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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yingyun Sun & Rui Mao & Zuyi Li & Wei Tian, 2016. "Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow," Energies, MDPI, vol. 9(3), pages 1-18, March.
    • Handle: RePEc:gam:jeners:v:9:y:2016:i:3:p:153-:d:64986
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    Citations

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    Cited by:

    1. Xuexia Zhang & Zhiqi Guo & Weirong Chen, 2017. "Probabilistic Power Flow Method Considering Continuous and Discrete Variables," Energies, MDPI, vol. 10(5), pages 1-17, April.
    2. Jun Liu & Xudong Hao & Peifen Cheng & Wanliang Fang & Shuanbao Niu, 2016. "A Parallel Probabilistic Load Flow Method Considering Nodal Correlations," Energies, MDPI, vol. 9(12), pages 1-16, December.

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