Decentralized Control of Multi-Area Power Systems

Benha University

Faculty of Engineering Shoubra

Department of Electrical Power and Machines

"Decentralized Control of Multi-Area Power Systems"

A Thesis Submitted to Faculty of Engineering (Shoubra)

Benha University

In Partial Fulfillment Of the Requirements

for the M.Sc.Degree in Electrical Engineering

(Power Division)

By

Eng / Mahmoud Nasr Sayed Mohamed Elsisi

Supervised By

Prof. Dr. Wagdy Mohamed Mansour

Faculty of Engineering (Shoubra)

Benha University

Dr. Mahmoud Soliman Ahmed Helal

Faculty of Engineering (Shoubra)

Benha University

Cairo - Egypt

2014

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i

Acknowledgment

First of all I would to thank Allah "God" for providing me with health

and patience to finish this thesis.

I would like to thank a lot of people for their support toward the

completion of this degree .Specifically Prof. Dr. Wagdy Mohamed Mansour,

advisor and committee chairman ,for his supervision, continues guidance

,encouragement and support he always offered during the preparation of this

thesis. He has always provided me with advice, useful discussions and

comments.

I wish to express my sincere gratitude to Dr. Mahmoud Soliman Helal for

his sincere help, great effort, helpful practical discussion, encouragement he

always offered. My enthusiasm in this thesis is inspired by his profound

knowledge in this area and his elegant research style. He has never hesitated to

spend any time or effort to guide my work.

Thanks are also to all members of electrical engineering department in

college of faculty of engineering (shoubra) for the great help.

I would like to express my gratitude and appreciation to my family for

their love, sacrifices and patience during my all years of study. And finally

many thanks to my wife for her support.

Mahmoud Nasr Sayed Mohamed Elsisi

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ii

ABSTRACT

Load Frequency Control (LFC) and Automatic Voltage Regulator (AVR)

are a very imperative issue in power system operation for providing

electric power with high quality and reliability. The objectives of LFC are

to minimize the transient deviations in area frequency and tie-line power

interchange and to ensure their steady state errors to be zeros. Objective of AVR

is to regulate the excitation of generator in order to match the reactive power

demand.

The main objective in this research work is to develop a new simple and

systematic way of designing Variable Structure Controller (VSC) and dual

Proportional-Integral (PI) controller to power system dynamic problems.

The validation of the proposed controllers is studied. The design of VSC and the

dual PI controller is considered as an optimization problem and uses Artificial

Bee Colony (ABC) and Genetic Algorithm (GA) in the design procedure.

Linear and nonlinear models of the investigated systems are considered. Results

have been compared with the conventional controller based on Zeigler-Nichols

(ZN) method. A decentralized load frequency control based VSC and dual PI

controller is proposed and results are compared with respect to the conventional

control. The interaction between AVR and AGC is reduced and the dynamic

behavior of the system is improved. Parallel processing is applied to two area

LFC and two area LFC with AVR. To demonstrate the decentralized control

and decoupling of each area in a multi area power system, a parallel

microprocessor network is obtained and simulated using

MATLAB/SIMULINK. Each area with its control is simulated and represented

as a microprocessor. A central processor is used to exchange the necessary data

for each area. The main idea of such parallel processing architecture is to reduce

the computation time, especially for large power system which consists of

several areas.

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iii

TABLE OF CONTENTS

ACKNOWLEDGMENT i

ABSTRACT ii

TABLE OF CONTENTS iii

LIST OF FIGURES vi

LIST OF TABLES ix

LIST OF SYMBOLS AND ABBREVIATIONS x

CHAPTER 1 INTRODCUTION 1

1.1 Research Motivation 1

1.2 Literature Review 2

1.3 Objectives of the Thesis 5

1.4 Thesis Outline 5

CHAPTER 2 MODELING OF ELECTRICAL POWER SYSTEM 8

2.1 Introduction 8

2.2 LFC And Modeling Of Various Components 9

2.2.1 Generator Model 9

2.2.2 Load Model 10

2.2.3 Turbine Model 12

2.2.4 Governor Model 12

2.2.5 State Space Model Of LFC 13

2.3 Generator Voltage Control System 14

2.3.1 Amplifier Model 15

2.3.2 Exciter Model 15

2.3.3 Generator Model 15

2.3.4 Sensor Model 16

2.3.5 State Space Model Of AVR 16

2.4 LFC-AVR System Model 17

2.5 LFC In the Multi Area System 20

2.6 Generation Rate Constraint (GRC) 23

CHAPTER 3 PROPOSED CONTROLLERS 24

3.1 Introduction 24

3.2 Basic Concepts of VSC 25

3.2.1 Merits and Demerits of VSC 28

3.2.2 Proposed Design Method of VSC 29

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iv

3.3 Basic Concepts of Dual PI Control 31

3.3.1 Proposed Design of Dual PI Control 33

3.3.1.1 Discontinuous Mode 33

3.3.1.2 Continuous Mode 35

CHAPTER 4 CHAPTER INTELLIGENCE OPTIMIZATION TECHNIQUES 36

4.1 Introduction 36

4.2 Genetic Algorithm 36

4.3 ABC Optimization Algorithm 38

4.4 4.4 Performance Index 42

CHAPTER 5 APPLICATION OF THE PROPOSED CONTROLLER TO THE

POWER SYSTEM

43

5.1 Introduction 43

5.2 Proposed VSC Design For A Single Area Power System 44

5.3 Proposed I, PI, and dual PI controller Design for A Single area Power system 47

5.3.1 The Frist Test Case 49

5.3.2 The Second Test Case 51

5.3.3 The Third Test Case 56

5.4 Design of Decentralized LFC Based VSC, Dual PI Controller Using ABC

and GA.

58

5.4.1 Proposed VSC Design For Two Area Interconnected Power System. 59

5.4.2 Proposed Dual PI Control Design For Two Area Interconnected Power

System.

61

5.4.3 The Frist Test Case 61

5.4.4 The Second Test Case 64

5.4.5 The Third Test Case 68

5.5 Design of AVR System by PID Controller 70

5.6 LFC and AVR System 74

5.6.1 LFC and AVR For Single Area Power System 75

5.6.2 LFC and AVR For Two Area Power System 79

CHAPTER 6 PARALLEL PROCESSING APPLICATION 85

6.1 Introduction 85

6.2 Single area LFC as Microprocessor 87

6.3 AVR as Microprocessor 89

6.4 LFC and AVR for single area power system as Microprocessor 90

6.5 Two area LFC by parallel processing 91

6.6 LFC and AVR for two area power system by parallel processing 94

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v

CHAPTER 7 CONCLUSIONS 99

7.1 Summary and Conclusions 99

7.2 Contributions 99

7.3 Future Work 100

REFERENCES 101

APPENDIX 112

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vi

LIST OF FIGURES

Figure 1.1 Chart of the thesis. 7

Figure 2.1 Schematic diagram of LFC and AVR of a synchronous generator. 8

Figure 2.2 The schematic representation of LFC system. 9

Figure 2.3 The block diagram representation of generator. 10

Figure 2.4(a) The block diagram representation of the generator and load. 11

Figure 2.4(b) The simplified block diagram representation of the generator and load. 11

Figure 2.5 The turbine model. 12

Figure 2.6 The block diagram representation of the governor. 13

Figure 2.7 The block diagram representation of the LFC. 13

Figure 2.8 A real model of AVR system. 15

Figure 2.9 Closed-loop block diagram of AVR. 16

Figure 2.10 LFC-AVR block diagram of single area power system. 18

Figure 2.11 Block schematic of interconnected areas. 22

Figure 2.12 Nonlinear turbine model with GRC. 23

Figure 3.1(a) Block diagram of VSC. 27

Figure 3.1(b) Regions divided by the switching lines 27

Figure 3.2 Phase trajectories 28

Figure 3.3 Block diagram of VSC. 30

Figure 3.4 Relay dual-mode control 32

Figure 3.5 Error signal without controller. 32

Figure 3.6 Block diagram for the proposed dual. 35

Figure 4.1 Flow chart of Genetic Algorithm. 38

Figure 4.2 The behavior of honey bee foraging for nectar 39

Figure 4.3 Flow chart of Artificial Bee Colony. 41

Figure 5.1 Single area LFC system excluding nonlinearities. 45

Figure 5.2 Single area LFC system with GRC. 46

Figure 5.3(a) Change in frequency due to using ABC technique in case of single area LFC linear model.

49

Figure 5.3(b) Change in frequency due to using GA technique in case of single area LFC linear model.

50

Figure 5.3(c) Change in frequency due to using ABC and GA techniques in case of single area LFC linear model.

51

Figure 5.4(a) Change in load disturbance in case of single area LFC linear model. 51

Figure 5.4(b) Change in frequency of single area LFC linear model due to using ABC in case of change in load disturbance.

52

Figure 5.4(c) Change in frequency of single area LFC linear model due to using GA in case of change in load disturbance.

52

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vii

Figure 5.4(d) Change in frequency of single area LFC linear model by dual PI controller in case of change in load disturbance.

53

Figure 5.5 Change in frequency due to using ABC technique in case of single area LFC nonlinear model.

54

Figure 5.6 Change in frequency due to using GA technique in case of single area LFC nonlinear model.

55

Figure 5.7 Change in frequency due to using ABC and GA techniques in case of single area LFC nonlinear model.

55

Figure 5.8 Change in frequency of single area LFC nonlinear model by VSC optimized by ABC in case of change of TG and TT by±25%.

56

Figure 5.9 Change in frequency of single area LFC nonlinear model by VSC optimized by GA in case of change of TG and TT by±25%.

57

Figure 5.10 Change in frequency of single area LFC nonlinear model by dual PI controller optimized by GA and ABC in case of change of TG and TT by±25%.

57

Figure 5.11 Proposed decentralized VSC controllers applied to two area 59

Figure 5.12 Two area power system model. 59

Figure 5.13(a) Change in frequency of first. 62

Figure 5.13(b) Change in frequency of second area. 63

Figure 5.13(c) Change in Ptie. 63

Figure 5.14(a) Change in load disturbance of area1 and area2. 64

Figure 5.14(b) Change in frequency of first area by ABCVSC in case of Change in load disturbance of area1 and area2.

65

Figure 5.14(c) Change in frequency of second area by ABCVSC in case of change in load disturbance of area1 and area2.

65

Figure 5.15(a) Change in frequency of first area by GAVSC in case of Change in load disturbance of area1 and area2.

66

Figure 5.15(b) Change in frequency of second area by GAVSC in case of Change in load disturbance of area1 and area2.

66

Figure 5.16(a) Change in frequency of first area by dual PI controller optimized by GA and ABC in case of Change in load disturbance of area1 and area2.

67

Figure 5.16(b) Change in frequency of second area by dual PI controller optimized by GA and ABC in case of Change in load disturbance of area1 and area2.

67

Figure 5.17 (a)-(b) Change in frequency of area1 and area2 by ABCVSC in case of change of T12 by±50%.

68

Figure 5.18 (a)-(b) Change in frequency of area1 and area2 by GAVSC in case of change of T12 by±50%.

69

Figure 5.19 (a)-(b) Change in frequency of area1 and area2 by dual PI controller optimized by GA and ABC in case of change of T12 by±50%.

70

Figure 5.20 Closed-loop block diagram of AVR. 72

Figure 5.21 Output voltage of AVR due to using GA and ZN. 74

Figure 5.22 LFC-AVR block diagram of single area system. 75

Figure 5.23 The change of frequency of single area LFC by VSC optimized by ABC in 76

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viii

case of with and without AVR.

Figure 5.24 The change of frequency of single area LFC by VSC optimized by GA in case of with and without AVR.

77

Figure 5.25 The change of frequency of single area LFC by VSC optimized by GA and ABC in case of with AVR.

78

Figure 5.26 Output voltage of AVR due to using GA in case of with and without LFC . 78

Figure 5.27 AGC-AVR block diagram of two area power system. 80

Figure 5.28 (a)-(b) Change in frequency of area1 and area2 by ABCVSC in case of with and without AVR.

81

Figure 5.29 ( a)-(b) Change in frequency of area1 and area2 by GAVSC in case of with and without AVR.

82

Figure 5.30 ( a)-(b) Change in frequency of area1 and area2 by GAVSC and ABCVSC in case of with AVR.

83

Figure 5.31 ( a)-(b) output voltage of area1 and area2 in case of with and without LFC. 84

Figure 6.1(a) Multi area electrical power system by parallel processing 86

Figure 6.1(b) Computations of parallel multi processors. 87

Figure 6.1(c) Computations of cascaded multi processors. 87

Figure 6.2(a) Original Single area LFC. 88

Figure 6.2(b) Single area LFC as microprocessor. 88

Figure 6.2(c) Change in frequency of single area LFC as microprocessor and original model by ABC based VSC.

88

Figure 6.3(a) Original AVR. 89

Figure 6.3(b) AVR as microprocessor. 89

Figure 6.3(c) Output voltage of AVR as microprocessor and original model. 89

Figure 6.4(a) Original LFC and AVR for single area power. 90

Figure 6.4(b) LFC and AVR for single area power system as microprocessor. 90

Figure 6.4(c) Change in frequency of single area LFC with AVR as microprocessor and original model by ABC based VSC.

91

Figure 6.4(d) Output voltage of AVR with LFC as microprocessor and original model by GA based PID controller.

91

Figure 6.5(a) Original two area LFC. 92

Figure 6.5(b) Two area LFC by parallel processing 93

Figure 6.5(c) Change in frequency of first area by ABC based VSC. 93

Figure 6.5(d) Change in frequency of second area by ABC based VSC. 94

Figure 6.6(a) Original LFC and AVR for two area power system. 95

Figure 6.6(b) LFC and AVR for two area power system by parallel processing. 96

Figure 6.6(c) Change in frequency of first area by ABC based VSC.

97

Figure 6.6(d) Change in frequency of second area by ABC based VSC.

97

Figure 6.6(e) Output voltage of first AVR by GA based PID controller.

98

Figure 6.6(f) Output voltage of second AVR by GA based PID controller.

9

98

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ix

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ix

LIST OF TABLES

Table 5-1 (a) Control parameters and performance indices in different designs for linear model.

47

Table 5-1 (b) Control parameters and performance indices in different designs for nonlinear

model.

47

Table 5-2 (a) Control parameters and performance indices in different designs for linear

model.

48

Table 5-2 (b) Control parameters and performance indices in different designs for nonlinear

model.

48

Table 5-3 Control parameters and performance indices in different designs. 60

Table 5-4 Control parameters and performance indices of dual PI and conventional I controller.

61

Table 5.5 AVR system parameters 73

Table 5.6 Control parameters, Performance index, Overshoot and settling time. 73

Table 5.7 Control parameters Of VSC by GA and ABC 76

Table 5.8 Control parameters 79

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x

LIST OF SYMBOLS AND ABBREVIATIONS

R : Speed regulation due to governor action (Hz p.u.MW-1).

