IEEE Systems, Man and Cybernetics Magazine - July 2021 - 36

increasing complexity of system order and variations in
system parameters.
Extension to Two-Area Power Systems
With GDB Nonlinearity in Both Areas
To demonstrate the performance of the proposed controller,
in this section, a two-area nonreheater power system with
GDB nonlinearity in both areas is considered. The GDB is
defined as the magnitude of the total speed change within
which there is no change in the governor valve position [7],
[42]. It is mentioned by the researchers in [42] that the GDB
influences the speed and magnitude of the primary frequency
response. It also causes an oscillation in the system [7].
Furthermore, the existing literature also suggests that the
simulation results of the frequency response match the
actual response of the system when the GDB is included in
the model [42], [43]. Thus, it is nontrivial to test the proposed
controller against an LFC system with the GDB.
The two-area power system model with GDB nonlinearity
is shown in Figure 5. In [7], the authors proposed an
improved ACO (IACO) fuzzy PID controller for the considered
system. In [34], the authors proposed a hybrid BFO
(hBFO) and PSO (hBFO-PSO)-based PI controller, and, in
[32], a crazy PSO (CPSO)-based PI controller was proposed
for the considered system. The system model shown in Figure
5 has an identical nonreheater plant in both areas, connected
through a tie line. The components of the
nonreheater plant are a governor with deadband, turbine,
and generator load model. In the considered system, controller
K ,1area
ler K ,2area
has components 45
has components kk
,,
12
,, and k ,3
kk and k .6
The parameter values for this model are given in the
" Parameter Values for Interconnected Two-Area Power
Systems With GDB " section in " Additional Information. "
For this system, kl
m is -10, ku
m is 10, and md1
the GSA, the number of agents N is 30, ()G 0c
6f= ,, . In
is 100, b is
and controlArea
1
b1
R1
1
+
+
-
+
0.8 -
0.2
π
1 + sTsg1
GDB
a12
-
+
+
b2
-
R2
1
1 + sTsg2
GDB
k6
0.8 -
0.2
π
s
x6
1 + sTt2
Kt2
k5
x5
+
s
x3
k3
+
+ +
k2
1 + sTt1
Kt1
∆Ptie
Tie Line
a12
∆Pd2
-
-
+ +
+
Area 2
Figure 5. An interconnected two-area power system with the GDB along with the proposed controller.
Table 3. The performance of two-area thermal power systems
with GDB [7] by the proposed method.
T f1
ISE
Method
(×10−5)
379.828
34.8
0.0119
ITAE
(×10−3)
CPSO-PI [32] 224.086 703.45
hBFO509.7
PSO-PI
[34]
IACO-FPID [7]
Proposed
5.834
6.4
6.258
0.147
-10.1
-0.82
36 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE July 2021
1.87
2.78
0.653
0.041
-4.3
-0.008
1.64
1.58
0.1199
0.08
-1.2
-0.016
1.15
1.41
Mos (Hz)
(×10−4)
46
55
Mus (Hz)
(×10−3)
-34.2
-33.7
ts (s)
11.19
10.85
Mos (Hz)
(×10−4)
35
48
Tf2
Mus (Hz)
(×10−3)
-37.2
-36.2
ts (s)
12.11
10.95
M os (p.u. MW)
(×10−4)
TPtie
M us (p.u. MW)
(×10−3)
-9.4
-9.2
ts (s)
11.23
9.43
1 + sTps2
Kps2
k4
x4
∆f2
+
x2
∆Pd1
x7
2πT12
s
+
-
-
-
1 + sTps1
Kps1
∆f1
x1
k1
IEEE Systems, Man and Cybernetics Magazine - July 2021

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