Multi-stage sliding mode control design with optimal state estimator for load frequency regulation in hybrid-source...

The rapid growth of renewable energy sources (RES) and the increasing complexity of modern power systems (PSs) have introduced significant challenges for automatic load frequency control (LFC), including large uncertainties, disturbances, and reduced system inertia. These issues limit the effectiveness of conventional control strategies and may threaten system stability and reliability. To address these problems, this paper proposes a novel multi-stage sliding mode control (SMC) scheme integrated with an optimal state estimator (OSE) for LFC in multi-area hybrid PSs (HPSs) consisting of conventional thermal, hydro, and gas units together with battery and flywheel energy storage and renewable sources such as photovoltaic and wind power. The OSE is first designed to provide accurate state feedback under uncertain operating conditions, thereby improving control robustness. Based on these estimates, a new multi-term sliding surface is formulated to ensure fast dynamic response and strong resilience against system uncertainties. The stability of the proposed approach is mathematically validated, and extensive simulations are performed under various load changes, uncertainty scenarios, and communication delay in both isolated and interconnected HPSs. The results demonstrate that the proposed controller outperforms recently developed SMC-based approaches by reducing overshoot and undershoot by up to 46.4%, undershoot by up to 48.1%, and shortening settling time by up to 23.8%, while also eliminating chattering. These improvements highlight the robustness, reliability, and practical applicability of the proposed scheme for future complex PSs with high RES penetration.