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

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 gener...

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Vydáno v:IET renewable power generation Ročník 10; číslo 9; s. 1450 - 1458
Hlavní autoři: Li, Jinghua, Zhu, Dunlin
Médium: Journal Article
Jazyk:angličtina
Vydáno: The Institution of Engineering and Technology 01.10.2016
Témata:
Approximation
Approximation methods
approximation theory
Cholesky decomposition method
Cholesky methods
Clustering
clustering methods
Computer simulation
importance sampling
Latin hypercube sampling
Mathematical analysis
Metal matrix composites
moment matching
moment‐matching‐clustering methods
observed original scenarios
original discrete probability distribution
probability
Research Article
stochastic programs
Stochasticity
wind farms
Wind power
wind power generation
wind turbines
clustering methods
approximation theory
probability
Cholesky methods
Cholesky decomposition method
moment-matching-clustering methods
observed original scenarios
importance sampling
original discrete probability distribution
wind farms
Latin hypercube sampling
stochastic programs
wind power generation
wind turbines
moment matching
ISSN:1752-1416, 1752-1424
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:1752-1416
1752-1424
DOI:10.1049/iet-rpg.2015.0568