AGC for autonomous power system using combined intelligent techniques

AGC for autonomous power system using combined intelligenttechniques

Y.L. Karnavas, D.P. Papadopoulos *

Department of Electrical and Computer Engineering, Electrical Machines Laboratory, Democritos University of Thrace, 671 00 Xanthi, Greece

Received 2 July 2001; received in revised form 18 February 2002; accepted 26 February 2002

Abstract

In the present work two intelligent load frequency controllers have been developed to regulate the power output and system

frequency by controlling the speed of the generator with the help of fuel rack position control. The first controller is obtained using

fuzzy logic (FL) only, whereas the second one by using a combination of FL, genetic algorithms and neural networks. The aim of the

proposed controller(s) is to restore in a very smooth way the frequency to its nominal value in the shortest time possible whenever

there is any change in the load demand etc. The action of these controller(s) provides a satisfactory balance between frequency

overshoot and transient oscillations with zero steady-state error. The design and performance evaluation of the proposed

controller(s) structure are illustrated with the help of case studies applied (without loss of generality) to a typical single-area power

system. It is found that the proposed controllers exhibit satisfactory well overall dynamic performance and overcome the possible

drawbacks associated with other competing techniques. # 2002 Elsevier Science B.V. All rights reserved.

Keywords: Frequency control; Controller design; Fuzzy logic; Genetic algorithms; Neural networks

1. Introduction

Many investigations in the area of automatic genera-

tion control (AGC) of isolated and of interconnected

power systems have been reported in the past [1�/5] and

a number of control strategies have been proposed to

achieve improved performance. The proportional-plus-

integral (PI) control approach is successful in achieving

zero steady-state error in the frequency of the system,

but it exhibits relatively poor dynamic performance as

evidenced by large overshoot and transient frequency

oscillations [1]. Moreover, the transient settling time is

relatively large. In the application of optimal control

techniques, the controller design is normally based on a

fixed parameter model of the system derived by a

linearization process. Power system parameters are a

function of the operating point. Therefore, as the

operating conditions change, system performance with

controllers designed for a specific operating point most

likely will not be satisfactory [2]. Consequently, the

nonlinear nature of the load frequency control (LFC)

problem makes it difficult to ensure stability for all

operating points when an integral or a PI controller is

used [6,7].

The application of adaptive control theory to the LFC

problem has also found acceptance because of its role in

eliminating some of the problems associated with

classical and modern control. Self-tuning regulators,

model reference adaptive control as well as variable

structure control are used under the heading of adaptive

control [8�/11].

In recent years, modern ‘intelligent’ methods such as

artificial neural networks (ANN), fuzzy logic (FL) and

genetic algorithms (GA), have gained increasing interest

for applications in the LFC problem. Some such

applications using ANNs and generalized neural net-

work can be found [12�/14]. The last methods have some

deficiencies, such as: large number of neurons in hidden

Abbreviations: ANN, artificial neural network; CIC, conventional

integral controller; CPIC, conventional proportional plus integral

controller; FL, fuzzy logic; FLLFC, fuzzy logic based load frequency

controller; GA, genetic algorithm; MLFFNN, multi layered feed

forward neural network; NNGAFLC, neural network driven by a

genetic algorithm tuned fuzzy logic controller.

* Corresponding author. Tel.: �/30-541-079721; fax: �/30-541-

027955

E-mail address: [email protected] (D.P. Papadopoulos).

Electric Power Systems Research 62 (2002) 225�/239

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layers for complex function approximation, very large

training time required [12], large number of unknowns

(some of them are inaccessible state variables) to be

determined for which the use of estimators must be

adopted [13]. Applications of FL along with neural nets

and GA based FL control has also been reported [14�/

16]. The drawbacks of these methods include fixed

parameters of the fuzzy sets of the fuzzy variables as

well as large computational time for the rule base to be

examined. In other words, the considerable time needed

for response when fuzzy set theory is applied makes the

practical realization quite difficult.

In this paper two intelligent controllers for the LFC

problem are developed and applied in connection with

the power system under study. The first one is based on

FL with fixed parameters and was designed for studying

its performance and compare it to that of a conventional

integral controller (CIC) and also to that of a conven-

tional PI controller (CPIC). The second one, uses a

combination of GA, FL and neural networks and its

related performance is compared to these of the previous

ones. Especially for the second one, the following ideas

were formulated to overcome the deficiencies mentioned

above:

�/ The off-line use of a variable structure fuzzy logic

controller (FLC). The controller will provide an

additive signal, which can be interpreted as the

optimal value of the proportional gain of a PI

structure LFC. The use of a FLC is adopted to attain

satisfactory control in a wide area of operating

conditions.

�/ The off-line use of a GA for the continuousdetermination of the parameters of the FLC.

�/ The off-line continuous training of an ANN with the

signals provided by the FLC output. Additionally,

the ANN will provide the optimal value of the

integral gain of the CIC. The use of the ANN is

incorporated here to learn system dynamics.

�/ The on-line (direct use) of a suitably pre-trained/re-

trained ANN for instantaneous controller response.

The above ideas have been incorporated in the

proposed LFC structure developed in this work. The

designed controller is actually an on-line neural net-

work, driven by a genetic algorithm based fuzzy logic

controller (NNGAFLC).

The last controller structure design is applied for

simulation purposes to a typical single-area power

system and its obtained performance has been compared

to the associated ones of a CIC, a CPIC and also to that

of the designed FLC.

The paper is organized as follows: In Section 2,

general considerations of the PI controller are presented.

