Frequency regulation of microgrid employing evolutionary game theory-based PID controller with RNN-based disturbance observer

This study develops an evolutionary game theory (EGT)-based proportional-integral-derivative (PID) controller integrated with a recurrent neural network (RNN)-based disturbance observer (DOB) for robust frequency regulation in a hybrid standalone microgrid. The EGT mechanism enables optimised controller tuning based on interactions with the operating environment, while the RNN-DOB estimates and compensates for unknown plant disturbances. Lyapunov analysis establishes the boundedness of the estimation error and guarantees closed-loop stability. Comprehensive comparisons with benchmark controllers demonstrate the effectiveness of the proposed approach under various load and renewable generation disturbances. The superiority of the proposed approach is established both quantitatively and qualitatively, with MAE values of 1.276×10−3, 3.196×10−3, and 1.675×10−3 p.u., and the corresponding RMSE values of 8.159×10−3, 8.055×10−3, and 2.501×10−3 p.u. under the considered disturbance scenarios, while maintaining low peak deviations. Beyond these quantitative results, the proposed scheme exhibits consistent frequency regulation under parameter uncertainties, constant and time-varying communication delays, and cyber-attacks, demonstrating enhanced robustness and resilience. Furthermore, validation using the IEEE 39-bus New England test system demonstrates the scalability of the proposed approach to a larger power-system benchmark. These findings establish the EGT-PID+RNN-DOB as a stable, robust, and resilient control framework for frequency regulation under diverse operating conditions.