Approximation formulas for the distribution system: the loss function and voltage dependence

The distribution system loss function and voltage dependence are examined, and useful approximations derived that are analogous to the loss formulae used in the transmission system. The approximation are used to estimate the losses and voltages in the distribution system under the conditions of varying the capacitive susceptance of capacitors installed in the system about the level corresponding to minimum losses and varying the tap setting of transformers about the nominal tap setting. Theory is compared to load flow calculations, and a simple quadratic function is shown to be accurate in estimating the losses and to be consistently slightly conservative, where by conservative it is meant that it overestimates the losses. The structure of the quadratic function is determined. A linear function is shown to be accurate for estimating voltages