A quadratic formulation for the optimal allocation of fault indicators

Faults are an inherent part of power distribution systems, and fault indicators play a crucial role in self-healing smart distribution systems by assisting in fault detection and location. However, the effectiveness of fault indicators depends on their number and location in the distribution system. This paper addresses the optimal decisions on the allocation of fault indicators in distribution networks to minimize the expected fault location time. To build upon the existing knowledge, a comprehensive review of the literature on the allocation of fault indicators is provided. Additionally, a novel approach is given by formulating the fault location time as a quadratic function of the network’s section sizes. From a relationship established between the fault indicator allocation problem and connected edge-partitions, a mathematical model and a metaheuristic are developed. To evaluate the proposed methodologies, a benchmark comprising 19 networks is employed, including the largest network solved for this problem to date. The results demonstrate the superiority of the new methodologies over previous approaches, as evidenced by the quality of the solutions and their optimality gaps.