Skip to main content

Advertisement

SpringerLink
Log in

Analysis and research on chaotic dynamics behaviour of wind power time series at different time scales

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

With the continuous growth of wind power access capacity, the impact of intermittent and volatile wind power generation on the grid is becoming more and more obvious, so the research of wind power prediction has been widely concerned. The dynamic behavior of wind power time series is the external performance of complex nonlinear and multi-scale phenomena. Before choosing an appropriate prediction model, it is of great significance to analyze the characteristics of wind power time series for wind power grid system. At the same time, different sampling time scales of wind power also have an important impact on its dynamic characteristics. In this study, the chaotic dynamics behaviour of wind power time series at different time scales is discussed. The research methods include stationarity and white noise judgment, power spectral density analysis, autocorrelation function analysis, probability distribution, the Hurst index, 0–1 test algorithm for chaos, correlation dimension, maximum Lyapunov exponent, Kolmogorov entropy, recurrence plot, and information entropy method are adopted to study the chaotic dynamic behavior of wind power time series at different time scales. The actual wind power data of a wind farm at different time scales are taken as the research object for the case study. The case study results draw the following conclusions: (a) The wind power time series is non-stationary and non-white noise. (b) The direct-current and low frequency components parts store the main energy. (c) In the long-term, wind power is unpredictable. (d) The output level of wind power depends on the time scales. (e) The wind power time series obeys the fractal Brownian motion. (f) Wind power time series has chaotic characteristic. (g) Wind power time series has fractal characteristics. (h) As the time scales changes, so does the maximum prediction horizon. (i) With the decrease of time scales, the information loss rate has also declined. (j) Wind power at large time scales is more chaotic. The research results of this study have certain theoretical value and practical significance for grasping the fluctuation law of wind power and improving the prediction accuracy of wind power.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

The source code used to support the findings of this study is available from the corresponding author upon request. The original data of the wind power can be downloaded at https://zenodo.org/record/3874348#.XtdzOlUzaCo.

Abbreviations

DC:

Direct-current

PSD:

Power spectral density

LB:

Ljung-Box

R/S:

Re-scaling range

G-P:

Grassberger-Procccia

WP_10min:

Wind power time series with time scale of 10 min

WP_20min:

Wind power time series with time scale of 20 min

WP_30min:

Wind power time series with time scale of 30 min

WP_40min:

Wind power time series with time scale of 40 min

WP_1hour:

Wind power time series with time scale of 1 h

WP_2hour:

Wind power time series with time scale of 2 h

WP_3hour:

Wind power time series with time scale of 3 h

WP_4hour:

Wind power time series with time scale of 4 h

WP_6hour:

Wind power time series with time scale of 6 h

WP_8hour:

Wind power time series with time scale of 8 h

WP_12hour:

Wind power time series with time scale of 12 h

WP_1day:

Wind power time series with time scale of 1 day

\(P_{i}\) :

The output level of wind power

\(F_{{pi}}\) :

The probability of the i-th output level

\(P_{{i\min }}\) :

The minimum output level of wind power

\(P_{{i\max }}\) :

The maximum output level of wind power

N:

The total number of wind power time series

\(F_{{cpi}}\) :

The cumulative probability distribution of the output less than or equal to the ith output level

H :

Hurst index

R :

Adjustment range

n :

The amount of time series samples

S :

Standard deviation

\(\alpha\) :

The fractal dimension of the time series

\(M(n)\) :

Mean shift function

\(K_{c}\) :

Asymptotic growth rate

\(C(r)\) :

Correlation dimension

\(\tau\) :

Delay time

m :

Embedded dimension

\(H(u)\) :

Heaviside function

\(\varepsilon\) :

Standard deviation of the time series

\(\tau _{w}\) :

Optimal embedding window

\(\lambda _{1}\) :

Maximum Lyapunov exponent

T :

The maximum prediction horizon of time series

K :

Kolmogorov entropy

\(K_{2}\) :

Second order Renyi entropy

\(P(l)\) :

Probability density of diagonal distribution

References

  • Abedinia O, Zareinejad M, Doranehgard MH, Fathi G, Ghadimi N (2019) Optimal offering and bidding strategies of renewable energy based large consumer using a novel hybrid robust-stochastic approach. J Clean Prod 215:878–889

    Article  Google Scholar 

  • Adeniji AE, Olusola OI, Njah AN (2018) Comparative study of chaotic features in hourly wind speed using recurrence quantification analysis. AIP Adv 8(2):025102

    Article  Google Scholar 

  • Awrejcewicz J, Krysko VA, Yakovleva TV, Pavlov SP, Krysko VA (2018) Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam. Chaos 28(5):053102

