Development of a three-phase power-flow calculation method for distribution systems with automatic handling of arbitrary winding connections of transformers

Single-phase loads and photovoltaic generation cause three-phase imbalance in distribution systems, and prospective growth of normal chargers of electric vehicles may even increase the imbalance. The analysis of such unbalanced systems requires the three-phase power-flow calculation. Since existing methods require the admittance matrices of three-phase transformers, they must be derived for all possible winding connection patterns in advance to its computer-code implementation. This paper proposes a three-phase power-flow calculation method which formulates circuit equations using the modified nodal analysis, making it possible to automatically handle any winding connection. The power-flow constraints are then embedded into the circuit equations using a fixed-point iteration. Newton-Raphson, backward/forward sweep and fixed-point iteration methods are the existing three categories of solution methods. Newton-Raphson methods may show convergence problems due to the high R/X ratios of distribution lines. Backward/forward sweep methods cannot be used, because loops are temporarily formed in a distribution system during circuit switching. These justify the use of a fixed-point iteration. In this paper, the proposed method is validated by practical examples.