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. 2025 Jul 1;15(1):21663.
doi: 10.1038/s41598-025-05547-3.

An optimal neural network to design generators and stabilizers for multi-machine power systems based on a promoted firefly algorithm

Xiujun Nie  1 , Nan Sun  2 , Buqin Wang  3 , Ganbar Akbari  4   5
Affiliations

An optimal neural network to design generators and stabilizers for multi-machine power systems based on a promoted firefly algorithm

Xiujun Nie et al. Sci Rep. .

Abstract

The purpose of this article is to investigate power system stabilizing (PSS) in multi-machine power systems. In this study, special attention has been given to the role of generator and network modelling which has a direct impact on PSS design. For this purpose, the most important generator models in a power system with several machines in the power network without connection to the infinite bus, and the network connected to the infinite bus have been simulated, and the effects of these models and the infinite bus on the dynamic conditions of the system have been considered. The results of the presented models and the desired network in PSS design have been investigated. To achieve this purpose, an optimal artificial neural network has been utilized, where the parameters of the PID controller are the network output. The network has been optimized by a new promoted version of the firefly algorithm for PSS design and the parameters of this controller in a number of specific working conditions in a multi-machine power system. The method of the optimized neural networks (ANN) has been used for communication and effective use of the parameters obtained through the promoted version of firefly algorithm in a continuous and wide workspace. Numerical simulations considering three-phase short-circuit situations show that ANN/PFF-PSS can decrease load angle overshoot (35.7%) and settling time (28.6%) compared to the conventional PSS. The recovery of voltage is improved also by 9.3%. Through an analysis of systems with and without an infinite bus, the robustness of the proposed stabilizer is validated and shown to be preferred for damping inter-area as well as intra-area oscillations in complicated power networks.

Keywords: Artificial neural network; Dynamic conditions; Infinite bus; Multi-machine power systems; Network modelling; PID controller; Power system stabilizer; Promoted firefly algorithm.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Connection between an individual reference D-Q and the main reference.
Fig. 2
Fig. 2
Power system with four generators.
Fig. 3
Fig. 3
Comparison of the results for the load angle (formula image– formula image).
Fig. 4
Fig. 4
Comparison of the results for the load angle (formula image– formula image).
Fig. 5
Fig. 5
Comparison of the results for the load angle (formula image– formula image).
Fig. 6
Fig. 6
Terminal voltage on bus B.
Fig. 7
Fig. 7
Block diagram of the PFF algorithm.
Fig. 8
Fig. 8
Power system with three generators.
Fig. 9
Fig. 9
Comparison of the results for the load angle (formula image– formula image).
Fig. 10
Fig. 10
Comparison of the results for the load angle (formula image– formula image) for MMPSW and MMPS.
Fig. 11
Fig. 11
Load angle response to three-phase short circuit for p = 1 and q = 0.2 in inter-zone mode.
See this image and copyright information in PMC

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