## 4 Experimental Validation
### Experimental Results  
The Bode plots obtained analytically were validated using the experimental setup shown in Figure 13, following the method described in the previous section. In Figure 14, the analytical \(\Delta P/\Delta\omega_{g}\) NFP Node plots are shown, with the measured points overlapping on the curves. For the three curves, each measured dot shares the same color as its corresponding analytical line. A total of 16 measurements were performed for each case, extracting one point for the magnitude and another for the phase from each measurement--96 measurements in total. All measured points exhibit a clear trend, validating the analytical expressions developed for the basic case. The largest deviations appear at the highest frequencies, where measurement perturbations and errors become more prominent, particularly around 90\({}^{\circ}\) of phase shift. Nonetheless, these discrepancies remain within acceptable limits. In Figure 15, the analytical \(\Delta P\)-\(\Delta P^{*}\) Bode plots are shown, again with the corresponding measured points overlapping. As in the previous case, 16 measurements were taken for each configuration, resulting in another set of 96 points. The experimental results show a consistent trend that aligns with the theoretical curves. In addition to the base case Bode plot, this work also evaluated the potential of increasing the control bandwidth of the active power setpoint, as well as the inclusion of the classic POD control structure and the proposed POD-P structure. The Bode plots and analytical transfer functions for these three cases are shown in earlier figures. However, the validation of the first two alternatives was excluded. Increasing the bandwidth through alternative techniques complicates the POD-P algorithm and interferes with the inherent control of the GFM system. For the second case, adding the classic POD structure not only alters the GFM control characteristics but could also compromise the stability of the inverter. Therefore, the focus of this study is on the validation of the transfer function and Bode plot corresponding to the proposed POD-P algorithm. Validating non-relevant cases would not contribute meaningful information to the reader, and the validation of an unstable control design may not be feasible. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Var Name** & **Value** \\ \hline \multirow{3}{*}{Base values} & \(S_{b}\) & 625 W \\  & \(v_{b}\) & 200 V \\  & \(\omega_{b}\) & 314 rad/s \\ \hline \multirow{3}{*}{LCL filter} & \(L_{c}\) & 0.1 pu \\  & \(R_{c}\) & 0.006 pu \\  & \(C_{f}\) & 0.05 pu \\  & \(R_{f}\) & 0.08 pu \\  & \(L_{t}\) & 0.05 pu \\ \hline \multirow{2}{*}{Inverter} & \(f_{sw}\) & 10 kHz \\  & \(v_{dc}\) & 300 Vdc \\ \hline \multirow{3}{*}{PSL and RPC setpoints} & \(p^{*}\) & 0 pu \\  & \(\omega_{r}^{*}\) & 1 pu \\  & E & 1 pu \\ \hline \multirow{3}{*}{Grid} & \(v_{g}\) & 1 pu \\  & \(\omega_{g}\) & 1 pu \\ \cline{1-1}  & \(L_{g}\) & 0.1 pu \\ \cline{1-1}  & \(R_{g}\) & 0 pu \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental setup parameters. In Figure 16, the analytical \(\Delta P/\Delta\omega_{g}\) NFP Bode plot of the proposed POD-P control and its equivalent base case are shown. The measured points can be seen overlapping. In total, 11 additional measures were taken at low frequencies to obtain a better accuracy at those frequencies. The measured operation points correspond almost perfectly to the  
Figure 14: \(\Delta P/\Delta\omega_{g}\) NFP Bode plots for different sets of parameters with overlapping measurements (dots). (**a**) H = 2.5 s and (**b**) H = 5 s.  
Figure 15: \(\Delta P/\Delta P*\) Bode plots for different sets of parameters with overlapping measurements (dots). (**a**) H = 2.5 s and (**b**) H = 5 s.  
theoretical results. The Bode plot of the proposed POD-P algorithm shows that a POD-P structure can work properly in a GFM-based IBR, without interacting negatively with each other. The inherent GFM characteristics are not modified, while the provided damping at the selected frequency increases.