# DC Cabling of Large-Scale Photovoltaic Power Plants
## 4 Impact of Temperature on Cable Losses
For a temperature of \(71.25\,^{\circ}\mathrm{C}\), the values are \(I_{\rm SC}=10.49\,\mathrm{A}\), \(U_{\rm I}=46.67\,\mathrm{V}\), \(P_{\rm P}=364.71\,\mathrm{W}\), \(U_{\rm I}=39.45\,\mathrm{V}\), and \(I_{\rm I}=9.87\,\mathrm{A}\). \(I_{\rm SC}\) and \(U_{\rm O}\) are catalog values, while \(I_{\rm I}\) and \(U_{\rm I}\) are obtained according to Equations (37) and (38), where \(\gamma\) is determined by Equation (44). Table 2 shows the changes in solar module voltage at the maximum power point, the solar module current at the maximum power point, the cell temperature, and the coefficient \(\gamma\) as a function of ambient temperature changed from \(-10\,^{\circ}\mathrm{C}\) to \(50\,^{\circ}\mathrm{C}\). It is assumed that the insolation is \(1000\,\mathrm{W}\,\mathrm{/}\,\mathrm{m}^{2}\). \[U_{\text{O}}(T) = U_{\text{O,STD}}\cdot\left[1+\frac{k_{\text{u}}}{100}(T_{\text{ C}}-25\,^{\circ}\text{C})\right],\]3 Change in the characteristic values of current and voltage of the solar module for cell temperatures \(25\,^{\circ}\mathrm{C}\) (solid blue line) and \(71.25\,^{\circ}\mathrm{C}\) (red dashed line). The results of different methods of determining the values of current, voltage, and power as a function of temperature at the maximum power point and for \(G=1000\,\mathrm{W}/\mathrm{m}^{2}\) are given in \[U_{\text{O}}(T) = U_{\text{O,STD}}\cdot\left[1+\frac{k_{\text{u}}}{100}(T_{\text{ C}}-25\,^{\circ}\text{C})\right],\]4  
Columns 2 and 3 represent the calculated values of currents and voltages with correction of the coefficients \(k_{\mathrm{i}}\) and \(k_{\mathrm{u}}\) by the factors \(\gamma\) and \(\theta\). Columns 4 and 5 represent the calculated values of currents and voltages without correction of the coefficients \(k_{\mathrm{i}}\) and \(k_{\mathrm{u}}\), (\(\gamma=1\) and \(\theta=1\)). Column 6 represents the power calculated based on currents and voltages determined without coefficients \(\gamma\) and \(\theta\) (columns 4 and 5). Column 7 represents the power calculated based on the nominal power and the coefficient \(k_{\mathrm{p}}\). Column 8 represents the power calculated based on the current and voltage with coefficients \(\gamma\) and \(\theta\) (columns 2 and 3). Column 7 corresponds to the closest power values because it is determined based on catalog data specified by the manufacturer. Power data calculated according to the proposed method are given in column 8, and the absolute error is below 0.09%. Column 6 represents the data according to the catalog coefficients \(k_{\mathrm{i}}\) and \(k_{\mathrm{u}}\) given for the short-circuit current \(I_{\mathrm{SC}}\) and the open-circuit voltage \(U_{\mathrm{O}}\). The maximum absolute error for column 6 is 8.58%. Based on previous results, the correction of the coefficients \(k_{\mathrm{i}}\) and \(k_{\mathrm{u}}\) should be performed when calculating currents and voltages outside the points \((0,I_{\mathrm{SC}})\) and \((U_{\mathrm{O}},0)\). The change in resistance according to the change in temperature is determined by:  
\[U_{\text{O}}(T) = U_{\text{O,STD}}\cdot\left[1+\frac{k_{\text{u}}}{100}(T_{\text{ C}}-25\,^{\circ}\text{C})\right],\]5  
where \(R_{0}\) is the resistance at room temperature \(T_{0}\) (\(25\,^{\circ}\mathrm{C}\)), \(T\) is the operating resistance temperature, and \(\alpha_{T}\) is the temperature coefficient. The temperature coefficient of copper is \(0.003\,92\,^{\circ}\mathrm{C}^{-1}\). If the ambient temperature (\(T_{\mathrm{a}}\)) is known, it can be assumed that the temperature of the cable at operating current (\(I_{1}\)) will be equal to or lower than the cell temperature. The cell's temperature is determined based on the energy of solar radiation, which is converted into thermal energy on the cell, plus thermal energy, which is released on the cable inside the solar module due to the flow of the current. The conductors between the modules are connected to the cables on the solar module. This leads to heat transfer from the solar module (which is warmer) to the cables. In addition to this heat, the cables