Then the characteristics of a typical model of a single-

area power system are given (with and without a reheat

turbine) to which the associated controllers will be

applied. Finally, the derivation of the optimal gains of

the CIC and the CPIC, which will be used for

comparison purposes, is conducted. Section 3 reviewsthe main aspects of the three modern intelligent

techniques. An FLC is also designed and applied to

the above single-area power system. Last, in Section 4

an effort is made to improve the performance of the

FLC design of Section 3 by incorporating the second

AGC structure, proposed in this paper, which combines

the three modern intelligent methods.

Some simulation cases are being investigated to showthe relative goodness of the control strategies employed.

It is to be pointed out that the use of a tunable

(adaptive) controller with a fixed PI structure could be

sufficient to deal with slow-changing power system

parameters and operating conditions. On the other

hand, in cases where such operating conditions can

become abnormal or even hard to deal with, a controller

with a more ‘nervous’ behavior may be justified. Theprimary motivation of this work is to explore, based on

appropriate simulation results, the behavior of such

controller(s), in order to extract meaningful information

so that further work concerning the integration of

simple as well as more ‘sophisticated’ controller designs

may be conducted.

2. Main aspects concerning AGC controller design

2.1. Qualitative PI control considerations

The general practice in the design of a LFC is to

utilize a PI structure. This gives adequate system

response considering the stability requirements and the

performance of its regulating units. Another approach

to this problem, with good results, is the use of moderncontrol theory. Usually, conventional controllers of

fixed structure and constant parameters are tuned for

one operating condition and can give optimal or sub-

optimal power system performance for that condition.

Since, the characteristics of the power system elements

are non-linear, the conventional controllers may not be

capable of providing the desired performance for all

operating conditions [6,17,18]. In this case the responseof the PI controller is not satisfactory enough and large

oscillations may occur in the system [10]. Thus, the

integrator gain must be set to a level that provides a

compromise between fast transient recovery and low

overshoot in the dynamic response of the overall system

[8,19,20]. Consequently, this type of controller may be

relatively slow and not allow the designer to take easily

into account possible system non-linearities. Latestefforts are made, as another approach, to develop

controllers (based on intelligent control techniques)

capable in dealing with such non-linearities and at the

Y.L. Karnavas, D.P. Papadopoulos / Electric Power Systems Research 62 (2002) 225�/239226

same time secure improved system performance [14].

Nowadays, many vertically integrated utilities which

participate in AGC schemes use simple and heuristically

tuned controllers. This approach is largely a conse-quence of the inherent uncertainties in dynamic models

of power system components and the lack of reliable

data needed for sophisticated models.

From an industrial point of view, it is known that

most PI or PID controllers have their parameters set

(tuned) either manually or in an automatic way.

However, in the manual mode, the parameter tuning

depends on the operator’s experience, while in theautomatic mode there is a need of a time period in

which the plant must run several cycles of operation

before the ‘auto’ function can produce the associated

parameter values. This tuning procedure is not always

possible in an autonomous power system (e.g. in a

wind�/diesel plant installed in an isolated island) because

of the need to serve the load continuously and the

fluctuations in the power generation produced by thewind turbines. In addition the system while in ‘auto’

mode may experience a different operating condition

than usual and the values of the obtained parameters

may result in counteractive controller tuning.

From the above it is clear that, in some cases, there

may be a need for a controller which can be adjusted

continuously on-line and be capable of handling any

non-linearities or parameter uncertainties that maysometime appear in the actual power plant. The aim

of the present work is to facilitate a hardware imple-

mentation with automatic good performance and with-

out the need of the exact plant parameter knowledge. A

practical implementation of the proposed controller will

consist of two dedicated hardware blocks. The first one

will act off-line and be responsible for optimum PI

parameter evaluation considering the possible inherentnon-linearities, while the second one will act like an on-

line parameter database. Finally it should be mentioned

that the intelligent controllers developed in this work

may be seen as being a form of parameter adaptive PI

controllers.

2.2. Model of power system under study

Fig. 1 shows a well known block diagram used for the

LFC of a typical single-area power system [2,13] along

with the additional new signal U (t). The presence of

U (t) denotes the existence of the proportional gain Kp,

whereas the absence of U (t) means Kp�/0 and this

leads to an integral controller only. The dynamic model

in state-space variable form, obtained from the asso-ciated transfer functions, is

X�AX�BU; Y�CX (1)

where

X� [Df DPt DPg DPscp]T; U� [DPd U(t)]T;

Y� [Df ]

are the state vector, the control vector and the output

variable, respectively. The nominal parameter values

(i.e. gains and time constants of the turbine, governor

and power system blocks in per unit) used in this study

are shown in Table 1 from which the values of theelements of the system matrices A, B and C may be

easily computed. For comparison purposes between the

conventional controllers (CIC and CPIC) and the two

proposed intelligent controllers, the same values of these

parameters are used [1,2,10,13]. In addition an integra-

tion-absolute-error-time (IAET) criterion of the follow-

ing form [21] is used in this work, i.e.

