Capacitor placement in large-sized radial distribution networks

The capacitor-placement problem consists of finding specific locations to install capacitor banks in an electrical distribution network. Consequently, the losses are reduced due to the compensation of the reactive component of power flow. This problem can be formulated as a nonlinear mixed-integer optimisation model and its solution has represented a challenge for many optimisation methods in the past decades. This work proposes a new method, based on evolutionary algorithms, capable of solving large network instances that appear in real-world settings. Our evolutionary approach makes use of a memetic algorithm that employs a hierarchical organisation of the population in overlapping clusters. This structure leads to special selection and reproduction schemes, which improve the algorithm's overall performance. Computational tests were executed with two small-sized instances, usually utilised as a test set in previous works, and with two real large-sized distribution networks. Tests include a sensitivity analysis of the algorithm to the optimisation's critical parameters such as the energy cost, the maximum budget available to acquire and install the capacitors, and the amortization term of the investment.