Performance evaluation-of-hybrid-intelligent-controllers-in-load-frequency-control-of-multi-area-interconnected-power-systems

Performance Evaluation of Hybrid Intelligent
Controllers in Load Frequency Control of Multi
Area Interconnected Power Systems
Surya Prakash and Sunil Kumar Sinha
Abstract—This paper deals with the application of artificial
neural network (ANN) and fuzzy based Adaptive Neuro Fuzzy
Inference System(ANFIS) approach to Load Frequency Control
(LFC) of multi unequal area hydro-thermal interconnected power
system. The proposed ANFIS controller combines the advantages of
fuzzy controller as well as quick response and adaptability nature of
ANN. Area-1 and area-2 consists of thermal reheat power plant
whereas area-3 and area-4 consists of hydro power plant with electric
governor. Performance evaluation is carried out by using intelligent
controller like ANFIS, ANN and Fuzzy controllers and conventional
PI and PID control approaches. To enhance the performance of
intelligent and conventional controller sliding surface is included.
The performances of the controllers are simulated using
MATLAB/SIMULINK package. A comparison of ANFIS, ANN,
Fuzzy, PI and PID based approaches shows the superiority of
proposed ANFIS over ANN & fuzzy, PI and PID controller for 1%
step load variation.
Keywords—Load Frequency Control (LFC), ANFIS, ANN &
Fuzzy, PI, PID Controllers, Area Control Error (ACE), Tie-line,
MATLAB / SIMULINK.
I. INTRODUCTION
OAD frequency control is part of Automatic Generation
Control (AGC) which is defined as the regulation of
power out put of controllable generator within prescribed limit
in response to change in system frequency or tie-line loading
or the relation of these two each other. Many developments
have taken place in the structure of power system since its
inception. All over the world, most of the power utilities have
been operating in interconnected fashion due to numerous
economical, technical and environmental considerations. The
power transmission network plays an important role in
transporting electrical power in bulk from one power pool to
other and to distantly located load centers. Main objective of
Automatic
Generation Control (AGC) is to balance the total system
generation against system load losses so that the desired
frequency and power interchange with neighboring system is
Surya Prakash is with Department of Electrical & Electronics Engineering,
Sam Higginbottom Institute of Agriculture, Technology & Sciences-Deemed
University, Allahabad, India. (Email: sprakashgiri0571@yahoo.com).
S K Sinha is with Department of Electrical Engineering, Kamala Nehru
Institute of Technology, Sultanpur-UP, India. (Email:
sinhask98@engineers.com).
maintained. Any mismatch between generation and demand
causes the system frequency to deviate from the nominal
value. This high frequency deviation may lead to system
breakdown. AGC comprises a load frequency control (LFC)
loop and an automatic voltage regulator (AVR) loop
interconnected power systems regulate power flows and
frequency by means of an AGC. LFC system provides
generator load control via frequency zero steady-state errors
of frequency deviations and optimal transient behavior are
objectives of the LFC in a multi-area interconnected power
system [1], [2]-[5].
Literature survey shows that most of earlier work in the
area of LFC pertains to interconnected thermal system and
relatively lesser attention has been devoted to the LFC of
multi area interconnected hydro-thermal system [7]. The PI &
PID controllers are very simple for implementation and gives
better dynamic response, but their performances deteriorate
when the complexity in the system increases due to
disturbances like load variation boiler dynamics [6], [7].
Therefore, there is need of a controller which can overcome
this problem. The Artificial Intelligent controllers like Fuzzy
and Neural control approaches are more suitable in this
respect. Fuzzy system has been applied to the load frequency
control problems with rather promising results. [8], [9], [15],
[16], [19], [20], [25]. The salient feature of these techniques is
that they provide a model- free description of control systems
and do not require model identification when selecting the
specific number of membership function [9], so this has some
limitation to over come this Artificial Neural Network (ANN)
and ANFIS controllers are introduced, those have advance
adaptive control configuration [10], [20], [21]. LFC or AGC is
one of the most important issues in electric power system
design and operation for supplying sufficient and reliable
electric power with good quality. The main aim of LFC for
power system are to ensure zero steady state error for
frequency deviations, to minimize unscheduled tie line power
flows between neighboring control areas and to maintain
acceptable overshoot and settling time on the frequency and
tie line power deviation [22], [23], [24].
