A Hybrid Systems View of Inverse Problems in Power System Dynamics

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

0114725 Hiskens Interactions between continuous dynamics and discrete events are an intrinsic part of power system dynamic behavior. Physical devices such as generators exhibit continuous dynamics. On the other hand, event-driven discrete behavior is normally associated with rule-based components. Examples include protection devices and market-dispatch rules. Analysis should accurately capture those interactions. This project will attempt to develop a unified hybrid systems approach to managing power systems. The project will make novel contributions in three fundamental areas: modeling, analysis and algorithms. Earlier work has shown that many hybrid systems can be modeled by a differential-algebraic (DAE) structure that incorporates impulsive action and switching within the algebraic constraints. This representation will be used as the basis for exploring model structures that best satisfy the competing requirements of generality, utility and computational efficiency. To analyze the behavior of switched DAE systems, stability results for (non-switched) DAEs will be combined with existing stability analysis tools for switched ODEs. Lyapunov stability theory underlies this analysis. Algorithms will be developed to address parameter uncertainty, parameter estimation, border-collision bifurcations, critically stable trajectories, boundary value problems, optimal control, switching and issues of uniqueness in forwards and reverse time.