Research Journal of Applied Sciences, Engineering and Technology 4(15): 2375-2381, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: February 02, 2012
Accepted: March 06, 2012
Published: August 01, 2012
Steam-Hydraulic Turbines Load Frequency Controller Based on Fuzzy
Logic Control
1,4
Ali M. Yousef, 2Jabril A. Khamaj and 3,4Ahmad Said Oshaba
Electrical Engineering Department Faculty of Engineering, Assiut University, Egypt, 71516,
2
Mechanical Engineering Department Faculty of Engineering Jazan University, KSA
3
Power Electronics and Energy Conversion Department, Electronics Research Institute, Egypt
4
Electrical Engineering Department Faculty of Engineering Jazan University, KSA
1
Abstract: This study investigates an application of the fuzzy logic technique for designing the load-frequency
control system to damp the frequency and tie line power oscillations due to different load disturbances under
the governor deadzones and GRC non-linearity. Integral controller are designed and compared with the
proposed fuzzy logic controller. To validate the effectiveness of the proposed controller, two-area load
frequency power system is simulated over a wide range of operating conditions and system parameter changes.
Further, comparative studies between the conventional PID control and proposed efficient fuzzy logic load
frequency control are included on the simulation results. Programs Matlab software are developed for
simulation. The digital results prove the power of the present fuzzy load-frequency controller over the
conventional. PID controller in terms of fast response with less overshoot and small settling time.
Keywords: Fuzzy logic controller, PID controller, steam-hydraulic turbines
INTRODUCTION
Power systems have complex and multi-variable
structures. Also they consist of many different controls
blocks. Most of them are non linear. Power systems are
divided into control areas connected by tie lines. From the
experiments on the power systems, it can be seen that
each area need to its system frequency and tie line power
flow to be controlled. Frequency control is accomplished
by two different control actions in interconnected two area
power system: primary speed control and supplementary
or secondary speed control actions as in Ertugrul and
Ilhan (2005), El-Sherbiny et al. (2001) and El-Sherbiny
et al. (2002). The secondary loop takes over the fine
adjustment of frequecy by resetting the frequency error to
zero through integral action. The relationship between the
speed and load can be adjusted by changing a load
reference set point input.
Load-Frequency Control (LFC) is important in
electric power system design and operation. Moreover, to
ensure the quality of the power supply, it is necessary to
design a LFC system, which deals with the control of
loading of the generator depending on the frequency. The
conventional proportional plus integral controller is
probably the most commonly used. It is well known that
power systems are non-linear and complex, where the
parameters are a function of the operating point and the
loading in a power system is never constant. Further, the
two area power system composed of steam turbines
controlled by integral control only, is sufficient for all
load disturbances and it does not work well. Also, the
non-linear effect due to governor deadzones and
Generation Rate Constraint (GRC) complicates the
control system design. Further, if the two area power
system contains hydro and steam turbines, the design of
LFC systems is important. There are different control
strategies that have been applied, depending on linear or
non-linear control methods as in Saadat (1980), Kothari
et al. (2000) and found in Anju and Sharma (2011). With
the advent of fuzzy logic theory, various applications for
it have been established as in Pan and Liaw (1989),
Saravuth et al. (2006) and as in Yusuf and Ahmed (2004).
It is considered that the fuzzy logic control system works
well with non-linear systems. The present study utilizes
the fuzzy logic control technique control to design the
LFC system for two area power systems. The proposed
technique is added to the integral control LFC system as
a supplementary signal to improve the power system
stability and response characteristics. Also, the non-linear
effect due to governor dead zones or GRC are
Corresponding Author: Ali M. Yousef, Electrical Engineering Department Faculty of Eng., Assiut University, Egypt, 71516,
Electrical Engineering Department Faculty of Engineering Jazan University, KSA
2375
Res. J. Appl. Sci. Eng. Technol., 4(15): 2375-2381, 2012
 Pr 2  1 / T1  Pr 2  1 / R2 T1  f 2  1 / T1  E x 2
considered as in Yousef (2011). The types of turbines
employed in the two area power system, steam-hydro, are
studied with the proposed fuzzy logic control technique.
 1 / T1  U p1
 X E 2   1 / T2  X E 2   Pr 2 [1 / T2 
TR / T1T2 ]  TR / T1T2 R2  f 2
MATERIALS AND METHODS
The system investigated comprises an
interconnection of two areas load frequency control. The
model is steam-hydraulic turbines. The linearized
mathematical models of the first order system are
represented by state variables equations as follows:
 E x 2   K E 2 [ B2  f 2  a12 *  Ptie ]
The tie line power as:
 Ptie  2T12 [  f 1   f 2 ]
For steam area as:
 f = !1/Tp1)f1+kp1/Tp1)Pg1!kp1/Tp1)Ptie
The overall system can be modeled as a multivariable system in the form of:
!kp1/Tp1)Pd1
x  Ax (t )  Bu(t )  Ld (t )
 P g1 = !1/Tr1)Pg1+)Pr1[1/Tr1!Kr1/Tt1]
+Kr1/Tt1)XE1
 P r1 = 1/Tt1)XE1!1/Tt1)Pr1
) X E1 = ! 1/R1Tg1)f1 ! 1/Tg1)XE1 + 1/Tg1)Ex1
+1/Tg1)Up1