Jfre�gT

0

jDf (t)jtdt (2)

The above described model does not consider the

effect of generation rate constraint (GRC). In practice,

there exists a maximum limit on the rate of change in the

generating power of a conventional power plant (e.g.

steam, diesel etc.). Hence, if the response of the applied

controller and/or the load change are too fast under

transient conditions, then system non-linearities will

prevent its achievement. It follows that a controllerdesigned for the unconstrained situation may not be

suitable when the GRC is considered. Previous works

indicate that in the presence of GRC, the dynamic

responses of the system experience larger overshoots and

longer transient settling times, compared to the case

without considering the GRC [1,9]. Moreover, if the

parameters of the applied controller are not chosen

properly the system may become unstable. For testingfurther the effectiveness of the proposed controllers, the

GRC is taken into account by replacing the non-reheat

turbine (linear) block DPt/DPg in Fig. 1 with the reheat

turbine (non-linear) block of Fig. 2. The generation rate

limitation d is set to 0.028 p.u.MW/s which is a typical

value, e.g. in diesel-electric generator sets (up to 4 MW)

installed in autonomous power stations in Greek

islands.

2.3. Systematic selection of gain values for CIC and

CPIC for best system performance

The tuning of the values of the gains Ki and Kp was

achieved using a systematic exhaustive search (according

to the IAET criterion) with and without GRC. Fig. 3

shows the effect Kp has on selecting the value of Ki.

From Fig. 3a and b it is clear that in the absence of

GRC, the best tuned gain values of the CIC and CPICare Ki�/0.306 and Ki�/0.5659 and Kp�/0.733 respec-

tively. In the presence of GRC the Ki�/0.1794 in both

the CIC and CPIC case whereas Kp�/0.0 for the CPIC

Y.L. Karnavas, D.P. Papadopoulos / Electric Power Systems Research 62 (2002) 225�/239 227

case (any value for Kp other than zero, results in more

oscillatory responses with quite large amplitudes and the

transient settling time is relatively large, which agrees

with [9]). This means that with GRC being present, only

a simple CIC is preferable than a PI based on the IAET

criterion. The parameter values, along with the Jfre

values obtained from the several computations con-

ducted with and without GRC, are shown in Table 2. As

mentioned before the CIC and CPIC gain values

obtained will be used and their resulting performance

will be compared to the associated one of the proposed

intelligent controllers.

3. Overview of used intelligent techniques

3.1. Fuzzy logic controller

The FL control [22,23] involves essentially the deriva-tion of a control law from heuristic and imprecise

(‘fuzzy’) rules. Since the mathematical models of power

system problems are usually non-linear, the controller

design becomes a really difficult task. FL control has

been applied to such system models and has been shown

to give by comparison improved performance [24�/26].

Fig. 4 shows a schematic representation of a typical

closed-loop fuzzy control system. The reference signal

and plant output, which are crisp values but non-fuzzy

variables, must be fuzzified by a fuzzification procedure.

Similarly, the fact that the controlled plant can not

directly respond to FL controls accounts for the reason

why the FL control signal generated by the fuzzyalgorithm must be defuzzified by defuzzification before

applied to control the actual plant. A rule base consists

of a set of fuzzy rules. The data base contains the

membership functions of the fuzzy subsets. A fuzzy rule

may contain fuzzy variables and fuzzy subsets charac-

terized by membership functions and a conditional

statement. The fuzzy control algorithm consists of

executing an ordered sequence of fuzzy rules by theconcepts of fuzzy implication and the compositional

rules of inference. Essentially a FLC is a deterministic

model-free, non-linear and robust controller.

3.1.1. FLC design procedure

For the LFC problem one encounters a situationwhere the power system is not amenable to conventional

output feedback in all points of the operating region.

Therefore the possibility of using a fuzzy logic load

frequency controller (FLLFC) will be explored for this

purpose. Next are outlined the necessary steps involved

in the pertinent controller design [23] (Fig. 4):

3.1.1.1. Fuzzification. Where precise numerical values

obtained by measurements are converted to membership

values of the various linguistic variables (e.g. ‘Positive

Small’). For the FLLFC the inputs are the frequency

variation (error) and the change in error defined as:

Fig. 1. Transfer function model of the LFC for a typical single area power system.

Table 1

Nominal parameters of a typical single-area power system

R [Hz/p.u.MW] D [p.u.MW/Hz] Kg Tg [s] Kt

2.4 0.00833 1 0.08 1

Tt [s] Kps Tps [s] DPd [p.u.MW] Ki

0.3 1 20 *variable *see explanation in text

Fig. 2. A non-linear turbine model with GRC.


input 1 : error�Df �fnom�ft�et

input 2 : change in error�Det�et�et�1�cet (3)

with the sampling interval chosen as 1 ms (which is

acceptable from a practical point of view).

The inputs are categorized as belonging to the various

linguistic variables with their corresponding member-

ship values. In general a membership function of alinguistic variable V is represented as shown in Fig. 5.

The fuzzy sets of each linguistic variable adopted in this

work are: NVL: Negative Very Large; NL: Negative

Large; NM: Negative Medium; NS: Negative Small;

ZR: Zero; PS: Positive Small; PM: Positive Medium;

PL: Positive Large; PVL: Positive Very Large. Each

fuzzy set has a triangular shape (except of the two

outermost ones which have a trapezoidal shape) and isdetermined by three parameters (i.e. for the fuzzy set

ZeRo of the linguistic variable V , these parameters are

�/p1V , 0, p1

V ). Consequently, if a linguistic variable is

supported by N fuzzy sets, then the total number of

parameters needed is N�/1, considering that the zero

value is fixed at the center of ‘ZR’ fuzzy set. Finally the

membership value of an input signal with amplitude x in

the particular linguistic variable V is denoted bym [V (x )]. Using the above mentioned notations the

membership functions for the designed FLLFC of the

three variables (et , cet , Ut) used are shown in Fig. 6.