L
World Academy of Science, Engineering and Technology
Vol:7 2013-05-26
637 International Science Index Vol:7, No:5, 2013 waset.org/Publication/12180

Vol:7 2013-05-26
Fig. 1 MATLAB Model of four area hydro-thermal reheat power system
The main objectives of the present paper are the
following:
1. To consider four area hydrothermal system under
perturbation in a single area and simultaneously in all
areas, and then obtain system dynamic responses with
Fuzzy, ANN and ANFIS, PI and PID controllers.
2. To present a systematic and comprehensive approach for
designing ANN, Fuzzy and ANFIS based controller.
3. To compare the results of all five controllers to
investigate the superiority of controller.
4. To compare the ANFIS controller results with already
published result of Swati[26], Sudha[27] and Parmar[28]
and, then analyze the dynamic performance obtained with
the above control strategy, i.e., ANFIS based controller.
II. MULTI AREA POWER SYSTEM INVESTIGATED
The four area power system connected by tie-line is shown
in Fig. 1.
A. Modeling of the Tie-Line
Considering area 1 has surplus power and transfers to area
2.
P12 = Power transferred from area 1 to 2 through tie line.
Then power transfer equation through tie-line is given by
V . V
P 1 2
= δ δ (1)
X . Sin( 1 - 2)
12
12
where
1 δ and 2 δ = Power angles of end voltages V1 and V2
of equivalent machine of the two areas respectively.
X12 = reactance of tie line.
The order of the subscripts indicates that the tie line power
is define positive in direction 1 to 2.
For small deviation in the angles and the tie line power
changes with the amount i.e. small deviation in 1 δ and 2 δ
changes by Δδ1 andΔδ 2,
Power P12 changes to P12 + Δ P12
Therefore, Power transferred from Area 1 to Area 2 as
given in [11] is
T o P s f s f s
π
( ) 2 ( ) ( )
( ) 12 1 2
Δ = Δ −Δ (2)
s
T0 = Torque produced
In this paper, the performance evaluation based on ANN,
Fuzzy and ANFIS control technique for four areas
interconnected thermal-hydro power plant is proposed. The
sliding concept arises due to variable structure concept. The
objective of VSC has been greatly extended from stabilization
to other control functions. The most distinguished feature of
VSC is its ability to result in very robust control systems and
external disturbances [12], [13].
B. Objective of Control Areas
The main objective of the control areas are as follows:

1. Each control area as for as possible should supply its own
load demand and power transfer through tie line should
be on mutual agreement.
2. Each control areas should controllable to the frequency
control. [11]
In an isolated control area case the incremental power
(ΔPG − ΔPD) was accounted for by the rate of increase of
stored kinetic energy and increase in area load caused by
increase in frequency. The state variable for each of areas are
ΔPi (i = 1,...., 4) and state space equation related to the
variables are different for each areas.
ΔP1(k) = ΔP12(k) + a41ΔP41(k) (3)
ΔP2(k) = ΔP23(k) + a12ΔP12(k) (4)
ΔP3(k) = ΔP34(k) + a23ΔP23(k) (5)
ΔP4(k) = ΔP41(k) + a34ΔP34(k) (6)
Tie-line bias control is used to eliminate steady state error
in frequency in tie-line power flow. This states that the each
control area must contribute their share to frequency control in
addition for taking care of their own net interchange.
12180
Publication/org/Let ACE1 = area control error of area 1
waset.ACE2 = Area control error of area 2
ACE3 = Area control error of area 3
2013 ACE4 = Area control error of area 4
5, In this control, ACE1, ACE2 and ACE3 are made linear
No:combination of frequency and tie line power error [11].
7, Vol:ACE1 = Δ P + b Δ f (7)
12 1 1 Index ACE2 = Δ P + b Δ f (8)
23 2 2 Science ACE3 = Δ P + b Δ f (9)
34 3 3 ACE4 = Δ P + b Δ f (10)
International 41 4 4 Where the constant b1, b2, b3 & b4 are called area frequency
bias of area 1, area 2, area 3 and area 4 respectively.
