Intelligent Frequency Regulation of Hybrid Renewable Power Systems Using Covariance Matrix Adaptation Evolution Strategy

Maintaining frequency stability in modern interconnected power systems has become increasingly challenging due to the growing penetration of renewable energy sources, energy storage systems, and hybrid AC/DC transmission networks. This study proposes an intelligent load frequency control strategy based on a Covariance Matrix Adaptation Evolution Strategy (CMA-ES)-optimized PID controller for interconnected multi-area power systems. The proposed approach is evaluated on several power system configurations, including two-area and three-area systems as well as hybrid AC/DC networks incorporating hydroelectric and thermal generating units, high-voltage direct-current transmission links, superconducting magnetic energy storage, and renewable energy integration. The controller parameters are optimized using CMA-ES and validated through extensive simulations under step load disturbances. To ensure robustness, the optimization process is repeated over 100 independent runs. The proposed method is compared with Particle Swarm Optimization, Gray Wolf Optimization, and Honey Badger Algorithm-based PID controllers using both dynamic performance measures and error-based performance indices. Simulation results demonstrate that the CMA-ES-based controller consistently achieves faster settling times, smaller frequency deviations, lower Tie-line Power oscillations, and improved damping characteristics across all investigated scenarios. In the two-area system, the proposed method reduces the Integral of Time Absolute Error by approximately 73.5% compared with the Gray Wolf Optimization approach. For more complex hybrid systems incorporating high-voltage direct-current links and energy storage units, substantial reductions in performance indices are also achieved. Furthermore, the proposed controller effectively mitigates oscillations caused by renewable power fluctuations and enhances inter-area coordination. The results confirm that CMA-ES provides an effective and robust framework for frequency regulation in modern interconnected power systems with high renewable energy penetration.