## 4 Results and Discussion
### Performance Evaluation
#### 4.1.2 Threshold Performance  
After training the estimation model, we utilized the model and calculated the residuals between the measured values and estimated values. By using the same dataset as the estimation model, we trained the DRL-DT agent. Therefore, we used the dataset of 2015 for training and the dataset of 2016 for testing. To set \(\beta\) and \(\gamma\), we searched 0.01 and 0.05 and, then, formed from 0.1 up to 0.9 by increasing 0.1 of \(\beta\). We found that the \(F_{1}\) score was best when \(\beta\) was 0.1. Figure 12 shows the performance of DRL-DT in terms of recall, precision, and \(F_{1}\) score.  
To compare our proposed method with benchmark methods, we implemented existing statistical threshold approaches [15, 49], a DNN classifier, and a DRL classifier. The classifiers had 7 input nodes for features (irradiance \(D_{t}\), ambient temperature \(T_{t}\), wind speed \(W_{t}\), humidity \(H_{t}\), the error of an estimated power \(e_{t}^{p}\), the error of an estimated current \(e_{t}^{l}\), the error of an estimated voltage \(e_{t}^{l}\)). Two output nodes were used to represent normal operation and inverter fault. Softmax function was used as an activation function in the output layer. In the case of the statistical approaches, fault labels were not required for the threshold. However, DNN classifier and DRL classifier required fault labels. Thus, we categorized the label-free groups according to whether fault labels were used or not. The used statistical approaches, and our proposed scheme, were label-free. We denoted the statistical approaches using dynamic thresholds of DT-1 [49] and DT-2 [15], and these approaches only used residuals between the estimated and measured values. In the case of the DNN and DRL classifiers, fault data and labels were used when they were trained. Figure 13 shows a comparison between the proposed scheme and benchmark approaches. The inverter fault data in the NIST canopy dataset had a relatively simple pattern that sharply decreased in a specific time period. Thus, the supervised manner (with fault labels) could almost completely classify inverter faults and normal data, showing an \(F_{1}\) score of 0.99. Among the label-free approaches, we observed that our proposed method showed the best performance, which was closest to the performance of the supervised manner, showing an \(F_{1}\) score of 0.94. As a result, the proposed scheme provided a 5.67% higher \(F_{1}\)-score, compared with the DT-2. The summary of the model performances are described in Table 2. The recall and precision curves were compared in Figure 14. We observed that DRL-DT  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Training Error**} & \multicolumn{2}{c}{**Validation Error**} & \multicolumn{2}{c}{**Test Error**} \\ \hline  & MAE & SMAPE & MAE & SMAPE & MAE & SMAPE \\ AC power [kW] & 4.99 & 4.34 & 5.48 & 6.32 & 8.26 & 8.30 \\ Current [A] & 15.75 & 5.16 & 16.02 & 6.88 & 25.18 & 7.87 \\ Voltage [V] & 6.61 & 1.95 & 6.80 & 2.33 & 11.38 & 3.17 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Power generation estimation performance of the estimation model based on DNNs.  
Figure 12: PV inverter fault detection performance of the proposed DRL-DT as a function of \(\beta\).  
As a result, various environmental variables, such as temperature, should also be considered to set more accurate threshold values. Both DT-1 and DT-2 used the threshold values of look-up tables, based on irradiance interval, which faces difficulties in considering various environmental variables. our proposed scheme could mitigate such difficulties and improve the accuracy of threshold values by using the DRL agent.