*Article* **A Novel Vector Control Strategy for a Six-Phase Induction Motor with Low Torque Ripples and Harmonic Currents**

**Hamidreza Heidari 1,\*, Anton Rassõlkin 1, Toomas Vaimann 1, Ants Kallaste 1, Asghar Taheri 2, Mohammad Hosein Holakooie <sup>2</sup> and Anouar Belahcen 1,3**


Received: 25 January 2019; Accepted: 19 March 2019; Published: 21 March 2019

**Abstract:** In this paper, a new vector control strategy is proposed to reduce torque ripples and harmonic currents represented in switching table-based direct torque control (ST-DTC) of a six-phase induction motor (6PIM). For this purpose, a new set of inputs is provided for the switching table (ST). These inputs are based on the decoupled current components in the synchronous reference frame. Indeed, using both field-oriented control (FOC) and direct torque control (DTC) concepts, precise inputs are applied to the ST in order to achieve better steady-state torque response. By applying the duty cycle control strategy, the loss subspace components are eliminated through a suitable selection of virtual voltage vectors. Each virtual voltage vector is based on a combination of a large and a medium vector to make the average volt-seconds in loss subspace near to zero. Therefore, the proposed strategy not only notably reduces the torque ripples, but also suppresses the low frequency current harmonics, simultaneously. Simulation and experimental results clarify the high performance of the proposed scheme.

**Keywords:** direct torque control; duty cycle control; harmonic currents; six-phase induction motor; torque ripple

## **1. Introduction**

With the emergence of power electronic devices and adjustable-speed drives, multiphase machines have attracted wide attention for special applications in the naval, automotive, and aerospace industries [1,2]. The key features of these machines are high reliability, fault tolerant operation, low rate of power switches, low torque pulsation and low dc-link voltage [3–7]. Among multiphase motors, multiple three-phase winding motors have received more interest due to their advantage of compatibility with conventional three-phase technology. Considering this benefit, the asymmetrical 6PIM, which is composed of two sets of three-phase windings spatially shifted by 30 electrical degrees, seems desirable for many applications.

Direct Torque Control (DTC) is a simple and powerful scheme for variable speed 6PIM drives that provides high-performance torque and stator flux control [8]. However, it suffers from some serious drawbacks, including high torque ripples and low-frequency current harmonics, which can strikingly degrade the performance of the drive system [9,10]. A great deal of effort has been invested in alleviating DTC high torque ripples, which mostly includes the modification of the hysteresis controller [11,12], amending the switching table (ST) [13,14], or replacing hysteresis controllers with other control strategies to provide Pulse Width Modulation (PWM)-based DTC [15]. A global minimum torque ripple using modified switching pattern has been proposed in [16]. In [17], the torque ripples have been reduced by applying active and zero voltage vectors in each sampling period using a predictive DTC. With regard to a large number of voltage vectors in six-phase voltage source inverter (VSI), elimination of loss subspace components seems possible through the vector space decomposition (VSD) model. Aiming to reduce harmonic currents, elimination of *z*<sup>1</sup> − *z*<sup>2</sup> (loss subspace) components using the duty cycle concept in DTC is proposed in [9,12] for a five-phase induction motor, and a six-phase permanent magnet motor, respectively. Moreover, harmonic currents have been reduced by adding an inductance filter to the 6PIM drive system [18]. On the other hand, structure reconfiguration of 6PIM to minimize both harmonic currents and torque ripples has been done in [4]. On the other hand, field-oriented control (FOC) can be easily applied to many types of electrical machines [19].

The main focus of this paper is on the parallel torque ripple and harmonic current reduction in vector control of a 6PIM. To achieve these goals, a new vector control scheme is proposed, using a combination of DTC FOC concepts to moderate steady-state torque ripples. To reduce harmonic currents, twelve virtual voltage vectors are introduced by combination of large and single medium voltage vectors (e.g., 48 and 57 in Figure 1a, respectively). The duration of each voltage vector is determined such that the average volt-seconds in the *z*<sup>1</sup> − *z*<sup>2</sup> subspace becomes near to zero. Consequently, low-frequency current harmonics experience a considerable reduction, current will be much smoother, and the efficiency of the drive system will be increased.

**Figure 1.** 6PIM model in (**a**) *α* − *β*, (**b**) *z*<sup>1</sup> − *z*<sup>2</sup> bspaces.

The rest of this paper is organized as follows: in Section 2, 6PIM modeling is presented. The conventional DTC and its drawbacks such as torque ripples and harmonic currents are discussed in Section 3. The proposed method to reduce torque ripples and harmonic currents is presented in Section 4.

#### **2. 6PIM Modelling**

There are two common methods for modelling of 6PIMs: double *d* − *q* [20] and VSD [21]. According to the VSD approach, the machine's parameters are mapped into active and loss subspaces, which makes the control strategy more convenient and efficient. Moreover, the VSD method can easily be extended to other types of motors. In this study, the 6PIM modelling is based on the VSD strategy. According to this modelling technique, a 6PIM with near-sinusoidal distributed windings is modelled in three orthogonal subspaces, which are commonly named as the *α* − *β*, *z*<sup>1</sup> − *z*2, and *o*<sup>1</sup> − *o*<sup>2</sup> subspaces. The produced voltage space vectors by switching states of a two-level six-phase voltage source inverter in the *α* − *β*, *z*<sup>1</sup> − *z*<sup>2</sup> subspaces are shown in Figure 1. Among these subspaces, only the *α* − *β* components share useful electromechanical energy conversion, while *z*<sup>1</sup> − *z*<sup>2</sup> and *o*<sup>1</sup> − *o*<sup>2</sup> components do not generate any electromechanical energy in the air-gap and just produce losses. The fundamental components and also harmonics of the order 12*n* ± 1(*n* = 1, 2, 3 . . .) are mapped

into the *α* − *β* subspace. The losses of 6PIM are mapped into the *z*<sup>1</sup> − *z*<sup>2</sup> and *o*<sup>1</sup> − *o*<sup>2</sup> subspaces which include harmonics by the order of 6*n* ± 1(*n* = 1, 3, 5 . . .) and 3*n*(*n* = 1, 2, 3 . . .), respectively. By the assumption that the stator mutual leakage inductance is ignored, the components of *z*<sup>1</sup> − *z*<sup>2</sup> and *o*<sup>1</sup> − *o*<sup>2</sup> subspaces have the same form [21]. Since the active and loss components are investigated separately, it is clear that the control of 6PIM will be more efficient by using VSD. Additionally, isolation of the neutral points of two three-phase windings, makes the *o*<sup>1</sup> − *o*<sup>2</sup> subspace losses become zero [21].
