Parallel control structure scheme for load frequency controller design using direct synthesis approach

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 1, February 2020, pp. 47~60
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i1.pp47-60  47
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Parallel control structure scheme for load frequency controller
design using direct synthesis approach
Anand Kumar, Md Nishat Anwar
Department of Electrical Engineering, National Institute of Technology Patna, India
Article Info ABSTRACT
Article history:
Received Jan 2, 2019
Revised Aug 28, 2019
Accepted Aug 30, 2019
This paper presents load frequency controller design for a single area as well
as the multi-area thermal power system using direct synthesis approach with
parallel control structure (PCS) scheme. The set-point and load frequency
controller has been designed for frequency regulation and maintains tie-line
power within a pre-specified limit for LFC power system. The proposed
controller has been implemented for single-area, two-area, and four-area
thermal power system for frequency regulation. The proposed method shows
impressive simulation results compared with existed control method.
The robustness of the proposed method has been examined with the help
maximum sensitivity and parametric variation in the nominal power system.
Keywords:
IAE
Load frequency control (LFC)
Maximum sensitivity
parallel control structure
PID control Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Anand Kumar,
Departement of Electrical Engineering,
National Institute of Technology Patna,
Ashok Rajpath, Patna 800005, Bihar, India.
Email: anand.ee15@nitp.ac.in
1. INTRODUCTION
In power system, the frequency and tie-line power exchange deviate from its nominal value due to
change in load and other abnormality. In load frequency control (LFC) retain the system frequency and
tie-line power exchange between two areas at its nominal (pre-defined) value [1]. Many researchers have
studied different design techniques for LFC in an interconnected power to maintain its frequency and tie-line
power exchange at its pre-specified value i.e. available in the literature [2, 3].
A lot of research has been done in the LFC system for improvement in frequency deviation as well
as tie-line power exchange between others area. Various controller design technique has been implemented
for LFC system such as fractional order Proportional-Integral-Derivative (FOPID) [4], Proportional-integral-
derivative-acceleration (PIDA) [5, 6], Model predictive control (MPC) [7, 8], Fuzzy logic controller
(FLC) [9, 10], internal model control (IMC) [11-14], cascade control [15, 16], sliding mode control
(SMC) [17, 18], direct synthesis (DS) approach [19-21], variable structure control [22], active-disturbance-
rejection-control (ADRC) [23-24], H∞ control [25], two degree of freedom (2DoF) control [26, 27],
coefficient diagram method [28] etc.
Debbarma and Dutta [4] have proposed FOPID controller for LFC power system using flower
pollination algorithm to obtain an optimum value of controller gain and the authors also utilize Electric
vehicles as a source in frequency regulation of power system. Raju et al. [5] presents PID plus double
derivative (PID+DD) controller based on ant-lion optimization technique for frequency regulation in multi-
area thermal power system and provide improved performance in terms of settling time (ts), peak value.
The authors also applied random step load at a different time in the three-area thermal power system and
show better robustness of double derivative controller. Guha et al. [6] proposed double derivative PID
controller with the application of multiverse optimization technique for frequency regulation in multi-area

