# A Short-Circuit Current Calculation Model for Renewable Power Plants Considering Internal Topology
## 2 Classification and Control Strategies of N-SMSs
### Response Characteristics of SCC in N-SMSs  
During steady-state operation, the grid-connected converter of the N-SMSs adopts a steady-state grid connection control strategy, with a reactive power command of 0 to achieve unit power factor operation. When a short-circuit fault occurs externally to the N-SMSs, the voltage at the point of common coupling (PCC) drops. If the voltage falls to the threshold for LVRT, the converter control strategy switches to LVRT mode. At this point, the \"power-voltage\" outer loop of the dual-loop control structure is locked, and the command value for the current inner loop is directly given by (5). Consequently, the SCC response process during this period is determined by the parameters of the PI controller in the current inner loop, the transfer function of the converter, and the transfer function of the filtering circuit. During the fault, only the command value of the current inner loop's PI controller changes. Therefore, investigating the time-domain response characteristics of the current inner loop is essential to consider its impact on the transient process of SCC. Due to the control strategy employed to suppress negative-sequence currents, the reference value for negative-sequence current is set to zero during both normal operation and fault conditions. During faults, only the reference value for the positive-sequence current in the dual-PI current inner loop changes. Therefore, the impact of the positive-sequence current inner loop on the transient process of SCC is considered by studying its time-domain characteristics. Figure 3 illustrates the structure of the q-axis current inner loop. The term \(K_{\text{ip}}+K_{\text{ii}}/\text{s}\) represents the transfer function of the PI controller in the current inner loop, where \(K_{\text{ip}}\) and \(K_{\text{ii}}\) are the proportional and integral coefficients, respectively. The term \(K_{\text{PWM}}/(T_{\text{PWM}}/\text{s}+1)\) represents the transfer function of the inverter, which is a first-order inertia element. Here, \(K_{\text{PWM}}\) is the inverter gain, and \(T_{\text{PWM}}\) is the inertia time constant. The term \(1/(Ls+R)\) represents the transfer function of the terminal filtering circuit, where \(L\), \(R\) are the inductance and resistance, respectively, of the connection between the terminal and the external grid. Based on this, the open-loop transfer function of the current inner loop can be written as follows:  
\[\frac{i_{\text{q}}}{i_{\text{q}}}^{*}~{}=~{}G_{\text{iq}}(s)~{}=~{}\frac{K_{ \text{PWM}}K_{\text{ip}}(s~{}+~{}\frac{K_{\text{ii}}}{K_{\text{ip}}})}{sL(s~{}+~ {}R/L)(sT_{\text{PWM}}~{}+~{}\mathbf{1})} \tag{6}\]  
Figure 3: The positive-sequence \(q\)-axis current inner loop. After the fault, the reference current changes. Considering a typical unit step change, the output current is as follows:  
\[i_{\text{q}}\ =\ \frac{\mathbf{1}}{s}\frac{G_{\text{iq}}(s)}{\mathbf{1}\ +\ G_{\text{iq}}(s)} \tag{7}\]  
A study [20] utilized fault recording data to verify the parameters of the current inner loop, resulting in a unit step response adjustment time of 8.5 ms for the current inner loop, as shown in Figure 4. This indicates that when the reference value experiences a step change after the fault, the current inner loop will control the output current to match the reference current value within several milliseconds, leading to a very short transient process. The SCC quickly transitions into a steady-state process after the fault. However, because the change in the reference value is not necessarily a step change, the actual response time of the current inner loop may be slightly longer. Simulations using a typical permanent magnet synchronous generator model show that the SCC enters a steady state in approximately 10 ms. The average response time of SF\({}_{6}\) circuit breakers is from 40 ms to 100 ms, providing a theoretical basis for determining the applicability of the proposed SCC calculation model.