# A Short-Circuit Current Calculation Model for Renewable Power Plants Considering Internal Topology
## 3 Practical SCC Calculation Model for Renewable Power Plants
### SCC Calculation Method for Renewable Power Plants Under LVRT  
In the steady state following a fault, N-SMSs can be treated as voltage-controlled current sources. With the PCC voltage known, determining the steady-state voltage at the generator terminals and the injected current becomes a power flow calculation problem. Power flow calculations typically use iterative methods, which can be complex. Given that renewable power plants often utilize chain or radial topologies [23], this paper proposes a simplified method for calculating steady-state SCCs based on these topological characteristics. The following outlines the calculation steps using the chain topology illustrated in Figure 7.  
(1) Number the internal lines and nodes of the renewable power plant.  
Assign numbers to the internal lines and nodes of the renewable power plant. The first node in the system is the PCC, numbered as (0). The nodes representing N-SMSs are numbered sequentially. The line number corresponds to the number of the N-SMSs at the endpoint of that line.  
(2) Construct the loop-branch incidence matrix \(C\).  
Based on the topology, derive the loop-branch incidence matrix \(C\), where the rows represent loops and the columns represent branches. If a loop passes through a particular branch, the corresponding element in the matrix is set to 1; otherwise, it is set to 0. Using the line information, construct the loop-branch reactance matrix \(X\) as follows:  
\[X=CX_{1} \tag{16}\]  
where  
* \(X_{1}\) is the column vector of branch reactance. (3) Calculate the terminal voltage of the N-SMSs. The voltage equations between adjacent nodes are given by \[U_{i}-U_{j}\ =\ \frac{\mathbf{3}}{2}I_{\text{qs}}X_{i}\ =\ \frac{\mathbf{3}}{2}\sum I_{x}X_{i}\] (17) where
* \(U_{i}\) and \(U_{j}\) are the fault steady-state voltages of two adjacent non-synchronous power nodes.
* \(X_{i}\) is the line reactance of branch \(i\),
* \(I_{\text{qs}}\) is the reactive current injected by node \(i+1\), which is the sum of the reactive current supplied by node \(i+1\) and the downstream asynchronous machine, and the reactive current generated by each asynchronous machine is determined by the low voltage crossing strategy, namely, \[I_{\text{qs}}\ =\ 1.5\times(0.9-U_{x})I_{\text{N}}\] (18)  
The linear Equations (13) and (14) for the machine terminal voltage can be listed as follows:  
\[\begin{bmatrix}U_{1}-U_{0}\\ \vdots\\ U_{i}-U_{j}\\ \vdots\\ U_{n}-U_{m}\end{bmatrix}\ =\ \frac{9}{4}I_{N}\boldsymbol{C}^{T}\begin{bmatrix}X_{1} (0.9-U_{1})\\ \vdots\\ X_{i}(0.9-U_{i})\\ \vdots\\ X_{n}(0.9-U_{n})\end{bmatrix} \tag{19}\]  
(4) Calculate the SCC of the renewable power plant.  
Figure 7: Renewable power plant internal loop.  
According to the terminal voltage and LVRT strategy, the SCC of each non-synchronous machine is calculated, and the SCC of the plant is obtained by summation.  
\[\left\{\begin{array}{l}i_{\text{d,i}}\ =\ i_{\text{d,i}^{*}}\ =\ \min(i_{\text{d0}},J_{\text{dmax}} ^{*})\\ i_{\text{q,i}}\ =\ i_{\text{q,i}^{*}}\ =\ 1.5(0.9-U_{i})I_{\text{N}}\end{array}\right. \tag{20}\]  
\[I\ =\ \sum_{i\ =\ 1}^{n}I_{i} \tag{21}\]