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 10, No. 1, February 2020 : 47 - 60
48
hydro-thermal power system and also consider generation rate constraint (GRC) and governor dead band
(GDB) as non-linearity in the system model. Model predictive control is the modern technique for LFC in
the power system. Linear matrix inequality (LMI) scheme is used to obtain MPC controller gain for LFC in
three areas thermal power system by Shiroei et al. [7]. Ersdal et al. [8] has used MPC for frequency
regulation in the Nordic power system using Kalman filter estimation technique. Sakia et al. [9] have
proposed fuzzy logic plus integral double derivative (FIDD) controller for LFC in the three-area power
system based on bacterial foraging algorithm. Fuzzy logic along with adaptive MPC technique has been
proposed by Kayalvizhi and Kumar [10] for LFC in micro-grid.
Tan [11-13] presents a PID controller via 2DoF-IMC for frequency regulation problem in single-
area as well as a multi-area power system. The authors proposed Anti-GRC strategy to minimize the problem
associated with the application of generation rate constraint in LFC [11]. Saxena and Hote [14] proposed
a robust PID controller via internal model control (IMC) technique for LFC problem in a single area as well
as the multi-area power system. Das et al. [15] have proposed cascade PD-PID controller for LFC in three-
area thermal power system along with GRC using bat-algorithm and its response is superior to PI, PD, PID
controller. Das et al. [16] proposed cascade PI-PD controller optimized using a flower-pollination algorithm
and its performance are improved compared to classical PI, PD, PID controller. It shows that cascade control
performance is better than the classical control technique. Sliding mode controller (SMC) has been designed
by Vrdoljak et al. [17] for LFC in the power system based on state estimation approach and its controller also
work in a non-minimum phase system. However, the sliding mode controller requires knowledge of full state
feedback using state estimation technique. Mi et al. [18] proposed SMC to regulate frequency deviation and
tie-line power exchange for the multi-area power system. The authors used Lyapunov stability to confirm
the frequency is zero. Chen and Seborg [19] presents PID controller design using DS approach for first and
second order system with time delay and its simulation results reveal the better disturbance rejection. Padhan
and Majhi [20] present a new PID tuning method for LFC power system and its controller gains are obtained
by Laurent series expansion of controller transfer function. Anwar and Pan [21] presents a PID controller for
LFC in single as well as multi-area thermal power system using DS method in the frequency domain.
The variable control structure is used to design the Proportional-integral (PI) controller for LFC in
the multi-area power system by Ray et al. [22]. Fu and Tan [23] present the ADRC technique for LFC in
multi-area power system along with the communication delays. The ADRC controller gain is obtained using
the IMC approach. Linear active disturbance rejection controller (LADRC) design has been proposed
by Tang et al. [24] based on the hybrid particle swarm optimization approach for LFC in wind power plant.
Peng et al. [25] proposed H∞ controller for LFC in the networked-based multi-area power system. Debbarma
et al. [26] proposed 2DoF-proportional-integral with double derivative (2DoF-PIDD) controller for frequency
regulation in the three-area thermal power system and controller parameter is obtained using the firefly
algorithm (FA) technique. 2DoF-PID controller has been designed based on teaching learning-based
optimization technique to regulate frequency deviation and tie-line power exchange for multi-area power
system by Sahu et al. [27]. Load frequency controller has been designed by Bernard et al. [28] based on
Coefficient diagram method (CDM) for two-area as well as three area power system.
The parallel control structure (PCS) is also named as 2DoF control structure has been discussed
by Karungaran and Wenjian [29]. Figure 1 shows the generalized form of the PCS which has the ability to
tune the controller to get the desired set-point response and load-disturbance response independently.
The modified PCS scheme has been used to design a PID controller for an unstable process system with
small time delay using DS approach by Ajmeri and Ali [30].
The above literature motivates to design a controller for LFC problem using PCS scheme.
The nomenclature used in this paper is elaborated in Appendix A. In this paper, the PCS scheme has been
used to design PID load frequency controller for a multi-area thermal power system using DS approach.
The major contribution of this paper is as summarized below:
a. The new control structure to design a PID controller for LFC in the thermal power system.
b. The set-point controller and load frequency controller has been designed via pole-placement using direct
synthesis approach.
c. Robustness of the controller has been analysed using uncertainty in the system parameter and random
load has been applied to the system.
d. The proposed PID controller performance has been compared with existing PID design methods for
a single area as well as the multi-area LFC system.
The whole paper is described in five chapters as follows: In chapter 1 described the introduction of
the paper. The problem formulation of the multi-area thermal power system is elaborated in chapter 2.
Controller design methodology for LFC using DS approach has been discussed in chapter 3. In chapter 4
discussed the simulation results of the different case studied of the power system and at last conclusion of the
paper is described in chapter 5.

