IEEE Systems, Man and Cybernetics Magazine - January 2023 - 54

(. ). ()sin
-01
6
53tt and shown in Figure S1(b) (available at
https://doi.org/10.1109/MSMC.2022.3208393) [27]. The performances
are demonstrated while considering the nominal
system parameters (Appendix B, available at https://
doi.org/10.1109/MSMC.2022.3208393) as well as the perturbed
system parameters. Variations of
!25 % and !50 %
in parameters kps and Tps are considered. In the proposed
analysis, variations for each parameter are considered
individually as well as simultaneously. Here, the controller
gains obtained using objective O1 are considered. The performances
of the system with all such variations are tabulated
in Table S1 (available at https://doi.org/10.1109/
MSMC.2022.3208393).
It is noted that the proposed method has maintained
system stability considering variations in system parameters
and input disturbances. For instance, a
1
tion in the parameter kps yields d 21 .,
0.002
0.0015
0.001
0.0005
−0.0005
−0.001
−0.0015
−0.002
0.0005
010203040506070
−0.0005
29 30 31 32
Time (s)
(a)
0.005
0.01
−0.005
−0.01
0102030
Nominal
+50% of Nominal kps and Tps
+25% of Nominal kps and Tps
−25% of Nominal kps and Tps
−50% of Nominal kps and Tps
Figure 3. The output responses of the LFC system by
the proposed method considering the nominal and
perturbed system parameters with the (a) variable step
load disturbances and (b) sinusoidal disturbances.
54 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE January 2023
+50 % varia8826827
and a -50%
variation in the parameter kps yields ..5 5952236 In the
proposed method, the 1d value corresponding to the cond
2
1
troller gains obtained using objective O1 is 10.81075, which
satisfies both 1
os
p
us
p
d ranges related to the !50 % variations of
kps. It is observed from the results that the values of ISE for
all such variations are significantly low. The values of
,,
MM and ts with the perturbed system parameters are
on par with the performances by the nominal system
parameters. The output responses of the system considering
the variable step and sinusoidal load disturbances are
shown in Figure 3(a) and (b), respectively. In Figure 3, variations
in parameters kps and Tps are considered. It is noted
that the system responses with all such variations are stable
and very close to each other. The results presented
through Table S1 and Figure 3 testify to the fact that the
proposed method maintains the system stability and performances
against the variations in system parameters
and input disturbances.
0.002
−0.002
40 45 50 55
40 50 60 70
Time (s)
(b)
Comparative Study
The comparative analysis is performed against popular techniques
from the existing literature for three different sets of
system parameters, represented by Examples 1-3 (available
at https://doi.org/10.1109/MSMC.2022.3208393). Here, previously
mentioned values of GSA parameters and a load disturbance
of 0.01 p.u. are considered.
The system parameters of Example 1 as given in
Appendix B (available at https://doi.org/10.1109/MSMC.
2022.3208393) are considered, and the comparative analysis
features some state-of-the-art control techniques,
like the physically referenced feed-forward SFC (PFSFC)
[13], an SFC [11], variants of the PID controller based on
internal model control (IMC) [28], the Laurent series
(LS) [29], direct synthesis (DS) [25], linear matrix
inequality (LMI) [5], and the Ziegler-Nichols (ZN) method
[4], as well as optimization algorithms like particle
swarm optimization (PSO) and GSA. The randomly
drawn controller gains from the chosen ranges in [11]
might not guarantee system stability. Therefore, the
stability of the system with such controller gains needs
to be tested by satisfying (8). Thus, according to the
method of [11], the stability checking for the controller
gains through GSA was performed in each iteration for
each agent. Furthermore, the number of decision variables
was three (equal to the number of controller
components). However, in the proposed method, the
number of decision variable is only one. The controller
gains
12 14 273==(
., .,kk8 163
and k3 =- 449 336
.) corresponding
to O1 are considered for Example 1, and the
results are presented through Table 2 and Figure 4(a).
The proposed method has obtained the minimum ISE
of
0 .00949 10 5
-
#
It is observed that the maximum peak ()Mp
in comparison with the cited works.
has
improved significantly from all cited works. Improvements
in the settling time (ts) from some of the cited
works are also observed.
∆F (Hz)
∆F (Hz)

https://www.doi.org/10.1109/MSMC.2022.3208393 https://www.doi.org/10.1109/MSMC.2022.3208393 https://www.doi.org/10.1109/MSMC.2022.3208393 https://doi.org/10.1109/MSMC.2022.3208393 https://doi.org/10.1109/MSMC.2022.3208393 https://www.doi.org/10.1109/MSMC.2022.3208393 https://www.doi.org/10.1109/MSMC.20223208393 https://www.doi.org/10.1109/MSMC.20223208393

IEEE Systems, Man and Cybernetics Magazine - January 2023

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