Numerical method for probabilistic load flow computation with multiple correlated random variables

Abstract

Grid complexity is increasing progressively as the deepening penetration of renewable power generation and unpredictable demand, which necessitates an exhaustive assessment of system parameters in a probabilistic manner. In this study, the authors employ a dimensional reduction integral method to tackle the above problems challenged by dimensionality. Their approach transforms the multivariate raw moments into a linear sum of several one-dimensional integrals, which could be solved by Gauss quadrature. To handle the correlation between non-Gaussian input variables, Nataf transformation is used to map the inputs into the independent normal domain. Instead of commonly used series expansion such as A-type Gram-Charlier, Edgeworth or Cornish-Fisher, the probability distributions of output variables can be better approximated by C-type Gram-Charlier series with the calculated moments. The salient feature of the proposed method is demonstrated in a modified IEEE 118-bus test system with respect to both accuracy and run times.