*4.3. Performance under Non-Unity Power Factor Conditions*

With respect to the V2G system, the adjustment of active and reactive power was an essential task. To evaluate the gird-connection performance under the non-unity power factor conditions, two cases where the power factor angle ϕ was suddenly changed from 0 to π/6 and from 0 to –π/6 were implemented, respectively. The results are presented in Figure 9.

**Figure 8.** Dynamic performance of four MPC methods (20 V/div, 10 A/div, 5 ms/div): (**a**) MPC1; (**b**) MPC2; (**c**) MPC3; (**d**) Proposed MPC.

**Figure 9.** Performance of non-unity power factor conditions (20 V/div, 10 A/div, 5 ms/div): (**a**) Dynamic performance under the condition of ϕ is suddenly changed from 0 to π/6; (**b**) Steady-state performance under ϕ is π/6; (**c**) Dynamic performance under the condition of ϕ is suddenly changed from 0 to -π/6; (**d**) Steady-state performance under ϕ is -π/6.

From Figure 9a,c, it can be found that excellent dynamic response can be achieved when ϕ had a sudden change. In particular, from Figure 9b, the phase current *ia* was shifted about π/6 with respect to *ea* and the peak-value of the phase current had a slight increase, which can be explained by the fact that *iq ref* desires a non-zero value under non-unity power factor condition. A similar result can be seen in Figure 9d, and a shifted angle of –π/6 of phase current can be generated. These results validated that excellent performance under non-unity power factor conditions can be obtained using the proposed MPC.
