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Title: 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 » and parameters are also investigated.« less

Authors:
; ; ORCiD logo; ;
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}
}

Works referenced in this record:

Probabilistic Load Flow
journal, May 1974


Probabilistic Load Flow Method Based on Nataf Transformation and Latin Hypercube Sampling
journal, April 2013


Review of probabilistic load flow approaches for power distribution systems with photovoltaic generation and electric vehicle charging
journal, September 2020


Propagating Uncertainty in Power Flow With the Alternating Direction Method of Multipliers
journal, July 2018


Second-Order Trajectory Sensitivity Analysis of Hybrid Systems
journal, May 2019


Probabilistic load flow calculation based on sparse polynomial chaos expansion
journal, April 2018


Probabilistic Power Flow Analysis Based on the Stochastic Response Surface Method
journal, May 2016


Probabilistic Power Flow Calculation Using Non-Intrusive Low-Rank Approximation Method
journal, July 2019


The Homogeneous Chaos
journal, October 1938


The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
journal, January 2002


Probabilistic equivalence and stochastic model reduction in multiscale analysis
journal, August 2008


Propagating Uncertainty in Power System Dynamic Simulations Using Polynomial Chaos
journal, January 2019


Basis-Adaptive Sparse Polynomial Chaos Expansion for Probabilistic Power Flow
journal, January 2017


Probabilistic Power Flow Calculation and Variance Analysis Based on Hierarchical Adaptive Polynomial Chaos-ANOVA Method
journal, September 2019


Data-Driven Arbitrary Polynomial Chaos-Based Probabilistic Load Flow Considering Correlated Uncertainties
journal, July 2019


Probabilistic load flow methodology for distribution networks including loads uncertainty
journal, March 2019


A Data-Driven Nonparametric Approach for Probabilistic Load-Margin Assessment Considering Wind Power Penetration
journal, November 2020


Data-driven uncertainty analysis of distribution networks including photovoltaic generation
journal, October 2020


Probabilistic power flow analysis of microgrid with renewable energy
journal, January 2020


An efficient Nataf transformation based probabilistic power flow for high-dimensional correlated uncertainty sources in operation
journal, March 2020


A Versatile Probability Model of Photovoltaic Generation Using Pair Copula Construction
journal, October 2015


C-Vine Copula Mixture Model for Clustering of Residential Electrical Load Pattern Data
journal, May 2017


A general framework for data-driven uncertainty quantification under complex input dependencies using vine copulas
journal, January 2019


Factor copula models for multivariate data
journal, September 2013


Remarks on a Multivariate Transformation
journal, September 1952


Orthogonal polynomials—Constructive theory and applications
journal, May 1985


Calculation of Gauss quadrature rules
journal, May 1969


Data-driven polynomial chaos expansion for machine learning regression
journal, July 2019


Generalized Injection Shift Factors
journal, September 2017


Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions
journal, January 2012


Probabilistic load flow calculation with quasi-Monte Carlo and multiple linear regression
journal, June 2017


A Short-Term Nodal Voltage Phasor Forecasting Method Using Temporal and Spatial Correlation
journal, September 2016