Nonlinear Stability Analysis of a Reduced-Order Wind Turbine VSC-grid model Operating in Weak Grid Conditions

In a wind turbine generator (WTG), the behaviour of the Phase-Locked Loop (PLL) under weak grid conditions becomes complex and requires nonlinear analysis to assess the WTG control performance and system stability. This paper introduces a quasi-static reduced-order VSC-grid model of a WTG and evaluates its performance for large-signal disturbances such as changes in current set points and grid short circuit ratio. The time-domain expression for a synchronous reference frame PLL is considered with its nonlinearity intact. Based on the analytical model, a V-δ mechanism is established to identify the PLL synchronisation instability events relevant to a WTG operation. Further, for PLL stable operation, a globally valid stability boundary is discussed. The complex nonlinear PLL dynamics are addressed using phase portraits, where it is shown that the results have direct implications on robust PLL gain tuning guidelines.