Now Δ PR , Δ PR , Δ PR and Δ PR are mode integral
1 2 3 4 of ACE1, ACE2, ACE3 and ACE4 respectively.
Control methodology used (FLC & ANN) is mentioned in
the next preceding sections.
III. CONTROL METHODOLOGY
A. Automatic Controller
The task of load frequency controller is to generate a
control signal Ui that maintains system frequency and tie-line
interchange power at predetermined values. The proportional
and integral (PI) control scheme is shown in Fig. 2 [30].
639 Vol:7 2013-05-26
Fig. 2 Conventional PI Controller Installed on ith Area
T
i
T
= − ∫ = − ∫ Δ + Δ (11)
U K ( ACE ) dt K ( P B f )
dt i i i tiei i i
0 0
Taking the derivative of equation (11) yields;
i i ( i ) i ( tie i i i ) U = −K ACE = −K ΔP + B Δf (12)
B. Fuzzy Logic Controller
Fuzzy logic is a thinking process or problem-solving
control methodology incorporated in control system
engineering, to control systems when inputs are either
imprecise or the mathematical models are not present at all.
Fuzzy logic can process a reasonable number of inputs but the
system complexity increases with the increase in the number
of inputs and outputs, therefore distributed processors would
probably be easier to implement. Fuzzification is process of
making a crisp quantity into the fuzzy (Ross, 1995). They
carry considerable uncertainty. If the form of uncertainty
happens to arise because of imprecision, ambiguity, or
vagueness, then the variable is probably fuzzy and can be
represented by a membership function.
Defuzzification is the conversion of a fuzzy quantity to a
crisp quantity, just as fuzzification is the conversion of a
precise quantity to a fuzzy quantity. There are many methods
of defuzzification, out of which smallest of maximum method
is applied in making fuzzy inference system. The Fuzzy logic
control consists of three main stages, namely the fuzzification
interface, the inference rules engine and the defuzzification
interface [15], [16]. For Load Frequency Control the process
operator is assumed to respond to variables error (e) and
change of error (ce). The fuzzy logic controller with error and
change in error is shown in Fig. 3.

Fig. 3 Model of Fuzzy Logic Controller
The variable error is equal to the real power system
frequency deviation ( Δ f ). The frequency deviation Δ f , is
the difference between the nominal or scheduled power
system frequency (fN) and the real power system frequency (f).
Taking the scaling gains into account, the global function of
the FLC output signal can be written as.
Δ Pc = F [ n c e(k), n ce ce(k)]
(13)
where ne and nce are the error and the change in error scaling
gains, respectively, and F is a fuzzy nonlinear function. FLC
is dependant to its inputs scaling gains (Ha, 1998). A label set
corresponding to linguistic variables of the input control
signals, e(k) and ce(k), with a sampling time of 0.01 sec is
given Attempt has been made to examine with Seven number
of triangular membership function (MFs) namely Negative
Big(NB), Negative Medium(NM), Negative Small (NS),
Zero(ZO), Positive Small(PS), Positive Medium (PM) and
Positive Big(PB) are used. The range on input (error in
frequency deviation and change in frequency deviation) i.e
universe of discourse is -0.25 to 0.25 and -0.01 to 0.01 The
numbers of rules are 49.
TABLE I
FUZZY INFERENCE RULE FOR FUZZY LOGIC CONTROLLER
Input e(k)
ce(k)
NB NM NS ZO PS PM PB
NB PB PB PB PB PM PM PS
NM PB PM PM PM PS PS PS
NS PM PM PS PS PS PS ZO
ZO NS NS NS ZO PS PS PS
PS ZO NS NS NS NS NM NM
PM NS NS NM NM NM NB NB
PB NS NM NB NB NB NB NB
C. Artificial Neural Network (ANN) Controller
ANN is information processing system, in this system the
element called as neurons process the information. The signals
are transmitted by means of connecting links. The links
process an associated weight, which is multiplied along with
the incoming signal (net input) for any typical neural net. The
output signal is obtained by applying activations to the net
input. The field of neural networks covers a very broad area
[17], [18].
