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1. DESIGN OF FUZZY SELF-TUNED LOAD FREQUENCY CONTROLLER FOR POWER SYSTEM
T.A.S.JAGADEESH Dr.R.VIJAYA SHANTI, Asst.Professor, Andhra University
Abstract: In the present paper, Self-Tuning fuzzy Controller is
designed for a multi-machine power system. Conventional PID
gains are obtained using Ant Colony System (ACS).Basing these
gains, Fuzzy Controller gains are designed for solving Load
Frequency Control (LFC) problem in a power system. The proposed
controller is tested on different loading conditions of a practical
thermal, hydel interconnected systems. The proposed controller
shows its efficiency when compared with conventional integral
controller & ACS-PID controller under different non-linearity’s like
Generation Rate Constraint (GRC).
Key words:
Load Frequency Control; Self-Tuning fuzzy Controller,
Generation Rate Constraints.
1. Introduction:
The problem of controlling the power output of a generator of a
closely knit electric area so as to maintain the scheduled frequency.
All the generators in such an area constitute a coherent group. So
that all the generators will speed up and slow down together
maintaining their relative power angles. Such an area is identified as
a control area. The boundaries of a control area will generally
coincide with that of an individual Electric Board Company [1].
These perturbations disturb the normal operation of the power
system. A very well known PI/PID controller are used after many
investigations and these controllers are used over half a centuries in
the industrial control and automation process. The PI/PID
controllers are simple for implementation [2, 3], design and low cost
for linear systems. Whenever an operating condition change, the
PID controller which is based on linearized model parameters will
also vary the PID controller gains which are designed at operating
conditions gives an optimal response at one operating condition
gives a suboptimal response at other operating condition. And
another drawback of PID controllers is human control of an
experienced operator is essential.So,in order to overcome these
drawbacks and to get some optimal response at all operating
conditions self tuning of PID controllers using Fuzzy logic
controllers come into action. Zeigler Nicolas method the most
widely used tuning method and is very simple but it is not
guaranteed one which will gives an effective response due to the
changes that may happen during the process running time of the
operating conditions. So, in recent years, Fuzzy logic controllers and
fuzzy sets tools are used for designing of fuzzy self tuning of PID
gains. This controller is used to update the PID controller gains pK
IK DK to meet closed loop system performance.
Several control techniques based on Fuzzy and Takagi-Sugeno
(TS) Fuzzy control system theory have been applied to LFC and
Power system as a tool to improve the system performance [8, 9]
The different loading conditions which we applied to self tuned
fuzzy logic controllers in the presence of system non-linearity GRC
&uncertain parameters are taken from the Egyptian power system
load frequency control during summer and winter of 2008[12] and
the gains of pK IK DK of the system can be self-tuned on-line
using output of the system and the simulated results are designed in
the MATLAB/SIMULINK are observed on comparison of proposed
fuzzy self tuned-PID & ACS-PID controller.
2. The Conventional Integral & PID System Modeling.
Assumptions are considered for Power system installed generation
capacity and peak load are estimated as 23400MW and 18970MW,
in 2008[12].The Approximated installed capacity of Non-reheat,
Reheat, and Hydro electric Power stations are given as.
1. Non-reheat generating units represent by gas turbine Power
stations represents approximately 25% of the installed capacity.
2. Reheat generating Units represent by the majority of the thermal
stations and combined cycle Power stations which are approximated
as 63% of the installed capacity.
3. Hydro electric Power stations are approximated as 15% of
installed capacity.
Fig (1) shows the block diagram of the Power system LFC model is
represented by SIMULINK is given below.
The Parameters of this model are divided into two sets. The first set
of parameters does not depend on system operating conditions. The
other set of parameters varies with the time according to the
operating condition. The data required to calculate the changing
parameters are concerned with the data of each generator including
status (ON or OFF),type of unit (Non-reheat,reheat,hydro),unit
rating (MW),unit Output (MW) for the operating condition under
study, inertia of the unit, and spinning reserve of the unit in
percentage of the unit rating.
The simulink model considers the generating rate constraints GRC
for different units. The applied values for GRC are 0.1P.UMW/min
and 0.2p.uMW/min. for the reheat turbines and non reheat turbines,
respectively. The GRC of hydro plants is neglected since its actual
value is much greater corresponding to the time durations of
practical disturbances [2].
The dynamic equations of this model can be written in the state-
space form as:
( ) ( ) ( )x t Ax t Bu t= +& (1)
Where
1 2 2 3( ) [ ( ) ( ) ( ) ( )]x t F t P t P t V P G t t= ∆ ∆ ∆ ∆ ∆ ∆
( )F t∆ = 1( )x t = the incremental frequency deviation Hz
1( )P t∆ = 2 ( )x t = incremental change in non-reheat plant in p.u
MW.
2()P t∆ = 3()x t = incremental changes reheat plant output in p.u
MW.
2V∆ = 4()x t = incremental opening in steam valve of reheat
plant output in p.u MW
3( )P t∆ = 5( )x t = incremental change in hydro plant output in p.u
MW
()Gt∆ = 6( )x t = incremental opening in hydro plant inlet vane in
p.u MW
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ISBN:378-26-138420-0255

