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The distribution system reconfiguration problem is concerned with finding the state of switches (open or closed) so as to optimize some objective function, typically the total loss, the load distribution among network sections, or the total cost within a planning period. This work focuses on the minimization of total loss. This problem has been studied over the past 30 years through various techniques. The diversity of approaches underlines the great difficulty associated with this problem, which arises from the exponential growth of the number of possible solutions with the number of binary variables that describe the state of switches. An additional difficulty stems from the quadratic relationship between the total loss and the remaining continuous variables that represent the electrical current flowing trough network branches. Constraints such as Kirchhoff ́s Current Law and maximum branch loading are taken into account in the problem formulation. The problem is then solved through Mixed-Integer Non-Linear Programming. Binary variables are determined using both Depth-First Search and the Branch-andBound method. The first technique does not usually allow the identification of the optimal solution, but requires very low processing times. Moreover, it does provide high-quality sub-optimal solutions. The latter allows the identification of the optimal solution in smallor medium-size networks, but its application in large networks, with more than 100 switches, is prohibitively time consuming. Two different implementations were developed for both methods. Continuous variables are computed through the standard Newton Method with second derivatives, which is particularly well suited for quadratic functions such as the total loss. In addition, in all study cases it was possible to verify the nonexistence of local minima, thus eliminating the main drawback of the method. The proposed methodology was applied in three distribution systems, two of them with 28 and 37 switches and the third one with 1128 branches and 129 switches.

Reconfiguração de redes de distribuição através de programação não-linear inteira mista.