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.