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. 2015 Jan 24;10(1):e0115123.
doi: 10.1371/journal.pone.0115123. eCollection 2015.

A Nonlinear Dynamics Approach for Incorporating Wind-Speed Patterns Into Wind-Power Project Evaluation

Free PMC article

A Nonlinear Dynamics Approach for Incorporating Wind-Speed Patterns Into Wind-Power Project Evaluation

Ray Huffaker et al. PLoS One. .
Free PMC article


Wind-energy production may be expanded beyond regions with high-average wind speeds (such as the Midwest U.S.A.) to sites with lower-average speeds (such as the Southeast U.S.A.) by locating favorable regional matches between natural wind-speed and energy-demand patterns. A critical component of wind-power evaluation is to incorporate wind-speed dynamics reflecting documented diurnal and seasonal behavioral patterns. Conventional probabilistic approaches remove patterns from wind-speed data. These patterns must be restored synthetically before they can be matched with energy-demand patterns. How to accurately restore wind-speed patterns is a vexing problem spurring an expanding line of papers. We propose a paradigm shift in wind power evaluation that employs signal-detection and nonlinear-dynamics techniques to empirically diagnose whether synthetic pattern restoration can be avoided altogether. If the complex behavior of observed wind-speed records is due to nonlinear, low-dimensional, and deterministic system dynamics, then nonlinear dynamics techniques can reconstruct wind-speed dynamics from observed wind-speed data without recourse to conventional probabilistic approaches. In the first study of its kind, we test a nonlinear dynamics approach in an application to Sugarland Wind-the first utility-scale wind project proposed in Florida, USA. We find empirical evidence of a low-dimensional and nonlinear wind-speed attractor characterized by strong temporal patterns that match up well with regular daily and seasonal electricity demand patterns.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.


Fig 1
Fig 1. Proposed procedure for integrating nonlinear dynamic methods into wind project evaluation.
Fig 2
Fig 2. Data.
(A) The typical daily electric demand load for hot and cold seasons. (B) Power curve for General Electric 1.6–100 turbine. (C) Preprocessed six-hour wind-speed record from April 1, 2009 through March 31, 2012 (4380 observations).
Fig 3
Fig 3. Signal Detection.
Fourier power spectrum of preprocessed wind velocity series showing dominant frequency associated with a diurnal oscillation (0.25 Hz).
Fig 4
Fig 4. 1st Stage SSA.
Plots of preprocessed wind velocity record (black line) and extracted trend series (grey line) reconstructed from EOFs 1, 4, and 5.
Fig 5
Fig 5. 2nd Stage Eigenspectrum.
EOF pairs 1, 2 and 3, 4 as the basis of possible oscillatory components in the preprocessed wind velocity series.
Fig 6
Fig 6. 2nd Stage Oscillations.
(A) The graphs of the eigenvectors associated with EOFs 1 and 2 oscillate with identical frequency in phase quadrature. (B) The scatterplot of these eigenvectors results in a four-sided polygon reflecting a four-cycle of 6-hour blocks, i.e., a diurnal oscillation. (C) The graphs of the eigenvectors associated with EOFs 3 and 4 oscillate with identical frequency in phase quadrature. (D) The scatterplot of these eigenvectors gives a circular polygon reflecting a relatively low-frequency cycle of 100 six-hour blocks (25 days).
Fig 7
Fig 7. Signal Detection.
The continuous wavelet spectrum of first-stage SSA residuals verifies stationary power at the dominant frequency of the diurnal oscillation.
Fig 8
Fig 8. w-Correlations.
The w-correlation matrix shows required statistical independence of EOF pairs 1, 2 and 3, 4. Lighter shaded boxes indicate low w-correlations.
Fig 9
Fig 9. 2nd Stage SSA.
(A) Plots of preprocessed wind-speed series (black line) and denoised series reconstruction (grey line). (B) Plots of extracted diurnal oscillation (black line) and 25-day oscillation (grey line).
Fig 10
Fig 10. Phase Space Reconstruction.
Wind speed dynamics evolve along a nonlinear low-dimension attractor reconstructed from lagged copies of the denoised and detrended SSA-reconstructed series. The attractor exhibits the dominant four-cycle of six-hour blocks giving the diurnal oscillation. The inset highlights the internal structure of the attractor by plotting only the first 200 points.
Fig 11
Fig 11. Wind power supply.
(A) Wind power (MW) generated on the reconstructed attractor per turbine per 6-hour interval from April 2009 through March 2012. (B) The percentage of total wind power generated during “hot” season months (April through October). The largest percentage of wind power is generated during the peak afternoon demand period (12:00–18:00). (C) The percentage of total wind power generated during “cold” season months (November through March). The largest percentage of power is generated during the peak morning demand period (6:00–12:00), the lowest percentage is generated during the peak evening demand period (18:00–24:00).
Fig 12
Fig 12. Sugarland Wind’s average annual supply rates per household.
Wind power (MWh) generated along the reconstructed attractor for 114 turbines and 60,000 households planned for Sugarland Wind (grey boxes) supplies 22%–26% of average annual electricity consumption per household in Florida (black boxes) for 2009–2010, 2010–11, and 2011–12.
Fig 13
Fig 13. Out-of-Sample Forecasting (1 week).
Out-of-sample forecasts successfully project reconstructed diurnal and lower-frequency oscillations.

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