## 5 Case Study  
A flow chart representing the steady-state power quality evaluation method presented in this paper is shown in Figure 5.  
Step 1. Establish the original matrix. Figure 5: The flow chart of the steady-state power quality evaluation. In this study, we measured the data of the photovoltaic grid-connected point in the Dynamic Simulation Laboratory of Tianjin University for two weeks by using the Fluke 435 II power quality analyzer. The measurement was set with 3 s as a recording point, and the data were used as a group every 24 h. For the measured data, we took 10 min as a time unit, and chose the maximum probability of 95% in each dataset as the final data typical value [40,43]. Then, the measured data are shown in Table 5.  
Step 2. Determine the BO vector, the OW vector, the \(\text{BO}_{\text{M}}\) vector and the \(\text{OW}_{\text{M}}\) vector. According to the authors of [32,44,45], we could obtain the triangular fuzzy matrix by combining Equations (9)-(12), as shown in Table 6.  
The elements of the \(\text{BO}_{\text{M}}\) vector and the \(\text{OW}_{\text{M}}\) vector could be obtained by Equations (13) and (14), as shown in Table 7.  
Step 3. Calculate the central weight of each index and conduct consistency check. The central weight of each index and the value of \(\xi\) could be determined by substituting the data in Table 7 into the optimization problem in Equation (18), as presented in Table 8. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Power Quality Indices** & **BO** & **OW** \\ \hline \(x_{1}\) & (1 1 1) & (4 4.5 5) \\ \(x_{2}\) & (2 2.5 3) & (1.5 1.8 2.1) \\ \(x_{3}\) & (3.1 3.4 3.7) & (1.4 1.7 2.0) \\ \(x_{4}\) & (3.1 3.4 3.7) & (1.4 1.7 2.0) \\ \(x_{5}\) & (1 1.5 2) & (3 3.3 3.6) \\ \(x_{6}\) & (4 4.5 5) & (1 1 1) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The triangular fuzzy matrix of power quality index. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Time** & \(x_{1}\)**/**Hz** & \(x_{2}\)**/**(\%)** & \(x_{3}\)**/**(\%)** & \(x_{4}\) & \(x_{5}\)**/**(\%)** & \(x_{6}\)**/**(\%)** \\ \hline Day 1 & 0.021 & 1.640 & 0.207 & 0.498 & 9.600 & 0.406 \\ Day 2 & 0.013 & 1.580 & 0.183 & 0.741 & 9.800 & 0.297 \\ Day 3 & 0.017 & 1.640 & 0.196 & 0.512 & 9.600 & 0.302 \\ Day 4 & 0.015 & 1.610 & 0.199 & 0.525 & 10.600 & 0.377 \\ Day 5 & 0.011 & 1.330 & 0.193 & 0.523 & 10.800 & 0.313 \\ Day 6 & 0.014 & 1.650 & 0.192 & 0.293 & 8.300 & 0.364 \\ Day 7 & 0.014 & 1.773 & 0.132 & 0.204 & 8.100 & 0.403 \\ Day 8 & 0.035 & 1.824 & 0.195 & 0.398 & 9.888 & 0.298 \\ Day 9 & 0.036 & 2.011 & 0.191 & 0.495 & 8.294 & 0.295 \\ Day 10 & 0.035 & 2.041 & 0.186 & 0.400 & 8.091 & 0.438 \\ Day 11 & 0.035 & 1.863 & 0.195 & 0.520 & 8.010 & 0.478 \\ Day 12 & 0.035 & 1.863 & 0.214 & 0.402 & 8.169 & 0.412 \\ Day 13 & 0.035 & 1.401 & 0.200 & 0.518 & 8.319 & 0.357 \\ Day 14 & 0.035 & 1.842 & 0.200 & 0.507 & 8.281 & 0.503 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Deviation values of measured data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Power Quality Indices** & **BO** & **OW** \\ \hline \(x_{1}\) & (1 1 1) & (4 4.5 5) \\ \(x_{2}\) & (2 2.5 3) & (1.5 1.8 2.1) \\ \(x_{3}\) & (3.1 3.4 3.7) & (1.4 1.7 2.0) \\ \(x_{4}\) & (3.1 3.4 3.7) & (1.4 1.7 2.0) \\ \(x_{5}\) & (1 1.5 2) & (3 3.3 3.6) \\ \(x_{6}\) & (4 4.5 5) & (1 1 1) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The triangular fuzzy matrix of power quality index. Since \(m_{BW}=m_{16}=4.5\), the CI could be determined by Equation (21) and CI = 1.9586. Then, the CR could be determined by Equation (20), and CR = 0.1115. The CR is near to zero and far from one, thus the consistency of the overall comparisons is acceptable. Step 4. Calculate the interval weight of each index. The radius in interval weight of each index could be determined by the optimization problem in Equation (26) based on the central weight of each index and the BO and OW vectors. The radius in interval weight of each index is presented in Table 9.  
Then, the interval weight of each index could be obtained, as presented in Table 10.  
Step 5.