Identification of Umbrella Constraints in DC-Based Security-Constrained Optimal Power Flow

Security-constrained optimal power flow (SCOPF) problems are essential tools to transmission system operators for long-term and operational planning and real-time operation. The general goal of SCOPF problems is to optimize electricity network operation while ensuring that operational and planning decisions are consistent with technical limits under both pre- and post-contingency states. The solution of SCOPF problems is challenging because of the inherent size and scope of modern grids. As empirical evidence and longstanding operator experience show, relatively few of the constraints of SCOPF problems actually serve to enclose their feasible region. Hence, all those constraints not contributing directly to set up the SCOPF feasible space are superfluous and could be discarded. In light of this observation, this paper proposes an optimization-based approach for identifying so-called umbrella constraints in SCOPF problems where the network operation is approximated by the dc power flow. Umbrella constraints are constraints which are necessary and sufficient to the description of the feasible set of an SCOPF problem. The resulting umbrella constraint discovery problem (UCD) is a convex optimization problem with a linear objective function. For SCOPF problems of practical importance, the UCD is also quite large and requires the use of a decomposition technique. In this paper, we concentrate on an SCOPF formulation for preventive security generation dispatch. We show that by removing superfluous constraints, the resulting sizes of SCOPF problems are much smaller and can be solved significantly faster.