Mixed Integer Optimization of the Flow Pattern for Stochastic Feeder Reconfiguration

Mixed-integer conic programming provides an approach to solving the Optimal Feeder Reconfiguration (OFR) problem with guarantees on the quality of the solution. Integrating renewable generation into the distribution network and its associated variability renders stochastic OFR, which simultaneously considers several snapshots of the network, a more viable approach. While the established mixed-integer conic program for deterministic OFR can be extended to the stochastic case, the resulting optimization problem that still uses the bus injection relaxation is challenging to solve. This paper proposes a new mixed integer conic optimization of the flow pattern for solving the stochastic OFR. The new optimization framework exploits the perspective reformulation to obtain a tighter relaxation for stochastic OFR, which improves computational performance, and a feasibility pump heuristic to give a feasible solution. The mixed integer optimization of the flow pattern can also provide an initial solution to the mixed integer conic program employing the bus injection relaxation, giving rise to a hierarchical solution approach. Numerical results on stochastic OFR show that the hierarchical approach provides much-improved system performance compared to solutions considering a single snapshot. In addition, the proposed feasibility pump heuristic gives rise to network configurations close to global optimality in several test instances.