3.1.1.2. Fuzzy control. Where the heuristic rules of theknowledge base are used to determine the fuzzy

controller action. For example the FLLFC employs a

rule: IF et is ZeRo AND cet is Positive Small THEN

controller action (Ut ) is Positive Small. The part ‘et is

ZeRo AND cet is Positive Small’ defines another

linguistic variable. Though it is possible to derive a

membership value for this variable in many possible

ways the rule that has been chosen (due to its simplicity)is

mASB(V1;V2)�min(mA(V1);mB(V2)) (4)

In the above example A : ‘ZeRo’, B : ‘Positive Small’,

A S /B : ‘ZeRo AND Positive Small’, V1�/et , V2�/cet .

Two sets of fuzzy rules used in this work are given in

Tables 3 and 4. These sets (which are the so called fuzzyassociative matrices (FAM)) are actually a visual

Fig. 3. Effect of the gain value of Kp on the optimal Ki setting value.

(a) Without GRC, (b) with GRC.

Table 2

CIC and CPIC gain values (Kp, Ki) along with the corresponding Jfre

values obtained, with and without GRC

Without GRC (non-reheat turbine) With GRC (reheat turbine)

CIC CPIC CIC CPIC

Ki 0.3060 0.5659 0.1794 0.1794

Kp �/ 0.7330 �/ 0.000

Jfre 0.361289 0.210001 0.616409 0.616409

Fig. 4. Block diagram of a typical closed-loop fuzzy control system.

Fig. 5. Generic form of triangular type membership functions for

fuzzy subsets of a variable V .


representation of all the possible combinations of the

linguistic variables plus the corresponding fuzzy con-troller action.

3.1.1.3. Defuzzification. It should be noted that various

rules (nr) may be in operation for a certain set of (et ,

cet ), each recommending possibly different fuzzy con-

troller actions. These have to be combined in a certain

way to obtain a precise numerical output corresponding

to the actual controller action. The well known center of

gravity defuzzification method has been used because of

its simplicity:

Du�Xnr

j�1

mjuj=Xnr

j�1

mj (5)

where mj is the membership value of the linguistic

variable recommending the fuzzy controller action,

and uj is the precise numerical value corresponding to

that fuzzy controller action. Since the FLLFC action

corresponds to an increment Du , this type of controller

will give zero steady-state error for an input step change

in the reference or any step disturbance.The membership functions, knowledge base and

method of defuzzification essentially determine the

controller performance. As mentioned before their

choice is heuristic, though a rough estimate of the

parameter values can be obtained from our knowledge

of steady-state characteristics and previously simulated

open-loop behavior. These have to be tuned after

evaluation of the performance using repetitive simula-

tions.The FLLFC offers many more tunable parameters

than the CIC or the CPIC gains. Moreover, since the

final output U (t) is a combination of the recommended

actions of many rules (which themselves operate on

combinations of the inputs (et , cet )), the controller is

more robust to changes in power system parameters or

controller operating conditions than a conventional

controller.

3.1.2. Results of testing the designed FLLFC

To demonstrate the efficiency of the proposed

FLLFC controller, several simulations were performed.

From all these the following cases are considered:

FAM used Total no. of rules Parameters used

Table 3

Fuzzy associative matrix of the proposed FLLFC controller with 81 rules

et

cet NVL NL NM NS ZR PS PM PL PVL

NVL PVL PVL PL PL PM PM PS PS ZR

NL PVL PL PL PM PM PS PS ZR NS

NM PL PL PM PM PS PS ZR NS NS

NS PL PM PM PS PS ZR NS NS NM

ZR PM PM PS PS ZR NS NS NM NM

PS PM PS PS ZR NS NS NM NM NL

PM PS PS ZR NS NS NM NM NL NL

PL PS ZR NS NS NM NM NL NL NVL

PVL ZR NS NS NM NM NL NL NVL NVL

Table 4

Fuzzy Associative Matrix of the proposed FLLFC controller with 12

rules

et

cet NM NS ZR PS

NS PM PS PS ZR

ZR PS PS ZR NS

PS PS ZR NS NS Fig. 6. Membership functions for the fuzzy variables of the proposed

FLLFC.


Appendix (Continued)

FAM used Total no. of rules Parameters used

Case 1 See Table 3 81 See Table 5

and Fig. 6

Case 2 See Table 3 81 See Table 6and Fig. 6

Case 3 See Table 4 12 See Table 7

and Fig. 6

A step load demand disturbance of DPd�/0.1 p.u. is

applied and the Df system output is obtained. Fig. 7

depicts the simulation results for the above three cases

without considering the GRC, whereas Fig. 8 depicts

analogous result with GRC. The simulation results of

Figs. 7 and 8 and others not shown here, amply indicatethat the designed FLLFC is relatively insensitive to

operating point variations and it is also stable in a wide

operating region. Based on the results of Fig. 7 one

clearly sees that the transient behavior of the frequency

deviation (Df) in the case of the CIC displays by

comparison to the other two controllers (CPIC and

FLLFC) higher first swing, less oscillations and lower

settling time. On the other hand, in the case of the

FLLFC, by comparison to the CPIC case, the Df has

oscillations with lower amplitude and shorter settling

time. With respect to Fig. 8 one sees that the Df

variation is the same for the CIC and CPIC cases,

whereas in the FLLFC case the corresponding Df

variation has by comparison more oscillations with

lower amplitude and shorter settling time. The IAET

criterion gives the values shown in Table 8, where Case 3

exhibits quite better performance although 5 fuzzy sets

have been used for each linguistic variable and only 12

rules (instead of 9 fuzzy sets and 81 rules used in Cases 1

and 2). From the above it is clear that the FLLFC is

highly dependent on the data base parameters. Thismeans that an initial tuning in the design of a FLC as

well as an algorithm to change continuously the data

base parameters is needed. This will be explored by

incorporating a GA in the control structure. In the

following the simulation results of Case 3 of the FLLFC

design will be kept to be compared with the associated

ones which will be obtained from the NNGAFLC to be

developed.

