Stochastic OPF by constraint relaxation

This paper describes an algorithm for the solution of the stochastic optimal power flow problem. The stochastic OPF minimizes the total cost of a base case operating state plus the expected cost of recovery from contingencies such as line or generator outages. The algorithm presented is based on a relaxation method in which constraints are modeled only as they become active. This method efficiently models all transmission constraints using a rank-one update to the distribution matrix. Numerical examples illustrate the dramatic reduction in problem size achieved in practice by constraint relaxation. They also confirm that the expected cost of a dispatch that accommodates failures according to their probability of occurrence is less than the cost of a preventive operating mode.