Design Fuzzy-PI Based Controller for Load Frequency Control of Thermal - Thermal Area Interconnected Power System

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ISSN No: 2456
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Design Fuzzy-PI Based Controller
Thermal - Thermal Area Interconnected Power System
Ajay Kumar Maurya
1
Ph.D. Scholar, Department of Electrical Engineering,
1
Lecturer, Department of Electrical & Electronics Technology,
2
Professor, Department of Electrical Engineering, IFTM University, Moradabad, UP, India
3
Associate Professor, Department of EEE, SRMS College of Engineering and Technology, Bareilly, UP, India
ABSTRACT
This paper presents how to design proportional
integral controller and Fuzzy-PI based controller for
efficiently load frequency control. Loads on the
electrical system always vary in relation to that time,
which results in diversity of frequency, causing
frequency control problems to be loaded. The
frequency difference is highly undesirable and the
maximum allowable difference in frequency is ± 0.5
Hz. This paper load frequency control is done by PI
controller, which is a conventional controller. This
type of controller is slow and the controller does not
allow the designer to keep in mind the potential
change in operating conditions and non
the generator unit. To overcome these flaws, new
intelligent controllers like Fuzzy-PI Controller are
presented to extinguish tie-line power due to deviation
in frequency and various load disturbances.
The effectiveness of the proposed controller has been
confirmed using the MATLAB / SIMULINK
software. The results show that the PI-fuzzy controller
provides fast response, little undershoots and
negligible overshoot with small state transfer time to
reach the final stable position.
KEY WORDS: PI controller, Fuzzy controller, two
area power system, load frequency control
1. INTRODUCTION
For large power systems consisting of interconnected
control areas, load frequencies, it is important to keep
the frequency and the inter-area energy close to the
planned values. The mechanical input power is used
to control the frequency of the generators
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ISSN No: 2456 - 6470 | Volume - 3 | Issue – 1 | Nov
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PI Based Controller for Load Frequency Control
Thermal Area Interconnected Power System
Ajay Kumar Maurya1
, Dr. G. K. Banerjee2
, Dr. Piush Kumar
Ph.D. Scholar, Department of Electrical Engineering, IFTM University, Moradabad, U
ical & Electronics Technology, Federal TVET Institute, Addis Ababa , Ethiopia
Department of EEE, SRMS College of Engineering and Technology, Bareilly, UP, India
This paper presents how to design proportional
PI based controller for
efficiently load frequency control. Loads on the
electrical system always vary in relation to that time,
which results in diversity of frequency, causing
frequency control problems to be loaded. The
frequency difference is highly undesirable and the
m allowable difference in frequency is ± 0.5
This paper load frequency control is done by PI
controller, which is a conventional controller. This
type of controller is slow and the controller does not
allow the designer to keep in mind the potential
ange in operating conditions and non-linearity in
the generator unit. To overcome these flaws, new
PI Controller are
line power due to deviation
in frequency and various load disturbances.
effectiveness of the proposed controller has been
confirmed using the MATLAB / SIMULINK
fuzzy controller
provides fast response, little undershoots and
negligible overshoot with small state transfer time to
PI controller, Fuzzy controller, two
area power system, load frequency control
For large power systems consisting of interconnected
control areas, load frequencies, it is important to keep
area energy close to the
planned values. The mechanical input power is used
to control the frequency of the generators, and the
change in frequency and line voltage is measured,
which is a measure of the change in rotor angle. A
well designed power system should be able to
guarantee the acceptable quality of the power supply
by keeping the frequency and voltage levels
tolerable limits.
Changes in the network load mainly affect the system
frequency, while the reactive power is less sensitive to
frequency changes and depends mainly on voltage
fluctuations. Thus, the control of the active and
reactive power in the power grid is treated separately.
The load frequency control is mainly concerned with
the control of the system frequency and the active
power, while the automatic voltage regulator loop
regulates the changes of the reactive power and
voltage magnitude. Load frequency control is the
basis of many advanced concepts of large scale
control of the power system.
The load frequency control (LFC) controls the actual
power and frequency. MATLAB provides an
excellent environment
programming. It has great flexibility and utility for
engineering applications. SIMULINK is a visual
modeling tool, which works on MATLAB shell. The
goal of the load frequency control (LFC) is to
maintain zero steady state errors in a multi area
interconnected power system.
and frequency from the nominal values, when there is
any mismatch in real power and reactive power
generations and demands. It can be provided by
sensitivity analysis that mismatches in the real power
balance affects primarily the sys
Research and Development (IJTSRD)
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1 | Nov – Dec 2018
Dec 2018 Page: 928
or Load Frequency Control of
Thermal Area Interconnected Power System
Dr. Piush Kumar3
versity, Moradabad, Uttar Pradesh, India
Federal TVET Institute, Addis Ababa , Ethiopia
Department of EEE, SRMS College of Engineering and Technology, Bareilly, UP, India
change in frequency and line voltage is measured,
which is a measure of the change in rotor angle. A
well designed power system should be able to
guarantee the acceptable quality of the power supply
by keeping the frequency and voltage levels within
Changes in the network load mainly affect the system
frequency, while the reactive power is less sensitive to
frequency changes and depends mainly on voltage
fluctuations. Thus, the control of the active and
power grid is treated separately.
The load frequency control is mainly concerned with
the control of the system frequency and the active
power, while the automatic voltage regulator loop
regulates the changes of the reactive power and
ad frequency control is the
basis of many advanced concepts of large scale
The load frequency control (LFC) controls the actual
MATLAB provides an
for modeling and
great flexibility and utility for
engineering applications. SIMULINK is a visual
modeling tool, which works on MATLAB shell. The
goal of the load frequency control (LFC) is to
maintain zero steady state errors in a multi area
interconnected power system. The change in voltage
and frequency from the nominal values, when there is
any mismatch in real power and reactive power
generations and demands. It can be provided by
sensitivity analysis that mismatches in the real power
balance affects primarily the system frequency, but

