An exact optimization strategy for the restoration problem in radial distribution systems with switches allocated in a reduced number of circuits
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In this paper, an adapted mathematical model is presented to the optimization of the restoration problem in radial electric power distribution systems with the existence of a reduced number of switches, which is the typical characteristic of real distribution systems. The restoration problem consists in restoring the maximum possible of loads after the de-energization of parts of the system due to the occurrence of a permanent fault or due to the execution of expansion projects or preventive maintenance. The preparation and the implementation of the restoration plan should be performed in the shortest time possible. In the proposed mathematical model, the objective is to maximize the restoration of de-energized loads and to minimize the number of switching operations necessary for the reestablishment of these loads. The mathematical model formulated is of mixed-integer second order conic programming and can be efficiently solved by commercial solvers based on exact optimization techniques, such as the branch and bound method. Tests were performed simulating permanent faults in a 53-bus distribution system adapted to the proposed problem. The results obtained show the robustness and the efficiency of the mathematical model adapted to solve this problem.