3203949 . robust decentralized controller design via ai to enhance power system dynamic performance

8/13/2019 3203949 . Robust Decentralized Controller Design via Ai to Enhance Power System Dynamic Performance

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Zagazig University

Faculty of Engineering

Electrical Power and Machines Department

ROBUST DECENTRALIZED CONTROLLER

DESIGN VIA AI TO ENHANCE POWER

SYSTEM DYNAMIC PERFORMANCE

Prepared by

EHAB SALIM ALI MOHAMMED SALAMA

M.Sc. & B.Sc. in Electrical Engineering, Faculty of

Engineering ,Zagazig University

A Thesis

Submitted to the Faculty of Engineering in Partial Fulfillment of the

Requirements For The Degree of Doctor of Philosophy (Ph.D.) in

Electrical Engineering

Supervised By:

Prof. Dr. M. E.Mandour Prof. Dr. Z. S. El-RazazProf. of Electrical power Prof. of Electrical power

Zagazig university Zagazig university

2006


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Zagazig University

Faculty of Engineering

Electric Power and Machines Department

ROBUST DECENTRALIZED CONTROLLER DESIGN

VIA AI TO ENHANCE POWER SYSTEM DYNAMIC

PERFORMANCE

Prepared by

EHAB SALIM ALI MOHAMMED SALAMA

A Thesis Submitted in Partial Fulfillment of the Requirements for the

Degree of Ph.D. in Electrical Engineering.

Approved by the examining committee

Prof. Dr. M. M. El-Metwally

Prof. Dr. F. M. A. Bendary

Prof. Dr. M. E. Mandour

Prof. Dr. Z. S. El-Razaz

2006


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Acknowledgement

First of all, I would like to express all thanks to God and I look forward for hisassistance.

My deep appreciation goes to Prof Dr. M. E. Mandour and Prof. Dr. Z. S. El-

Razaz for their valuable guidance, suggestions, continuous encouragement during the

progress of this work Moreover, my thanks go to the staff of the electrical power and

machines department.

My special thanks are for my mother for her prayers for me, which were a greathelp to me to complete this work. And I am really grateful to my wife for her great

help and co-operation.

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ABSTRACT

Power systems are modeled as large-scale systems composed of a set of small-

interconnected subsystems. It is generally impossible to incorporate many feed back

loops into the controller design for large scale interconnected systems and is also too

costly even if they can be implemented. These motivate the development of

decentralized control theory where each subsystem is controlled independently on its

local available information.

On the other hand, the operating conditions of power systems are always varying to

satisfy different load demands. Control systems are therefore required to have the

ability to damp the system oscillations that might threaten the system stability as the

load demand increases. However, as power systems are large-scale nonlinear systems

in nature, the applications of conventional power system stabilizer (PSS) are limited.

There is thus a need for controllers, which are robust to changes in the system

operating condition. Robust controllers based on control theory are particularly

suited for this purpose.

H

This thesis proposes two robust decentralized controllers for multimachine power

system instead of using a complex centralized controller. The first one is based on

theory, and results in high order controller. The second controller is a

proportional integral (PI) type, and is tuned by a novel robust performance as the first

one, but it is more appealing from an implementation point of view. In more detail,

the second control design is first cast into the robust

H

H control design in terms of

linear matrix inequalities (LMI) in order to obtain robustness against system operating

conditions. An additional constraint is that the structure of the controller is predefined

as a PI type, which is ideally practical for industry. In order to obtain the optimal

controller parameters with regards to the

H and controller structure constraints,

genetic algorithms (GAs), a powerful probabilistic search technique is used to find the

control parameters of the PI controller.

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To treat the problem of possible adverse interaction between multiple decentralized

controllers, three global control strategies are introduced in this thesis. The first,

which is a multi-input multi-output (MIMO) centralized with effective

communicated information. The second is the reduced centralized based on the

balanced truncation method. While the third is based on two level PSS. The

simulation results show that the proposed controllers ensure adequate damping for

widely varying system-operating conditions.

H

H

III


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Abbreviations

AI Artificial Intelligence

ANN Artificial Neural Network

ASVC Advanced Static Var Compensator

FACTS Flexible AC Transmission System

GA Genetic Algorithms

LFC Load Frequency Control

OC Optimal Control

PI Proportional Integral Controller

PID Proportional Integral Differential Controller

PSO Particle Swarm Optimization

PSS Power System Stabilizer

LMI Linear Matrix Inequalities

LQ Linear Quadratic

SA Simulated Annealing

SAPSS Simulated Annealing Based Power System Stabilizer

SMIB Single Machine Infinite Bus

SSV Structure Singular Values

STATCOM Static Compensator

SVC Static Var Compensator

TCSC Thyristor Controlled Series Capacitor

TS Tabu Search

UPFC Unified Power Flow Controller

Vref Reference Voltage

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List of Symbols

Angular speed.

The deviation from nominal values.

V Infinite bus voltage.

tV Generator terminal voltage.

ejX

eR + Transmission line resistance and inductance.

fdE Exciter voltage.

aT

aK , Gain and time constant of the excitation system.

fT

fK ,

Gain and time constant of the field system.

mT Mechanical input torque.

eT Electrical torque.

dI ,

qI d-and q-axis terminal current respectively.

Ido, Iqo d -and q-axis nominal current respectively.

j Inertia coefficient, H

j2= .

VqoVdo, The nominal voltage in d and q axes in p.u.

qE' Internal voltage behind in p.u.d

X'

qoE Q axis voltage.

Torque angle in rad.

do` Time constant of excitation system in sec.

B Rated angular speed.

dX ,

qX d-and q-axis reactance of the generator respectively.

'dX The d- axis transient reactance of the generator.

H Inertia constant.

DQ A state weighting matrix.

DR A control weighting matrix.

K Controller.

DCBA ,,, The state space equation.

V


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rD

rC

rB

rA ,,, The state space equation of reduced-order model.

kD

kCB

kA k ,,, The state space equation of controller.

clD

clC

clB

clA ,,, The state space equation of closed loop system.

CA = coupling block matrix A.ijA

DA = decoupling block matrix A.iiA

C

B = coupling block matrix B.ijB

D

B = decoupling block matrix B.iiB

CC = coupling block matrix C.ijC

DC = decoupling block matrix C.iiC

lu Local control signal.

gu

Global control signal.

tx )( Denote the state vector.

tW )( The vector of input disturbance.

tu )( The vector of control input.

ty )( The vector of measured variables.

tZ )( The vector of error signals.

)(sZWT The closed loop transfer matrix from the disturbance W to the

regulator output Z.

(gopt) The norm of the transfer function .)(sZWT

ST ,

dT The change in the synchronizing and damping torque

component respectively.

s

K ,

d

K The synchronizing and damping torque coefficient respectively.

Kp, Ki PI controller gains.

wT Washout time constant.

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Contents

Contents

page

Acknowledgment

Abstract

Abbreviations

List of Symbols

Contents

List of Figures

List of Tables

I

II

IV

V

VII

X

XIV

Chapter 1 Introduction

1.1 Power System and Robust Control Technique. 1

1.2 Power System Modes of Oscillation. 2

1.3 Power System Stabilizers. 3

1.4 Decentralized Control. 4

1.5 Conflict Between Centralized and Decentralized

Controller in PSS Design.

