## 4 Validation
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Units** \\ \hline \(V_{M}\) & \(240\sqrt{2}\) & V \\ \(\omega\) & \(2\pi\cdot 50\) & rad/s \\ \(L_{f}\) & 350 & \(\mu\)H \\ \(C_{f}\) & 10 & \(\mu\)F \\ ESR(\(L_{f1}\)) & 50 & m\(\Omega\) \\ ESR(\(C_{f}\)) & 316 & m\(\Omega\) \\ \(S_{R}\) & 11 & kVA \\ \(V_{R}\) & 400 & V \\ \(k\) & 0.94 & - \\ min(PF) & 0.5 Leading/Lagging & - \\ \hline \end{tabular}
\end{table} 
Table 1: System parameter values. Three simulations (PSIM 2025 software was used) and matching experiments were carried out under rated loading \(S_{R}\) (cf. Table 1) under three following power factor values: PF = 0.5 (leading), PF = 1 (unity), PF = 0.5 (lagging) with the former representing the design point (cf. (21)). The results are depicted in Figures 6-11. Experimental waveforms were acquired using a 4-channel oscilloscope, hence only two out of three AC-side quantities (i.e., two voltages and two currents) are shown simultaneously while all the three are given in corresponding simulation results. It should also be emphasized that due to the fact that the three-phase mains in the Applied Energy Laboratory (experimental site) is typically polluted with non-negligible harmonic content (well-evident in the experimental waveforms), the currents generated by the inverter also possess noticeable harmonic constituents due to simplified control system adopted (cf. Figure 4b) which does not consider harmonic elimination for brevity. Nevertheless, such characteristics do not affect the proposed methodology feasibility. It is well-evident that all simulation results accurately match their experimental counterparts even though the former consider purely sinusoidal AC-side voltage and currents. Figures 6 and 7 demonstrate operational waveforms of the system under rated loading with leading power factor of PF = 0.5 (i.e., AC-side currents lead corresponding AC-side voltages by 60\({}^{\circ}\)). It is well-evident that under these conditions, a single tangency point between positive part of grid voltages and positive split DC link voltage \(v_{DC1}\) exists, as indicated by black circles in Figure 7, as expected. On the other hand, split DC link voltages are kept below 376 V (=0.94-400) at all time. Such a behavior accurately validates the design point (cf. (21)), simultaneously satisfying (15) and (18). Note that even though experimental waveforms of AC-side voltages are slightly distorted (due to harmonic content pollution), split DC link voltages are sinusoidal at triple-grid-frequency. This supports the above-made claim regarding negligible influence of AC-side current harmonic content on split DC-link voltages behavior particular and the proposed methodology feasibility in general. Similar conclusion may be drawn regarding operation under other power factor values as well. It is also evident that positive AC-side voltage peaks and valleys of split DC link voltage \(v_{DC1}\) are slightly shifted due to nonzero PF and are expected to approach each other in case the value of leading power factor is further decreased (cf. Figure 3). Figures 8 and 9 demonstrate operational waveforms of the system under rated loading with unity power factor (here, AC-side currents are in-phase with corresponding AC-side voltages). It is well-evident  
Figure 5: Graphical solution of (15) and (18) to obtain (20). that under these conditions no tangency point between positive grid voltage parts and the corresponding split DC link voltage \(v_{DC1}\) exists, as expected. On the other hand, split DC link voltages are kept below 376 V (=0.94\(\cdot\)400) at all times, as required. It is also evident that positive AC-side voltage peaks are synchronized with instances where \(v_{DC1}=-v_{DC2}=0.5\)\(v_{DC}\). Such a behavior is well in line with performance previously revealed by the Authors in [36]. Figures 10 and 11 demonstrate operational waveforms of the system under rated loading with lagging power factor of PF = 0.5 (i.e., AC-side currents lag corresponding voltages by 60\({}^{\circ}\)).