∆f : Incremental change in frequency (Hz).

∆f1 : Incremental change in frequency for area 1 (Hz).

∆f2 : Incremental change in frequency for area 2 (Hz).

∆P ref1 : Incremental change in reference set power in area 1 (p.u.MW).

∆P ref2 : Incremental change in reference set power in area 2 (p.u.MW).

∆PL : Incremental change in Load disturbance (p.u.MW).

∆PL1 : Load disturbance area 1 (p.u.MW).

∆PL2 : Load disturbance area 2 (p.u.MW).

∆Pm : Incremental change in mechanical power (p.u.MW).

∆Pm1 : Incremental change in mechanical power for area1 (p.u.MW).

∆Pm2 : Incremental change in mechanical power for area2 (p.u.MW).

∆Pref : Incremental change in reference set power (p.u.MW).

∆Ptie : Incremental change in tie-line power.

∆Pv : Incremental change in governor valve position (p.u.MW).

∆Pv1 : Incremental change in governor valve position for area 1.

∆Pv2 : Incremental change in governor valve position for area 2.

∆δ : Incremental change in rotor angle (rad).

ABC : Artificial bee colony .

ABCDVSC : Artificial bee colony based decentralized variable structure controller.

ABCVSC : Artificial bee colony based variable structure controller.

ACE : Area control error.

AI : Artificial intelligence.

AVR : Automatic voltage regulator.

BFOA : Bacterial foraging optimization algorithm.

CIC : Conventional integral controller.

D : load damping constant.

D : Decentralized.

ess : Steady state error.

FLPI : Fuzzy logic based proportional integral.

GA : Genetic algorithm.

GADVSC : Genetic algorithm based decentralized variable structure controller.

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xi

GAVSC : Genetic algorithm based variable structure controller.

GRC : Generation rate constraint.

GT : Genetic-tabu.

Gt(s) : Transfer Function (TF) of the turbine.

H : Generator inertia constant (s).

ICA : Imperialist competitive algorithm.

ISE : Integrated square of the error.

ITAE : Integral of time multiplied by absolute-error value.

K1 : Change in electrical power for small change in stator emf.

K2 : Change in terminal voltage for small change in rotor angle.

K3 : change in terminal voltage for small change in stator emf.

KA : Amplifier gain.

KD : Derivative gain.

KE : Exciter gain.

KG : Generator gain.

KI : Integral control gain.

KP : Proportional gain.

KR : Amplifier gain.

LFC : Load frequency control.

Mp : Maximum overshoot.

MTS : Multiple tabu search.

Pe : Electrical power.

PI : Proportional – integral controller.

PID : Proportional – integral – derivative controller.

Ps : Synchronizing power coefficient.

PSO : Particle swarm optimization.

T : Transpose of a matrix.

TA : Amplifier time constant.

Tc : The computation time for the central processor.

Tcm : The computation time of cascade processing.

Td : The computation time for data transfer between all microprocessors and the central processor.

Te : Electrical torque.

TE : Exciter time constant.

Tg : Governor time constant (s).

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xii

TG : Generator time constant.

Tm : Mechanical torque.

TP : The total computation time using parallel microprocessors.

tr : Rise time.

TR : Amplifier time constant.

ts : Settling time.

Ts : The computation time for each microprocessors.

Ts : The computation time of single processing of each area.

U : Control signal.

Ve : Error voltage (p.u).

VE : Exciter voltage (p.u).

VF : Field voltage (p.u).

VR : Sensor voltage (p.u).

Vref : Refrence voltage (p.u).

VS : Sensor voltage (p.u).

VSC : Variable structure control.

Vt : Terminal voltage (p.u).

Xtie : Tie-line reactance.

ZN : Ziegler-Nichols.

β : The weighting factor.

Τt : Turbine time constant (s).

ωs : Synchronous angular speed (rad/s).

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CHAPTER 1

INTRODUCTION

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Chapter1 INTRODUCTION

1

Chapter One

INTRODUCTION

1.1 Research Motivation

Everyone desires an uninterrupted power supply. But it is always not

possible for a system to remain in normal steady state, since both the active and

reactive power demands are continually changing with rising and falling trend

[1-2]. In modern interconnected networks, where a number of utilities are

interconnected and power is exchanged between them over tie-lines, the

Load Frequency Control (LFC) and Automatic Voltage Regulator (AVR)

problems are major requirements. Excitation of generator must be regulated

in order to match the reactive power demand; otherwise bus voltage falls

beyond the permitted limit. The mechanical input power to the generator is

used to control the frequency of output electrical power and to maintain the

power exchange between the areas as scheduled. In modern interconnected

power system, manual control is not feasible. Hence automatic equipments

are installed on each generator. The objective of control strategy is to

generate and deliver power in an interconnected power system as

economically and reliably as possible while maintaining the voltage and

frequency within permissible limits. In order to get better performance from any

controller, its parameters need good optimization. The conventional methods

face some difficulties to achieve this purpose, such as complex mathematical

equations for large systems [3]. Novel Artificial Intelligence (AI) techniques

offer some challenges for parameters optimization of controllers. This thesis

concentrates on a novel AI technique for tuning the proposed controllers of LFC

and AVR as well as parallel technique applied to two areas LFC and two area

LFC with AVR.

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2

1.2 Literature Review

The voltage and frequency controllers have gained importance with the

growth of interconnected system and have made the operation of power

system more reliable. A lot of studies have been made in the past about the

LFC. In the literature, some control strategies have been suggested based on the

conventional linear control theory [4]. Gain scheduling is a controller design

technique used for non-linear systems. Therefore, a gain scheduling controller

can be used for this purpose. In this method, since parameter estimation is not

required, control parameters can be changed very quickly. In addition, gain

scheduling application is easier than both automatic tuning and adaptation of

controller parameters methods [5]. However, the transient Response for this

controller can be unstable because of abruptness in system

parameters. Besides, it cannot be obtained accurate linear time variant

models at variable operating points [6]. Evolutionary algorithm caused

serious concern in the optimization fields, various evolutionary algorithms

emerged in endlessly. In [7] Bacterial Foraging Optimization Algorithm

(BFOA) is used for optimal designing of Proportional – Integral (PI) controller

for LFC in two area interconnected power system. In [8] Multiple Tabu

Search (MTS) algorithm is used in design of a Fuzzy Logic based

Proportional Integral (FLPI) for LFC in two area interconnected power system

. In [9] hybrid Genetic-Tabu search algorithm (GT) is used for tuning the

elements of a Proportional – Integral – Derivative (PID) controller which is

applied in a multi Area LFC. In [10] Imperialist Competitive Algorithm (ICA)

is used for tuning the parameters of a PID controller which is applied in a multi

area LFC. In [11] GA, Particle Swarm Optimization (PSO) and fuzzy

Algorithm based PID are used for automatic load frequency control of a

multi area power system. In [12] BFOA is used to find the parameters

optimization of nonlinear LFC considering PID for a power system. A large

number of researchers have pointed out that the implementation of

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3

centralized controller has certain difficulties when the complexity of

interconnected areas increase. These difficulties can be traced to the need

of enormous instrumentation and telemetering of the required data to a

central processing unit [13]. The application of a decentralized control strategy

to the LFC problem has found wide acceptance because of its role in

eliminating some of the problems associated with other centralized or multi-

level control strategies [14-16]. The main desirable features of decentralized

LFC are the following:

(i) It should provide better transient response and improved stability margin.

(ii) The Area Control Error (ACE) should be zero at steady state, i.e. frequency

and tie line power deviation should be zero under steady state.

(iii) The control law should be independent of disturbance.

(iv) Each area controller should use its own area output information.

A number of decentralized control methods has been employed in the design of

decentralized LFC in order to achieve better dynamic performance [17].

Among various types of load frequency controllers, the most widely

employed is the conventional PI controller. The PI controller is very simple for

implementation and gives better dynamic response, but their performance

deteriorates when the complexity in the system increases [18]. The PI control

strategy has slightly smaller deviation at the first peak than integral control

strategy but settling time for only integral control is less. The response with

the PI controller is more oscillatory than the integral controller [19]. Control

system performance can be improved significantly by allowing the controller to

switch from one mode to another. For instance, for certain linear systems

switching from a proportional controller to integral controller in a feedback loop

may provide a fast response, small over shoot, and no offset [20]. Based upon

the above-mentioned facts, it is desirable to adopt a dual–mode controller

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4

involving both proportional and integral controller. The proportional controller

acts when rate of change of the error is sufficiently large, whereas the integral

controller would be better one when the rate of change of the error is small.

Another type of controller, Variable Structure Controller (VSC) is a viable

high-speed switching feedback control (for example, the gains in each feedback

path switch between two values according to some rules). This VSC law

provides an effective and robust means of controlling nonlinear plants [21]. But

there are some problems facing the use of proposed controllers such as tuning

its parameters. To overcome this problem, some of evolutionary algorithm are

used.

Evolutionary algorithm caused serious concern in the optimization

fields, various evolutionary algorithms emerged in endlessly. Recently,

global optimization technique like Genetic Algorithm (GA) has attracted the

attention in the field of controller parameter optimization. Unlike other

techniques, GA is a population based search algorithm, which works with a

population of strings that represent different solutions. Therefore, GA has

implicit parallelism that enhances its search capability and the optimization can

be located swiftly when applied to complex optimization problems.

Unfortunately recent research has identified some deficiencies in GA

performance [22]. This degradation in efficiency is apparent in applications

with highly complicated objective functions (i.e. difficult where parameters

being optimized are highly correlated). Also, the premature convergence of GA

degrades its performance and reduces its search capability. To overcome the

limitations associated with GA, colonies of social insects such as ants and

bees have sense ability known as swarm intelligence [23]. This highly

organized behavior enables the colonies of insects to solve problems beyond

capability of individual members by functioning collectively and interacting

primitively amongst members of the group [24-27].

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5

The large power system problems are such as the large time of

computation. With increase number of areas in the cascaded system as a result

of that the time of computation increases, and because the time is important.

The emergence of parallel processing architectures, and fast network

computation opened new opportunities and challenges to apply these recent

technologies to solve power system problems. High efficiency is usually hard to

reach because computation and communication takes too much time during

each calculation time-step, thus for the solution of large scale power system

networks, it is possible to substantially reduce the computation time if special

proposed parallel processing hardware and parallel programming were used

[28-29]. There are various types of commercially available parallel processing

computers: carrier, shared-memory multi-processor computers, and distributed-

memory parallel computers, and real time digital simulator [30].

1.3 Objectives of the Thesis

Based on the previous literature review, this thesis concentrates on

applying a novel AI technique for optimal tuning of VSC and dual PI controller

parameters for single area and multi-area power systems. A decentralized load

frequency based on VSC and dual PI controller is proposed and compares it

with respect to the conventional control. The tuning of proposed controllers by

Artificial Bee Colony (ABC) and GA is used to enhance the dynamic behavior

of systems and to reduce the coupling effect between AVR and AGC. Also this

thesis proposes the application of parallel processing on two area LFC and two

area LFC with AVR.

1.4 Thesis Outline

The chapters of the thesis are organized as follows:

Chapter 1: Gives a brief theoretical background of LFC and AVR

problems, various types of controllers and the iterative heuristic

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6

optimization algorithms. This chapter also includes the objectives as

well as outline of the thesis.

Chapter 2: Presents the modeling of the power system components

such as generators, speed controllers, transmission lines (tie-lines) and

electrical loads. It also describes the models used throughout this

thesis in order to demonstrate the feasibility of the proposed

controllers.

Chapter 3: Gives a brief theoretical background of VSC and the dual

PI controller. Furthermore, the proposed design of VSC and dual PI

controller is then explained.

Chapter 4: Gives a brief theoretical background of optimization

algorithms (GA and ABC) used in the design procedure.

Chapter 5: Includes the application of the proposed VSC design

and dual PI controller to the LFC problem. This includes single and

two areas LFC systems. The systems were studied with and without

nonlinearities in the models. Also PID controller is applied to AVR.

Furthermore, the interaction between LFC and AVR was studied.

Chapter 6: Studies the application of parallel technique to multi area

electrical power system.

Chapter 7: Includes conclusion as well as contributions reached in the

thesis. Moreover, direction for future research in this subject is also

suggested.

The thesis also includes:

References.

Appendix.

The flow chart of thesis is shown in Figure 1.1.

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7

ELECTRICAL POWER SYSTEM

Single area

LFC

By

I ,PI,dual PI and VSC

Optmized by

GA and ABC

As

microprocessor

AVR

By

PID controller

Optmized by

GA and ZN

As

microprocessor

LFC with AVR

BY

PID and VSC

Optmized by

GA and ABC

As

microprocessor

Two area

LFC

By

dual PI and VSC

Optmized by

GA and ABC

By

parallel technique

LFC with AVR

By

PID and VSC

Optmized by

GA and ABC

By

parallel technique

Figure 1.1 Chart of the thesis.

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CHAPTER 2

MODELING OF ELECTRICAL

POWER SYSTEM COMPONENTS

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MODELING OF ELECTRICAL POWER SYSTEM Chapter2

8

Chapter Two

MODELING OF ELECTRICAL POWER SYSTEM

2.1 Introduction

Nowadays loads are continuously changing. If the load on the system is

increased the speed of turbine is reduced before the governor can adjust the

input of steam to the new load. As the change in output of system becomes

smaller, the position of governor moves to set point to maintain a constant

speed. On the other hand, the generator excitation system controls generator

voltage and reactive power flow using AVR. In order to study the behavior of a

dynamic system via feedback control, a proper mathematical model is essential.

Generally there are a number of system components of AGC loop and AVR

loop that are important to the dynamic study of the power systems . Schematic

diagram of LFC and AVR of a synchronous generator is shown in Figure 2.1 as

given in [31].

Figure 2.1 Schematic diagrams of LFC and AVR of a synchronous

generator.

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9

2.2 LFC and Modeling of Various Components

The LFC objective is to control the frequency deviation by maintaining

the real power balance in the system. The main functions of the LFC are to

maintain the constant frequency with incremental load change, control the tie-

line flows and distribute the load among the participating generating units. The

control (input) signals are the tie-line deviation ∆Ptie (measured from the tie-

line flows), and the frequency deviation ∆f (obtained by measuring the angle

deviation ∆δ). These error signals ∆f and ∆P tie are amplified, mixed and

transformed to a real power signal, which then controls the valve position.

Depending on the valve position, the turbine (prime mover) changes its output

power to establish the real power balance [32]. For the analysis purpose, the

model for each block in Figure 2.2 is required.

