Dimension reduction method for probabilistic power flow calculation

In this study, the probabilistic power flow (PPF) problem is modelled as a multiple integral with an implicit integrand. A detailed discussion is given about the dimension reduction (DR) method for solving PPF. To accommodate the dependency of the input random variables, Nataf transformation is introduced to map PPF problems in the independent standard normal space. Emphasis is put on the computational burden of DR method. Based on Taylor expansion, a deep sight is given in the residual error of univariate DR (UDR) method. Using the first four standardised central moments from UDR method, the generalised lambda distribution is employed to represent the probability distribution of the output variable. Finally, an IEEE-118 case is performed to check the proposed method.