## 3 Short-Circuit Current Calculation Considering Power Fluctuation
### Real-Time Short-Circuit Current Calculation Considering Fluctuation in DGs and Loads  
Based on the abovementioned analysis, it can be seen that the DGs and loads at each node of the distribution network have a strong randomness due to the influence of solar radiation and electricity consumption patterns. Their influence on the distribution network short-circuit current calculation can be summarized as follows:  
1. In the short-circuit calculation, the node voltage value before the fault time should be obtained in real time by considering the source-load stochasticity, which cannot be  
Figure 3: Cluster analysis of residential loads: (**a**) ten households; (**b**) fifty households; (**c**) one hundred and fifty households; (**d**) three hundred households. simplified to the rated voltage. It can be derived that the voltage changed because of the volatility in DGs and loads at each node of the distribution network throughout the day and 24 h. In the meantime, the short-circuit current of each branch is directly determined via the voltage at each node after the fault based on Equation (7);
2. In the short-circuit calculation, DGs in distribution networks can be equivalent to voltage-controlled current sources according to the LVRT strategies. According to Equations (10)-(12), the output current of DGs after the fault will change from the output current at the pre-fault moment. If the output current of a DG at the node \(j\) before and after the fault changed by \(\Delta I_{\text{IIDC},j}\), this updated injected current \(\Delta I_{\text{IIDC},j}\) is directly determined by the post-fault DG terminal voltage. It will also be indirectly affected by the DG output power before the fault moment. Therefore, the proposed real-time short-circuit calculation method for distribution networks that takes into account the source-load stochasticity is proposed; the flowchart of our proposed is shown in Figure 4.  
The main procedures include the typical daily curves of DGs and the electricity loads calculation, continuous power flow calculation, short-circuit current calculation without LVRT strategies, and short-circuit calculation with LVRT strategies. The detailed steps are given as follows:  
1. During the normal operation stage, the distributed DGs and load nodes of the distribution network are equivalent to PQ nodes, and the nodes of the distribution network connected to the main network are equivalent to the balanced node. Then, taking into account the source-load stochasticity, the voltage of each node is calculated at each moment of the whole day based on traditional power flow calculation algorithms, as well as the current of each branch. In the results, the voltage at the node \(i\) in the normal operation at the time \(t\) is denoted as \(\dot{V}_{i}^{(0)}(t)\), and the branch current between the node \(m\) and node \(n\) is denoted as \(\dot{I}_{m,n}^{(0)}(t)\), and the injected current of the DG at the node \(j\) is denoted as \(I_{IIDC,j}^{(0)}(t)\);
2. The external power system connected to the whole distribution network is equivalent to a current source with an internal resistance. And the node conductance matrix \(\mathbf{Y}\) and impedance matrix \(\mathbf{Z}\) of the distribution network are constructed according to the topology and parameters of the distribution network;
3. When a fault occurs at node \(f\) at moment \(t\), the initial voltage of each node of the distribution network and the short-circuit current of each branch are calculated using Equations (5)-(7) under the assumption that the there is no change in the output current of DGs, and then, the initial value of the short-circuit current calculation results of the distribution network can be obtained. In the results, the initial fault  
Figure 4: An illustrative flowchart of our proposed method. voltage at node \(i\) is noted as \(\dot{V}_{i,f}^{(0)}(t)\), and the initial fault current in the branch circuit between node \(m\) and node \(n\) is noted as \(\dot{I}_{m,n,f}^{(0)}(t)\);
4.