**1. Introduction**

For the sake of fast development of electric vehicle (EV), pertinent research and studies, such as on motor drive [1], battery charger [2] and vehicle to grid (V2G), have received ever-increasing concern. In particular, the V2G system is increasingly emphasized due to its distinct advantages in terms of both EVs and the grid. With respect to EVs, the function can be expanded through the V2G system, and hence, the cost-effectiveness is increased [3]. Meanwhile, for the power grid, V2G creates some interesting features, e.g., the active and reactive power adjustment, the load balance and the frequency regulation, as well as the improvement of the efficiency, stability and reliability [4–6].

As a mobile energy storage unit, the capacity of a single EV is inevitably limited, such as the 4 kWh of the Toyota Prius plug-in hybrid EV and the 85 kWh of the Tesla Model S [3]. Therefore, with respect to the power grid, an individual V2G operation is insufficient and insufficient. However, research on V2G operation for the single EV is still meaningful to alleviate the undesired influence on the grid, especially the current harmonics. This paper concerns the V2G operation of single EV, as shown in Figure 1a. In essence, a V2G structure of the single EV is an inverter connected with the grid and powered by the EV battery. Generally, the mainstream control strategies of the inverter consist of hysteresis current control (HCC) method and proportional-integral (PI) or proportional resonance (PR) controller based on the pulse width modulation (PWM). Particularly, the classical HCC method introduces non-uniform switching frequency, thereby leading to its limited application [7]. To counter this issue, the hysteresis band was modified to operate a uniform switching frequency, while the updated process will inevitably complicate the calculation [8]. With respect to modulation-based control schemes, PI-PWM schemes are utilized to regulate the output current, voltage or power [9]. To obtain better power factor correction performance under the full range of modulation index, a hybrid modulation scheme was provided in [10], where the conventional space vector PWM (SVPWM) was combined with the virtual-vector-based SVPWM. In addition, it should be noticed that the PR-PWM regulator is an alternative solution in terms of the elimination of the steady-state error [11]. Normally, modulation-based PI or PR control strategies feature a good steady-state performance at expenses of reduced dynamic performance, while the parameters tuning in the PI or PR controller is a time-consuming and complex task as well. Another modulation-related method is the combination of model-based dead-beat and the SVM (DB-SVM) strategy [12]. Unlike PI (or PR)-PWM methods, the reference voltage vector in the DB-SVM scheme is directly determined according to the discretized mathematical model of inverter, leading to a faster dynamic response.

**Figure 1.** Vehicle to grid (V2G) system for the single vehicle: (**a**) Representational figure; (**b**) The circuit topology.

Recently, the model predictive control (MPC) algorithm has come into the focus of attention since it is characterized by a fast dynamic response, feasible implementation of multi-objective control and strong dynamic decoupling performance [13–21]. It has to be mentioned that the MPC method has some drawbacks, including unfixed switching frequency, lower steady-state performance and undesired computation burden [22], and hence, this limits its implementation in industrial application. To perform the constant switching frequency as well as better steady-state performance, numerous improved MPC methods have been presented. In [23], an MPC using discrete space vector modulation (DSVM) is provided while it yields a higher computation burden [24,25], since 12 vectors must be evaluated during one sampling period. Moreover, a novel MPC scheme based on the space vector modulation (SVM) concept is studied and implemented for a three-level inverter in [26], where the optimum voltage vector is generated through nullifying the derivative of the cost function. In addition, an improved MPC with second modification has been successfully developed for a three-level converter in [27], where the duty-ratios of three vectors are reasonably regulated to achieve a better steady-state performance. In particular, when compared with the DB-SVM method, this scheme can readily realize the multi-objective control by the employment of cost function. Unfortunately, the computation burden is ultra high due to the second optimization for mickle combinations of cost function values [28]. On the whole, these improved arts are to extend the active voltage vector region (AV2R), which will be

discussed in Section 2.2, while the computation burden is highly increased, thus complicating the optimization process.

To achieve enhanced AV2R and improved steady-state performance, this paper studies an MPC method in conjunction with SVM concept. Meanwhile, the good dynamic performance of traditional MPC is retained and fixed switching frequency can be acquired in a manner two adjacent active vectors and two null vectors are applied during one sampling period. Significantly, a formal mathematical methodology is conducted in terms of duty ratio calculation for null and active vectors. Moreover, an SVM-based PWM generation method is studied, aiming at reducing the on/off losses and unifying the switching frequency.

This paper is organized as follows: in Section 2, the mathematical model of two-stage grid-connected inverter for V2G is given and analyzed, which consists of a three-phase inverter and a DC/DC converter. Meanwhile, three existing MPC methods for inverter are analyzed and then the AV2Rs in these methods are elaborated. The proposed MPC method that comprises the duty-ratio calculation of the null vector and active vectors determination is conducted in Section 3, where the implementation of AV2R in the proposed method is also discussed. In Section 4, experimental results are examined to verify the effectiveness of the proposed method. Finally, conclusions are presented in Section 5.
