Predictions of Surface Solar Radiation on Tilted Solar Panels using Machine Learning Models: A Case Study of Tainan City, Taiwan
Abstract
:1. Introduction
2. Study Site and Data
2.1. Ground Weather Data Set {A}
2.2. Satellite Remote-Sensing Data Set {B}
2.3. Sun Position Data Set {C}
2.3.1. Declination Angle
2.3.2. Hour Angle
2.3.3. Zenith Angle
2.3.4. Elevation Angle
2.3.5. Azimuth Angle
3. Methodology and Models
3.1. Procedures of the Methodology
3.2. Machine Learning
3.2.1. Multilayer Perceptron Neural Networks
3.2.2. Random Forests
- Step 1:
- Determine the number of decision trees required to construct RFs.
- Step 2:
- Use bootstrapping to generate new training data in existing ones. Both new and existing training data are equivalent in volume.
- Step 3:
- Use the data derived through bootstrapping to generate classification and regression trees. If the number of independent variables is P during the generation of the trees, then branching is performed on randomly selected nodes whose number of independent variables is lower than .
- Step 4:
- Repeat Steps 2 and 3 until the number of decision trees as determined in Step 1 is reached.
- Step 5:
- Analyses are performed using all decision trees. If the dependent variables are categorical, and the variable that appears the most frequently in the decision trees is deemed to be the output. If dependent variables are continuous, then the average of the prediction results from all the trees is used as the output.
3.2.3. k-Nearest Neighbor
4. Experiments and Modeling
4.1. Data Partition and Combination Cases
- Dataset combination 1: ground weather dataset, denoted by {A}.
- Dataset combination 2: ground weather dataset and satellite remote-sensing dataset ({A,B}).
- Dataset combination 3: ground weather dataset and solar position dataset ({A,C}).
- Dataset combination 4: ground weather dataset, satellite remote-sensing dataset, and solar position dataset ({A,B,C}).
4.2. Model Parameter Setup and Calibration
4.3. Forecasting Solar Irradiance in t + 1 through the Four Dataset Combinations
4.3.1. Results of Dataset Combinations
4.3.2. Evaluation
- Regarding (Figure 6a), the improvement rate was the highest in RF (100%), followed by kNN (93.6%), MLP (87.7%), and LR (23.1%).
- Regarding (Figure 6b), the improvement rate was the highest in RF (99.9%), followed by MLP (95.4%), kNN (89.4%), and LR (44.6%).
- Regarding (Figure 6c), the improvement rate was the highest in RF (98.4%), followed by MLP (94.3%), kNN (91%), and LR (47.3%).
4.4. Forecasting Solar Irradiance across Different Forecast Horizons
4.4.1. Prediction Results as Represented by MAE, RMSE, and r
4.4.2. Predicted vs. Observed Changes in Solar Irradiance
4.4.3. Prediction Errors across Seasons
5. Deriving Equations for Solar Irradiance Received by a Tilted Solar Panel
5.1. Estimating Theoretical Clear-Sky Solar Irradiance
5.1.1. Theoretical Values of GC, IC, and DC
5.1.2. Solar Incident Angle (Θ) and Global Irradiance with Tilted Solar Panels (Gtilt)
5.2. Estimating Observed and Predicted Solar Irradiance with Tilted Solar Panels
5.2.1. Estimating the Observed and Predicted Direct Irradiance and Diffuse Horizontal Irradiance
5.2.2. Estimating the Observed and Predicted Global Irradiance with the Solar Panels Set at a Tilted Position
6. Estimating Solar Irradiance with the Solar Panels Set at a Tilted Position
6.1. Estimating the Observed and Predicted Values of Global Horizontal Irradiance and Diffuse Horizontal Irradiance
6.2. Estimating the Observed and Predicted Global Irradiance with Solar Panels set at Different Tilt Angles
6.3. Total Annual Global Irradiance in Relation to Different Solar-Panel Tilt Angles
6.3.1. Total Annual Global Irradiance and Its Increase Rate
6.3.2. Total Annual Global Irradiance at Different Solar-panel Tilt Angles
7. Conclusions
