Contingency constrained optimal power flow solutions in complex network power grids

The optimal power flow problem is concerned with finding a proper operating point for a power network while attempting to minimize a cost function and satisfy network constraints. We analyze the optimal power flow problem subject to contingency constraints and investigate the relationship between the cost of the optimal power flow problem and network topology. We find that when the network topology is that of a small world graph or a scale-free graph, the optimal power flow problem is robust in terms of satisfying contingency constraints.