Where

Tm : Mechanical torque

Te : Electrical torque

Pe : Electrical power

Pm : Mechanical power

2.2.1 Generator Model

The generated power and the electrical load constitute the power system.

Using the swing equation, the generator can be modeled by [32]:

Where

(2.1)

Figure 2.2 The schematic representation of LFC system.

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10

Where

By expressing the speed deviation in Pu.

This relation can be represented as shown in Figure2.3.

Figure 2.3 The block diagram representation generator model.

2.2.2 Load Model

The load on the system is composite consisting of frequency independent

component (ΔPL ) and a frequency dependent component (ΔPf). The load can

be written as

ΔPe = ΔPL+ ΔPf

Where

ΔPe is the change in the load.

∆δ is the incremental change in rotor angle (rad).

H is the generator inertia constant (s).

ωs is the synchronous angular speed (rad/s).

(2.2)

(2.3)

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11

ΔPL is the frequency independent load component.

∆ Pf is the frequency dependent load component.

ΔPf = D Δ

Where, D is called frequency characteristic of the load (also called as damping

constant) expressed in percent change in load. For 1% change in frequency. If

D=1.5%, then a 1% change in frequency causes 1.5% change in load. The

combined generator and the load (constituting the power system) can then be

represented as shown in Figure 2.4 (a).

Figure 2.4(a) The block diagram representation of the generator and load.

Eliminating the simple feedback loop in Figure 2.4 (a), results in the

block diagram of Figure 2.4 (b).

Figure 2.4 (b) The simplified block diagram representation of the generator and

load.

(2.4)

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12

2.2.3 Turbine Model

The turbine can be modeled as a first order lag as shown in the Figure 2.5.

Where

∆Pv is the incremental change in governor valve position (p.u.MW).

Gt(s) is the Transfer Function (TF) of the turbine.

∆Pm is Incremental change in mechanical power (p.u.MW).

2.2.4 Governor Model

Governor can similarly modeled as shown in Figure 2.6. The output of

the governor is given by:

Where

∆Pref is the reference set power.

∆ω/R is the power given by governor speed characteristic.

R is the speed droop.

The hydraulic amplifier transforms this signal ∆Pg into valve/gate position

corresponding to a power ∆PV. Thus

(2.7)

(2.5)

(2.6)

Figure 2.5 The turbine model.

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13

All the individual blocks can now be connected as shown in Figure 2.7 to

represent the complete LFC loop.

2.2.5 State Space Model of LFC

The dynamic Equations corresponding to the block diagram shown in

Figure 2.7 can be written as

Governor model:

VP

=

∆Pref -

∆ -

∆PV

Turbine model:

=

∆Pv -

∆Pm mP

Rotating mass and load model:

=

ΔPm-

ΔPL-

Δ

Figure 2.6 The block diagram representation of the governor.

(2.8)

(2.9)

(2.10)

Figure 2.7 The block diagram representation of the LFC.

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14

The model defined by Equations (2.8)-(2.10) can be rewritten in the state space

form as

=A x(t)+B u(t)+E w(t) ( )x t

Where

x(t)=[Δ (t),ΔPm(t),ΔPv(t)]T

u(t)=[ΔPref]

w(t)=[ΔPL]

A=

[

]

B=

E=

2.3 Generator Voltage Control System

The voltage of the generator is proportional to the excitation (flux)

of the generator. The excitation is used to control the voltage. Therefore, the

voltage control system is also called as excitation control system or AVR.

For the generators, the excitation is provided by a device (another

machine or a static device) called exciter. Depending on the way the DC

supply is given to the field winding of the alternator (which is on the rotor), the

exciters are classified as Direct Current (DC) exciters, Alternating Current (AC)

exciters and static exciters. According to [32] a real model of AVR system is

shown in Figure 2.8.

(2.11)

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15

Figure 2.8 A real model of AVR system.

By referring to Figure 2.8 which contains the different blocks of AVR

system, the model of each block can be obtained in following sections.

2.3.1 Amplifier Model

The transfer function of amplifier model is

Where KA is a gain and TA is a time constant.

2.3.2 Exciter Model

The transfer function of exciter model is

Where KE is a gain and TE is a time constant.

2.3.3 Generator Model

The transfer function of generator model is

Where KG is a gain and TG is a time constant.

(2.12)

(2.13)

(2.14)

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16

2.3.4 Sensor Model

The transfer function of sensor model is

Where KR is a gain and TR is a time constant.

2.3.5 State Space Model of AVR

The dynamic Equations corresponding to the block diagram shown in

Figure 2.9 can be written as:

Amplifier model:

RV

=

Vref

VS

VR

Exciter model:

FV

=

VR -

VF

Generator model:

tV

=

VF -

Vt

Sensor model:

SV

=

Vt -

VS


form as

( )X t

=A x(t)+B u(t)

Figure 2.9 Closed-loop block diagram of AVR.

system.

(2.15)

(2.16)

(2.17)

(2.18)

(2.19)

(2.20)

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17

Where

x(t)=[ VR VF Vt VS]T

u(t)=[Vref]

A=

[

]

B= [

,0,0,0]

2.4 LFC-AVR System Model

If the effect of voltage on real power is considered, the following

linearized equation is obtained:

Where

K1 is the change in electrical power for small change in stator emf.

Ps is the synchronizing power coefficient.

Also including the small effect of rotor angle upon generator

terminal voltage is considered as follows.

Where

K2 is the change in terminal voltage for small change in rotor angle.

K3 is the change in terminal voltage for small change in stator emf.

(2.21)

(2.22)

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18

Finally, modifying the generator field transfer function to include effect

of rotor angle, the stator emf can be expresed as

The above constants depend upon the network parameters and operating

conditions [31].

The dynamic Equations corresponding to the block diagram shown in Figure

2.10 can be written as

VP

=

∆Pref

∆

∆PV

mP

=

∆Pv

∆Pm

=

ΔPm

ΔPL

Δ

Δδ E

'

(2.23)

(2.24)

(2.25)

(2.26)

Figure 2.10 LFC-AVR block diagram of single area power system.

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19

=Δ

RV

=

Vref

VS

VR

FV

=

VR -

VF

E

=

VF

Δδ

E

'

SV

=

E

'

Δδ

VS


form as

( )X t

=A x(t)+B u(t)+E w(t)

Where

x(t)=[ΔPv(t) , ΔPm(t),Δ (t),Δδ(t),VR,VF,E',Vs]

T

u(t)=[ΔPref, ΔVref]T

w(t)=[ΔPL]

The matrices given in Equation (2.32) are known as:

A is 8 ×8 system matrix.

B is 8 × 2 input vector.

E is 8 × 1 disturbance vector.

These matrices are given as:

(2.27)

(2.28)

(2.29)

(2.30)

(2.31)

(2.32)

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20

A=

[

]

Bt=[

]

Et=*

+

2.5 LFC in the Multi Area System

In a multi-area system, the interaction between different areas

(subsystem) is through the tie-line power exchange. Changes in tie-line power

flows affect to the power balance in the corresponding areas. Considering area i

in an nth-area system. Corresponding to the change in load demand by ∆ PLi let

the tie-line schedule deviation be ∆Ptie,i. then

∑

Where ∆Ptie,ij is the change in tie-line power flow over the line connecting the

area i and j. Further, ( as illustrated in [32] ):

(2.33)

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21

| || |

Where | | | | are the voltage magnitudes at the tie-line ends in areas i

and j, respectively and Xij is the reactance of the same tie-line and δ ij the

phase shift between nominal bus voltages.

Equation (2.33) can be linearized for small deviation in the tie-line flow

∆Ptie,ij from the nominal value, i.e.,

| |

δ

δ

Let

| |

δ

δ

Then,

For a frequency deviation of ∆fi in the ith area

(∫

∫

)

( ) ∑

Taking the laplace transforms on both sides

∑

Thus, for the case of multi-area interconnected system [32],

(2.34)

(2.35)

(2.36)

(2.38)

(2.37)

(2.39)

(2.40)

(2.41)

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22

Taking the laplace transforms on both sides and rearranging terms

[ ]

if

(

) (

) (

) (

)

.

The block schematic of an ith control area in an interconnected system is

shown in Figure2.11.

The dynamics of the turbine can be expressed as :

miP

(

) (

)

The dynamics of the governor can be expressed as:

ViP

(

) (

) (

)

The total tie-line power change between area-i and the other areas can be

calculated as:

Figure 2.11 Block schematic of interconnected areas.

(2.42)

(2.43)

(2.45)

(2.46)

(2.44)

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23

,tie iP

∑

In a multi-area power system, in addition to regulating area frequency, the

supplementary control should maintain the net interchange power with

neighboring areas at scheduled values. This is generally accomplished by

adding a tie-line flow deviation to the frequency deviation in the supplementary

feedback loop. A suitable linear combination of frequency and tie-line power

changes for area i , is known as the ACE,

, .i tie i i iACE P B f

Bi is the frequency bias factor of area i

Bi=Di +1/Ri

2.6 Generation Rate Constraint (GRC)

In real power system, there exists a maximum limit on the rate of the

change in the generation power. GRC is taken into account by adding limiter to

the turbine input and also to the integral control part to prevent excessive

control action [33]. It is assumed that generation units belonging to the same

type of generation will have the same GRC. The GRC would significantly

influence the dynamic responses of power systems. In case where GRC is

considered, the system will present larger overshoots and longer settling times,

compared with the case where GRC is not considered. Typical value for GRC is

taken as 0.1p.u MW/min [33]. Nonlinear turbine model with GRC is shown in

Figure 2.12.

(2.47)

(2.48)

(2.49)

Figure 2.12 Nonlinear turbine model with GRC.

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CHAPTER 3

PROPOSED CONTROLLERES

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Chapter3 PROPOSED CONTROLLERS

24

Chapter Three

PROPOSED CONTROLLERS

3.1 Introduction

Many control strategies for LFC have been proposed since the 1970s e.g.,

[4-12]. Power systems always contain parametric uncertainties. In the design of

a controller, the uncertainties have to be considered. Otherwise, if the real

plant differs from the assumed plant model, a controller design based on

classical approaches may not ensure the stability of the overall system.

Based on the concepts of discontinuous control as illustrated in [16-20], dual-

mode control can improve the system performance. The early work on VSC was

conducted by Russian authors before four decades. Interest in this method

evolved after the comprehensive work and translation made by Utkin [34]. Pan

and Liaw [35] proposed an adaptive PI controller adaptation. Concepts of

variable structure systems have subsequently been utilized in many applications

and engineering problems including power systems, aerospace , and robotics

[36]. Recently, several authors [34-36] have applied the concept of VSC to the

design of load-frequency controllers. The VSC controller changes the

system control structure in accordance with some law of structural change,

which improves the dynamic performance and makes the controller

insensitive to the plant parameter changes. Various adaptive control

techniques have been also proposed for dealing with parameter variations.

This chapter starts by reviewing some of the basic concepts of VSC.

Merits and demerits of VSC are also mentioned. The basic concept of dual PI

control is also discussed in this chapter.

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25

3.2 Basic Concepts of Variable Structure Control

The fundamental requirement of this theory, as proposed by most authors,

is to find the necessary and sufficient conditions for the existence of a sliding

mode regime on a designed sliding hyper-plane. Other requirements include the

conditions that guarantee hitting the sliding hyper-plane from any location in

the state space, the conditions for the stability of the sliding mode, and the

conditions for invariance in sliding regime. Furthermore, sliding mode reaching

condition is the condition under which states of the system are guaranteed to

move towards and reach a sliding surface. There are various methods of

defining this condition [34]. One of the conditions is the Lyapunov function-like

reaching condition is defined as follows:

V =

σ

2

Where σ is switching hyper planes,

V

=

σ< 0

The direct switching function approaches are defined by

These conditions for achieving a sliding regime are discussed in details in [33-

34].

The basic concept of VSC can be illustrated by the following example

[37]: Consider a second-order system described by the following equations,

x y

2y y x u

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)

(3.2)

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26

u x

Where

{

and

s(x,y)= xσ

σ=0.5x + y

Figure 3.1(a) shows a block diagram of the system. s(x, y) is called the

switching surface. It consists of the product of two functions x = 0 and

σ = 0.5x + y = 0. These functions represent switching lines that divide the phase

plane into regions according to the sign of s(x, y) as shown in Figure 3.1(b).

The main regions are defined as follows,

Region I: s(x , y) = xσ > 0, ψ = 4, and the model is described as

x y

2 4 2 5y y x x y x

The phase trajectory of such system is shown in Figure 3.2(a).

Region II: s(x , y) = xσ < 0, ψ =- 4, with state equations

x y

2 4 2 3y y x x y x

The system is shown in the phase plane as in Figure 3.2(b).

The above two models show unstable trajectories.

(3.7)

(3.8)

(3.9)

(3.10)

(3.11)

(3.12)

(3.6)

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27

The trajectory of the whole system is formed by combining the

trajectories of the two subsystems depending on the location of the

representative point in the phase plane with respect to the two regions. The

trajectory of the whole system, as illustrated in Figure 3.2 (c), is stable.

The phase trajectory can be divided into two phases:

1) Reaching mode: where the trajectory moves toward the sliding surface from

any point in the phase plane.

2) Sliding mode: where the trajectory is maintained on the sliding surface and

moves towards the origin of the phase plane. During this mode the dynamics

of the system can be described as follows:

Figure 3.1(b) Regions divided by the switching lines

Figure 3.1 (a) Block diagram of VSC.

x y u

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28

σ=0.5x + y=0.5x+ x

The dynamics of the system are therefore of lower order during the sliding

mode. This type of control is called variable structure control because the

controller changes the system structure from that of Equation (3.10) to

Equation (3.12) model depending on the location of the representative point

in the phase plane.

3.2.2 Merits and Demerits of Variable Structure Control

The advantages of obtaining a sliding motion are: reduction of the order

of the system and increase the sensitivity to parameter variations. This allows

the design of a robust controller against uncertainties in the parameters of the

system. Furthermore, VSC allows the determination of the closed-loop

dynamics of nonlinear system in a desired manner. This can be done by

Figure 3.2 Phase trajectories

(3.13)

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29

multiplying each state variable by a certain gain as a pole placement design

and varying the coefficients of the sliding surface. The problem associated with

VSC design is the selection of the feedback gains. Generally, the gains are

chosen by trial and error such that they will satisfy certain system performance

requirements. Recently, the problem of VSC feedback gains selection has been

considered by [38]. Their approach essentially was to try all allowable values of

the feedback gains and evaluate a performance index for each possible set of

feedback gains. The optimal feedback gains selected are those which minimize

the performance index. This approach is numerically intensive especially for

large numbers of feedback gains. Furthermore, in conventional design methods

of the switching surface for the VSC for a nonlinear system, various

transformations of the differential equations to a suitable canonical form is

required [39]. These transformations are complicated and are not always

possible. This thesis try to solve the problems which facing VSC by using

iterative heuristic optimization algorithms such as GA and ABC.

