# DC Cabling of Large-Scale Photovoltaic Power Plants
## 2 Serial-Parallel Topology (SP)  
Serial-parallel topology (SP) is realized by connecting the \(N_{\text{M}}\) modules in series (in so-called \"strings\") and then connecting \(N_{\text{S}}\) strings in parallel, where \(N_{\text{S}}\) is the number of strings, and \(N_{\text{M}}\) is the number of modules in the string. The module and the inverter parameters are used to select the number of modules in the strings and the number of strings in parallel. The types of modules and inverter parameters are chosen according to the predicted power of the power plant, that is, the available area [21]. The parameters of the inverter and the solar module for the configuration of SP topology are provided by the manufacturer, as shown in Table 1.  
One array is formed as \(N_{\text{S}}\times N_{\text{M}}\), where \(N_{\text{S}}\) is the number of strings, and \(N_{\text{M}}\) is the number of modules in the string (Figure 1).  
The number of modules in a string can be determined by the equation:  
\[N_{\text{M}}=\left\lfloor\frac{U_{\text{DC}\text{min}}+U_{\text{DC}\text{max}} }{2\cdot U_{\text{PN}}}\right\rfloor. \tag{1}\]  
The following condition must be met:  
\[N_{\text{M}}\cdot U_{\text{O}}<U_{\text{max}}. \tag{2}\]  
The number of strings in the array can be calculated as:  
\[N_{\text{S}}=\left\lfloor\frac{P_{\text{INV}}}{N_{\text{M}}\cdot\frac{\text{G}} {1000}\cdot P_{\text{P}}}\right\rfloor, \tag{3}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Inverter Parameters** & **Label** \\ \hline Power & \(P_{\text{INV}}\) \\ Maximum DC input voltage & \(U_{\text{max}}\) \\ Minimum operating voltage & \(U_{\text{DC}\text{min}}\) \\ Maximum operating voltage & \(U_{\text{DC}\text{max}}\) \\ Maximum input current & \(I_{\text{IN}}\) \\ \hline
**Solar Module Parameters** & **Label** \\ \hline Maximum power & \(P_{\text{P}}\) \\ Maximum power voltage due to MPP & \(U_{\text{PN}}\) \\ Maximum power current due to MPP & \(l_{\text{PN}}\) \\ Open-circuit voltage & \(U_{\text{O}}\) \\ Short-circuit current & \(I_{\text{SC}}\) \\ Maximum system voltage & \(U_{\text{max}\text{P}}\) \\ Current temperature coefficient & \(k_{\text{i}}\) \\ Voltage temperature coefficient & \(k_{\text{u}}\) \\ Power temperature coefficient & \(k_{\text{p}}\) \\ Nominal operating cell temperature & NOCT \\ Dimensions & L \(\times\) W \\ \hline \hline \end{tabular}
\end{table}
Table 1: Inverter and solar module parameters.  
where \(G\) is the maximum insolation at the location of the FPV power plant [\(W/m^{2}\)]. \(P_{\rm P}\) is the nominal power of the module measured under standard test conditions (insolation \(1000\,W/m^{2}\) and solar cell temperature \(T_{\rm C}=25\,^{\circ}\)C). The number of modules per array is as follows:  
\[N_{\rm P}=N_{\rm S}\cdot N_{\rm M}. \tag{4}\]  
The usable power of the inverter can be calculated:  
\[P_{\rm INVK}=N_{\rm P}\cdot\frac{G}{1000}P_{\rm P}. \tag{5}\]  
The total number of arrays in the system can be determined by the equation:  
\[N_{\rm A}=\left\lfloor\frac{P}{P_{\rm INVK}}\right\rfloor, \tag{6}\]  
where \(P\) is the predicted power of the plant.  
The block structure of one large-scale FPV power plant is presented in Figure 2.  
The basic building block is an array that is multiplied \(N_{\rm A}\) times, where \(N_{\rm A}\) is the number of arrays in the PV plant [21]. The value of \(N_{\rm A}\) may vary from a few tens to a few thousand. It can be shown that the system performance is at its maximum when the array performance is at its maximum. This stems from the fact that the system, up to the point of connection to the network, is realized as a simple sum of an array.