## 4 Simulation Results and Discussion  
In this section, we will show the performance of the 2L-VSI using the conventional M\({}^{2}\)PC and the proposed ANN-M\({}^{2}\)PC. To assess its performance, it is of paramount importance to check several system behaviors feeding both linear and nonlinear loads. The steady-state behavior, transient response performance, harmonic spectrum, and the total harmonic distortion of both control schemes will be investigated as well. Table 2 summarizes the system parameters, which were used for both control strategies, while Figure 9 shows the simulink modeling for the simulation results. Figure 8: Switching pattern of the applied vectors when the optimal sector is: (**a**) odd, (**b**) even. Figure 9: Simulink model for the proposed ANN-M\({}^{2}\)PC. Figure 10 shows the converter output voltage (\(V_{o,\alpha_{g}}\)) controlled by the M\({}^{2}\)PC and the proposed ANN-M\({}^{2}\)PC feeding a linear \(RL\) load. Both controllers are following a voltage reference as the only objective of their cost function. In addition, the load current is shown in Figure 11. It gives an insight on the performance of the 2L-VSI using the ANN-M\({}^{2}\)PC compared to M\({}^{2}\)PC during the instant of load change at 0.1 s. That gives a fair comparison as the available opportunity is equal for both controllers by tracking only the voltage at every sampling time based on the CF definition as in (23), but with different approaches for dwell-time calculations. It has been detected that the error from the reference of the conventional tracking algorithm is high. The error at some points in time can be spiky, resulting in a risk of stability issues based on the intended application. This outcome is verified when the error difference is calculated for both the conventional and proposed algorithms, as shown in Figure 12.  
Using the proposed algorithm leads to a better power quality compared to the conventional M\({}^{2}\)PC. In addition, two important aspects have been retained by using the proposed \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Input voltage & \(V_{dc}\) & 700 V \\ Filter inductance & \(L_{f}\) & 2 mH \\ Filter capacitance & \(C_{f}\) & 50 \(\mu\)F \\ Switching frequency & \(F_{sw}\) & 10 kHz \\ Sampling time & \(T_{s}\) & 100 \(\mu\)s \\ Nominal RMS output voltage (L-L) & \(V_{o,ref}\) & 380 V \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the studied 2L-VSI. Figure 11: Dynamic performance of the load current in both control algorithms when the load is stepped-up at 0.1 s: (**a**) conventional M\({}^{2}\)PC, (**b**) proposed ANN-M\({}^{2}\)PC. Figure 12: Tracking error of the phase voltage: (**a**) conventional M\({}^{2}\)PC, (**b**) proposed ANN-M\({}^{2}\)PC. Figure 10: Dynamic performance of the output voltage in both control algorithms when the load is stepped-up at 0.1 s: (**a**) conventional M\({}^{2}\)PC, (**b**) proposed ANN-M\({}^{2}\)PC. algorithm, firstly, the algorithm can still accept adding more constraints into its operating cost function. Another aspect is that the fast response and the fixed-switching frequency are achieved, while the power quality is significantly enhanced. This is illustrated in Figure 13 by calculating the THD for both conventional and proposed algorithms at different sampling times. It is clear that the proposed approach has a superior performance compared to the conventional M\({}^{2}\)PC, as it has lower THD by around 50% in all the tested sampling intervals. Moreover, Figures 14 and 15 show how the output voltage and current at the same ground of truth have incredibly enhanced and give better shape, respectively. That is a direct result of achieving an optimal switching state, as shown in Figure 16. As it may be noticed that in the proposed ANN-M\({}^{2}\)PC, the algorithm always keeps the sector selection in a certain time span repetitive and that behavior will introduce better quality compared to the conventional M\({}^{2}\)PC.