A Generalized Computationally Efficient Copula-Polynomial Chaos Framework for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections
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 typesmore »
- Authors:
- Publication Date:
- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)
- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE), Wind Energy Technologies Office (EE-4W); USDOE Grid Modernization Laboratory Consortium
- OSTI Identifier:
- 1833353
- Report Number(s):
- NREL/JA-5D00-81311
MainId:82084;UUID:381fcc73-0471-4329-a78f-7c2aa4481f23;MainAdminID:63380
- DOE Contract Number:
- AC36-08GO28308
- Resource Type:
- Journal Article
- Journal Name:
- International Journal of Electrical Power & Energy Systems
- Additional Journal Information:
- Journal Volume: 136
- Country of Publication:
- United States
- Language:
- English
- Subject:
- MATHEMATICS AND COMPUTING,POWER TRANSMISSION AND DISTRIBUTION,SOLAR ENERGY; copula; nonlinear correlations; photovoltaic; polynomial chaos expansion; probabilistic power flow; PV
Citation Formats
Ye, Ketian, Zhao, Junbo, Zhang, Yingchen, Liu, Xiaodong, and Zhang, Hongming. A Generalized Computationally Efficient Copula-Polynomial Chaos Framework for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections. United States: N. p., 2021.
Web. doi:10.1016/j.ijepes.2021.107727.
Ye, Ketian, Zhao, Junbo, Zhang, Yingchen, Liu, Xiaodong, & Zhang, Hongming. A Generalized Computationally Efficient Copula-Polynomial Chaos Framework for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections. United States. https://doi.org/10.1016/j.ijepes.2021.107727
Ye, Ketian, Zhao, Junbo, Zhang, Yingchen, Liu, Xiaodong, and Zhang, Hongming. 2021.
"A Generalized Computationally Efficient Copula-Polynomial Chaos Framework for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections". United States. https://doi.org/10.1016/j.ijepes.2021.107727.
@article{osti_1833353,
title = {A Generalized Computationally Efficient Copula-Polynomial Chaos Framework for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections},
author = {Ye, Ketian and Zhao, Junbo and Zhang, Yingchen and Liu, Xiaodong and Zhang, Hongming},
abstractNote = {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.},
doi = {10.1016/j.ijepes.2021.107727},
url = {https://www.osti.gov/biblio/1833353},
journal = {International Journal of Electrical Power & Energy Systems},
number = ,
volume = 136,
place = {United States},
year = {Mon Nov 01 00:00:00 EDT 2021},
month = {Mon Nov 01 00:00:00 EDT 2021}
}
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