Table 5

Case 1 of parameter values corresponding to membership functions of

the input/output variables of the proposed FLLFC (Fig. 6)

p1 p2 p3 p4 p5

et 0.05 0.10 0.20 0.40 0.80

cet 0.0005 0.00125 0.0025 0.0050 0.0100

Ut 0.05 0.10 0.30 0.50 0.80

Table 6



p1 p2 p3 p4 p5

et 0.05 0.10 0.20 0.40 0.80

cet 0.002 0.004 0.008 0.012 0.020

Ut 0.05 0.10 0.30 0.50 0.80

Table 7



p1 p2 p3 p4a p5

a

et 0.35 0.89 1.00

cet 0.37 0.63 1.00

Ut 0.40 0.51 1.00

a Not used.

Fig. 7. Frequency variation of a typical single-area power system with

load step change DPd�/0.1 p.u.MW and without GRC. (a) Case 1, (b)

Case 2, (c) Case 3. /(*)/ designed FLLFC, ( �/ �/ �/ �/ �/) CPIC with Ki�/

0.5659 and Kp�/0.733, (*/) CIC with Ki�/0.306.


3.2. Genetic algorithms

A GA is a global search technique based on the

operations of natural genetics and a Darwinian survival-

of-the-fittest with a randomly structured information

exchange. GA related research has received increasing

interest owing to its advantages over conventional

optimization techniques. Given an optimization pro-

blem, a GA encodes the parameters concerned into a

finite bit binary string that is called a chromosome. A

chromosome population is subsequently formed, each

representing a possible solution to the optimization

problem. Each chromosome is then evaluated according

to its fitness function.

Three basic operators ‘reproduction’, ‘crossover’ and

‘mutation’, i.e. similar to genetic evolution, are thenperformed. The reproduction task randomly selects a

new generation of chromosomes. The crossover involves

exchanging parts of two chromosomes. With the cross-

over operation, more chromosomes are generated. The

genetic search space is thus extended and more com-

plete. Mutation is the random alteration of the bits in

the string. For the binary representation mutation task

simply flips the state of a bit from 1 to 0, or vice versa.The mutation operation is usually associated with

helping to re-inject any information that may be vital

to the performance of a search process. Elitism is the

procedure where the best individual is replicated into

next generation. Finally the string having the largest

value of fitness function is found and then decoded to

obtain the parameters of a fuzzy controller.

A GA, capable of searching for a population ofchromosomes rather than a single chromosome, can

arrive at the globally optimal point rapidly and simul-

taneously avert locking at a local optima. In addition,

GA works with a coding of parameters rather than the

parameters themselves, thereby freeing itself of the

limitations (e.g. continuity and derivative existence) of

conventional techniques such as gradient methods [27].

3.3. Artificial neural networks

It is well known that the use of an ANN offers a

significant speed advantage, due to its parallel nature,

and could be implemented in real-time while the

implementation of a complicated conventional control-

ler is not always possible in real-time. Many of the

ANNs applications in control areas involve learning the

control system dynamics and incorporating them, insome way to the overall system controller. The ap-

proaches differ in the methods used for such incorpora-

tion, the learning and adaptation of the ANN. One

approach is to train the ANN off-line to learn the

system dynamics and employ it as a feed-forward

controller as shown in Fig. 9a. In another approach

the ANN is employed as a replacement for the plant

dynamics evaluation inside the model-based controlalgorithm as shown in Fig. 9b. In the present work a

combination of these two approaches is used.

Actually two identical ANNs (ANN-I, ANN-II) are

employed. The first one is trained off-line, using the

input and output of the FLLFC driven by the GA, and

the second one is acting like an on-line controller. At the

beginning of the on-line operation, the synapses among

the ANN-II neurons will give the same output as theANN-I neurons for the same input. As the off-line

controller operation continues the ANN-II starts learn-

ing the plant dynamics and also updates itself.

Fig. 8. Frequency variation of a typical single-area power system with

load step change DPd�/0.1 p.u.MW and with GRC. (a) Case 1, (b)

Case 2, (c) Case 3. Designed FLLFC /(*)/; CIC (or CPIC) with Ki�/

0.1794 (*/).

Table 8

Jfre values for the three FLLFC simulation cases

Case 1 Case 2 Case 3

Without GRC 0.157878 0.150673 0.143946

With GRC 0.346607 0.325105 0.283582


4. Developed AGC scheme and simulation results

4.1. Developed AGC structure

Summarizing Section 3 it can be said that intelligent

control concepts are mainly based on the following three

optional approaches: (a) expert systems as adaptive

elements in a control system, (b) fuzzy calculations as

decision-producing elements in a control system, and (c)

neural nets as compensation elements in a control

system. The proposed in this work controller designprocedure as a result of the above features consists of

the following parts:

4.1.1. Stage 1: fuzzy part

It is shown in Section 3.1.1 that the output U (t) of the

FLLFC can be expressed in terms of e , ce and the

parameters pe1; pe

2; pce1 ; pce

2 ; pU1 ; pU

2 (where the index‘t ’ is omitted for notation simplification purposes).

