Fuzzy logic controller in interconnected electrical power systems for load-frequency control

Fuzzy logic controller in interconnected electrical power

systems for load-frequency control

Ilhan Kocaarslan*, Ertugrul Cam

Faculty of Engineering, Kırıkkale University, 71450 Yahsihan, Kırıkkale, Turkey

Received 5 May 2004; revised 17 May 2005; accepted 23 June 2005

Abstract

This study presents an application of a fuzzy gain scheduled proportional and integral (FGPI) controller for load-frequency control of a

two-area electrical interconnected power system. Model simulations of the power system show that the proposed FGPI controller is effective

and suitable for damping out oscillations resulted from load perturbations. The current FGPI results were compared against those from a

conventional proportional and integral (PI) controller, a fuzzy logic controller and a FGPI controller proposed by Chang and Fu (Chang C. S.,

Fu W. Area load-frequency control using fuzzy gain scheduling of PI controllers. Electr Power syst Res 1997; 42: pp. 145–152). Two

performance criteria were utilized for the comparison: settling times and overshoots of the frequency deviation and absolute error integral.

The comparison study indicated that the proposed FGPI controller has better performance than the other three controllers.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Power plant; Load-frequency control; Fuzzy logic control application

1. Introduction

In power systems, active and reactive power flows

function independently. Therefore, different control blocks

are used to control them. The automatic generation control

(AGC) is the major technique for solving this problem [1].

Interconnected electrical power systems operate together

adjusting their power flows and frequencies at all areas by

AGC. In this study, a two-area power system is considered

to control power flows. A power system has a dynamic

characteristic meaning that it can be affected by disturb-

ances and changes at the operating point [2,3]. Given that

frequencies at the areas and power flows in tie-lines produce

unpredictable load changes and also, generated and demand

powers are not equal. Such difficulties are taken care of by

AGC systems which are also called load-frequency control

(LFC) and are being improved over the years [4]. Load-

frequency control, a technical requirement for the proper

0142-0615/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijepes.2005.06.003

* Corresponding author. Tel.: C90 318 357 35 71; fax: C90 318 357

24 59.

E-mail addresses: [email protected] (I. Kocaarslan), ikocaarslan@

yahoo.com (I. Kocaarslan).

operation of an interconnected power system, is very

important for supplying reliable electric power with good

quality. The goals of the LFC are to maintain zero steady

state errors in a multi-area interconnected power system and

to fulfill the requested dispatch conditions [5].

During last decades, several studies on the load-

frequency control in interconnected power systems have

been presented in the literature. Different control strategies

have been suggested based on the conventional linear

control theory [6–8], among others. Since, the dynamics of a

power system even for a reduced mathematical model is

usually nonlinear, time-variant and governed by strong

cross-couplings of the input variables, the controllers have

to be designed with special care [9]. Thus, a gain scheduling

controller had been used for nonlinear systems by some

researcher e.g. [5]. In this method, control parameters can be

changed very quickly since parameter estimation is not

required, and thus system outputs are obtained faster with

higher quality as compared with conventional controllers.

However, in the same method, the transient response can be

unstable because of abruptness in system parameters. Also,

accurate linear time invariant models cannot be obtained at

variable operating points [5].

Recently, FGPI controllers have been proposed to solve

the above mentioned difficulties in power systems. For

Electrical Power and Energy Systems 27 (2005) 542–549

www.elsevier.com/locate/ijepes

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Nomenclature

Ki integral gain constant

Kp proportional gain constant

Ri regulation constant

Tg speed governor time constant

Tt turbine time constant

Tp power system time constant

A system matrix

B input matrix

L disturbance matrix

x(t) state vector

u(t) control vector

d(t) disturbance vector

Dfi frequency deviation from nominal value in

Area-i

DP12 change in tie-line power between two-area

DPd,iZDPL,i load demand increment in Area i

bi frequency bias factor in Area i

Ta settling time of proposed controller

Tb settling time of the conventional PI controller

Tc settling time of the conventional I controller

Td settling time of the fuzzy logic controller

a12 synchronizing power coefficient

I. Kocaarslan, E. Cam / Electrical Power and Energy Systems 27 (2005) 542–549 543

example, [5] and [10] developed different fuzzy rules for the

proportional and integral gains separately and showed that

response of power systems can be further improved using

fuzzy logic controller [11].