International Journal of Trend in Scientific Research and
leaves the bus voltage essentially unaffected.
control system is essential to cancel the effects of the
sudden load changes and to keep the frequency at the
nominal value [3–5]
1.1 TWO-area power system model
A two-area interconnected thermal power system as
shown in Fig. 1 is considered. The system is widely
used in literature for the design and analysis of AGC
[7]. In Fig. 1, B1 and B2 are the frequency bias
parameters; ACE1 and ACE2 are area control errors;
X1 and X2 are the control outputs from the controller;
R1 and R2 are the governor speed regulation
parameters in p.u. Hz; TH1 and TH2
governor time constants in seconds; Δ
are the governor output command (p.u.);
are the turbine time constant in seconds;
ΔPT 2 are the change in turbine output powers;
and ΔPE2 are the load demand changes;
are the power system gains; TP1 and TP2
system time constant in seconds;
incremental change in tie line power (p.u.);
Δf2 are the system frequency deviations in Hz. The
relevant parameters are given in Appendix A.
Figure 1: Two area Thermal–Thermal plant with
conventional PI controller
1.2 Modeling of the tie-line
The well known power transfer equation is
1 2o
1 2 1 2
V V
P s in ( )
x
   
Where 1 and 2 are the angles of end voltages V
and V2 respectively. The sequence of subscript
indicates that the tie line defines positive in power
direction 1 to 2.
International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456
leaves the bus voltage essentially unaffected. So, a
control system is essential to cancel the effects of the
sudden load changes and to keep the frequency at the
area interconnected thermal power system as
shown in Fig. 1 is considered. The system is widely
used in literature for the design and analysis of AGC
are the frequency bias
are area control errors;
are the control outputs from the controller;
are the governor speed regulation
are the speed
ΔPH1 and ΔPH2
are the governor output command (p.u.); TT1 and TT 2
are the turbine time constant in seconds; ΔPT1 and
are the change in turbine output powers; ΔPE1
are the load demand changes; KP1 and KP2
2 are the power
system time constant in seconds; ΔPTie is the
incremental change in tie line power (p.u.); Δf1 and
are the system frequency deviations in Hz. The
relevant parameters are given in Appendix A.
Thermal plant with
conventional PI controller
The well known power transfer equation is
(1)
are the angles of end voltages V1
The sequence of subscript
positive in power
For tiny deviation in the angles and the tie line
changes with the power amount
1 2
12 1 2 1 2
V V
P cos( )( )
x
       
