Multi-objective optimization of the balancing of phases in primary distribution circuits

• Presents a new multi-objective formulation.
• Minimizes the neutral current at the desired points of the circuit.
• Minimizes the energy losses and the number of reconnected elements.
• A test example with all the needed data is solved.

The primary distribution systems are among the more unbalanced three-phase networks. The unbalance of the phase currents causes two fundamental problems in the circuits: the increase of energy losses in the primary feeders and the presence of a high neutral current in normal operating status that makes it difficult the detection of ground faults by corresponding protections. These circuits are always protected at the substation. Nevertheless, other protections can also be located downstream in some sections or laterals of the circuit. Additionally, a circuit or some section of it can be supplied from another adjacent circuit in emergency conditions. In all the points where a ground fault protection is used, the maximum current of imbalance must be reduced to a minimum considering the several operating conditions that can change the circuit topology. This paper formulates the problem of phase balancing as a multi-objective optimization problem that minimizes: the neutral current at the desired points of the circuit, the energy losses in the primary feeders and the number of reconnected elements to achieve these objectives. The Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to develop the optimization application, which has shown a very successful performance in the solution of the phase balancing problem. A test example with all the needed data is solved to show the advantages of the presented approach.