## 5 Case Study
Calculate the value of \(S_{i}^{\pm},R_{i}^{\pm}\), and \(Q_{i}^{\pm}\) of each day's power quality data. Based on the interval VIKOR method introduced in this paper, the \(S_{i}^{\pm},R_{i}^{\pm}\), and \(Q_{i}^{\pm}\) of each day's power quality data could be determined by Equations (32)-(37), as shown in Table 11.  
According to Equations (38)-(40), the values of PPI of each dataset (including the upper boundary values of each level) could be determined, and the results are presented in Table 12. \begin{table}
\begin{tabular}{c c} \hline \hline
**Indices** & **Interval Weight** \\ \hline \(x_{1}\) & (0.2951, 0.3725) \\ \(x_{2}\) & (0.1242, 0.1556) \\ \(x_{3}\) & (0.1007, 0.1091) \\ \(x_{4}\) & (0.1007, 0.1091) \\ \(x_{5}\) & (0.2069, 0.2845) \\ \(x_{6}\) & (0.0321, 0.1095) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The interval weight of the index. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time-** & \(S_{i}^{\pm}\) & \(R_{i}^{\pm}\) & \(Q_{i}^{\pm}\) \\ \hline Day 1 & (0.6015, 0.7969) & (0.2795, 0.3528) & (0.6046, 0.8317) \\ Day 2 & (0.5838, 0.7837) & (0.2920, 0.3686) & (0.6171, 0.8522) \\ Day 3 & (0.6083, 0.8100) & (0.2857, 0.3607) & (0.6189, 0.8520) \\ Day 4 & (0.5872, 0.7781) & (0.2889, 0.3646) & (0.6135, 0.8425) \\ Day 5 & (0.5994, 0.7954) & (0.2951, 0.3725) & (0.6305, 0.8650) \\ Day 6 & (0.6678, 0.8809) & (0.2904, 0.3666) & (0.6575, 0.8986) \\ Day 7 & (0.6810, 0.8941) & (0.2904, 0.3666) & (0.6643, 0.9054) \\ Day 8 & (0.5817, 0.7733) & (0.2576, 0.3252) & (0.5566, 0.7718) \\ Day 9 & (0.5983, 0.8006) & (0.2561, 0.3232) & (0.5624, 0.7824) \\ Day 10 & (0.6129, 0.8115) & (0.2576, 0.3252) & (0.5726, 0.7914) \\ Day 11 & (0.6040, 0.8016) & (0.2576, 0.3252) & (0.5680, 0.7863) \\ Day 12 & (0.6159, 0.8164) & (0.2576, 0.3252) & (0.5741, 0.7939) \\ Day 13 & (0.6139, 0.8181) & (0.2576, 0.3252) & (0.5731, 0.7948) \\ Day 14 & (0.5997, 0.7942) & (0.2576, 0.3252) & (0.5658, 0.7825) \\ Level 1 & (0.7960, 1.0586) & (0.2498, 0.3153) & (0.6530, 0.9011) \\ Level 2 & (0.6179, 0.8227) & (0.1874, 0.2421) & (0.4535, 0.6534) \\ Level 3 & (0.4398, 0.5868) & (0.1453, 0.1998) & (0.2893, 0.4590) \\ Level 4 & (0.2617, 0.3509) & (0.1145, 0.1574) & (0.1447, 0.2647) \\ Level 5 & (0.0836, 0.1150) & (0.0836, 0.1150) & (0, 0.0704) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The values of the \(S_{i}^{\pm},R_{i}^{\pm}\), and \(Q_{i}^{\pm}\). The PPI value of the daily power quality with the PPI value of the level upper boundary is compared in Figure 6.  
We intuitively can see that the power quality belongs to Level 2 almost every day in Figure 6. Only the PPI value of the power quality on Days 6 and 7 is slightly lower than the upper boundary of Level 1. Therefore, we can conclude that the power quality level of the monitoring point belongs to Level 2. The power quality of the monitoring point is good, which meets the requirements of Chinese national photovoltaic grid connection, and has little effect on the power quality of the local grid. To verify the feasibility of the method proposed in this paper, we selected several comprehensive power quality evaluation methods introduced in other publications to evaluate the data in this paper and the results are shown in Table 13.