line under its control. Figure 4.5 shows

the apparent impedance Z0 locus movement in the R0-X0 plane at Bus 136 for Line 136-

135 of the reduced 30-bus system depicted in Figure 4.1. This locus size increase is due

to a three-phase fault on one of the two parallel lines connecting Bus 127 to Bus 129. It

can be seen that the path taken by the apparent impedance locus that is recorded by the

out-of-step relay present on Line 136-135 varies in magnitude once the fault is cleared.

As displayed in Figure 4.5, the locus movement is towards the tripping area of the relay

represented by a circle. We observe that in this case, the apparent impedance does not

enter the tripping area of the out-of-step relay.

The process has been further simplified in Figure 4.6. Here, the magnitude of the

apparent impedance, Z0, is plotted against time for the same contingency simulation as

described above. The out-of-step relay trips if the value of Z0 falls below 1.0 p.u.. This

representation of the apparent impedance locus and relay tripping area on the basis of line

impedance helps to identify the out-of-step locations in a very simple manner.

46

Figure 4.5: Apparent impedance path of line 135-136.

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8Ro in p.u

Legend:F = Fault on Line 127-129FC = Fault ClearedR = Successful ReclosureSimulation = 1.0 sec

F = 0.1- sec

F = 0.1+ sec

FC = 0.2- sec

FC = 0.2+ sec

R = 0.45 - sec

R = 0.45+ sec

Simulation Ends 1.0 sec

Line Impedance

t = 0.75 sec

Xo in

p.u

.

47

Figure 4.6: Apparent impedance path of Line 135-136.

0

1

2

3

4

5

6

7

8

9

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time in seconds

Zo in

p.u

.

F -

F +

Relay Tripping Zone

FC -

FC +

R -R +

Simulation Ends

Legend:F =Fault on Line 127-129FC=Fault Cleares (Breakers open)R =Reclosure (Breakers close)Simulation 1.0 sec

48

Chapter 5 Simulation Results To verify the validity of the three conjectures stated in Section 4.1, simulations are

performed on the 30-bus and the 517-bus systems for different contingency scenarios.

These conjectures describe the effect of fault location, fault intensity, loading conditions

and network-configuration on the location of the out-of-step operations that may occur in

a power system.

The three conjectures are verified in the following order. First, the existence of a

time delay between the occurrences of two out-of-step operations, called cascading

effect, is demonstrated. Next, the out-of-step blocking and transfer tripping scheme is

studied; this provides the rational behind the proposed controlled separation scheme.

Finally, this scheme is applied to the 30-bus and 517-bus systems to evaluate its ability to

split a network into generation-load balanced parts.

5.1 Simulations performed on the 517-bus system

A complete description of the 517-bus system is given in Section 4.2. As depicted in

Fig. 4.2, this system is made up of four subsystems, namely, Subsystem E, F, G, and H;

the latter are connected pair-wise via Tie-Lines e-f, e-g, g-h and f-h. Various

contingency scenarios were simulated on Subsystem E while locations M1, M2, M3 and

M4 were monitored for out-of-step operations. The contingencies for which results were

recorded are described in the subsequent sections. These simulations are categorized

according to the conjectures that are being assessed.

49

5.1.1 Checking the Out-of-step Cascading Effect

Simulations were carried on the 517-bus system to verify the second conjecture, which

states that out-of-step operations occur sequentially when a disturbance is applied to the

system. The system has a power plant sited at Bus 65, which consists of a 450-MVA

generator connected to a 500-MVA step-up transformer hooked at Bus 64. The total

system load and generation are 21,630 MW and 22,100 MW, respectively. A 35-degree

phase-shifting transformer is present between Tie-Line f-h at the receiving end.

The parameters of Line 64-132 are given in Table 5.1 while those of the tie-lines

are shown Table 5.2. In Table 5.1, V is the bus voltage expressed in kV and in per unit

while the bus angle θ is given in degrees at the “from bus” end; P and Q are respectively

double-circuit line active and reactive power flows in MW and MVAR at the “from bus”

end; R, X and B are the single-circuit line resistance, reactance, and shunt susceptance,

respectively, all expressed in per unit on the 230-kV voltage basis and the 100-MVA

system basis. Table 5.2 gives the values of the tie-line power flows and of other

parameters.

Table 5.1: Parameters of Line 64-132.

