Load Frequency Control Using Fuzzy Gain Scheduling

8/7/2019 Load Frequency Control Using Fuzzy Gain Scheduling

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Load Frequency Control Using Fuzzy Gain Scheduling

Of PI Controller.

Document BySANTOSH BHARADWAJ REDDYEmail: [email protected]

Engineeringpapers.blogspot.comMore Papers and Presentationsavailable on above site

ABSTRACT:

In this paper, a fuzzy gain scheduled proportional and integral (FGPI)

controller was developed to regulate and to improve the frequency deviation

in a two-area electrical interconnected power system. Also, a conventional

proportional and integral (PI), and a fuzzy logic (FL), controllers were used

to control the same power system for the performance comparison. Two

performance criteria were utilized for the comparison. First, settling times

and overshoots of the frequency deviation were compared. Later, theabsolute error integral analysis method was calculated to compare all the

controllers. The Simulation results show that the FGPI controller developed

in this study performs better than the other controllers with respect to the

settling time and overshoot, and absolute error integral of the frequency

deviation.

Keywords-Two area power system; Load-Frequency control; Fuzzy logic

controller

1. INTRODUCTION:

Large scale power systems are normally composed of control areas or

regions representing coherent groups of generators. The various areas are
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interconnected through tielines. The tie-lines are utilized for contractual

energy exchange between areas and provide inter-area support in case of

abnormal conditions. Area load changes and abnormal conditions, such asoutages of generation, lead to mismatches in frequency and scheduled power

interchanges between areas. These mismatches have to be corrected through

supplementary control.

Load Frequency Control (LFC) of interconnected systems is defined as

the regulation of power output of generators within a prescribed area, in

response to change in system frequency, tie-line loading, or the relation of

these to each other; so as to maintain scheduled system frequency and/or

established interchange with other areas within predetermined limits [1].

Many investigations have been reported in the past pertaining to load

frequency control of a multi-area interconnected power system. In the

literature, some control strategies have been proposed based on classical

linear control theory .However, because of the inherent characteristics of the

changing loads, the operating point of a power system changes continuously

during a daily cycle. Thus, a fixed controller may no longer be suitable in all

operating conditions. There are some authors who have applied variablestructure control [3] to make the controller insensitive to system parameters

change. However, this method requires information on the system states

which are very difficult to know completely. In view of this, a new area load

frequency controller based on fuzzy gain scheduling of PI controller is

proposed in this paper. Gain scheduling is a technique commonly used in

designing controller for non-linear systems. Its main advantage is that

controller parameters can be changed very quickly in response to changes in

the system dynamics because no parameter estimation is required. Besides

being an effective method to compensate for non-linear and oth

predictable variations in the system dynamics, it is also simpler

implement than automatic tuning or adaptation. However, the transient


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response can be unstable because of abruptness in system parameters.

Besides,

it is impossible to obtain accurate linear time invariant models at variableoperating points. Some fuzzy gain scheduling of PI controllers have been

proposed to solve such problems in power systems [4] and [5] that

developed different fuzzy rules for the proportional and integral gains

separately. Fuzzy logic control presents a good tool to deal

complicated, non-linear and indefinite and time-variant systems [6]. In this

paper, the rules for the gains are chosen to be identical in order to improve

the system performance. The comparison of the proposed FGPI, the

conventional PI controllers, and the fuzzy logic controller suggests that the

overshoots and settling time with the proposed FGPI controller are better

than the rest.

2. TWO AREA POWER SYSTEM:

An interconnected power system can be considered as being divided into

control areas which are connected by tie lines. In each control area, all

generators are assumed to form a coherent group. The power system is

subjected to local variations of random magnitude and duration. Hence, it is

required to control the deviations of frequency and tie-line power of each

control area.

An uncontrolled two-area interconnected power system is shown in Figure

1 where, f is the system frequency (Hz), iR is regulation constant (Hz/per

unit), gTis speed governor time constant (sec), tTis turbine time constant

(sec) and pT is power system time constant (sec).

The overall system can be modelled as a multi-variable system in form of

)()()( tdLtuBtxAx ++= , (1)


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Where 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.

X(t)=[f1 Pg1 Pd1 Ptie12 f2 Pg2 Pd2 ]T

[ ]21)( uutu = T

[ ]21)( dd PPtd =

T,

where denotes deviation from the nominal values. 1u and 2u are the

control outputs inFigure1. The system output, which depends on area control error (ACE)

shown as

)()()()(

2

1

2

1 txCAA

tytyty (2)

iiitiei fbPACE += , ,


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Where bi is the frequency bias constant, if is the frequency deviation and

itieP, is the change in tie-line power for areai and C is the output matrix

[4].

Fig.1: Two Area Interconnected System

3. FUZZY LOGIC IN POWER SYSTEMS:

Fuzzy set theory and fuzzy logic establish the rules of a nonlinear mapping

[6]. The use of fuzzy sets provides a basis for a systematic way for the

application of uncertain and indefinite models [4]. Fuzzy control is based on

a logical system called fuzzy logic is much closer in spirit to human thinking

and natural language than classical logical systems [5,6]. Nowadays fuzzy

logic is used in almost all sectors of industry and science. One of them is

load-frequency control [2]. The main goal of load-frequency control in

interconnected power systems is to protect the balance between production

and consumption. Because of the complexity and multi-variable conditions

of the power system, conventional control methods may not give satisfactory

solutions.