3.2.1 Proposed Design Method of VSC

This thesis try to tune the parameters of the VSC using iterative heuristic

optimization algorithms. These parameters of the VSC include both the

switching vector values and the switching feedback gains. The conventional

VSC control laws are used for the designed system. A block diagram of the

VSC is shown in Figure 3.3, where the control law is a linear state feedback

whose coefficients are piecewise constant functions. Consider the linear time-

invariant controllable system given by

X AX BU

Where

nX R is the state vector.

(3.14)

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30

mU R is the control input vector.

n nA R is the system matrix.

n mB R is the input matrix.

The VSC control law for the system of Equation (3.14) are given by

Where the feedback gains are given as

And

, i=1,2……………., m

are the switching vectors iCWhere

To find the optimal values of the switching vector and the switching

feedback gains iterative heuristic optimization algorithms such as GA and ABC

are used.

ψ ∑ ψ

i=1, 2,…………m

{

(3.15)

(3.16)

Figure 3.3 Block diagram of VSC.

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3.3 Basic Concepts of Dual PI Control

An example of a relay system is essential to understand a dual-mode

control system [40]. A relay system as shown in Figure 3.4(a) and having the

closed loop state equation,

x F x g u

( )u sign k x

Where

K' is the gain matrix.

F is the state distribution matrix.

g is the control distribution matrix.

x is the state vector.

The dual-mode control has two modes of operation. In one mode, the

discontinuous mode, the input to the relay is either a fixed negative value, and

sign changes occur instantaneously. In the other mode, known as the continuous

mode or the linear mode, the relay input is zero and the output fluctuates

between its maximum and minimum limits with an average sliding value that

could alternatively be realized by a linear state feedback control law.

Typically, for a large initial state, the controller will operate first in the

discontinuous mode and then, when the states are sufficiently small, it will enter

the linear mode and remain in this mode even on reaching the zero state. A

typical state trajectory and the corresponding control input are shown in Figure

3.4.b and Figure 3.4.c respectively.

(3.17)

(3.18)

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Figure 3.4 Relay dual-mode control .

system.

Figure 3.5 Error signal without controller.

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For the linear mode, the states obey the following Equations [40]

K' X = 0 | |

And if is non-zero

The bounded hyper plane defined by Equation (3.17) is termed as the singular

bounded hyper plane. A ‘Singular strip’ is a portion of the singular bounded

hyper plane with the property that the solutions of the Equation (3.17) starting

in the singular strip remain in the singular bounded hyper plane. The input X(t)

is considered here as the rate of change of the area control error ,

( ( )) /d ACE t dt , as shown in Figure 3.5.

3.3.1 Proposed Design of Dual PI Control

It is proposed that the control structure be switched during the

discontinuous mode. The type of structure (P controller or I controller) to be

used during the discontinuous mode depends upon the particular problem and

switching can be performed on a simple criterion such as rate of change of the

error staying within a singular strip.

3.3.1.1Discontinuous Mode

The control system will operate in this mode when the rate of change of

the error signal, as shown in Figure 3.5 exceeds specified limit. In the

discontinuous mode, the control should switch between two different controller

in the feedback loop until the rate of change of the error signal trajectory enters

the singular strip permanently. The time at which these changes occur is

determined in accordance with the current value of the derivative of the error

signal. Based on the properties of the proportional and the integral control, the

system response can be improved by employing a variable structure concept

X

(

)

(3.19)

(3.20)

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that combines useful properties of both the control action during the

discontinuous mode. The control law employed during the transient period that

is the discontinuous mode is switched between Equations (3.21) and (3.23)

depending upon the magnitude of the rate of change of the error signal.

For |

|

Where

ACE(t) is an error signal at a particular instant.

ε is a very small positive constant indicating the specified limit of rate

of change of the error signal.

ε =Kc ∆PL

Where Kc is scaling factor and

For |

|

∫

Then if the parameters Kp, Ki and Kc are suitably selected, one can ensure a high

quality transient response. By choosing a suitable value of Kp, one makes sure

that speed of the system is high. Whenever the rate of change of error falls

within the specified error bound |

| , the integrator starts

accumulating the error. But if the error exceeds the bound the integrator resets

to zero. This continuous switching between the proportional and integral control

strategies quickly brings the system to the continuous mode when |

|

.

(3.21)

(3.23)

(3.22)

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3.3.1.2 Continuous Mode

When the rate of change of the error signal remains within the specified

limit i.e.|

| the system will operate in the continuous mode.the

integral control strategy is best able to meet the LFC requirements when the

system enters the continuous mode. Thus the control law during the continuous

mode would be

∫

Where tε<t is the time at which the error enters the region |

| and

remains in this region. The integral control will then eliminate the steady state

error remaining in the system. The proposed control scheme is shown in Figure

3.6. To find the optimal values of Kp , Ki and Kc an iterative heuristic

optimization algorithms such as GA and ABC are used.

(3.24)

Figure 3.6 Block diagram for the proposed dual.

Mode. Controller

ACE(t) |

|

KP

( )iK ACE t dt

YES

NO

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CHAPTER 4

INTELLEGENCE OPIMIZATION

TECHNIQUES

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Chapter4 INTELLIGENCE OPTIMIZATION TECHNIQUES

36

Chapter Four

INTELLIGENCE OPTIMIZATION TECHNIQUES

4.1 Introduction

The operating point of the power system changes in a daily cycle due to the

inherent nature of the changing load. This poses the difficulty in optimizing the

conventional controller gains. Thus it may fail to provide the best dynamic

response .The growth in size and complexity of electric power systems along

with increase in power demand has necessitated the use of intelligent systems

that combine knowledge, techniques and methodologies from various sources for

the real-time control of power systems [41]. In practice different conventional

control strategies are being used for LFC. Yet, the limitations of conventional PI

and PID controllers are: slow and lack of efficiency and poor handling of

system nonlinearities. Artificial Intelligence techniques like Fuzzy Logic,

Artificial Neural networks, GA , Particle Swarm Optimization (PSO) and

ABC can be applied for LFC, which can overcome the limitations of

conventional controls. This chapter gives an overview of GA and ABC

techniques, which are used in this thesis.

4.2 Genetic Algorithm

GA is powerful domain independent search technique inspired by

Darwinian Theory of evolution. It was invented by John Holland and his

colleagues in 1970s [42] and was successfully applied to many engineering and

optimization problems and to various areas of power system such as economic

dispatch, unit commitment , reactive power planning , power plant control , and

Generation expansion planning [43]. GA is an adaptive learning heuristic that

imitate the natural process of evolution to progress toward the optimum by

performing an efficient and systematic search of the solution space. A set of

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solutions, described as a population of individuals, are encoded as binary

strings, termed as Chromosomes. This population represents points in the

solution space. A new set of solutions, called Offsprings, are created in a new

generation (iteration) by crossing some of the strings of the current generation.

This process is called Crossover. Furthermore, the Crossover is repeated at

every generation and new characteristics are introduced to add diversity. The

process of altering some of the strings of the Offsprings randomly is known as

Mutation.

The basic steps of GA can be described as follows:

Step1: Generation of Initial population of solutions represented by

Chromosomes.

Step 2: Evaluation of the solutions generated using the fitness function which

is usually the objective function of the problem under study.

Step 3: Selection of individual solutions that have higher fitness value. There

are different selection methods such as Roulette wheel selection,

Stochastic selection, and Ranking-based selection.

Step4: Generation of new offsprings from the selected individual solutions.

This is done for certain number of generations using two main

operations:

- Crossover: There are various crossover operators; the most common is the

one- point crossover. In one-point crossover, one bit in each solution, of two

given binary coded solutions, is determined randomly and then swapped to

generate two new solutions.

- Mutation: Incremental random changes applied in the selected offsprings by

altering randomly some its bits. Mutation is usually probabilistically applied to

only few members of the population and therefore has a small value.

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Step 5: Steps 2 to 4 are repeated until a predefined number of generations have

been produced. The flow chart of GA is shown in Figure 4.1.

4.3 Artificial Bee Colony optimization algorithm

The ABC algorithm is proposed by Karaboga [44-46] in 2005, and the

performance of the ABC is analyzed in 2007 [45].In a real bee colony, there

are some tasks performed by specialized individuals. These specialized bees try

to maximize the nectar amount stored in the hive by performing efficient

Figure 4.1 Flow chart of Genetic Algorithm.

Yes

Yes Done

Done

Generation =Generation+1

Genetic operators Reproduction Crossover Mutation

Simulate the system and evaluate the

performance index

Randomly generate the initial population

Is convergence Obtained?

Is generation maximum?

No

No

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division of labour and self-organization. The minimal model of swarm-

intelligent forage selection in a honey bee colony, that ABC algorithm adopts,

consists of three kinds of bees: employed bees, onlooker bees, and scout bees.

Half of the colony comprises employed bees and the other half includes the

onlooker bees. Employed bees are responsible from exploiting the nectar

sources explored before and giving information to the other waiting bees

(onlooker bees) in the hive about the quality of the food source site which they

are exploiting. Onlooker bees wait in the hive and decide a food source to

exploit depending on the information shared by the employed bees. Scouts

randomly search the environment in order to find a new food source depending

on an internal motivation or possible external clues or randomly. The behavior

of honey bee foraging for nectar is shown in Figure 4.2.

The Main steps of the ABC algorithm are given below [45]:

Step 1: Initialize the food source positions.

Step 2: Each employed bee produces a new food source in her food source

site and exploits in the better source.

Figure 4.2 The behavior of honey bee foraging for nectar

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Step 3: Each onlooker bee selects a source depending on the quality of her

solution, produces a new food source in selected food source site and

exploits the better source.

Step 4: Determine the source to be abandoned and allocate its employed bee

as scout for searching new food sources.

Step 5: Memorize the best food source found so far.

Step 6: Repeat steps 2-5 until the stopping criterion is met.

In the first step of the algorithm xi (i = 1,2, — , SN), solutions are randomly

produced in range of parameters where SN is the number of the food sources.

In second step of the algorithm, for each employed bee, whose total number

equals to the all of the number of food sources, a new source is produced by

( )

Where

φij is a uniformly distributed real random number within the range [-1,1].

k is the index of the solution chosen randomly from the

colony(k=int(rand*SN+1), j = 1,2, — ,D

D is the dimension of problem.

After producing vi, this new solution is compared to xi solution and the

employed bee exploits the better source. In the third step of the algorithm, an

onlooker bee chooses a food source with the probability

∑

Where

fiti is the fitness of the solution xi.

(4.1)

(4.2)

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After all onlookers are distributed to the sources, sources are checked

whether they are to be abandoned. If the number of cycles that a source cannot

be improved is greater than a predetermined limit, the source is considered to be

exhausted. The employed bee associated with the exhausted source becomes a

scout and makes a random search in problem domain by

(

)

Where

rand is random number within the range [0,1].

The flow chart of ABC could be simplified as is shown in Figure 4.3.

Figure 4 .3 Flow chart of Artificial Bee Colony.

(4.3)

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42

4.4 Performance Index

The design of a control system is an attempt to meet a set of

specifications, which define the overall performance of the system in

terms of certain measurable quantities. A number of dynamic performance

measures i.e. peak overshoot (Mp), rise time (tr), peak time (tp), settling time

(ts) and steady state error (ess), have been introduced for step and higher order

inputs. These measures have to be satisfied simultaneously in design and

hence the design necessarily becomes a trial and error procedure. If,

however, a single performance index could be established on the basis of

which one may describe the suitability of the system response, then the

design procedure will become logical and straightforward. Therefore

performance index is a function of the variable system parameters. The other

desirable features of a performance index are its sensitivity, i.e. its ability to

clearly distinguish between an optimum and non-optimum system, its

sensitivity to parameter variations and the ease of its analytical

computation or its on-line analogical or digital determination[19]. The

Integrated Square of the Error (ISE) is taken as a performance index in this

study to measure the appropriateness of the system .The ISE represent in the

form of.

∫

(4.4)

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CHAPTER 5

APPLICATION OF THE

PROPOSED CONTROL TO THE

POWER SYSTEM

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Chapter5 APPLICATION OF THE PROPOSED CONTROLLERS TO THE POWER SYSTEM

43

Chapter Five

APPLICATION OF THE PROPOSED CONTROLLERS TO

THE POWER SYSTEM

5.1 Introduction

LFC is one of the most important subjects concerning power system

engineers in the last decades. An exact forecast of real power demand is

impossible due to random changes in the load and therefore an imbalance

occurs between the real power generation and the load demand (plus

losses) [47]. In a single area, a turbine connected to a synchronous generator

produces mechanical power. Control system is required to detect the load

changes and command the steam valve to open or close more so that the turbine

increase or decrease its mechanical power production and stabilize the

shaft speed and hence the system frequency. Modern real power systems

constitute interconnected neighboring areas. The study of interconnected

systems is essential to improve the dynamic behavior of power systems.

Studies conducted in the past have shown that area-frequencies and tie-

line power can undergo prolonged fluctuations following a sudden change

in power in an interconnected power system [48]. The main cause of

these fluctuations is the nonlinearities present in the system such as GRC.

A multi-area LFC system constitutes a number of single areas connected by tie

lines. These tie lines allow the flow of power between the areas. Consequently,

a disturbance in one area influences the frequency of other areas as well

as the tie lines power flow. The objective of the LFC is to minimize deviations

of both frequency of all areas and tie line power interchanges. This chapter

studies the application of the proposed design of VSC and dual PI

controller to single and two area power systems. The effect of including the

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44

nonlinearities into the models is also considered. To control the terminal

voltage, PID controller is applied to the AVR. The relationship between LFC

and AVR for the single and two area power systems is also included.

5.2 Proposed VSC Design for a Single Area Power System

The model for LFC of a non-reheat turbine for single area power

system excluding nonlinearities is shown in Figure 5.1 [32]. The model shows

the feedback of the change in frequency to turbine through speed regulator and

an integral controller. The dynamic model in state variable form can be

obtained from the transfer function model and is given as:

( )X t

=A X (t) +B u (t) +E w (t)

Where

X is a 4-dimensional state vector.

u is 1-dimensional control force vector.

w is 1-dimensional disturbance vector.

A is 4 ×4 system matrix.

B is a 4 × 1 input vector.

E is 4 × 1 disturbance vector.

A=

[

]

B=,

-

(5.1)

CHAPTER FIVE APPLICATION OF THE PROPOSED CONTROLLER TO THE LOAD FREQUENCY CONTROL & AUTOMATIC VOLTAGE REGULATOR

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E=[

]

Where

X1 is the change in frequency (p.u).

X2 is the incremental changes in generator output (p.u. MW).

