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.

中文翻译：

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考虑有功功率控制环和无功功率控制环之间高阶非线性相互作用的并网 VSG 暂态稳定分析

功率变换器系统的暂态稳定性问题引起了人们的广泛关注。通常，由于多个级联控制环路，变流器系统表现出高阶非线性动态，这成为暂态稳定性分析的障碍。考虑到有功功率和无功功率控制回路之间的动态耦合，并网虚拟同步发电机（VSG）系统是一个三阶非线性系统。包括等面积准则（EAC）在内，许多传统方法仅适用于二阶系统，无法完全捕捉阻尼效应。为了填补这一空白，提出了一种新的迭代 EAC 方法来处理三阶 VSG 系统的暂态稳定性。首先，通过积分代换导出输出电压与功率角的隐式关系。从能量方面来看，通过迭代计算，用代数方程逼近电压、功角和频率之间的动态关系。非线性阻尼的影响也被完全定量地捕捉到。与之前的研究相比，保守性和计算量都有所提高。此外，还推导了不同扰动形式和程度下的临界间隙角。此外，还讨论了限流器的影响和不同控制器参数的影响。基于RT-Lab进行仿真和半实物实验验证了所提方法的准确性。