2. The system model matrices A & B are displayed in the Appendix.
The three loading conditions of Power system are considered to
design ACS-based PI and PID gains.
3. Design of Fuzzy self-tuning of PID controller.
The Proposed design procedure includes two steps:
1. Finding the optimal gains of PID which Controls the system.
2. Design of fuzzy logic control (FLC), with self-tuning capabilities.
3. General Expressions for PID controller
The of a PI controller is given below:
( ) I
p D
K
K s K K s
s
= + + (2)
Where pK IK and DK are proportional, integral and differential
gains respectively.
( ) ( )*U s K s F= − ∆ (3)
Where ( )U s =output and, F∆ is the incremental frequency
deviation.
4. Design of a Controller
The below Fig(1) shows the Two input and one output variables of
conventional fuzzy logic system
X1
Y
Y
X2
Fig (1) Fuzzy Logic system
The Fig (2) shows below the Fuzzy logic controller with various
control schemes
Fig (2) A fuzzy controller with control system structure
The below Fig (3) shows Designed Fuzzy self tuned PID controller
The designs steps of fuzzy self tuning can be summarized as
follows:
1-Write the PID controller by the following equation:
( )
( )p I D
de t
U K K e t dt K
dt
= + +∫ (4)
This equation can also be written as:
2 2 2
( )
( )P I D
de t
U K K e t dt K
dt
= + ∫ +
(5)
Where:
2pK = PK * 1PK , 2IK = IK * 1IK , 2DK = DK * 1DK are the gain
outputs from fuzzy controller.
The input member ship functions of e and ∆e as shown in the fig (4,
5, 6) and are represented in the rule base are:
{ PB-Positive Big, PM-Positive Medium, PS-Positive Small, Z-
Zero, NB-Negative Big, NM-Negative Medium, NS-Negative
Small} and the outputs are represented in rule base as {B-Big, VB-
Very Big, MB-Medium Big, S-Small, MS-Medium Small};
The output membership functions are:
ZE-Zero Error, MS-Medium Small, S-Small, M-Medium, B-Big,
MB-Medium Big, VB-Very Big
Where:
e : error input normalizing gain.
∆e : Change in error input
normalizing gains.
The rule base for KP1 is shown in the table below.
∆e
e NB NM NS ZE PS PM PB
NB VB VB VB VB VB VB VB
NM MB MB MB MB B MB VB
NS B B B B MB B VB
ZE ZE ZE ZE MS S S S
PS B B B B MB B VB
PM MB MB MB MB B MB VB
PB VB VB VB VB VB VB VB
Fig (4) Rule base for determining 1pK
Fuzzy Logic System
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ISBN:378-26-138420-0256

