The stability of the grid-connected voltge source converter (VSC) with limits of phase locked loop (PLL) is investigated in this letter. The studied system is a nonlinear switched system that consists of three subsystems and a switching rule that connects switching between these subsystems. It is proved that the three subsystems share one common Lyapunov function, and the derivation of the constructed Lyapunov function for each subsystem with respect to time is negative. As a result, one conservative stability region for the studied switched system is derived, and the system can be asymptotically stable under arbitrary switching within the derived stability region. Numerical results show that implementing limits of PLL is one simple and effective approach to enhance the system stability of VSCs.

中文翻译：

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基于通用Lyapunov函数的锁相环极限VSC稳定性分析


本文研究了具有锁相环 (PLL) 限制的并网电压源转换器 (VSC) 的稳定性。研究的系统是一个非线性切换系统，由三个子系统和连接这些子系统之间切换的切换规则组成。证明了三个子系统共享一个共同的Lyapunov函数，并且每个子系统构造的Lyapunov函数对时间的导数都是负的。结果，导出了所研究的切换系统的一个保守稳定区域，并且系统在导出的稳定区域内的任意切换下都可以渐近稳定。数值结果表明，实施PLL限制是提高VSC系统稳定性的一种简单有效的方法。