6

1.6 Thesis Objectives. 7

1.7 Outline of The Thesis. 8

Chapter 2 Review of Literature

2.1 Introduction. 11

2.2 Previous Work. 11

2.3 Contributions of This Thesis. 24

Chapter 3 Modeling of Power Systems


3.2 System Equations. 26

3.3 Block Diagram Simulation. 28

3.4 State Space Formulation. 32

3.5 Formulation of The System Model. 35

3.6 System Under Study. 393.7 State Space Equations. 42

VII


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Contents

Chapter 4 Centralized and Decentralized Controllers


4.2 Large Scale Controllers. 46

4.3 System Representation. 48

4.3.1 State and Output Feedback 49

4.4 Design of The Optimal Decentralized Controller. 50

4.5 Design of The Sub optimal Decentralized Controller. 52

4.6

H Robust Controller. 53

4.6.1 Linear Matrix Inequality (LMI). 56

4.6.2 Robust

H Control Design Via LMI. 58

4.7 Robust Controller Design Via Reduced Order Model. 60

4.8 Limitations and Shortcomes of Previous Mentioned

Controllers.

62

4.9 Proposed Robust Control Design Via GALMI. 63

4.9.1 An Overview of Genetic Algorithms. 64

4.9.2 An Overview of Particle Swarm Optimization. 66

4.10 Global Controller Design. 68

4.11 Proposed Two Level PSS Controller Design. 71

Chapter 5 Robust Controller Design for Single Machine Infinite

Bus


5.2 Dynamic Model of SMIB. 73

5.3 Implementation of

H Controller. 76

5.4 Balanced Truncation

H Controller Implementation. 78

5.5 Implementation of GALMI Controller. 85

5.6 Recommendation for Multimachine System 93

Chapter 6 Robust Decentralized Controller Design for

Multimachine System


6.2 Evaluation of Multimachine System. 96

6.2.1 System Modes Classification. 96

6.2.2 Block Diagram Simulation of Multimachine

System.

98

6.2.3 Response of The System Without Controller. 100

6.2.4 Effect of Loading on System Dynamic. 101

VIII


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Contents

6.3 Implementation of Optimal Controller. 102

6.4 Implementation of Sub optimal Controller. 107

6.5 Fixed Modes Problem Formulation. 111

6.6 Centralized and Decentralized Controller Design Via.

H

113

6.7 Dynamic Model of Multimachine System 120

6.8 Simulation and Evaluation of GALMI 122

6.9 Implementationof Global Controller 125

6.10 Implementation of The Proposed Two Level Controller 131

6.11 System Performance With Two Subsequence

Disturbances

135

Chapter 7 Conclusions and Recommendations

7.1 Conclusions of This Thesis. 137

7.2 Recommendations for Future Work. 138

References 140

Appendix A 147

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List of Figures

List of Figures

Chapter 1 IntroductionFigure (1.1) Block diagram of PSS. 3

Figure (1.2) Schematic diagram of centralized controller. 5

Figure (1.3) Schematic diagram of decentralized controller. 6

Chapter 2 Review of literature


Figure (3.1) Machine-infinite bus. 26

Figure (3.2) The block diagram of a single machine adopted to

be used in Simulink Toolbox.

31

Figure (3.3) Conversion from machine axes to common frame

axes.

35

Figure (3.4) Block diagram representation of a single machine

connected to the network.

39

Figure (3.5) System under study. 40

Figure (3.6) Matrix Q1. 42

Figure (3.7) Matrix Q2. 43

Figure (3.8) Matrix A0. 44

Figure (3.9) Matrix Gxs. 45

Chapter 4 Decentralized and Centralized Controllers

Figure (4.1) Flow chart of the controllers 47

Figure (4.2) Generalized block diagram of

H . 54

Figure (4.3) Flow chart of the GA optimization 65

Figure (4.4) Flow chart of the PSO optimization 67

Figure (4.5) Flow chart of the local and global controller 70

Figure (4.6) Proposed two level PSS design 72

Chapter 5 Robust Controller Design for Single Machine

Infinite Bus

Figure (5.1) Response of for 0.1 p.u step in Vref for testedoperating point

77

Figure (5.2) Response of for 0.1 p.u step in Vref for tested

operating point.

78

Figure (5.3) Response of for 0.1 p.u step in Vref for first

operating point

80


operating point

80

Figure (5.5) Change in control signal for 0.1 p.u step in Vref 81

Figure (5.6) Bode plot of the transfer function for first

operating point.

82

X


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List of Figures

Figure (5.7) Response of for 0.1 p.u step in Vref for

second operating point.

83


second operating point.

83

Figure (5.9) Response of for 0.1 p.u step in Tm for second

operating point.

84


operating condition

85

Figure (5.11) change in control signal for 0.1 p.u step in Vref 86

Figure (5.12) Variations of objective function 87

Figure (5.13) Variations of Kp 87

Figure (5.14) Variations of Ki 88

Figure (5.15) Response of for different values of (gopt)

for P=1.0, Q=0.4

90


second operating condition.

91

Figure (5.17) Response of for 0.1 p.u step in Tm for second

operating condition.

92

Figure (5.18) Bode plot of the transfer function. 92

Chapter 6 Robust Decentralized Controller Design For

Multimachine System

Figure (6.1) System under study. 96Figure (6.2) The block diagram of the system under study. 99

Figure (6.3) Response of12

to 0.1 p.u step in Vref. 100

Figure (6.4) Response of to 0.1 p.u step in Vref.12

100

Figure (6.5) Open loop poles (mechanical modes) for the 9

bus, 3 machine system.

102


w for 0.1 step in Vref of Gen. (1) 106




for 0.1 step in Vref of Gen. (1) 110



Figure (6.10a) Schematic of centralized output feedback

controller.

114

Figure (6.10b) Schematic of decentralized output feedback

controller.

114

XI


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List of Figures

Figure (6.11) The response of12

w for light load condition. 115


w for light load condition. 115

Figure (6.13) The response of

12

w fornormal load condition. 116


w fornormal load condition. 117


w for heavy load condition. 119


w for heavy load condition. 120


for light load condition with

three PI local decentralized controllers.

123

Figure (6.18) Response of 12 for normal load condition with


124


w for heavy load condition with


125


for light load condition due to

different robust global controllers.

126


w for light load condition due to


127


for normal load condition due

to different robust global controller.

128


w for normal load condition due

to different robust global controllers.

128


for heavy load condition due to


130


w for heavy load condition due to


131

Figure (6.26) Region in the left hand side of a vertical line 131

Figure (6.27) Comparison of13

response for normal load

condition with different robust damping global

controllers.

132

Figure (6.28) Comparison of12w response for normal load

condition with different robust damping globalcontrollers.

133

XII


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List of Figures


w response for heavy load


controllers.

134


w response for heavy


controllers.

134

Figure (6.31) Response of12w under two subsequence

disturbances.

135


w under two subsequence

disturbances.

136

XIII


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List of Tables

List of Tables




Table (3.1) Bus data for the base case (Load flow) on the 100

MVA Base.

40

Table (3.2) Transmission lines and transformer data all values

are in p.u. on 100 MVA base.

41

Table (3.3) Generator data: Reactance values are in pu on a

100-MVA base.

41

Chapter 4 Decentralized and Centralized Controllers

Chapter 5 Robust Controller Design for Single Machine

Infinite Bus

Table (5.1) Eigenvalues of closed loop system with different

controllers.

