## 2 The Selection of the Fault Feature
### Analysis of Internal Parameters of Photovoltaic Array Equivalent Circuit in Fault State  
If the photovoltaic array malfunctions, the internal parameters of the photovoltaic array equivalent circuit will change, and these differences contain the most abundant fault feature information, directly reflecting the state that the photovoltaic array is in. Figure 1 presents the equivalent circuit model of photovoltaic module [17], \(I_{\text{ph}}\) is the photovoltaic current generated by the photovoltaic module, \(I_{\text{D}}\) is the current through the diode, \(I_{\text{sh}}\) is the current flowing through the shunt resistance \(R_{\text{sh}}\), \(R_{\text{s}}\) is the series resistance, and \(I\) is the output current of the photovoltaic module. Figure 1: The equivalent circuit model of photovoltaic module. As the equivalent circuit model of photovoltaic module shows that the photovoltaic module output current is:  
\[I=I_{\mathrm{ph}}-I_{\mathrm{D}}-I_{\mathrm{sh}}=I_{\mathrm{ph}}-I_{0}\bigg{\{} \mathrm{exp}\bigg{[}\frac{\mathrm{q}(U+IR_{\mathrm{s}})}{n\mathrm{k}T}\bigg{]}-1 \bigg{\}}-\frac{IR_{\mathrm{s}}+U}{R_{\mathrm{sh}}} \tag{1}\]  
In the Formula, \(I_{0}\) is the reverse saturation current of the diode, \(U\) is the output voltage of the photovoltaic module, \(\mathrm{q}\) is the electron charge (1.60218 \(\times\) 10\({}^{-19}\) Coulomb), \(n\) is the ideality factor of the diode, \(\mathrm{k}\) is the Boltzmann's constant (1.38066 \(\times\) 10\({}^{-231}\) J/K), and \(T\) is the absolute temperature of photovoltaic module. In an actual solar power station, there are five major connection types of photovoltaic array: series structure, parallel structure, serial-parallel (SP) structure, total-cross-tied (TCT) structure, and bridge-linked (BL) structure, among which the SP structure is the most widely used; therefore, this paper studies the photovoltaic array of the SP structure. Figure 2 is an equivalent circuit model of photovoltaic array, of which the type of the photovoltaic array is \(M\)\(\times\)\(N\), \(M\) is the number of photovoltaic modules in a photovoltaic string, and \(N\) is the number of photovoltaic strings in a photovoltaic array. Furthermore, Figure 3 is the equivalent circuit model of Figure 2.  
Figure 3: The equivalent circuit model of photovoltaic array. Figure 2: The equivalent circuit model of photovoltaic array. \(I^{\prime}\), \(U^{\prime}\) are the output current and voltage of the photovoltaic array, respectively; \(I_{\mathrm{ph}}\)\({}^{\prime}\) is the photovoltaic current generated by the photovoltaic array; and, \(R_{\mathrm{s}}\)\({}^{\prime}\), \(R_{\mathrm{sh}}\)\({}^{\prime}\) are the series resistance and shunt resistance of the photovoltaic array, respectively. In the literature [18], the output current of photovoltaic array is:  
\[I^{\prime}=NI_{\mathrm{ph}}-\ Nl_{0}\bigg{\{}\mathrm{exp}\bigg{[}\frac{ \mathrm{q}(U^{\prime}+I^{\prime}R_{\mathrm{s}}(M/N))}{MnkT}\bigg{]}-\ 1\bigg{\}}-\frac{U^{\prime}+\frac{M}{N}I^{\prime}R_{\mathrm{s}}}{\frac{M}{N}R _{\mathrm{sh}}} \tag{2}\]  
The above analysis shows that \(I_{\mathrm{ph}}\)\({}^{\prime}=NI_{\mathrm{ph}}\), \(R_{\mathrm{s}}\)\({}^{\prime}=MR_{\mathrm{s}}/N\), and \(R_{\mathrm{sh}}\)\({}^{\prime}=MR_{\mathrm{sh}}/N\). For the model, its internal equivalent parameters \(I_{\mathrm{ph}}\)\({}^{\prime}\), \(R_{\mathrm{s}}\)\({}^{\prime}\), and \(R_{\mathrm{sh}}\)\({}^{\prime}\) is proportion to \(I_{\mathrm{ph}}\), \(R_{\mathrm{s}}\), and \(R_{\mathrm{sh}}\) of the photovoltaic module. From Figures 1-3 and the above analysis, it shows that under the same test condition, \(I_{\mathrm{ph}}\), \(R_{\mathrm{s}}\), and \(R_{\mathrm{sh}}\) of the faulty photovoltaic module are zero when there is a short-circuit fault in the photovoltaic array; thus, the \(I_{\mathrm{ph}}\) of its string keeps constant, \(R_{\mathrm{s}}\) and \(R_{\mathrm{sh}}\) decreases, and then the \(I_{\mathrm{ph}}\)\({}^{\prime}\) is basically unchanged, while \(R_{\mathrm{s}}\)\({}^{\prime}\) and \(R_{\mathrm{sh}}\)\({}^{\prime}\) decrease.