X3 is the incremental changes in governor valve position (p.u. MW).

X4 is the incremental changes in integral control.

The control objective in the LFC problem is to keep the change in

frequency as close to zero as possible when the system is subjected to

load disturbance ∆PL=0.2 p.u when system nonlinearities are not considered

and ∆PL=0.005 p.u when system nonlinearities are considered. The model in

Figure 5.1 excludes system nonlinearities while Figure 5.2 [32] shows the same

model when the nonlinearities, such as GRC, is included. The GRC is

caused by the mechanical and thermodynamic constraints in practical

steam turbines systems. It imposes limits on the rate of change of generated

power. A typical value of 0.1p.u. /min has been chosen in this study [19]. The

model of Figure 5.2 also has a limiter on the integral control values to prevent

excessive control.

Figure 5.1 single area LFC system excluding nonlinearities.

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The design procedure explained in chapter 3 is applied to design a VSC

for a single area LFC when excluding nonlinearities and also when including

nonlinearities. The performance index used for optimization procedure is given

as follows:

∫

Where

J is performance index

Δ is the deviation in frequency.

The parameters of the systems under study of Figure 5.1and Figure 5.2 are

given below:

H = 5 , D= 0.8 , Tt = 0.5 , Kt =1 , Tg = 0.2 , Kg =1 , R = 0.05 .

The proposed VSC design using GA and ABC described in

Chapter 4 has been applied to minimize the performance indices for

optimal selection of the switching vector and feedback gains. Table 5-1 (a)

shows the control parameters and performance indices in different designs in

case of linear model. Table 5-1 (b) presents control parameters and performance

indices in different designs in case of nonlinear model.

(5.2)

Figure 5.2 single area LFC systems with GRC.

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ABC GA

C=[9.35 0.019 0.002 3.534]T

=[50 44.4779 50 41.17] α

K = 9.3838

C=[32.209 0.166 0.029 13.311 ]T

α=[8.27 7.162 28.198 8.548]

K = 9.3838

Control

Parameters

7.243*10-8 4.7832*10-7 Performance

Indices

Table 5-1 (b) Control parameters and performance indices in different designs for nonlinear model.

ABC GA

C=[14.5323 0.5511 1.0722 0.7]T

=[7.5169 0 25.1347 0] α

K = 9.3838

C=[1.633 0.905 0.032 0.141 ]T

α=[2.203 0.695 0.028 0.047]

K = 9.3838

Control

Parameters

1.1*10-6 1.437*10-6 Performance

Indices

5.3 Proposed I, PI, and Dual PI Controller Design for a Single Area Power

System

The proposed I, PI, and dual PI controller design are applied on the same

model for LFC of a non-reheat turbine which is shown in Figure 5.1 and

Figure 5.2 but without the feedback integer controller ( ), which is shown in

the figures .

The design procedure explained in Chapter 3 is applied to design a dual

PI controller for a single area LFC excluding nonlinearities and including

nonlinearities. The performance index was used for optimization procedure it is

given in Equation 5.2.

The parameters of the proposed I, PI, and dual PI controller are design

using GA and ABC described in Chapter 4. These techniques are used to to

minimize the performance index as well as the optimal values of the gains

of each controller. Table 5-2 (a) shows control parameters and performance

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48

indices in different designs in case of linear model. Table 5-2 (b) shows control

parameters and performance indices in different designs in case of nonlinear

model.


ABC GA

Dual PI

Controller

PI

Controller

I

controller

Dual PI

controller

PI

controller

I

controller

Controller type

KP=45.117

KI=9.383

Kc=0.024

KP=23.784

KI=9.606

KI=9.383 KP=45.117

KI=9.383

Kc=0.024

KP=23.784

KI=9.606

KI=9.383 Control

Parameters

1.087*10-4

1.303*10-4

2.457*10-4

1.087*10-4

1.303*10-4

2.457*10-4

Performance

Indices

Table 5-2 (b) Control parameters and performance indices in different designs for nonlinear model.

ABC GA

Dual PI

Controller

PI

Controller

I

controller

Dual PI

controller

PI

Controller

I

Controller

Controller

type

KP=6.867

KI=2.013

Kc=0.035

KP=0

KI=1.23

KI=1.23 KP=6.867

KI=2.013

Kc=0.035

KP=0

KI=1.23

KI=1.23 Control

parameters

1.516*10-6

1.752*10-6

1.752*10-6

1.516*10-6

1.752*10-6

1.752*10-6

performance

indices

It is noticed that the paramerters of I, PI and dual PI controller using the

GA are the same as when using ABC technique.

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5.3.1 The Frist Test Case

Figure 5.3 (a) shows the comparison of the responses of the resultant

frequency for a single area LFC using different types of controllers, I, PI, dual

PI controller and VSC due to a 0.2 p.u step load disturbance. All of controllers

parameters are optimized using ABC technique as shown in tables 5.1 (a) and

5.2 (a). It is found that the response of the frequency using the proposed VSC

technique has smaller over shoot, smaller settling time and smaller performance

index compared to the other types of controllers. It is clear also from Figure 5.3

(a) that the proposed dual PI controller has better performance than I and PI

controller, where the response has shorter settling time and smaller overshoot.

Because of the short rising time and settling time of the frequency

response using VSC technique, an amplified figure of this part is shown beside

the main response.

Figure 5.3(a) Change in frequency due to using ABC

technique in case of single area LFC linear model.

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Figure 5.3 (b) shows the same comparisons, but using GA optimization

technique. The responses of the frequency deviations when using I, PI, and dual

PI controller are the same as Figure 5.3 (a), because they have the same

parameters using ABC technique. It is clear that the VSC is also better than

other controllers.

Figure 5.3 (c) shows the frequency deviations for the single area LFC

linear model using the proposed optimization techniques, ABC and GA. It is

concluded that, the response using ABC technique based VSC is considerably

improved in comparison with the response using GA based VSC in terms of less

settling time and smaller overshoot.

Figure 5.3(b) Change in frequency due to using GA

technique in case of single area LFC linear model.

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5.3.2 The Second Test Case

In order to validate the proposed VSC and dual controllers due to change

in load disturbance according to Figure 5.4(a), Figure 5.4 (b) , Figure 5.4 (c) ,

and Figure 5.4 (d) , show that the change in frequency of single area LFC linear

model by ABC and GA based VSC and dual PI controller, respectively. It is

found that the frequency response using ABC technique based VSC has shorter

settling time and smaller over shoot.

Figure 5.3( c ) Change in frequency due to using ABC and

GA techniques in case of single area LFC linear model.

Figure 5.4(a) Change in load disturbance in case of single

area LFC linear model.

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Figure 5.4(b) Change in frequency of single area LFC linear model

due to using ABC in case of change in load disturbance.

Figure 5.4( c ) Change in frequency of single area LFC linear

model due to using GA in case of change in load disturbance.

Scaling of switching feedback gains

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The proposed ABC based VSC, dual PI, and I controller have been also

applied to single area LFC nonlinear model with 0.05 p.u step load disturbance.

The controllers parameters are optimized using ABC technique and shown in

tables 5.1 (b) and 5.2 (b).

It is clear from table 5.2(b) that the value of KP of PI controller optimized

by ABC and GA equal to zero and the value of KI of PI controller equal the

value of KI of I controller, According to this I controller is only used.

It is clear from Figure 5.5 that the response of the frequency using the

proposed VSC technique has smaller over shoot, shorter settling time and

smaller performance index compared to the other types of controllers.

Also, it can be concluded form Figure 5.5 that the proposed dual PI

controller is better than the I controller.

Figure 5.4(d) Change in frequency of single area LFC linear model by

dual PI controller in case of change in load disturbance.

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54

Another comparison is applied between the proposed VSC, dual PI, and I

controller, but using GA optimization technique. It is clear from Figure 5.6 that

the frequency response using VSC is also better than the response using other

controllers when applied on single area LFC nonlinear model.

It is found that the frequency responces using I, and dual PI controller,

Figure 5.6 are the same as Figure 5.5 because they have the same parameters

using ABC technique.

Figure 5.7 shows the frequency response of single area LFC nonlinear

model using ABC and GA based VSC. The ABC based VSC response has a

smaller settling time, smaller over shoot and smaller performance index

compared to GA based VSC.

Figure 5.5 Change in frequency due to using ABC

technique in case of single area LFC nonlinear model.

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Figure 5.6: Change in frequency due to using GA

technique in case of single area LFC nonlinear model.

Figure 5.7 Change in frequency due to using ABC and GA

techniques in case of single area LFC nonlinear model.

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5.3.3 The Third Test Case

Parameters variation test is also applied to validate the effectiveness of

the proposed controllers. Figure 5.8, Figure 5.9 and Figure 5.10 show the

frequency response with the proposed ABC and GA based VSC and dual PI

controller in case of change of TG and TT by±25%. It is clear that the system is

stable with the change in parameters. From this test the validation of the

proposed controllers is verified.

Figure 5.8 Change in frequency of single area LFC

non linear model by VSC optimized by ABC in case of

change of TG and TT by±25%.

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Figure 5.9 Change in frequency of single area LFC

non linear model by VSC optimized by GA in case of

change of TG and TT by±25%.

Figure 5.10 Change in frequency of single area LFC non

linear model by dual PI controller optimized by GA and

ABC in case of change of TG and TT by±25%.

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5.4 Design of Decentralized LFC based VSC and Dual PI Controller using

ABC and GA.

In the dynamical operation of power systems it is usually important

to aim for decentralization of control action to individual areas. This aim

should coincide with the requirements for stability and load-frequency

scheduling within the overall system. In a completely decentralized control

scheme, the feedback controls in each area are computed on the basis of

measurements taken in that area only [14-16]. This implies that no inter

change of information among areas is necessary for the purpose of LFC. The

advantages of this operating philosophy are apparent in providing cost

savings in data communications and in reducing the scope of the monitoring

network .In the load-frequency control, it is necessary that the system

frequency and the inter area tie-line power are kept as near to the scheduled

values as possible through control action. The important requirement for

system stability may be conveniently met by adopting a global policy for

design, based for example on well-established principles of pole placement

or optimal control by state feedback. Where such an approach is to be used

with decentralized control, the state vector for the entire system should be

made available for the generation of local feedback control signals in all areas.

This requirement may be met if a reconstruction of the whole system state

vector is made within each area only, i.e. if the system state vector is

observable from area measurements. However, even if the observability

condition is satisfied, the resulted controllers with appropriately

designed observers are normally quite complicated and this approach is

not suitable for a large power system where the total number of the state

variables are large [26]. In this section, application of the proposed VSC

design and proposed dual PI controller design to two area interconnected

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power system is investigated and the results are compared with the

conventional I controller [32].

5.4.1Proposed VSC Design for Two Area Interconnected Power System

Figure 5.11 illustrates the idea of using decentralized VSC for each area.

Xi represents the internal states of the ith area. Ui is the supplementary control

signal going to the ith area. The decentralized VSC is applied to the two area

system [49]. GA and ABC were used to obtain the optimal settings of each

controller. A model of two area LFC system [32] is shown in Figure 5.12.

Figure 5.11 Proposed decentralized VSC controllers applied to two area

LFC.

areas

Figure 5.12 Model of two area LFC system.

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Dell

Text Box

Dell

Stamp


60

The design procedure explained in Chapter 3 is applied to design a VSC

for a two area LFC. The performance index, J, used for optimization procedure

is given below.

∫ (

)

The parameters of the system under study are given in [32] as below:

The optimization techniques , GA and ABC , described in chapter 4 based

VSC has been applied to minimize the performance indices for optimal

selection of the switching vector and feedback gains. The system is subjected

to a step load change of 0.2p.u in both areas; simultaneously .Table 5-3 shows

the control parameters and the performance indices in the different proposed

optimization techniques.

Table 5-3 Control parameters and performance indices in different designs.

ABC GA

C1=[-1.153 0.029 0.174 9.46 ]T

α1=[6.351 9.9776 7.4213 6.4953]

C2=[-1.006 0.031 0.184 7.331 ]T

α2=[5.7818 5.6381 7.2669 10]

K1=0.7249 , K2=1

C1=[-0.701 0.016 0.089 3.431 ]T

α1=[0.709 1.824 0.13 0.605]

C2=[-0.508 0.042 0.104 2.953 ]T

α2=[0.873 2.192 0.696 0.276]

K1=0.217 , K2=0.457

Control Parameters

0.0074 0.0418 Performance Indices

TG1=0.2 s

TT1=0.5 s R1=0.05

D1=0.6 , H1=5 , T12=2

TG2=0.3 s

TT2=0.6 s R2=0.0625

D2=0.9 , H2=4 , a12=-1

(5.3)

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5.4.2 Proposed Dual PI Control Design for Two Area Interconnected Power

System.

The proposed dual PI control design is applied to the model of two area

LFC system shown in Figure 5.12 instead of the integral controller shown in the

figure. The same objective function for optimization procedure is given in

equation 5.3.

The optimization techniques , GA and ABC , described in chapter 4 based

the proposed dual PI controller has been applied to minimize the

performance index for optimal selection gains of the proposed dual PI

controller. The system is subjected to a step load change of 0.2p.u in both areas,

simultaneously. Table 5-4 shows the optimized control parameters and

performance indices of dual PI controller and conventional I controller .

Table 5-4 Control parameters and performance indices of dual PI and conventional I controller.

ABC GA

Dual PI

Controller

Dual PI

controller

Conventional I

Controller

Controller Type

KP1=1.4294

KI1=0.2529

KC1=0.497

KP2=1.5

KI2=0.279

KC2=0.814

KP1=1.4294

KI1=0.2529

KC1=0.497

KP2=1.5

KI2=0.279

KC2=0.814

KI1=0.3

KI2=0. 3

Control Parameters

0.1996 0.1996 0.2858 Performance Index

5.4.3 The First Test Case

Step load changes of 0.2p.u are applied to the two area system at the same

time. All types of controller's parameters are optimized using ABC and GA

techniques and obtained in tables 5.3 and 5.4. The frequency deviation of the

first area ∆f1, the frequency deviation of the second area ∆f2 and tie line

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power signal are shown in Figures 5.13 (a-c), respectively. It is clear from

these figures that oscillations are greatly attenuated using the proposed ABC

and GA based VSC. Hence, a comparisons to the Conventional Integral

Controller (CIC) , GA and ABC based dual PI controller and the proposed

VSC technique enhance the system stability and improves the damping of the

power system. Also, it is clear from these figures that the frequency response

using ABC based VSC is better than GA based VSC. Table 5.4 shows that the

dual PI controller parameters are same in case of using GA and ABC

optimization techniques. Figures 5.13 (a-c) show that the responses of the

system give a better performance using the dual PI controller in comparison

with the conventional I controller.

Figure 5.13(a) Change in frequency of first area .