In accordance with the concept of "electrical stiffness"
of synchronous machines, we define
coefficient" of a line
𝑇 =
| | | |
cos (
Thus the equation (2) can be written as
o
1 2 1 2P T ( )      
Figure 2: Conventional Two Area System: Basic
Block Diagram
The frequency deviation is related to
angle by the formula
1 d ( )
f
2 dt
   
 

or d ( )
dt
 
 
or 2 2    
Thus the equation (3.4) can be written as
 t t
o
12 1 20 0
P 2 T f dt f dt      
Taking Laplace transformation of equation

o
12 1 2
2 T
P (s) f (s) f (s)
s

    
The above equation can be represented as in figure (3)
Figure 3: Block Diagram Representation of a Tie
Line
Similarly the incremented tie line power expected
from area 2 is given by

o
12 2 1
2 T
P (s) f (s) f (s)
s

    
Development (IJTSRD) ISSN: 2456-6470
Dec 2018 Page: 929
For tiny deviation in the angles and the tie line
changes with the power amount
12 1 2 1 2P cos( )( )        (2)
In accordance with the concept of "electrical stiffness"
of synchronous machines, we define "synchronizing
(𝛿 − 𝛿 ) (3)
Thus the equation (2) can be written as
1 2 1 2P T ( )       (4)
Figure 2: Conventional Two Area System: Basic
Block Diagram
The frequency deviation is related to the reference
1 d ( )
2 dt
   1 d( )
2 dt



d ( )
2 f
 
 
0
2 2
t
f d t    
Thus the equation (3.4) can be written as
t t
12 1 20 0
P 2 T f dt f dt      
Taking Laplace transformation of equation
12 1 2P (s) f (s) f (s)     (5)
The above equation can be represented as in figure (3)
Figure 3: Block Diagram Representation of a Tie –
Similarly the incremented tie line power expected
12 2 1P (s) f (s) f (s)    

The power balance equation for single area can be
given by
So for the double area, the equation should be
modified as follows
1 1
1 1 1 1 1 2
2 ( )
T E
o
H d f
P P B f P
f d t

       
  1
T1 E1 12 1 1 1
o
2H
P (s) P (s) P (s) s f (s) B f (s)
f
        
If 𝑇 = 𝐾 =
Equation (6) can be written as
1 P1 T 1 E 1 1 2f (s) G (s) P (s) P (s) P (s)      
P 1
P 1
P 1
K
G (s )
1 sT


Thus the complete block diagram representation of
two area load frequency control is given in figure (1).
2. Ziegler -Nichols Rule Based Tuning
For comparison the PID controller was tuned using
conventional Ziegler –Nichols tuning rule based on
the critical gain Ku and critical period P
Ku and Pu were calculated from the sustained
oscillations of the output by employing only
proportional controller. The sustained oscillation
response with proportional controller under critical
gain is shown in Figure (4). As per the Ziegler
Nichols rule the settings for PID controller parameter
are given in the following table [1]. Controller
parameters calculated for conventional controller are
given in Table [2].
Table 1: Ziegler-Nichols tuning rules
Type of control Gc(s) K
Proportional (P) Kc
0.5
K
Proportional–
Integral(PI) c
i
1
K 1
sT
 
 
 
0.45K
Proportional-
Integral-
Derivative (PID)
c d
i
1
K 1 sT
sT
 
  
 
