Multi‐Input Backstepping Control for Transient Stability Enhancement in Power Systems With PMSG‐Based Wind Turbines and UPFC

This paper addresses the enhancement of power system stability by incorporating the coordinated operation of Permanent Magnet Synchronous Generator (PMSG) and Unified Power Flow Controller (UPFC). A multi‐input backstepping control strategy is designed to improve the power system's transient performance, while its asymptotic stability is rigorously verified through Lyapunov's direct method. The proposed control law acts on both PMSG and UPFC inputs to increase the system's critical clearing time under fault conditions. The full nonlinear dynamics of the PMSG and UPFC are explicitly integrated into the control scheme. To achieve optimal performance, the Particle Swarm Optimisation (PSO) algorithm is employed to fine‐tune the gains of the controller. Furthermore, a second‐order sliding‐mode observer (SOSMO) is implemented to estimate the time derivatives of selected voltage signals. The designed controller also incorporates physical and operational constraints on control inputs, synchronous generator variables, and system currents and voltages. The effectiveness and robustness of the proposed approach are validated through simulations conducted on the standard New England 39‐bus test system and also the 118‐bus system. Comparative results with a similar system utilising a Doubly‐Fed Induction Generator (DFIG) demonstrate that the proposed controller achieves superior transient stability and robustness against parameter uncertainties, as well as variations in fault location and timing.