79

Table (5.2) Comparison between three controllers for first

operating point

89

Table (5.3) Comparison between GA and PSO. 89

Chapter 6 Robust Decentralized Controller Design For

Multimachine System

Table (6.1) A part of the participation matrix corresponding to

the mechanical modes.

97

Table (6.2) System modes after classification. 97

Table (6.3) The eigenvalues, and frequencies associated with

the rotor oscillation modes of the system.

98

Table (6.4) Loading conditions for the 9 bus, 3 machine

system ( in p.u).

101

Table (6.5) Open loop eigenvalues of the rotor oscillation

modes of the system.

102

Table (6.6) System modes with optimal decentralized

controller and centralized one.

105

Table (6.7) The eigenvalues, and damping ratios associated

with the rotor oscillation modes of the system for

both controllers.

105

Table (6.8) System modes with sub optimal decentralized and

centralized controller.

109

Table (6.9) The eigenvalues, and damping ratios associated

with the rotor oscillation modes of the system for

both controllers.

109

Table (6.10) System modes with variable controller. 112

XIV


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List of Tables

Table (6.11) Eigenvalues of closed loop system with

centralized and decentralized controllers for 1.0

p.u (normal load).

118

Table (6.12) Eigenvalues of closed loop system for different

operating conditions with three GALMI

controllers.

123

Table (6.13) Eigenvalues of closed loop system with global and

reduced global controller for 1.00 p.u (normal

load).

129

XV


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Chapter 1

Introduction

1.1 Power System and Robust Control Technique

Power systems are usually large nonlinear systems, which are often subject to low

frequency oscillations when working under some adverse loading conditions. The

oscillation may sustain and grow to cause system separation if no adequate damping

is available. To enhance system damping, the generators are equipped with power

system stabilizers (PSSs) that provide supplementary feedback stabilizing signals in

the excitation systems. PSSs enhance the power system stability limit by improving

the system damping of low frequency oscillations associated with the

electromechanical modes. Many approaches are available for PSS design, most of

which are based either on classical control methods or on intelligent control strategies.

Power systems continually undergo changes in the operating condition due to changes

in the loads, generation, and in the transmission network resulting in accompanying

changes in the system dynamics. A well-designed stabilizer has to perform

satisfactorily in the presence of such variations in the system. In other words, the

stabilizer should be robust to changes in the system over its entire operating range.

The nonlinear differential equations, which simulate the behavior of a power system,

can be linearized at a particular operating point to obtain a linear model, which

represents the small signal oscillatory response of the power system. Any variation in

the operating condition of the system may cause a variation in the system model. For

a different variation in the operating conditions of a particular system a set of a linear

models, each corresponding to one particular operating condition may be generated.

Since, at any given instant, the actual plant could correspond to any model in this set,

a robust controller would have to impart adequate damping to each one of these entire

sets of linear models.

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Robust control technique has been applied to power system controller design since

1980s. The main advantage of this technique is that it presents a natural tool for

successfully modeling plant variations. Several studies, which will be mentioned in

previous work, have been devoted to the design of power system controllers for PSS

and/or FACTS devices using

H . In these studies, many classical control

objectives such as disturbance attenuation, robust stabilization of power systems are

expressed in terms of performance and tackled by

H

Hsynthesis techniques.

The control problem is to find a controller that minimizes

H where

= )(sZWT and represents the norm of the transfer function of the output (Z)

to the disturbance (W). In other words, minimize the energy of the output signals (Z)

for a given set of exogenous signals (W). All these studies produce a controller, which

is robust. These controllers provide added damping to the system under a wide

range of operating conditions.

1.2 Power System Modes of Oscillation

An electrical power system consists of many individual elements connected together

to form a large, complex system capable of generating, transmitting and distributing

electrical energy over a large geographical area. Due to these interconnections of

elements, a large variety of dynamic interactions are possible to done which may

affect on the system.

The stability problem involves the study of the electromechanical oscillations inherent

in power systems [1]. Power systems exhibit various modes of oscillation due to

interactions among system components. Power systems usually have two distinct

forms of oscillations.

1- Local modes are associated with the swinging of units at a generating station

with respect to the rest of the power system. The term local is used because the

oscillations are localized at one station or a small part of the power system.

Typical local-mode frequency range from 0.8-2.0 Hz.

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2- Inter-area modes are associated with the swinging of many machines in one

part of the system against machines in other parts. They are caused by two or

more groups of closely coupled machines being interconnected by weak ties.

Typically have a frequency in the range from 0.1-0.8 Hz.

Undamped oscillations once started often grow in magnitude over the span of many

seconds. Sustained oscillations in the power system are undesirable for many reasons.

They can lead to fatigue of machine shafts, cause excessive wear of mechanical

actuators of machine controllers and also make system operation more difficult. It is

therefore desirable that oscillations are well damped. So PSS is necessary to provide

appropriate damping of undesirable oscillations caused by disturbances.

1.3 Power System Stabilizers

The basic function of a power system stabilizer is to extend the stability limits by

adding damping to generator rotor oscillations by controlling its excitation using

auxiliary stabilizing signal(s). To provide damping, the stabilizer must produce a

component of electric torque, which is in phase with rotor speed deviations. The

oscillations of concern typically occur in the frequency range of approximately 0.1 to

2.0 Hz, and insufficient damping of these oscillations may limit the ability to transmit

the power. The block diagram used in industry is shown in Figure (1.1). It consists of

a washout circuit, phase compensator (lead-lag circuit), stabilizer gain and limiter [2].

Figure (1.1) Block diagram of PSS

KSTAB

Stabilizer gain Washout Lead-Lagumax

umin

usTw

1+sTw

1+sT11+sT2

1+sT31+sT4

Lead-Lag

The phase compensation block provides the appropriate phase lead characteristic to

compensate for the phase lag between the exciter input and generator electrical

torque. The required phase lead can be obtained by choosing the values of time

constants .41,....,TT

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The signal washout block serves as a high pass filter, with the time constant high

enough to allow signals associated with oscillations in speed to pass as it. Without it,

steady changes in speed would modify the terminal voltage. It allows the PSS to

respond only for a change in the speed. From the viewpoint of the washout function,

the value of is not critical and may be in the range of 1 to 20 seconds.

WT

WT

The stabilizer gain determines the amount of damping introduced by PSS.

Ideally the gain should be set at a value corresponding to maximum damping.

However, in practice the gain is set to a value that results in satisfactory damping of

the critical system modes without compromising the stability of other modes.

STABK

In order to restrict the level of generator terminal voltage fluctuation during transient

conditions, limits are imposed on PSS outputs.

1.4 Decentralized Control

The complexity and high performance requirements of present day industrial

processes place increasing demands on control technology. The orthodox concept of

driving a large system by a central controller has become unattractive for either

economic or reliability reason. New emerging notions are subsystems,

interconnections, parallel processing, and information constraints, to mention a few.

In complex system, where databases are developed around the plants with distributed

sources of data, a need for fast control action in response to local inputs and

perturbations dictates the use of distributed (that is, decentralized ) information and

control structures.

The accumulated experience in controlling complex system suggests three basic

reasons for using decentralized control structures:

1- dimensionality ,

2- information structure constraints, and

3- uncertainty.