0.6K
The power balance equation for single area can be
So for the double area, the equation should be
1 1 1 1 1 2P P B f P       
T1 E1 12 1 1 1P (s) P (s) P (s) s f (s) B f (s)         (6)
1 P1 T 1 E1 12f (s) G (s) P (s) P (s) P (s)      
Thus the complete block diagram representation of
two area load frequency control is given in figure (1).
Nichols Rule Based Tuning
For comparison the PID controller was tuned using
Nichols tuning rule based on
and critical period Pu. Values of
were calculated from the sustained
oscillations of the output by employing only
nal controller. The sustained oscillation
response with proportional controller under critical
gain is shown in Figure (4). As per the Ziegler-
Nichols rule the settings for PID controller parameter
are given in the following table [1]. Controller
s calculated for conventional controller are
Nichols tuning rules
Kc Ti Td
0.5
Ku
- -
u0.45K uP
1.2
-
u0.6K uP
2
uP
8
Figure 4: System response with proportional
controller under critical gain
Table 2: Controller Parameters for conventional
controller
Kc T
0.45.Ku= 0.66 Pu /1.2 =
3. Different types of controllers
3.1 PI - Controller
The 'PI' controller will eliminate forced oscillations
and steady state error, which will
operation of the on-off controller and the 'P'
controller, respectively. However, starting an integral
mode has a negative impact on the response speed and
overall stability of the system.
Therefore, the PI controller does not increase the
reaction rate. It can be expected because the PI
controller has no means of predicting what will
happen to the bug in the near future. This problem can
be solved by introducing a derivative mode that is
able to predict what will happen to the error in the
near future and thus reduce it [13]
3.2 Fuzzy Controller
The general architecture of a fuzzy controller is
depicted in Figure (5) [14]. The origin of a fuzzy
controller is an fuzzy inference engine (FIS), which
includes fuzzification,, knowledge base evalu
and defuzzification in the data flow.
systems are the error and the change in the error of the
feedback loop, while the output is the control action.
There are 7 trapezoidal membership functions in each
input i.e.NB (Negative Big), NM (Negative Medium),
NS (Negative Small), Z (Zero), PS (Positive Small),
PM (Positive Medium), PB (Positive Big). The
mamdani rule base adopted here and the
0 0.5 1 1.5 2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Time (sec)
FrequencyDeviation(Hz.)
Pu = 1.2
Dec 2018 Page: 930
Figure 4: System response with proportional
controller under critical gain
Table 2: Controller Parameters for conventional
controller
i Ki
/1.2 = 1
Kc/Ti =
0.66
Different types of controllers
The 'PI' controller will eliminate forced oscillations
and steady state error, which will result in the
off controller and the 'P'
controller, respectively. However, starting an integral
mode has a negative impact on the response speed and
overall stability of the system.
Therefore, the PI controller does not increase the
eaction rate. It can be expected because the PI
controller has no means of predicting what will
happen to the bug in the near future. This problem can
be solved by introducing a derivative mode that is
able to predict what will happen to the error in the
ear future and thus reduce it [13]
The general architecture of a fuzzy controller is
depicted in Figure (5) [14]. The origin of a fuzzy
controller is an fuzzy inference engine (FIS), which
includes fuzzification,, knowledge base evaluation
in the data flow. The inputs to the
systems are the error and the change in the error of the
feedback loop, while the output is the control action.
There are 7 trapezoidal membership functions in each
NM (Negative Medium),
NS (Negative Small), Z (Zero), PS (Positive Small),
PM (Positive Medium), PB (Positive Big). The
mamdani rule base adopted here and the
2.5 3 3.5 4
Time (sec)
Ku = 1.467

