Clustering Electrical Customers with Source Power and Aggregation Constraints: A Reliability-Based Approach in Power Distribution Systems

Abstract

Reliability is an important issue in electricity distribution systems, with strict regulatory policies and investments needed to improve it. This paper presents a mixed integer linear programming (MILP) model for clustering electrical customers, maximizing system reliability and minimizing outage costs. However, the evaluation of reliability and its corresponding nonlinear function represent a significant challenge, making the use of mathematical programming models difficult. The proposed heuristic procedure overcomes this challenge by using a linear formulation of reliability indicators and incorporating them into the MILP model for clustering electrical customers. The model is mainly defined on a density-based heuristic that constrains the set of possible medians, thus dealing with the combinatorial complexity associated with the problem of empowered p-medians. The proposed model proved to be effective in improving the reliability of real electrical distribution systems and reducing compensation costs. Three substation cluster scenarios were explored, in which the total utility compensations were reduced by approximately USD 86,000 (1.80%), USD 67,400 (1.41%), and USD 64,000 (1.3%). The solutions suggest a direct relationship between the reduction in the compensation costs and the system reliability. In addition, the alternative modeling approach to the problem served to match the performance between the distribution system reliability indicators.