A Lyapunov Framework for Nested Dynamical Systems on Multiple Time Scales With Application to Converter-Based Power Systems

• 成果类型: Article
• 署名作者: Subotic, Irina; Gross, Dominic; Colombino, Marcello; Doerfler, Florian
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3047368
• 发表日期: 2021
• 页码: 5909-5924
• 关键词: Power system stability; asymptotic stability; Power system dynamics; Stability criteria; oscillators; Lyapunov methods; Analytical models; stability of NL systems; network analysis and control; MODEL; controller reduction; virtual oscillator control; electrical power systems

摘要

In this article, we present a Lyapunov framework for establishing stability with respect to a compact set for a nested interconnection of nonlinear dynamical systems ordered from slow to fast according to their convergence rates, where each of the dynamics is influenced only by the slower dynamics and the successive fastest one. The proposed approach explicitly considers more than two time scales, it does not require modeling multiple time scales via scalar time constants, and provides analytic bounds that make ad-hoc time-scale separation arguments rigorous. Motivated by the technical results, we develop a novel control strategy for a grid-forming power converter that consists of an inner cascaded two-degree-of-freedom controller and dispatchable virtual oscillator control as a reference model. The resulting closed-loop converter-based ac power system is in the form of a nested system with multiple time scales. We apply our technical results to obtain explicit bounds on the controller set points, branch powers, and control gains that guarantee almost global asymptotic stability of the multiconverter ac power system with respect to a prespecified solution of the ac power flow equations. Finally, we validate the performance of the proposed control structure in a case study using a high-fidelity simulation with detailed hardware validated converter models.