# DC Cabling of Large-Scale Photovoltaic Power Plants
## 4 Impact of Temperature on Cable Losses
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(T_{\mathrm{a}}\) [\({}^{\circ}\mathrm{C}\)] & \(T_{\mathrm{C}}\) [\({}^{\circ}\mathrm{C}\)] & \(U_{\mathrm{1}}\) [V] & \(I_{\mathrm{1}}\) [A] & \(\gamma\) \\ \hline \(-10\) & 21.25 & 46.35 & 9.62 & 1.789966 \\ \(0\) & 31.25 & 44.26 & 9.70 & 1.770358 \\ \(10\) & 41.25 & 42.22 & 9.78 & 1.751579 \\ \(20\) & 51.25 & 40.22 & 9.86 & 1.733567 \\ \(30\) & 61.25 & 38.26 & 9.95 & 1.716263 \\ \(40\) & 71.25 & 36.34 & 10.03 & 1.699619 \\ \(50\) & 81.25 & 34.45 & 10.12 & 1.683589 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Change in solar panel parameters with change in temperature. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(T_{\mathrm{a}}\) [\({}^{\circ}\mathrm{C}\)] & \multicolumn{2}{c}{\(\gamma=1.789966\)} & \multicolumn{2}{c}{\(\gamma=1\)} & \multicolumn{2}{c}{\(P\) [W]} \\ \cline{2-7}  & \(I_{\mathrm{1}}\) [A] & \(U_{\mathrm{1}}\) [V] & \(I_{\mathrm{1}}\) [A] & \(U_{\mathrm{1}}\) [V] & \(1\) & \(2\) & \(3\) \\ \hline \(-10\) & 9.62 & 46.34 & 9.63 & 46.05 & 443.6 & 446.1 & 445.7 \\ \(0\) & 9.70 & 44.26 & 9.68 & 44.73 & 433.0 & 429.8 & 429.5 \\ \(10\) & 9.78 & 42.22 & 9.73 & 43.41 & 422.3 & 413.5 & 413.2 \\ \(20\) & 9.87 & 40.22 & 9.78 & 42.09 & 411.5 & 397.3 & 397.0 \\ \(30\) & 9.95 & 38.26 & 9.82 & 40.77 & 400.6 & 381.0 & 380.7 \\ \(40\) & 10.03 & 36.34 & 9.87 & 39.45 & 389.5 & 364.7 & 364.4 \\ \(50\) & 10.11 & 34.45 & 9.92 & 38.13 & 378.3 & 348.4 & 348.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Three different methods of calculating the power of the solar module at the maximum power point as a function of temperature. are also heated due to the current flowing through them. The value of the resistance of the cable at ambient temperature can be determined according to:  
\[R=R_{0}(1+\alpha_{T}\cdot(T_{\mathrm{C}}-T_{0})). \tag{46}\]  
Considering these corrections to the resistance amounts \(R_{1}^{\prime}\) and \(R_{2}^{\prime}\), the estimation of losses can be obtained with the ambient temperature taken into consideration as follows:  
\[R_{1}^{\prime}(T_{\mathrm{a}}) = R_{1}^{\prime}(1+0.00392\cdot(T_{\mathrm{C}}-T_{0})), \tag{47}\] \[R_{2}^{\prime}(T_{\mathrm{a}}) = R_{2}^{\prime}(1+0.00392\cdot(T_{\mathrm{C}}-T_{0})). \tag{48}\]  
The cables have standard cross-sections and resistances whose values are given by the manufacturers (\(\Omega\,\mathrm{km}^{-1}\)). In addition to the stated values, data on nominal cable currents and linear mass density for copper and aluminum are given in Table 4[27]. For economic reasons, using aluminum instead of copper may be an option. Table 4 shows, in addition to the parameters of copper conductors, the parameters of aluminum conductors for larger amounts of current \(I_{\mathrm{N}}\). When replacing a copper conductor with an aluminum one, the same current capacity should be provided. This requires equivalents with a larger cross-section, as indicated in the table, so an aluminum conductor with a cross-section of \(95\,\mathrm{mm}^{2}\) is used in place of a \(35\,\mathrm{mm}^{2}\) copper conductor cross-section, with comparable nominal currents of \(218\,\mathrm{A}\) and \(216\,\mathrm{A}\). The longitudinal resistance of aluminum conductors with this cross section is less than the resistance of the equivalent copper conductors. The same applies to the other substitute values listed in Table 4.