# Selection of a Photovoltaic Panel Cooling Technique Using Multi-Criteria Decision Analysis
## 3 MCDM Approach to Evaluate PV Panel Cooling Methods Evaluation
### Determine the Best and Worst PV Panel Cooling Methods for a Given Criterion  
By multiplying each element of the normalized decision matrix above by its associated entropy weight \(\mathrm{EW_{j}}\), the decision matrix is obtained using the below Equation (12).  
\[\mathrm{V_{ij}}=\mathrm{EW_{j}}*\mathrm{N_{ij}} \tag{12}\]  
The following Equations (13) and (14) are used, respectively, to obtain the best and worst solutions from the output of the aforementioned Equation (12).  
\[\mathrm{V^{+}}=\mathrm{Best\,solution}=\{\mathrm{V_{1}^{+},\ldots,V_{j}^{+}, \ldots,V_{n}^{+}}\} \tag{13}\]  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Evaluation Criterion (j)** & **Entropy Weight Values (\(\mathrm{EW_{j}}\))** \\ \hline C1 \({}^{\$}\) & 0.039418 \\ \hline C2 & 0.24979 \\ \hline C3 & 0.057353 \\ \hline C4 & 0.24979 \\ \hline C5 & 0.098977 \\ \hline C6 & 0.216416 \\ \hline C7 & 0.041632 \\ \hline C8 & 0.046626 \\ \hline \hline \end{tabular} Note. \({}^{\$}\) Refer to Table 5.  
\end{table}
Table 8: Entropy weight \(\mathrm{E_{j}}\) values for each PV panel cooling assessment criterion (j).  
In Equation (13)  
\[\mathrm{V_{j}^{+}}=\left\{\mathrm{maxi}\left(\mathrm{V_{ij}}\right)\text{ for maximization criteria j; mini }\left(\mathrm{V_{ij}}\right)\text{ for minimization criteria j}\right\}\]  
\[\mathrm{V^{-}}=\text{Worst soultion}=\left\{\mathrm{V_{1}^{-}},\ldots\mathrm{ V_{j}^{-}},\ldots\mathrm{V_{n}^{-}}\right\} \tag{14}\]  
In Equation (14)  
\[\mathrm{V_{j}^{-}}=\left\{\mathrm{mini}\left(\mathrm{V_{ij}}\right)\text{ for minimization criteria j; maxi}\left(\mathrm{V_{ij}}\right)\text{ for maximization criteria j}\right\}\]  
Calculate Each Alternative PV Panel Cooling Method's Proximity to the Best Solution for a Specific Criterion before Rating the Alternatives  
For a given alternative PV panel cooling method for a given criterion, its proximity from the best ideal cooling strategy and its proximity from the worst cooling strategy is calculated using Equations (15) and (16), respectively.  
\[\mathrm{D_{i}^{+}}=\sqrt{\sum_{j}\left(\mathrm{V_{j}^{+}}-\mathrm{V_{ij}} \right)} \tag{15}\]  
\[\mathrm{D_{i}^{-}}=\sqrt{\sum_{j}\left(\mathrm{V_{j}^{-}}-\mathrm{V_{ij}} \right)} \tag{16}\]  
For a given PV panel cooling method, its closeness to the ideal PV panel cooling method is obtained using Equation (17).  
\[\mathrm{C_{i}}=\frac{\mathrm{D_{i}^{-}}}{\mathrm{D_{i}^{+}}-\mathrm{D_{i}^{-}}} \tag{17}\]  
In Equation (17) above, the \(\mathrm{C_{i}}\) value ranges between one and zero. The alternative PV panel cooling method i with the maximum positive value of \(\mathrm{C_{i}}\) is ranked number one. Thus, the decision matrix of the 3 cooling climatic zones and the corresponding eight cooling strategies and 30 evaluation criteria are established according to the data in Table 7. The normalized decision matrix is established, and the weighted decision matrix is estimated (refer to Table 9), and then the best solution and the worst solution values are obtained by using Equations (13) and (14), respectively.