## 4 Simulation and Verification
### Simulation Model
On a rainy day, the output power of DGs reduce significantly, and the voltage at node 27 drops to 0.9756 at 13:00. Hence, the short-circuit current is also affected by the weather change. In this paper, the system impedance is set as 0.5 \(\Omega\) with a three-phase short-circuit fault with a resistance of 0.1 \(\Omega\) at node 20. For the traditional short-circuit analysis method, all electrical loads remain the same and have equal-rated power. Then, the short-circuit current in some selected branches in case 1 is given in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Branch** & **Normal Current/kA** & **Short-Circuit Current/kA** & **Branch** & **Normal Current/kA** & **Short-Circuit** \\  & & & & & **Current/kA** \\ \hline
1–2 & 0.2236 & 0.9155 & 8–9 & 0.1511 & 0.9277 \\ \hline
3–28 & 0.0051 & 0.0043 & 9–42 & 0.1052 & 0.1043 \\ \hline
3–59 & 0.0103 & 0.0087 & 9–10 & 0.0441 & 0.8214 \\ \hline
3–4 & 0.2082 & 0.9054 & 11–55 &When ignoring load fluctuation in case 1, it can be derived that the current in branches through which the short-circuit flows increases significantly when the fault occurred. Take branch 1-2 as an example, which is between node 1 and node 2: its normal current equals 0.2236 kA. Once the fault occurred, the short-circuit current reaches 0.9155 kA. The over-current protection device would be activated, and the fault feeder would be cut off. Because the fluctuation in electrical load would affect the node voltage, the fault current in branches would change over time. In the first case, when the fluctuation in the load is taken into account during the calculation of the short-circuit current, the short-circuit current in the branches would change over time. As shown in Figure 10, the short-circuit currents in branches 1-2, 4-5, and 11-12 vary with time. For the short-circuit current in branch 1-2, the minimum value is 0.8946 kA at 4:00, and the maximum value is 0.9155 kA at 20:00. A similar analysis can also be used for branch 4-5; the results show that the short-circuit current may vary from 0.8792 kA to 0.9161 kA. In other words, the maximum short-circuit current is 1.042 times the minimum value for branch 4-5 because of the fluctuation in loads. The short-circuit current in some other selected branches in case 1 is given in Table 5 with the consideration of the fluctuation in loads. As given in Table 5, the short-circuit current in the fault loop is much bigger than the rated normal current; the ratio of the short-circuit current to the rated normal current varies from 4.0 to 39.5. It can be used for the setting calculation of the over-current protection. In the meantime, the short-circuit current varies during the whole day with consideration of the load fluctuation. In the selected branches, the short-circuit current changes with a variation of 2%-7% for the branches in the fault loop. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Branch**} & \multirow{2}{*}{**Rated Normal Current/kA**} & \multicolumn{2}{c}{**Short-Circuit Current/kA**} & \multicolumn{2}{c}{**Short-Circuit Current/kA**} \\ \cline{3-8}  & & **4.00** & **20:00** & **Branch** & **Rated Normal Current/kA** & **4:00** & **20:00** \\ \hline
1–2 & 0.2236 & 0.8946 & 0.9155 & 8–9 & 0.1511 & 0.8677 & 0.9277 \\ \  
In the second and third case, different scales of DGs have access to the 69-node distribution network. The fault currents are also influenced by the output power and LVRT strategies of the DGs. Therefore, the fault currents of some selected branches in case 2 at different times on sunny days, cloudy days, and rainy days are given in Table 6, while the results in case 3 are given in Table 7 when a three-phase short-circuit fault occurred at node 20. As given in Tables 6 and 7, the short-circuit current in case 2 is obviously different from that that in case 3. Take branch 1-2 as an example, the corresponding short-circuit current in case 2 equals 1.20 at 4:00, while the current in case 3 equals 0.9606.