A Mixed-Integer Linear Programming Model for Simultaneous Optimal Reconfiguration and Optimal Placement of Capacitor Banks in Distribution Networks

Optimal capacitor placement and network reconfiguration are well-known methods to minimize losses, enhance reliability, and improve the voltage profile of electric distribution networks (EDNs). Distribution network reconfiguration (DNR) consists of altering the system topology by changing the states of ties and sectionalizing switches, while the optimal placement of capacitors (OPCAs) involves sizing and finding the optimal location of capacitor banks within the distribution network for reactive power control. DNR and OPCAs are challenging optimization problems involving both integer and continuous decision variables. Due to the nature of these problems (combinatorial optimization problems), most approaches that deal with DNR and OPCAs resort to metaheuristic techniques, and they are limited to applications in small-size distribution networks. Although these techniques have proven to be effective when dealing with non-convex optimization problems, their main drawbacks lie in the fact that they require the fine-tuning of several parameters and do not guarantee the finding of a globally optimal solution. This paper presents a mixed-integer linear programming (MILP) model to solve simultaneous DNR and OPCAs in radial distribution networks. The proposed model can be solved by commercially available software; it guarantees to obtain globally optimal solutions and requires low computational effort when compared with metaheuristic techniques employed for the same purpose. Several tests were carried out on seven benchmark EDNs ranging from 33 to 417 buses. In all cases, the proposed methodology was able to replicate the results reported in the specialized literature. Regarding the DNR alone, a novel solution was found for the 119-bus test system which is 1.86 % better than that previously reported in the specialized literature. Furthermore, new solutions are reported for the simultaneous optimal DNR and OPCAs for medium and large-size EDNs. The power loss reduction in the test system ranged from 21.12 % to 68.93 % evidencing the positive impact of the proposed approach in EDNs.