In recent decades, various technologies of the motor have been quickly developed. Some research is on the controller to improve the mechanical performance of the motor [
4,
5]. A controller of DC-link voltage of the three-phase PWM rectifier has been proposed in [
4]. In this controller, an Artificial Bee Colony (ABC) optimization method is used to optimize the type-2 fuzzy neural network (T2FNN) controller. As a result, the proposed controller has a better dynamic response than the traditional T2FNN controller. Based on the proportional + derivative type-2 fuzzy neural network (PD-T2FNN), a controller is proposed in [
5] for DC-link voltage control of the PWM rectifier. Compared with traditional PD, proportional + integral, and T2FNN controllers, the proposed controller has superior performance in the transient and steady-state responses under various working conditions. The pulse width modulation (PWM) strategy is another research hotspot for motor drive systems, which directly influences the inverter system efficiency and the quality of the output waveform [
6,
7]. The overmodulation PWM strategy is widely applied in electric vehicles, mining equipment and other motor drive fields. For example, an overmodulation control strategy has been used in the medium-speed range for motor drive control of the TOYOTA hybrid system II (THS II), and the output of the shaft torque has been increased by a maximum of approximately 30% in this range [
8]. For a single-phase inverter operating in the overmodulation region, an improved SPWM method is proposed in [
9] to eliminate the third harmonic. Thus, the total harmonic distortion is reduced and current quality is improved. For three-phase motors, an overmodulation space vector pulse width modulation (SVPWM) strategy based on Fourier series expansion of the reference voltage is proposed in [
10], and maximum utilization of the dc-link voltage can be achieved. However, the calculation amount is large. Another SVPWM strategy based on the superposition principle for a three-phase motor operating in the overmodulation range is developed in [
11]. This strategy does not need to calculate the control angle or the hold angle, and it is easy to implement digitally. However, the voltage harmonic components in the overmodulation region are large. Modulation functions of carrier-based PWM which are equivalent to this SVPWM strategy are investigated in [
12]. However, these modulation functions are based on the superposition principle and are not universal. Ref. [
13] has proposed a method that combines Space-Vector Modulated Direct Torque Control (DTC-SVM) and conventional DTC. In the linear region, the DTC-SVM is used, which provides low THD and low torque ripple, while in the overmodulation region, the conventional DTC is applied. The transition between these two methods is smooth, and the DC bus voltage is fully employed. In [
14], an SVPWM strategy exploiting the Lagrangian method to minimize the harmonic voltage in the overmodulation range is proposed for a five-phase voltage source inverter (VSI). However, this method adopts suboptimal solutions under specific conditions instead of the optimal solution. The comprehensive relationship between the carrier-based PWM and SVPWM techniques for a five-phase motor operating in the linear modulation range is explained in [
15]. For six-phase motors, there are two major models [
16]: the double synchronous reference frame (double
d-q) model [
17,
18] and the vector space decomposition (VSD) model [
19,
20]. In the double
d-q model, the SVPWM strategy is similar to the traditional three-phase VSI. In [
17], the proposed current control scheme based on the double
d-q model uses four identical PI regulators for all current loops. In this way, the two sets of three-phase stator currents are independently controlled and kept balanced. However, the decoupling voltage required by this method is complex. An indirect field-oriented control (FOC) scheme for a six-phase induction machine is proposed in [
18]. The unbalanced current between the two sets of three-phase windings is eliminated, and this scheme is applicable to a six-phase machine with any arbitrary angle of displacement between the two sets. However, many sensors are used in this method, which increases the cost of industrial application. For the VSD model, two-vector SVPWM is the simplest modulation strategy, which will generate many 6n ± 1 (n = 1, 3, 5, …) harmonic voltage components [
19]. The commonly used SVPWM strategies are four-vector modulation techniques. An SVPWM strategy synthesizing the reference voltage vector using four adjacent large voltage vectors (4L) is proposed in [
20], which can keep the harmonics in the Z
1 − Z
2 subspace at a minimum level within the linear modulation range. However, the harmonic distortion factor of this strategy has not been studied. Based on [