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Because the amount of computation required to analyze and control a large-scale

system grows faster than its size, it is beneficial to decompose the system into

subsystems, and design controls for each subsystem independently based on local

subsystem dynamics and its interconnections. In this way, special structure features

of a system can be used to devise feasible and efficient decentralized strategies for

solving large control problems previously impractical to solve by one shot

centralized methods.

A restriction on what and where the information is delivered in a system is a standard

feature of interconnected systems. For example, the standard automatic generation

control in power system is decentralized because of the cost of excessive information

requirements imposed by a centralized control strategy over distant geographic areas.

The structure constraints on information make the centralized methods for control and

estimation design difficult to apply, even to systems with small dimensions.

It is a common assumption that neither the internal nor the external nature of complex

systems can be known precisly in deterministic or stochastic terms. Decentralized

control strategies are inherently robust with respect to a wide variety of structure and

unstructured perturbations in complex systems[3].

Figures (1.2-1.3) represent a schematic diagram of centralized and decentralized

controller respectively.

K

G-1 G0 G1 G2

Figure (1.2) Schematic diagram of centralized controller

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G-1 G0 G1 G2

K -1 K 0 K 1 K 2

Figure (1.3) Schematic diagram of decentralized controller

1.5 Conflict Between Centralized and Decentralized Controller in

PSS Design

Two basic approches are avaliable for designing PSS. The first approach is to use a

multi-input multi-output centralized controller which would require a significant

amount of system wide communication. With this approach, the controller success

heavily depends on the communication which can be a serious disadvantage. Also a

controller failure might paralyze the whole network. So centralization is undesirable.

The second approach is the decentralized controller schemes, which have a number of

advantages. From which its operation requires a local signal so it is easy to design as

a hardware. So a failure of one controller has no detrimental effect on the

performance of the other controllers. Also the dependence on communication between

control stations is greatly reduced.

In the centralized PSS, the control signal to a machine is a function of the outputs for

all the machines. This affects on the gain matrix of centralized PSS for multimachine

power system by making it full. So a transmitted signals among the generating units is

needed. For this the centralized controller system is complex to design and

implement.

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In the decentralized PSS, the control signal for each machine should be a function of

its output only. So the gain matrix should have a zeros for all offdiagonal terms. For

this the decentralized control scheme is preferable.

1.6 Thesis Objectives

For large power systems comprising many interconnected machines, the PSS

parameter tuning is a complex task due to the presence of several poorly damped

modes of oscillation. The problem is further complicated by continuous variation in

power system operating conditions. To meet modern power system requirements,

controllers have to guarantee stability and robustness over a wide range of system

operating conditions. Thus the robustness is one of the major issues in power system

controllers design. So the recently developed

H synthesis is the way to handle

these requirements.

The main objectives of the thesis:

1- Design a robust controller for single machine infinite bus (SMIB)

a) Design a robust controller based on the

H .

b) Design a reduced controller based on balanced truncation method.

c) Design a proportional integral (PI) controller using the genetic algorithms

(GAs), which is well known as the new generation of the artificial

intelligence (AI). The parameters of the PI controller are tuned to mimic

the robust performance of the

H optimal one designed in (a). In other

word, the parameters of the PI controller have to obtain the same as that

of . More specifically, GAs is used to obtain the control parameters

of the PI controller subject to the

H

H constraints in terms of linear matrix

inequalities (LMI). Hence, this control design is called GALMI.

d) Another optimization tool, which is particle swarm optimization (PSO) is

used to tune PI controller and ensure a best solution.

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2- Design a robust controller for multimachine system

a) Design a centralized and decentralized robust controller based on the

optimal control method for PSS.

H

b) Design a GALMI for each area instead of the robust local decentralized

controller.

H

3- Design global controller to coordinate between the decentralized controllers

and ensure stability of the interconnected system.

a) Design a global controller based on multi-input multi-output (MIMO)

centralized controller.

H

b) Design a global controller based on reduced MIMO centralized

controller via balanced truncation method.

H

c) Design a global controller based on two level PSS. The parameters of PI

controller are selected to shift the undamped mechanical modes of

oscillation to the left hand side of vertical line in the complex s- plane by

GA.

1.7 Outline of The Thesis

The general description of the thesis is as follow:

Chapter 1: Discuss power system modes of oscillation and the classical structure of

PSS in brief. Also, conflict between centralized and decentralized controller in PSS

design are investigated. Moreover, introduces the reader to the thesis objectives and

outlines of their chapters.

Chapter 2: Performs a survey of the previous work, which discusses the relevant

work in the area of tuning PSS and robust control.

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Chapter 3: Presents the steady state and dynamic models of a SMIB and

multimachine power system. The mathematical formulations have been manipulated

in details. The machine models have been formulated in state-space form.

Chapter 4: Illustrates the design of centralized and decentralized controllers using

optimal and sub-optimal method for multimachine power system. Moreover, three

robust controllers are proposed. The first is based on

H theory, and results in a

high number of states, which represents the order of controller. The second controller

is a reduced order controller based on balanced truncation. The third is the PI

controller, has a simple structure, which is more appealing from an implementation

point of view, and it is tuned by GAs to achieve the same robust performance as thefirst one. More specifically, GAs optimization is used to tune the control parameters

of the PI controller subject to the

H constraints in terms of LMI. Hence, the third

control design is called GALMI. Particle swarm optimization (PSO), which is another

optimization technique, is used to tune the PI controller and ensure the best solution.

The previous controllers are further extended for designing centralized and

decentralized controller for multimachine power system based on . Moreover,

three global control strategies are introduced in this thesis to coordinate between the

decentralized controllers and ensure stability of the interconnected system. The first

utilizes a MIMO centralized

H

H controller system. The second is based on reduced

MIMO centralized controller via balanced truncation method. The third strategy

utilizes a two level PSS based on PI controller.

H

Chapter 5: The implementation and application of the three robust controllers are

illustrated for SMIB system. The first one is based on

H theory, and results in a

high order controller. The second controller is the reduced one based on balanced

truncation. The third controller design is based on GAs and is called GALMI. PSO is

used instead of GAs to redesign the third controller. The performance of the

implemented controllers is obtained for different operating conditions.

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Chapter 6: In this chapter, the implementation of the decentralized and centralized

controller based on optimal control theory and a comparison between them is

presented. Also the problem of fixed mode is presented. Moreover, a novel robust

decentralized controller with a simple structure is introduced based on the

optimal control method for PSS in multimachine area. The parameters of the PI

controller are tuned to mimic the robust performance of the decentralized one.

GALMI is used to obtain the control parameters of the PI controller. A global

controller is developed by reduced centralized controller based on minimum

communicated information to coordinate the local decentralized controllers. The

reduced controller is achieved by using the balanced truncation method. Another

global controller, which is more appealing from an implementation point of view, ispresented based on two level PSS to damp both local and interarea modes. Objective

function is presented using GA to allow the selection of the stabilizer parameters. The

effectiveness of the suggested techniques in damping local and interarea modes of

oscillations in multimachine power systems is verified under various operating

conditions to demonstrate their robust performance.

H

Chapter 7: highlights the significant contributions of the present work and draws the

scope for future work in this area.

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Chapter 2

Review of Literature

2.1 Introduction

Power systems are modeled as large nonlinear highly structured systems. Conventional

linear control is limited since it can only deal with small disturbances about an operating

point. Two important issues for power systems control are robustness and a decentralized

structure. The robustness issue arises to deal with sources of uncertainties, which mainly

come from the varying network topology, and the dynamic variation of the load. Since

physical limitation on the system structure makes information transfer among subsystems

unfeasible, decentralized controllers for multimachine systems must be used.

