Solar and Wind Data Recognition: Fourier Regression for Robust Recovery
<p>Case study Location, Midland, TX, USA [<a href="#B29-BDCC-08-00023" class="html-bibr">29</a>].</p> "> Figure 2
<p>Integrating Solar and Wind Power Into the Existing Electric Grid.</p> "> Figure 3
<p>A Hierarchical Methodology for Predicting DNI, DHI, and Wind Speed.</p> "> Figure 4
<p>Fourier Series-based Network.</p> "> Figure 5
<p>Original DHI versus Forecasted DHI.</p> "> Figure 6
<p>Original DNI versus Forecasted DNI.</p> "> Figure 7
<p>Zoomed-in Original DHI versus Forecasting DHI.</p> "> Figure 8
<p>Zoomed-in Original DNI versus Forecasted DNI.</p> "> Figure 9
<p>Original Wind Speed versus Forecasted Wind Speed.</p> "> Figure 10
<p>Zoomed-In Original Wind Speed versus Forecasted Wind Speed.</p> "> Figure 11
<p>Magnitude Spectrum.</p> "> Figure 12
<p>Phase Spectrum.</p> "> Figure 13
<p>DHI Residuals.</p> "> Figure 14
<p>DNI Residuals.</p> "> Figure 15
<p>Wind Speed Residuals.</p> "> Figure 16
<p>Histogram of DHI residuals.</p> "> Figure 17
<p>Histogram of DNI Residuals.</p> "> Figure 18
<p>Histogram of wind speed residuals.</p> "> Figure 19
<p>RMSE with Different Adjustment.</p> ">
Abstract
:1. Introduction
2. Model Site Description and Data Collection
3. Regression-Based Fourier Model and Parameter Estimation
3.1. Regression-Based Fourier Model Formulation
3.2. General Model Description
4. Results and Discussions
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviation
Individual data points for variables A and B, respectively. | |
The means of variables A and B. | |
y(t) | The signal that changes over time and needs to be predicted. |
The signal’s total time duration l. | |
h | The time increment between each signal sample. |
k | An index representing a specific time instant. |
Unknown constant coefficients in a mathematical series used for prediction. | |
The Nyquist frequency, half of the sampling angular frequency . | |
N | The number of data points in the signal. |
A vector used in the prediction process. | |
A vector representing the predicted signal. | |
ϵ | A small positive constant. |
T | The fundamental period of the signal. |
The fundamental angular frequency. | |
Y | A vector containing all the signal’s sampled data points. |
The predicted or approximated signal at a specific time instant. | |
M | A constant term in the mathematical series. |
The angular frequency at which the signal is sampled. | |
W | A vector containing coefficients used for prediction. |
Φ | A matrix of vectors used in the prediction process. |
A mathematical operation involving the pseudo-inverse matrix. | |
I | The identity matrix. |
n | The number of observations in the dataset. |
The actual values. | |
The predicted values. |
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Al-Aboosi, A.F.; Muñoz Vazquez, A.J.; Al-Aboosi, F.Y.; El-Halwagi, M.; Zhan, W. Solar and Wind Data Recognition: Fourier Regression for Robust Recovery. Big Data Cogn. Comput. 2024, 8, 23. https://doi.org/10.3390/bdcc8030023
Al-Aboosi AF, Muñoz Vazquez AJ, Al-Aboosi FY, El-Halwagi M, Zhan W. Solar and Wind Data Recognition: Fourier Regression for Robust Recovery. Big Data and Cognitive Computing. 2024; 8(3):23. https://doi.org/10.3390/bdcc8030023
Chicago/Turabian StyleAl-Aboosi, Abdullah F., Aldo Jonathan Muñoz Vazquez, Fadhil Y. Al-Aboosi, Mahmoud El-Halwagi, and Wei Zhan. 2024. "Solar and Wind Data Recognition: Fourier Regression for Robust Recovery" Big Data and Cognitive Computing 8, no. 3: 23. https://doi.org/10.3390/bdcc8030023
APA StyleAl-Aboosi, A. F., Muñoz Vazquez, A. J., Al-Aboosi, F. Y., El-Halwagi, M., & Zhan, W. (2024). Solar and Wind Data Recognition: Fourier Regression for Robust Recovery. Big Data and Cognitive Computing, 8(3), 23. https://doi.org/10.3390/bdcc8030023