Computational algorithms for unstable and stable (load flow) equilibria of a power system

Fast parallel algorithms to compute unstable equilibria in the state space of a large electric power system are introduced and analyzed. The approach utilizes cluster separation. The algorithm proposed for finding stable equilibria is a novel and is much faster in parallel implementation than the sparse Newton-Raphson technique. The algorithm proposed for finding unstable equilibria is not only novel but is the only available algorithm for computing unstable equilibria. Necessary and sufficient conditions for stability and instability checking have been developed. These conditions give some indications how the (N-1) unstable equilibria can be located through cluster structures. Simulation results are also given to show the convergence of the algorithms. Time-complexity analysis of parallel implementation is described and shows the potential of the algorithms