## 4 Simulation and Verification
### Simulation Model  
In a traditional 69-node distribution network, the electric loads are constant. In the field, the load would change at every time point. Based on the cluster results shown in Figure 4, four types of load curves are given in Figure 5. The maximum load power and the corresponding curve are given in Table 1.  
For the DGs in the selected 69-node distribution network, three typical daily output power curves are calculated based on the cluster results in Figure 2, which are shown in Figure 6. Type 1, type 2, and type 3 of daily output power curves are related to a sunny day, cloudy day, and rainy day, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Node** & **Maximum Power/kW** & **Type of Load Curve** & **Node** & **Maximum Power/kW** & **Type of Load Curve** \\ \hline  
& 1 & Total & 3802.1 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum power and typical load curves for all loads in the 69-node distribution network. In the meantime, the short-circuit current is analyzed in three different scenarios in this paper. The topological structures of the distribution network in these three scenarios are shown in Figure 7.  
As shown in Figure 7a, in the first case, there are no DGs in the 69-node distribution network. In the second case shown in Figure 7b, six DGs are connected into the distribution network, and the total rated capacity of these DGs are 50% of the total maximum load power. Different from the second case, there are six DGs connected into different nodes in the third case, which is shown in Figure 7c, and the total rated capacity of these DGs are 70% of the total maximum load power. Figure 5: Four typical daily load curves according to the cluster analysis results. Figure 6: Three typical daily output power curves of DGs in the distribution network. The location and capacity of DGs in the second case is given in Table 2, while the information in the third case is given in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Access Node of DGs** & **Capacity of DGs/kW** & **Access Node of DGs** & **Capacity of DGs/kW** \\ \hline
6 & 304.2 & 35 & 380.2 \\ \hline
16 & 304.2 & 44 & 152.1 \\ \hline
27 & 380.2 & 54 & 380.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The location and capacity of DGs in the second case. Figure 7: Topological structures of the distribution network in short-circuit analysis scenarios: (**a**) the first case; (**b**) the second case; (**c**) the third case. shown in Figure 8a: the lowest voltage reaches 0.956 p.u. at 20:00, while its highest voltage reaches 0.980 p.u. at 4:00, nearly 1.025 times the lowest voltage value. In the meantime, due to the output power of distributed DGs, the voltages at node 27 in the second case and third case are obviously different from that in the first case. At 13:00, the voltage at node 27 in the first case, second case, and third case, is 0.9721, 0.9922, 0.9927, respectively. In other words, the voltage at some node may change 2.1% because of the output power of DGs. In addition, the voltages at some nodes in the second case are different from that at the same node in the third case. Take node 54 as an example, which is shown in Figure 8b: at 14:00, the voltage at node 54 in the first case, second case, and third case is 0.9453, 0.9508, 0.9585, respectively. The fluctuation in output power of the DGs would affect the node voltage at different times; hence, the short-circuit current, which is determined by the node voltage, should be calculated considering the fluctuation in renewable resources and electricity loads. Due to the different output power on a sunny day, cloudy day, and rainy day, which is shown in Figure 5, the node voltage would be different. As shown in Figure 9, take node 27 in case 3 as an example: the voltage at node 27 equals 0.9927 at 13:00 on a sunny day, while it equals 0.9849 at 13:00 on a cloudy day. The node voltage would also change with the weather.