## 4 Design Procedures and Simulation Results
### Summary of Simulations  
The simulation results are summarized in Table 2 in terms of parameters like the minimum frequency, maximum ROCOF, settling time, peak power, and energy exchange. The settling time is defined here as the time required for the frequency to return to and stay within \(\pm\)0.25 Hz of the final steady-state frequency after a disturbance. The energy exchange was calculated over the time period where the inverter exchanges power with the system. With all three topologies, the minimum frequency and ROCOF were reduced by similar amounts. The peak power delivered by the inverter varied slightly, with the highest value of 1929 W for the VSG topology. The most pronounced differences were in the settling time for the frequency and the energy exchange. Compared to systems with no virtual inertia, the settling time has increased in all three cases. This was expected as adding virtual inertia slows down the frequency dynamics. The ISO8528-5 standard for generators sets recommends a settling time of 10 s [20]. The settling time, however, increased to 13.2 s with synchronverter and an even higher value of 17.7 s and 17.9 s with the Ise lab's and VSG respectively. This led to a relatively higher energy exchange in these two topologies of 3.8 Wh and 4.9 Wh compared to that 0.8 Wh with the synchronverter. Moreover, there was a short-energy recovery period in the power plot of the synchronverter as seen in Figure 12c which led to a lower energy exchange estimate for the synchronverter.  
Therefore, by appropriate selection of the parameters for the topologies through the time constant \(T_{f}\) and/or the inertia constant \(H\), similar inertial response can be achieved in terms of frequency deviation reduction and power exchange from the inverter. Based on the topology, the exact dynamics represented by the system may vary. The selection of a particular topology depends on the application and the desired level of replication of the dynamics of the SG. Topologies like the synchronverter and the Ise lab's topology may be more suitable for isolated power system as they can operate autonomously as grid forming units, as well as for reasons discussed in Section 3. The VSG topology on the other hand behaves more like a grid following unit with added inertial response capabilities  
Figure 14: Simulation results from a virtual synchronous generator: (**a**) system frequency after a step-increase of 2 kW load; (**b**) ROCOF after a step-increase of 2 kW load; (**c**) increase in inverter power as a response to system frequency decrease [45; 46].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **No VI** & **Synchronverter** & **Ise Lab** & **VSG** \\ \hline Minimum Frequency & 57.3 Hz & 58.1 Hz & 58.6 Hz & 58.3 Hz \\ Maximum ROCOF & 1.9 Hz/s & 1.5 Hz/s & 1.6 Hz/s & 1.7 Hz/s \\ Settling time & 11.3 s & 13.2 s & 17.7 s & 17.9 s \\ Peak power delivered & 0 W & 1825 W & 1800 W & 1929 W \\ Energy exchanged & 0 Wh & 0.8 Wh & 3.8 Wh & 4.9 Wh \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance comparison of systems without virtual inertia (VI), and VI implemented through synchronverter, Ise lab’s and virtual synchronous generator (VSG) topologies.  
and is more suited towards interconnected operations. The synchronverter or Ise lab's topology are more suitable for a closer approximation of SG dynamics. If the main aim, however, is to make the DG unit responsive to frequency changes, the VSG approach provides a far simpler implementation.