A Quantitative Approach for Convergence Analysis of a Singularly Perturbed Inverter-Based Microgrid

Abstract

A reduced-order model of a converter-dominated microgrid system may not resemble its full-order system associated with uncertainties. This paper aims to provide a singular perturbation-based contraction framework for model order reduction in converter-dominated uncertain microgrid systems. For this purpose, the concerned microgrid system is modeled as a generalized multi-timescale system, and certain sufficient conditions are derived such that convergence between the trajectories of the uncertain full-order and the corresponding reduced-order model can be guaranteed. The contraction theory-based strategy also provides explicit parameter-dependent expressions for quantifying discrepancies. The derived results are utilized to analyze the inverter-based microgrid system’s convergence behavior and obtain uncertainty bounds on its parameters. Further, the effects of modeling uncertainties and different loading conditions on the reduced-order model’s validity are also discussed. It is observed that for any uncertainty associated with the microgrid parameters that are within the bounds of checkable conditions, the states of the reduced-order microgrid model converge to that of the uncertain full-order system. Further, it is also shown that the obtained discrepancy expressions are more precise than state of the art.