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Fig. 4 Neural Network as Function Approximator
Neural network architecture the multilayer perceptron as
unknown function are shown in Fig 5, which is to be
approximated. Parameters of the network are adjusted so that
it produces the same response as the unknown function, if the
same input is applied to both systems. The unknown function
could also represent the inverse of a system being controlled;
in this case the neural network can be used to implement the
controller [17].
D. NARMA-L2 Control
The ANN controller architecture employed here is a Non
linear Auto Regressive Model reference Adoptive Controller.
This controller requires the least computation of the three
architectures. This controller is simply a rearrangement of the
neural network plant model, which is trained offline, in batch
form. It consists of reference, plant out put and control signal.
The controller is adaptively trained to force the plant output to
track a reference model output. The model network is used to
predict the effect of controller changes on plant output, which
allows the updating of controller parameters. In the study, the
frequency deviations, tie-line power deviation and load
perturbation of the area are chosen as the neural network
controller inputs [17]. The outputs of the neural network are
the control signals, which are applied to the governors in the
area. The data required for the ANN controller training is
obtained from the designing the Reference Model Neural
Network and applying to the power system with step response
load disturbance. After a series of trial and error and
modifications, the ANN architecture provides the best
performance. It is a three-layer perceptron with five inputs, 13
neurons in the hidden layer, and one output in the ANN
controller. Also, in the ANN plant model, it is a three-layer
perceptron with four inputs, 10 neurons in the hidden layer,
and one output. The activation function of the networks
neurons is trainlm function.300 training sample has been
taken to train 300 no of epochs. The proposed network has
been trained by using the learning performance. Learning
algorithms causes the adjustment of the weights so that the
controlled system gives the desired response.
E. Hybrid Neuro Fuzzy (HNF) Controller
In recent years, Hybrid Neuro-Fuzzy (HNF) approach has
considerable attention for their useful applications in the fields
like control, pattern recognition, image processing, etc [20],
[26]. In all these applications there are different neuro-fuzzy
applications proposed for different purposes and fields. HNF

results are obtained from fusion of neural network and fuzzy
logic.
1. Neuro Fuzzy Modeling
The general algorithm for a fuzzy system designer can be
synthesized as Fuzzification, Fuzzy Inference and
Defuzzification [29]. From the beginning, a fuzzy-style
inference must be accepted and the most popular are
Mamdani-style inference and Sugeno-style Inference [14],
[19], [20].
Fig. 5 Architecture of a Two-Input Sugeno Fuzzy Model with Nine
Rules
The basic steps followed for designing the ANFIS
controller in MATLAB/Simulink is outlined:
1. Draw the Simulink model with fuzzy controller and
simulate it with the given rule base.
2. The first step for designing the ANFIS controller is
collecting the training data while simulating the model
with fuzzy controller.
3. The two inputs, i.e., ACE and d(ACE)/dt and the output
signal gives the training data.
4. Use anfisedit to create the ANFIS .fis file.
5. Load the training data collected in Step 2 and generate the
FIS with gbell MF’s.
6. Train the collected data with generated FIS up to a
particular no. of Epochs.
7. Save the FIS. This FIS file is the neuro-fuzzy enhanced
ANFIS file[29]
2. Training and Checking: ANFIS
The number of epoch is determined according to the above
parameters and to the excepted error measure fixed by the
user. The training and checking data are given below:
Number of nodes: 53, Number of linear parameters: 16,
Number of nonlinear parameters: 24, Total number of epoch:
80, Number of training data pairs: 51, Number of checking
data pairs: 51, Number of fuzzy rules: 16.
The range of error is as below:
1 0.000527979 0.00470353
2 0.000611368 0.00492588
The gbell MFs is taken. The frequency deviationΔf , is the
difference between the nominal or scheduled power system
frequency (fN) and the real power system frequency (f).
