Transient Stability Analysis for Grid-Tied VSG Considering High-Order Nonlinear Interactions Between Active and Reactive Power Control Loops

Transient stability issues of power converter systems have attracted much attention. Generally, the converter systems behave in high-order nonlinear dynamics due to multiple cascaded control loops, which become obstacles for transient stability analysis. Considering the dynamic coupling between active power and reactive power control loops, the grid-tied virtual synchronous generators (VSG) system is a third-order nonlinear system. Including the equal area criterion (EAC), many conventional methods are only applicable to second-order systems and cannot fully capture damping effects. To fill this gap, a novel iterative EAC method is proposed to handle the transient stability of the third-order VSG system. First, an implicit relationship from the output voltage to the power angle is derived by integral substitution. From energy aspects, the dynamic relations between voltage, power angle, and frequency are approximated by algebraic equations through iterative calculation. The impact of nonlinear damping is also fully captured quantitatively. Both conservatism and quantity of computation are improved compared with previous studies. Furthermore, the critical clearing angles under different disturbance forms and degrees are derived. In addition, some discussions about current limiters' influence and different controller parameters' influence are given. Simulation and hardware-in-the-loop experiments based on RT-Lab are conducted to verify the accuracy of the proposed method.