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. 2016 Jan 7;11(1):e0146284.
doi: 10.1371/journal.pone.0146284. eCollection 2016.

Influence of Sub-Daily Variation on Multi-Fractal Detrended Fluctuation Analysis of Wind Speed Time Series

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Free PMC article

Influence of Sub-Daily Variation on Multi-Fractal Detrended Fluctuation Analysis of Wind Speed Time Series

Xianxun Wang et al. PLoS One. .
Free PMC article

Abstract

Using multi-fractal detrended fluctuation analysis (MF-DFA), the scaling features of wind speed time series (WSTS) could be explored. In this paper, we discuss the influence of sub-daily variation, which is a natural feature of wind, in MF-DFA of WSTS. First, the choice of the lower bound of the segment length, a significant parameter of MF-DFA, was studied. The results of expanding the lower bound into sub-daily scope shows that an abrupt declination and discrepancy of scaling exponents is caused by the inability to keep the whole diel process of wind in one single segment. Additionally, the specific value, which is effected by the sub-daily feature of local meteo-climatic, might be different. Second, the intra-day temporal order of wind was shuffled to determine the impact of diel variation on scaling exponents of MF-DFA. The results illustrate that disregarding diel variation leads to errors in scaling. We propose that during the MF-DFA of WSTS, the segment length should be longer than 1 day and the diel variation of wind should be maintained to avoid abnormal phenomena and discrepancy in scaling exponents.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist. This commercial affiliation, POWERCHINA Kunming Engineering Corporation Limited, does not alter the authors' adherence to PLOS ONE policies on sharing data and materials.

Figures

Fig 1
Fig 1. Wind speed processes.
Fig 2
Fig 2. MF-DFA plots of the two schemes for 1# WSTS.
(a) Log—log plots; (b) h(q)~q plots, and; (c) f(α) ~ α plots.
Fig 3
Fig 3. Log—log plots of WSTS.
(a) plot of the 1# WSTS; (b) plot of the 2# WSTS; …, and; (j) plot of the 10# WSTS. The legend is same as in Fig 2a.
Fig 4
Fig 4. Log—log plots of the inter-day shuffled WSTS.
(a) plot of the 1# WSTS; (b) plot of the 2# WSTS; …, and; (j) plot of the 10# WSTS. The legend is same as in Fig 2a.
Fig 5
Fig 5. Log—log plots of the intra-day shuffled WSTS.
(a) plot of the 1# WSTS; (b) plot of the 2# WSTS; …, and; (j) plot of the 10# WSTS. The legend is same as in Fig 2a.
Fig 6
Fig 6. The h(q) ~ q plots of the short range scheme of our WSTSs.
Fig 7
Fig 7. The h(q) ~ q plots of 100 surrogate series for each WSTS (mean and error bar).

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References

    1. Ackermann T. (Ed.). Wind power in power systems, 2nd ed. Chichester: John Wiley; 2012.
    1. Craig A., Rudolf I Howard (Ed.). Wind power and hydropower integration: concepts, considerations and case studies. Hauppauge, NY: Nova Science Publishers Inc; 2012.
    1. Feng T, Fu Z-T, Deng X, Mao J-Y. A brief description to different multi-fractal behaviors of daily wind speed records over China. Physics Letters A. 2009; 373(45): 4134–4141.
    1. Sun B, Yao HT. Multi-fractal detrended fluctuation analysis of wind speed time series in wind farm. Transactions of China electrotechnical society. 2014; 29(6): 204–210.
    1. Peng C-K, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL. Mosaic organization of DNA nucleotides. Physical Review E. 1994; 49(2): 1685. - PubMed

Publication types

Grant support

This study was supported by the Major Program of National Natural Science Foundation of China, grant number: 51239004, (URLs: http://npd.nsfc.gov.cn/fundingProjectSearchAction.action), Recipient: Yadong Mei; and the Program of National Natural Science Foundation of China, grant number: 51479140 (URLs: http://npd.nsfc.gov.cn/fundingProjectSearchAction.action), Recipient: Yadong Mei. The funder provided support in experiment field and tools. The POWERCHINA Kunming Engineering Corporation Limited provided support in data collection. The funder and the commercial company did not have any additional role in the study design, data analysis, decision to publish, or preparation of the manuscript. The specific roles of the authors are articulated in the ‘author contributions’ section.
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