Voltage distribution constant versus losses in medium-voltage distribution transformer: A polynomial interpolation approach

•Equation to describe the α-factor behavior depending on the load losses.•Application of polynomial interpolation depends on the number of parameters involved.•The equations have low error viable in transformer of distribution design.•The algorithm for interpolation used a matrix approach.

This paper aims to calculate an estimate of the initial stress voltage distribution in the transformer windings through their losses (that can be reduced by varying the construction parameters such as conductor section and size of the core window) through the numerical interpolation applied in capacitances of distribution transformers 30, 45, 75 and 112.5 kVA, 15 kV class. The calculations of the projects were organized into sets, with simultaneous variation of three construction parameters, totaling analysis of 10,648 projects of each power transformers arranged in three-dimensional arrays. The equation of the constant voltage distribution (α-factor) according to the losses through the quadratic polynomial and cubic splines for the of LV and HV windings is formulated.