Therefore, the performance of the control system

primarily relies on the shapes of the membership

functions. However, to apply fuzzy control, the values

of the above parameters must be initially determined in

an optimal manner. Therefore, a performance index

must be defined as well as an algorithm to search for the

optimal values of the above parameters. Herein, theperformance index is defined as the reciprocal of the

summation of the sum of both the weighted absolute of

error and the weighted absolute of change of error, i.e.

F �1=Xnpop

j�1

(w1jejj�w2jcejj) (6)

where w1 and w2 are performance weights, and the larger

magnitude of weight is related to the corresponding

transient response which is of more relevant concern. In

this manner, large values of the fitness function F

indicate a better performance. In searching for the

optimal values of the parameters

pe1; pe

2; pce1 ; pce

2 ; pU1 ; pU

2 that maximize the fitness

function, a suitable algorithm must be adopted which

can satisfy the following requirements: (a) the ability to

handle non-linearities such as those of the yielded fuzzy

rules, and (b) the ability to generate an optimal solutionrapidly without being stuck at a local optima.

4.1.2. Stage 2: GA part

Section 3.2 clearly illustrated why a GA satisfies the

above requirements and can obviously be applied to

search for the optimal values of

pe1; pe

2; pce1 ; pce

2 ; pU1 ; pU

2 of the designed FLLFC.

Moreover, the CIC’s gain Ki will be searched also by

the GA. In the present application the first step involves

encoding the values of pe1; pe

2; pce1 ; pce

2 ; pU1 ; pU

2 ; Ki

into a binary string of fixed-length, in which the lengthof the string is determined by compromising the resolu-

tion accuracy and computational speed. Without loss of

generality it is assumed that there are N bits for each

value of pe1; pe

2; pce1 ; pce

2 ; pU1 ; pU

2 ; Ki, respectively. In

this manner the values of pe1; pe

2; pce1 ; pce

2 ; pU1 ; pU

2 ; Ki,

which determine the shape of the corresponding mem-

bership functions are transformed into a string that has

3N�/3N�/N�/7N bits as follows:

S� S1|{z}pe

1

S2|{z}pe

2

S3|{z}pce

1

S4|{z}pce

2

S5|{z}pU

1

S6|{z}pU

2

S7|{z}Ki

;

Si �00 . . . 001|fflfflfflfflfflffl{zfflfflfflfflfflffl}N bit

i�1 . . . 7(7)

where S represents the chromosome in the GA solution

and Si a parameter representation.In addition to encoding the parameters, several

important genetic parameters in the GA searching

procedure must be chosen, i.e. the generation number,

population size, crossover rate, mutation rate etc. The

parameters used in this work are shown in Table 9.

The details of the proposed GA-based fuzzy con-

troller design procedure are summarized as follows:

Step 1 Determine the number of fuzzy subsets forfuzzy variables et , cet , U (t) (Fig. 6) and the

fuzzy control decision table (Table 4).

Step 2 Define the fitness function as given in Eq. (6).

Fig. 9. Forms of ANN incorporations: (a) ANN as a feed-forward

controller, (b) ANN as an adaptive controller.

Table 9

Typical GA parameters

Parameter Value

Maximum no of generations a 1

No of population size 100

Uniform crossover Yes

Crossover probability 0.5

Elitism Yes

Mutation probability 0.01

Creep mutations Yes

Creep mutation probability 0.02

a Single function evaluation.


Step 3 Determine the generation number, populationsize, the crossover rate and the mutation rate.

Step 4 Give the range and length of bit strings for pe1;

pe2; pce

1 ; pce2 ; pU

1 ; pU2 and Ki, produce an initial

generation of chromosomes in a randommanner.

Step 5 Calculate the error et and change of error cet .

Execute fuzzification, fuzzy inference, defuzzi-

fication phases and fuzzy control law for all

populations in this generation. Meanwhile,

evaluate the fitness values of all populations

in this generation.Step 6 Reproduce a new generation by the roulette

wheel selection.Step 7 Crossover the pair of populations in the new

generation according to the crossover ratedetermined in Step 3.

Step 8 Mutate the populations in the new generationaccording to the mutation rate determined inStep 3.

Step 9 Reserve the population having the largestfitness value in the old generation to the newgeneration.

Step 10 Decode the chromosome (represented by abinary string) having the largest fitness valuei n t o i t s c o r r e s p o n d i n g v a l u e s o fpe

1; pe2; pce

1 ; pce2 ; pU

1 ; pU2 and Ki.

Step 11 R e p l a c e t h e o l d v a l u e s o fpe

1; pe2; pce

1 ; pce2 ; pU

1 ; pU2 with the new ones.

Step 12 Repeat Steps 5 to 11 while training the ANN-I.

4.1.3. Stage 3: ANN part

As it is known there are many kinds of neural

networks. In this application the most appropriate

have been proven the multi-layer feed-forward neural

network (MLFFNN), which learn using the back

propagation algorithm [28]. Such networks are designedto learn non-linear function mappings and their ‘train-

ability’ allows on-line learning of the changing system

behavior. The employment of the MLFFNN is to

evaluate in real-time the dynamics of the power gen-

erating system under study. The used ANN architecture

is shown in Fig. 10. The neural network current outputs,

i.e. U (t) and CIC’s gain Ki, can be determined from the

current values et , cet , the past values of these parameters(et�1, cet�1) and the past value of U (t).