Over the last four decades, considerable amounts of research have been done in the area

of design and application of robust and decentralized control for power system, which are

discussed in the following section.

2.2 Previous Work

The optimal output decentralized (local) and global control of a power system consisting

of three interconnected synchronous machines is considered in [4]. A computational

method is introduced which enables the optimal output control (either global or local) of

a complete system to be found, thereby allowing realistic configurations to be studied.

The main question considered in this paper is as follows: given a multimachine, what are

the advantages, if any of feeding back the outputs of other machines in a system to

control a given machine? How does the performance of such a control system (termed

global control) compare with the overall system performance obtained by controlling

each machine from its own outputs (termed local decentralized control)?

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The load and frequency control of a multi-area interconnected power system is studied in

[5]. In this problem, the system is assumed to be subject to unknown constant

disturbances, and it is desired to obtain, if possible, robust decentralized controllers so

that the frequency and tie-line /net-area power flow of the power system are regulated.

The problem is solved by using some structural results recently obtained in decentralized

control, in conjunction with a parameter optimization method, which minimizes the

dominant eigenvalue of the closed-loop system. A class of minimum order robust

decentralized controllers, which solve this general multi-area load, and frequency control

problem is obtained. Application of these results is then made to solve the load and

frequency control problem for a power system consisting of nine synchronous machines

(described by a 119th-order system).

A method of coordinating multiple adaptive PSS units in a power system is presents in

[6]. The method is based on decentralized adaptive control scheme. Self-tuning adaptive

controllers are used as PSS units on given generators. The generators that tend to strongly

dynamically interact are coordinated by communication the controlled inputs between

them. The communicated information is used in such a way that the controllers are not

dependent on one another and is robust to any communication failures. Simulation results

that compare non-coordinated controllers with coordinated ones are presented for a 17

machines system. Two different system-operating points are tested. It is shown that better

system damping is obtained if the adaptive PSS units on the strongly coupled generators

are coordinated.

The design of a controller for a (TCSC) thyristor controlled series compensator to

enhance the damping of an inter area oscillation in a large power system is presented in

[7]. It describes a comprehensive and systematic way of applying the control design

algorithm in power systems. Two methods to obtain a satisfactory reduced order system

model, which is crucial to the success of the design, are describes.

H

H

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An optimal control method is outlined to deal with uncertainties in power system

modeling and operation as they affect the design of a PSS [8]. It focuses on the design

process for PSS using a nominal model with an uncertainty description, which represents

the possible perturbation of a synchronous generator around its normal operating point.The uncertainties are due to incomplete knowledge of the physical system in the model

formulation process and system abnormal operating conditions. This excitation controller

enables the power system to remain stable over a wide range of operating condition.

H

The design of a robust controller for generator excitation systems is used to improve the

steady state and transient stabilities [9]. The unique approach used is to first treat the

nonlinear characteristics of the system as model uncertainties at the controller design

stage using robust methodology. The performance of the controller has been evaluated

extensively by non-linear simulation. It is concluded that the robust controller provides

better damping to the oscillatory modes of the system than the conventional PSS in all the

cases studied.

In [10], a model matching robustness design procedure based on optimization

theory for the robust redesign of nominal operating conditions and tunes the nominal

control law to enhance the robustness with respect to the off nominal operating

conditions. The procedure is applied to the design of a PSS for a single machine infinite

bus system, which has a range of possible operating conditions. The results show that the

redesign controller contains features similar to the nominal controller, but yet improves

significantly the damping of the machine swing modes at the off nominal conditions.

H

Design of a robust controller for a Static Var Compensator (SVC) to improve the

damping of power system is presented [11]. The main contributions of this paper are to

formulate and to solve the power system damping control problem using robust

optimization techniques, and to synthesize the controller with explicit consideration of

the system operating condition variations. Nonlinear simulations using PSCAD/EMTDC

have been conducted to evaluate the performance of the closed loop system. The results

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have indicated the performance of the closed loop system. The results have indicated that

the designed controller can provide damping to the system under a wide range of

operating conditions.

In [12], the usual trial and error attempts for selection of performance weights are

discarded, that is the main problem in design of a robust

H power system stabilizer

(PSS), and instead a systematic and automated approach based on Genetic Algorithms

(GAs) is proposed. The resulting

H PSS performs quite satisfactory under a wide

range of turbo generator operating conditions and is robust against unmodelled low

damped torsional modes. It also provides sufficient robustness against significant changes

in configuration and parameters.

In [13], a new PSS design for damping power system oscillations focusing on interarea

modes is described. The input to the PSS consists of two signals. The first signal is

mainly to damp the local mode in the area where PSS is located using the generator rotor

speed as an input signal. The second is an additional global signal for damping interarea

modes. Two global signals are suggested; the tie line active power and speed difference

signals. The choice of PSS location, input signals and tuning is based on modal analysis

and frequency response information. These two signals can also be used to enhance

damping of interarea modes using SVC located in the middle of the transmission circuit

connecting the two oscillating groups. The effectiveness and robustness of the new

design are tested on a 19-generator system having characteristics and structure similar to

the Western North American grid.

A method to design sub optimal robust excitation controllers based on control

theory is presented [14]. The sub optimal controller results from additional constraints

that are imposed on the standard optimal

H

H solution. Global stability constraints are

incorporated into the algorithm to ensure stability of the interconnected system

under decentralized control. Furthermore, a lyapunov-based index is used to evaluate the

H

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robustness properties of the closed loop. In order to obtain a reduced order controller, the

method of balanced truncation is used. The sub optimal

H controllers are output

feedback controllers. These controllers posses superior robustness as compared to CPSS

and optimal controllers.H

A method based on optimal control is presented for the design of power system

controllers aimed at damping out electromechanical oscillations [15]. By imposing

decentralization and output feedback as constraints to the control problem, the resulting

controller structures are compatible with those employed by electric utilities. On the other

hand, the use of formulation based on the Chandrasekhar equations allows that sparsity

be exploited by the optimal control algorithm. This makes the method applicable to largesystems. The performance of the proposed method is assessed through its application to

two multimachine systems: the 10 machine New England system and a large power

system based on the South Southeast Brazil interconnected network.

A systematic robust decentralized design procedure based on the optimization

technique for tuning multiple FACTS devices is presented [16]. The design procedure

uses a model matching robustness formulation and requires the design of a parameter toachieve decentralized control. The approach is used to design damping controllers for an

SVC and a TCSC to enhance the damping of the interarea modes in a 3 area 6 machine

system. The feedback signals for the controllers are synthesized from the local voltage

and current measurements.

H

A new method of designing a robust

H PSS to deal with some limitations of the

existing PSS (standard PSSs) is presented [17]. These limitations includeH

H

(i) the inability to treat the system uncertainty when a stable nominal plant becomes an

unstable perturbed plant

(ii) the cancellation of the plants poorly damped poles by the controllers zeros.

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The proposed multiple inputs single output controller for the excitation system is based

on the numerator denominator uncertainty representation which is not restricted in the

modeling of uncertainty as compared to the standard additive or multiplicative

uncertainty representation. Furthermore, the bilinear transformation has been used in the

design to prevent the pole zero cancellation of the poorly damped poles and to improve

the control system performance. Simulation results have shown satisfactory performance

of this PSS for a wide range of operating conditions and good stability margin as

compared to both the conventional PSS and the standard

H PSS.