V

(kV)

V

(p.u)

θ

(°)

P

(MW)

Q

(MVar)

R

(p.u.)

X

(p.u.)

B

(p.u.)

230

1.037

-4.5

122.2

15.4

0.0049

0.0304

0.0570

50

Table 5.2: Initial operating conditions for checking the cascading case.

Tie

V

(kV)

V

(p.u)

θ

(°)

P

(MW)

Q

(MVar)

R

(p.u.)

X

(p.u.)

B

(p.u.)

e-f

345

1.002

-21.7

-56.0

-51.1

0.006318

0.067500

1.15830

e-g

500

0.998

-35.0

110.6

-67.7

0.000567

0.011025

0.78300

g-h

345

1.058

-14.1

400.8

-46.9

0.006318

0.067500

1.15830

f-h

500

1.060

-2.5

-342.7

-30.4

0.000567

0.011025

0.78300

One typical simulation result is depicted in Figure 5.1. In this case, a three-phase

fault was applied adjacent to Bus 64 on one of the 230-kV double transmission lines

connecting Bus 64 to Bus 132. The fault was placed at 0.1 second and was cleared at

0.25 second. Therefore, the total fault duration lasted 9 cycles on the 60-Hz basis. The

circuit breakers on both ends of the single-circuit transmission line operated

simultaneously to open and re-close the line at 0.5 seconds. Consequently, the total

reclosing duration was 15 cycles. The resulting apparent impedance locus is displayed in

Figure 5.1. It can be seen that the apparent impedance at Bus e of Tie-Line e-f has

entered the relay tripping zone at time 0.605 second while that at Bus g of Tie-Line g-h

has entered the relay tripping zone at time 1.185 second. Consequently, there is a time

interval of 0.58 second, or approximately 35 cycles, between the two out-of-step

51

operations monitored at points M1 and M2. Therefore, we conclude that the out-of-step

operations do occur with sufficient time interval between two successive out-of-step

operations, depicting a cascading behavior. During this time interval, necessary relay

blocking and transfer-tripping operation can be performed to split the system into

disconnected parts having each a minimal load-generation imbalance.

Figure 5.1: Simulation result that illustrates the cascading effect.

0

2

4

6

8

10

12

14

16

18

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5Time in seconds

Zo in

p.u

.

Legend:

F = Fault on Line 64-132 in E-System FC = Fault Clears R = Breakers Reclose

e-f Tie trips at 0.605 sec.

e-f Tie Tripps g-h Tie trips

R

R

FC

FC

F

g-h Tie

e-f Tie

Relay Tripping Zone

g-h Tie trips at 1.185 sec. or 35 cycles later

52

5.1.2 Effect of the Initial Fault Locations on Out-of-step Operations

A series of simulations were carried out on the 517-bus system for different initial fault

locations to demonstrate the first conjecture given in Section 4.1. The latter states that

the location of the out-of-step operation is independent of the locations of the initial

faults.

Figure 5.2 depicts the results of two simulated cases. In both cases, two identical

three-phase faults were applied and the apparent impedance paths for all the four tie-lines

were monitored. In the first simulated case, a fault was placed adjacent to Bus 64 on one

of the 230-kV double-circuit transmission line connecting Bus 64 to Bus 132. In the

second simulated case, a fault was placed adjacent to Bus 47 on one of the 230-kV

double circuit transmission line connecting Bus 47 to Bus 33. To Bus 47 is connected

Power Plant #48 sited in System E. The parameter values for Lines 64 -32 and 47-33 are

shown in Table 5.1 and Table 5.3, respectively. In both simulated cases, the initial fault

was placed at time 0.1 second and cleared at 0.25 second, yielding a fault-duration of 9

cycles. The reclosing duration was 12 cycles and 15 cycles for the first and second

simulation cases, respectively.

Table 5.3: Parameters of Line 47-33.

V

(kV)

V

(p.u)

θ

(°)

P

(MW)

Q

(MVar)

R

(p.u.)

X

(p.u.)

Bs

(p.u.)

230

1.032

-6.2

344.1

108.2

0.00920

0.09800

0.04770

53

It can be seen from Figure 5.3 that the apparent impedance paths for Tie-Line g-h

enters the tripping area of the out-of-step relay at 1.30 seconds in the first simulated case

and at 1.26 seconds in the second simulated case. Therefore, it can be inferred that for

different initial fault locations with the same fault duration, it is Tie-Line g-h that is

subject to out-of-step operations [4].

