RMS+：增强传统电路模型以捕捉锁相环不稳定性

Electrical circuits are modelled with a constant admittance matrix for steady-state studies and for dynamic studies involving synchronous machines. It is widely considered that this model, called RMS model, is also suitable for capturing low-frequency oscillations in networks with inverters; however, this idea has been challenged by recent research of the Phase-Locked Loop. The EMT model, in contrast, accounts for the dynamics of all circuit components, but its high computational cost limits its application in the analysis of bulk power systems. This paper introduces RMS+, a new circuit model constructed from the raw data of the system, that captures the PLL interactions with the network while reducing the number of state variables. The theoretical framework includes the theory of dynamical systems, particularly, of slow-fast systems. The underlying assumption is that there must be a time-scale separation between the electromagnetic transients, and the PLL dynamics. In this sense, this paper discusses the advantage of the RMS+ model for the analysis of synchronization stability of networks with Grid-following Voltage Source Converters. The model is implemented in a modal analysis tool, and validated in three test networks: a Single Converter Infinite Bus system, a modified version of the WSCC nine-bus system; and the 39-bus system.