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access icon free Combination of moment-matching, Cholesky and clustering methods to approximate discrete probability distribution of multiple wind farms

  • Author(s): Jinghua Li 1, 2  and  Dunlin Zhu 1, 2
    • View affiliations
    • Affiliations: 1: Guangxi Key Laboratory of Power System Optimization and Energy Technology, Guangxi University, Nanning 530004, People's Republic of China ;
      2: School of Electrical Engineering, Guangxi University, Nanning 530004, People's Republic of China
  • Source: Volume 10, Issue 9, October 2016, p. 1450 – 1458
    DOI:  10.1049/iet-rpg.2015.0568 , Print ISSN 1752-1416, Online ISSN 1752-1424
© The Institution of Engineering and Technology
Received 02/12/2015, Accepted 10/06/2016, Revised 29/05/2016, Published 13/06/2016

This study focuses on approximating a reduced discrete probability distribution (RDPD) of wind power from the original discrete probability distribution (ODPD), consisting of a large number of observed original scenarios (OSs), to relieve the burden of solving stochastic programs of wind power generation. The proposed method, namely, the MMCC method, aims to achieve high approximation accuracy and computational efficiency by combining an improved moment-matching (MM) method with the clustering (C) method and the Cholesky decomposition (CD) method. First, the C method is used to reduce the number of OSs by minimising the space distance between the reduced scenarios (RSs) and the OSs. Next, the CD method is used to rectify the correlation of the RSs to satisfy that of the ODPD. Finally, the RS probabilities are optimally determined by the MM method in order to minimise the stochastic features (first four moments and correlation matrix) between the RDPD and the ODPD. Simulations of RDPD approximation for three wind farms with 10, 20, 40, 60, 80, and 100 scenarios were carried out using the Latin hypercube sampling, importance sampling, C, moment-matching-clustering (MMC), and MMCC methods. The results showed that the MMCC method exhibits the best performance in terms of capturing the features of the ODPD.

Inspec keywords: wind turbines; approximation theory; probability

Other keywords: moment matching; moment-matching-clustering methods; importance sampling; wind farms; clustering methods; original discrete probability distribution; wind power generation; Latin hypercube sampling; observed original scenarios; Cholesky methods; stochastic programs; Cholesky decomposition method

Subjects: Other topics in statistics; Wind power plants; Interpolation and function approximation (numerical analysis)

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