A stochastic power flow method based on polynomial normal transformation and quasi Monte Carlo simulation

Most common sampling methods adopted in stochastic power flow (SPF), such as simple random sampling (SRS) and Latin hypercube sampling (LHS), are of low accuracy due to their incapability in generating sampling sequences of low discrepancy. In this paper, a SPF method based on polynomial normal transformation and quasi Monte Carlo simulation method is proposed. This method utilized the numerical characteristics of input variables to reconstruct the distribution of their own by polynomial normal transformation, meanwhile, singular value decomposition is adopted to handle the scenario of non-positive definite correlation matrix. At last, Sobol sequences are generated as samples of input variables, then Monte-Carlo simulation method is adopted to attain the probability distribution and numerical characteristics of bus voltage and branch power. The test on IEEE 30 and IEEE 118 systems demonstrate the validity of the proposed method. The simulation results suggested that, compared to Latin hypercube sampling with the same sample size, the proposed method is more effective, which not only has the advantages of high accuracy and calculating efficiency, but also has better convergence characteristics.