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

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