 E x1   K E 1 B1 f 1   Ptie

where A is system matrix, B and L are the input and
disturbance distribution matrices.
x(t),u(t) and d(t) are system state, control signal and
load changes disturbance vectors, respectively:
x(t) = [)f1 )Pg1 )Prl )XE1 )EX1 )f2 )Pg2 )Pr2 )XE2 )EX2
)Ptie]T
(2)
For hydraulic area as:
 f2   1 / Tp2  f 2  k p2 / Tp 2  Pg 2  k p2 / Tp2
* a12 *  Ptie  k p 2 / Tp 2  Pd 2
 Pg 2    Pg 2 [1/.5Tw  (1/.5T2  TR /.5T1T2 )]
  X E 2 [1/.5Tw  1/.5T2 ]  TR /.5T1T2 R2  f 2
 1

 T p1

0



0

 1

 R1T g 1
  K E 1 B1
A  
0



0


0



0


0

 2 T12
K p1
T p1
1
T r1
0
0
K
1
 r1 )
Tr1
Tt1
1
Tt1
1
Tg1
0
0
0
0
0
0
K r1
Tt 1
1
Tt 1
1
T g1
0
0
0
0
0
0
(
0
0
(1)
u(t) = [u1 u2]T
(3)
d(t) = [)Pdl )Pd2]T
(4)
ACEi = )ptie, i + bi )fi
(5)
y(t) = Cx(t)
(6)
)ptie(t) = )ptie, 1 (t) = ! )ptie, 2(t)
(7)
 K p1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
T p1
0
0
0
0
0
0
0
1
T p2
 TR
. 5T1T 2 R 2
1
R 2 T1
TR
T1T 2 R 2
 K E 2 B2
 2 T12
0
K p2
0
0
0
0
0
 K E1
K p2
 a 12
Tp2
0
Tp2
TR
1
1


