## 4 Simulations and Experimental Results
Figure 9: Comparison of the output performance of MPC in steady-state operation (three-phase output current, A-phase reference current, line-to-line voltage, load phase voltage, a-phase current (FFT)): (**a**) conventional MPC, (**b**) multi-vector MPC, and (**c**) proposed D-MPC. The output performance of the conventional MPC, multi-vector MPC, and the proposed D-MPC was compared during the transient states by varying the output current, as shown in Figure 11. The comparison criteria are identical to those used in the steady-state analysis. The conventional MPC exhibited rapid response characteristics; however, it demonstrated a relatively lower output current quality. The multi-vector MPC demonstrated improved output performance when compared with the conventional MPC using multiple vectors, but it presented increased losses due to higher switching frequency. The proposed D-MPC achieved rapid response characteristics similar to the conventional MPC while applying multiple vectors and demonstrated that discontinuous intervals are preserved even under low-load conditions. This indicates that a discontinuous control technique can be applied via switching patterns in low-load regions to suppress unnecessary switching operations, thereby potentially reducing the switching losses. Additionally, the output current performance exhibited results similar to those of the multi-vector MPC. The performances of the conventional MPC, multi-vector MPC, and the proposed D-MPC were compared during the transient states by varying the output frequency, as shown in Figure 12. The comparison criteria were identical to those used in the steady-state analysis. Figure 11: Comparison of the output performance of MPC in the transient-state operation with current magnitude changes from 15 A to 7.5 A (three-phase output current, a-phase reference current, line-to-line voltage, load phase voltage): (**a**) conventional MPC, (**b**) multi-vector MPC, and (**c**) proposed D-MPC. The conventional MPC exhibited rapid response characteristics; however, it exhibited a tendency towards degraded output current quality under low-frequency conditions. The multi-vector MPC improved the output performance when compared with the conventional MPC by utilizing multiple vectors; however, this presents the disadvantage of increased switching losses. The proposed D-MPC exhibited rapid response characteristics similar to those of the conventional MPC while applying multiple vectors and demonstrated superior output current performance even under low-frequency conditions. Furthermore, the discontinuous switching intervals were consistently maintained in the high-current regions, regardless of the frequency variations. This demonstrates that the discontinuous control technique presents consistent switching suppression effects independent of the frequency changes, thereby preventing unnecessary switching operations and reducing the switching losses. We performed a comparative analysis for the conventional MPC, multi-vector MPC, and the proposed D-MPC across various sampling frequency conditions, as shown in Figure 10. Figure 10a presents a comparison of the current error performances of each method. The current error is calculated as follows:  
\[error(i_{x})=\frac{1}{N}\sum_{k=1}^{N}\left|i_{x,ref}-i_{xo}\right|\left(x=a.b.c\right) \tag{13}\]  
where \(i_{x,ref}\) denotes the reference currents for each phase, and \(i_{xo}\) denotes the measured load currents. With N set to 10,000, the error represents the average of these values. Figure 12: Comparison of the output performance of MPC in the transient-state operation with frequency variations from 60 Hz to 30 Hz (three-phase output current, a-phase reference current, line-to-line voltage, load phase voltage): (**a**) conventional MPC, (**b**) multi-vector MPC, and (**c**) proposed D-MPC. The proposed D-MPC method presents a lower current error when compared with the conventional MPC across all the sampling frequency ranges, despite implementing multiple vectors.