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

Yingyun Sun, Rui Mao, Zuyi Li and Wei Tian
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Yingyun Sun: State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
Rui Mao: State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
Zuyi Li: Robert W. Galvin Center for Electricity Innovation, Illinois Institute of Technology, Chicago, IL 60616, USA
Wei Tian: Robert W. Galvin Center for Electricity Innovation, Illinois Institute of Technology, Chicago, IL 60616, USA

Energies, 2016, vol. 9, issue 3, 1-18

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 (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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