Int J Elec & Comp Eng ISSN: 2088-8708 
Parallel control structure scheme for load frequency controller design using direct synthes… (Anand Kumar)
49
2. PROBLEM FORMULATION
The parallel control structure (PCS) as shown in Figure 1, which has the nominal model of the plant
(Mn) and actual model of the plant (Ma) is considered to design set-point controller (Kc1) and load-
disturbance controller (Kc2) for load frequency control. The controller Kc1 is used to regulate the set-point
response of the system while Kc2 is used to regulate load-disturbance of the system. The closed-loop response
(∆f) of the PCS is given by d
KM
M
KM
KM
KM
KM
rf
ca
a
ca
cn
cn
ca





























22
2
1
1
11
1
1
(1)
Where r, d, ∆f are the reference input, load disturbance and process output (change in frequency deviation) of
the system. Under nominal condition (Ma=Mn), ∆f may be represented as follows:
d
KM
M
KM
KM
rf
cn
n
cn
cn



















21
1
11
(2)
2.1. Single area power system
The PID controller Kci(s) has been used to maintain the load frequency control of the thermal power
system, which may be written as
sK
s
K
KsK di
ii
pici )( (i=1,2) (3)
Where Kpi, Kii, Kdi are the proportional, integral, derivative constants of ith controller, respectively.
The linearized model of the single-area thermal power system as shown in Figure 2, which is used to design
the controller parameter. The transfer function of the power system model from u to ∆f as shown in
Figure 1 is
Written as
RTTT
TTT
u
f
M
ptg
ptg
n




1
(4)
Where Tg, Tt, Tp are the transfer function of the governor, turbine & generator and load respectively. R is
the speed regulation of the governor.
2.2. Multi-area power system
The controller design technique of single-area power system is extended to a multi-area power
system. The change in frequency, as well as tie-line power exchange between areas, also varies from its
pre-specified value due to load demand fluctuates in a multi-area power system. Area control error (ACE) is
the combination of the small change in frequency deviation and tie-line power exchange and that ACE is
minimized by using a controller gain parameter. The schematic block diagram of a multi-area power system
is shown in Figure 3. The ACE of the ith
area may be represented as
ACEi= ∆ptie,i+βi∆fi (5)
Where βi is the frequency bias factor. The tie-line power exchange (∆ptie,i) between area ith
and other area is
given by












  






N
ij
j
N
ij
j
jijiij
N
ij
j
tieijtiei ftft
s
pp
1 11
1
(6)
Where tij is the synchronizing power coefficient of the multi-area power system. The transfer function model
of the multi-area power system can be represented as
ipitigi
pitigi
ini
RTTT
TTT
M


1
 (7)

 ISSN: 2088-8708
50
The load frequency control in a multi-area power system is as same as single area power system
where the tuning of each single area system is independently with consideration in the modified plant model
as given in (7).
Figure 1. The schematic block diagram of
the parallel control structure
Figure 2. Single-area thermal power system
Figure 3. Schematic block diagram of the control area i
3. CONTROLLER DESIGN METHODOLOGY
In this paper, the parallel control structure (PCS) has been used to design PID controller using direct
synthesis (DS) approach. The Parallel control structure (PCS) has also known as two degrees of freedom
control structure [30] because the set-point controller and load disturbance controller are tuned independently
of each other. Figure 1 shows a basic block diagram of the parallel control structure (PCS). In DS approach,
a desired transfer function of the system is considered for the closed loop transfer function of the system.
By approximating the desired transfer function with closed-loop transfer function of the system,
a mathematical expression of the controller is obtained in terms of the desired transfer function and
the closed-loop transfer function of the system. In PCS decouples the regulatory (load-disturbance rejection)
problem from servomechanism (set-point tracking) problem.
3.1. Set-point tracking controller (Kc1)
The desired set-point closed-loop transfer function Psp(s) (from r to Δf) of the power system is
considered as given by
nsp
Ts
sP
)1(
1
)(

 , (8)
where T is the time constant of the desired set-point reference model, n is the order of the desired set-point
reference model.

51
From (2), the closed loop set-point transfer function (Pr,f) from (∆f to r) may be written as
nc
nc
fr
MK
MK
P
1
1
,
1
 (9)
The closed-loop characteristic equation from (9) may be written as
01 1  nc MK (10)
In the direct synthesis (DS) technique, the controller has been designed by equating the closed loop
set-point transfer function model with that of the desired set-point reference model, which may be written as
)()(, sPsP spfr  (11)
The following aspects have been assumed to obtain such desired performance matching of LFC
system using DS approach:
a. To obtain the desired transient response, the pole of the desired set-point reference model at Ts 1
may be assumed as the pole of the closed-loop system which results in the following equation.
01 1  nc MK for Ts 1 (12)
Or,
RsTsTsT
sK
ptg
c
1
)()()(
1
)(1  (13)
Using (3), (13) may be written as
Z
RsTsTsTT
K
TKK
Ts
ptg
d
ip 









