1. Introduction

The multiphase motor reliability is high and valuable for small torque ripples [1], which makes it suitable for electric vehicle [2], wind power generation [3], ship propulsion [4], and also for electric aircraft [5].

DTP-PMSM is an asymmetric six-phase motor with two sets of three-phase winding with a shift of 30 degrees. In this motor, the voltage vector in α, β subspace is projected to the x, y harmonic subspace, which generated the harmonic current in the x, y subspace. When using a voltage vector to control a dual three-phase motor, it is necessary to eliminate its influence on the x, y harmonic subspace. Therefore, the conventional vector control and direct torque control methods of three-phase PMSM are unsuitable for DTP-PMSM [6].

To eliminate the current harmonics of the DTP-PMSM, the four-vector space vector pulse width modulation (SVPWM) method is proposed in [6, 7]. The four vectors of the α, β subspace are used to synthesize the desired vectors, which can minimize the amplitude of synthesis vector of the x, y subspace and thus achieve the minimum harmonic current of the x, y subspace [8, 9]. Adopt two-zero sequence injection PWM and three-phase decoupling methods to reduce the harmonic current in the x, y subspace, respectively. To apply DTC in DTP-PMSM and effectively eliminate the harmonic current in x, y subspace, the dual zero sequence injection PWM method is used to DTC [10]. The four-vector SVPWM method can also be applied to DTC to reduce the DTP-PMSM harmonic current [11]. All of these harmonic current elimination methods for DTP-PMSM have a vector pulse width readjustment process, which is complicated to implement.

Model predictive control (MPC) has the advantages of being easy to achieve [12], multiobjective control [13], and suitable for nonlinear systems. Recently, with the wide application of MPC in motor control [14], many scholars have already discussed it in multiphase motors [15–18]. Zhang et al. [15] combine four-vector SVPWM with MPC for harmonic current suppression to achieve better dynamic performance and robustness when motor parameters change. According to the distribution characteristics of the four amplitude vectors of DTP-PMSM, a virtual vector with a zero amplitude in the x, y subspace is synthesized in advance to perform MPC to suppress harmonic currents [16–18]. The virtual vector MPC (VV-MPC) method proposed in [16] uses the largest and the second amplitude vector of α, β subspace to synthesize 12 virtual vectors with a zero amplitude in the x, y subspace. Then, these 12 virtual vectors are applied to MPC. Based on [16, 17], MPC is used to select two virtual vectors and their action time from 12 virtual vectors for synthesis. Luo and Liu [18] use 36 vectors to synthesize 24 virtual vectors with zero amplitude in the x, y subspace, and then combine the deadbeat method and MPC to control the system.

In actual systems, due to asymmetry and dead-time effects, the harmonic currents in the x, y subspace still exist [16, 19], even the amplitude of virtual vectors in the x, y subspace is zero. At this time, since the amplitude of the virtual vector in the x, y subspace is zero, it cannot be adjusted to reduce the actual harmonic current in the x, y subspace. In addition, the cost function does not include the harmonic currents of x, y subspace in [16–18]. Therefore, the closed-loop adjustment of the harmonic current cannot be realized.

2. Model of DTP-PMSM

The structure of neutral point isolation DTP-PMSM and its driver system studied in this paper are shown in Figure 1.

When the two neutral points of the system are isolated, there is no current in the o1 and o2 subspaces, so it is not considered in this article.

Among them, α, β subspace is the subspace of motor energy conversion, including the fundamental wave and k = 12m ± 1 (m = 1,2,3, …) harmonics. The x, y subspace contains k = 6m ± 1(m = 1,3,5, …) harmonics, and the o1, o2 subspace contains k = 3 m (m = 1,3,5, …) harmonics. Since the two neutral points of the system are isolated, there is no current in the o1, o2 subspace, so it is not considered in this article.

3. Vector Selection Based on DTC

From characteristics (1) and (3), it can be seen that the L4 vector with the largest amplitude in the α, β subspace corresponds to the L1 vector with the smallest amplitude in the x, y subspace, and the corresponding vector position changes. From formula (5), it can be seen that when k = 1, α, β subspace is obtained and, when k = 5, x, y subspace is obtained. From this, the following conclusion can be drawn.

In the α, β subspace, two adjacent L4 vectors are with a difference of △θ = π/6 angle, and the angle difference corresponding to the L1 vector on the x, y subspace should be k × △θ = 5×π/6 = 5π/6.

The above conclusion is consistent with the vector positions in Figure 2, so the three largest L4 vectors V1, V2, and V3 that are arbitrarily continuous in the α, β subspace, which correspond to the smallest L1 vectors in the x, y subspace, have the following spatial position relationships, as shown in Figure 3.

According to the principle of volt-second balance, the combination of these three maximum amplitude voltage vectors can make the volt-second voltage amplitude in the x, y subspace zero or a specified value. To achieve the closed-loop adjustment of the actual harmonic currents, it is necessary to combine the three continuous vectors in real time according to the actual harmonic currents to achieve the voltage required to eliminate the harmonic currents at the volt-second balance level.

According to the above analysis, combined with the rule of the DTC vector table, the largest 12 vectors can be divided into 4 groups, and each group includes 3 adjacent vectors whose angles differ by 30 degrees. Taking the motor stator flux linkage in sector S1 as an example, DTC vector (Table 1) can be obtained according to Figure 2(a).

