Iterative Equal Area Criterion for Transient Stability Analysis of Grid-tied VSG with High-order Dynamics

Transient stability issues of power converter systems have attracted much attention. Generally, the converter systems are high-order nonlinear due to multiple cascaded control loops, which become obstacles for transient stability analysis. However, many conventional methods, including the well-known Equal Area Criterion, are only applicable for second-order systems without considering damping effects. To fill this gap, an iterative Equal Area Criterion is proposed to handle the transient stability of higher-order systems. Considering the dynamic coupling between active power control and reactive power control loops, the grid-tied VSG system is a typical third-order nonlinear system. Firstly, an implicit equation from the output voltage to the power angle is derived by integral substitution. Then, the dynamic relations between voltage, power angle and frequency are approximated by algebraic equations by iterative calculation of accelerating and decelerating area. The impact of nonlinear damping is also fully captured quantitatively. Both conservatism and complexity are improved compared with previous studies. Simulation and hardware-in-the-loop (HIL) experiment based on RT-Lab are performed to verify the accuracy of the proposed method. By the idea of iterative approximation, the EAC method may release new vitality and be extended for higher- order power converter systems with complicated dynamics.