The decentralized load frequency controller design problem presented [18]. It is shown

that, subject to a condition based on the structure singular values (SSV), each local area

load frequency controller can be designed independently. The stability condition for the

overall system can be stated as to achieve a sufficient interaction margin and a sufficient

gain and phase margin defined in classical feedback theory during each independent

design. It is demonstrated by computer simulation that within this general framework,

very local controllers can be designed to achieve satisfactory performances for a sample

two-area power system and a simplified four-area power system. Under the designed

framework based on the structure singular values, other design methods for local area

controllers may be applied.

In [19], the design of linear robust decentralized fixed structure power system damping

controllers using GA is presented. The designed controllers follow a classical structure

consisting of a gain, wash out stage and two lead lag stages. To each controller is

associated a set of three parameters representing the controller gain and the controller

phase characteristics. The GA searches for an optimum solution over the parameter

space. Controller robustness is taken into account as the design procedure considers a

prespecified set of operating conditions to be either stabilized or improved in the sense of

damping ratio enhancement. A truly decentralized control design is achieved as the loop

control channels are closed simultaneously. The approach is used to design SVC and

TCSC damping controllers to enhance the damping of the interarea modes in a three-area

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six-machine system. Local voltage and current measurements are used to synthesis

remote feedback signals.

A new decentralized nonlinear voltage controller for multimachine power systems is

introduced [20]. A decentralized nonlinear voltage controller is developed by use of the

robust control theory. Performance of this controller in a three-machine example system

is simulated. The simulation results show that both voltage regulation and system

stability enhancement can be achieved with this controller regardless of the system


In [21], coordinated optimal decentralized controller design of excitation and TCSC

control for improving damping of overall power systems is discussed. Decentralized and

coordinated control is indispensable to power system because power systems are large

scaled and geographically distributed over large area. In particular, FACTS devices need

decentralized and coordinated control more and more. One present the decentralized

controller based on the only local available output variable of each subsystem. Simulation

of 3 machine and 9 bus with 1 TCSC show that decentralized controller has the

reasonable performance compared to centralized controller.

A novel method for the design of TCSCs in a meshed power system is developed [22].

The selection of the output feedback gains for the TCSC controllers is formulated as an

optimization problem and the simulated annealing (SA) algorithm is used to find the

solution. Using this method, the conflicting design objectives, such as the improvement

in the damping of the critical modes, any deterioration of the damping of the non-critical

modes and the saturation of the controller actuators, can be simultaneously considered. It

is also shown that the SA algorithm can be used to design robust controllers, which

satisfy the required performance criteria over several operating conditions. This control

scheme can be easily implemented as only the measurable signals local to each TCSC

location are used to control the TCSCs (decentralized control).

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In [23], one presents a new setup for analyzing the stability of a multimachine power

system with parameter variations. This method is based on SSV, which allows

computation of an effective measure for robustness in the presence of real parametric

uncertainty. Once the robustness problem has been set up it becomes amenable to the

application of synthesis tools for robust controller design. This technique is applied to

the robust stability assessment of a 4-machine test system specifically designed to

analyze the effect of control on the interarea.

In [24], numerical simulations and testing results of the new method is presented for

stability robustness of multimachine power systems. The approach is based on SSV tools.

The variations of operating conditions are treated as structured uncertainty. Simulation

results for a test system have shown excellent accuracy of robust stability assessment for

a wide range of operating conditions.

In [25], a systematic procedure for the design of decentralized controllers for

multimachine power systems is presented. The robust performance in terms of (SSV or

) is used as the measure of control performance. A wide range of operating conditions

was used for testing. Simulation results have shown that the resulting controllers

would effectively enhance the damping torques. Providing better robust stability and/or

performance characteristics both in the frequency and time domain compared to

conventionally designed PSSs.

A robust decentralized excitation control of multimachine power systems is introduced

[26]. One concerned with the design of decentralized state feedback controller for the

power system to enhance its transient stability and ensure a guaranteed level of

performance when there exist variations of generator parameters due to changing load

and/or network topology. It is shown that the power system can be modeled as a class of

interconnected systems with uncertain parameters and interconnections. One develops a

guaranteed cost control technique for the interconnected system using a linear matrix

inequality ( LMI ) approach. A procedure is given for the minimization of the cost by

employing the powerful LMI tool. The designed controller design is simulated for a

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three-machine power system example. Simulation results show that the decentralized

guaranteed cost control greatly enhances the transient stability of the power system in the

face of various operating points, faults in different locations or changing network

parameters.

Robust design of multimachine PSSs using SA optimization technique is presented [27].

This approach employs SA to search for optimal parameter settings of a widely used

conventional fixed structure lead lag PSS (CPSS). The parameters of this simulated

annealing based power system stabilizer (SAPSS) are optimized in order to shift the

system electromechanical modes at different loading conditions and system

configurations simultaneously to the left in the s-plane. Incorporation of SA as a

derivative free optimization technique in PSS design significantly reduces the

computational burden. One of the main advantages of this approach is its robustness to

the initial parameter settings. In addition, the quality of the optimal solution does not rely

on the initial guess. The performance of the SAPSS under different disturbances and

loading conditions is investigated for two multimachine power systems. The eigenvalue

analysis and the nonlinear simulation results show the effectiveness of the SAPSSs to

damp out the local as well as the interarea modes and enhance greatly the system stability

over a wide range of loading conditions and system configurations.

Robust design of multimachine (PSSs) using the Tabu Search (TS) optimization

technique is presented [28]. This approach employs TS for optimal parameter settings of

a widely used conventional fixed structure lead lag PSS (CPSS). The parameters of this

stabilizer are selected using TS in order to shift the system poorly damped

electromechanical modes at several loading conditions and system configurations

simultaneously to a prescribed zone in the left hand side of the s-plane. Incorporation of

TS as a derivative free optimization technique in PSS design significantly reduces the

computational burden. In addition, the quality of the optimal solution does not rely on the

initial guess. The performance of this PSS under different disturbances and loading

conditions is investigated for multimachine power systems. The eigenvalue analysis and

the nonlinear simulation results show the effectiveness of the designed PSSs in damping

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out the local as well as the interarea modes and enhance greatly the system stability over

a wide range of loading conditions and system configurations.

Several control design techniques namely, the classical phase compensation approach, the

synthesis, and a linear matrix inequality technique, are used to coordinate two power

system stabilizers to stabilize a 5-machine equivalent of the South/Southeast Brazilian

system [29]. The open loop system has an unstable interarea mode and cannot be

stabilized using only one conventional power system stabilizer. Both centralized and

decentralized controllers are considered. The different designs are compared and several

interesting observations are provided.

An effective method for designing coordinated

H PSSs to improve the damping of

local and interarea oscillations is presented [30]. Target modes types of inputs of the PSS,

and effective locations for each controller are examined using the participation factor and

residue concept. To realize coordination of the controllers, a method for constructing the

effective reduced model for this design is presented, minimizing the uncertainty for each

controller. With such a small uncertainty, a tight design, which yields marginal

robustness, can be realized, increasing the performance of each controller as well as that

of the total system. The influence of the reduced model on the controller characteristics is

discussed. The effectiveness of this design is demonstrated through nonlinear numerical

simulation in a five machine seven bus system under two critical operating conditions.

