Wind farm power prediction based on wavelet decomposition and chaotic time series
Highlights
► A useful model based on wavelet transform, chaotic time series and GM (1, 1) method is presented for wind farm power forecasting. ► In the proposed method, the wind farm power is decomposed into several components from high to low frequencies by the wavelet transform, and the characteristic of each decomposed components is identified. ► Each component is respectively predicted by weighted one-rank-region method or GM (1, 1) according to their different characteristics. ► The final forecasted result is obtained by summing the predicted results of all the decomposed components.
Introduction
The intermittence and uncertainty of wind power increases the instability of its interconnected power grid, with the large-scale wind power parallel in the power grid. It also has significant influence on the load distribution and the reasonable quality of power supply. In order to improve overall power system scheduling reasonableness, safety and economy, it is very important to predict wind farm power timely and accurately (Damousis et al., 2004, Kusiak et al., 2009, Landberg, 1999, Louka et al., 2008, Mabel and Fernandez, 2008, Pinson and Kariniotakis, 2004, Ramirez-Rosado et al., 2009).
The actual wind power output variation is very complicated and difficult to establish its mathematical model, due to the power generation is known to be highly influenced by wind speed, wind direction, pressure, temperature, etc. meteorological data, and wind fields, topography, vegetation, surrounded by obstacles. Furthermore, it also is affected by the wheel hub height, power curve, mechanical drive, control strategy, and many other factors of the wind turbine itself (Damousis et al., 2004, Kusiak et al., 2009, Landberg, 1999, Louka et al., 2008, Mabel and Fernandez, 2008, Pinson and Kariniotakis, 2004, Ramirez-Rosado et al., 2009).
In this paper, a wind farm power prediction model is constructed based on wavelet transform, chaotic theory, and GM(1, 1) model. The wavelet transform is used to decompose the non-stationary wind farm power time series into several detail parts associated with high frequencies and an approximate part associated with low frequencies. After identifying their characteristics, the weighted one-rank local-region method or GM(1, 1) model is employed to make a short-term prediction for each part, respectively. Finally, the ultimate prediction result for the whole wind farm power is obtained by summing all predicted results. And the proposed method is applied to Dongtai wind farm which situates in the east of China, the predicted results is encouraging.
Section snippets
Wavelet transform
The wavelet transform is a mathematical tool for nonlinear and non-stationary signal analysis (Magosso et al., 2009, Shahriar et al., 2005, Yao et al., 2000, Zhang et al., 2001). It allows the decomposition of a signal into contributions from both the space and scale domains through a dilation and translation processes.
For a given square integrable signal x(t), its continuous wavelet transform is defined aswhere ψ(t) is the mother wavelet, the a, b are scale
Reconstruction of the phase-space
Wind farm power is affected by many factors, is a complex and nonlinear time series. In order to predict the time series using chaotic theory, an important step is determining the presence of chaotic property. A method for reconstructing a phase-space from a single time series has been presented by Takens (1981). When wind turbine is running, if the dynamics of a power time series {x(i)}, (i = 1, 2, … , n), are embedded in the m-dimensional phase-space (m ⩾ 2d + 1, where d is the correlation dimension),
Chaotic prediction of wind farm power
If the chaotic property of wind farm power can be determined, it can be predicted using chaotic method and the prediction results are valid for small prediction steps. In this paper, the weighted one-rank local-region method (Lv, Lu, & Chen, 2002) is used to predict the wind farm power. The detail process to formulate the weighted one-rank local-region method is described as follows:
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Step 1. Find nearest neighbor points.
In phase-space, assuming that Yki is the adjacent point of the center point Y
Wind farm power prediction based on wavelet decomposition, chaotic time series and GM(1, 1) model
This section provides a schematic overview of a forecasting procedure based on wavelet decomposition, chaotic time series and GM(1, 1) model. Due to wind farm power is highly nonlinear and non-stationary, it is very difficult to predict accurately. In order to improve prediction accuracy, the wavelet decomposition method is used to decompose the wind farm power to several detail parts associated with high frequencies and an approximate part associated with low frequencies. The basic idea is to
Case study
To demonstrate the effectiveness and reliability of the proposed method, we use the actual power generation data for a wind turbine of Dongtai wind farm which situates in the east of China as an illustrating example. In this paper, though the data is generated with a wind turbine, the proposed method applies to large numbers of data. The detailed analysis steps as follows:
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Step 1: Pre-processing of original data.
The actual wind turbine output power time series from the wind farm is depicted in
Conclusion
In this paper, a prediction model is constructed by combining wavelet transform, chaotic theory, and GM(1, 1) model. We use wavelet transform to decompose the power into different scales, this can reduce the non-stationary of the power time series and enhance the prediction accuracy. By analyzing the characteristics of the decomposition of the wind farm power, the forecasting strategies of weighted one-rank local-region and GM(1, 1) are applied to predict each scale individually. In the end,
Acknowledgements
This work is supported by the National Basic Research Program (973 Program) (No. 2007CB210304) and China Postdoctoral Science Foundation funded project (No. 20090460273).
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