    Article  Google Scholar 

  • Bokde N, Fejoo A, Villanueva D, Kulat K (2019) A review on hybrid empirical mode decomposition models for wind speed and wind power prediction. Energies 12(2):254

    Article  Google Scholar 

  • Di CL, Wang TJ, Yang XH, Li SL (2018) Technical note: An improved Grassberger-Procaccia algorithm for analysis of climate system complexity. Hydrol Earth Syst Sci 22(10):5069–5079

    Article  Google Scholar 

  • Ding JF, Cai J (2020) Two-side coalitional matching approach for joint MIMO-NOMA clustering and BS selection in multi-cell MIMO-NOMA systems. IEEE Trans Wirel Commun 19(3):2006–2021

    Article  Google Scholar 

  • Ding XX, Li QC, Lin L, He QB, Shao YM (2019) Fast time-frequency manifold learning and its reconstruction for transient feature extraction in rotating machinery fault diagnosis. Measurement 141:380–395

    Article  Google Scholar 

  • Drisya GV, Asokan K, Kumar KS (2018) Diverse dynamical characteristics across the frequency spectrum of wind speed fluctuations. Renew Energy 119:540–550

    Article  Google Scholar 

  • Fang LD, Zeng QQ, Faraj Y, Zhao N, Wei ZH, Li XT (2019) Analysis of chaos characteristics of gas-liquid two-phase flow noise. Flow Meas Instrum 22(10):5069–5079

    Google Scholar 

  • Fluck M, Crawford C (2018) A fast stochastic solution method for the Blade Element Momentum equations for long-term load assessment. Wind Energy 21(2):115–128

    Article  Google Scholar 

  • Fortuna L, Nunnari G, Nunnari S (2016) Analysis of wind speed time series. In: Nonlinear modeling of solar radiation and wind speed time series. SpringerBriefs in energy. Springer, Cham, pp 29–40. https://doi.org/10.1007/978-3-319-38764-2_3

  • Fu WL, Wang K, Zhou JZ, Xu YH, Tan JW, Chen T (2019a) A hybrid approach for multi-step wind speed forecasting based on multi-scale dominant ingredient chaotic analysis. KELM Synch Optim Strategy Sustain 11(6):1804

    Google Scholar 

  • Fu WL, Wang K, Li CS, Tan JW (2019b) Multi-step short-term wind speed forecasting approach based on multi-scale dominant ingredient chaotic analysis, improved hybrid GWO-SCA optimization and ELM. Energy Convers Manag 187:356–377

    Article  Google Scholar 

  • Gao W, Darvishan A, Toghani M, Mohammadi M, Abedinia O, Ghadimi N (2019) Different states of multi-block based forecast engine for price and load prediction. Int J Electr Power Energy Syst 104:423–435

    Article  Google Scholar 

  • Ghadimi N, Akbarimajd A, Shayeghi H, Abedinia O (2018) Two stage forecast engine with feature selection technique and improved meta-heuristic algorithm for electricity load forecasting. Energy 161:130–142

    Article  Google Scholar 

  • Guan HJ, Dai ZL, Guan S, Zhao AW (2019) A neutrosophic forecasting model for time series based on first-order state and information entropy of high-order fluctuation. Entropy 21(5):455

    Article  Google Scholar 

  • Hong PT, Binh CT (2018) A note on exponential stability of non-autonomous linear stochastic differential delay equations driven by a fractional Brownian motion with Hurst index > 1/2. Statist Probab Lett 138:127–136

    Article  MATH  Google Scholar 

  • Jiang YX, Guo SJ, Deng SP (2019a) Denoising and chaotic feature extraction of electrocardial signals for driver fatigue detection by Kolmogorov Entropy. J Dyn Syst Meas Control Trans ASME 141(2):021013

    Article  Google Scholar 

  • Jiang P, Wang B, Li HM, Lu HY (2019b) Modeling for chaotic time series based on linear and nonlinear framework: application to wind speed forecasting. Energy 173:468–482

    Article  Google Scholar 

  • Karakasidis TE, Andreadis I, Fragkou D (2019) On a topological classification of recurrence plots: Application to noise perturbed molecular dynamics time series. Chaos 29(2):023113

    Article  Google Scholar 

  • Karthikeyan A, Rajagopal K, Mathew D (2018) Fractional order nonlinear variable speed and current regulation of a permanent magnet synchronous generator wind turbine system. Alex Eng J 57(1):159–167

    Article  Google Scholar 

  • Kazimierczuk AH (2019) Wind energy in Kenya: A status and policy framework review. Renew Sustain Energy Rev 107:434–445

    Article  Google Scholar 

  • Khodaei H, Hajiali M, Darvishan A, Sepehr M, Ghadimi N (2018) Fuzzy-based heat and power hub models for cost-emission operation of an industrial consumer using compromise programming. Appl Therm Eng 137:395–405

