Reduced MIP formulation for transmission topology control

The standard optimal power flow minimizes generation costs subject to a fixed transmission network topology. Although the co-optimization of network topology and generation resources results in significant congestion cost avoidance, it requires the solution of a mixed integer program (MIP), which is in general intractable for even moderate size systems. The current MIP formulations use the Bθ power flow model, which does not scale with the number of switchable lines or with the number of monitored/contingent facilities, and as such is not amenable to developing tractable topology control (TC) heuristics. This paper introduces the shift factor MIP formulation of the TC problem, where line openings are emulated through the use of flow-cancelling transactions. The shift factor formulation is very compact and its size is a function of the number of pairs of monitored/contingent transmission elements and the number of switchable lines. Simulation results on the IEEE 118-bus test system show the superior computational performance of the shift factor formulation as compared to the Bθ formulation for small to medium switchable sets.