Acknowledgments
Conflicts of Interest
References
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Data Set | Attribute | Unit | Min–Max | Mean | Standard Deviation |
---|---|---|---|---|---|
Ground weather | Atmospheric pressure | hPa | 973.8–1031.5 | 1011.2 | 5.72 |
Wind speed | m/s | 0–18.4 | 2.83 | 1.70 | |
Precipitation | mm | 0–95 | 0.23 | 1.91 | |
Temperature | °C | 5.6–35.9 | 24.3 | 5.38 | |
Relative humidity | % | 23–100 | 74.0 | 10.17 | |
Radiation | w/m2 | 0–1125.00 | 162.04 | 249.38 | |
Satellite Remote-sensing | Aerosol optical depth | - | 0.18–10.74 | 2.80 | 1.56 |
Water vapor | cm | 0.15–77.21 | 37.47 | 13.72 | |
Cirrus reflectance | - | 0.25–67.42 | 2.92 | 4.99 | |
Cloud fraction | - | 0.93–100 | 68.50 | 28.76 | |
Sun Position | Declination angle | Deg. | −23.45–23.45 | −0.01 | 16.58 |
Hour angle | Deg. | −165.00–80.00 | 7.50 | 103.83 | |
Zenith angle | Deg. | 0.01–179.99 | 90.00 | 43.83 | |
Elevation angle | Deg. | −89.99–89.99 | 0.00 | 43.83 | |
Azimuth angle | Deg. | −90.00–90.00 | 0.00 | 65.09 |
Model Case | MLP | RF | kNN | |
---|---|---|---|---|
Learning Rate | Momentum | Size of Each Bag | Number of Neighbors | |
Dataset {A} | 0.5 | 0.2 | 40 | 30 |
Dataset {A, B} | 0.1 | 0.1 | 25 | 25 |
Dataset {A, C} | 0.1 | 0.2 | 45 | 30 |
Dataset {A, B, C} | 0.1 | 0.3 | 30 | 25 |
Performance | Case {A} | Case {A,B} | Case {A,C} | Case {A,B,C} |
---|---|---|---|---|
MAE | 62.52 | 63.23 | 39.33 | 39.42 |
RMSE | 104.45 | 104.67 | 76.78 | 76.75 |
r | 0.924 | 0.923 | 0.960 | 0.961 |
Season | Performance | t + 1 | t + 6 | ||||||
---|---|---|---|---|---|---|---|---|---|
MLP | RF | kNN | LR | MLP | RF | kNN | LR | ||
Spring | MAE (w/m2) | 39.4 | 37.4 | 41.1 | 57.9 | 76.0 | 68.5 | 70.6 | 123.1 |
rMAE | 0.209 | 0.198 | 0.218 | 0.307 | 0.403 | 0.363 | 0.374 | 0.652 | |
RMSE (w/m2) | 74.6 | 73.8 | 80.0 | 89.0 | 125.6 | 129.7 | 135.2 | 184.5 | |
rRMSE | 0.395 | 0.391 | 0.424 | 0.472 | 0.665 | 0.687 | 0.716 | 0.978 | |
r | 0.964 | 0.965 | 0.959 | 0.950 | 0.896 | 0.888 | 0.876 | 0.767 | |
Summer | MAE (w/m2) | 50.7 | 47.6 | 48.8 | 67.8 | 84.9 | 78.7 | 75.2 | 134.7 |
rMAE | 0.232 | 0.217 | 0.223 | 0.310 | 0.388 | 0.360 | 0.344 | 0.616 | |
RMSE (w/m2) | 96.5 | 93.1 | 95.9 | 110.6 | 134.0 | 140.1 | 134.4 | 201.6 | |
rRMSE | 0.441 | 0.426 | 0.438 | 0.506 | 0.613 | 0.640 | 0.614 | 0.922 | |
r | 0.950 | 0.954 | 0.951 | 0.933 | 0.906 | 0.901 | 0.906 | 0.805 | |
Autumn | MAE (w/m2) | 36.2 | 34.1 | 36.8 | 56.0 | 72.4 | 63.7 | 63.8 | 107.6 |
rMAE | 0.218 | 0.205 | 0.222 | 0.338 | 0.436 | 0.384 | 0.384 | 0.648 | |
RMSE (w/m2) | 72.1 | 70.8 | 73.4 | 89.3 | 122.2 | 123.7 | 121.3 | 170.1 | |
rRMSE | 0.434 | 0.426 | 0.442 | 0.538 | 0.736 | 0.745 | 0.731 | 1.025 | |
r | 0.962 | 0.964 | 0.962 | 0.941 | 0.892 | 0.892 | 0.892 | 0.781 | |
Winter | MAE (w/m2) | 29.4 | 28.5 | 30.7 | 52.4 | 64.6 | 53.8 | 57.1 | 104.9 |
rMAE | 0.214 | 0.207 | 0.223 | 0.382 | 0.470 | 0.392 | 0.416 | 0.764 | |
RMSE (w/m2) | 59.4 | 57.8 | 61.5 | 79.2 | 108.4 | 104.1 | 109.1 | 157.9 | |
rRMSE | 0.432 | 0.421 | 0.448 | 0.577 | 0.790 | 0.758 | 0.795 | 1.150 | |
r | 0.968 | 0.969 | 0.966 | 0.940 | 0.884 | 0.893 | 0.880 | 0.725 |
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Wei, C.-C. Predictions of Surface Solar Radiation on Tilted Solar Panels using Machine Learning Models: A Case Study of Tainan City, Taiwan. Energies 2017, 10, 1660. https://doi.org/10.3390/en10101660
Wei C-C. Predictions of Surface Solar Radiation on Tilted Solar Panels using Machine Learning Models: A Case Study of Tainan City, Taiwan. Energies. 2017; 10(10):1660. https://doi.org/10.3390/en10101660
Chicago/Turabian StyleWei, Chih-Chiang. 2017. "Predictions of Surface Solar Radiation on Tilted Solar Panels using Machine Learning Models: A Case Study of Tainan City, Taiwan" Energies 10, no. 10: 1660. https://doi.org/10.3390/en10101660