## 5 Results and Discussion  
The control algorithms were implemented in the dSPACE controller with a DS1007 power dual-core 2 GHz processor board. The computational delay of exact _Ts_ has been compensated as in [23]. The overall parameters of the test setup and simulation model can be seen in Table 1. The conventional (CMPC), improved (IMPC), MPC scheme with a modulator (M\({}^{2}\)PC), and periodic (PMPC) are tested experimentally using a Danfoss three-phase 2L-VSC with an output _LC_ filter, as seen in Figures 4 and 5. An input rectifier is connected to a dc-link and fed by the main utility through a delta star transformer. The experimental validation is divided twofold: a) The investigation of the THDv for all control algorithms, where the THDv was investigated with a 600 V dc-link and line to line output voltage which is equal to 400 V rms; and b) the investigation of the losses for the 2L-VCS using the same parameters up to 8 kW. In the losses investigation, four sets of the test have been carried out, feeding a linear load. The first and second tests consider using conventional and improved predictive algorithms. The third test is feeding a linear load, where the M\({}^{2}\)PC algorithm is deployed. The fourth test considers using the periodic predictive algorithm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Quantity** \\ \hline S & 15 kVA \\ \(V_{a_{s}}\) & 230 V (rms) \\ \(V_{d_{c}}\) & 600 V \\ \(f_{g}\) & 50 Hz \\ \(f_{s_{w}}\) & \(\approx\)5 kHz \\ \(L_{f}\) & 3 mH \\ \(C_{f}\) & 40 \(\mu\) F \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters for the simulation and experimental setup  
Figure 4: Schematic diagram of the experimental setup. In line with previous studies, firstly the control algorithms should be validated with the selected circuit parameters. This kind of test implies that the control algorithms should work efficiently at the same conditions. In Figure 6a-d, it is notable that the discussed MPC control algorithms in this paper are working properly, applying the same power levels and using the same parameters. The total harmonics distortion of the applied control algorithms has been measured, and the results are included to show the importance of each control algorithm in providing a better power quality. For a fair evaluation, the switching frequency values have been considered to be approximately similar, and around 5 kHz for all algorithms. Figure 7 demonstrates that slightly superior results are achieved with the periodic control algorithm, which provides similar power quality but not using a modulator, compared to the CMPC and IMPC performance. It can be noticed that M\({}^{2}\)PC gives the accepted power quality and meets the grid requirement. Due to the unavoidable variations in the switching frequency using FCS-MPC, the switching states have high commutation values at higher power compared to those at lower power. Take into consideration that the calculated average is still approximately the same. In addition, FCS-MPC depends on the model of the converter associated with a physical filter to predict its future values. Based on that, changing in the measured values influences the predicted values directly and therefore, the actuations of the inverter are instantly influenced and that affects the THDv. Moreover, spectrum analysis shows the magnitude and frequency concentration for the current signals of the four MPC algorithms, as it is shown in Figure 8a-d. These results and findings are particularly important when investigating the efficiency of the power converter under different control operations. Figure 5: Experimental setup. Figure 6: Obtained \(I_{\alpha\beta}\) currents using different MPC schemes, where the output power is 4 kW. (**a**) Conventional predictive scheme; (**b**) improved scheme from the conventional way; (**c**) periodic MPC scheme; and (**d**) MPC scheme with modulator. Figure 7: Total harmonics distortion of the voltage (THDv) for different MPC schemes at 5 kHz switching frequency (average).