Prediction of Horizontal Daily Global Solar Irradiation Using Artificial Neural Networks (ANNs) in the Castile and León Region, Spain
Abstract
:1. Introduction
2. Materials and Methods
2.1. Horizontal Daily Global Solar Irradiation Data
- −
- Mean of means temperature = 11.1 °C.
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- Maximum mean temperature = 16.7 °C.
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- Minimum mean temperature = 5.5 °C.
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- Average rainfall = 515 mm.
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- Average number of days with rainfall same or above 1 mm = 75.
- −
- Average number of clear days = 83.
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- Average yearly number of sun hours = 2673 h.
2.2. The Prediction of Horizontal Daily Global Solar Irradiation Using ANNs
- −
- [H(t)], horizontal daily global solar irradiation of the current day MJ/(m2·d).
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- [H(t−1)], horizontal daily global solar irradiation a day delayed, MJ/(m2·d).
- −
- [H(t−2)], horizontal daily global solar irradiation two days delayed, MJ/(m2·d).
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- [J(t)], number of the day of the year (1…365), adimensional.
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- [Kt(t)], daily clearness index, adimensional, which is calculated as the relation between the incident global solar irradiation over the earth surface (H), and the extraterrestrial solar irradiation (H0), which is calculated for each particular day as a function of the latitude [3].
2.3. The Prediction of Horizontal Daily Global Solar Irradiation Using Classic Models
2.3.1. CENSOLAR Typical Year
2.3.2. Weighted Moving Mean with Partial Autocorrelation
2.3.3. Linear Regression
2.3.4. Fourier Analysis
2.3.5. Markov Analysis
- −
- All data series were rounded and a corresponding state was assigned making use of MATLAB ‘round’ function.
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- Maximum and minimum value of the data series was found for the horizontal daily global solar irradiance by using MATLAB ‘max’ and ‘min’ functions, resulting in 33 possible states.
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- A probability matrix was created using the transitions or change of state of the existing data series.
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- A Markov transition matrix (MTM) probability matrix was created with a transitions number for each data series state.
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- MTM is normalized by dividing each element by the value of the sum of all the elements in a line, which results in the normalized Markov transition matrix (NMTM), where the sum of all the line element has 1 as a value.
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- The state change probability has been calculated for the day after based on the state of the current day, multiplying the state vector of the current day by NMTM vector, ending with a vector in which the position where the highest value is located, will be the state with the highest probability to occur the day after.
3. Results
3.1. Results of Simulations with the Artificial Neural Networks Models
3.2. Results of the Classic Models
3.2.1. CENSOLAR Typical Year
3.2.2. Weighted Moving Mean (WMM) with Partial Autocorrelation
3.2.3. Linear Regression
3.2.4. Fourier Analysis
3.2.5. Markov Analysis
4. Discussion
5. Conclusions
- (1)
- Use of other explicative variables, such as humidity, temperature, atmospheric pressure, or cloudiness, which contribute to changes in the evolution of solar radiation, mainly the days in which sudden changes in the weather occurs, and moments when ANN models present their worst results.
- (2)
- Division of input data for the different times/seasons of the year that have similar characteristics and the generation of models for each of them.
- (3)
- Use of predictions from the national meteorological services as input data for the ANN models, instead of the historic data registered in the area.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
AIC | Akaike information criterion, adimensional. |
ANN | Artificial neural networks. |
BP-LM | Back-propagation Levenberg-Marquardt algorithm. |
CENSOLAR | Centro de Estudios de la Energía Solar (Spain). |
d | Day |
DW | Durbin-Watson coefficient, adimensional. |
FA | Forecast accuracy, adimensional. |
GP | Genetic programming. |
GPML | Gaussian process machine learning. |
GUI | Graphical User Interface. |
H | Incident global solar irradiation over the earth surface, MJ/(m2·d). |
