## 3 Results and Discussion
### QRLSTM PV Interval Prediction Simulation  
The pre-processed data was feature-constructed, and then divided into a training set and a test set in a ratio of 4:1. Firstly, to improve the prediction accuracy, the historical data were clustered into three types according to the weather conditions, using the FCM-Frechet clustering method mentioned in Section 2.3. Then, the QRLSTM prediction model was  
Figure 4: Flow chart of overall power-stealing identification. mean that the prediction effect of the interval is better. The calculation formulas of the two evaluation indicators are shown in Equations (12) and (13). \[\left\{ \begin{array}{l}I_{i}^{\alpha}=\left[L_{i}^{\alpha},U_{i}^{\alpha}\right] \\ \xi_{i}^{\alpha}=\left\{\begin{array}{ll}0&y_{i}\
otin I_{i}^{\alpha}\\ 1&y_{i}\in I_{i}^{\alpha}\\ PICP=\frac{1}{N_{interval}}\sum\limits_{i=1}^{N_{interval}}\xi_{i}^{\alpha} \end{array}\right.\left(i=1,2,\cdots,N_{interval}\right)\,,\end{array} \right. \tag{12}\]  
where \(I_{i}^{\alpha}\) represents the \(i\)-th interval at a certain confidence level; \(L_{i}^{\alpha}\) and \(U_{i}^{\alpha}\) are, respectively, the lower and upper bounds of the corresponding interval; and \(\xi_{i}^{\alpha}\) indicates whether the actual value \(y_{i}\) is within the prediction interval--1 represents that it is in the interval, 0 represents it is not. \(N_{interval}\) is the number of intervals. The probability that the actual value \(y_{i}\) falls within the interval should not be less than or close to the set confidence level, which means that the prediction model is effective. \[\left\{ \begin{array}{l}\delta_{i}^{\alpha}=U_{i}^{\alpha}-L_{i}^{\alpha}\\ PINAW=\frac{1}{N_{interval}}\sum\limits_{i=1}^{N_{interval}}\delta_{i}^{ \alpha}\,,\end{array} \right. \tag{13}\]  
where \(\delta_{i}^{\alpha}\) is the width of the \(i\)-th interval. The smaller the _PINAW_ index is, the smaller the obtained prediction interval is. Tables 1-3 show the comparison of the evaluation indicators of the two interval prediction models on three similar days. \begin{table}
\begin{tabular}{c c c c} \hline
**Confidence Levels** & **Model** & **PICP (\%)** & **PINAW (KW)** \\ \hline
85\% & QRLSTM & 88.05 & 3.35 \\  & QRNN & 86.49 & 4.57 \\
90\% & QRLSTM & 95.18 & 3.76 \\  & QRNN & 92.58 & 5.02 \\
95\% & QRLSTM & 99.67 & 4.29 \\  & QRNN & 96.43 & 5.63 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of evaluation indicators on similar-day 1. \begin{table}
\begin{tabular}{c c c c} \hline
**Confidence Levels** & **Model** & **PICP (\%)** & **PINAW (KW)** \\ \hline
85\% & QRLSTM & 86.05 & 4.71 \\  & QRNN & 82.11 & 6.37 \\
90\% & QRLSTM & 92.18 & 5.16 \\
90\% & QRNN & 89.58 & 6.94 \\  & QRLSTM & 96.67 & 5.78 \\  & QRNN & 95.00 & 7.53 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of evaluation indicators on similar-day 2. \begin{table}
\begin{tabular}{c c c c} \hline
**Confidence Levels** & **Model** & **PICP (\%)** & **PINAW (KW)** \\ \hline
85\% & QRLSTM & 85.05 & 5.86 \\  & QRNN & 80.11 & 8.37 \\
90\% & QRLSTM & 88.18 & 6.43 \\  & QRNN & 84.58 & 9.08 \\
95\% & QRLSTM & 95.00 & 7.19 \\  & QRNN & 88.43 & 9.83 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of evaluation indicators on similar-day 3. From Tables 1-3, it can be seen that on different similar days, with the increase of confidence level, the prediction interval coverage probability will increase, and the prediction interval normalized average width will also increase. It can be seen from Table 1 that the interval coverage of the two methods exceeds the corresponding confidence level on similar-day 1. When the confidence level is 95%, the QRLSTM method can even achieve close to 100% coverage, and the average width of the interval is also smaller than that of the QRNN method. At other confidence levels, it can also be concluded that the prediction accuracy of the QRLSTM method is higher than that of the QRNN method on similar-day 1.