## 2 Observing-System and Power-System Considerations
### Mathematical Modeling of the Power System
#### 2.4.3 Low-Temperature Characteristics of PV Panel  
The PV panel is the major power-generation unit of the power system in this study. The environmental characteristics of the installation location of the power-supply system are described in Section 2.1. We do not understand the power-generation characteristics of photovoltaic panels at low temperatures. Therefore, the characteristics of PV panels at low temperatures require a comprehensive study. The key parameters of the PV panel have been described as follows:  
\[\left\{\begin{array}{l}I=I_{sc}(1-\sigma_{1}(exp(\sigma_{2}\cdot V))-1)\\ \sigma_{1}=\left[\left(I_{sc}-I_{mp}\right)/I_{sc}\right]\frac{V_{mp}}{V_{mp}- Vmp}\\ \sigma_{2}=(1/V_{oc})ln[(1+\sigma_{1})/\sigma_{1}]\\ i_{sc}(R,T)=I_{sc}\cdot\frac{R}{K_{c}}\cdot[1+a(T-T_{r})]\\ v_{oc}(R,T)=V_{oc}\cdot ln[e+b(R-R_{r})]\cdot[1-c(T-T_{r})]\\ i_{mp}(R,T)=I_{mp}\cdot\frac{R}{K_{r}}\cdot[1+a(T-T_{r})]\\ v_{mp}(R,T)=V_{mp}\cdot ln[e+b(R-R_{r})]\cdot[1-c(T-T_{r})]\end{array}\right. \tag{3}\]  
where \(I_{sc}\) is the short circuit current (A); \(V_{oc}\) is the open circuit voltage (V); \(I_{mp}\) is the optimum operating current (A); \(V_{mp}\) is the optimum operating voltage (V). \(I_{sc}\), \(V_{oc}\), \(I_{mp}\) and \(V_{mp}\) can be found in Table 2. \(\sigma_{1}\) and \(\sigma_{2}\) are the are parameters for the convenience of describing the model; \(i_{sc}(R,T)\) is the short circuit current (A) at radiation intensity \(R\) (Wh/m\({}^{2}\)/day) and ambient temperature \(T\) (\({}^{\circ}\)C); \(v_{oc}(R,T)\) is the open circuit voltage (V) at the same conditions as \(i_{sc}(R,T)\); \(i_{mp}(R,T)\) and \(v_{mp}(R,T)\) are the optimum operating current (A) and voltage (V) at radiation intensity \(R\) (Wh/m\({}^{2}\)/day) and ambient temperature \(T\) (\({}^{\circ}\)C), respectively; \(R_{r}\) is the reference value of 1000 W/m\({}^{2}\); \(T_{r}\) is the reference temperature of 25 \({}^{\circ}\)C; \(a\) is 0.0025; \(b\) is 0.0005; \(c\) is 0.00288.  
Based on the established PV panel parameter model as shown in Equation (3), the temperature was set 0 \({}^{\circ}\)C. Simultaneously, radiation intensities of 1000, 800, 600, and 400 W/m\({}^{2}\) were selected for the PV panel. Then, the output characteristics were tested (Figure 6). Figure 6a shows the open circuit voltage and short circuit current of the PV panel. At the same temperature, as radiation intensity decreased, the open circuit voltage and short circuit current of the PV panel would gradually decrease. Figure 6b shows the output power of the PV panel. The output power of the PV panel also increased as the radiation intensity increased. When radiation intensity was kept constant at  
\begin{table}
\begin{tabular}{c c} \hline
**Characteristics** & **Value** \\ \hline Rated power & 10 W (1 min average at 10 m/s) \\ Peak power & 12 W \\ Cut-in speed & 3 m/s \\ Cut-off speed & 40 m/s \\ Temperature range & \(-\)60–10 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table}
Table 3: Key specifications of the TYUT wind turbine.  
1000 W/m\({}^{2}\) and ambient temperature was raised from \(-\)50 \({}^{\circ}\)C to \(-\)20 \({}^{\circ}\)C, the output characteristics of the PV panel were as shown in Figure 6c,d. Figure 6c shows that the open circuit voltage of the PV panel increased as the temperature decreased, but the short circuit current decreased. Figure 6d shows that the maximum power point of the PV panel increased with decreasing temperature. Although the short circuit current of the PV panel was reduced, the maximum output power point increased in the low-temperature environment.