3. ANFIS (Adaptive Neuro-Fuzzy Inference System)
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This is more complex than Fuzzy inference System (FIS),
but users have some limitations: only zero-order or first-order
Sueno fuzzy models, AND Method: Prod, OR Method: max,
Imlication Method: prod, Aggregation Method: max,
Defuzzification Method: wtaver(weighted average). On the
other hand, users can provide to ANFIS their own number of
MFs(num MFs) both for input and outputs of the fuzzy
controller, the number of training and checking data sets
(numPts), the MF’s type (mfType), the optimization criterion
for reducing the error measure(usually defined by the number
of the squired difference between actual and linearized N
curve) [20], [26].
The great advantage of Neuro-fuzzy design method
comparing with fuzzy design method consists in the small
number of in put and output MFs (usually 2…4), which
implies the same maximum number of rules. Thus, the rule
base and the occupied memory became very small.
IV. SIMULATION AND RESULTS
In this presented work, different models of four area hydro-thermal
reheat interconnected power system have been
developed by using fuzzy logic, ANN and ANFIS and PI, PID
controllers to illustrate the performance of load frequency
control using MATLAB/SIMULINK package. The parameters
used for simulation are given in appendix [12]. Frequency
deviation plots for thermal and hydro cases are obtained
separately for 1% step load change in system frequency and
tie-line power as shown in Fig. 6-26 respectively.
Dynamic responses of four areas power system using PI
controller is are given below:
Time
Change in frequency
Fig. 6 Change in frequency (thermal plant) – with PI controller (Δf)
Time
Change in
Fig. 7 Change in frequency (Hydro plant)- with PI controller(Δf)

Time (sec)
Fig. 8 Change in Tie-line power(thermal plant) with PI control
Fig. 9 Change in Tie-line power (hypothermal plant) with PI control
Fig. 10 Change in Tie-line power (thermal-hydro plant) with PI
control
The developed model with PI controller has been simulated
and responses obtained above in Fig. 6-10 reveals that PI
controller reduces the steady state error in frequency deviation
and also maximum peak over shoot. The settling time is
limited to 64 sec. in case of frequency deviation of thermal
plant and 70 sec. for hydro plant. The deviation in the tie-line
power is also limited to 70 sec.
The dynamic responses of four areas power system using
PID controller is are given below:
Time (sec)
Fig. 11 Change in frequency (thermal plant) – with PID controller
(Δf)
Time (sec)
Fig. 12 Change in frequency (hydro plant)- with PID controller (Δf)
Time (sec)
Fig. 13 Change in Tie-line power (thermal plant) with PID control (Δ
P tie)
Fig. 14 Change in Tie-line power (hydro plant) with PID control
(Δ P tie)
The developed model with PID controller has been
simulated and responses obtained above in Fig. 11-14 reveals
that PID controller reduces the steady state error in frequency
deviation and also maximum peak over shoot. The settling
time is limited to 60 sec. in case of frequency deviation of
Time (sec)
Change in Tie-line
Change in frequency
Time (sec)
Time (sec)
Change in Tie-line
Change in Tie-line
Change in frequency
Change in Tie-line Power Change in Tie-line
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thermal plant and 60 sec. for hydro plant. The deviation in the
tie-line power is also limited to 60 sec. The Number of
oscillations are also reduced. Dynamic responses of four areas
power system using Fuzzy controller is are given below:
Time (sec)
Fig. 15 Change in frequency (thermal plant) – with Fuzzy
controller
Fig. 16 Change in frequency (hydro plant) – with Fuzzy controller
Fig.17 Change in Tie-line power (thermal plant) with Fuzzy
Controller
Time (sec)
Fig.18 Change in Tie-line power (hydro plant) with Fuzzy Controller
The developed model with Fuzzy controller has been
simulated and responses obtained above in Fig. 15-18 reveal
that fuzzy controller further reduces the steady state error in
frequency deviation and also maximum peak over shoot. The
settling time is limited to 45 sec. in case of frequency
deviation of thermal plant and 48 sec. for hydro plant. The
deviation in the tie-line power is also limited to 45 sec. The
settling time and peak over shoot is much lesser than the PI
and PID controller. Dynamic responses of four areas power
system using ANN controller is are given below:
Time (sec)
Fig. 19 Change in frequency (Thermal plant) with ANN controller
Time
Change in frequency
Fig. 20 Change in frequency (hydro plant) with ANN controller
Time (sec)
Time (sec)
Change in frequency
Change in Tie-line
Change in Tie-line
Change in frequency
Change in frequency
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Fig. 21 Change in Tie-line power (hydro thermal plant) with ANN
Fig. 22 Change in Tie-line power (thermal hydro plant) with ANN
The developed model with Artificial Neural Network
(ANN) controller has been simulated and responses obtained
above in figure 19-22 reveal that ANN controller further
reduces the steady state error in frequency deviation and also
maximum peak over shoot. The settling time is limited to 40
sec. in case of frequency deviation of thermal plant and hydro
plant as well. The deviation in the tie-line power is also
limited to 30 sec. The settling time and peak over shoot is
much lesser than the PI, PID and Fuzzy controllers.
