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Hybrid dynamical systems modeling of power systems

B. G. Odunlami, M. Netto, Y. Susuki

TL;DR

The paper tackles the challenge of accurately modeling modern power systems where rapid discrete events and mode changes accompany continuous dynamics due to high renewable penetration. It surveys hybrid dynamical system formalisms—hybrid automata, switched systems, mixed logical dynamical systems, and set-oriented frameworks—and analyzes their suitability for modeling, estimation, control, and verification tasks in converter-dominated grids. Through a comparative study and a grid-connected inverter example, the work clarifies the strengths and limitations of each framework, offers guidelines for model selection, and identifies key research gaps in scalability, differentiability of resets, and real-time verification. The findings provide a practical roadmap for applying HDS methods to improve reliability, resilience, and performance of renewable-rich power systems, with implications for control design, state estimation, and safety verification.

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

Hybrid dynamical systems modeling of power systems

TL;DR

The paper tackles the challenge of accurately modeling modern power systems where rapid discrete events and mode changes accompany continuous dynamics due to high renewable penetration. It surveys hybrid dynamical system formalisms—hybrid automata, switched systems, mixed logical dynamical systems, and set-oriented frameworks—and analyzes their suitability for modeling, estimation, control, and verification tasks in converter-dominated grids. Through a comparative study and a grid-connected inverter example, the work clarifies the strengths and limitations of each framework, offers guidelines for model selection, and identifies key research gaps in scalability, differentiability of resets, and real-time verification. The findings provide a practical roadmap for applying HDS methods to improve reliability, resilience, and performance of renewable-rich power systems, with implications for control design, state estimation, and safety verification.

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

Paper Structure

This paper contains 31 sections, 22 equations, 12 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Overview of HDS modeling frameworks
  3. Set-oriented modeling framework
  4. Illustrative example
  5. Set-valued generalization for uncertain dynamics
  6. Hybrid automaton modeling framework
  7. Switched systems modeling framework
  8. Mixed logical dynamical systems modeling framework
  9. Model equivalence and other relevant frameworks
  10. Model selection of HDS methods in power systems
  11. Non-differentiable reset maps in model selection
  12. Comparative study of HDS and purely continuous for modeling and estimation
  13. Grid-connected inverter under mode switching
  14. Safety verification and reachability analysis
  15. Applications in power systems
  16. ...and 16 more sections

Figures (12)

  • Figure 1: Overview of proposed review and hybrid dynamical systems topics.
  • Figure 2: Illustrative example: Single generator–load bus with switching between two identical transmission lines.
  • Figure 3: Hybrid automata model.
  • Figure 4: Phase portrait of a single generator–load bus system with switching between two identical transmission lines using five modeling formalisms.
  • Figure 5: Variation of voltage in d- and q-axes for hybrid and continuous models.
  • ...and 7 more figures