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Figure 5.13(c ) Change in Ptie.

Figure 5.13(b) Change in frequency of second area.

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5.4.4 The Second Test Case

The change in load disturbance is one of the tests, which is applied to the

two area system in order to validate the robustness of the proposed controllers.

Figure 5.14 (a) shows the change in load disturbance, which is applied on both

areas simultaneously, to test the validity of the proposed ABC and GA based on

VSC and dual PI controller.

Figure 5.14 (b-c), Figure 5.15 (a-b) and Figure 5.16 (a-b) show the

responses of the frequency using the mentioned proposed optimization

techniques based the proposed controllers. Results proved that proposed

controllers are robust, which guarantee the effectiveness and robustness of the

system under change of load disturbance.

Figure 5.14(a) Change in load disturbance of area1 and area2.

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Figure 5.14(c ) Change in frequency of second area by

ABCVSC.

Figure 5.14(b) Change in frequency of first area by ABCVSC.

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Figure 5.15( b) Change in frequency of second area by GAVSC.

Figure 5.15(a) Change in load disturbance of area1 and area2.

Figure 5.15(a) Change in frequency of first area by GAVSC.

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Fig 5.16(a) Change in frequency of first area by dual PI

controller optimized by GA and ABC.

Fig 5.16(b) Change in frequency of second area by dual PI

controller optimized by GA and ABC.

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5.4.5The Third Test Case

A parameter variation test is also applied to assess the robustness of the

proposed controller. Figure 5.17 (a-b),Figure 5.18 (a-b) and Figure 5.19 (a-b)

show the change in frequency of area1 and area2 using the proposed ABC and

GA based VSC and dual PI controller in case of change of T12 by±50%. It is

clear that the system is stable with the proposed controllers. The system

response with the proposed ABC based VSC is more robust and gives better

dynamic performances.

(a)

Figure 5.17 Change in frequency of area1 and area2 by

ABCVSC in case of change of T12 by±50%.

(b)

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Figure 5.18 Change in frequency of area1 and area2

by GAVSC in case of change of T12 by±50%.

(a)

(b)

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70

5.5 Design of PID Controller for AVR

At the view of power system, the excitation system must contribute for

the voltage control and enhancement of system stability. In substation grid so


dual PI controller optimized by GA and ABC in case of

change of T12 by±50%.

(a)

(b)

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71

many equipment are connected to control stability. An AVR is one of them to

control the voltage fluctuations. In power system basically there are two types

of power active power and reactive power. The voltage regulator in an

excitation system controls the output of the exciter so that the generated

voltage and reactive power change in desired way. For achieving this, so

many methods are suggested such as PI, PD and PID controller. In this thesis ,

the PID controller is chosen due to its robustness and better transient

response as well as dynamic response, but there are some problems facing

the use of PID controller such as tuning its parameters. To overcome this

problem, the genetic algorithm is used. Previous works on AVR system with

self tuning control was initiated in the years of 1990s [50] . Sweden bank and

coworkers [51] carried out the classical self-tuning control techniques to

the AVR system in 1999. After this study, Finch [52] used a generalized

predictive control technique as a self-tuning control algorithm in the same

year. Since the conventional self-tuning control methods contains more

mathematical calculation due to the complexity of the power systems

such as nonlinear load characteristics and variable operating points. The usage

of artificial intelligence based self-tuning controllers was preferred by

researchers from the beginning of 2000. In particular, self-tuning PID

type controllers which were tuned with the optimization methods based on

artificial intelligence have been initiated to carry out to the AVR system since

then. Gaing [53] suggested a PSO based self tuning PID controller for

AVR system, and compared the results with that of GA based methods in

2004 . In 2006, Kim [54] developed the hybrid method which contains

genetic algorithm and bacterial foraging optimization technique in order

to improve the performance of PID self-tuning controller in AVR

system. In this section GA is used for tuning of PID controller and The

performance of the proposed technique has been evaluated with the

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comparison of the conventional ZN. The AVR system model controlled by the

PID controller can be expressed by Figure 5.20.

The transfer function of PID controller is

Where

KD is the derivative gain.

KI is the integral control gain.

KP is the proportional gain

The performance index was used for optimization procedure is described

as [55]:

Where W is the performance criterion described by

( )( ) ( )

Where

β is the weighting factor.

ITAE is an integral of time multiplied by absolute-error value and it is defined

by

∑ | |

( )

Figure 5.20 Closed-loop block diagram of AVR.

system.

(5.4)

(5.5)

(5.7)

(5.6)

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Where

i * + is an index.

ti is the i-th sampling time

ei is the absolute error value in the i-th sampling time.

The AVR system of a generator has the following parameters [38] in table 5.5,

Figure 5.20, are given below:

Table 5.5 AVR system parameters

Gain Time constant

Amplifier KA=10 TA=0.1

Exciter KE = 1 TE = 0.4

Generator KG= 1 TG = 1.0

Sensor KR=1 TR= 0.05

Best control parameters selected and Performance index by GA for the

AVR system with β=1and control parameters and Performance index selected

by ZN [56] and system performance (overshoot and settling time) by different

optimization technique described in Table 5.6.

Table 5.6 Control parameters, Performance index, Overshoot and settling time.

ZN PID controller GA PID controller

Controller parameters

KP = 0.729 KI = 1.1156

KD=0.119

KP = 0.462 KI = 0.178

KD=0.124

Performance Index

2.1529 0.6101

Overshoot 0.6113 0.0044

Settling time 3.4941 1.0236

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From Table 5.6 and Figure 5.21, the response of the output voltage of the

AVR due to GA based PID controller has a shorter settling time, smaller over

shoot and smaller performance index compared to the response of ZN based

PID controller.

5.6 Load Frequency Control and Automatic Voltage Regulator system.

LFC mainly refers to real time frequency control loop to match the

area generation changes corresponding to change in area load in order to meet

tie-line flows and to maintain frequency at nominal value. Another control loop,

usually assumed to be decoupled from above control loop, of the generator

excitation system maintains generators voltage and reactive power flow [38]. In

an interconnect power system load frequency control and automatic voltage

regulator equipment are installed for each generator. The controller of LFC and

Figure 5.21 output voltage of AVR due to using

GA and ZN.

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AVR are set for a particular operating condition. Many researchers in the area

of LFC of isolated and interconnected power system have been reported in the

previous sections but they have not considered the effect of AVR. This section

presents a study of interaction between exciter AVR with frequency control

loop of LFC for single and two area power systems. Frequency control loop of

LFC with VSC and the switching vector and gain vector are optimized by GA

and ABC. AVR with PID controller and gains of controller are optimized by

GA.

5.6.1 LFC and AVR for Single Area Power System.

Model of LFC and AVR for single area power system [38] is shown in

Figure 5.22.

The LFC and AVR of single area power system have the following

parameters [38], Figure 5.22, are given below:

Figure 5.22 LFC-AVR block diagram of single area system.

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KT=1 , TT=0.5 , Kg=1 , Tg=0.2 , KA=10 , TA=0.1, KE=1 , TE=0.4 ,

KG=1, TG=1 , KR=1 , TR=0.05 , H=5 , R=0.05 , D=0.8 , Ps=1.5 ,

K1=0.2 , K2=-0.1 , K3=0.5 , K4=1.4 .

The control parameters of VSC by GA and ABC are in Table 5.7.

Table 5.7 Control parameters of VSC by GA and ABC

ABC GA

C=[9.35 0.019 0.002 3.534]T

=[50 44.4779 50 41.17] α

K=9.383

C=[32.209 0.166 0.029 13.311 ]T

α=[8.27 7.162 28.198 8.548]

k=9.383

Control Parameters

of VSC

Controller parameters of PID controller optimized by GA are given as:

KP = 0.462, KI = 0.178, KD=0.124 .

It is clear from Figure 5.23 that the coupling between LFC and AVR

affect on the response of the frequency using the proposed ABC based VSC

technique due to a step load disturbance 0.2p.u. It is found that the settling

time and over shoot of the response are increased but the system still retains the

damping characteristics with applying the proposed ABC based VSC

technique.

Figure 5.23 the change of frequency of single area LFC by VSC

optimized by ABC in case of with and without AVR.

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Figure 5.24 shows the frequency response of the same system but with

GA based VSC. It is found that the system with AVR has longer settling time

and large over shoot compared with the system without AVR.

Figure 5.25 shows that the frequency deviations for the single area LFC

is improved by the ABC based VSC in comparison with the GA based

VSC in terms of less settling time and overshoot in case of with AVR. Also it

is clear from figure the coupling effect between LFC and AVR is reduced by

applying the proposed ABC based VSC on the system.

Figure 5.26 shows that the coupling between LFC and AVR not only

affect on the frequency response of the system but also affect on the output

voltage response of the system. It is clear from figure that the settling time of

the output voltage is increased due to the coupling between LFC and AVR. Also

it is clear the coupling between LFC and AVR has the same effect on output

voltage in case of LFC by ABC based VSC and GA based VSC.

Figure 5.24 the change of frequency of single area LFC by

VSC optimized by GA in case of with and without AVR.

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Figure 5.25 the change of frequency of single area LFC by

VSC optimized by GA and ABC in case of with AVR.

Figure 5.26 Output voltage of AVR due to using GA in

case of with and without LFC .

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5.6.2 LFC and AVR for Two Area Power System.

Model of LFC and AVR for two area power system [38] is shown in

Figure 5.27.The parameters of the system under study [38], Figure 5.27, are

given below:

Kg2=1, Tg2=0.3 , TT2=0.6 , R2=0.0625 , D2=0.9 , H2=4 , a12=-1 , Kg1=1 ,

Tg1=0.2 , TT1=0.5 , R1=0.05 , D1=0.6 , H1=5 , T12=2 , KA=10 , TA=0.1, KE=1

, TE=0.4, KG=1 , TG=1 , KR=1 , TR=0.05 , Ps=1.5 , K1=0.2 , K2=-0.1 ,

K3=0.5, K4=1.4 .

The control parameters of VSC by GA and ABC are given in table 5.8.

Table 5.8 Control parameters of VSC by GA and ABc

ABC GA

C1=[-1.153 0.029 0.174 9.46 ]T

α1=[6.351 9.9776 7.4213 6.4953]

C2=[-1.006 0.031 0.184 7.331 ]T

α2=[5.7818 5.6381 7.2669 10]

KI1=0.7249 , KI2=1

C1=[-0.701 0.016 0.089 3.431 ]T

α1=[0.709 1.824 0.13 0.605]

C2=[-0.508 0.042 0.104 2.953 ]T

α2=[0.873 2.192 0.696 0.276]

KI1=0.217 , KI2=0.457

Control parameters

Controller parameters of PID controller optimized by GA are given as:

KP = 0.462, KI = 0.178, KD=0.124 .

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It is clear from Figure 5.28 (a-b) and Figure 5.29 (a-b) that the coupling

between LFC and AVR affect on the response of the frequency of area1 and

area2 using the proposed ABC based VSC and GA based VSC technique due to

a step load disturbance 0.2p.u in each area. It is found that the settling time and

over shoot of the response are increased due to the coupling between LFC and

AVR but the system remain retains the damping characteristics with applying

the proposed ABC and GA based VSC technique.

Figure 5.27 LFC-AVR block diagram of two area power system.

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(a)


ABCVSC in case of with and without AVR.

(b)

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Figure 5.30 (a-b) shows that the frequency response for the two area

LFC by the ABC based VSC gives a superb damping performance in

comparison with the GA based VSC in terms of less settling time and

overshoot in case of with AVR .

(b)

(a)

Figure 5.29 Change in frequency of area1 and area2 by GAVSC

in case of with and without AVR.

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Figure 5.31 (a-b) shows that the coupling between LFC and AVR affect

on the output voltage response of the system. It is clear from figure that the

output voltages of area1 and area2 have large settling time in case of with LFC

from in case of without LFC. Also it is clear that the coupling between LFC and

AVR has the same effect on output voltage in case of LFC by ABC based VSC

and GA based VSC.

(a)

(b)

Figure 5.30 Change in frequency of area1 and area2 by GAVSC

and ABCVSC in case of with AVR.

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(a)

(b)

Figure 5.31 output voltage of area1 and area2 in case of with and

without LFC.

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CHAPTER 6

PARALLEL PROCESSING

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Chapter6 PARALLEL PROCESSING APPLICATION

85

Chapter Six

PARALLEL PROCESSING APPLICATION

6.1 Introduction

Recent advances in computer technology will certainly have a great

impact on the methodologies used in power system expansion and

operational planning as well as in real-time control. Parallel processing

appear to be among the most promising ones of these new developments

[57-58]. Parallel processing consists in the use of multiple microprocessors to

exploit concurrency in the computation job. The main advantage of parallel

processing in power system applications is the speed up of computations

in order to make viable the solution of problems intractable in conventional

computers. The gain obtained in moving an application to a parallel

microprocessor has been usually measured in terms of speedup and

efficiency of the parallel processing implementation when compared to the

sequential version. In multi area electrical power system, each individual area

can be represented as microprocessor. The tie line between areas can be

represented as central processor. The central processor takes the change in

frequency of each area and gives the tie line power of each individual area. Each

microprocessor takes its tie line power from central processor and gives its

change in frequency to the central processor. This chapter demonstrates only

how to simulate each area with its controller as a single microprocessor and also

how to represent the multi area power system as parallel microprocessor. Figure

6.1(a) shows such network with the necessary interchange data between the

central processor and the different microprocessors. It is noted that the resultant

responses for each configuration using the parallel processing is the same as the

original system represented in Chapter 5.

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86

In order to calculate the time of computations of parallel multi processors,

the following Equation is obtained:

Tp = Ts +Tc+Td

Where

TP is the total computation time using parallel microprocessors.

Ts is the computation time for each microprocessors.

Td is the computation time for data transfer between all microprocessors

and the central processor.

Tc is the computation time for the central processor.

Also, the computation time of cascade processing using conventional PC

can be calculated by the following Equation:

1

N

cm si

i

T T

Where

Tcm is the computation time of cascade processing.

Ts is the computation time of single processing of each area.

If Ts of each microprocessor are equal, the following equations can be obtained:

Tcm=N*Tsi

cm cmp c d

T TT T T

N n

Figure 6.1(a) Multi area electrical power system by parallel processing.

(6.1)

(6.2)

(6.3)

(6.4)

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87

It can be concluded from Equation 6.3 , Equation 6.4 , Figure 6.1(b) and

Figure 6.1(c) that the computation time of parallel micro processors is shorter

than the computation time of conventional pc, specially for large power system.

The simulation of the parallel computation technique is verified using

MATLAB/SIMULINK, due to the unavailability of real parallel system.

