## 3 Methodology
### Dataset
#### 3.1.2 Data Analysis  
First, we analyzed the linear relationship between the PV generation data and weather data to identify which weather feature dominantly affected the power generation of PV systems in the NIST dataset, by investigating Pearson's correlations as follows:  
\[r_{XY}=\frac{\sum_{i=1}^{N}(X_{i}-\overline{X})(Y_{i}-\overline{Y})}{\sqrt{ \sum_{i=1}^{N}(X_{i}-\overline{X})^{2}}\sqrt{\sum_{i=1}^{N}(Y_{i}-\overline{Y}) ^{2}}} \tag{1}\]  
where \(r_{XY}\) denotes a correlation coefficient between different random variables (irradiance, humidity, and etc.), \(X\) denotes PV generation, \(Y\) denotes environment variables, and \(i\) denotes a sample index, where \(N\) is the number of samples for each random variable. \(\overline{X}\) and \(\overline{Y}\) denote sample mean values, respectively.  
Irradiance, ambient temperature, relative humidity, wind speed, and snow depth were considered to be environment variables. Canopy was selected among the three PV types. The power generation data was measured at the inverter of the PV system. The heatmap of the correlation matrix for PV generation and the local weather data fields during 2015 in the NIST dataset are illustrated in Figure 3. We could identify that irradiances mainly affected the power generation of the PV system, while ambient temperature and humidity showed weaker correlations with power generation. Even though the ambient temperature showed positive correlations with the power generation, because irradiance effects were related to temperature, it was reported that the temperature increase actually reduced power generation output [55]. To observe this, we empirically divided the data into different irradiance intervals (e.g., 0-100, 100-200,..., 900-1000). We could observe that power generation decreased, and variation increased, when ambient temperature increased, as shown in Figure 4. This meant that the ambient temperature had negative correlations with power generation when it was decoupled from irradiance. Figure 5 also shows that the negative correlation relationship became stronger in high irradiance intervals. Especially, wind speed and snow depth seemed to have no correlations with power generation. Nevertheless, we observed that snow depth affected power generation in some periods, which is illustrated in Figure 6. The weather station, which measured the snow depth, was somewhat far from the PV systems. We had relatively fewer snow fall event periods compared to other weather conditions. This might have caused the very weak correlation between power generation and snow depth. For the implementation of our proposed scheme and benchmark models, we excluded the few periods when snow fell. Regarding wind speed, we could not directly observe an impact on power generation. However, it was reported that wind speed had an extreme effect the temperature of PV cells, equivalent to a cooling effect of 15-20 \({}^{\circ}\)C at wind speeds of 10 m/s [56; 57], closely related to the efficiency of PV panels [55]. Therefore, we considered four environmental variables: irradiance, ambient temperature, humidity, and wind speed.  
Figure 4: Scatter plot of power generation and ambient temperature within the irradiance interval (600\(\sim\)700 [W/m\({}^{2}\)]).  
Figure 5: Correlation coefficients between ambient temperature and power generation in different irradiance intervals.  
Figure 3: Heatmap of a correlation matrix for PV generation and local weather data fields in the NIST dataset.  
In addition, we observed some inverter faults in the dataset, and they were labeled by an expert who was managing the PV systems. It was also observed that AC power, current and voltage sharply decreased and increased in the PV system within a short time period, while irradiance showed a normal pattern, as illustrated in Figure 7.  
Figure 6: Profiles of power generation and local weather for 21 days in February 2015.  
Figure 7: Typical inverter fault patterns observed in the NIST dataset.