Perspective Reformulations of the Two-Level Service Restoration Problem

This article presents the two-level service restoration problem, which involves finding a reconfigured network suitable for serving the loads while a fault affecting some components is attended to. The first stage minimizes the actual branch overload in the reconfigured network. In contrast, the second stage chooses the network structure that maintains an acceptable voltage profile while preserving the overload level of the first stage. The two-level solution paradigm differs from some real-life implementations of service restoration programs based on the secure flow pattern concept, which employs successive branch openings to minimize a load balancing index. The proposed two-level service restoration problem is solved using a sequence of two mixed-integer conic programs, for which solvers that guarantee global optimality are available. The presented perspective reformulation combines tight relaxations in mixed-integer conic programming with the polyhedral representation to expedite the search for the reconfigured network. Numerical results are reported on networks that have over 900 switchable branches. The results demonstrate that while the secure flow pattern implementation relying on branch opening provides results close to the globally optimal load balancing, much improvement to the actual branch overloads and voltage profile is attained from the proposed two-level service restoration problem.