Open Access

ARTICLE

A Hybrid MZOA-PSO Optimized Cascaded PI(1+DD)-PI-PID Controller for Frequency Stability of Interconnected Power Systems with Renewable Energy and Electric Vehicles

AL-Wesabi Ibrahim¹, Hassan M. Hussein Farh^2,*, Jiazhu Xu^1,*, Mohamad A. Alawad², Ahmed Alqurashi³, Abdullrahman A. Al-Shamma’a²

1 College of Electrical and Information Engineering, Hunan University, Changsha, China
2 Electrical Engineering Department, College of Engineering, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
3 Electrical Engineering Department, College of Engineering and Architecture, Umm Al-Qura University, Makkah, Saudi Arabia

* Corresponding Authors: Hassan M. Hussein Farh. Email: ; Jiazhu Xu. Email:

(This article belongs to the Special Issue: Advanced Artificial Intelligence and Machine Learning Methods Applied to Energy Systems, 2nd Edition)

Computer Modeling in Engineering & Sciences 2026, 148(1), 22 https://doi.org/10.32604/cmes.2026.081371

Received 28 February 2026; Accepted 15 April 2026; Issue published 27 July 2026

Abstract

Load frequency control (LFC) in interconnected power systems has always been a challenging task in the presence of uncertainty and variability in the power systems arising primarily due to the integration of renewable energy sources and the impact of electric vehicles on the power system. Although various PI/PID and other advanced control strategies have been employed for LFC in power systems, the existing methods have shown some limitations in terms of dynamic flexibility and robustness in the presence of nonlinearities and couplings in the power systems. Moreover, the optimization methods employed for the tuning of the controllers have shown some limitations in terms of the balance between global and local search abilities of the optimization functions. To overcome the limitations of the existing methods and optimization functions, a hybrid Modified Zebra Optimization Algorithm-Particle Swarm Optimization (MZOA-PSO) is presented in this paper for the optimization of a cascaded PI(1+DD)-PI-PID controller for LFC in power systems. The MZOA enhances the original ZOA by chaotic initialization, adaptive parameter control, and Lévy-flight foraging to improve the global search ability, while PSO ensures efficient local search ability. The optimizer is first validated using four benchmark functions, achieving the global optimum for the Booth and Zakharov functions, a mean value of 2.13 × 10⁻²⁸ with a 98% success rate for Rosenbrock, and 3.21 × 10⁻⁸¹ for Schwefel 2.22. Under a 1% step load perturbation, the proposed controller achieves a 13 s settling time, zero negative deviation in Area 2, a maximum positive excursion of 0.10 Hz, and tie-line undershoot limited to −0.10 p.u. Under random load variations, deviations remain within ±0.03 Hz and ±0.02 p.u. Under RES and EV integration, the peak frequency deviation is reduced to 0.46 Hz in Area 1. These results confirm that the proposed hybrid MZOA-PSO tuned cascaded controller provides improved damping, faster stabilization, and stronger robustness for modern interconnected LFC systems.

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Keywords

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