Distribution Transformer Loading: Probabilistic Modeling and Diversity Factor

For planning purposes, the loading of assets in electric power distribution circuits is often modelled in terms of a diversified load. The temporal and probabilistic nature of the load is a sum of several individual loads of various levels and characteristics. The diversity factor of such circuits is the ratio of the sum of the individual non-simultaneous load asset ratings energized by that circuit to the total peak simultaneous demand. The diversity factor is temporal and probabilistic in nature. In this paper, the probability density of the load factor is described and modelled for power distribution loads. The model used is the ratio of two dependent bivariate normal random variables. The resulting probability density is termed a ratio density and a recent algebraic formulation of the ratio density is used. The probabilistic model is compared to results obtained by others. The potential impact of electric vehicle charging loads is applied to the sizing of distribution power supply assets using diversity loading strategies for Level 1 and single phase Level 2 EV chargers. The probabilistic method is offered as an added tool to the conventional, fixed diversity factor method in distribution engineering.