(
)
. 5T w .5T 2 .5T1T 2
0
1
T1
0
0
0
0
2376
(
T
1
 R )
T 2 T1T 2
0
0
1
1

(
)
. 5T w .5T 2
1
T1
1
T2
0
0
0
0
0
0
0
0
0
0
 K E 2 a 12
0


























Res. J. Appl. Sci. Eng. Technol., 4(15): 2375-2381, 2012

0
B
0

0
0
1
Tg1
0
0
0
  K p1

T
L   p1

 0

0
0
0
0
0
0
0
0
1
T1
0
0
0
0
0
0
0
0
0
0
0
0
 K p2
Tp2
0
0
0
0
0
0
0
0

0

0


0


0

TT1,TT2 = Turbine time constant (s) of area No. 1 and
area No. 2
= Plant model time constant (s)
Tp
= Plant gain
Kp
R
= Speed regulation due to governor action
(HZ/p.u. MW)
= The integral control gain
KE
T
Effect of governor dead zones non-linearity: Figure 1
shows the power system block diagram with governor
dead zones. The described of governor dead zones D(v)
by the following function:
T
m(v-d), if v $d
D[v] = 0, {if-d # v # d
{m(v+d) if v #d
where,
)f1, )f2
)Pg1, )Pg2
)XE1,)XE2
)Pd1,)Pd2
)EX1,)EX2
)Pd1,)Pd2
Tg1,Tg2
= The frequency deviation (HZ) of area No.
1 and area No. 2
= The change in generator output (p.u. MW)
of area No. 1 and area No. 2
= The change in governor value position
(p.u. MW) of area No. 1 and area No. 2
= The change in turbine values (p.u. MW) of
area No. 1 and area No. 2
= The change in integral control of area No.
1 and area No. 2
= Load disturbance (p.u. MW) of area No. 1
and area No. 2
= Governor time constant (s) of area No. 1
and area No. 2
Effect of GRC non-linearity: The block diagram of the
plant model with Generation Rate Constraint (GRC) given
by  Pg  0.0017 p.u. MW/s is shown in Fig. 1
Fuzzy logic control: Fuzzy logic has an advantage over
other control methods due to the fact that it does not
sensitive to plant parameter variations. The fuzzy logic
control approach consists of three stages, namely
fuzzification, fuzzy control rules engine and
defuzzification. To design the fuzzy logic load frequency
control, the input signals is the frequency deviation at
sampling time and its change. While, its output signal is
the change of control signal )U(k). When the value of
Fig. 1: Two-Area (Steam-Hydraulic Turbines) load frequency control with governor deadzone and GRC nonlinearity
2377
Res. J. Appl. Sci. Eng. Technol., 4(15): 2375-2381, 2012
LN
MN
SN
Z
SP
MP
LP
Fig. 2: Three-stage of fuzzy logic controller: u, membership
degree
Fig. 3: Fuzzy logic power system stabilizer
Table 1: Fuzzy logic control rules
d )f
-------------------------------------------------------------------------)f
LN
MN
SN
Z
SP
MP
LP
LN
LP
LP
LP
MP
MP
SP
Z
MN
LP
MP
MP
MP
SP
Z
SN
SN
LP
MP
SP
SP
Z
SN
MN
Z
MP
MP
SP
Z
SN
MN
MN
SP
MP
SP
Z
SN
SN
MN
LN
MP
SP
Z
SN
MN
MN
MN
LN
LP
Z
SN
MN
MN
LN
LN
LN
:
:
:
:
:
:
:
Large negative membership function
Medium negative
Small negative
Zero
Small positive
Medium positive
Large positive
PID power system stabilizer: PID controllers are
dominant and popular and, have been widely used
because one can obtain the desired system responses and
it can control a wide class of systems. This may lead to
the thought that the PID controllers give solutions to all
requirements, but unfortunately, this is not always true as
in Datta et al. (2000). In this work, the PID optimal tuning
method used is found in Kristiansson and Lennartson
(2002). In this method, the parameters of PID controller
satisfying the constraints correspond to a given domain in
a plane. The optimal controller lies on the curve. The
design plot enables identification of the PID controller for
desired robust conditions and in particular, gives the PID
controller for lowest sensitivity. By applying this method,
trade-off among high frequency sensor noise, low
frequency sensitivity, gain and phase margin constraints
are also directly available.
The transfer function of a PID controller is given by:
K(s) = Kp(1+1/Tls+TDs)
(8)
where Kp,Kp/Tl and KpTD represent the proportional,
integral and derivative gains of the controller respectively.
Define
n 
1
TI TD
and

