Chess Optimizer for Load Frequency Control of Three-Area Multi-Source Renewable Energy Based on PID Plus Second Order Derivative Controller

Renewable energy sources such as solar and wind are increasingly integrated into multi-area power systems. However, their fluctuating and unpredictable characteristics pose challenges for sustaining system stability. Therefore, automatic generation control (AGC) is essential for the continual regulation of power and frequency in the system. This article presents the use of a Proportional–Integral–Derivative plus second-order derivative (PID+DD) controller for load frequency control in a three-area multi-source power system, which includes a thermal reheat power plant with a generation rate constraint (GRC) representing the maximum permissible change rate of generation output of 5% per min , a hydroelectric power plant with a GRC of 370% per min, and a wind power plant where wind speeds vary across areas. The power generation ratio of the three areas is 1:2:4. The controller parameters were tuned using a Chess Optimizer (CO), a metaheuristic inspired by chess move complexity and planning, with specific weights assigned to each type of chess piece. Two load change scenarios were studied: a 10% step load perturbation (10% SLP) and a random load pattern (RLP). Furthermore, experimental results based on the Integral of Time-weighted Absolute Error (ITAE) indicate that the PID+DD controller tuned by the Chess Optimizer achieved the lowest steady-state error in both scenarios (10% SLP and RLP). In Case 1 (SLP), it achieved an ITAE of 25.5072, representing a 9.70% reduction compared to the PID controller and a 1.96% reduction compared to the PI controller. In Case 2 (RLP), it achieved an ITAE of 88.0654, representing a 1.14% reduction compared to the PID controller and a 2.03% reduction compared to the PI controller. These improvements contribute to enhanced oscillation damping, reduced overshoot and undershoot, and improved frequency stability, demonstrating the practical applicability of the proposed approach in future smart grids with high renewable energy penetration.