Complex-Frequency Synchronization of Converter-Based Power Systems
Xiuqiang He, Verena Häberle, Florian Dörfler
TL;DR
The paper tackles stability of converter-based power systems under multivariable P/\theta and Q/V coupling by introducing a complex-frequency framework. It shows that grid-forming dVOC is equivalent to a complex-droop controller, enabling a fast linear complex-frequency synchronization on the time scale of rocov and frequency followed by slower voltage stabilization on a linearized power-flow basis. The authors derive both time-domain and frequency-domain stability criteria, including parametric (bar{\delta}, bar{\gamma}) conditions and an admittance-based Nyquist test, and validate the approach with nonlinear EMT simulations and case studies on nonuniform networks and mixed generator-converter systems. The methodology provides a practical, generalizable stability analysis tool for microgrids and HVDC-connected offshore wind, with potential extensions to systems containing synchronous machines. Overall, the work offers a tractable, linearized treatment of a nonlinear, multivariable stability problem via complex-frequency synchronization and demonstrates its efficacy through theory and simulations.
Abstract
In this paper, we study phase-amplitude multivariable dynamics in converter-based power systems from a complex-frequency perspective. Complex frequency represents the rate of change of voltage amplitude and phase angle by its real and imaginary parts, respectively. This emerging notion is of significance as it accommodates the multivariable characteristics of power networks where active and reactive power are inherently coupled with both voltage amplitude and phase. We propose the notion of complex-frequency synchronization to study the phase-amplitude multivariable stability issue in a power system with dispatchable virtual oscillator-controlled (dVOC) converters. To achieve this, we separate the system into linear fast dynamics and approximately linear slow dynamics. The linearity property makes it tractable to analyze fast complex-frequency synchronization and slower voltage stabilization. From the perspective of complex frequency and complex-frequency synchronization, we provide novel insights into the equivalence of dVOC and complex-power-frequency droop control, stability analysis methods, and stability criteria. Our study offers a practical solution to address challenging stability issues in converter-based power systems.