1 TI
2 TD
as the controller's
natural frequency and the damping coefficient,
respectively. Then the PID transfer function can be
written as:
K ( s)  K P
 n2  2 n s  s2
2 n s
(9)
The optimal PID controller parameters values were:
Kp = 2, TI = 0.6 and KD =1
Fig. 4: Membership functions of the fuzzy regulator
the control signal at sampling time [k-1] (U(k-1)) is added
to the output signal of fuzzy logic controller, the required
control signal U(k) is obtained. Figure 2 shows the threestage of fuzzy logic controller. While the fuzzy logic
control system is described in Fig. 3. The fuzzy control
rules are illustrated in Table 1. The membership function
shapes of error and derivative error and the gains are
chosen to be identical with triangular function for fuzzy
logic control. However, this horizontal axis range is taken
different values because of optimizing controller. The
membership function sets of FLC for two areas are shown
in Fig. 4
where,
RESULTS AND DISCUSSION
To validate the effectiveness of the proposed fuzzy
controllers, the power system under study is simulated
and subjected to different parameters changes. The power
system frequency deviations are obtained. Further a
various types of turbines (steam and hydro) are simulated.
Also a comparison between the power system responses
using the conventional integral and PID control system
and the proposed fuzzy logic controller is studied as
follows and the system parameters are:
Nominal parameters of the hydro-thermal system
investigated:
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Res. J. Appl. Sci. Eng. Technol., 4(15): 2375-2381, 2012
f = 60 HZR1 = R2 = 2.4 HZ/per unit MW
Tg1 = 0.08 s Tr = 10.0 s Tt = 0.3s
TR = 5 s D1 = D2 = 0.00833 Mw/HZ
T1 = 48.7 s T2 = 0.513 s, Tg2 = 0.08s
Tt1 = Tt2 = 0.3 s Kr1 = Kr2 = 1/3
Pd1 = 0.05 p.u. MW
B1 = B2 = 0.425
Pd2 = 0.0
Tr1 = Tr2 = 20 s, T12 = 0.0707 s
The integral control gain Ki = 1 pu
0.010
0
P tie
-0.005
Without
Integral
Fuzzy
-0.020
-0.025
0
10
20
30
40
50
60
70
80
Time
Fig. 7: Tie-line power deviation response due to 0.5 p.u. load
disturbance in area-1 of the two-area power system with
and without integral and proposed fuzzy logic control
0
f1
-0.010
-0.015
Without
Integral
Fuzzy
0.005
Deviation P tie
0.005
-0.005
Deviation P tie
-0.010
0.005
-0.015
Tg1 = Tg2 = 0.1
0
-0.020
-0.005
0
10
20
30
40
50
60
70
P tie
-0.025
80
Time
-0.010
-0.015
Fig. 5: Frequency deviation response of area-1 due to 0.5 p.u.
load disturbance in area-1 of the two-area power system
with and without integral and proposed fuzzy logic
control
Without
Integral
Fuzzy
-0.020
-0.025
0
10
20
30
40
50
60
70
80
Time
0.015
Without
Integral
Fuzzy
0.010
Fig. 8: Tie-line power deviation response due to 0.5 p.u. load
disturbance in area-1 of the two-area power system with
and without integral and proposed fuzzy logic control at
increased 20% in Tg
0.005
F2
0
-0.005
0.010
-0.010
0.005
-0.015
Deviation of F1
Tg1 = Tg2 = 0.1
0
f1
-0.020
-0.025
0
10
20
30
40
50
60
70
-0.005
-0.010
80
Time
-0.015
Fig. 6: Frequency deviation response of area-2 due to 0.5 p.u.
load disturbance in area-1 of the two-area power system
with and without integral and proposed fuzzy logic
control
-0.020
Figure 5 shows the frequency deviation response of
area-1 due to 0. 5 p.u. load disturbance in area-1 of the
two-area power system with and without integral and
proposed fuzzy logic control. Figure 6 shows the
frequency deviation response of area-2 due to 0.5 p.u.
load disturbance in area-1 of the two-area power system
with and without integral and proposed fuzzy logic power
deviation response due to 0.5 p.u. load disturbance in
area-1 of the two-area power system with and without
Without
Integral
Fuzzy
-0.025
0
10
20
30
40
50
60
70
80
Time
Fig. 9: Frequency deviation response of area-1 due to 0.5 p.u.
load disturbance in area-1 of the two-area power system
with and without integral and proposed fuzzy logic
control of model-2 at increased 20% in Tg
control. Figure 7 shows the tie-line power deviation
response due to 0.5 p.u. load disturbance in area-1 of the
two-area power system with and without integral and
proposed fuzzy logic control. Figure 8 depicts the tie-line
integral and proposed fuzzy logic control at increased
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Res. J. Appl. Sci. Eng. Technol., 4(15): 2375-2381, 2012
Tt = 0.5, Tr = 20
0.010
0
Tg1 = Tg2 = 0.1
0.005
-0.005
P tie
0
f2
Deviation P tie
0.005
Deviation of F2
0.015
-0.005
-0.010
-0.010
-0.015
-0.015
-0.020
Without
Integral
Fuzzy
-0.020
70
-0.025
-0.025
0
10
20
30
40
50
60
80
Without
Integral
Fuzzy
0
10
20
30
Time
Fig. 10: Frequency deviation response of area-2 due to 0.5 p.u.
load disturbance in area-1 of the two-area power
system with and without integral and proposed fuzzy
logic control at increased 20% in Tg
50
60
70
80
Fig. 13: Tie-line power deviation response due to 0.5 p.u. load
disturbance in area-1 of the two-area power system