Figure 5.2: Apparent impedance paths for Tie-Line g-h.

5.1.3 Effect of the Fault Intensities on the Out-of-step Operations

A series of simulations were carried out on the 517-bus system for fault intensities to

demonstrate the first conjecture given in Section 4.1. The latter states that the location of

the out-of-step operation is independent of the severity of the initial faults.

0

2

4

6

8

10

12

14

16

18

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Time in seconds

Zo in

p.u

.

Legend:F1 = Fault on Line 64-132 in E-System F2 = Fault on Line 47-33 in E-System F1C & F2C = Faults clear in 0.15 sec ( 9 cycles )R1 = Reclosure after 12 cyclesR2 = reclosure after 15 cyclesg-h Tie trips with F1 at 1.30 sec.g-h Tie tips with F2 at 1.26 sec.

Relay Tripping Zone

F1 & F2

F1C & F2C

R1

R2

g-h Tie Trips for F2

g-h Tie Trips for F1

54

Figure 5.3 displays the apparent impedance paths of two simulated cases with a

three-phase fault placed on one of the double-circuit Line 64-132 that is adjacent to

Bus 64 in the 517-bus system. The fault-clearing-time period was 9 cycles for the first

simulated case and 12 cycles for the second simulated case. In both cases, the reclosing

period for the circuit breakers was 15 cycles while the apparent impedance path for Tie-

Line e-f entered the tripping area of the out-of-step relay at 0.615 second. From

Figure 5.3, it can be inferred that the location of the out-of-step operation always occurs

on Tie-Line e-f for all simulated fault intensities, hence verifying the first conjecture.

Figure 5.3: Apparent impedance path of Tie-Line e-f for different fault intensities. 5.1.4 Effect of Out-of-step Blocking on Tie-lines A series of simulations were executed on the 517-bus system to verify the second

conjecture stated in Section 4.1. To this end, we study the impact of blocking a tripping

operation by means of out-of-step relays.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

Time in seconds

Log

(Zo)

in p

.u. o

n Li

ne's

Z

Legend:

F1 & F2 = Faults on Line 64-132 in E-System F1C = Fault Clears in 0.15 sec ( 9 cycles )F2C= Fault Clears in 0.2 sec ( 12 cycles )R1 & R2 = Reclosure after 15 cyclese-f Tie trips at 0.615 - sec.e-f Tie trips at 0.615+ sec.

F1 & F2

F1C F2C

R1 R2

Zone

55

Figure 5.4 illustrates this impact on Tie-Line e-f. Here, the initial operating

conditions together with the initial fault location are the same as those of the contingency

case described in Figure 5.1. In Figure 5.4, we observe that Tie-Line e-f trips at time

0.605 second while Tie-Line g-h trips at time 1.185 seconds since at these times, the

apparent impedance locus enters the relay tripping area. In the simulated cases, the out-

of-step relay on Tie-Line e-f tie is armed. This relay recognizes the out-of-step operation

and blocks the relay from tripping Tie-Line e-f. Subsequent to the out-of-step blocking

operation, the out-of-step relay located on Tie-Line g-h, which is not armed, trips Tie-

Line g-h at time 1.26 seconds.

Figure 5.4: Impact on Tie-Line g-h of blocking the out-of-step relay of Tie-Line e-f.

0

2

4

6

8

10

12

14

16

18

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Time in seconds

Zo in

p.u

.

Legend:F = Fault on Line 64-132 in E-System FC = Fault ClearsR = Reclosuree-f Tie trips at 0.615 sec.g-h Tie trips at 1.260 sec. or 40 cycles later

e-f Tie is Blocked

g-h Tie Allowed to Trips

F

FC

FC

R

R

Relay Tripping Zone

56

5.1.5 Impact of Changes in the Loading Conditions A series of simulations were carried out on the 517-bus system to demonstrate that the

location of out-of-step operation depends on system loading conditions. To this end,

these simulations were performed under peak load and light load operating conditions

without altering the network configuration and without changing the number of operating

generators in the system. The total system load was 21,630 MW for the peak-load case

and 17,300 MW for the light-load case. A total of 38 generators were operating to

provide 22,100 MW and 17,640 MW in the first and second case, respectively. Table 5.2

and Table 5.4 give the initial operating conditions for the tie-lines for both cases. From

Figure 5.5, it can be inferred that Tie-Line g-h trips at time 1.26 seconds when the system

was operating under the peak-load condition and it does not trip under the light-load

operating condition. These results clearly demonstrate that the location of out-of-step

operation depends on system loading conditions.

