Complex-Frequency Synchronization of Converter-Based Power Systems

In this paper, we study the phase-amplitude coupled dynamics in converter-based power systems from the complex-frequency perspective. A complex-frequency quantity represents the rate of change of the voltage amplitude and the phase angle by its real and imaginary parts, respectively. This emerging notion is of significance as it accommodates the multivariable characteristics of general power systems where active and reactive power are inherently coupled with both the voltage amplitude and phase. We propose the notion of complex-frequency synchronization to study the phase-amplitude coupled stability of a power system with grid-forming virtual oscillator-controlled converters. To do so, we formulate the system into a linear fast system and another linear slow system. This linearity property makes it tractable to analyze fast complex-frequency synchronization and slower voltage stabilization. From the perspective of complex-frequency synchronization, we provide novel insights into the equivalence of virtual oscillator control to complex-power-frequency droop control, the stability analysis methodologies, and the stability criteria. Our study provides a practical solution to address challenging stability issues in converter-dominated power systems.