A mixed-integer conic approximation for optimal pole-swapping in asymmetric bipolar DC distribution networks

Abstract

This paper deals with the optimal pole-swapping problem in bipolar asymmetric distribution networks by proposing a mixed-integer conic approximation (MICA) model to minimize the total grid power losses for a particular load condition. The non-convex relation between voltage and power in the constant power loads is relaxed through equivalent cones. The effect of the neutral wire’s connection is considered in the proposed MICA model via an auxiliary variable associated with the total current drained to the earth in the case of a solidly grounded connection. Numerical comparisons with three combinatorial optimization methods (black-hole optimization, sine-cosine algorithm, and the Chu & Beasley genetic algorithm) and a mixed-integer quadratic approximation in two test feeders composed of 21 and 85 buses demonstrate the effectiveness of the proposed MICA model. Reductions of about 3.9411 and 10.1706% were obtained after applying the MICA model to the optimal pole-swapping problem. All numerical validations were carried out in the MATLAB programming environment, using the convex disciplined tool known as CVX with the Gurobi solver.