Figure 5.5: Light Load and Peak load case results (38 generators in operation)

0 2 4

6 8

10 12

14 16 18 20

22 24

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Time in seconds

Zo in

p.u

.

F

FC

R

Peak-Load

Light-Load

g-h Tie Trips

g-h Tie Doesn't Trip

Legend:F = Fault on Line 64-132 in E-System FC = Fault ClearedR = breakers ReclosedUnder Peak-Load, g-h Tie Trips at 1.260 sec.Under Light-Load, g-h Tie Doesn't Trip

Relay Tripping Zone

57

Table 5.4: Initial operating conditions for the light-load case

Tie

V

(kV)

V

(p.u)

θ

(°)

P

(MW)

Q

(MVar)

e-f

345

1.072

-12.4

-192.7

-35.4

e-g

500

1.071

-22.7

172.8

-73.6

g-h

345

1.102

-8.3

165.6

-45.8

f-h

500

1.102

8.3

-188.4

-54.1

5.1.6 Impact of the Changes in Network Configuration The impact of changes in network configuration on the location of out-of-step operation

was studied by executing few simulations. Figure 5.6 shows the results obtained for two

different simulated cases. In these cases, the network configuration is different. In the

first case, 38 generators producing 17,640 MW are serving a total system load of

17,300 MW. The initial operating conditions for the first case are similar to those of the

light-load case shown in Table 5.4. Both the total system load and power generation are

reduced by 20% when compared to the peak-load case of Section 5.1.5. In the second

simulated case, the total number of generators present in the network is reduced to 24.

The initial operating conditions of the tie-lines for this case are shown in Table 5.5. The

58

steam units along with the combustion units present in the system have been shut down

but the total load and power generation are kept to the same level as those of the first

case.

It can be observed from Figure 5.6 that the apparent impedance locus recorded for

Tie-Line e-f for the simulated case with 38 generators is quite different from the second

case with 24 generators. In the second case, the apparent impedance path enters the

tripping area of the relay while in the first case, it does not. Consequently, we infer that

the location of out-of-step operation depends on the network and/or generation

configuration.

Table 5.5: Initial operating conditions for the reduced network

Tie

V

(kV)

V

(p.u)

θ

(°)

P

(MW)

Q

(MVar)

e-f

345

1.061

-8.9

-280.8

-6.1

e-g

500

1.068

-11.9

40.8

-68.7

g-h

345

1.198

-4.4

85.0

-33.6

f-h

500

1.193

15.2

-168.

-57.2

59

Figure 5.6: Apparent impedance path for the two network configurations. 5.1.7 Impact of Out-of-step Blocking and Tripping Operations Figures 5.7 and 5.8 display the results of the simulations that are executed to illustrate

out-of-step blocking and transfer tripping schemes. In this simulation, the total generation

capacity of the E-system and G-system of the 517-bus test system is 10% more than those

of Systems F and H. The initial operating condition for this simulation case is shown in

Table 5.6. In this simulation case, the initial three-phase fault is placed on one of the

double-circuit lines present that are adjacent to Bus 64 for a period of 9 cycles. From the

results obtained in the earlier sections, we can infer that Tie-Line e-f trips at around 0.6

second followed by Tie-Line g-h, which trips around 1.185 seconds or 35 cycles later.

Consequently, the system splits into two unbalanced parts. Therefore, in order to avoid

such system separation, the out-of-step tripping and blocking scheme is initiated.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time in seconds

Log(

Zo) i

n p.

u.

Legend:F = Faults on Line 64-132 in E-SystemFC = Faults ClearedR = Breakers Reclosede-f Tie Under Light-Load Condition with 38 Generators.e-f Tie Under Same Load Condition but with 24 generators

38 GeneratorsLight-Load

24 GeneratorsSame Load

F

FC

Relay Tripping Zone

R

60

As shown in Figures 5.7 and 5.8, the tripping of Tie-Line e-f is blocked while the

tripping is transferred to out-of-step relays located on Tie-Lines e-g and f-h. Because Tie-

Line g-h does not trip, the 517-bus system separates into two balanced parts.