 1
1
11
1
)()()(
1
(14)
b. To obtain better steady state performance of the power system by matching the frequency response of
the two systems at very small frequency point (say 0.001  rad/s) which results in the following
expression.
)()(,  jPjP SPfr  (15)
The (15) may be written as
)(
)()(1
)()(
1
1



jP
jMjK
jMjK
SP
nc
nc


(16)
))(1(
)(
1


jPM
jP
K
SPn
SP
c

 (17)
The expression of PID controller parameter for LFC may be obtained by using (3) and (17)
as given by
RjTjTjTjP
jP
jK
j
K
K
tgpSP
SP
d
i
p
1
)()()(
1
)(1
)(
1
1
1 













(18)
Assuming
RjTjTjTjP
jP
X
tgpSP
SP 1
)()()(
1
)(1
)(












, the (18) may be written as

 ISSN: 2088-8708
52
  ]Im[Re)( 1
11 XjX
k
KjK i
dp 

 (19)
By separating real and imaginary parts of (19), we get the following two equations as given by.
]Re[1 XK p  (20)
]Im[)
1
(1 XkK id 



 (21)
The (14), (20) and (21) may be arranged in matrix form as given by



































]Im[
]Re[
1
0
001
11
1
1
1
X
X
Z
K
K
KTT
d
i
p


(22)
By solving the. (22), the PID controller gain for set-point response will be obtained.
3.2. Load-disturbance controller (Kc2)
The desired load-disturbance closed-loop transfer function PLD(s) (from ∆Pd to Δf) of the power
system is considered as given by
nLD
Ts
Ks
sP
)1(
)(

 , (23)
where T is the time constant of the desired load-disturbance reference model, n is the order of
the desired load-disturbance reference model and the constant gain 21 iKK  . To ensure the frequency
deviation of the system at steady state is zero due to one zero at the origin is placed in the desired
load-disturbance reference model as in (23).
From (2), the closed loop load-disturbance transfer function (Pd,f) from (∆f to d) may be written as
nc
n
fd
MK
M
P
2
,
1
 (24)
The closed-loop characteristic equation from (24) may be written as
01 2  nc MK (25)
In the direct synthesis (DS) technique, the controller has been designed by equating the closed loop
load-disturbance transfer function model with that of the desired load-disturbance reference model, which
may be written as
)()(, sPsP LDfd  (26)
The following aspects have been assumed to obtain such desired performance matching of LFC
system using DS approach:
a. To obtain the desired transient response, the pole of the desired load-disturbance reference model at
Ts 1 may be assumed as the pole of the closed-loop system which results in the following equation.
01 2  nc MK for Ts 1 (27)
Or,
RsTsTsT
sK
ptg
c
1
)()()(
1
)(2  (28)

53
Using (3), (28) may be written as
Z
RsTsTsTT
K
TKK
Ts
ptg
d
ip 









 1
2
22
1
)()()(
1
(29)
b. To obtain better steady state performance of the power system by matching the frequency response of
the two systems at very small frequency point (say 001.0 rad/s) which results in the following
expression.
)()(,  jPjP LDfd  (30)
The (30) may be written as
)(
)()(1
)(
2



jP
jMjK
jM
LD
nc
n


(31)
)(
1
)(
1
2
 jMjP
K
nLD
c  (32)
Or,
RjTjTjTjP
K
tgpLD
c
1
)()()(
1
)(
1
2 

(33)
The expression of PID controller parameter for LFC may be obtained by using (3) and (33)
as given by
RjTjTjTjP
K
jK
j
K
K
tgpld
i
d
i
p
1
)()()(
1
)(
2
2
2
2 











(34)
Assuming
s
Ts
jP
W
n
ld
)1(
)(
1 


and
RjTjTjT
Y
tgp
1
)()()(
1


, the (34) may be written as
  ])Im[]Im[(])Re[Re()( 22
2
22 YWKjYWK
k
KjK ii
i
dp 

 (35)
By separating real and imaginary parts of (35), we get the following two equations as given by.
]Re[]Re[22 YWKK ip  (36)
]Im[])Im[
1
(22 YWkK id 



 (37)
The (29), (36) and (37) may be arranged in matrix form as given by








































]Im[
]Re[
]Im[
1
0
0]Re[1
11
2
2
2
Y
Y
Z
K
K
K
W
W
TT
d
i
p


(38)
By solving the (38), the PID controller gain for load-disturbance will be obtained.