defuzzification process is centroid method. The fuzzy
rules are shown in Table [3].
Figure 5: Structure of fuzzy logic controller
Table 3: Fuzzy Rule Base
E
∆E
NB NM NS ZE PS
NB PB PB PB PB PM
NM PB PM PM PM PS
NS PM PM PS PS PS
ZE NS NS NS ZE PS
PS ZE NS NS NS NS
PM NS NS NM NM NM
PB NS NM NB NB NB
A fuzzy system is described by a set of IF
rules and uses diverse membership functions. To
solve the load-frequency control problem in fuzzy
controller, controller inputs are Area Control Error
and derivative of Area Control Error and its
considered as the control signal. The member ship
function uses in fuzzy logic controller for Error,
change in Error and output is shown in figure (5).
Figure 5: Membership functions of inputs (E,
and output
3.3 PI- Fuzzy Logic Controller
A Fuzzy-PI controller designed based on a linear
model of power system under the loading condition
FLC designed to eliminate the need for continuous
defuzzification process is centroid method. The fuzzy
Structure of fuzzy logic controller
Table 3: Fuzzy Rule Base
PM PB
PM PS
PS PS
PS ZE
PS PS
NM NM
NB NB
NB NB
A fuzzy system is described by a set of IF-THEN
rules and uses diverse membership functions. To
frequency control problem in fuzzy
controller, controller inputs are Area Control Error
and derivative of Area Control Error and its output are
considered as the control signal. The member ship
function uses in fuzzy logic controller for Error,
change in Error and output is shown in figure (5).
Membership functions of inputs (E, ΔE)
PI controller designed based on a linear
model of power system under the loading condition
FLC designed to eliminate the need for continuous
operator attention and used automatically to adjust
some variables the process variable is kept
reference value. A FLC consists of three sections
Namely, fuzzifier, rule base, and defuzzifier.
Fuzzy-PI controller structure is shown in Figure (6).
Figure 6: PI-Fuzzy Logic controller in Simulink
4. Results and Simulation
Performed simulations using PI and Fuzzy
controllers applied to a two area interconnected power
systems. The developed system is simulated with 10
% step load disturbance in area 1. Due to this the
change in dynamic responses of the system has been
observed, as shown in below Figures. It is examine
from the output responses that the proposed Fuzzy
Controller is stable and less oscillations and the
settling time also improved considerably. Also this
output justified that this interconnection is valid for
Thermal-Thermal systems. For conventional PI
controller and Fuzzy-PI controller, the main objective
is to improve the control performance
4.1 Uncontrolled case
The frequency changes in area
10% step load perturbation is shown in figure (7).
There is a steady state error in the response.
Figure 7: Two area Thermal
(Uncontrolled) with a disturbance of
area-1: Frequency deviation of area
4.2 Controlled Case with Proportional plus
Integral Controller
The frequency changes in area
10% step load perturbation is shown in figure (8) and
(9). (10% step load perturbation is given in area
Dec 2018 Page: 931
attention and used automatically to adjust
process variable is kept at the
reference value. A FLC consists of three sections
Namely, fuzzifier, rule base, and defuzzifier. The
controller structure is shown in Figure (6).
zzy Logic controller in Simulink
simulations using PI and Fuzzy-PI
controllers applied to a two area interconnected power
systems. The developed system is simulated with 10
% step load disturbance in area 1. Due to this the
change in dynamic responses of the system has been
hown in below Figures. It is examine
from the output responses that the proposed Fuzzy-PI
Controller is stable and less oscillations and the
settling time also improved considerably. Also this
output justified that this interconnection is valid for
Thermal systems. For conventional PI
PI controller, the main objective
is to improve the control performance
The frequency changes in area-1 and area-2 for the
10% step load perturbation is shown in figure (7).
There is a steady state error in the response.
Two area Thermal-Thermal plant
disturbance of 10 % in
1: Frequency deviation of area -1 and area – 2
Controlled Case with Proportional plus
The frequency changes in area-1 and area-2 for the
(9). (10% step load perturbation is given in area -1).

The steady state error is zero in this case. The
frequency deviation of area-1 is much more
Figure 8: Two area Thermal-Thermal plant
(Controlled with PI) with Disturbance of 10 % in
(Controlled with PI) with a Disturbance of 10 % in
area-1: Frequency deviation of ar
4.3 Controlled Case with Fuzzy-PI Controller
The frequency changes in area-1 and area
(11). (10% step load perturbation is given in
frequency deviation of area-1 is much more
0 5 10 15 20 25 30 35
Time (Second)
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
1 is much more
Thermal plant
Disturbance of 10 % in
1: Frequency deviation of area -1
Thermal plant
PI Controller
1 and area-2 for the
(11). (10% step load perturbation is given in area -1).
1 is much more
(Controlled with Fuzzy-PI) With disturbance of 10
% in area-1: Frequency deviation of area
(Controlled with Fuzzy-PI) With Disturbance of 10
% in area-1: Frequency deviation of area
4.4 Comparison between PI and Fuzzy
Controller
Figure 12: Comparison result between Fuzzy
and PI controller with Disturban
40 45 50
Area 2
PI Controller
Dec 2018 Page: 932
With disturbance of 10
wo area Thermal-Thermal plant
With Disturbance of 10
Comparison between PI and Fuzzy-PI
Figure 12: Comparison result between Fuzzy-PI

