A Quasi-Monte Carlo approach for radial distribution system probabilistic load flow

Monte Carlo simulation (MCS) is a numerical method to solve the probabilistic load flow (PLF) problem. Comparing to analytical methods, MCS for PLF has advantages such as flexibility, general purpose, able to deal with large nonlinearity and large variances, and embarrassingly parallelizable. However, MCS also suffers from low convergence speed and high computational burden, especially for problems with multiple random variables. In this paper, we proposed a Quasi-Monte Carlo (QMC) based method to solve the PLF for radial distribution network. QMC uses samples from low-discrepancy sequence intended to cover the high dimension random sample space as uniformly as possible. The QMC method is particularly suitable for the high dimension problems with low effective dimensions, and has been successfully used to solve large scale problems in econometrics and statistical circuit design. In this paper, we showed that the PLF for radial distribution system has the similar properties and can be a good candidate for QMC method. The proposed method possesses the advantage of MCS method and significantly increases the convergence rate and overall speed. Numerical experiment results on IEEE test feeders have shown the effectiveness of the proposed method.