Parallel processing for the steady state solutions of large-scale non-linear models of power systems

Parallel algorithms are presented for solving large-scale systems of algebraic polynomial equations. The algorithms are based on the so-called probability-one homotopy method and they guarantee finding all the roots. The algorithms are used to obtain all steady-state solutions of the load flow for a three-bus power system. A special probability-one homotopy method is tailored for the load flow to reduce the computational complexity while guaranteeing that all solutions are found. Numerical implementation of the procedures will exploit inherent parallelism in the techniques, providing efficient execution on massively parallel distributed-memory multiprocessors