Phase Balancing in Power Distribution Grids: A Genetic Algorithm with a Group-Based Codification

Phase balancing is an optimization problem which can reduce power losses in modern power distribution grids. The problem consists on phase swapping of the loads at the feeder level in order to reduce the unbalance of the grid. Despite being a classic problem, it is still relevant since unbalance is a common phenomena in power distribution grids and can be intensified by the uncoordinated use of distributed resources such as renewable energies and electric vehicles, among other single phase loads. Being a combinatorial problem, phase balancing requires heuristic algorithms whose codification must be carefully designed. In addition, high penetration of renewable energies makes the problem stochastic. This chapter shows a genetic algorithm which solves efficiently the problem, considering a detailed model of the power flow. A novel codification is proposed based on the identification of symmetries on the intrinsic structure of the problem by using the concept of group, an algebraic structure that can be easily combined with the conventional genetic algorithm. Simulations results on the IEEE test systems demonstrate the efficiency of the proposed method.