Analytical goal programming model for optimal restoration of distribution systems

This paper presents a optimization approach for solving the distribution systems´ restoration problem. The problem is formulated as a goal programming model aiming to establish the combination of devices to be operated in order to maximize the number of customers restored in the post-fault period as well as to minimize the time required by the network reconfiguration process. This approach considers devices with arbitrary switching times, allowing the modeling of operation of automatic and manual switches. The viability of restoration is ensured through operational and topological constraints, including the system´s voltage profile, spare capacity and the radial post-reconfiguration topology. A linear version of the power flow in terms of nodal injection of current is proposed in order to take into account such constraints. The equations are formulated as functions of the state of available sectionalizing switches in the feeder. A case study using a real distribution feeder is used to demonstrate the technique and the optimal solutions of the model obtained in reduced processing times.