An Analytic Approach to Probabilistic Load Flow Incorporating Correlation Between Non-Gaussian Random Variables

  • Yu Huang Kauno technologijos universitetas
  • Qingshan Xu
  • Xianqiang Jiang
  • Yang Yang
  • Guang Lin
Keywords: Probabilistic load flow, Gaussian mixture model, Correlation, Gram-Charlier expansion.


This paper presents a cumulant-based method for probabilistic load flow (PLF) analysis which incorporates correlation between input random variables. Our approach can approximate non-Gaussian variables of all kinds (e.g. different load profiles or renewable power injections) accurately using the Gaussian mixture model (GMM), which also facilitates the computation of cumulants in a straightforward numerical way. Multiple correlations can be easily handled by transforming correlated variables into a combination of uncorrelated ones. To reduce the deviations introduced by traditional series expansions such as Edgeworth or Cornish-Fisher series, we use C-type Gram-Charlier series instead, which can better predict the probabilistic tail regions and have good convergence property as well. The good performance of the proposed method is verified using the IEEE 30 test system in terms of accuracy and efficiency.