In this study, a FGPI controller was designed with

seven triangular membership functions to LFC application

in a two-area power system for generating electricity with

good quality. In the design of the controller, rules for the

gains (Kp and Ki) are chosen to be identical in order to

improve the system performance. The proposed controller

was compared with three different controllers: a conven-

tional PI controller, a fuzzy logic controller and another

FGPI controller designed by [5]. Settling times and

overshoots of the systems and absolute integral values

were utilized as comparison criteria to evaluate the

performance of controllers. It was shown that the

proposed FGPI controller generally has better perform-

ance than the other controllers.

2. Interconnected electrical power systems

Interconnected power systems consist of many control

areas connected by tie-lines. The block scheme of an

uncontrolled two-area power system is shown in Fig. 1.

(2*

∆Ptie1

Control Area-1

Control Area-2

∆Ptie2

a12

U1

U2

Fig. 1. The block scheme of an uncon

All blocks are generally nonlinear, time-variant and/or

non-minimum phase systems [12]. In each control area, the

generators are assumed to form a coherent group. Loads

changing at operating point affect both frequencies in all

areas and tie-line power flow between the areas [13]. As

known that power systems have parametric uncertainties

and they must have small oscillations in the magnitude of

transient frequency. Their speed control must be taken care

of as quickly as possible [12]. The load-frequency control

generally is accomplished by two different control actions in

interconnected two-area power systems: (a) the primary

speed control and (b) supplementary or secondary speed

control actions. The former performs the initial vulgar

readjustment of the frequency by which generators in the

control area track a load variation and share it in proportion

to their capacities. This process typically takes place within

2–20 s. The latter takes over the fine adjustment of the

frequency by resetting the frequency error to zero through

an integral action. The relationship between the speed and

load can be adjusted by changing a load reference set point

input. In practice, the adjustment of the load reference set

point is accomplished by operating the speed changer

motor. The output of each unit at a given system frequency

can be varied only by changing its load reference, which in

effect moves the speed-droop characteristic up and down.

pi*T12)/s

Load

Load

+

--

∆f1

∆f2

trolled two-area power system.

I. Kocaarslan, E. Cam / Electrical Power and Energy Systems 27 (2005) 542–549544

This control is considerably slower and goes into action

only when the primary speed control has done its job. In this

case, response time may be of the order of 1 min.

3. Power system model used

The two-area interconnected power system used in this

study is displayed in Fig. 2 where f is the system frequency

(Hz), Ri is regulation constant (Hz per unit), is speed

governor time constant (s), Tt is turbine time constant (s), Tp

is power system time constant (s) and DPL1,2 is load demand

increments.

The overall system can be modeled as a multi-variable

system in the following form:

_x Z AxðtÞCBuðtÞCLdðtÞ; (1)

in which A is the system matrix, B and L are input and

disturbance distribution matrices, x(t), u(t) and d(t) are state,

control and load changes disturbance vectors, respectively.

xðtÞ Z ½Df1 DPg1 DPy1 DP12 Df2 DPg2 DPy2�T

uðtÞ Z ½u1 u2�T dðtÞ Z ½DPd1 DPd2�

T;

where D denotes deviation from the nominal values and u1

and u2 are the control outputs in Fig. 2.

The system output, which depends on area control error

(ACE) given in Fig. 3, is written as follows:

Fig. 2. The two-area interconnected p

yðtÞ Zy1ðtÞ

y2ðtÞ

" #Z

ACE1

ACE2

" #Z CxðtÞ (2)

ACEi Z DP12 CbiDfi; (3)

where bi is the frequency bias constant, Dfi is the frequency

deviation and DP12 is the change in tie-line power for area i

(iZ1 for area 1 and iZ2 for area 2) and C is the output

matrix [14].