20], several new discontinuous SVPWM strategies for six-phase VSIs have been proposed, and the harmonic current of each strategy has been completely studied [
21]. The results demonstrate that the performance of these strategies is affected by the parameter
kσxy, which is defined as the ratio of the total (α − β) referred-to-stator leakage inductance to the (Z
1 − Z
2) leakage inductance. However, only the 4L strategy has been analysed, not other strategies; for example, the two large vectors plus two medium vectors (2L + 2M) strategy. The double zero-sequence injection PWM method is studied for the asymmetrical six-phase motors in [
22]. This method can reduce the calculation amount, but the flux harmonic distortion factor (HDF) in the Z
1 − Z
2 subspace is higher than that in the SVPWM strategies. Using the SVPWM method, a zero CMV (ZCMV) strategy is proposed in [
23] to eliminate the common mode voltage (CMV) for asymmetric six-phase motors. In this strategy, the turn-on/off moment of each phase is shifted, and the peak value of total CMV is suppressed to 0 in theory. To reduce the CMV for asymmetric six-phase motors, three SVPWM schemes, namely, CMV2, CMV3, and DCMV3, are proposed in [
24]. Although their CMV suppression effects are the same, their harmonic performances are different. The DCMV3 has better harmonic performance in the high modulation region for leakage coupling coefficients
ξ = 1 to 2. If
ξ = 6.2, the CMV2 performs better in the higher modulation region, while the DCMV3 generates superior quality waveforms in the lower modulation region. A modified SVPWM technique that divides the
α − β subspace into 24 sectors is proposed in [
25]. It provides lower current THD, but it only focuses on the linear range and does not involve the overmodulation range.
When a motor operates in the overmodulation region, low-order voltage harmonic components in the Z
1 − Z
2 subspace are unavoidable. However, harmonic impedance in the Z
1 − Z
2 subspace is only composed of the stator resistance and leakage inductance; thus, even low-level harmonic voltages can induce large harmonic currents. Therefore, it is necessary to suppress the harmonic components in the Z
1 − Z
2 subspace. In [
26], a general
n-phase SVPWM technique is proposed for overmodulation regions, which forces the zero-vector duty cycle δ
0 to zero for the entire sector, and it effectively suppresses voltage harmonic components in the Z
1 − Z
2 subspace. However, this technique is only applicable to odd
n. An SVPWM strategy for six-phase voltage source-inverter-fed six-phase split-phase induction motors is presented in [
27]. The approach is based on three-phase space vector modulators that can be operated in both the linear and overmodulation regions. However, it does not consider harmonic suppression in the Z
1 − Z
2 subspace. Through extending the three-phase VSI overmodulation method to the six-phase VSIs, Ref. [
28] has proposed an SVPWM strategy that divides the overmodulation regions into two sections. In section I, the amplitude of reference voltage is proportional to the modulation index. In section II, due to the phase correction algorithm, the distortion of phase voltage is reduced. Although the traditional four-vector overmodulation strategy (TFOS) [
29] can suppress the harmonic voltage components in the overmodulation range, the harmonic component content is still quite large and will be compared with the proposed strategy.
The control objective of this paper is to synthesize the reference voltage in the
α −
β subspace and simultaneously minimize the harmonic components in the Z
1 − Z
2 subspace when a six-phase asymmetric motor fed by two-level six-phase VSI operates in the overmodulation range. A novel SVPWM strategy, namely, harmonic suppression overmodulation strategy (HSOS), is proposed in this paper, which can effectively achieve this objective. The main innovation is that the optimization models consisting of an objective function and constraint conditions are built, and the external point method is adopted to minimize the harmonics in the Z
1 − Z
2 subspace. The main contribution is that the proposed HSOS can reduce the content of the 5th harmonic by about 20% and the
THDZ1Z2 of the four harmonics (namely, the 5th, 7th, 17th and 19th) by about 21% when it is compared with the TFOS. The rest of this paper is organized as follows: The basic theory of the six-phase two-level VSI model is described in
Section 2. In
Section 3, the existing method TFOS is briefly introduced at first, and then the proposed HSOS is deduced in detail. The simulation and experiment are carried out in
Section 4 and
Section 5, respectively. In these two sections, harmonic content of line voltage and current in these two strategies are compared, and the validity of the proposed HSOS is verified.