Convex Optimization Methods for the Restoration Topology and the Switching Sequence Restoration in Distribution Systems

The restoration process in an electrical distribution system (EDS) tries to reestablish the service for the disconnected loads after a fault through the opening/closing of interconnection switches. Most of the restoration methods define the topology of the EDS in terms of the corresponding switching operations that minimize the not-served power. However, the sequence and operation time in which these switches are operated are usually disregarded, which is critical for identifying the energy not supplied. In that context, two convex models are studied in this paper to solve the restoration process (identification of topology and sequence). The identification of the restoration topology is based on a previous convex proposal, while novel formulations are presented for the sequence problem minimizing the energy not supplied over the set of steps representing the restoration process. A mixed-integer conic programming model is first obtained; then, a linearization technique is applied to obtain a mixed-integer linear programming formulation, which requires less computational effort to solve. Tests performed on two feeders of the IEEE 53-node system demonstrate that both models can obtain the optimal switching restoration sequence. It is also concluded that the linear formulation outperforms the conic model in terms of solution time.