4. The proposed FGPI controller

Originally developed by Zadeh in 1965 fuzzy logic

(FL) is today implemented in all industrial systems all

over the world. It is much closer in spirit to human

thinking and natural language than classical logical

systems [15]. Therefore, it is not required a mathematical

model or certain system parameters [1]. According to

many researchers, there are some reasons for the present

popularity of FL control. First, FL can easily be applied to

most industrial applications in industry. Second, it can

deal with intrinsic uncertainties by changing controller

parameters. Finally, it is appropriate for rapid

applications.

Fuzzy logic has been applied to industrial systems as a

controller in various applications. For the first time, FL was

applied to control theory by Mamdani in 1974 [16]. A fuzzy

controller is formed by fuzzification of error, inference

ower system used in this study.

1R1

+

+

2*pi*T12

s∆P12

∆f1

∆f2

b1

a12

Controller

Controller +

–

Turbine-Generator2

–

+

–

+

–

Power System2

∆Pd2

1R2

b2

+

+

Turbine-Generator1

a12

–

+–

Power System1

–

+

∆Pd1

ACE1

ACE2

Fig. 3. Two-area power system with controllers [10].


mechanism and defuzzification levels. Therefore, an analog

signal is taken from output of the FL controller. For systems,

human experts prepare linguistic descriptions as fuzzy rules

which are obtained based on step response experiments of

the process, error signal, and its time derivative [10]. In

general, conventional FL controllers are not suitable for

system controlling since they cannot produce reliable

transient response. Also, they are unable to decrease

steady-state errors down to zero [17]. Thus, a fuzzy gain

scheduling PI (FGPI) controller is proposed in this study to

maintain load-frequency control in the two-area power

system. The main goal of the load-frequency control in the

interconnected power systems is to protect the balance

between production and consumption [17].

Table 1

Fuzzy logic rules for the proposed FGPI and FL controllers

DACE(k)

ACE(k) LN MN SN

LN LP LP LP

MN LP MP MP

SN LP MP SP

ZE MP MP SP

SP MP SP ZE

MP SP ZE SN

LP ZE SN MN

LN, Large Negative; MN, Medium Negative; SN, Small Negative; ZE, Zero; SP

By taking ACE as the system output, the control vector

for the conventional PI controller can be given in the

following forms:

upiðtÞ ZKKpACEiK

ðKiðACEiÞdt

ZKKpðDPtie;i CbiDfiÞK

ðKiðDPtie;i CbiDfiÞdt (4)

Most of experiments and simulation studies applied to

the power systems have shown that the conventional

controllers have large overshoots and long settling times

[6]. Also, optimizing time for control parameters, especially

ZE SP MP LP

MP MP SP ZE

MP SP ZE SN

SP ZE SN MN

ZE SN MN MN

SN SN MN LN

MN MN MN LN

MN LN LN LN

, Small Positive; MP, Medium Positive; LP, Large Positive.

µ

–10

(c)

–6.5 –3 0 3 6.5 10

LN MN SN ZE SP MP LP

X=Kp, Ki

µ

–1

(b)

–0.78 –0.36 0 0.36 0.78 1.2


X=∆ACE(k)

µ

–0.1

(a)

–0.065 –0.03 0 0.03 0.065 0.1


X=ACE(k)

Fig. 5. Membership functions for the proposed FGPI controller of (a) ACE,

(b) DACE, (c) Kp, Ki.

(a) µ



PI controllers, is very long and the parameters cannot be

determined exactly [18].

