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

• Published in: IET renewable power generation 2018-08, Vol.12 (11), p.1295-1303
• Main Authors: Huang, Yu, Xu, Qingshan, Yang, Yang, Jiang, Xianqiang
• Format: Article
• Language: English
• Subjects: approximation theory; C‐type Gram‐Charlier series; dimensional reduction integral method; exhaustive system parameter assessment; Gauss quadrature; grid complexity; integral equations; integration; load flow; modified IEEE 118‐bus test system; multiple correlated random variables; multivariate raw moments; Nataf transformation; nonGaussian input variables; numerical method; one‐dimensional integrals; power grids; probabilistic load flow computation; probability distributions; renewable power generation; Research Article; statistical distributions; unpredictable demand
• ISSN: 1752-1416; 1752-1424; 1752-1424
• DOI: 10.1049/iet-rpg.2017.0067

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.