Parallel Implementations of the Power System Transient Stability Problem on Clusters of Workstations

Power system transient stability analysis computes the response of the rapidly changing electrical components of a power system to a sequence of large disturbances followed by operations to protect the system against the disturbances. Transient stability analysis involves repeatedly solving large, very sparse, time varying non-linear systems over thousands of time steps. In this paper, we present parallel implementations of the transient stability problem in which we use direct methods to solve the linearized systems. One method uses factorization and forward and backward substitution to solve the linear systems. Another method, known as the W-Matrix method, uses factorization and partitioning to increase the amount of parallelism during the solution phase. The third method, the Repeated Substitution method, uses factorization and computations which can be done ahead of time to further increase the amount of parallelism during the solution phase. We discuss the performance of the different methods implemented on a loosely coupled, heterogeneous network of workstations (NOW) and the SP2 cluster of workstations.