Hybrid dynamical systems modeling of power systems

Abstract: The increasing integration of renewable energy sources has introduced complex dynamic behavior in power systems that challenge the adequacy of traditional continuous-time modeling approaches. These developments call for modeling frameworks that can capture the intricate interplay between continuous dynamics and discrete events characterizing modern grid operations. Hybrid dynamical systems offer a rigorous foundation for representing such mixed dynamics and have emerged as a valuable tool in power system analysis. Despite their potential, existing studies remain focused on isolated applications or case-specific implementations, offering limited generalizability and guidance for model selection. This paper addresses that gap by providing a comprehensive overview of hybrid modeling approaches relevant to power systems. It critically examines key formalisms, including hybrid automata, switched systems, and piecewise affine models, evaluating their respective strengths, limitations, and suitability across control, stability, and system design tasks. In doing so, the paper identifies open challenges and outlines future research directions to support the systematic application of hybrid methods in renewable-rich, converter-dominated power systems