Numerical simulation of Stochastic Differential Algebraic Equations for power system transient stability with random loads

This paper summarizes numerical methods for Stochastic Differential Algebraic Equations (SDAEs) with which power system are modeled. The loads are modeled as random variables which appear in algebraic equations. The properties of numerical methods for Differential Algebraic Equations (DAE) and Stochastic Differential Equations (SDE) are reviewed and the first-order backward euler method is proposed for SDAE in power system transient stability simulation. Illustration examples are given on a single-machine-infinite-bus (SMIB) system.

I Introduction

Transient stability analysis in power systems plays an important role in dynamic security assessment to validate the system's ability to remain in synchronism following a major disturbance such as a short circuit. Usually a large set of nonlinear differential-algebraic equations (DAEs) is used to describe system behavior, which can be called semi-explicit index-l DAEs of the form

$$\eqalignno{\dot{x} & = f(x, y)&\hbox{(1a)}\cr 0 & = g(x, y)&\hbox{(1b)}}$$ where and are the vectors of differential variables and algebraic variables respectively and and are sufficiently differentiable vector functions of the same dimensions as and , respectively.