Fuzzy set theory and fuzzy logic establish the rules of a

nonlinear mapping [19]. The use of fuzzy sets provides a

basis for a systematic way for the application of uncertain

and indefinite models [20]. Fuzzy logic shows experience

and preference through membership functions (MFs) which

have different shapes depending on the experience of system

experts [21]. For the proposed FGPI, the Mamdani fuzzy

inference engine was selected and the gain ranges of the

controller are chosen different from [5] to improve outputs

of the power system. In their study, Chang and coworkers

[5] employed two MFs (Big and Small) for the inference

mechanisms of the gains whereas same inference mechan-

ism was realized by seven triangular MFs (see Table 1) for

both the FGPI and FL controllers. Using the same

normalization procedure, Cam and Kocaarslan in an earlier

study [22] have compared their proposed FGPI controller

with [5] and two other controllers. They have shown that

their FGPI controller have better performance than other

controllers. In the current study, further improvements were

made to [22] by changing the MF intervals of the ACE,

DACE, Kp and Ki. Defuzzification has been performed by

the center of gravity method in all studies. The appropriate

rules used in our study are given in Table 1. The rules, which

belong to the MFs, were obtained in the same way for each

fuzzy logic controller. They were formed based on the error

(e) and its time derivative (de). For instance, if e is highly

bigger than the set value and de is increased rapidly, then the

output of the controllers is also expected to be big.

Therefore, U is increased and output of the system

µ

X=Kp, Ki–1 –0.65 –0.3 0 0.3 0.65 1


(c)

µ

–1 –0.65 –0.3 0 0.3 0.65 1

LN MN SN ZE SP MP LP(b)

X=∆ACE(k)

µ

–1

(a)

–0.65 –0.3 0 0.3 0.65 1


X=ACE(k)

Fig. 4. Membership functions for the FL controller of (a) ACE, (b) DACE,

(c) Kp, Ki.

approaches to the set value. Other rules were also obtained

by using the same procedure.

The shapes of the error and derivative error membership

functions were chosen to be identical with triangular

(b) µ

–0.038 –0.028 –0.018 0 0.018 0.028 0.038X=∆ACE(k)

–0.027 –0.017 –0.011 0 0.011 0.017 0.027X=ACE(k)

(c)

0.07 1.4K=Kp, Ki

BigSmallµ


Fig. 6. Membership functions for FGPI controller of [5] (a) ACE, (b)

DACE, (c) Kp, Ki.

Table 2

Two-area power system parameters

TgZ0.08 B1Z0.425

R1Z2.4 B2Z0.425

R2Z2.4 T12Z0.086

TpZ20 KpZ120

TtZ0.3 a12ZK1

0 2 4 6 8 10 12 14 16 18 20–0.6

–0.4

–0.2

0

0.2

0.4

0.6

0.8

1

1.2

t(sec)

Chg

Kp

Chang’s FGPI

FLC

Proposed FGPI


function for the three fuzzy logic controllers. However, the

shapes of Kp and Ki membership functions of the FL and the

proposed FGPI controller are different from that of [5].

Additionally, intervals of the MFs were taken different

values in order to further improve outputs of the proposed

FGPI controller. The membership function sets of FL for

ACE, DACE, Kp and Ki for the conventional FL controller,

the proposed controller and for [5] are shown in Figs. 4–6,

respectively.
Fig. 8. Changes of Kp for the two-area power system (For PI, KpZ0.05).
5. Results and analyses

Simulations were performed to a two-area intercon-

nected electrical power system using four different

controllers: a conventional PI, a FGPI proposed by Chang

and coworkers, a conventional FL and a new FGPI proposed

in this study. The same system parameters [23], given in

Table 2 were used in all controllers and a comparison was

carried out.

The gain changes produced by simulations are shown in

Figs. 7 and 8.

Two performance criteria were utilized for the compari-

son: settling times and overshoots of the frequency

deviation and absolute error integral. The frequency

deviation plots were obtained with Matlab 6.0-Simulink

software [24] and therefore, settling times and overshoots of

the frequency deviation of the controllers were compared

0 2 4 6 8 10 12 14 16 18 20–0.6

–0.4

–0.2

0

0.2

0.4

0.6

0.8

1

1.2

t(sec)

Chg

Ki

Chang’s FGPI

FLC

Proposed FGPI

Fig. 7. Changes of Ki for the two-area power system (For PI, KiZ0.5).

against each other. The comparison results are provided in

Table 3.

