**3. Proposed MPC Method**

From the aforementioned analysis, although MPC2 and MPC3 schemes can provide a better performance, both of them are weak if they stack up against the conventional PI-SVPWM method, which can yield an AV2R of the whole hexagon area. In order to address this issue, a four-vector-based MPC is proposed, in which two adjacent active vectors along with two null vectors are applied during each sampling period. In this way, a modulation-like behavior can be realized, yielding the desired steady-state performance and unifying the switching frequency. Meanwhile, it should be mentioned that the excellent dynamic response inherent to the classical MPC can be retained. The control diagram of the proposed MPC is presented in Figure 3. Each part is elaborated as follows.

**Figure 3.** Control block of the proposed MPC method.

## *3.1. Determination for Two Active Voltage Vectors*

In the classical MPC, an optimal vector can be selected through the evaluation of cost function. Based on this concept, two active vectors are selected with a two-stage cascaded algorithm.

The first stage is to determine the optimal vector using conventional MPC. It is noteworthy that the number of voltage vector candidates is six (*V*1-*V*6) instead of eight. For the sake of convenience, the optimal vector is counted as *u*1. Next, the second stage is to decide the suboptimal vector (termed as *u*2) from the vectors adjacent to the optimal one. For instance, supposing that the optimal vector is *V*1, then *V*<sup>2</sup> and *V*<sup>6</sup> are the two adjacent vectors and selected as the candidates associated with the suboptimal vector. Then, if the cost function value generated by *V*<sup>2</sup> is smaller than that generated by *V*6, *V*<sup>2</sup> will be selected as the suboptimal vector and vice versa. In the same manner, the candidate vectors can be picked out for the other cases (as listed in Table 1), and the suboptimal vector can be determined.


**Table 1.** Optimal vector and corresponding candidates associated with the suboptimal vector.
