# A Short-Circuit Current Calculation Model for Renewable Power Plants Considering Internal Topology
## 4 Results  
In order to verify the feasibility of the method proposed in this paper, combined with the actual engineering, a detailed model of a renewable power plant, as shown in Figure 8, was built in PSCAD. The plant mainly includes a wind turbine, back-to-back converters, box converters and main converters. The wind turbine is connected to the box transformer (0.69 kV/35 kV) through back-to-back converters, then to the 35 kV bus through the collection line, and then to the 220 kV system through the main transformer (35 kV/220 kV). Due to the similarity of the collecting lines, the calculation example includes one collecting line with ten wind turbines, each rated at 2 MW capacity (permanent magnet direct drive). The spacing of the units is selected as 1 km, and the basic wind speed is set as 10 m/s. The main parameters of the wind farm are shown in Table 1. The grid-connected inverter adopts the control strategy shown in Figure 2. The fault occurs at the location indicated by the red arrow. The sum of the equivalent impedances of the AB and BC sections of the line is \(Z_{\text{ac}}\) = (2.43 + 6.91j) \(\Omega\). The impedance of the AB section is \(Z_{\text{ab}}\), and let \(\gamma\) = \(Z_{\text{ab}}/Z_{\text{ac}}\). By changing \(\gamma\), the fault location can be adjusted. The greater the value of \(\gamma\), the closer the fault is to the PCC. Set \(\gamma\) to 0.25, 0.5, and 0.75, and set the short-circuit impedance Z to 1 \(\Omega\), 2 \(\Omega\), and 3 \(\Omega\), respectively. A three-phase short-circuit fault is applied at t = 1 s, with the fault point located at point B marked by the red arrow in Figure 8. The fault lasts for 0.5 s.  
The method proposed in Sections 3.1 and 3.2 was used to calculate the fault steady-state voltage at the end of each wind turbine in the wind farm, and the simulation results were compared, as shown in Figure 9 and Table 2. In Figure 9, the terminal voltage of the ten wind turbines at different fault locations and transition impedances is shown. The dashed lines represent the simulation results, and the solid lines represent the calculated values. \begin{table}
\begin{tabular}{c c c} \hline
**Type** & **Parameter** & **Value** \\ \hline
35 kV line & Impedance & 0.13 + 0.23j \(\Omega\)/km \\ \hline \multirow{2}{*}{Box-type transformer} & Transformation ratio & 0.69/35 kV \\  & Capacity & 2.24 MW \\  & Impedance & 6.39\% \\ \hline \multirow{3}{*}{Main transformer} & Transformation ratio & 35/220 kV \\  & Capacity & 100 MW \\ \cline{1-1}  & Impedance & 13.54\% \\ \hline \end{tabular}
\end{table} 
Table 1: Main component parameters of permanent magnet wind field. Figure 8: Sketch diagram of the detailed wind farm model. Table 2 shows the maximum relative error between the simulated and calculated voltage values of the wind turbines under different fault conditions. The calculation method for the relative error is as follows:  
\[relative\ error\ =\ \frac{calculated\ value-simulated\ value}{simulated\ value}\times\mathbf{100\%}. \tag{22}\]  
Table 3 presents the simulated SCC of the wind farm and PCC voltage under different fault conditions, the calculation values using the single-machine multiplication method, and the calculation values obtained using the method proposed in this paper. The calculation errors relative to the simulated values were also computed according to Equation (20). \begin{table}
\begin{tabular}{c c c} \hline \hline \(\gamma\) & **Short Circuit Impedance/\(\Omega\)** &
\begin{tabular}{c} **Maximum Wind Turbine Voltage** \\ **Relative Error/\%** \\ \end{tabular} \\ \hline  & 1 & 4.23 \\
0.25 & 2 & 0.95 \\  & 3 & \(-\)2.20 \\ \hline  & 1 & 2.24 \\
0.50 & 2 & \(-\)2.26 \\  & 3 & \(-\)3.44 \\ \hline  & 1 & \(-\)2.29 \\
0.75 & 2 & \(-\)4.00 \\  & 3 & \(-\)4.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum voltage error of wind. Figure 9: Fault steady-state voltage of each wind turbine in the different fault situations. (**a**) \(\gamma\) = 0.25; (**b**) \(\gamma\) = 0.50; (**c**) \(\gamma\) = 0.75.