Figure 13: Comparison result between Fuzzy
and PI controller in with Disturbance of 10 % in
The comparison of peak undershoots; Peak Overshoot
and Settling Time via PI controller and Fuzzy
controller are given in Table [3].
Table 3: Thermal-Thermal plant: PI Controller Vs
Fuzzy-PI Controller
Peak
Undershoot
Peak
Overshoot
Two
Area
Area
-1
Area
-2
Area
-1
Area
-2
PI
Control
ler
-
0.15
57
-
0.06
29
0.02
97
0.00
03
PI-
Fuzzy
Control
ler
-
0.13
20
-
0.05
62
0.00
27
0.00
00
5. Conclusion
In this paper a new technique Fuzzy-PI controller is
designed for automatic load frequency control of
interconnected Thermal - Thermal systems. The
controller performances Fuzzy-PI approach is in work
for a Load Frequency Control for Generation of
Interconnected Power System. The proposed
controller can handle the non-linearity and at the same
time faster than other conventional controllers. Also
the simulation results are compared with a
conventional other controller. From the Result shown
in figure (8) to figure (13). The results obtained for
double area Thermal-Thermal plant shows the
superiority such controllers over the conventional PI
controllers. In Fuzzy-PI Controller the settling time
has been reduced in area1 and area 2 are 5.63 sec and
6.30 sec respectively. It is explicit that the
Figure 13: Comparison result between Fuzzy-PI
The comparison of peak undershoots; Peak Overshoot
and Settling Time via PI controller and Fuzzy-PI
Thermal plant: PI Controller Vs
Settling
Time(Sec)
Are
a-1
Are
a-2
12.8
8
14.8
5
7.25 8.55
PI controller is
designed for automatic load frequency control of
Thermal systems. The
PI approach is in work
for a Load Frequency Control for Generation of
nected Power System. The proposed
linearity and at the same
time faster than other conventional controllers. Also
the simulation results are compared with a
conventional other controller. From the Result shown
figure (13). The results obtained for
Thermal plant shows the
superiority such controllers over the conventional PI
PI Controller the settling time
has been reduced in area1 and area 2 are 5.63 sec and
spectively. It is explicit that the
performance in term of settling time and overshoot of
fuzzy-PI controller is better. There is no steady state
error. So fuzzy-PI controller shows its effectiveness
over the conventional PI controller.
The result shows that the proposed intelligent
controller is having improved dynamic response and
at the same time faster than conventional
APPENDIX
Parameter
KP1 = KP2 120 Hz. / p.u. MW
KH1 =KH2 1 Hz. / p.u. MW
KT1 =KT2 1 Hz. / p.u. MW
TP1 = TP2
TH1 =TH2 0.08 Sec.
TT1 = TT2
B1 = B2 0.425 p.u. MW / Hz.
R1 = R2 2.4 Hz. / p.u. MW
To 0.0867 p.u. MW/Hz
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Dec 2018 Page: 933
performance in term of settling time and overshoot of
PI controller is better. There is no steady state
PI controller shows its effectiveness
over the conventional PI controller.
hat the proposed intelligent
controller is having improved dynamic response and
at the same time faster than conventional controller
Value
120 Hz. / p.u. MW
1 Hz. / p.u. MW
1 Hz. / p.u. MW
20 Sec.
0.08 Sec.
0.3 Sec.
0.425 p.u. MW / Hz.
2.4 Hz. / p.u. MW
0.0867 p.u. MW/Hz
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Saravuth Pothiya, Issarachai Ngamroo, Suwan
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imal Fuzzy Logic based PI Controller using
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1027, October 2003

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