Terminal Voltage and Load Frequency Regulation in a Nonlinear Four-Area Multi-Source Interconnected Power System via Arithmetic Optimization Algorithm

The increasing integration of renewable energy sources (RES) and rising energy demand have created challenges in maintaining stability in interconnected power systems, particularly in terms of frequency, voltage, and tie-line power. While traditional load frequency control (LFC) and automatic voltage regulation (AVR) strategies have been widely studied, they often fail to address the complexities introduced by RES and nonlinear system dynamics such as boiler dynamics, governor deadband, and generation rate constraints. This study introduces the Arithmetic Optimization Algorithm (AOA)-optimized PI(1+DD) controller, chosen for its ability to effectively optimize control parameters in highly nonlinear and dynamic environments. AOA, a novel metaheuristic technique, was selected due to its robustness, efficiency in exploring large search spaces, and ability to converge to optimal solutions even in the presence of complex system dynamics. The proposed controller outperforms classical methods such as PI, PID, I–P, I–PD, and PI–PD in terms of key performance metrics, achieving a settling time of 7.5 s (compared to 10.5 s for PI), overshoot of 2.8% (compared to 5.2% for PI), rise time of 0.7 s (compared to 1.2 s for PI), and steady-state error of 0.05% (compared to 0.3% for PI). Additionally, sensitivity analysis confirms the robustness of the AOA-optimized controller under ±25% variations in turbine and speed control parameters, as well as in the presence of nonlinearities, demonstrating its potential as a reliable solution for improving grid performance in complex, nonlinear multi-area interconnected power systems.