Sliding Mode Control Based on PID Switching Surface Design for Terminal Voltage and Load Frequency Control in Multi‐Area Power Systems

ABSTRACT

This paper presents a two‐stage decentralised sliding mode control (SMC) framework for the regulation of terminal voltage and load frequency control in multi‐area power systems (MAPS) with solar energy integration. Unlike conventional studies that treat automatic voltage regulation (AVR) and load frequency control (LFC) as decoupled subsystems, a combined state‐space model of MAPS is first formulated to capture the electromechanical coupling between the two loops while representing load disturbances, parameter uncertainties, and solar power output fluctuations. Based on this model, a decentralised PID switching surface of SMC is designed for each control area, and the asymptotic stability of the sliding motion is rigorously established through a Lyapunov‐based theorem whose sufficient conditions are derived as solvable linear matrix inequalities (LMIs). A continuous robust sliding mode control (CRSMC) law is then synthesised to drive the system trajectories onto this surface and remain on it thereafter, while the continuous control structure substantially attenuates the chattering phenomenon inherent to conventional SMC schemes. The results show that the proposed controller preserves closed‐loop stability under wide‐range parameter uncertainty, achieves markedly reduced frequency and voltage overshoot, faster settling time, and near‐complete rejection of solar power disturbances relative to the existing strategies. These findings confirm that the proposed PID switching surface combined with the continuous decentralised SMC law offers a theoretically grounded and practically effective solution to the combined voltage–frequency regulation problem in multi‐area power systems with solar energy integration.