    Article  Google Scholar 

  • Li X, Hu T, Wang Y, Li T, Wang T, Ren Z (2019) Multiple spatial scales chaos characterization in runoffseries by the 0–1 test algorithm. Tecnol Ciencias Del Agua 10(4):182–194

    Article  Google Scholar 

  • Liang C, Wang P, Han XQ, Qin WP, Jia YB, Yuan TJ (2018) Battery energy storage selection based on a novel intermittent wind speed model for improving power system dynamic reliability. IEEE Trans Smart Grid 9(6):6084–6094

    Article  Google Scholar 

  • Liu H, Chen C (2019) Data processing strategies in wind energy forecasting models and applications: a comprehensive review. Appl Energy 249:392–408

    Article  Google Scholar 

  • Mseddi A, Le Ballosi S, Aloui H, Vido L (2019) Robust control of a HESG for a wind energy application. Electric Power Syst Res 168:250–260

    Article  Google Scholar 

  • Ng YK, Leung SY (2019) Estimating the finite time Lyapunov exponent from sparse Lagrangian trajectories. Comput Phys Commun 26(4):1143–1177

    Article  MATH  Google Scholar 

  • Nie CX (2019) Applying correlation dimension to the analysis of the evolution of network structure. Chaos Solitons Fractals 123:294–303

    Article  MATH  Google Scholar 

  • Niu T, Wang JZ, Lu HY, Du P (2018) Uncertainty modeling for chaotic time series based on optimal multi-input multi-output architecture: Application to offshore wind speed. Energy Convers Manag 156:597–617

    Article  Google Scholar 

  • Saeedi M, Moradi M, Hosseini M, Emamifar A, Ghadimi N (2019) Robust optimization based optimal chiller loading under cooling demand uncertainty. Appl Therm Eng 148:1081–1091

    Article  Google Scholar 

  • Safari N, Chung CY, Price GCD (2018) Novel multi-step short-term wind power prediction framework based on chaotic time series analysis and singular spectrum analysis. IEEE Trans Power Syst 33(1):590–601

    Article  Google Scholar 

  • Schembri F, Sapuppo F, Bucolo M (2012) Experimental classification of nonlinear dynamics in microfluidic bubbles’ flow. Nonlinear Dyn 67(4):2807–2819

    Article  Google Scholar 

  • Senyange B, Manda BM, Skokos CH (2018) Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices. Phys Rev E 98(5):052229

    Article  Google Scholar 

  • Tian ZD (2020) Short-term wind speed prediction based on LMD and improved FA optimized combined kernel function LSSVM. Eng Appl Artif Intell 91:103573

    Article  Google Scholar 

  • Tian ZD, Li SJ, Wang XH (2020) A prediction approach using ensemble empirical mode decomposition-permutation entropy and regularized extreme learning machine for short-term wind speed. Wind Energy 23:177–206

    Article  Google Scholar 

  • Wang XD, Song CQ (2019) Analysis on nonlinear dynamic characteristic of synchronous generator rotor system. Complexity 2019:3603172

    Google Scholar 

  • Wang C, Zhang HL, Fan WH, Ma P (2017) A new chaotic time series hybrid prediction method of wind power based on EEMD-SE and full-parameters continued fraction. Energy 138:977–900

    Article  Google Scholar 

  • Wang C, Zhang HL, Fan WH, Ma P (2018) Analysis of chaos in high-dimensional wind power system. Chaos 28(1):013102

    Article  Google Scholar 

  • Wang B, Li W, Chen XH, Chen HH (2019) Improved chicken swarm algorithms based on chaos theory and its application in wind power interval prediction. Math Probl Eng 2019:1240717

    Google Scholar 

  • Xu M, Shang PJ, Qi Y, Zhang S (2019) Multiscale fractional order generalized information of financial time series based on similarity distribution entropy. Chaos 29(5):053108

    Article  Google Scholar 

  • Yuan LG, Zheng S, Alam Z (2019) Dynamics analysis and cryptographic application of fractional logistic map. Nonlinear Dyn 96(1):615–636

    Article  MATH  Google Scholar 

Download references

Funding

This study was funded by the Natural Science Foundation of Liaoning Province (Grant No. 2020-MS-210).

Author information

Authors and Affiliations

  1. School of Artificial Intelligence, Shenyang University of Technology, Shenyang, 110870, China

    Zhongda Tian

Authors
  1. Zhongda Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhongda Tian.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tian, Z. Analysis and research on chaotic dynamics behaviour of wind power time series at different time scales. J Ambient Intell Human Comput 14, 897–921 (2023). https://doi.org/10.1007/s12652-021-03343-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-021-03343-1

Keywords

Search

Navigation