 ISSN: 2088-8708
54
4. SIMULATION RESULTS AND DISCUSSIONS:
In this part, simulation results of a single area, two area and four-area thermal power system has
been considered and show the major advantages of the proposed PID controller design method.
Case study 1: A single-area LFC power system with non-reheated thermal turbine (NRTT) [21] is
considered with the following parameters 120pk , 20pt , 3.0tt , 08.0gt , R=2.4. The desired set-
point and load disturbance transfer function model is considered with T=0.18, n=3. The proposed set-point
PID controller is obtained as Kc1(s) =0.1728+0.7870/s+0.1418s and load- disturbance PID controller is
obtained as Kc2(s) =3.4001+7.0835/s+0.5187s. The load demand ∆Pd=0.01 p.u. at t=0 sec is applied in LFC
power system to verify the performance of the proposed controller. The frequency regulation of the proposed
PID controller is as shown in Figure 4 and its comparative performance of the proposed method is compared
with that of prevalent designed techniques such as Anwar and Pan [21], Padhan and Majhi [20], Tan [11].
The detailed analysis of case study 1 is given in Table 1. The simulation results of case study 1 reveal that
the frequency deviation (∆f), the integral of absolute error (IAE), and settling time (ts) are minimum value
compared to Anwar and Pan [21], Padhan and Majhi [20], Tan [11]. The percentage improvement of peak
value w.r.t Tan is as shown in Table 1 measured with the given formula as
( ) ( )
( )
(39)
To analyses, the robustness of the proposed PID controller, -50% parameter variation in kp and tp of
nominal plant model and frequency deviation of the perturbed plant is shown in Figure 5. The maximum
sensitivity is defined as  )()(11max 2
0


jMjKM ncs 

. The lowest value of Ms indicates the robustness
of the system.
Figure 4. Frequency deviation response for case
study 1 with nominal plant
study 1 with -50% variations in pk and pt
Table 1. Comparative performance of case study 1
Method Kp2 ki2 Kd2 Ms
Nominal plant Perturbed plant
Peak value
(x10-3
)
% Improvement
in term of Peak
value w.r.t Tan
ts
(sec)
IAE
(x10-3
)
Peak value
(x10-3
)
ts
(sec)
IAE
(x10-3
)
Proposed PID 3.40 7.08 0.51 1.92 6.12 54.32 1.02 1.94 6.12 1.02 1.93
Anwar & Pan [21] 1.52 2.50 0.27 1.74 9.02 32.68 1.74 4.20 8.97 1.73 4.20
Padhan & Majhi [20] 1.49 1.30 0.235 1.77 9.6 28.35 4.07 7.68 9.52 4.09 7.68
Tan [11] 0.40 0.63 0.183 1.24 13.4 - 3.51 15.8 13.3 3.58 15.8
Case study 2: A single-area thermal power system with Re-heated turbine (RTD) [21] has been
considered with the following parameters as given by
120pk , 20pt , 3.0tt , 08.0gt , R=2.4, 2.4rt and c = 0.35