Dynamic responses of four areas power system using
ANFIS controller is are given below:
Fig. 23 Change in frequency (Thermal plant) with ANFIS controller
Time (sec)
Fig. 24 Change in frequency (Hydro plant) with ANFIS controller
Fig.25 Change in Tie-line power (thermal hydro plant) with
ANFIS
Fig. 26 Change in Tie-line power (thermal hydro plant) with
ANFIS
The developed model with ANFIS controller has been
simulated and responses obtained above in Fig. 23-26 reveal
that ANFIS controller further reduces the steady state error in
frequency deviation and also maximum peak over shoot. The
settling time is limited to 18 sec. in case of frequency
deviation of thermal plant and 17 sec. for hydro plant. The
deviation in the tie-line power is also limited to 15 sec. for
thermal and 27 sec. for hydro plant. The settling time and
peak over shoot is much lesser than the PI, PID, Fuzzy and
ANN controllers.
The above simulation results shows that the proposed
ANFIS based controllers tracks the load changes and achieve
good robust performance than conventional PI, PID and other
intelligent control(Fuzzy & ANN) approach with 1% load
variation in power system. Conventional PI, PID and
Intelligent (Fuzzy and Neuro-Fuzzy) control approach with
inclusion of slider gain provides better dynamic performance
and reduces the steady state error and oscillation of the
frequency deviation and the tie line power flow in each area in
Change in Tie-line Power
Time
Time (sec)
Change in Tie-line Change in
Time (sec)
Time (sec)
Change in Tie-line Power
Change in Tie-line
Time (sec)
Change in
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hydro-thermal combination of four area interconnected power
system. Settling time and maximum peak overshoot in
transient condition for both change in system frequency and
change in tie-line power are given in table II & III,
respectively.
TABLE II
COMPARATIVE STUDY OF SETTLING TIME
Control
lers
Area
1
(sec)
Area
2
(sec)
Area
3
(sec)
Area
4
(sec)
Therma
l-thermal
(sec)
Hydro-thermal
(sec)
PI 64 64 70 65 65 70
PID 60 60 60 50 62 60
Fuzzy 45 45 45 48 40 45
ANN 40 40 40 40 30 35
ANFIS 18 18 17 17 15 27
TABLE III
COMPARATIVE STUDY OF PEAK OVERSHOOTS
Control
lers
Δf
Area 1
(pu)
Δf
Area 2
(pu)
Δf
Area 3
(pu)
Δf
Area 4
(pu)
ΔP tie
Thermal-thermal
(pu)
ΔP tie
Hydro-thermal
(pu)
PI -0.055 -0.055 -0.067 0.066 -0.0145 -0.05
PID -0.049 -0.049 -0.057 -0.062 0.005 -0.0042
Fuzzy -0.059 -0.06 -0.068 -0.065 0.005 -0.012
ANN -0.038 -0.038 -0.055 -0.051 -0.006 -0.013
ANFIS -0.061 -0.061 -0.054 -0.054 -0.052 -0.045
By varying 1% step load, the above responses reveals that
the steady state error in dynamic change in frequency and tie-line
power are reduced to zero and settling time and peak
overshoot is plotted and tabulated in Table II and Table III.
