## 3 System Design
### Mathematical Modeling of the Power System  
#### 3.2.1 PV Array  
The polycrystalline panels were assembled by Taiyuan University of Technology in this study. The PV panels can be mainly divided into solar cells made of polymers, silicon materials, and sensitized nanomaterials [20] and silicon PV are mostly used. Advantages and disadvantages of different silicon solar cells are shown in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Name** & **Advantages** & **Disadvantages** \\ \hline Monocrystalline silicon & High conversion efficiency, mature technology and small footprint & Expensive and high requirement for incident angle of sunlight \\ \hline \multirow{4}{*}{Polysilicon} & The conversion efficiency is higher than that of amorphous silicon, the manufacturing cost is lower than that of monocrystalline silicon, and the low requirement for incident angle of sunlight \\ \cline{1-1}  & Minimum requirement for incident angle of sunlight \\ \cline{1-1}  &
\begin{tabular}{c} Minimum requirement for incident angle of \\ sunlight and high acceptance rate of \\ astigmatism \\ \end{tabular} & Low conversion efficiency \\ \cline{1-1}  & & \\ \end{tabular}
\end{table} 
Table 2: Advantages and disadvantages of different silicon solar cells. Figure 3: (**a**) Atmospheric conditions, (**b**) Schematic of the renewable energy system. As shown in Table 2, monocrystalline silicon solar cells and polycrystalline silicon solar cells have higher conversion efficiency and smaller size than amorphous silicon solar cells. The monocrystalline silicon solar cells and the polycrystalline silicon solar cells have different appearances due to different manufacturing processes. When assembled into PV panels, the monocrystalline silicon materials cannot be covered. In terms of efficiency of use, monocrystalline silicon solar cells and polycrystalline silicon solar cells are not much different, the former being 1%-2% more than the latter. Due to the different manufacturing processes used, the polycrystalline silicon solar cells are cheaper to produce than the monocrystalline silicon solar cells. Thus, the polycrystalline silicon solar cells are used in this study. All the PV panels were designed to be positioned in a fixed direction, facing north. The key specifications of the PV panels are presented in Table 3.  
A total of 350 PV panels can be used to form a 120 V, 105 KW PV array. The principle of power generation of solar cell is that the solar radiation emits photons to the induction plate of the photovoltaic cell to produce a photoelectric effect, causing internal electrons to move, thereby generating current. Equivalent circuit of the solar cell is shown in Figure 4.  
According to equivalent circuit of the solar cell, relevant calculating equations are as follows:  
\[I=I_{L}-I_{d}-I_{sh} \tag{1}\]  
\[I_{sh}=\frac{IR_{sh}+V}{R_{sh}} \tag{2}\]  
The characteristics of the internal PN junction of the solar cell can be described as follows:  
\[I_{d}=I_{0}\left\{\exp\left[\frac{q(IR_{sh}+V)}{\lambda KT}-1\right]\right\} \tag{3}\]  
Substituting Equations (2) and (3) into Equation (1) for calculation, relevant calculating equation is as follows:  
\[I=I_{L}-I_{0}\left\{\exp\left[\frac{q(IR_{sh}+V)}{\lambda KT}-1\right]\right\} -\frac{IR_{sh}+V}{R_{sh}} \tag{4}\]  
Figure 4: Equivalent circuit of the solar cell. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Characteristics** & **Value** & **Unit** \\ \hline Open circuit voltage (V\({}_{\text{oc}}\)) & 42.64 & V \\ Optimum operating voltage (V\({}_{\text{mp}}\)) & 34.96 & V \\ Short circuit current (I\({}_{\text{sc}}\)) & 9.48 & A \\ Optimum operating current (I\({}_{\text{mp}}\)) & 8.59 & A \\ Maximum power at STC \({}^{1}\) (P\({}_{\text{max}}\)) & 300 & W \\ Operating temperature & \(-50\) to 85 & \({}^{\circ}\)C \\ Size & \(1956\times 992\times 50\) & mm \\ \hline \hline \end{tabular} \({}^{1}\) Standard test conditions.  
\end{table} 
Table 3: Key specifications of the photovoltaic (PV) panels.