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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]