## 5 Experiment Verification  
Based on the system parameter values listed in Table 1, experiments were carried out on a 1-kW three-phase VSM prototype to validate the effectiveness of the proposed inertia analysis and design method. Figure 10 illustrate a photo of the experimental prototype. As seen, a three-phase \(LC\)-filtered power electronic converter was employed as the hardware of the VSM, while the control algorithms were executed on a dSPACE control platform (dSPACE Microlabbox). For simplicity, the VSM acts as the only generator fed by resistive loads, where transmission lines, transformers, and other factors are ignored. The energy storage of the VSM emulates the kinetic energy of the synchronous generator to support the islanded grid for frequency regulation. The frequency regulation structure of the VSM is presented in Figure 3, where the frequency variation signal \(\Delta\omega_{r}\) was integrated to obtain the angle signal \(\Delta\theta\). Then the ac output voltage reference \(V_{arg\prime}\) of the VSM can be determined according to \(\Delta\theta\). A standard double-loop controller, i.e., outer voltage-loop and inner current-loop controller, was incorporated to achieve the voltage control of the VSM, and its design guideline can be found in [30]. Figure 11 demonstrate the steady-state experimental waveforms of the VSM. As seen, the VSM provides voltage support through converting the constant dc-link voltage vdc into three-phase ac output voltages \(v_{x}\) (\(x=a,\,b,\,c\)) of sinusoidal waveforms. In the steady-state where the generated power, rated power of the VSM, and load power are equivalent, the frequency of \(v_{x}\) (\(x=a,\,b,\,c\)) is the rated frequency of 50 Hz. Since the load is purely resistive, the waveforms of load current follow those of ac voltages. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Symbol** & **Value** \\ \hline Droop coefficient & \(R\) & 0.05 \\ Speed governor coefficient & \(T_{G}\) & 7/0.1 s \\ Damping coefficient & \(D\) & 1.0 \\ Inertia coefficient & \(H\) & 10/5 s \\ Initial inertia coefficient & \(H_{0}\) & 5 s \\ Rated frequency & \(f_{br}\) & 50 Hz \\ Maximum frequency nadir & \(|f_{r,peak}|_{max}\) & 0.2 Hz \\ Maximum ROCOF & \(|df_{r}(t)/dt|_{max}\) & 0.5 Hz/s \\ Dc-link voltage & \(V_{dc}\) & 400 V \\ Ac voltage (rms) & \(V_{a}\) & 110 V \\ Switching frequency & \(f_{s}\) & 10 kHz \\ Dc-link capacitance & \(C_{dc}\) & 2.82 mF \\ Filter capacitance & \(C_{f}\) & 5 \(\mu\)F \\ Filter inductance & \(L_{j}/L_{g}\) & 1.0 mH \\ Power rating & \(P_{rated}\) & 1 kW \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameter values. Figure 10: A photo of the experimental prototype. Under a 3% step-up load change, frequency responses of the VSM with \(T_{G}\) = 7 s are shown in Figure 12. As seen, more frequency oscillations, larger frequency deviation and overshoot, and greater ROCOF can be observed for the case of \(H\) = 5 s as compared with the case of \(H\) = 10 s, i.e., the case of optimal design. As mentioned in Section 3.2, a \(T_{G}\) of 7 s specifies a relatively large time constant for the speed governor. Under this condition, the system always remains underdamped, i.e., \(\zeta\) < 1. Consequently, most of the performance indices for frequency regulation, such as frequency nadir, overshoot, and ROCOF, can be improved as the inertia coefficient \(H\), together with the damping factor \(\zeta\), increases. It can be observed from Figure 12 that the requirement of frequency nadir is satisfied for the case of \(H\) = 10 s. However, the case of \(H\) = 5 s fails to comply with this requirement even though it allows faster frequency recovery.