## 4 Conclusions  
Daily line loss rate is a critical indictor for power-supply corporations as it greatly affects their profits. In order to better manage the level of line losses and provide guidance for the construction and operation of low-voltage transformer regions, it is concerned with developing an efficient method to compute benchmark values for daily line loss rates. Based on the benchmarks, reasonable intervals of the daily line loss rates can be further obtained, which are able to help discover abnormal line loss rate values, as well to help operators to check and confirm those irregular operating conditions. However, the number of studies is limited that research on calculating benchmark values of daily line loss rates and eliminating outlier from collected line loss rate data. As a result, a regression calculation method based on RNN is proposed in this study. It consists of DAE, three main paths, dropout layers, Huber loss function, L2 regularization and ten outputs. The benchmarks are calculated according to the mean values of the ten outputs. After error analysis, reasonable intervals can be obtained to detect outliers of original line loss rate samples.  
From the case study and comparison results, conventional ANN model fails to calculate results of benchmarks, as it cannot deal with outliers. KNN, DTR and the proposed RNN are proved applicable in the case study, where the proposed RNN outperforms the other two models. It shows both high accuracy and robustness among all the testing models. Furthermore, according to the final result obtained from the proposed RNN, there are about 13% outliers in the overall data points.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indicator** & **Proposed RNN** & **KNN** & **DTR** & **ANN** \\ \hline mean (\%) & 2.03 & 1.03 & \(-4.81\) & \(-5.83\times 10^{6}\) \\ std (\%) & 0.80 & \(185.69\) & \(194.78\) & \(1.87\times 10^{7}\) \\ min (\%) & 0.00 & \(-8.13\times 10^{4}\) & \(-8.13\times 10^{4}\) & \(-8.26\times 10^{7}\) \\ max (\%) & 33.61 & 100.00 & \(100.00\) & \(4.49\times 10^{6}\) \\ \(l_{a}\) (\%) & 0.81 & \(-1.80\) & \(-1.80\) & \(-1.17\times 10^{6}\) \\ \(u_{a}\) (\%) & 3.36 & 5.25 & 5.24 & \(2.80\times 10^{6}\) \\ \(q1\) (\%) & 1.76 & 0.84 & 0.84 & \(3.23\times 10^{5}\) \\ \(q2\) (\%) & 2.09 & 1.65 & 1.65 & \(8.47\times 10^{5}\) \\ \(q3\) (\%) & 2.40 & 2.60 & 2.60 & \(1.32\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: The robustness analysis results of different testing models.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indicator** & **Proposed RNN** & **KNN** & **DTR** & **ANN** \\ \hline Mean absolute error (MAE, \%) & 1.46 & 0.70 & 5.01 & \(7.26\times 10^{6}\) \\ Mean squared error (MSE, \%\({}^{2}\)) & 13.70 & 574.58 & \(3.90\times 10^{3}\) & \(3.54\times 10^{14}\) \\ Huber loss & 4.44 & 5.90 & 48.19 & \(7.26\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: The accuracy analysis results of different testing models.  
The percentage of regions only occupy about 20% that hold no missing and abnormal values of line loss rates within a month, indicating a low dependability of the acquisition equipment. Therefore, a reliable monitoring and management system for line loss data is still necessary nowadays in power grid.  
Writing original draft preparation, W.W. and L.C.; reviewing and editing, Y.Z., B.X. and H.Z.; supervision, G.X. and X.L.  
This research is supported by Science and Technology Project of Jiangsu Frontier Electric Technology Corporation, called \"Research on key techniques of line loss benchmark value modeling in low-voltage transformer area by data-driven model\" (project ID. OFW-18553-WF).  
The authors declare no conflict of interest.