Identification of the phase connectivity in distribution systems through constrained least squares and confidence-based sequential assignment

This paper addresses the customer-phase identification problem in three-phase distribution grids including three-phase customers characterized by aggregated energy measurements. The proposed technique first solves a relaxed problem, in which the binary nature of the variables is ignored, which leads to a constrained, least-squares estimation, using as inputs the active and reactive energy readings provided by the smart meters, along with the energy delivered by each phase at the head of the feeder. With the estimated values of the decision variables, and their corresponding variances, a confidence-based selection technique is then applied for the sequential assignment of the customer with the highest joint probability of being connected to one of the three phases but not to the other two. The performance of the proposed procedure is assessed with five different scenarios in terms of accuracy for increasing number of loads and measurement errors. The robustness of the algorithm is additionally tested in the presence of model errors, and its performance is compared to that of existing methods.