Hybrid Power Rate Reaching Law–Based Sliding Mode Control for Grid-Connected PMSG Wind Energy Systems

This paper presents a sliding mode control framework for a grid-connected permanent magnet synchronous generator–based wind energy conversion system using a hybrid power rate reaching law (HPRRL). The dynamic model of the wind turbine and back-to-back converter system connected to the grid is first established. The proposed reaching law is then introduced which combines nonlinear power rate shaping with sliding variable-dependent gain modulation, enabling fast convergence for large tracking errors while maintaining smooth behavior near the sliding surface. Unlike conventional exponential and integral reaching laws with fixed convergence characteristics, the proposed formulation provides flexible reaching dynamics with reduced chattering. The HPRRL is now incorporated into the outer loop sliding mode controllers to achieve rotor speed regulation for maximum power point tracking and dc-link voltage regulation for grid-side power control. A unified stability analysis is further presented through a Lyapunov-based approach, confirming the closed loop stability of the proposed controller framework. Finally, simulation results under various wind profiles show that the proposed HPRRL achieves nearly 41% lower speed overshoot, reduces the settling time from about 0.56 s to 0.24 s, achieves over 75% reduction in dc-link voltage overshoot, and lowers grid current THD by nearly 38% compared with existing SMC-based reaching laws. Also, the effectiveness of the proposed framework is further supported through real-time testing using the OPAL-RT simulator platform.