A Generalized Computationally Efficient Copula-Polynomial Chaos Framework for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections: Article No. 107727

Ketian Ye, Junbo Zhao, Yingchen Zhang, Xiaodong Liu, Hongming Zhang

Research output: Contribution to journalArticlepeer-review

23 Scopus Citations

Abstract

This paper develops a general computationally efficient copula-polynomial chaos expansion (copula-PCE) framework for power system probabilistic power flow that can handle both linear and nonlinear correlations of uncertain power injections, such as wind and PVs. A data-driven copula statistical model is used to capture both nonlinear and linear correlations of uncertain power injections. This allows us to resort to the Rosenblatt transformation to transform correlated variables into independent ones while preserving the dependence structure. It paves the way for leveraging PCE for surrogate modeling and uncertainty quantification of power flow results. To further improve the computational efficiency of the proposed method without sacrificing accuracy, two strategies are developed and unified together. Specifically, the branch flow sensitivity analysis (BFSA) is used to select an appropriate number of outputs that need PCE surrogate modeling while the analysis of variance (ANOVA) scheme enables us to reduce the number of basis functions and coefficients evaluations for each PCE surrogate. Simulations carried out on the IEEE 57-bus and 118-bus and PEGASE 1354-bus systems show that the proposed framework can obtain better accuracy and computational efficiency than the existing PCE-based methods with linear correlation assumption and other Monte Carlo-based methods. The sensitivities to different copula types and parameters are also investigated.
Original languageAmerican English
Number of pages10
JournalInternational Journal of Electrical Power and Energy Systems
Volume136
DOIs
StatePublished - 2022

NREL Publication Number

  • NREL/JA-5D00-81311

Keywords

  • copula
  • nonlinear correlations
  • photovoltaic
  • polynomial chaos expansion
  • probabilistic power flow
  • PV

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