Security-constrained optimal power flow (SCOPF) problems are becoming increasingly important in short-term operations planning tasks in modern power systems. Traditionally, the objective of SCOPF problems is to find the generation operating point either minimizing generation costs or maximizing network loading. The most important feature here is that the optimal operating point has to be feasible both under healthy and contingency conditions, where contingencies generally include line and generation asset failures. In other words, solutions to SCOPF problems are essentially passive and defensive in nature presupposing that the network operator has too little time or ways to mitigate the effects of a sudden failure. As practical electricity networks are quite large, the ensuing size of SCOPF problem instances are very large too---for example, the small IEEE 30 node system with 41 lines and 38 allowable single line contingencies results in a SCOPF containing 3184 inequalities.
Evidence from research and industry practice is showing that security-constrained optimal power flow problems are ultimately constrained by very few of those inequalities---for example, the Brazilian national system operator claims that it needs only about 130 inequalities to represent the N-1 secure operation of its 50,000 node network! These few inequalities are part of what we call the umbrella contingency set of networks. The inequalities which are members of the set of umbrella contingencies are both necessary and sufficient to ensure the security of the entire system as they form an "umbrella" over all the other contingencies. So far, however, there was no systematic method to identify which contingencies are members of the umbrella set.
In this talk, we formulate the umbrella contingency discovery problem (UCD) for SCOPF problems with linear network models. The UCD is formulated first as a mixed-integer linear program and we show how that it can be reformulated as a linear program. We also show that the resulting UCD is easily decomposable and lends itself well to parallel computation. We provide preliminary results from standard test networks and show how the UCD is promising as a pre-processing step to speed up SCOPF solutions.