Fast Contingency Evaluation Using Concentric Relaxation

A fast method for evaluating contingencies either in real time in an actual emergency or for security monitoring is introduced. This method begins with treating the system or a piece of it (a float) as electrically rigid and then gradually relaxing the results tier by tier to account for the actual flexibility of the transmission. The diagonally dominant or dispersive nature of the power system is utilized. Speed of computation is derived from this exploitation of the structure of the problem which also allows explicit solutions for the intermediate steps. Solutions can be obtained in the vicinity of the contingency or at secondary sites like weak cutsets within the system. Computer illustrations of the method are provided and the convergence of the proposed algorithms is proven. No "equivalent" network is used.