# DC Cabling of Large-Scale Photovoltaic Power Plants
## 4 Impact of Temperature on Cable Losses  
Temperature is an important parameter when considering the operation of PV systems [31; 32; 33; 34; 35]. The temperature changes the parameters of the solar module (\(I_{\text{SC}},U_{\text{O}},P_{\text{P}}\)) as well as the resistances of the DC conductors \(R_{1}^{\prime}\) and \(R_{2}^{\prime}\). Solar modules are tested for current, voltage, and power under standard conditions (STC) of \(1000\,\text{W}/\text{m}^{2}\) insolation and \(25\,^{\circ}\text{C}\) solar cell temperature. For these values, catalog data are given for modules; such data includes short-circuit current \(I_{\text{SC}}\), open-circuit voltage \(U_{\text{O}}\), maximum power \(P_{\text{P}}\), operating current at maximum power \(I_{\text{PN}}\), and operating voltage at maximum power \(U_{\text{PN}}\). The power plant operates in a temperature range that can vary from \(-20\,^{\circ}\text{C}\) to \(45\,^{\circ}\text{C}\). The relations that connect the catalog data with the real data are given below [33; 34; 35]:  
\[I_{\text{SC}}(T,G) = I_{\text{SC,STD}}\cdot\left[1+\frac{k_{\text{i}}}{100}(T_{\text{ C}}-25\,^{\circ}\text{C})\right]\cdot\frac{G}{1000}, \tag{32}\] \[U_{\text{O}}(T) = U_{\text{O,STD}}\cdot\left[1+\frac{k_{\text{u}}}{100}(T_{\text{ C}}-25\,^{\circ}\text{C})\right],\] (33) \[P(T) = P_{\text{P,STD}}\cdot\left[1+\frac{k_{\text{P}}}{100}(T_{\text{ C}}-25\,^{\circ}\text{C})\right],\] (34) \[FF = \frac{I_{\text{PN}}\cdot U_{\text{PN}}}{I_{\text{SC}}\cdot U_{ \text{O}}}. \tag{35}\]  
A nominal operating temperature of a solar cell is measured for insulation \(800\,\text{W}/\text{m}^{2}\) and \(20\,^{\circ}\text{C}\) ambient temperature. For these values, the nominal temperature of the cell (NCOT) is given as catalog data. \[T_{\text{C}}=T_{\text{a}}+\bigg{(}\frac{\text{NCOT}-20\,^{\circ}\text{C}}{800 \,\text{W}/\text{m}^{2}}\cdot G\bigg{)}. \tag{36}\]Cell temperature \(T_{\rm C}\) can be calculated by Equation (36) if the insolation \(G\), the ambient temperature \(T_{\rm a}\), and the NCOT are known. The short-circuit current and open-circuit voltage at this cell temperature can be determined according to Equations (32) and (33). There is a change in the current-voltage characteristic of the solar panel and thus a change in the operating point compared to the nominal point. The current and voltage \((I_{1},U_{1})\) at the point of maximum power at this temperature are different compared to the nominal values \((I_{\rm PN},U_{\rm PN})\). This change is a linear function of temperature [34] and depends on the temperature coefficients. Temperature coefficients can be represented as a linear combination of the catalog coefficients \(k_{\rm i}\) and \(k_{\rm u}\), so Equations (32) and (33) can be written:  
\[I_{1}(T,G) = I_{\rm PN}\cdot\left[1+\frac{\gamma k_{\rm i}}{100}(T_{\rm C}-25 \,^{\circ}\!{\rm C})\right]\cdot\frac{G}{1000}, \tag{37}\] \[U_{1}(T) = U_{\rm PN}\cdot\left[1+\frac{\theta k_{\rm u}}{100}(T_{\rm C}-2 5\,^{\circ}\!{\rm C})\right]. \tag{38}\]  
Power as a function of cell temperature is determined by Equation (34) if the catalog parameter \(k_{\rm p}\), nominal power \(P_{\rm p}\), and cell temperature \(T_{\rm C}\) are known [34]. The same value of power is given by the product of current and voltage at that temperature obtained by Equations (37) and (38) [36]. This gives the relation of the coefficients \(k_{\rm i},k_{\rm u},k_{\rm p},\gamma k_{\rm i},\theta k_{\rm u}\) as follows:  
\[k_{\rm p}=\gamma\cdot k_{\rm i}+\theta\cdot k_{\rm u}+\gamma\cdot k_{\rm i} \cdot\theta\cdot k_{\rm u}\frac{T_{\rm C}-25\,^{\circ}\!{\rm C}}{100}. \tag{39}\]  
The coefficients \(\gamma k_{\rm i}\) and \(\theta k_{\rm u}\) are coefficients of change in current and voltage at the maximum power point (MPP) as a function of temperature. Equation (39) express the fact that coefficients \(\gamma k_{\rm i}\) and \(\theta k_{\rm u}\) depend on temperature if \(k_{\rm p}\) is treated as a constant coefficient.