ODE Transformations of Nonlinear DAE Power Systems

TL;DR

This paper introduces two mathematical transformations that convert nonlinear DAE power system models into ODE models, making them easier to analyze and control while preserving their full nonlinear structure.

Contribution

The paper presents novel transformations that convert nonlinear DAE power system models into equivalent ODE models, facilitating the application of existing control and estimation techniques.

Findings

Transformations retain full nonlinear DAE structure

Models are effective and computationally scalable

Enables use of ODE-based control algorithms

Abstract

Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator transients and the algebraic one captures network power flow. While the literature on control and monitoring for ordinary differential equation (ODE) models of power systems is indeed rich, that on DAE systems is \textit{not}. DAE system theory is less understood in the context of power system dynamics. To that end, this letter presents two new mathematical transformations for nonlinear DAE models that yield nonlinear ODE models whilst retaining the complete nonlinear DAE structure and algebraic variables. Such transformations make (more accurate) power system DAE models more amenable to a host of control and state estimation algorithms designed for ODE dynamical systems. We showcase that the proposed models are effective, simple, and computationally scalable.