*4.1. Steady-State Performance Comparison*

At first, the steady-state performance comparison was carried out. The *d*-axis current reference *id ref* was set to 8 A and the power factor angle ϕ was set to 0. In this case, the inverter was operated under the unity power factor condition. The total harmonic distortion (THD) analysis was conducted using the fast Fourier transform (FFT) tool of the MATLAB/Simulink powergui block.

The results are presented in Figure 7. It can be observed that the four MPC methods yielded sinusoidal output currents and the peak-value of currents was about 8 A. Meanwhile, the unity power factor operation could be realized. However, MPC1, MPC2 and MPC3 provided THDs of 19.73%, 15.68% and 17.28%, respectively. Comparatively, the THD generated with the proposed MPC was within 10%. This extreme improvement was as expected since the proposed MPC can extend the AV2R to the whole hexagon instead of some points or lines in the existing arts. In other words, the proposed MPC can create a continuous-changed control signal, while the existing methods just created step-changed signals. This comparison proves that the steady-state performance can be greatly enhanced and the tracking accuracy can be realized using the proposed MPC.

**Figure 7.** Steady-state performance of four MPC methods (20 V/div, 10 A/div, 5 ms/div): (**a**) MPC1; (**b**) MPC2; (**c**) MPC3; (**d**) Proposed MPC.