In the analysis of the simulation results, the frequency

deviation results were also used to calculate the absolute

error integral for the controllers given in Eq. (5):

Ie Z

ðN0

½rðtÞKxðtÞ�2$dt (5)

where r(t) and x(t) were taken as the reference and the

output of the frequency deviation signals, respectively. dt

was assumed to be 1 s for both the FL and the two FGPI

controllers, and 10 s for the PI controller. Table 4 contains

the absolute error integral of each controller.

Frequency deviations of area 1 after a sudden load

change are shown in Fig. 9. Settling times for 5% band of

the step change and maximum overshoots are shown in

Table 3. Performance comparison of the proposed controller

versus the remaining ones indicates that the system response

with the proposed controller has a quite shorter settling time

Table 3

System performances for all controllers on settling times and overshoots for

frequency deviation of area 1

Controllers Df1

Settling time (for 5% band

of the step change)

Maximum overshoots

Time

(s)

Percent ratio

(other/

FGPI*100)

Magnitude

(Hz)

Percent ratio

(other/

FGPI*100)

The proposed

FGPI (ta)

3.47 100 K0.0194 100

Conventional

PI (tb)

4.37 125 K0.0271 140

Chang’s FGPI

(tc)

7.21 208 K0.0226 116

FLC (td) 17.13 498 K0.0152 78

Table 4

System performances for all controllers with absolute error integral for

frequency deviation of area 1

Controllers Absolute error

integral

Ratio (Other/FGPI)

The proposed FGPI 0.0025 –

Conventional PI 0.0062 2.48

Chang’s FGPI 0.0043 1.72

FLC 0.0040 1.6


and lower magnitude in overshoots. Simulations have been

repeated with various instantaneous load changes and a

success has been obtained for all.

As shown in Table 3, the settling time of the proposed

FGPI controller is substantially shorter than that of the other

three controllers. As for the overshoots, the best perform-

ance was obtained by the FL controller closely followed by

the FGPI controller. This suggests that the fuzzy logic

control concept is suitable for such power system in

reducing overshoots of the frequency deviation. However,

the overall results indicate that lowering the settling times

without any conventional controller is impossible. Given

these outcomes, fuzzy logic control and conventional

control techniques together can be applied to the optimiz-

ation of a controller in power systems. FGPI controller was

therefore preferred in this study. As shown in Table 3, the

FGPI controller seems to be the optimum control technique

for use in such two-area interconnected power systems. An

examination of the absolute error integral values in Table 4

indicates that the proposed controller has the smallest

absolute error integral value. It is 1.6, 2.48 and 1.72 times

smaller than that of FL, PI and Chang’s FGPI controllers,

respectively. Therefore, the proposed controller seems to be

more advantageous than the others fulfilling the demand for

the two-area interconnected power systems.

0 2 4 6 8 10 12 14 16 18 20

t(sec)

0.03

0.025

0.02

0.015

0.01

0.005

0

0.005

0.01

0.015

df1

(Hz)

Chang’s FGPI Controller

Proposed FGPI Controller

Conventional PICtll

Fuzzy Logic Controller

Fig. 9. Deviation of frequency of area 1(DPd, iZ0.01 p.u.).

6. Conclusions

In this paper, a new fuzzy gain scheduling of PI

controller was investigated for automatic load-frequency

control of a two-area interconnected electrical power

system. In the simulations, the horizontal ranges of

membership functions of the FL and the two FGPI

controllers were taken differently in order to decrease

the oscillations of frequency deviation in all areas. The

number of rules for the inference mechanisms is

increased from two MFs as in [5] to seven MFs in

the proposed controller, so that the controller perform-

ance was improved by increasing the rule numbers to

49. It has been therefore shown that the proposed

control algorithm is effective and provides significant

improvements in system performance. The proposed

controller is very simple and easy to implement, since

it does not require any information about the system

parameters. According to the experimental results, it

performs significantly better than other controllers in the

settling time and absolute error integral while it

performs closer in the overshoot magnitude. In con-

clusion, the proposed fuzzy gain scheduling PI controller

is recommended to generate good quality and reliable

electric energy.

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Fuzzy logic controller in interconnected electrical power systems for load-frequency control