Mathematical representation of radiality constraint in distribution system reconfiguration problem

•Distribution systems are modeled as planar graphs.•The proposed model is used to formulate radiality constraint for network optimization.•This formulation is proven to be more efficient than other variants.•Network reconfiguration is formulated as a mixed-integer programming problem.•The formulated problem can be solved to its global optimum using available solvers. Distribution systems are most commonly operated in a radial configuration for a number of reasons. In order to impose radiality constraint in the optimal network reconfiguration problem, an efficient algorithm is introduced in this paper based on graph theory. The paper shows that the normally followed methods of imposing radiality constraint within a mixed-integer programming formulation of the reconfiguration problem may not be sufficient. The minimum-loss network reconfiguration problem is formulated using different ways to impose radiality constraint. It is shown, through simulations, that the formulated problem using the proposed method for representing radiality constraint can be solved more efficiently, as opposed to the previously proposed formulations. This results in up to 30% reduction in CPU time for the test systems used in this study.