IEEE Systems, Man and Cybernetics Magazine - January 2023 - 56

0.002
−0.012
−0.01
−0.008
−0.006
−0.004
−0.002
−0.014
Tan (IMC-PID)
−0.005
−0.01
01 2
Time (s)
(a)
0 × 10−4
−6
−4
−2
−8
0.0005
0.001
−0.002
−0.0015
−0.001
−0.0005
51015
Time (s)
(b)
Paliwal (LQR)
Padhan (LS-PID)
Khodabakhshian (MPR-PID)
Anwar (DS-PID)
Proposed
0 × 10−4
−3
−2
−1
0 1 23 45
20 25 30
Padhan (LS-PID)
Anwar (DS-PID)
Singh (LMI-PID)
Singh (PFSFC)
Ghosh (ZN-PID-PSO)
Ghosh (SFC-GSA)
Proposed
02 46 810
computation, unlike in the existing literature. The
improvements in the system performances are demonstrated
through a set of results considering four objectives.
The proposed controller is also tested against
time-varying load disturbances while considering the
nominal and perturbed system parameters to analyze the
performances of the LFC system.
The suitability of the proposed method is demonstrated
through a comparative analysis featuring three different
sets of system parameters, state-of-the-art control techniques
(e.g., IMC, PID, SFC, and LQR), and optimization
techniques (e.g., LMI and PSO) from the existing literature.
The results and the comparative study confirm that the
proposed method successfully maintains system stability
and improves system performances considering different
system parameters, variations in input disturbances, and
system parameters. A system of the nth order would have
()n
21- constraints from the necessary and sufficient
conditions of Routh-Hurwitz criteria. In the future, the
authors endeavor to work with these constraints to
explore solutions of the stability problem in interconnected
LFC systems.
Acknowledgment
This work was supported by the Ministry of Education and
Mathematical Research Impact Centric Support, Science
and Engineering Research Board, Government of India,
for the project " Dynamics of Power Grids Through Complex
Network Theory: A study of Vulnerability, Stability,
and Synchronization " (Sanction MTR/2021/000484). This
article has supplementary downloadable material available
at https://doi.org/10.1109/MSMC.2022.3208393, provided
by the authors.
0.0005
−0.0005
20
02 46 810
40
60
Time (s)
(c)
Figure 4. The comparative responses of the LFC
system considering the system parameters from
(a) Example 1, (b) Example 2, and (c) Example 3.
the fact that the proposed method of minimizing the timedomain
objective within the defined range improves the
system performances in comparison with some of the
methods from the existing literature.
Conclusion
In this article, a generalized range to ensure the stability
and a GSA-based process to optimize the performances
of an LFC system are proposed. Moreover, the number of
decision variables to get the controller gains and to use in
the optimization algorithm is reduced for efficient
56 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE January 2023
Gundes (FCS)
Anwar (DS-PID)
Kumar (DS-PID)
Kumar (DS-PIDA)
Proposed
80 100
About the Authors
Arabinda Ghosh (phee16023@nitsikkim.ac.in) is with the
Department of Electrical and Electronics Engineering,
National Institute of Technology Sikkim, Ravangla 737139,
India. He is a Student Member of IEEE.
Anjan Kumar Ray (akray.nits@gmail.com) is with
the Department of Electrical and Electronics Engineering,
National Institute of Technology Sikkim, Ravangla
737139, India. He is a member of IEEE.
Omkar Singh (omkar20singh@gmail.com) is with
the Department of Electrical and Electronics Engineering,
National Institute of Technology Sikkim, Ravangla
737139, India.
Mo Jamshidi (mojamshidi4@gmail.com) is with the
Department of Electrical and Computer Engineering, University
of Texas at San Antonio, San Antonio, TX 78249
USA. He is a Fellow of IEEE.
References
[1] R. K. Sahu, S. Panda, and S. Padhan, " Optimal gravitational search algorithm for
automatic generation control of interconnected power systems, " Ain Shams Eng. J.,
vol. 5, no. 3, pp. 721-733, Sep. 2014, doi: 10.1016/j.asej.2014.02.004.
∆F (Hz)
∆F (Hz)
∆F (Hz)
https://www.doi.org/10.1109/MSMC.2022.3208393 http://dx.doi.org/10.1016/j.asej.2014.02.004
IEEE Systems, Man and Cybernetics Magazine - January 2023

Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - January 2023
