Direct Torque Control of Dual Three-Phase Permanent Magnet Synchronous Motor

In this paper a direct torque control strategy for dual three-phase permanent magnet synchronous motor (DTP-PMSM) is presented, the machine has two sets of three-phase stator windings spatially phase shifted by 30 electric degrees. In order to reduce the stator harmonic current, torque and flux are controlled based on regulators and Vector Space Decomposition technique. The proposed approach has the benefits of low stator current distortion and low torque ripple. The validity and the efficiency of the selected technique are confirmed by simulation results.


Introduction
In the domain industry, conventional three-phase electric machines are mainly used. Recently, the use of electric machines with more than three phases has significantly increased, particularly for high power applications such as system propulsion. These machines usually known as multiphase machines which are existing in the domain various that is automobile, avionics, and maritime [2][3][4][5][6][7][8]; and provide several significant advantages such as lower torque pulsations and higher reliability [1]. Dual-Three Phase (DTP) Machines are characterized by the multiphase structure having two sets of three-phase stator windings within the same stator frame, and are spatially shifted by 30 electrical degrees [1]. Among all DTP machines used, the Dual Three Phase Permanent Magnet Synchronous Motor (DTP-PMSM) is the most used one. It has a high fault tolerance and reliability [9]. A high-performance control of DTP-PMSM is based on the Vector Space Decomposition (VSD) [10]. The VSD theory for DTP induction motor was presented in [10]. In relation to the VSD strategy, the overall machine model is transformed into three decoupled subspaces, written in three independent space coordinates, identified as, (α, β) torque-component , (z1, z2) harmonic-component and (o1, o2) zero-sequence, respectively [11][12][13][14][15][16][17]. Direct Torque Control (DTC) for DTP has been studies in recent years. The key problem of such a system is the occurrence of harmonic current in stator windings [18].
This control and VSD theory are introduced into DTC of dual three-phase induction motor [19,20]. Torque and flux control based on regulators [21,22] and VSD technique * Fouad Labchir: labchirfouad69@gmail.com [23,24] of DTP-PMSM is proposed in this paper. It can reduce the torque ripple and harmonic current. When applying the DTC for the DTP-PMSM, important harmonic stator currents are usually observed. These currents cause losses in the stator and thus effect the machine's efficiency. According to the VSD technique, the basic DTC does not permit the control of the harmonics that seem in the subspace (z1, z2). The rest of this paper is structured as follows: in section 2, the machine model will be described based on VSD. Section 3 relates the conventional (DTC) approach. Section 4 includes simulation results to approve the validity of the proposed technique. Finally, conclusion is drawn in section 5.

Modelling of machine's system
The DTP-PMSM model and VSI-fed drive are illustrate in two Figures 1and 2. The VSD theory [10] allows us to get an applied model appropriate for control. The latter is based on the decoupling transformation matrix which is expressed by (1): By means of this transformation, the complex system of motor is decomposed into three decoupled communally orthogonal subspaces (α, β), (z1, z2) and (o1, o2). The variables equations of the machine, under the assumptions [26] concerning sinusoidally distributed windings and the neglect of magnetic saturation and iron losses, can be represented in stationary frame by [11]: Where: Ld, Lq are direct and quadrature-axis inductances. Lz and Lo are the transformed inductance of stator selfleakage. Ψ PM is the flux linkage product by permanent magnet. θ is the rotor position angle.
The (α, β) current components contribute to the electromechanical energy conversion; However, the currents in (z1, z2) and (o1, o2) are all harmonics, independent of the resultant torque and produce stator loss [27,28]. In relation to change from stationary plane of (α, β) subspace to the rotating plane (d,q), the following transformation matrix is applied: In the (d-q) subspace:  the electric equation of the machine is shown as:  the mechanic equation of the machine is shown as: ( is the number of the pole pairs).  By the matrix T, the plane voltages function the device switch states can be expressed by:

DTC scheme
In the basic DTC for DTP-PMSM, torque and flux are estimated. Torque and flux regulators are used to create the inverter vectors by using a switching table, (Fig. 5). In the (α,β) subspace, the 12 maximum magnitude vectors, which form 12 sectors, are chosen as depicted in Figure 6. The select of these vectors allows to have the smallest amplitude vectors in the (z1, z2) subspace, and enables maximal exploitation of DC source.  The (α, β) subspace is decomposed into 12 sectors; each sector is bordered using two maximum vectors, as shown in Figure 6. When the stator flux positioned in sector k, vector viable for the rise of both flux and torque is V k+2 where the one answerable for their reduction is V k−4 and that responsible for the reduction of both flux and torque is V k−4 . Vector V k+3 leads to the reduction of the flux and the increase of the torque whereas vector V k−3 leads to the opposite process.
Torque and flux hysteresis regulators are employed to generate appropriate voltage vector according to table 1. The engendered torque and flux control signals and are defined by the following tables:

Signal
Value Condition

Simulations Results
The simulations with Matlab/Simulink environment, were accomplished by using a 240W prototype DTP-PMSM whose principal parameters are indicated in table 2 [25].  Figure 7 shows that the phase current using classical DTC strategy is not purely sinusoidal. Therefore the harmonic currents contain a big quantity of the 5th and 7th harmonics which are dominant (THD=42.6%) as shown in Figure 8. It is value mentioning that these stator current components do not contribute to the air gap flux and will only produce losses. Figure 9 represents the currents in (α, β) subspace having a low ripple and a regular trajectory for the proposed method.
In figure 10 (a), the performance of the torque is not affected by the presence of these harmonics. Figure 10 (b), shows the machine speed response; the velocity reaches its reference with good static and dynamic performance. This paper presents a conventional Direct Torque Control (DTC) strategy to control the DTP-PMSM. When using its technique, only the variables in the subspace (α, β) are controlled but significant harmonic current will be produced. These harmonics do not contribute to the electromechanical energy conversion, however increase the stator loss. The conventional DTC based on regulators and Vector Space Decomposition (VSD) theory proposed in this paper can resolve the problematic effectively. This method permits the elaborating of the most appropriate inverter voltage vector which allows not only the control of variables in ( , ) subspace but also the diminution of currents in the (z1, z2) subspace.The simulation results show that as well as the good dynamic response, this proposed technique can decrease the torque ripple and harmonic current and increase the system effectiveness.