55
The desired set-point and load disturbance transfer function model is considered with T=0.15, n=3.
The proposed set-point PID controller is obtained as Kc1(s) = 0.2864+0.9444/s+0.3211s and load- disturbance
PID controller is obtained as Kc2(s) = 8.139+19.03/s+1.0921s. The load demand ∆Pd=0.01 p.u.MW at t=0 sec
is applied in LFC power system to assure the performance of the proposed controller. The frequency
regulation of the proposed PID controller is as shown in Figure 6 and its comparative performance of
the proposed method is compared with that of prevalent designed techniques such as Anwar and Pan [21],
Padhan and Majhi [20] and Tan [11]. The detailed analysis of case study 2 is given in Table 2.
The simulation results of case study 2 reveal the frequency deviation (∆f), the integral of absolute error
(IAE), and settling time (ts) are much better than that of Anwar and Pan [21], Padhan and Majhi [20] and
Tan [11]. The percentage improvement of peak value w.r.t Tan [11] is as shown in Table 2.
To analyses, the robustness of the proposed PID controller, -50% parameter variation in kp and tp of
nominal plant model and frequency deviation of the perturbed plant is shown in Figure 7. In case study 2
the maximum sensitivity Ms is 2.37, which is lower than that of Anwar and Pan [21] Padhan and Majhi [20]
and Tan [11].
study 2 with nominal plant
study 2 with -50% variations in pk and p
Method Kp2 ki2 Kd2 Ms
Nominal plant Perturbed plant
Peak
value
(x10-3
)
%Improvement
in term of Peak
value w.r.t [20]
ts
(sec)
IAE
(x10-3
)
Peak
value
(x10-3
)
ts
(sec)
IAE
(x10-3
)
Proposed PID 8.13 19.03 1.09 2.39 7.06 29.4 1.8 3.82 7.03 1.8 3.77
Anwar & Pan [21] 10.60 2.50 2.57 1.76 4.75 52.5 3.64 4.0 4.73 3.65 4.0
Padhan & Majhi [20] 6.16 1.93 1.16 1.61 7.38 26.2 3.23 5.80 7.34 3.24 5.80
Tan [11] 2.79 1.27 0.787 1.32 10.0 - 7.4 11.4 10.0 7.4 11.4
Case study 3: A two area power system with NRT has been reported from [21] with the following
system parameter as 12021  pp kk , 2021  pp tt , 3.021  tt tt , 08.021  gg tt , R1=R2=2.4,
β1=β2=0.425.
The desired set-point and load disturbance transfer function model is considered with T=0.18, n=3.
The proposed set-point PID controller is obtained as Kc1(s) =-0.4065+1.8517/s+0.3336s and load-
disturbance PID controller is obtained as Kc2(s) =8+16.65/s+1.22s. The load demand ∆Pd=0.01 p.u. at t=0 sec
is applied in LFC power system to verify the performance of the proposed controller. The frequency
regulation of the proposed PID controller is as shown in Figures 8, 9, 10 and the simulation results of
the proposed design method are compared with that of Anwar and Pan [21], Tan [11]. The detailed analysis
of case study 3 is described in Table 3. The simulation results of case study 4 reveal that the percent
overshoot (%OS) in frequency deviation (∆f), the integral of absolute error (IAE), and settling time (ts) are
better than that of Anwar and Pan [21], Tan [11] in each area. The percent overshoot (%OS) in tie-line
power, settling time (ts), IAE is improved than that of Anwar and Pan [21] and Tan [11]. In case study 3
the maximum sensitivity Ms is 2.37, which is higher than that of Anwar and Pan [21] and Tan [11].

 ISSN: 2088-8708
56
Figure 8. Frequency regulation of area 1 for
case study 3
Figure 9. Frequency regulation of area 2 for
case study 3
Figure 10. Tie-line power exchange between area 1&2 for case 3
Method Kp2 Ki2 Kd2 Ms
Area 1
1
f
Area 2
2
f
Tie-line power
tie
P
%OS
(x10-3
)
ts
(sec)
IAE
(x10-3
)
%OS
(x10-3
)
ts
IAE
(x10-3
)
% OS
(x10-4
)
ts
(sec)
IAE
(x10-3
)
Proposed PID 8 16.65 1.22 2.37 5.82 2.86 1.10 2.02 2.86 0.35 0.63 1.54 0.30
Anwar and Pan [21] 3.55 5.95 1.22 1.75 6.38 3.2 1.80 2.50 2.82 0.17 8.50 2.57 0.87
Tan [11] 1.569 2.39660.525 1.43 9.92 3.32 4.18 5.32 3.9 0.65 18.06 3.42 2.09
Case study 4: A four area LFC power system with NRTT as shown in Figure 11 has been
considered from [13] with the following system parameter
Area No. 1: 1201 pk , 201 pt , 3.01 tt , 08.01 gt , R1=2.4, Area No. 2: 5.1122 pk , 252 pt ,
33.02 tt , 072.02 gt , R2=2.7, Area No. 3: 1253 pk , 203 pt , 35.03 tt , 07.03 gt , R3=2.5
Area No. 4: 1154 pk , 154 pt , 375.04 tt , 085.04 gt , R4=2.0
The synchronizing constants are 545.041322321141312  ttttttt and the frequency bias
constants are 425.04321   .