3. ∆e
e
NB NM NS ZE PS PM PB
NB M M M M M M M
NM M M M M M M M
NS S S S S S S S
ZE MS MS MS ZE MS MS MS
PS S S S S S S S
PM M M M M M M M
PB M M M M M M M
Fig (5) Fuzzy rule base for 1IK
∆e
e
NB NM NS ZE PS
PM
PB
NB ZE MS S M MB B VB
NM MS S M B B B VB
NS S M B MB VB VB VB
ZE M B MB MB VB VB VB
PS MB MB VB VB VB VB VB
PM B MB VB VB VB VB VB
PB VB VB VB VB VB VB VB
Fig(6) Fuzzy rule base for determining 1DK
3) The universe of discourse is normalized, the physical values is of
the normalizing gains is obtained by dividing the boundary values of
discourse of the input member ship functions of maximum of
original values of e and ∆e.
4) Defuzzification is a mathematical process used to convert a fuzzy
sets to real number and is a necessary step because fuzzy sets
generated by fuzzy inference in rules must be somehow
mathematically combined to come up with one single number as
output of a fuzzy controller output. Defuzzification is applied as a
final step to convert the fuzzy output to crisp value .Defuzzification
is a process which converts the range of values of output variables
into corresponding universe of discourse and it yields a non fuzzy
control action from an inferred fuzzy control action. One of the
Defuzzification methods is centroid method it is also called as centre
of gravity or centre of area defuzzification .The widely used COA
strategy the centre of gravity of the possibility distribution of a
control action.
1
1
( )
( )
r
i i
i
r
i
i
x x
u
x
µ
µ
=
=
=
∑
∑
Where ix a running point in the universe of discourse, and ( )ixµ
is its membership value in the member ship function
Results and Discussions:
The results show that system is responding effectively for
variation of uncertain parameters in the presence of nonlinearity
Generation Rate Constraints. The self tuned fuzzy controller meets
the required results of uncertain parameters over ACS –PID &
conventional Integral controller.
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ISBN:378-26-138420-0257

4. The following conditions are:
Case 1: Small disturbance in the system dP∆ =1%:-
In this a Small disturbance of 1% is applied to the power system
and can observed that the damping of the system frequency is
improved and simulation results shows that proposed FST-PID
controller has less overshoot & Quick settling time when compared
with Integral Controller and ACS-PID controller as shown in the
fig(7)and fig(8) below.
Fig(7) ∆F
∆U
Fig (8) System dynamic response for case (1)
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ISBN:378-26-138420-0258

5. Case 2: Disturbance Variations:
Fig (8) and fig(9) , illustrates the dynamic response of frequency
deviation F∆ and control input U∆ when a step of dP∆ = 1%
is applied,
during 5 ≤ t ≤ 30 seconds. It is clear that the oscillations are quickly
damped with the proposed FST-PID as compared to ACS-PID.
Besides,
the FST-PID settles faster whereas ACS-PID shows the opposite.
Fig (9) ∆F
∆U
Fig (10) System dynamic response for case (2)
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ISBN:378-26-138420-0259

6. Case 3: Tracking Disturbance Variations
Fig (9) and (10) show the dynamic response of F∆ and U∆
following a variation of as seen in Fig (12) and Fig (13). This
variation covers both tracking represented by the ramp and
regulation which represented by a step change. It is obvious from
Fig (12) and (13) that the system driven by FST-PID controller,
shows better performance and clearly improved than ACS- PID fast
response with relatively small overshoots).
a) Fig(12) ∆F
∆U
Fig(13) shows the system dynamic response
Operating conditions:
Condition1 Condition2 Condition3
H 4.9598 6.0168 5.8552
Pn1 0.2730 0.3112 0.2433
Pn2 0.7007 0.5200
0.6179
Pn3 0.1364 0.1798 0.1389
Where H: Equivalent Inertia constant of the system.
&
Pn1, Pn2, and Pn3: Nominal rated regulating power output
for non-reheat, reheat and
Hydro Plants (p.u MW)
List of symbols:
1) R1, R2 - 2.5(Hz/p.u MW)
2) R3 - (Hz/p.u MW)
3) D - 0.029(p.u MW/hz)
4) T1 & T2 –0.4Sec
5) T3 - 90sec
6) Tb -6sec
7) Td -5sec
8) wT -1.0sec
9) M - 0.5
10) LT - 2.5 sec/Hz
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ISBN:378-26-138420-0260

