# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 2 Proposed Solution
### Exploratory Data Analysis  
The distributed data is characterized by unique features at each site. However, to predict the GHI for the next \(\delta\) time step, the GHI values must be present in the dataset. This requirement is met by the stations considered. For instance, the features of 3 different stations, Natural Energy Laboratory of Hawaii Authority (NELHA), University of Louisiana at Lafayette (ULL), and Cal Poly Humboldt SoRMS (HSU), are described in Table 5. Two more stations were used in the training, namely, REL Flatirons Campus (NWTC) and the University of Florida (UFL). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **Equation** & **Optimal Value** & **Advantages** \\ \hline \(R^{2}\) & \(R^{2}=1-\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}{\sum_{i=1}^{n}(y_{i}-\hat{y })^{2}}\) & 1 & Indicates the proportion of variance explained by the model, making it easy to interpret. \\ RMSE & RMSE & \(\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}\) & 0 & Sensitive to large errors, providing a clear measure of model accuracy. \\ MAE & MAE & \(\frac{1}{n}\sum_{i=1}^{n}\left|y_{i}-\hat{y}_{i}\right|\) & 0 & Easy to understand and less sensitive to outliers compared to RMSE. \\ MAPE & MAPE & \(\frac{100\%}{n}\sum_{i=1}^{n}\left|\frac{y_{i}-\hat{y}_{i}}{y_{i}}\right|\) & 0\% & Expresses errors as a percentage, making it easier to interpret the relative size of errors. \\ Median AE & Median AE & \(\frac{1}{n}\) median(\(\left|y_{i}-\hat{y}_{i}\right|\)) & 0 & Robust to outliers, providing a more resilient measure of central tendency. \\ \(D^{2}\) & \(D^{2}=1-\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}{\sum_{i=1}^{n}(y_{i}-\hat{y })^{2}}\) & 1 & Similar to \(R^{2}\) but more suitable for specific types of regression models, offering additional flexibility. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression metrics. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameter** & **NELHA** & **ULL** & **HSU** \\  & **Units** & **Units** & **Units** \\ \hline Air temperature & ✓(\({}^{\circ}\) C) & ✓(\({}^{\circ}\) C) & \\ Avg wind direction (stdev) & ✓(\({}^{\circ}\)) & \\ Avg wind direction & ✓(\({}^{\circ}\) from N) & ✓(\({}^{\circ}\) from N) & \\ Avg wind speed & ✓(m/s) & ✓(m/s) & \\ CR1000 battery & ✓(VDC) & ✓(VDC) & \\ CR1000 temp & ✓(\({}^{\circ}\) C) & ✓(\({}^{\circ}\) C) & \\ Dew point temp & ✓(\({}^{\circ}\) C) & \\ Global horizontal & ✓(W/m\({}^{2}\)) & ✓(W/m\({}^{2}\)) & ✓(W/m\({}^{2}\)) \\ Global PAR & ✓(\(\text{\text{\text{\text{\text{\text{\text{\text{\text{\text@underline{\text{ \text{\textThe exploration of these features toward the development of an optimal solution was performed based on the queries described below. * What does the outlier study reveal? Outlier analysis, an essential step for detecting factors such as fluctuations in incident radiation, solar panel performance, and faults, was performed at the three sites. The presence of outliers can be attributed to various factors beyond those initially mentioned. Notably, outliers were observed in the GHI series across all stations, as shown in Figure 3. At the NELHA site, outliers were found in the global PAR, global UV-FPD, and global UV measurements. At the HSU site, outliers were present in the diffuse irradiance variants, direct normal irradiance, and to some extent, the airmass feature. Lastly, at the ULL station, outliers were detected in the GHI, DNI, DHI, and CR1000 temperature measurements. Outliers in solar irradiance data often result from rapid and unpredictable changes in environmental conditions, sensor inaccuracies, and calibration issues. For instance, GHI outliers across all stations may stem from sudden weather changes, such as cloud cover or precipitation, which impact the total solar radiation measured. At the NELHA site, outliers in global PAR, UV-FPD, and UV measurements could be due to local variations in vegetation or atmospheric conditions.