Probabilistic load flow calculation for three-phase unbalanced droop-regulated islanded microgrids based on low-rank approximation method

Abstract

For the characteristics of unbalanced nodes and constant frequency in the sagging control island microgrid, taking into account its three-phase asymmetry and the influence of uncertainty factors, a three-phase probability trend calculation method based on optimal multiplier Newton-Rafson method and low rank approximation method is proposed. First of all, the three-phase trend model of the sagging control island microgrid of frequency variables is established, solved by Newton-Rafson method, and the optimal multiplier is calculated by taylor-expanding high-order information of the current equation system, and the correction amount with optimal multiplier is corrected in iteration, which significantly improves the convergence of the algorithm. Then, the probability trend of the system is calculated by using the low rank approximation method. According to the principle of low rank approximation, the statistical equivalent proxy model of the trend distribution variable of concern is established by a relatively small number of determinized trend calculation samples, and its average value and standard deviation are calculated, and the probability characteristics such as probability density and cumulative probability distribution of the trend quantity can be obtained by a large number of input random variable samples to the proxy model. The results of the study prove the validity and accuracy of the algorithm.