7. Conclusion:
In this paper Self tuned FST-PID controller is designed and its
performances are compared with conventional Integral controller
&ACS-PID controller under different loading conditions. Simulation
results prove that the proposed controller shows the robust
performance with different non-linearity like GRC under dynamic
operating conditions. The simulation results shows that FST-PID
controllers is powerful in reducing the frequency deviations under a
variety of load perturbations of LFC for proposed power system.
The dynamic equations are:
A=
1
1 1 1
2
2 2 2
2
2 2 2
3
3
1 1 1
0 0
2 2 2 2
1
0 0 0 0
1 1
0 0 0
1
0 0 0 0
2 2 2 2 2 2
2 1 0
2 2 2 2
1
1 0
2 2 2 2
h h
d d d d
w w
d d d d
D
H H H H
Pn
R T T
mPn m
R T T T T
Pn
R T T
T D aT aT aT
a
H H H H T T T
T D aT aT aT
a
H H H H T
 
− 
 
− − 
 
 
  − −
−  
  
 − −


     − − − +    
      

− − − −  −    









a=
3
3 3
Pn
R T
B=
3 31 2 2
1 2 2 3 3
2*
0
Pn PnPn mPn Pn
T T T T T
 −− − −
 
 
Fig (14) The Simulink representation of a power system Load Frequency model
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ISBN:378-26-138420-0261

8. References:
1) Modern Power system analysis by D.P.Kotari, I.J.Nagarath
‘Third edition’.
2) Design of a Fuzzy Self-Tuning Optimal PID Load
Frequency Controller for the Egyptian Power System.
3) C. E. Fosha, O. I. Elgerd, “The megawatt-frequency control
problem: a new approach via optimal control theory”, IEEE
Trans. PAS, vol. 89, pp. 563–567, April 1970.
4) A. Khodabakhshian, N. Golbon, “Unified PID design for
load frequency control”, In Proc. 2004 IEEE Int. Conf. on
Control Applications (CCA), Taipei, Taiwan, pp. 1627–
1632, September 2004.
5) G.J. Silva, A. Datta, et al., “New results on the synthesis of
PID controllers”, IEEE, Transactions on Automatic Control,
47(2), pp. 241-252, 2002.
6) Keven M. Passino and Stephen Yurkovich, "Fuzzy Control",
Addison Wesley longnan, Inc., 1998.
7) G.R. Chen and T.T. Pham, "Introduction to fuzzy sets, fuzzy
logic, fuzzy control system", RC. Press,Boac Raton, FL,
USA, 2000.
8) Michall Petrov, Ivan Ganchev and Ivan dragotinov, “Design
Aspects of Fuzzy PID Control”, International conference on
soft computing, Mendel “99”, Brno, Czech Republic, 9-12
June, pp. 277-282, 1999.
9) H. A. Shayanfar and H. Shayeghi A. Jalili, " Takagi-Sugeno
Fuzzy Parallel Distribution Compensation Based Three-Area
LFC Design", International Journal on Technical and
Physical Problems of Engineering, Issue 8, Volume 3,
Number 3, pp. 55-64, Sept 20.
10) R. Dhanalakshmi and S. Palaniswami, "Application of Self-
Tuning Fuzzy Logic PI Controller in Load Frequency
Control of Wind-Micro Hydro-Diesel Hybrid Power
System", European Journal of Scientific Research ISSN
1450-216X Vol. 79 No. 3, pp. 317-327, 2012.
11) Zareiegovar G., Sakhavati A. , Nabaei V. and Gharehpetian
G. B., " A New Approach for Tuning PID Controller
Parameters of Load Frequency Control Considering System
Uncertainties”, 9th International Conference on Digital
Object, pp. 333 – 336, 2008.
12) Egyptian Electricity Holding Company, 2007/2008 Annual
Report.
http://www.egelec.com/annual%20report/2007.html.
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ISBN:378-26-138420-0262