Modeling and Transient Stability Analysis for Type-3 Wind Turbines Using Singular Perturbation and Lyapunov Methods

Wind turbines (WTs) are prone to transient instability during weak grid faults, which is caused by their complex interactions. However, it is a challenge to analyze the transient stability, due to high-order and strong nonlinearity. Moreover, the existing works mainly focus on a phase-locked loop (PLL) system while ignoring current control, which cannot fully reflect the transient instability mechanism. To fill this gap, this article studies the transient stability of type-3 WT considering both PLL and current control. First, to simplify the full model of type-3 WT, a slow–fast subsystem is established using the singular perturbation. Then, the sixth-order full model is simplified as a second-order slow subsystem and its small disturbance (i.e., fast subsystem). Based on it, Lyapunov's direct and indirect methods are adopted to analyze the stability of slow and fast subsystems, respectively. Meanwhile, the influence of various factors (e.g., the fault degree, grid inductance, current references, current controller, and PLL controller) on transient stability of type-3 WT is revealed. In addition, the proposed analytical method combining singular perturbation and Lyapunov methods is a new approach to studying transient stability, which can also be applied to other renewable energy resources. Finally, the analysis is validated by experiments.