ANNs are characterized by their topology, i.e. by the

number of interconnections, the node characteristics

that are classified by the type of non-linear elements

used, and the kind of learning rules implemented. A

MLFFNN is a layered network consisting of an input

layer, an output layer, and at least one layer of non-

linear processing elements. The non-linear processingelements, which sum the incoming signals and generate

output signals according to some predefined functions,

are called neurons or nodes. The neural network

developed is a three-layer feedforward network. The

standard back propagation algorithm with momentum

is used to train the network off-line. Along with the

following bipolar sigmoid transfer function for the

hidden neurons

yji �(2=1�exp(�bj

xi))�1 (8)

where xij is the input and yi

j is the output for the ithneuron in the jth network hidden layer. Here, b affects

the steepness of the curve. High values of b give a step-

like curve and lower ones give a smoother curve. The

gradient descent method was used to search for the

optimal settings of the weights. During the off-line

training the weights in the ANN were updated using

the delta rule. Application of the delta learning rule

eliminates the problem of the structured presentation ofthe training set by accumulating the weight changes over

several training presentations and making the applica-

tion all at once. Different learning rates, n , and

momentum rates, a , are used between consecutive layers

to achieve the most rapid learning. The values of the

parameters used in ANN-I and ANN-II is given in

Table 10.

4.2. Simulation cases

The dynamic subsystems, i.e. the power system, the

FLLFC and the GA are interfaced with each other as

Fig. 10. Architecture of used ANN.

Table 10

ANN-I and ANN-II parameters used

Parameter Value

No of layers 3

No of neurons (input, hidden, output) 5, 4, 2

Steepness parameter b 0.2

Learning rate n (off-line) Started 0.9, reduced to 0.3

Learning rate n (on-line) Fixed at 0.6

Momentum rate a (off-line) Started 0.6, reduced to 0.1

Momentum rate a (on-line) Fixed at 0.3


shown in Fig. 11. The designed NNGAFLC applied to a

typical single-area power system and some cases of

interest are being investigated. The cases studied aresummarized below:

Case 1 Step change DPd�/0.1 p.u.MW, withoutGRC. ANN-I trained by 50%.

Case 2 Step change DPd�/0.2 p.u.MW, withoutGRC. ANN-I trained by 50%.

Case 3 Step change DPd�/0.1 p.u.MW, with GRC.ANN-I trained by 90%.

Case 4 Step change DPd�/0.2 p.u.MW, with GRC.ANN-I trained by 90%.

In all above cases the power system parameters are

given in Table 1. In all above cases the weight matrix is

copied from ANN-I to ANN-II every 250 ms.

4.3. Results obtained

The results (frequency variation) for the above four

cases are: for Cases 1 and 2 are shown in Fig. 12 and for

Cases 3 and 4 in Fig. 13. The associated values of the

IAET criterion for the examined cases gives the values

shown in Table 11. From Fig. 12 and Fig. 13 and Table11 it is clear that the designed NNGAFLC gives the

overall best results, the FLLFC gives the second best

results by comparison to the associated ones of the

conventional controllers (CIC and CPIC). These results,

also, show that the behavior of the proposed controller

is more ‘nervous’ when the ANN’s involved are not

trained completely. In the opposite case the behavior of

the controller becomes smoother even if the disturbanceis larger and GRC is considered. This in fact proves the

general ability of ANNs to cope with non-linearities. It

should be noted, however, that for the shake of restoring

Fig. 11. Overall structure of proposed controller (NNGAFLC) connected to the power system under study.

Fig. 12. Frequency variation of a typical single-area power system,

without GRC. Step changes: (a) DPd�/0.1 p.u.MW, (b) DPd�/0.2

p.u.MW. Designed NNGAFLC /(*)/; designed FLLFC (Case 3 of

Section 3.1.2) (*/); CPIC ( �/ �/ �/ �/ �/ �/); CIC (-----).


the system frequency to its nominal value in the shortest

time possible, one allows greater number of oscillations

in the Df deviation.

Due to space limitations, only the variation of the

values of the FL data base parameters along with the

on-line integral gain variation of Case 1 are shown in

Fig. 14 and Fig. 15 respectively. As one can see from

these figures the final values of the parameters

Fig. 13. Frequency variation of a typical single-area power system,

with GRC. Step changes: (a) DPd�/0.1 p.u.MW, (b) DPd�/0.2

p.u.MW. Designed NNGAFLC /(*)/; designed FLLFC (Case 3 of

Section 3.1.2) (*/); CPIC ( �/ �/ �/ �/ �/ �/).

Table 11

Overall comparison of the Jfre values of the conventional and designed

controllers for Cases 1, 2, 3 and 4

Without GRC CIC CPIC FLLFC (Case 3

of Section 3.1.2)

NNGAFLC

DPd�0.1 p.u. 0.361 0.210 0.144 0.025

DPd�0.2 p.u. 0.433 0.254 0.168 0.041

With GRC

DPd�0.1 p.u. 0.616 0.616 0.283 0.075

DPd�0.2 p.u. 1.172 1.172 0.412 0.159

Fig. 14. Variation of parameters pe1; pe

2; pce1 ; pce

2 ; pU1 ; pU

2 (of the

FLC part of the NNGAFLC). Step change: DPd�/0.1 p.u.MW.


pe1; pe

2; pce1 ; pce

2 ; pU1 ; pU

2 are quite the same with the

corresponding values of Case 3 (Table 7) of the designed

FLLFC (Section 3.1.1). They are also the same with

those ones that formed one of the starting GA’s

chromosome population. This means that the GA at

last reached an optimal parameter combination (includ-

ing the integral gain Ki, which reaches the optimal value

found by the exhaustive search in Section 2.3) but this

combination was not optimal before. This points out the

need of adopting a well-tuned suitable search algorithm

for the overall controller’s parameters identification.

