The analysis of voltage regulation in residential distribution networks using the beta distribution model

Abstract

An analytical method for estimating single-phase consumer voltages in a three-phase low-voltage distribution system is developed. The starting point is the assumption of a beta model for the statistical distribution of the individual stochastic consumer load currents. The method is further based on a Taylor expansion of the first moment, together with the second moment of the consumer voltages. Practical implementation of the resultant algorithms is further enhanced by using an approximation for the quantile value of the incomplete beta function and an appropriate curve fit for the Gaussian probability function. The resulting formulation may be used in a simple computer program, such as a spreadsheet, and the results compare well with simulations.