Probabilistic techniques for three-phase load flow analysis

Some techniques are presented to obtain the probability density functions of phase-voltages in an unbalanced three-phase power system. The techniques are based on the Monte Carlo simulation applied to the non-linear and linear three-phase load flow equations, on convolution process and on the Pearson distributions. These methods are compared in terms of time execution and accuracy in the evaluation of phase-voltage and unbalance factor probability density functions and in particular regarding their 95^th percentiles, being these quantities the statistical measures of greatest interest in many international standards for power quality. Several numerical applications are presented and discussed with reference to the three phase unbalanced IEEE 13-bus distribution test system.