6.2 Single Area LFC as Microprocessor

Single area LFC (governor, turbine and rotating mass) with its controller

is shown in Figure 6.2(a). It can be simulated in a microprocessor chip using

any low level language. To represent this, MATLAB/SIMULINK is used to

represent such microprocessor as a subsystem, Figure 6.2(b). The change of

load power is the input to microprocessor. The change of frequency is the frist

output (out1) of the microprocessor and generation power is the second output

(out2) of the microprocessor.

Tc

Figure 6.1(b) computations of parallel multi processors.

Time

Ts1 Ts2

Tcm

Computations

Ts3

TsN

Time

Ts Td

Tp

Computations

Figure 6.1(c) computations of cascaded multi processors.

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88

Figure 6.2(c) shows the change in frequency of single area LFC as

microprocessor and original model by ABC based VSC. It is clear that single

area LFC as microprocessor and original model by ABC based VSC have the

same result.

Figure 6.2(b) Single area LFC as microprocessor.

Figure 6.2(a) Original Single area LFC.

Microprocessor

Figure 6.2(c) Change in frequency of single area LFC as

microprocessor and original model by ABC based VSC.

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89

6.3 AVR as Microprocessor

AVR (amplifier, exciter, sensor and generator) with controller can also be

represented as microprocessor. The reference voltage is the input to

microprocessor. The terminal voltage is the output of the microprocessor.

Original AVR is shown in Figure 6.3(a) and AVR as microprocessor is shown

in Figure 6.3(b).

Figure 6.3(c) shows output voltage of AVR as microprocessor and

original model. It is can be concluded that the output voltage of AVR as

microprocessor and original model are same.

Figure 6.3(b) AVR as microprocessor.

Figure 6.3(a) Original AVR.

Microprocessor

Figure 6.3(c) Output voltage of AVR as microprocessor and original

model.

by GA based PID controller.

.

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90

6.4 LFC and AVR for Single Area Power System as Microprocessor.

The representation of LFC and AVR with their control as a

microprocessor can also be done. Figure 6.4(a) shows the block diagram of a

single area power system. Such configuration can also be programmed in a

microprocessor. Figure 6.4(b) shows the single area LFC with AVR as a

subsystem using MATLAB/SIMULINK. The change of load power is the frist

input (in1) to microprocessor. The reference voltage is the second input (in2) to

microprocessor. The change of frequency is the frist output (out1) of the

microprocessor. The generation power is the second output (out2) of the

microprocessor. The terminal voltage is the third output (out3) of the

microprocessor.

Figure 6.4(b) LFC and AVR for single area power system as

microprocessor.

Figure 6.4(a) Original LFC and AVR for single area power.

Microprocessor

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91

It clears that from Figure 6.4 (c) and Figure 6.4 (d) that the result of

single area LFC with AVR as microprocessor is the same as original model.

6.5 Two Area LFC using Parallel Processing

The parallel processing is applied to two area LFC. Area1 with controller

can be represented as microprocessor (1). Area2 with controller can be

Figure 6.4(c) Change in frequency of single area LFC with AVR as

microprocessor and original model by ABC based VSC.

Figure 6.4(d) Output voltage of AVR with LFC as microprocessor and

original model by GA based PID controller.

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92

represented as microprocessor (2). The tie-line connection between the two area

is represented as central processor. The change of frequency of each area is the

input to central processor. The tie line power of each area is the output of the

central processor. Original two area LFC are shown in Figure 6.5 (a) and two

area LFC by parallel processing are shown in Figure 6.5(b).

Figure 6.5(c) and figure 6.5(d) show the change in frequency of first and

second area of original two area LFC and two area LFC using parallel

Microprocessor(1)

Central processor

Microprocessor(2)

Figure 6.5(a) Original two area LFC.

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93

processing by ABC based VSC. It is clear from these figures that the result of

original two area LFC and two area LFC using parallel processing by ABC

based VSC are same.

Figure 6.5(b) Two area LFC using parallel processing.


.

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94

6.6 LFC and AVR for Two Area Power System using Parallel Processing.

The parallel processing is applied to two area LFC with AVR. Area1

(governor, turbine and rotating mass) and Automatic voltage regulator1

(amplifier, exciter, sensor and generator) with controller can be represented as

microprocessor1. Area2 (governor, turbine and rotating mass) and Automatic

voltage regulator2 (amplifier, exciter, sensor and generator) with controller can

be represented as microprocessor2.The tie-line connection between the two

areas can be represented as central processor. The change of frequency of each

area is the input to central processor. The tie line power of each area is the

output of the central processor. Original LFC and AVR for two area power

system is shown in Figure 6.6 (a). LFC and AVR for two area power system

using parallel technique are shown in Figure 6.6(b).


.

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95

Figure 6.6(a) Original LFC and AVR for two area power system.

Microprocessor(1)

Central processor

Microprocessor(2)

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96

It is clear from Figure 6.6(c) and Figure 6.6(d) that the change of

frequency of frist and second area of LFC and AVR for two area power system

using parallel processing are same as original LFC and AVR for two area power

system.

Figure 6.6(b) LFC and AVR for two area power system using

parallel processing.

CHAPTER SIX PARALLEL TECHNIQUE APPLICATION

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97

It is clear from Figure 6.6(e) and Figure 6.6(f) that the output voltage of

frist and second AVR by GA based PID controller for two area power system

using parallel processing are same as original LFC and AVR for two area power

system.


.


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98

The microprocessors and parallel networks of the previous sections are

obtained and simulated using MATLAB/SIMULINK, due to unavailability of

real parallel system. It is noted that the resulting responses for each

configuration using the parallel processing is the same as the original systems

represented in chapter (5), But the feature that can be taken from the

application of parallel system is to reduce the time of computations.

Figure 6.6(e) Output voltage of first AVR by GA based PID controller.

.

Figure 6.6(f) Output voltage of second AVR by GA based PID controller.

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CHAPTER 7

CONCLUSIONS AND FUTURE

WORK

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CHAPTER 7

CONCLUSIONS AND FUTURE

WORK

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REFERENCES

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REFERENCES

101

REFERENCES

[1] Singh, Gurdeepinder, and RajniBala. "Automatic Generation &

Voltage Control of Interconnected Thermal Power System

Including Load Scheduling Strategy."‏International Journal of

Engineering and Advanced Technology (IJEAT),Vol. 1, No. 2,

2011, pp. 1-7.

[2] Sadeh, Javad. "Application of Power System Stabilizer in a

Combined Model of LFC and AVR Loops to Enhance System

Stability." Journal of Mathematics, Vol. 138, No. 1, 2010, pp. 1-5.

[3] Bandal, Vitthal, B. Bandyopadhyay, and A. M. Kulkarni. "Design

of power system stabilizer using power rate reaching law based

sliding mode control technique." Power Engineering Conference,

IPEC The 7th International. IEEE, 2005.

[4] Al-Musabi, Naji A. "Design of optimal variable structure

controllers: applications to power system dynamics." Diss.

Master’s thesis, King Fahd University of Petroleum and Minerals,

Dhahran, Saudi Arabia, 2004.‏

[5] Hussein, T. "A Genetic Algorithm for Optimum Design of PID

Controller in Load Frequency Control."‏World Academy of Science,

Engineering and Technology, Vol. 70, No. 1, 2012, pp. 1206-1209.

[6] DeCarlo, Raymond A., Stanislaw H. Zak, and Gregory P.

Matthews. "Variable structure control of nonlinear multivariable

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REFERENCES

102

systems: a tutorial." Proceedings of the IEEE, Vol. 76, No. 3, 1988,

pp. 212-232.

[7] Ali, E. S., and S. M. Abd-Elazim. "BFOA based design of PID

controller for two area Load Frequency Control with

nonlinearities." International Journal of Electrical Power &

Energy Systems, Vol. 5, No. 1, 2013, pp. 224-231.

[8] Pothiya, Saravuth, et al."Design of Optimal Fuzzy Logic based Pl

Controller using Multiple Tabu Search Algorithm for Load

Frequency Control." International Journal of Control Automation

and Systems, Vol. 4, No. 2, 2006, pp. 155-164.

[9] Soheilirad, M ;Karami, K. ; Othman, M.L. ; Farzan, P." PID

controller adjustment for MA-LFC by using a hybrid Genetic-Tabu

Search Algorithm." System Engineering and Technology (ICSET),

2013, pp. 197-202.

[10] Mohammad Soroush.A, S.M." Tuning of PID Controller for Multi

Area Load Frequency Control by Using Imperialist Competitive

Algorithm " J. Basic. Appl. Sci. Res, Vol. 2, No. 4, 2012, pp.3461-

3469.

[11] Mohamed. M .Ismail, M. A. Mustafa Hassan." Load Frequency

Control Adaptation Using Artificial Intelligent Techniques for One

and Two Different Areas Power System." international journal of

control, automation and systems, Vol. 1, No. 1, 2012, pp 12-23.

[12] Ali, E. S., and S. M. Abd-Elazim. "BFOA based design of PID

controller for two area Load Frequency Control with

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http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Soheilirad,%20M..QT.&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Karami,%20K..QT.&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Othman,%20M.L..QT.&newsearch=true

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Farzan,%20P..QT.&newsearch=true

http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6642157

http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6642157



REFERENCES

103

nonlinearities." International Journal of Electrical Power &

Energy Systems, Vol. 5, No. 1, 2013, pp. 224-231.

[13] Ray, Goshaidas, and Anil Kumar. "Decentralized adaptive PI

control strategies for frequency control of interconnected systems."

Kybernetika, Vol. 27, No. 5, 1991, pp. 458-478

[14] Yang, T-C., H. Cimen, and Q. M. Zhu. "Decentralized load-

frequency controller design based on structured singular values."

Generation, Transmission and Distribution, IEE Proceedings,Vol.

145, No. 1, 1998, pp. 7-14.

[15] Selvakumaran, S., and V. Rajasekaran. "Design of decentralized

biased dual mode controller for load frequency control of an

interconnected power system with AC/DC tie lines." IPEC

Conference Proceedings. IEEE, 2010.‏

[16] Velusami, S., and I. A. Chidambaram. "Decentralized biased dual

mode controllers for load frequency control of interconnected

power systems considering GDB and GRC non-linearities." Energy

Conversion and Management,Vol. 48, No. 5, 2007, pp. 1691-1702.

[17] Velusami, S., and I. A. Chidambaram. "Decentralized biased dual

mode controllers for load frequency control of interconnected

power systems considering GDB and GRC non-linearities." Energy

Conversion and Management,Vol.48, No.5, 2007, pp. 1691-1702.

[18] Prakash, Surya, and S. K. Sinha. "Load frequency control of three

area interconnected hydro-thermal reheat power system using

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REFERENCES

104

artificial intelligence and PI controllers." International Journal of

Engineering, Science and Technology,Vol.4, No.1, 2012, pp.23-37.

[19] Chatterjee, Kalyan. "Design of dual mode PI controller for load

frequency control." International Journal of Emerging Electric

Power Systems,Vol.11, No. 4, 2010, pp. 1-24.

[20] Samad, Tariq. "Perspectives in Control Engineering: Technologies,

Applications, and New Directions."Wiley-IEEE Press,2000.

[21] DeCarlo, Raymond A., Stanislaw H. Zak, and Gregory P.

Matthews,"Variable structure control of nonlinear multivariable

systems: a tutorial."Proceedings of the IEEE, Vol. 76, No. 3, 1988,

pp. 212-232.

[22] Kothari, D. P., and I. J. Nagrath. "Power system engineering." Tata

McGraw-Hill, 2008.

[23] Ferdowsi, Mohammad Hossein, A. V. Kamyad, and Khalil

Alizadeh. "A Study on Performance of Fuzzy And Fuzyy Model

Reference Learning PSS In Presence of Interaction Between LFC

and AVR Loops." Australian Journal of Basic & Applied Sciences,

Vol. 5, No. 12, 2011, pp. 258-263.

[24] Luo, Youxin, XiaoyiChe, and Zhaoguo Chen. "Optimization for

PID Control Parameters on Hydraulic Servo Control System Based

on Artificial Bee Colony Optimization Algorithm." Information

Engineering Letters, Vol. 2, No. 1, 2012, pp. 43-47.

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REFERENCES

105

[25] Yan, Gaowei, and C. Li. "An effective refinement artificial bee

colony optimization algorithm based on chaotic search and

application for PID control tuning." Journal of Computational

Information Systems, Vol.7, No. 9, 2011, pp. 3309-3316.

[26] Abachizadeh, Mahdi, Mohammad Reza Haeri Yazdi, and

AghilYousefi-Koma. "Optimal tuning of PID controllers using

artificial bee colony algorithm." Advanced Intelligent Mechatronics

(AIM), IEEE, 2010, pp. 379-384.

[27] Karaboga, Dervis, and BahriyeAkay. "A comparative study of

artificial bee colony algorithm." Applied Mathematics and

Computation, Vol. 214, No. 1, 2009, pp. 108-132.

[28] Falcão, Djalma M. "Parallel and distributed processing applications

in power system simulation and control." Revista SBA:

Controle&Automaçao, Vol. 5, No. 1, 1994, pp. 125-143.

[29] Lemaitre, C., and B. Thomas. "Two applications of parallel

processing in power system computation." Power Systems, IEEE

Transactions on, Vol. 11, No. 1, 1996, pp. 246-253.

[30] Ali, M.A., Mansour ,W.M. "A Proposed Approach for Online

Transient Stability of Multi - machine Power Systems Using

Parallel Microprocessors." Proceedings of The 6th ICEENG

Conference , Military Technical College, 2008, pp. 901-910.

[31] Rakhshani, Elyas, Kumars Rouzbehi, and Sedigheh Sadeh. "A new

combined model for simulation of mutual effects between LFC and

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REFERENCES

106

AVR loops" In Proc. Asia-Pacific Power and Energy

EngineeringConference, Vol. 2, No.1, 2009, pp. 1480-1485

[32] Hadi Saadat ." power system analysis" Tata Mcgraw hill, Ch: 12,

2002.

[33] Chan, Wah-Chun, and Yuan-Yih Hsu. "Automatic generation

control of interconnected power systems using variable-structure

controllers." Generation, Transmission and Distribution, IEE

Proceedings, Vol. 128, No. 5, 1981, pp. 269-279.

[34] Vadim, I. Utkin. "Survey paper variable structure systems with

sliding modes." IEEE Transactions on Automatic control, Vol. 22,

No. 2, 1977, pp. 212-222.

[35] Wang, Y., R. Zhou, and C. Wen. "Robust load-frequency controller

design for power systems." IEE Proceedings C (Generation,

Transmission and Distribution), Vol. 140, No. 1, 1993, pp. 11-16.

[36] Al-Yahmadi, Amer S., and T. C. Hsia. "Modeling and control of

two manipulators handling a flexible beam." Proceedings of World

Academy of Science, Eng. and Tech, 2005, pp. 147-150.

