A Computational Analysis of the Optimal Power Flow Problem

The optimal power flow problem is concerned with finding a proper operating point for a power network while attempting to minimize some cost function and satisfy several network constraints. In this report we analyze the optimal power flow problem subject to contingency constraints, which demands that there be enough power to meet demands in the network in the event of contingencies such as a fault in some transmission line or the loss of a generator. We develop numerical algorithms to handle this problem for the e− 1 security constrained optimal power flow problem. We also 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 quite robust in terms of satisfying contingency constraints.