In Table 1, 1 means need to increase, −1 means need to decrease, and 0 means need to maintain. When the motor rotates counterclockwise to sectors S2, S3, S4⋯S12, each vector in Table 1 also rotates counterclockwise according to the position in Figure 2(a). The selection of the zero vector follows the principle of minimum switching times.

4. The Proposed MPDTC

When implementing DTC on DTP-PMSM, according to Table 1, three vectors can be obtained at each step. To realize the real-time combination of these three vectors and the closed-loop control of harmonic currents, the MPC needs to be combined.

It can be seen that the cost function in (14) does not require adjustment factors and is simple and easy to implement.

On the basis of the above analysis, the system block diagram of the proposed MPDTC method is shown in Figure 4.

This control system is different from the general MPTC [12]. Firstly, according to the DTC rules, based on the feedback flux and torque errors, a group of three vectors is obtained from the DTC vector (Table 1). Secondly, according to the feedback harmonic current i_x, i_y, the cost function of formula (14) is used for prediction, and the optimal vector V^opt is selected from the group. Finally, the group of three vectors will be repeatedly selected in multiple prediction cycles, which are equivalent to the dynamic combination of the three vectors according to the real-time feedback i_x, i_y and realize the closed-loop control of i_x, i_y.

Compared with VV-MPC, MPDTC uses a dynamic combination of vectors instead of vector synthesis. Moreover, VV-MPC needs to select the optimal vector from the 12 vectors each time. In comparison, MPDTC only needs to select the optimal vector from 3 vectors, which greatly reduces the computational workload.

5. Simulation Research

In order to verify the effectiveness of the method proposed in this paper, Matlab/Simulink software is used for results’ verification. The parameters of DTP-PMSM used in the simulation are shown in Table 2 [22]. The speed is set to 3000 rpm. The DC link is set to 600 V. The sampling and control cycle is set to 10⁻⁵s. The initial torque of the motor is set to 3 N·m and a step change load of 16 N·m is given at t = 0.05 s.

To verify the steady-state and dynamic performance of the proposed MPDTC method, it is compared with the traditional DTC and the VV-MPC proposed in [16]. The steady-state and dynamic performance simulation results of the three methods are shown in Figure 5.

From the speed and torque simulation results in Figure 5, the proposed MPDTC method has the same fast torque and speed dynamic response performance as the other two methods. From the perspective of the six-phase current i_abcdef, the six-phase current of DTC is relatively messy in dynamic and steady-state processes. The proposed MPDTC method can always keep i_abcdef smooth and symmetrical in a dynamic and steady-state like VV-MPC. Since the complicated process of virtual vector synthesis makes virtual voltage vector more accurate in VV-MPC, the torque ripple in Figure 5(b) is smaller than the proposed MPDTC in Figure 5(c). However, the proposed MPDTC method has no vector synthesis process, and it is simple and easy to implement with less computational workload.

Because the smoothness and symmetry of the six-phase current are affected by the harmonic current components, it is necessary to further analyze the harmonic current simulation results, as shown in Figure 6.

It can be seen from Figure 6 that when traditional DTC is applied to DTP-PMSM, its harmonic currents i_x, i_y are larger, while VV-MPC and MPDTC can effectively suppress harmonic currents. The comparison of the i_x and i_y harmonic currents of the three methods is shown in Table 3.

Table 3 illustrates that the proposed MPDTC method can effectively suppress the harmonic currents in DTP-PMSM. Because of the accurate virtual voltage vector synthesized by VV-MPC, the i_x,i_y of VV-MPC is smaller than that of MPDTC in Table 3. If the real-time vector combination of MPDTC needs to be more accurate and precise, a higher control frequency is need for vector prediction and combination.

In actual systems, harmonic currents i_xand i_y will be generated due to system asymmetry and dead time. In order to verify MPDTC’s ability to suppress these harmonic currents produced by the systems, the following simulation adds interference harmonic currents on i_x, i_y. It can be seen from [19] that the main harmonic currents is the 5^th harmonics to the fundamental component due to dead time. In the following simulation, the 5^th (1250 Hz) harmonic current of 250 Hz fundamental component is added to i_x, i_y with an amplitude of 5A. In order to achieve better simulation results, the sampling and control cycle is set to 10⁻⁶s.The simulation result is shown in Figure 7.

From Figure 7, it can be seen that DTC and VV-MPC cannot effectively suppress the added 5^th harmonic current, but the MPDTC can effectively suppress the added 5^th harmonic current. The numeric of i_x,i_y and THD of the three methods are shown in Table 4.

The results in Table 4 shows that the MPDTC method is superior to DTC and VV-MPC in suppressing the added 5^th harmonic current, since MPDTC realizes the closed-loop control of i_x,i_y by using the dynamic combination of voltage vectors. At the same time, since the sampling and control period is set to 10⁻⁶s, the dynamic voltage vector combination during MPDTC control is more accurate, and the average values of i_x and i_y in Table 4 are less than those in Table 3.

6. Conclusion

The MPDTC proposed in this paper can make full use of the advantages of DTC and MPC to control DTP-PMSM. The method not only has the fast dynamic response performance of DTC but also reduces the number of prediction vectors of MPC and the computational workload of MPC.The method does not contain complex vector synthesis process, but can effectively suppress the harmonic current of dynamic and steady state. Based on the simplified cost function, it realizes the closed-loop control for harmonic current which can suppress the interference harmonic current. From simulation results, it is proved that the proposed method has an advantage over VV-MPC and DTC in DTP-PMSM.

Conflicts of Interest

The authors have no conflicts of interest regarding the publication of this study.