57
Figure 11. Four-area non-reheat thermal turbine (NRTT) system
A four-area interconnected thermal power system is studied to demonstrate the advantage of
the proposed controller. The area no.1, 2, 3 are interconnected to each other, while the area no. 4 is connected
with area 1 only and each area in power is non-reheated thermal turbine (NRTT). The desired set-point and
load disturbance transfer function model for each area are considered with T=0.30, n=3. The proposed
set-point PID controller for each area is obtained as
s
s
sKc 096.0
4722.0
0470.0)(11  , s
s
sKc 1272.0
4214.0
1245.0)(12  ,
s
s
sKc 1130.0
4533.0
0455.0)(13  , s
s
sKc 1160.0
5652.0
0202.0)(14 
The load- disturbance PID controller for each area is obtained as
s
s
sKc 3322.0
8599.1
2483.1)(21  , s
s
sKc 4937.0
6646.2
0189.2)(22 
s
s
sKc 3799.0
0122.2
403.1)(23  , s
s
sKc 3298.0
7192.1
0386.1)(24 
The simulation results of the proposed controller are observed by applying load demand ∆Pd=0.01
p.u.MW at t=1 sec in an area no. 1, 2 and load demand ∆Pd=0.01 p.u.MW at t=20 sec in an area no. 3, 4
simultaneously. The change in frequency deviation is shown in Figure 12 while tie-line power between
interconnected-area is shown in Figure 13. The simulation result of the proposed controller as shown in
Figure 12 and Figure 13 is compared with Tan [13] and observed that the proposed method is better than
Tan [13] in terms of frequency deviation and settling time.
Figure 12. Frequency regulation of four area power system in case study 4

 ISSN: 2088-8708
58
Figure 13. Tie-line power exchange of four-area power system in case 4
4.1. Random loading pattern (RLP)
To assure robustness of the proposed PID controller method, different step change in load applied at
particular interval of time in case study 1. The simulation results as shown in Figure 14 for case study 1
by applying random step change in load. The simulation results reveal the percent overshoot and settling time
is improved even that high magnitude of step load apply in LFC power system. Thus, the proposed design
technique is effective in LFC power system
Figure 14. Frequency regulation of case study 1 with RLP
5. CONCLUSION
In this article, the PCS scheme has been used to design the set-point and load-frequency controller
for a single-area and the multi-area power system using the DS approach. The proposed technique has been
considered for single-area reheat as well as non-reheated thermal turbine power system, two-area
non-reheated system, four-area non-reheated system. Proposed technique show better simulation response in
terms of percent overshoot, settling time, and IAE for the nominal system as well as the perturbed system.
Robustness of the proposed method has been analyzed with system parameter variation and the random load
applied at a particular time in the LFC power system. The main advantages of the proposed technique are to
improved percent overshoot and settling time compared to standard reported literature.
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60
BIOGRAPHIES OF AUTHORS
Anand Kumar: Received Bachelor of Engineering degree in Electrical and Electronic
Engineering from OIST, Bhopal, India, in 2013 and currently pursuing M.Tech-PhD dual degree
from NIT, Patna in Department of Electrical Engineering since 2015. His research interest
includes Load frequency control, Automatic voltage regulator, PID controller, PIDA controller.
Md Nishat Anwar: He obtained his bachelor and master degree in Electrical Engineering from
AMU, Aligarh, India. He obtained his Ph.D. from IIT (ISM), Dhanbad, India in 2015. He has
teaching experience of 4 years and currently working as an Assistant Professor in the Department
of Electrical Engineering, NIT Patna, India. His research interests include industrial control and
automation, PID controller, model predictive control and have several masters and Ph.D. students
working under him. His publication includes 4 papers in referred journals, 12 papers in
international conferences and 5 papers in national conferences.

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