## 5 Results
### IEEE 123-Node System  
In the case of the Base-GC configuration--that is, grid-connected base network without distributed generation--the short-circuit results of PMsP are presented in Column 3 of Table 6. These results are comparable with those of OpenDSS (see Table 1). In the case of the SG-M-GC and SG-M-I configurations--that is, grid-connected or islanded operation with multiple distributed synchronous generators--the results are presented in Column 4 and Column 5 of Table 6, respectively. These results are not directly comparable with results from OpenDSS as they are based on a flat start, while OpenDSS performs a pre-fault power flow to determine generator setpoints. In the case of the Gfl-M-GC configuration--that is, grid-connected operation with multiple grid-following inverter-interfaced generators--the short-circuit fault current results of PMsP were within 5% of the results produced with the PV inverter model of OpenDSS (note that the nominal current is 32.76 A). This demonstrated that the formulation of the grid-following inverter constraints (Section 2.3) is able to limit the current injected from the inverter during a fault. In the case of the GfrI-S-I configuration, a single grid-forming inverter-interfaced generator was placed near the substation at Bus 8 and became the main source of power for the islanded system. When the system experienced a heavy fault, the inverter went into current limiting mode and appeared as a current source, thereby limiting the fault currents to the maximum current that could be injected by the inverter. In the case of the GfrI-M-I and GflI-GrI-M-I configurations, multiple grid-forming (and grid-following) inverter-interfaced generators were placed throughout the islanded \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Node** & **Fault Phasing** & _Base-GC_ **Fault Current (A)** & _SG-M-GC_ **Fault Current (A)** & _SG-M-I_ **Fault Current (A)** \\ \hline
13 & LG & 4444.9 & 5914.654 & 3969.269 \\
13 & LL & 4954.2 & 6211.437 & 3914.959 \\
13 & 3P & 5517.3 & 7116.605 & 4559.597 \\
67 & LG & 2362.2 & 4788.279 & 3896.403 \\
67 & LL & 2933.1 & 5301.483 & 3969.117 \\
67 & 3P & 3285.6 & 6153.95 & 4598.621 \\
113 & LG & 1392.2 & 2987.6 & 2802.407 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of results for configurations Base-GC, SG-M-GC and SG-M-I of the IEEE 123-Node System. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Symbol** & **Value** & **Unit** \\ \hline Fundamental frequency & f & 60 & Hz \\ Line-line voltage & V & 480 & V \\ Inverter rated power & P & 50 & kW \\ DC-bus voltage & Vdc & 1800 & V \\ Output filter inductance & L & 18 & \(\mu\)F \\ Output filter capacitance & C & 250 & nF \\ Maximum rms output current & Imax & 70 & A \\ Cable resistance & Rc & 39 & m\(\Omega\) \\ Cable inductance & Lc & 70.8 & \(\mu\)H \\ Load real power & Pd & 25 & kW \\ Load reactive power & Qd & 12.5 & kW \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Hardware parameters. system according to Figure 5. This resulted in the faults being fed from multiple lines connected to the faulted bus. These configurations had fault currents less than the GfrI-S-I islanded configuration (Table 3) or any of the grid-connected configurations (Tables 1, 7, and 8). It can be concluded that there are two reasons for the lower currents in the multiple inverter configurations of Tables 7 and 8: (1) a difference in the lower capacity of the configurations, and (2) an increase in the electrical distances between the sources and the fault location. To the first point: The total capacity of the configurations with inverter-interfaced distributed generation was 5.7 MVA, while the single grid-forming inverter had a capacity of 6 MVA. PMsP partially bases the maximum fault current on the VA rating of the inverter, which explains why the 1165 A value seen in Table 8 was close to, but higher than the maximum fault currents in the multiple inverter configurations seen in the same table.