Due to limited damping, under critical and dynamically changing loading circumstances, the electrical power system penetrated with renewable energy sources (RES) is a complex nonlinear system that regularly causes substantial variations in tie-line active power and frequency. The power system's generation-demand equilibrium point moves as a result of a contingency, making it more difficult to reestablish a tolerable equilibrium point using common control techniques. The interesting capabilities of capacitive energy storage units (CES) combined with sophisticated control methods provide a noteworthy solution to improve network damping and enhance frequency regulation. The Gravitational Search Algorithm (GSA) is used in this work to optimize the tuning of an Active Disturbance Rejection Control (ADRC) regulator for LFC of a two-area hybrid system comprising a photovoltaic (PV) system, a thermal non-reheating system, and CES. To efficiently tune the controller settings, the GSA-ADRC method constructs and fixes a time-domain-based objective function. Based on settling times and other indicators, our proposed GSA-ADRC controller is compared to Firefly Algorithm-PI controller and Genetic Algorithm-PI controller inside a test system configuration with and without CES. The results of our simulations demonstrate that the proposed GSA-ADRC controller, combined with CES, outperforms the selected benchmark PI controllers.