H0 | Extraterrestrial solar irradiation, MJ/(m2·d). |
[H(t+1)] | Horizontal daily global solar irradiation of the day after, MJ/(m2·d). |
[H(t)] | Horizontal daily global solar irradiation of the current day, MJ/(m2·d). |
[H(t−1)] | Horizontal daily global solar irradiation a day delayed, MJ/(m2·d). |
[H(t−2)] | Horizontal daily global solar irradiation two days delayed, MJ/(m2·d). |
[H(t−10)] | Horizontal daily global solar irradiation ten days delayed, MJ/(m2·d). |
ITACyL | Agricultural Technological Institute in Castile and León (in Spanish), |
[J(t)] | Number of the day of the year, adimensional. |
[Kt(t)] | Daily clearness index, adimensional. |
LR | Linear regression model. |
MLP | Multilayer feed-forward perceptron. |
MPE | Mean percentage error, adimensional. |
MTM | Markov transition matrix. |
NMTM | Normalized Markov transition matrix. |
RMSE | Root mean square error, MJ/(m2·d). |
R2 | Coefficient of determination, adimensional. |
SIAR | Agroclimatic Information System for Irrigation (in Spanish). |
SVR | Support vector regression. |
WMM | Weighted moving mean model. |
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Model | Inputs | Model’s Architecture (1) | RMSE | R2 | DW | MPE | FA | AIC |
---|---|---|---|---|---|---|---|---|
ANN 1 | [H(t)] | (1-1-1) | 4.2609 | 0.7862 | 2.2632 | −0.2523 | 0.5884 | 4.2835 |
ANN 2 | [H(t−1), H(t)] | (2-6-1) | 4.1292 | 0.7988 | 1.9703 | −0.2517 | 0.5940 | 4.1733 |
ANN 3 | [H(t−2), H(t−1), H(t)] | (3-8-1) | 4.0204 | 0.8088 | 1.8543 | −0.2507 | 0.5938 | 4.0830 |
ANN 4 | [H(t), J(t)] | (2-5-1) | 3.8012 | 0.8299 | 1.9263 | −0.2154 | 0.6196 | 3.8427 |
ANN 5 | [H(t−1), H(t), J(t)] | (3-10-1) | 3.8467 | 0.8253 | 1.9061 | −0.2232 | 0.6160 | 3.9106 |
ANN 6 | [H(t−2), H(t−1), H(t), J(t)] | (4-7-1) | 3.8431 | 0.8253 | 1.8007 | −0.2032 | 0.6277 | 3.9261 |
ANN 7 | [H(t), Kt(t)] | (2-6-1) | 3.7703 | 0.8326 | 1.9183 | −0.2022 | 0.6324 | 3.8118 |
ANN 8 | [H(t), Kt(t), J(t)] | (3-7-1) | 3.8043 | 0.8297 | 1.8716 | −0.2273 | 0.6098 | 3.8662 |
Model | RMSE | R2 | DW | MPE | FA | AIC |
---|---|---|---|---|---|---|
CENSOLAR | 5.1829 | 0.6837 | 0.7092 | −0.1342 | 0.5286 | 5.2105 |
Weighted Moving Mean [H(t−1), H(t)] | 4.2582 | 0.7865 | 2.0952 | −0.1366 | 0.6589 | 4.3048 |
Weighted Moving Mean [H(t−10), H(t)] | 3.9810 | 0.8134 | 1.7265 | −0.1682 | 0.6493 | 4.2283 |
Linear Regression [H(t)] | 4.2434 | 0.7880 | 2.2880 | −0.2234 | 0.6103 | 4.2666 |
Fourier 1st Harmonic | 4.2747 | 0.7848 | 1.0439 | −0.2692 | 0.5294 | 4.2974 |
Fourier 2nd Harmonic | 4.2626 | 0.7861 | 1.0498 | −0.2629 | 0.5381 | 4.3086 |
Fourier 3rd Harmonic | 4.2675 | 0.7856 | 1.0474 | −0.2617 | 0.5388 | 4.3374 |
Fourier 4th Harmonic | 4.2618 | 0.7861 | 1.0499 | −0.2560 | 0.5466 | 4.3562 |
Fourier 5th Harmonic | 4.2465 | 0.7877 | 1.0575 | −0.2580 | 0.5439 | 4.3642 |
Fourier 6th Harmonic | 4.2552 | 0.7868 | 1.0532 | −0.2577 | 0.5444 | 4.3971 |
Fourier 7th Harmonic | 4.2537 | 0.7869 | 1.0539 | −0.2547 | 0.5490 | 4.4199 |
Fourier 8th Harmonic | 4.2557 | 0.7867 | 1.0529 | −0.2543 | 0.5495 | 4.4463 |
Markov [H(t)] | 4.3653 | 0.7756 | 2.4099 | −0.1525 | 0.6497 | 4.3892 |
Harmonics | Typical Annual Fourier Function | RMSE |
---|---|---|
1st | 4.417 | |
2nd | 4.372 | |
3rd | 4.370 | |
4th | 4.365 | |
5th | 4.360 | |
6th | 4.358 | |
7th | 4.355 | |
8th | 4.355 |
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Diez, F.J.; Navas-Gracia, L.M.; Chico-Santamarta, L.; Correa-Guimaraes, A.; Martínez-Rodríguez, A. Prediction of Horizontal Daily Global Solar Irradiation Using Artificial Neural Networks (ANNs) in the Castile and León Region, Spain. Agronomy 2020, 10, 96. https://doi.org/10.3390/agronomy10010096
Diez FJ, Navas-Gracia LM, Chico-Santamarta L, Correa-Guimaraes A, Martínez-Rodríguez A. Prediction of Horizontal Daily Global Solar Irradiation Using Artificial Neural Networks (ANNs) in the Castile and León Region, Spain. Agronomy. 2020; 10(1):96. https://doi.org/10.3390/agronomy10010096
Chicago/Turabian StyleDiez, Francisco J., Luis M. Navas-Gracia, Leticia Chico-Santamarta, Adriana Correa-Guimaraes, and Andrés Martínez-Rodríguez. 2020. "Prediction of Horizontal Daily Global Solar Irradiation Using Artificial Neural Networks (ANNs) in the Castile and León Region, Spain" Agronomy 10, no. 1: 96. https://doi.org/10.3390/agronomy10010096
APA StyleDiez, F. J., Navas-Gracia, L. M., Chico-Santamarta, L., Correa-Guimaraes, A., & Martínez-Rodríguez, A. (2020). Prediction of Horizontal Daily Global Solar Irradiation Using Artificial Neural Networks (ANNs) in the Castile and León Region, Spain. Agronomy, 10(1), 96. https://doi.org/10.3390/agronomy10010096