The Waveform Relaxation Algorithm for Systems of Differential/Algebraic Equations with Power System Applications

This paper reports the continuing effort of the authors towards establishing numerical algorithms suitable for simulating large power systemns dynamics on parallel computer architectures. The feasibility of the waveform relaxation algorithm for power system transient stability simulation was first established by the authors in [2]. In this report the transient stability simulation was approached as the problem of the numerically integrating a (typically large) set of ordinary differential equations (ODEs). Unfortunately, this model is valid in the 0-1 second range only. For longer time intervals the generating unit is described by the differential equations of the machine and the transmission network is modeled by algebraic equations in which the loads can be modeled with nonlinear voltage dependent characteristics. This leads to a more realistic transient stability problem, with the loads in the system prrved, which can be formulated as a set of differential/algebraic equations (DAEs). The principal thrust of this paper is therefore to extend the earlier results of [2] to power systems described by the set of DAEs. The basic formulation of the Waveform Relaxation algorithm for Differential/Algebraic Equations (WRDAE) is introduced here for the first time.