ANFIS controller has minimum settling time and peak
overshoot in frequency response than other four proposed
controller.
V. CONCLUSIONS
In this paper, automatic generation control of four area
interconnected hydro thermal power system is investigated. In
order to demonstrate the effectiveness of proposed method,
the control strategy based on Neuro-fuzzy, ANN and
conventional PI & PID technique is applied. The performance
of proposed controller is evaluated through the simulation.
The results are tabulated in Table II and III respectively.
Analysis reveals that the proposed technique gives good
results and uses of this method reduce the peak deviation of
frequencies, tie-line power, time error and inadvertent
interchange. It can be concluded that ANFIS controller with
sliding gain provides better settling performance than Fuzzy,
ANN and conventional PI &PID one. Therefore, the
intelligent control approach using Neuro-Fuzzy concept is
more accurate and faster than the fuzzy, ANN, PI and PID
control scheme even for complex dynamical system.
APPENDIX
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Parameters are as follows:
f = 50 Hz, R1 =R2= R3= R4 =2.4 Hz/ per unit MW, Tgi= 0.08
sec, Tpi=20 sec; P tie, max = 200 MW ; Tr = 10 sec ; Kr = 0.5, H1
=H2 =H3= H4 =5 sec ; Pri=2000MW, Tti = 0.3sec ;
Kp1=Kp2=Kp3 = Kp4 = 120 Hz.p.u/MW ;Kd =4.0;
Ki = 5.0 ; Tw = 1.0 sec; Di =8.33 * 10-3 p.u MW/Hz.;
B1=B2=B3=B4=0.425 p.u. MW/hz; ai=0.545;
a=2*pi*T12=2*pi*T23=2*pi*T34=2*pi*T41=0.545,
delPdi= 0.01
Nomenclature
i: Subscript referring to area (i=1,2,3,4)
f : Nominal system frequency
Hi: Inertia constant; Δ P Di : Incremental load change
ΔPgi : Incremental generation change
= P Di
fi
Di
Δ
Δ
; Tr : Reheat time constant
Tg: Steam governor time constant; Kr : Reheat constant,
Tt : Steam turbine time constant; Bi: Frequency bias
constant
Ri : Governor speed regulation parameter
Tpi : 2Hi / f * Di, Kpi: 1/ Di
Kt: Feedback gain of FLC
Tw : Water starting time, ACE : Area control error
P: Power, E : Generated voltage
V: Terminal voltage, δ Angle of the Voltage V
Δδ : Change in angle, ΔP: Change in power
Δf : Change in supply frequency;
ΔPc: Speed changer position
R: Speed regulation of the governor
KH : Gain of speed governor
TH : Time constant of speed governor
Kp : 1/B= Power system gain
Tp: 2H / B f0 = Power system time constant
ACKNOWLEDGMENT
This work is supported by the Department of Electrical
Engineering, Sam Higginbottom Institute of Agriculture,
Technology and Sciences-Deemed University, Allahabad-
India.
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Surya Prakash belongs to Allahabad-India, Received
his Bachelor of Engineering degree from The I E
(India) in 2003, He obtained his M.Tech. in Electrical
Engg.(Power System) from KNIT, Sultanpur-India in
2009. Presently he is Pursuing Ph. D in Electrical
Engg.(Power System)from, SHIATS-DU(Formerly
AAI-DU, Allahabad- India). His field of interest
includes power system operation & control, Artificial
Intelligent Control.
Dr. S. K. Sinha belongs to Varanasi and his date of
birth is 17th Apr 1962. He received the B.Sc. Engg
degree in Electrical from R.I.T. Jamshedpur, Jharkhand,
India, in 1984, the M. Tech. degree in Electrical
Engineering from Institute of Technology, B.H.U,
Varanasi, India in 1987, and the Ph.D. degree from IIT,
Roorkee, India, in 1997. Currently he is working as
Professor in the Department of Electrical Engineering,
Kamla Nehru Institute of Technology, Sultanpur, India.
His fields of interest includes estimation, fuzzy control,
robotics, and AI applications’-

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