A design method of damping controllers of two facts devices, namely synchronous

voltage source when it is used only for reactive shunt compensation, advanced static var

compensator (ASVC) and SVC is introduced [31]. The application of ASVC and SVC for

damping control is demonstrated and the comparison is made about the damping controlcapabilities paying attention to the difference in the design philosophy and detailed

dynamic performances. An important issue in designing this kind of controllers is to

suppress over voltage that appears under large disturbance. This over voltage problem

sometimes appears in the existing SVC system. To cope with this over voltage problem,

it uses the control sensitivity function to regulate indirectly the controller output so that

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the over voltage problem is treated in the design step. Another important issue is that one

point out the zero problems tends to appear inherent in a typical ASVC system making

the controller design difficult. To design robust controller under this condition, one

suggest to use the bilinear transform to design a robust

H optimal controller, it is

shown that this controller provides more robust stability and better performance for

additional damping for power system oscillations while suppressing over voltages.

Performance comparison is also made between ASVC and SVC cases.

A new PSS design method, which uses the numerator denominator perturbation

representation and includes the partial pole placement technique and a new weighting

function selection method is presented [32]. This overcomes certain conventionalPSS design algorithm limitations. A sixth order machine model is used to increase

the accuracy of selected weighting functions. A robust PSS has been successfully

designed for single and two machine systems by treating the highly nonlinear

characteristic of the power system as model uncertainty. The design is verified to have

better performance for a wide range of operating conditions when compared with the

conventional PSS designs.

H

H

The design of robust power system stabilizers, which place the system poles in an

acceptable region in the complex plane for a given set of operating and system

conditions, is introduced [33]. It therefore, guarantees a well-damped system response

over the entire set of operating conditions. The proposed controller uses full state

feedback. The feedback gain matrix is obtained as the solution of a LMI expressing the

pole region constraints for polytopic plants. The technique is illustrated with applications

to the design of stabilizers for a single machine and a 9 bus, 3 machine power system.

The design of robust control for the second generation of FACTS devices such as static

compensator (STATCOM), and unified power flow controller (UPFC) using a loop

shaping design via a normalized coprime factorization approach, where loop shape refers

to the magnitude of the loop transfer function L=GK as a function of frequency is

H

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presented [34]. Since method is based on classical loop shaping ideas, it is relatively easy

to implement. Furthermore, comparing it with the other methods of robust control,

it is more flexible and is not limited in its applications. Simulation of the system

following a disturbance is performed to demonstrate the effectiveness of the designedcontroller.

H

A robust controller for providing damping to power system transients through

STATCOM devices is presented [35]. The method of multiplicative uncertainty has been

employed to model the variations of the operating points in the system. A loop shaping

method has been employed to select a suitable open loop transfer function, from which

the robust controller is constructed. The design is carried out applying robustness criteria

for stability and performance. The proposed controller has been tested through a number

of disturbances including three phase faults. The robust controller designed has been

demonstrated to provide extremely good damping characteristics over a range of


A genetic algorithm based method is used to tune the parameters of a PSS [36]. This

method integrates the classical parameter optimization approach, involving the solution

of a Lyapunov equation, within a genetic search process. It also ensures that for any

operating condition within a predefined domain, the system remains stable when

subjected to small perturbations. The optimization criterion employs a quadratic

performance index that measures the quality of system dynamic response with in the

tuning process. The solution thus obtained is globally optimal and robust. This method

has been tested on two different PSS structures: the lead lag PSS and the derivative PSS.

System dynamic performance with PSS tuned using this technique is highly satisfactory

for different load conditions and system configurations.

A mixed sensitivity design of a damping device employing a UPFC is presented

[37]. The problem is posed in the LMI framework. The controller design is aimed at

providing adequate damping to interarea oscillations over a range of operating conditions.

H

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The results obtained in a two area four machine test system are seen to be very

satisfactory both in the frequency domain and through nonlinear simulations.

In [38], a robust PSS is designed using loop shaping design procedure. The resulting PSS

ensures the stability of a set of perturbed plants with respect to the nominal system and

has good oscillation damping ability. Comparisons are made between the resulting PSS, a

conventionally designed PSS and a controller designed based on the structure singular

value theory.

A decentralized controller for load frequency control (LFC) problem in power systems is

designed based on control technique formulated as a LMI problem [39]. To

achieve decentralization, interfaces between interconnected power systems control area

are treated as disturbances. The LMI control toolbox is used to solve such a constrained

optimization problem for LFC applications. The performance of this controller is

illustrated and compared with that of a conventional controller through simulation of a

two-area power system.

H

A LMI based robust controller design for damping oscillations in power systems is

presented in [40]. This controller uses full state feedback. The feedback gain matrix is

obtained as the solution of a LMI. The technique is illustrated with applications to the

design of stabilizer for a typical single machine infinite bus (SMIB) and a multimachine

power system. The LMI based control ensures adequate damping for widely varying

system operating conditions and is compared with conventional power system stabilizer

(CPSS).

2H

In [41], a design procedure of a H mixed sensitivity PSS is developed to improve

power system stability. A study system representing SMIB is investigated. The machine

accelerating torque is selected as input signal to the PSS. A comparison between system

response to disturbances for the

H and lead lag PSS is made. The simulation results

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show that the PSS ensures the stability of the system and has good damping ability

at a wide range of system loading.

H

The Particle Swarm Optimization (PSO) technique is used to develop a controller fordamping power system oscillations [42]. The speed deviation and its rate of change are

selected as input signals to the controller. The objective is to get optimal gains values of

the controller within pre-specified limits to improve the system dynamics. In order to

ensure the reliability of the PSO based controller, a comparison has made between the

effect of the developed controller and that of

H controller on the dynamic

performance of a SMIB. The simulation results show that the PSO based controller offers

effective damping to system oscillations in a wide range of operating conditions.

The application of PSO technique to optimize a PID controller parameters for LFC is

discussed [43]. The capability of the controller is investigated through variations the

magnitude of load disturbance. The simulation results show that the applied PSO based

PID controller has achieved good system performance. A comparative study results is

made between the controller and the designed one. The performance is shown to be

better for the new PID controller.

H

2.3 Contributions of This Thesis

There has been considerable amount of work done to develop new controllers in the area

of design and application of robust and decentralized control for power system. The

previous controllers are suffered from high dimension and practical implementation

especially in multimachine system. Moreover, none of them addresses the problem of

coordination of multiple controllers by means of global controller. This research has

filled this point since it has achieved the design, development, and testing of a simple low

order controller and global controller scheme to control and coordinate the actions of

decentralized controllers. The proposed controller provides a simple and effective scheme

to stretch the stability limit and to increase the loadability of the system.

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The main contributions of this thesis are summarized as follows:

A new controller is presented to design a robust PSS for a SMIB using PI controller. The

parameters of PI controller are obtained by GA to achieve the same performance of

H

based on output feedback in term of LMI. This controller, which is called GALMI, is

simpler than one. This controller succeeds in achieving a robust tuned PSS.

Moreover, it overcomes the difficulty of computation and high dimension of controller

system especially in multimachine environment. So it is more advantageous, in terms of

practicability and reliability.

H

The design of centralized and decentralized PSS for a multimachine power system usingoutput feedback is presented. In centralized controller, the control signal is a

function of output of all machines. In decentralized controller, the control signal to each

machine becomes a function of the output of that machine only.