The simulation results displayed in Tables 5.7, 5.8 and 5.9 are those obtained by

applying on the 517-bus system of the contingency scenarios that are described in

Sections 5.1.2, 5.1.3, and 5.1.5, respectively. These simulations demonstrate the validity

of the three conjectures stated in Section 4.1, which are related to the impact on out-of-

step operations of the fault location, fault intensity, and the network loading levels.

Figure 5.7: Apparent impedance locus of Tie-Line e-f (blocked) and Tie-Line g-h.

0

5

10

15

20

25

30

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Time in seconds

Zo in

p.u

.

Legend:F = Faults on Line 64-132 in E-System FC = Faults ClearedR = Breakers Reclosede-f Tie Blocked 0.6 sec.g-h Tie doesn't trip.

The effect of f-h & e-g Ties tripping

on g-h Tie

F

FC

FC R

R

e-f Tie

g-h Tie

Relay Tripping Zone

Blocked

61

Figure 5.8: The transfer tripping operation performed on Tie-Lines f-h and e-g.

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time in seconds

Log

(Zo)

in p

.u.

Legend:F = Fault on Line 64-132 in E-SystemFC = Fault Clears (Breakers Open)R = Breakers Reclosee-f Tie Blocked and e-g Tie Opens at 0.6 sec. e-f Tie Blocked and f-h Tie also opens at 0.6 sec. g-h Tie Does'n Trip

e-g Tie Tripsat 0.6 sec

f-h Tie Tripsat 0.6 sec.

F1 & F2

F1C & F2C

R1

R2

62

Table 5-6: Initial operating conditions for the out-of-step blocking

and transfer tripping simulation case.

Tie

V

(kV)

V

(p.u)

θ

(°)

P

(MW)

Q

(MVar)

e-f

345

0.997

-25.9

133.0

-70.8

e-g

500

0.957

-38.5

426.7

-46.6

g-h

345

1.055

-12.7

229.2

-31.7

f-h

500

1.067

-20.0

-144.3

-47.4

63

Table 5-7: Simulation results obtained using different initial fault locations. Beginning

of

Simulation

Initial

Fault

Location

Fault

Clearing

Circuit-

breaker

Reclosing

Tie-line

Tripping

End

of

Simulation

Cycles on

the

60-Hz basis

0

6

15

30

37

90

Z0 in p.u.

of

Tie-Line e-f

23.9

16.6

2.0

1.3

1.0

0.7

Cycles on

the

60-Hz basis

0

6

15

27

35

90

Z0 in p.u.

of

Tie-Line e-f

23.9

16.6

1.2

1.4

1.0

0.8

64

Table 5-8: Simulation results obtained using different initial fault intensities. Beginning

of

Simulation

Initial

Fault

Location

Fault

Clearing

Circuit-

breaker

Reclosing

Tie-line

Tripping

End

of

Simulation

Cycles on

the

60-Hz basis

0

6

15

21

76

90

Z0 in p.u.

of

Tie-Line g-h

16.2

12.6

10.5

14.3

1.0

0.8

Cycles on

the

60-Hz basis

0

6

18

21

71

90

Z0 in p.u.

of

Tie-Line g-h

15.9

12.6

10.0

16.4

1.0

0.5

65

Table 5-9: Simulation results obtained using different load levels. Beginning

of

Simulation

Initial

Fault

Location

Fault

Clearing

Circuit-

breaker

Reclosing

Tie-line

Tripping

End

of

Simulation

Cycles on

the

60-Hz basis

0

6

15

21

76

90

Z0 in p.u.

of

Tie-Line e-f

16.2

12.6

10.5

14.3

1.0

0.8

Cycles on

the

60-Hz basis

0

6

15

21

60

90

Z0 in p.u.

of

Tie-Line e-f

11.5

11.2

7.5

9.7

1.0

7

66

5.2 Simulations Performed on the 30-bus System

A series of dynamic stability simulations were carried out on the reduced 30-bus system,

which is displayed in Figure 4.1. In this figures, cross-marks indicate the locations where

the initial three-phase faults were placed. Out-of-step operations were monitored on

points M1, M2, M3 and M4.

