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Volume 9
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10.3390/en9030153
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Article

Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow

by
Yingyun Sun
1,
Rui Mao
1,*,
Zuyi Li
2 and
Wei Tian
2
1
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
2
Robert W. Galvin Center for Electricity Innovation, Illinois Institute of Technology, Chicago, IL 60616, USA
*
Author to whom correspondence should be addressed.
Energies 2016, 9(3), 153; https://doi.org/10.3390/en9030153
Submission received: 14 December 2015 / Revised: 18 February 2016 / Accepted: 19 February 2016 / Published: 3 March 2016
(This article belongs to the Special Issue Microgrids 2016)
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Abstract

An intrusive spectral method of probabilistic load flow (PLF) is proposed in the paper, which can handle the uncertainties arising from renewable energy integration. Generalized polynomial chaos (gPC) expansions of dependent random variables are utilized to build a spectral stochastic representation of PLF model. Instead of solving the coupled PLF model with a traditional, cumbersome method, a modified stochastic Galerkin (SG) method is proposed based on the P-Q decoupling properties of load flow in power system. By introducing two pre-calculated constant sparse Jacobian matrices, the computational burden of the SG method is significantly reduced. Two cases, IEEE 14-bus and IEEE 118-bus systems, are used to verify the computation speed and efficiency of the proposed method.
Keywords: probabilistic load flow; uncertainty quantification; Nataf transformation; generalized polynomial chaos; stochastic Galerkin method probabilistic load flow; uncertainty quantification; Nataf transformation; generalized polynomial chaos; stochastic Galerkin method

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MDPI and ACS Style

Sun, Y.; Mao, R.; Li, Z.; Tian, W. Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow. Energies 2016, 9, 153. https://doi.org/10.3390/en9030153

AMA Style

Sun Y, Mao R, Li Z, Tian W. Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow. Energies. 2016; 9(3):153. https://doi.org/10.3390/en9030153

Chicago/Turabian Style

Sun, Yingyun, Rui Mao, Zuyi Li, and Wei Tian. 2016. "Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow" Energies 9, no. 3: 153. https://doi.org/10.3390/en9030153

APA Style

Sun, Y., Mao, R., Li, Z., & Tian, W. (2016). Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow. Energies, 9(3), 153. https://doi.org/10.3390/en9030153

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