# A Short-Circuit Current Calculation Model for Renewable Power Plants Considering Internal Topology
## 3 Practical SCC Calculation Model for Renewable Power Plants
### The Calculation Method for the Steady-State Voltage at the Point of Common Coupling (PCC)  
The calculation method for the PCC voltage \(U_{\text{st}}\) shown in Figure 5 is as follows.  
When a short-circuit fault occurs outside the renewable power plant, the renewable power plant can be regarded as a large voltage divider. The minimum depth of the PCC voltage drop is related to both the fault impedance and the system impedance [14; 21]. A schematic diagram of an external fault at the renewable power plant is shown in Figure 6. The fault occurs at the location indicated by the red arrow.  
(1) Calculate the minimum depth of voltage drop using the short-circuit impedance:  
\[U_{\text{min}}\ =\ \left|\frac{Z}{Z\ +\ Z_{1}}\right|E \tag{11}\]  
where  
* \(U_{\text{min}}\) is the amplitude of the PCC voltage at the moment of the fault;  
Figure 5: SCC calculation flowchart.  
Figure 6: External fault of renewable power plant.  
* \(Z\) is the fault impedance;
* \(Z_{1}\) is the impedance from the fault point to the system;
* \(E\) is the voltage amplitude of the infinite bus, which can be taken as a per unit value of 1.  
In subsequent calculations, all variables are expressed in per unit values.  
(2) The reactive current injected by the renewable power plant into the system will raise the PCC voltage [22]. Therefore, according to the superposition theorem, the steady-state voltage at the PCC can be expressed as follows:  
\[U_{\text{st}}\ =\ U_{\text{min}}\ +\ \Delta U \tag{12}\]  
where  
* \(U_{\text{st}}\) is the steady-state voltage at the PCC during a fault in the renewable power plant;
* \(\Delta U\) is the voltage rise caused by the reactive power injected into the system by the renewable power plant.  
(3) During the fault steady-state period, neglecting the influence of active power on voltage and the resistance of the lines, the effect of reactive current on the voltage can be expressed as follows:  
\[\Delta U\ =\ \frac{3}{2}I_{\text{q}\Sigma}(\frac{ZZ_{1}}{Z_{1}\ +\ Z}\ +\ Z_{2}) \tag{13}\]  
where  
* \(I_{\text{q}\Sigma}\) is the reactive current provided by the renewable power plant during the fault;
* \(Z_{2}\) is the impedance from the renewable power plant to the fault point.  
(4) During the fault steady-state period, the reactive current is related to the terminal voltage of the generators. To simplify the calculations, ignore the differences between the various N-SMSs in the renewable power plant and use the single-machine multiplication method, treating the renewable energy source as a large-capacity N-SMSs. In this case, the reactive current provided by the renewable power plant can be expressed as follows:  
\[I_{\text{q}\Sigma}\ =\ 1.5N(0.9-U_{\text{st}})I_{\text{N}} \tag{14}\]  
where  
* \(N\) is the number of N-SMSs units within the renewable power plant.  
(5) When the fault conditions and parameters of the renewable power plant are known, only \(I_{\text{q}}\) and \(U_{\text{st}}\) remain unknown in (9) to (12). By solving these equations simultaneously, the steady-state voltage at the PCC during the fault can be determined as follows:  
\[\left\{\begin{array}{l}U_{\text{st}}\ =\ \frac{81N_{\text{t}}Z_{3}+40U_{ \text{min}}}{90N_{\text{N}}Z_{3}+40}\\ Z_{3}\ =\ \frac{ZZ_{1}}{Z_{1}+\ Z}\ +\ Z_{2}\end{array}\right. \tag{15}\]