Figure 5.9 displays the swing curves of several generating plants after placing a

three-phase fault on one of the parallel lines connecting Bus 139 to Bus 140. In this

simulation, the initial three-phase fault was placed on the system at 0.1 seconds. The fault

was cleared at 0.2 seconds by the opening of the circuit-breakers located on both ends of

the faulted Line 139-140. The line was renergized by reclosing the circuit-breakers at

0.5 seconds. It can be seen that two generating units, namely Gen-138-Hydro and Gen-

142-Hydro, had high accelerating speeds with respect to the others. This led to the

splitting of the system at Line 136-135, resulting in the formation of unbalanced load-

generation islands.

Figure 5-9: Transient stability swing curves obtained on the reduced 30-bus system.

0

50

100

150

200

250

300

350

400

450

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Time in seconds

Ang

ular

Pos

ition

- D

egre

es Fault adjacent to Bus 139 on oneof two parallel lines to Bus 140,Showing two coherent Groups

Successful Reclosure

Breakers Open

Fault

Gen 142, Hydro

Gen 138, Hydro

Gen 132, Steam Gen 101, Steam

Gen 124, Hydro

Gen 144, Hydro

67

5.3 Weak Link Identification of a Network Using a Clustering Method

Numerous simulations were performed on the 30-bus system to identify the clusters of its

network and thereby, to pinpoint the links connecting them, termed weak links. To this

end, a k-means clustering technique was applied to the Z-bus impedance matrix of this

system. This matrix is obtained by taking the inverse of the symmetric admittance Y-bus

matrix. This clustering method was executed by using the clustering toolbox of

MATLAB®.

Silhouette value was recorded for every simulation case to verify the

characteristic of the grouping that has been performed. A cluster having a silhouette value

closer to 1.0 unit is considered to enclose objects that exhibit a high degree of

similarities. After the clusters have been formed, the transmission lines connecting buses

that belong to two different clusters are the weak links of the network. When heavily

loaded, these weak links are anticipated to be the locations where out-of-step operation

may occur following a major disturbance on the system.

Figure 5.10 depicts the simulation results. We observe that eleven clusters are

formed. The mean silhouette value for the eleven clusters formed is 0.82, which is quite

high. Consequently, the weak links are the 11 branches connecting these clusters,

namely, Line 102-108, Line 108-112, Line 135 – 109, Line 136-135, Line 136-139, Line

120-123, Line 115-146, Transformer 144-145, Transformer 143-145, Transformer 148-

149 and Transformer 134-133.

68

s

H

H C S

S

H

H

HH

136M2

M1

M3

M4

101 102

136137

139 140

141142

135

133

134

127

129

128

120 118

123 124

115112

132

143

144145

146149148

109

108

Figure 5-10: Eleven clusters identified on the 30-bus system using k-means clustering

with mean silhouette value of 0.82.

69

Chapter 6

Conclusions

To decrease the risk of large-scale blackouts, appropriate control actions may be taken on

a power system when it undergoes a major disturbance. Few recognized control actions

are load shedding, generation curtailment, and controlled separation, to cite a few. In this

research work we have developed a new method aimed at performing controlled system

separation using current technologies. Here, a power system is split into islands having

minimal load-generation imbalance.

The proposed approach is based on three conjectures, which are stated and their

validity verified through extensive simulations performed on a 30-bus and a 517-bus

system. On these two test systems, it was verified the following two statements: (i) the

location of out-of-step operations is independent of the location and severity of the initial

fault; (ii) there is sufficient time gap between two out-of-step operations for initiating an

appropriate out-of-step blocking and tripping scheme.

The simulation results revealed that the location of out-of-step operation is highly

system specific and very much dependent on the prevailing system operating conditions.

Therefore, the determination of the out-of-step locations is a critical step to implement

the proposed method to any given power system. The study also revealed that it is

necessary that a power transmission network contains clusters of tightly connected buses

connected via few weak links. These weak interconnections can be identified by a

clustering method or past system experience. When these weak links are heavily loaded,

it is likely that they become the sites of out-of-step operation should the system

undergoes a major disturbance.

As a future work, more robust and effective methods for identifying the weak

links of a power transmission network should be developed. These methods may be

based on clustering techniques [23] applied to the Jacobian matrix of the dynamic model

70

of a power system. Here, both the synchronous machine model and the transmission

network model should be derived and linearized around an appropriate operating point.

71

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