5. Conclusions

A new LFC structure based on intelligent methods

was developed and applied successfully in this work. The

main advantages of the proposed controller may be

summarized as follows:

�/ The main feature of all AGC controllers used inpractice is retained, that is, the feedback is based only

on the error and the change in error of frequency

measurements, instead on the state variables of the

system. This means that measurements of all system

state variables are not needed, and that only the

measurement of the system frequency suffices.

�/ The adaptation property helps the controller to

stabilize the plant especially when the parametersmay vary widely and abruptly. Whereas, the robust-

ness property of the FLC and the search ability of the

GA, makes it possible for the controller to stabilize

the system even if there are certain errors in the

identification system.

�/ The required control effort is made off-line and does

not slow down the control process. Since the actual

controller is only the on-line ANN employed, theresponse of the controller is almost instantaneous due

to the memory-element properties it has. Such an

architecture ‘decentralizes’ the control of the overall

system and reduces the amount of information to be

exchanged between the plant and the controller. This

makes possible the implementation of the controller.

�/ The more economic operation of the power system,

since the loss of served load and the imposed excess ofload are much smaller.

The various simulation results clearly indicate that theproposed power system LFC depicts by comparison to

competing controllers superior performance and stabi-

lity properties. The designed procedure of the proposed

controller may be applied in multi-area power systems,

possibly with simpler structure and with careful exam-

ination of its potential properties.

Appendix A: Nomenclature

f , fnom, ft power system frequency, nominal value,

value at sampling instant t

Pt output signal of turbine block

Pg output signal of governor blockPscp speed changer position signal

U (t ) additional signal input to the existing

integral controller structure

Kps, Tps gain and time constant of power system

block

Kt, Tt gain and time constant of turbine block

Kg, Tg gain and time constant of governor block

Ki, Kp integral and proportional gains of a PIstructure controller

R governor droop parameter

X, Y, U state and output variable, and control

vector of a model in state-space form

A, B, C system matrices of a dynamic model in

state-space form

/[]T/ transpose of a matrix/vector

B frequency bias parameterJ performance index

et , cet error, change in error (at sampling instant

t)

m [R (x )] membership function value of fuzzy vari-

able R for an input point x

p1, p2, . . .,p5

coordinate parameters of the fuzzy vari-

ables

u output (defuzzified) value of the fuzzycontroller

F fitness function of the genetic algorithm

w1, w2 weight values used by the fitness function

S chromosome representation

Sj the j th gene of chromosome S

xij , yi

j input and output signal value of the ith

neuron element of the jth layer in a neural

networkb steepness parameter (saturation degree) of

a neural network element

n learning rate of a neural network element

Fig. 15. Integral control gain (Ki) variation (output of on-line ANN-II

of designed NNGAFLC).


a momentum rate of a neural network

element

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Biographies

Yannis L. Karnavas (1969), received the Diploma in

Electrical Engineering in 1994 from the Department of

Electrical and Computer Engineering (DE&CE) of

Democritos University of Thrace (DUTH), Greece. He

has been working (October 1995�/Febuary 1998, Octo-ber 2000�/) as a scientific associate of the Electrical

Machines Laboratory of the Higher Technological

Educational Institute of Kavala, Kavala, Greece. He is

currently pursuing his Ph.D. degree in Electrical En-

gineering in the DE&CE of DUTH and his research

interests include power system operation, industrial

process control and applications of artificial intelligence.

He is a Chartered Electrical Engineer and he engages intechnical studies. He is a member of the Technical

Chamber of Greece. He is an IEEE student member.

(Electrical Machines Laboratory, Department of Elec-

trical and Computer Engineering, Democritos Univer-

sity of Thrace, Vasilissis Sofias 12, 67100, Xanthi,

Greece. Tel.: �/30-541-079925; fax: �/30-541-071191,

[email protected]).

Professor Demetrios P. Papadopoulos (1942) received

the BSEE (1965), MSEE (1968) and Ph.D. (1970) in

Electrical Engineering from Marquette University, Mil-


[email protected]

waukee, WI, USA. During 1970�/1972 he was Assistant

Professor at the Department of Electrical Engineering of

Gonzaga University, Spokane, WA, USA. From 1972 to

1997 he was with the Public Power Corporation ofGreece working on special projects of power systems.

Since 1981 he is Professor and Director of the Electrical

Machines Laboratory of the Department of Electrical

and Computer Engineering at Democritos University of

Thrace (DUTH). From 1987 to 1988 he served as Vice-

Rector at DUTH and from 1989 to 1991 as General

Secretary of Eastern Macedonia-Thrace Region of

Greece. He is Senior Member of IEEE, Member of the

Technical Chamber of Greece, and also of the Societies

P??, ??P, ??? and S?. His research interests are in

electrical machines, and in power production with small

hydro, wind conversion and cogeneration systems.

(Electrical Machines Laboratory, Department of Elec-

trical and Computer Engineering, Democritos Univer-

sity of Thrace, GR-67100 Xanthi/Greece. Tel.: �/30-

541-079721; fax: �/30-541-027955; [email protected]

duth.gr).


[email protected]

[email protected]

AGC for autonomous power system using combined intelligent techniques

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