Modelling of random variation of three-phase voltage unbalance in electric distribution systems using the trivariate Gaussian distribution

This paper deals with probabilistic modelling of the random variation of three-phase voltage unbalance. With field measurement and an analysis of three-phase voltage unbalance, trivariate Gaussian distribution has been employed to model the random variation of three-phase voltages, and a simulation method based on the Monte Carlo technique has been developed to generate voltage data, the statistical properties of which are close to those of the measured voltages. Comparison of the probability distribution functions of the complex voltage unbalance factor between Monte Carlo simulation and the measurement is then carried out for validation