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The fuzzy controller for the single input, single output type of systems is

shown in Fig. 2 [3]. In this

proportional and integral gains, respectively. The fuzzy controller input canbe the derivative of e together with the signal E. The fuzzy controller block

is formed by fuzzification of E, the inference mechanism a

defuzzification. Therefore, Y is a crisp value, and u is a control signal for the

system.

Fig.2. The simple fuzzy controller

4. Fuzzy gain scheduled PI controller:

Gain scheduling is an effective way of controlling systems whose dynamics

change non-linearly with operating conditions [4]. It is normally used when

the relationship between the system dynamics and operating conditions are

known, and for which a single linear time-invariant model is insufficient. In

this paper, we use this technique to schedule the parameters of the PIcontroller according to change of the new area control error ACE, and

ACE, as depicted in Fig. 3.

Fig.3. The scheme of fuzzy gain scheduling.

By taking ACE as the system output, the control vectors for the conventional

PI and I controllers, respectively can be given in the following forms:

ui = -KPACEi- Ki (ACEi)dt

= - KP(Ptie,i+bifi) - Ki(Ptie,i+bifi)dt


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Fuzzy logic shows experience and preference through membership

functions, which have different shapes depending on the experience of

system experts. Same inference mechanism is realized by seven rules for thetwo FGPI and the FL controllers. The appropriate rules used in the study are

given in Table 1.

Fig.5. Membership functions for FL Controller of (a) ACE, (b) ACE, (c)

Kp, Ki


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Fig.6. Membership functions for FGPI Controller of (a) ACE, (b) ACE, (c)Kp, Ki

Membership functions shapes of the error and derivative error and the

gains are chosen to be identical with triangular function for both fuzzy logic

controllers. However, their horizontal axis ranges are taken different values

because of optimizing these controllers. The membership function sets of FL

for ACE, ACE, Kp and Ki are shown in Fig. 5, while the ones for FGPI

controller are shown in Fig.6. Defuzzification has also been performed by

the center of gravity method in all studies.

5. Simulation study.

Simulations were performed using the conventional PI, Fuzzy Logic (FL)

and the proposed FGPI controllers applied to a two-area interconnected

electrical power system. The same system parameters given in Tables 2 were

used in all controllers for a comparison.

Two performance criteria were selected in the simulation. The frequency

deviation graphs were first plotted with Matlab 7.0-Simulink software. Here,

settling times and overshoots of the frequency deviation of the controllers


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were compared against each other. The comparison results are provided in

Table 2 and 3.

Fig 7. a, b, c, d shows the responses for frequency deviation of area1 (f1)p.u (Pd1=0.01p.u.).

f11

Time(sec)Fig a. Without Controller

Fig 8. e,f shows the responses for Change in mechanical power in area1(Pm1).(ii)Change inmechanical power in area2(Pm2).Change in Tieline power (Ptie).

Time(sec)Fig b. With PI Controller

Time(sec)Fig b. With PI Controller

Time(sec)Fig c. With Fuzzy Logic Controller

f1


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Time(sec)Fig d. With FGPI Controller

Fig e. Without ControllerTable:1

Table:2

Controller

Frequency Deviation inarea 1 (f1)

Steady state error(ess)

FGPI -0.000067

FLC -0.00383

Conventional PI -0.00136

Controller

Frequency Deviation in area 1(f1)

Settlingtime(sec) (for

5% bandof the step

change)

MaximumOvershoot

(HZ)

FGPI 3.2 -0.013

FLC 6.2 -0.022

ConventionalPI

4.9 -0.024


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System performances for all controllers on settling times andovershoots for frequency deviation of area1.

System performances for all controllers with steady state error forfrequency deviation of area1.

6.CONCLUSION:

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

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 conclusion, the proposed fuzzy gain scheduling PI

controller is recommended to generate good quality and reliable electric

energy.

Appendix.

Two-area power system parameters:

Tg=0.08 B1=0.425

R1=2.4 B2=0.42

R2=2.4 T12=0.0Tp=20 Kp=

Tt=0.3 a12=1

References.


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[1]. Demiroren A, Yesil E. Automatic generation control with fuzzy logic

controllers in the power system including SMES units. Electr Power

Energy Syst 2004;26: 291305.

[2]. C am E, Kocaarslan I. Load frequency control in two area power

systems using fuzzy logic controller. Energy Conversion Manage 2005;

46:23343.

[3].Meliopoulos APS, Cokkinides GJ, Bakirtzis AG.Load-frequency

control service in a deregulated environment. Decision Support Syst 1999;

24:24350.

Document BySANTOSH BHARADWAJ REDDYEmail: [email protected]

Engineeringpapers.blogspot.comMore Papers and Presentationsavailable on above site
mailto:[email protected]:[email protected]

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Load Frequency Control Using Fuzzy Gain Scheduling