Joined Probabilistic Load Flow and Sensitivity Analysis of Distribution Networks Based on Polynomial Chaos Method

Due to the statistical uncertainty of loads and power sources found in smart grids, effective computational tools for probabilistic load flow analysis and planning are now becoming indispensable. In this paper, we describe a unified simulation framework that allows quantifying the probability distributions of a set of observation variables as well as evaluating their sensitivity to potential variations in the power demands. The proposed probabilistic technique relies on the generalized polynomial Chaos algorithm and on a regionwise aggregation/description of the time-varying load profiles. It is shown how detailed statistical distributions of some important figures of merit, which includes voltage unbalance factor in distribution networks, can be calculated with a two orders of magnitude acceleration compared to standard Monte Carlo analysis. In addition, it is highlighted how the associated sensitivity analysis is of guidance for the optimal allocation and planning of new loads.