Multi-linear Monte Carlo simulation for probabilistic three-phase load low

Several transmission and distribution systems are known to have unbalanced lines and line sections carrying a mixture of single, double, and three-phase loads; moreover, their steady-state conditions are affected by unavoidable uncertainties that require to analyze these systems with probabilistic approaches. In this article, a probabilistic three-phase load flow using a multi-linear simulation algorithm is proposed. The method properly extends to the field of unbalanced systems a probabilistic method proposed for balanced systems. Numerical examples on the three-phase unbalanced IEEE 13-bus and 34-bus distribution test systems are provided and discussed to illustrate the application of the proposed method. The results obtained with the proposed algorithm are compared with the ones obtained using a Monte Carlo simulation algorithm, which includes the non linear three-phase load flow equations. Copyright (C) 2006 John Wiley & Sons, Ltd.