Electric Power Systems Research 109 (2014) 1–7 Contents lists available at ScienceDirect Electric Power Systems Research jou rn al hom e page: www.elsevier.com/locate/epsr NSGA-II phase balancing of primary distribution circuits by the reconnection of their circuit laterals and distribution transformers Ignacio Pérez Abril ∗ Universidad Central de Las Villas, Centro de Estudios Electroenergéticos, Carretera Camajuani km 5, Santa Clara, Villa Clara, Cuba a r t i c l e i n f o Article history: Received 27 September 2013 Received in revised form 3 December 2013 Accepted 11 December 2013 Available online 31 December 2013 Keywords: Distribution systems NSGA-II Phase balancing a b s t r a c t The primary distribution circuits are unbalanced not only by the spread use of unbalanced three-phase transformer banks and single-phase distribution transformers, but also by the use of two-phase three- wire and single-phase two-wire circuit laterals. The unbalance of the phase currents produces two fundamental problems in the circuit: the energy losses in the primary conductors are increased and the presence of a high neutral current on normal operation make it difficult the detection of earth faults by the neutral over current relays. The present work implements an NSGA-II application for the phase balancing problem, which search for the minimal reconnection needed for the two-phase three-wire and the single-phase two-wire circuit laterals, as well as for the three-phase transformer banks and the single-phase distribution transformers, to minimize both: the energy losses and the maximum neutral current of the circuit. The successful performance of this application is achieved by the new definition of the set of independent variables, which permits the NSGA-II to optimize the selection of the elements to be reconnected. A test example with all the needed data is solved to shows the features of the presented approach. © 2013 Elsevier B.V. All rights reserved. 1. Introduction The primary distribution circuits are unbalanced not only by the spread use of unbalanced three-phase transformer banks and single-phase distribution transformers, but also by the use of two- phase three-wire and single-phase two-wire circuit laterals. The unbalance of the phase currents produces two fundamental problems in the circuit: the energy losses in the primary conduc- tors are increased and the presence of a high neutral current on normal operation make it difficult the detection of earth faults by the neutral over current relays. Several programming techniques as: genetic algorithms (GA) [1], differential evolution [2], parallel tabu search [3], ant colony search [4], etc. have been applied for the reconfiguration of the primary distribution feeders by proper switching operations [1–7]. This approach can improve the feeders operation, but requires the presence of enough sectionalizing switches. Another approach consists in the phase balancing of the dis- tribution circuits by the reconnection of their circuit laterals and distribution transformers to the primary circuit phases. Normally the reconnection of a few circuit elements can improve the primary ∗ Tel.: +53 42281055. E-mail address: iperez@uclv.edu.cu phase currents balance and reduce the energy losses in the primary circuit conductors. The phase balancing problem is formulated in [8] as a mixed integer programming problem with linear constraints. A second contribution uses the simulated annealing technique [9]. The pre- sented objective is the reduction of the circuit unbalance index. Searching for the phase balancing and the loss reduction, a GA is used to optimize the phase arrangement of the distribution transformers connected to the primary feeder [10]. However, the number of the needed reconnections is too high to be practical. A heuristic backtracking search algorithm is proposed in [11] to reconnect the circuit laterals, but only the minimization of the phase unbalance index of each line segment and branch is taken into account. Another application of simulated annealing is presented in [12], this approach combining phase balancing and feeder reconfigura- tion. An expert system to obtain a phase balancing strategy is proposed [13] which aim to reduce the neutral current and conse- quently avoid the tripping of the over-current relay of the neutral conductor. In [14,15], the immune algorithm is proposed to reconnect the circuit laterals and the distribution transformers to optimize a multi-objective function that considers: the unbalance of the phase currents, the customer service interruption cost and the labor cost to perform the optimal reconnection. 0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2013.12.006