H

A new simple algorithm is introduced to design robust decentralized PSS for a

multimachine power system using GALMIs. For each area, the decentralized controller

based on is replaced by GALMI. Moreover, a global controller is designed to deal

with the interactions, which is unconsidered in design of decentralized controllers.

H

A new application for a MIMO centralized

H controller is illustrated for designing a

high order global controller. Another two global controllers are introduced in this thesis

to treat the problem of possible adverse interaction between multiple decentralized

controllers and to overcome the problem of high order of centralized controller.

The first is based on the reduced centralized with minimum communicated

information. While the second is based on two level PSS. In this controller, not only is

the cost of implementation drastically reduced, but also, the risk of loss of stability due to

signal transmission failure is minimized. Moreover, it represents a simple global

controller to damp both local and interarea modes.

H

H

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Chapter 3

Modeling of Power Systems

3.1 Introduction

The nonlinear differential equations governing the behavior of a power system can be

linearized about a particular operating point, to obtain a linear model, which

represents the small signal oscillatory response of a power system. Variations in the

operating condition of the system result in the variations in the parameters of the

small signal model. A given range of variations in the operating conditions of a

particular system thus generates a set of linear models, each corresponding to one

particular operating condition. Since, at any given instant, the actual plant could

correspond to any model in this set, a robust controller would have to impart adequate

damping to each one of these entire sets of linear models. In this chapter, the

mathematical models for a power system required in formulating the stability problem

will be presented. The typical single machine infinite bus (SMIB) is shown in Figure

(3.1). The system data has been given in appendix A

Figure (3.1) Machine-infinite bus system

Xe Re

3.2 System Equations

The complete system has been simulated in state space representation. For simplicity

both the state and algebraic equations for (SMIB) are given below [1,2]:

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Machine Equations

Using the third order model for the synchronous machine, the differential equations,

which describe the machine dynamics, can be arranged as

dI

do

dX

dX

fdE

doq

E

doq

E

+

+

=

11& (3.1)

eT

mT

j

=1

& (3.2)

= B&

(3.3)

Static Exciter Equations

The differential equations that describe the static excitation system can be written as

sVaa

K

tVaa

K

fVaa

K

fdEa

fdE +

= 1

& (3.4)

sV

fa

fKa

K

tV

fa

fKa

K

fV

fa

fKa

K

ffd

E

fa

fK

fV +

+

=

1& (3.5)

Algebraic Equations

The linearized algebraic equations can be summarized as

qI

qX

dV = (3.6)

dI

dX

qE

qV += (3.7)

dI

qoI

dX

qX

qI

qoE

qE

qoI

eT

+= (3.8)

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qV

toV

qoV

dV

toV

doV

tV += (3.9)

The transmission network having an impedance ofe

jXe

R + , which is connected to

an infinite bus with voltage , is included in the following equations:

V

dI

eRV

qI

eX

dV =

+ ])

0cos([ (3.10)

qI

eRV

dI

eX

qV =

+ ])

0sin([ (3.11)

3.3 Block Diagram Simulation

One has to build the block diagram of every equation and all blocks are connected

together to form one block. For example, the machine equation. (3.1) is formed as

(Xd-X'd)I

d

Efd

+

+

1

1

+ sdo

E'q

The exciter is connected to this block by the voltagefd

E , i.e., the output of the

exciter is an input to the field winding of the machine.

+

+

-

-

Vref

Vt

Vs

EfdKa

(1+ as)

(1+ fS)

KfS

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The terminal voltage Vt that is a feedback signal to the exciter is formed by the

following block.

Iq

Id

E'q

-XqVd

VqX'd +

+

Vdo Vto

VqoVto

+

+

Vt

The electric torque equation (3.8) is formed in a block diagram as

Iq

Id

E'q

Eqo

X'd)(Xq- Iqo

Iqo

Te

+

+

-

The electric torque output signal from the previous block is an input to the block

diagram representing the swing equation, which is described by equation (3.2) and

(3.3).

Tm

Te

+

-

1

jS

o

S

29


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The transmission network equation (3.10,3.11) are formed in a block diagram as

shown below

V cos(0-)

Xe1/Re

+

+

Iq

Vd

Id

V sin(0-)

Xe1/Re

+

+

+

Id

Vq

Iq

The block diagram of a single machine adopted to be used in SIMULINK Toolbox is

developed as shown in Figure (3.2).

30


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31


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3.4 State Space Formulation

The system in general is described by a set of differential and algebraic equations in

the standard form as shown in equation (3.12)

(3.12)]][[]][[][

]][[]][[][

UDXCY

UBXAX

+=

+=&

Once the equations are obtained in this form the eigenvalues of the matrix A indicate

the stability of the system.

In general these equations can be written as shown previously but they can be

rearranged as follows:

(3.13)[ ] [ ][ ] [ ][ ]URXQY

XP +=

&

Where X, Y and U are the state space variables, while P, Q and R are real constant

matrices. The entries of these matrices are function of all system parameters and

depend on the operating condition. The P matrix of equation (3.13) can be partitioned

as follows:

[ ] (3.14)

=

xsG

oAI

P0

Where matrix I is an identity matrix of dimension , where is the number of

the state space variables. The P matrix is of dimension n x n where n is the total

number of states and algebraic variables. Matrix 0 is a null matrix. The matrix

snx

sn

sn

sG is

a square matrix of dimension wherev

nxv

nv

n is the total number of the algebraic

variables and matrixA0 is a very sparse matrix of dimension vnxns . Then the inverse

of P matrix is obtained by partitioning as follows:

(3.15)[ ]

=

1][0

1][1

xsG

xsG

oAI

P

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Thus the inverse of P matrix involves the inversion of the sG matrix, which ispartitioned in turn, and it is almost in a block form.

The Q and R matrices are partitioned as

=

=

DR

sR

R

CQA

QQ ,

Where is a matrix of dimension and matrixA

Qs

nxs

n C

Q is of dimensions

nxv

n

then the coefficient matrices of the state space are

DR

sGD,DoA

sRB

Co

AA

QA,c

Qxs

GC

1][

1][

==

=

=

It can be seen that the matrixAis obtained, as a sum of two matrices. The matrix

contains almost all the control parameters. The eigenvalues of the system matrix A

described by the equation (3.12) are indicative of the system performance.

A

Q

The system eigenvalues are related to the different modes in the system while the real

part is a measure of the amount of the damping and the imaginary part is related to the

natural frequency of the oscillation of the corresponding modes. System eigenvalues

are in general function of all control and design parameters; the change in any of these

parameters affects on the system performance. Hence, causes a shift in the whole

eigenvalue pattern. The amount of shift depends on the sensitivity of the different

eigenvalues as well as the amount of change in the parameter. The matrix P is shown

below.

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=

eR

eX

eX

eR

tV

qV

tV

dV

qEqXqXqI

dX

qX

fT

aT

fK

aK

aT

aK

j

d

dX

dX

P

001000000

000100000

0010

0

0

0

000000

00010000000

0001000000

0000100000

0000010000

0000001000

00000000100

0001

0000010

0

0

000000001

Equation (3.13) can be written in the form

[ ]sfTaTf

K

a

Ka

T

aK

fVfd

E

qE

V

V

qI

fT

aT

fKa

K

fT

fT

aT

fK

3203949 . robust decentralized controller design via ai to enhance power system dynamic performance

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