with and without integral and proposed fuzzy logic
control at change in Tt , Tr
Deviation of F1
0.015
40
Time
-3
4  10
P tie dev. Response in pu.
0.010
Tg1 = 0.5, Tr = 20
0.005
2
Kp = 0, ki = 0, kd = 0
0
-0.005
P tie
f1
0
-0.010
-0.015
-4
Without
Integral
Fuzzy
-0.020
10
20
30
40
50
60
70
W/o-control
PID-control
Fuzzy-control
-6
-0.025
0
-2
-8
80
0
10
20
30
Time
Fig. 11: Frequency deviation response of area-1 due to 0.5 p.u.
load disturbance in area-1 of the two-area power
system with and without integral and proposed fuzzy
logic control at change in Tt , Tr
0.005
0
Tg1 = 0.5, Tr = 20
F2
f2
-0.005
-0.010
-0.015
-0.020
-0.010
-0.015
-0.020
W/o-control
PID-control
Fuzzy-control
-0.035
0
-0.025
20
30
40
80
Kp = 0.02, ki = 0.2, kd = 0
-0.025
-0.030
Without
Integral
Fuzzy
10
70
-0.005
0
0
60
F2 dev. response in pu.
0.010
0.010
0.005
50
Fig. 14: Tie-line power deviation response due to 0.5 p.u. load
disturbance in area-1 of the two-area power system
with and without PID and proposed fuzzy logic control
Deviation of F2
0.015
40
Time (sec)
50
60
70
80
10
20
30
40
50
60
70
80
Time (sec)
Time
Fig. 12: Frequency deviation response of area-2 due to 0.5 p.u.
load disturbance in area-1 of the two-area power
system with and without integral and proposed fuzzy
logic control at change in Tt, Tr
Fig. 15: Frequency deviation response of area-2 due to 0.5 p.u.
load disturbance in area-1 of the two-area power
system with and without PID and proposed fuzzy logic
control
20% in Tg. Figure 9 depicts the frequency deviation
response of area-1 due to 0.05 p.u. load disturbance in
area-1 of the two-area power system with and without
integral and proposed fuzzy logic control at increased
20% in Tg. Moreover, Fig. 10 depicts the frequency
deviation response of area-2 due to 0.5 p.u. load
disturbance in area-1 of the two-area power system with
and without integral and proposed fuzzy logic control at
increased 20% in Tg. Figure 11 displays the frequency
deviation response of area-1 due to 0.5 p.u. load
2380
Res. J. Appl. Sci. Eng. Technol., 4(15): 2375-2381, 2012
Kp = 0.02, ki = 0.2, kd = 0
0.005
0
F1
proposed controller a comparison among the conventional
integral and PID controller and the proposed controller is
obtained. The effect of governor non-linear and GRC is
included in the simulation. The proposed controller proves
that it is robust to variations in dead zones non-linearity.
The digital simulation results
Proved and show the effectiveness of the power of
the proposed FLC over the conventional integral and PID
controller through a wide range of load disturbances. The
superiority of the proposed fuzzy controller is embedded
in the sense of fast response with less overshoot and/or
undershoot and less settling time.
F1 dev. Response in pu.
0.015
0.010
-0.005
-0.010
-0.015
-0.020
W/o-control
PID-control
Fuzzy-control
-0.025
-0.030
0
10
20
30
40
50
60
70
80
Time (sec)
REFERENCES
Fig. 16: Frequency deviation response of area-1 due to 0.5 p.u.
load disturbance in area-1 of the two-area power
system with and without PID and proposed fuzzy logic
control
Table 2: Time settling calculated in each control
Integral-control
PID-control
(Sec)
(Sec)
F1
50
40
F2
40
35
Tie-line power
30
28
Fuzzy control
(Sec)
30
29
25
disturbance in area-1 of the two-area power system with
and without integral and proposed fuzzy logic control at
change in turbine time constant (Tt) and Tr. Figure 12
displays the frequency deviation response of area-2 due to
0.5 p.u. load disturbance in area-1 of the two-area power
system with and without integral and proposed fuzzy
logic control at change in turbine time constant Tt and Tr.
Figure 13 shows the tie-line power deviation response of
area-1 due to 0.5 p.u. load disturbance in area-1 of the
two-area power system with and without integral and
proposed fuzzy logic control at change in turbine time
constant Tt and Tr. Figure 14 shows the tie-line power
deviation response due to 0.5 p.u. load disturbance in
area-1 of the two-area power system with and without
PID and proposed fuzzy logic control. Figure 15 depicts
the frequency deviation response of area-2 due to 0.5 p.u.
load disturbance in area-1 of the two-area power system
with and without PID and proposed fuzzy logic control.
Figure 16 shows the frequency deviation response of area1 due to 0.5 p.u. load disturbance in area-1 of the two-area
power system with and without PID and proposed fuzzy
logic control. Also, Table 2 displays the settling time
calculation at different controllers.
CONCLUSION AND RECOMMENDATIONS
The presents study design a load-frequency control
system using fuzzy logic controller for enhancing power
system dynamic performances after applying several
disturbances upon it. The proposed controller is robust
and gives good transient as well as steady-state
performance. To validate the effectiveness of the
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