[37] Al-Musabi, Naji A. "Design of optimal variable structure

controllers: applications to power system dynamics." Diss.

Master’s thesis, King Fahd University of Petroleum and Minerals,

Dhahran, Saudi Arabia, 2004.‏

[38] Bandal, Vitthal, B. Bandyopadhyay, and A. M. Kulkarni. "Design

of power system stabilizer using power rate reaching law based

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REFERENCES

107

sliding mode control technique." Power Engineering Conference,

IPEC , The 7th International. IEEE, 2005.

[39] Hsu, Liu, et al. "Output Feedback Sliding Mode Control for a Class

of Uncertain Multivariable Systems with Unmatched Nonlinear

Disturbances." Advances in Variable Structure and Sliding Mode

Control, 2006, pp. 195-225.

[40] Anderson and J. B. Moore. "Linear Optimal Control." Prentice-

Hall, Englewood Cliffs, N.J., 1971.

[41] Patel, R. N., S. K. Sinha, and R. Prasad. "Design of a Robust

Controller for AGC with Combined Intelligence Techniques."

Proceedings of World Academy of Science: Engineering &

Technology, Vol. 47, No.1, 2008, pp. 95-101.

[42] Mitchell, Melanie. "Genetic algorithms: an overview." Complexity,

Vol. 1, No. 1, 1995, pp. 31-39.

[43] Walters, David C., and Gerald B. Sheble. "Genetic algorithm

solution of economic dispatch with valve point loading." Power

Systems, IEEE Transactions on, Vol. 8, No. 3, 1993, pp. 1325-

1332.

[44] Karaboga, Dervis. "An idea based on honey bee swarm for

numerical optimization." Technical report-tr06, Erciyes university,

engineering faculty, computer engineering department, Vol. 200,

No. 1, 2005, pp. 1-10.

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REFERENCES

108

[45] Karaboga, Dervis, and Bahriye Basturk. "A powerful and efficient

algorithm for numerical function optimization: artificial bee colony

(ABC) algorithm." Journal of global optimization, Vol. 39, No. 3,

2007, pp. 459-471.

[46] Abedinia, Oveis, et al. "Design of robust PSS to improve stability

of composed LFC and AVR using ABC in deregulated

environment." 13th International conference on Artificial

Intelligence, 2011.‏

[47] Ghoshal, S. P. "Optimizations of PID gains by particle swarm

optimizations in fuzzy based automatic generation

control." Electric Power Systems Research, Vol. 72, No. 3, 2004,

pp.203-212.

[48] Grainger, John J., and William D. Stevenson. "Power system

analysis." New York: McGraw-Hill, 1994.

[49] Sadeh, Javad. "Application of Power System Stabilizer in a

Combined Model of LFC and AVR Loops to Enhance System

Stability." Journal of Mathematics,Vol. 138, No. 1, 2010, pp. 1-7.

[50] Bhati, Sapna, and DhiirajNitnawwre."Genetic Optimization Tuning

of an Automatic Voltage Regulator System."‏International Journal

of Scientific Engineering and Technology www.ijset.com ,Vol. 1,

No. 3, 2012, pp. 120-124.

[51] Swidenbank, E., M. D. Brown, and D. Flynn. "Self-tuning turbine

generator control for power plant." Mechatronics, Vol. 9, No. 5,

1999, pp. 513-537.

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REFERENCES

109

[52] Ibrahim, A. S., B. W. Hogg, and M. M. Sharaf. "Self-tuning

automatic voltage regulators for a synchronous generator." IEE

Proceedings D (Control Theory and Applications) ,Vol. 136, No. 5,

1989, pp. 843-848.

[53] Gaing, Zwe-Lee. "A particle swarm optimization approach for

optimum design of PID controller in AVR system." Energy

Conversion, IEEE Transactions on, Vol. 19, No. 2, 2004, pp. 384-

391.

[54] Kim, Dong Hwa, and Jae Hoon Cho. "A biologically inspired

intelligent PID controller tuning for AVR systems." International

Journal of Control Automation and Systems, Vol. 4, No. 5, 2006,

pp. 624-636.

[55] Ching-Chang, W., L. Shih-An and W. Hou-Yi. "Optimal PID

controller design for AVR system." Tamkang J. Sci. Eng,Vol.

12, No. 3, 2009, pp. 259-270.

[56] Skogestad, Sigurd. "Probably the best simple PID tuning rules in

the world." AIChE Annual Meeting, Reno, Nevada, 2001.‏

[57] Falcão, Djalma M. "Parallel and distributed processing applications

in power system simulation and control." Revista SBA:

Controle&Automaçao, Vol. 5, No. 1, 1994, pp. 125-143.

‏

[58] Lemaitre, C., and B. Thomas. "Two applications of parallel

processing in power system computation." Power Systems, IEEE

Transactions on, Vol. 11, No. 1, 1996, pp. 246-253.

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REFERENCES

110

[59] Elgerd, Olle Ingemar. "Electric energy systems theory: an

introduction." Tata McGraw-Hill Education, 1983.

[60] Rhif, Ahmed. "A high order sliding mode control with PID sliding

surface: Simulation on a torpedo." International Journal of

Information Technology, Control and Automation (IJITCA), Vol. 2,

No.1, 2012, pp. 1-13.

[61] Kundur P." Power system stability and control."McGraw-Hill,

1994.

[62] Filatov, Nikolai Michailovich, and Heinz Unbehauen. "Adaptive

dual control: Theory and applications."Springer, 2004.‏

[63] Malik, OP, A. Kumar, and GS Hope. "A load frequency control

algorithm based on a generalized approach." IEEE transactions on

power systems, Vol. 3, No. 2, 1988, pp. 375-382.

[64] Boiko, Igor. "Discontinuous control systems." Birkhäuser, Boston,

‏.2009

[65] Jidin, A. B., N. R. N. Idris, and N. D. Muhamad. "Sliding mode

variable structure control design principles and application to DC

drives." Power and Energy Conference, PECon , Proceedings.

National. IEEE, 2004, pp. 78-82.

[66] Bartoszewicz, Andrzej. "Variable Structure Control–from

Principles to Applications." International Symposium on System

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REFERENCES

111

Theory, Automation, Robotics, Computers, Informatics, Electronics

and Instrumentation, Craiova, Romania, 2007, pp.18-20.‏

[67] Vasanthi, S., M. Gopila, and I. Gnanambal. "Fuzzy AndPid

Excitation CONTROL System With AVR In Power System

Stability Analysis."‏International Journal of Engineering and

Advanced Technology (IJEAT),Vol. 1, No. 5, 2012, pp. 95-99.

[68] Murty, P. S. R. "Operation and control in power systems." BS

Publications, 2008.‏

[69] Al-Hamouz, Z. M., and H. N. Al-Duwaish. "A new load frequency

variable structure controller using genetic algorithms." Electric

Power Systems Research, Vol. 55, No. 1, 2000, pp. 1-6.

[70] Venkatachalam, Adhimoorthy, and Chidambaram

IlangiAkilandam. "Dual Mode Two-Layer Fuzzy Logic Based

Load-Frequency Controller for a Two-Area Interconnected Power

System with Super Capacitor Energy Storage Units using Control

Performance Standards Criterion."‏International Journal of

Engineering and Innovative Technology (IJEIT), Vol. 2, No.12,

2013, pp. 162-173.

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APPENDIX

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APPENDIX

112

APPENDIX

Genetic Algorithm and Direct Search Toolbox

This Toolbox is a collection of functions that extend the capabilities of

the Optimization Toolbox and the MATLAB numeric computing

environment.

These algorithms enable you to solve a variety of optimization problems

that lie outside the scope of the Optimization Toolbox.

All the toolbox functions are MATLAB M-files made up of MATLAB

statements that implement specialized optimization algorithms.

You can extend the capabilities of the Genetic Algorithm and Direct

Search Toolbox by writing your own M-files, or by using the toolbox in

combination with other toolboxes, or with MATLAB or Simulink.

Writing M-Files for Functions You Want to Optimize

To use the Genetic Algorithm and Direct Search Toolbox, you must first

write an M-file that computes the function you want to optimize

The M-file should accept a vector, whose length is the number of

independent variables for the objective function, and return a scalar

Example — Writing an M-File

The following example shows how to write an M-file for the function you want

to optimize. Suppose that you want to minimize the function

∫

(A.1)

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APPENDIX

113

Where

J the objective of the single area LFC by integral controller where the

deviation in frequency Δ is minimized.

Pc=

Where KI is the integral controller gain and Δ is function in KI .

The main object of GA is to find the best value of KI at which J is minimum

value.

Select New from the MATLAB File menu.

Select M-File. This opens a new M-file in the editor.

In the M-file, enter the following:

function J= my_fun(K)

global KI

KI=K(1);

sim('singleareaLFCbyI_controller')

%where singleareaLFCbyI_controller is the simulink model.

J=trapz(T,dw.^2);

% where T is the running time of simulink model and dw the deviation in

frequency.

end

Save the M-file in a directory on the MATLAB path.

Write global KI at the MATLAB command prompt.

(A.2)

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APPENDIX

114

Using the Genetic Algorithm Tool

To open the Genetic Algorithm Tool, enter gatool at the MATLAB

command prompt.

Figure A.1 single area LFC by integral controller simulink model.

Fitness function

Options

Number of

Variables

Start

Algorithm

Display Results

Figure A.2 Genetic Algorithm

Tool

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APPENDIX

115

Fitness function — The objective function you want to minimize. Enter

the fitness function in the form @fitnessfun, where fitnessfun.m is an M-

file that computes the fitness function.

Number of variables — The length of the input vector to the fitness

function. For the function my_fun described in Writing M-Files for

Functions You Want to Optimize, you would enter 1.

To run the genetic algorithm, click the Start button. The tool displays the

results of the optimization in the Status and results pane.

You can change the options for the genetic algorithm in the Options pane.

To view the options in one of the categories listed in the pane, click the +

sign next to it.

Displaying Plots

The Plots pane enables you to display various plots that provide

information about the genetic algorithm while it is running.

This information can help you change options to improve the

performance of the algorithm.

Figure A.3 Plots

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APPENDIX

116

Stopping Conditions for the Algorithm

The genetic algorithm uses the following conditions to determine when to stop:

Generations — The algorithm stops when the number of generations

reaches the value of Generations.

Time limit — The algorithm stops after running for an amount of time in

seconds equal to Time limit.

Fitness limit — The algorithm stops when the value of the fitness

function for the best point in the current population is less than or equal to

Fitness limit.

Stall generations — The algorithm stops when the weighted average

change in the fitness function value over Stall generations is less than

Function tolerance.

Figure A.4 Fitness value

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APPENDIX

117

Stall time limit — The algorithm stops if there is no improvement in the

objective function during an interval of time in seconds equal to Stall

time limit.

Function Tolerance — The algorithm runs until the weighted average

change in the fitness function value over Stall generations is less than

Function tolerance.

Nonlinear constraint tolerance — The Nonlinear constraint tolerance is not

used as stopping criterion. It is used to determine the feasibility with respect

to nonlinear constraints.

Figure A.5 Stopping criteria

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APPENDIX

118

Artificial bee colony algorithm

To use artificial bee colony algorithm you must first write an M-file that

computes the function you want to optimize

The M-file should accept a vector, whose length is the number of

independent variables for the objective function, and return a scalar

Example — Writing an M-File

The following example shows how to write an M-file for the function you

want to optimize. Suppose that you want to minimize the function

∫

Where

J the objective of the single area LFC by PI controller where the deviation

in frequency Δ is minimized.

Pc=

Where KP is proportional controller gain , KI is the integral controller gain and

Δ is function in KP and KI .

The main object of ABC is find best value of KP and KI at which J is minimum

value.

Select New from the MATLAB File menu.

Select M-File. This opens a new M-file in the editor.

In the M-file, enter the following:

(A.3)

(A.4)

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APPENDIX

119

function J= my_fun(Chrom)

global KP KI

x1=Chrom(:,1)

% x1 is the first Colum and all raw of Chrom

% first Colum of Chrom represent variable number one (KP)

% each raw of Chrom of first Colum represent value of KP

% number of raw of Chrom equal number of Employed Bees

x2=Chrom(:,2)

% x2 is the second Colum and all raw of Chrom

% second Colum of Chrom represent variable number two (KI)

% each raw of Chrom of second colum represent value of KI

for i=1:5

% i=1: number of employed bees

% each value i represent an employed bee

KP=x1(i); KI=x2(i);

sim('singleareaLFCbyPI_controller')

%where singleareaLFCby PI_controller is the simulink model.

J(i)=trapz(T,dw.^2);

end

% there is five possible solution of J for each cycle

% number of possible solution for each cycle equal the number of employed

bees

% at end of cycles the algorithm select the best solution

Save the M-file in a directory on the MATLAB path.

Write global KP KI at the MATLAB command prompt.

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APPENDIX

120

Using ABC algorithm

To use the ABC algorithm

open the running m-file of algorithm

Set ABC Control Parameters

ABCOpts = struct( 'ColonySize', 10, ... % Number of Employed Bees+

Number of Onlooker Bees

'MaxCycles', 100,... % Maximum cycle number in order to terminate the

algorithm

'ErrGoal', 1e-20, ... % Error goal in order to terminate the algorithm (not

used in the code in current version)

'Dim', 2, ... % Number of parameters of the objective function

'Limit', 150, ... % Control parameter in order to abandone the food source

'lb',0, ... % Lower bound of the parameters to be optimized

'ub',100, ... %Upper bound of the parameters to be optimized

Figure A.6 single area LFC by PI controller simulink model.

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APPENDIX

121

'ObjFun' , ' my_fun ', ... %Write the name of the objective function you want

to minimize

'RunTime',2); % Number of the runs

To run the ABC algorithm, click on the run option of the running m-file

of algorithm.

At the end of cycles the solution appear at the MATLAB command

prompt and mean of best function values appear in Figure A.7.

Figure A.7 Mean of best function values.

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Arabic

Summary

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جامعت بنها

كليت الهندست بشبرا

الكهربائيت قسم الهندست

مركىي ىً ببكاث الوىي الكهربي الالتحكم ال

المتعددة المنظىماث

رسالة مقدمة من

محمىد نصر سيد محمد السيسًالمهندس /

للحصىل علي

ىٍ الهندست الكهربائيت الماجستيردرجت

)ببكاث الوىٌ الكهربائيت(

رافتحت إش

هالل د / محمىد سليمان أحمد وجدي محمد منصىرأ.د /

ةكهربائيمدرس نظم القىي ال أستاذ نظم القىي الكهربائية والتحكم

جامعة بنها جامعة بنها

مصر –الواهرة

0214

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Decentralized Control of Multi-Area Power Systems

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