Efficiency improvement of dual three-phase permanent magnet synchronous motor using modified switching table DTC for electric ship propulsion

Received Sept 16, 2020 Revised May 2, 2021 Accepted July 12, 2021 A direct torque control using a classical switchingtable ST-DTC can be used to control the torque and thus the speed of Dual Three-Phase Permanent Magnet Synchronous Motor (DTP-PMSM). The principle is based on direct application of control sequence by using two hysteresis regulators and a switching table. A large stator current containing low order harmonics is produced during the application of the classic ST-DTC technique, this leads to higher losses affecting the efficiency of the machine. To allow a reduction of these harmonics a modified switching-table approach based DTC technique is examined. Indeed, an improved ST-DTC strategy, which consist of replacing the vectors of the classical table with synthetic vectors, is discussed. The simulation results confirm the validity of the selected strategy.


INTRODUCTION
Recently, the all-electric ship concept has become particularly important. Full electric propulsion systems for commercial and military shipping sector have been intensively developed. Electric propulsion offers potential advantages regarding flexibility in ship maneuvering, maintenance cost and vibration level [1], [2]. In the naval industry, three-phase electric machines are mainly the most used. Recently, the use of multiphase machines has grown considerably in several areas including naval propulsion, railway electric traction, electric vehicles, avionics, and high-power industrial applications [3]- [9]. Multiphase machines provide several important benefits in terms of torque quality and machine reliability [1]. The most interesting multiphase machines which attract a lot of interest is the dual three phase (DTP) ones. DTP machines has two sets of three-phase stator windings spatially shifted by 30 electrical degrees with two isolated neutrals [1].
Among all DTP machines the permanent magnet synchronous motor (DTP-PMSM) is the most used one [10]. A field oriented control of DTP-PMSM based on the vector space decomposition (VSD) was presented in [10]. The conventional VSD control for DTP induction motor was given in [11]. As specified by the VSD strategy, the machine model is transformed into three decoupled subspaces, identified as, (α, β) torque-component, (z 1 , z 2 ) harmonic-component and (o 1 , o 2 ) zero-sequence, respectively [12]- [18].  [19]. It is characterized by simple structure which is independent of machine parameters and allowing a fast torque response. When applying the DTC for the DTP-PMSM, important harmonic stator currents are usually observed. These currents cause losses in the stator and thus deteriorate the machine's efficiency. According to the VSD technique, the basic DTC does not allow the control of the harmonics that appear in the subspace (z 1 , z 2 ).
With the view to minimize harmonics and hence improve the machine's efficiency, a modified Switching Table based DTC for five phase synchronous machine is proposed in reference [20]. In this approach the selection of the appropriate voltage is done in two steps. The same technique applied to DTP-PMSM is presented in reference [21]. The disadvantage of this method is the necessity to locate the stator flux position not only in the ( , ) subspace but also in the (z 1 , z 2 ) subspace. Our contribution is to propose a modified switching table constituted by synthetic vectors allowing the torque control as well as the reduction of the currents in (z 1 , z 2 ) subspace. Figure 1 and Figure 2 illustrate the DTP-PMSM and VSI-fed drive. The two three-phase windings are identical with two independent neutral points [12]. The DTP-PMSM is complex and high order system. The mathematical model of the motor is simplified by assuming that the motor windings are distributed sinusoidally, saturation and magnetic losses are neglected [22]. To obtain a practical model proper for control, the voltage space decomposition VSD is used [11]. The VSD is based on the transformation matrix expressed by (1).
Current components in the (α, β) subspace produce air gap flux and create the torque. Currents in (z 1 , z 2 ) and (o 1 , o 2 ) are all harmonics, they don't contribute to the electromechanical conversion and produce stator losses [23], [24]. To change to the ( , ) rotating frame the following transformation matrix is applied: Machine model in the (d, q) plane: The electromagnetic torque is: : pole pairs number.

RESEARCH METHOD 3.1. Inverter voltage vectors
The inverter shown in Figure 1 can provide 64 different voltage vectors. Each vector is presented by the subscript decimal number, corresponding to binary numbers S a1 S b1 S c1 S a2 S b2 S c2 . Where (S = S a1 , S b1 , S c1 , S a2 , S b2 , S c2 ) are the device switch states. The phase voltages are expressed according to switch states by (9).
While (S = S a1 , S b1 , S c1 , S a2 , S b2 , S c2 ) are the states of switches, E is the DC voltage. The 64 voltage vectors projected in each subspace are given by (10).
We can notice from Figure 3 and Figure 4 that vectors of the outer dodecagon D 4 in (α, β) subspace map in the inner dodecagon D 1 of the (z 1 , z 2 ) subspace, the inner dodecagon D 1 of (α, β) subspace forms the outer dodecagon D 4 of (z 1 , z 2 ) subspace while the middle dodecagon space vector keeps the the same region.

Conventional ST-DTC
In the direct torque control scheme, torque and flux of DTP-PMSM are estimated. Two hysteresis comparators for torque and flux and a switching table are used to generate the inverter vectors as shown in Figure 5. The voltage vectors with the maximum amplitude divide the subspace (α, β) into 12 sectors as shown in Figure 6. This choice allows maximum use of the DC power supply and guarantees the application of low amplitude voltage vectors in the (z 1 , z 2 ) subspace. Each sector is delimited by two maximum vectors, as shown in Figure 6. When the stator flux is in the sector , the application of the vector V k+2 leads to the increase of the flux and the torque whereas the application of V k−4 causes their reduction. The application of the vector V k+3 produces the reduction of the flux and the increase of the torque, the opposite effect is produced by the vector V k−3 . In summary, the choice of the voltage vector is carried out according to the Table 1.  The generated torque and flux control signals and are defined as:

THE MODIFIED ST-DTC APPROACH
The modified switching table DTC approach allows the decreasing of the current harmonics by reducing the currents in subspace (z 1 , z 2 ). As shown in Figure 7 the sixty non-zero voltage vectors of the  12 }. Each group is composed of three vectors having the same direction, for the example 36 , 53 and 46 constitute the G 1 group. Given this remark, the vectors of the same group will have the same effects on the flux and the torque.
The vectors belonging to the same group in (α, β) subspace change the direction and the module in (z 1 , z 2 ) subspace. Indeed, for a given group the largest vector of the Dodecagon D 4 changes direction in subspace (z 1 , z 2 ) and its module becomes the smallest. The second vector of the group belonging to the Dodecagon D 3 keeps the same module but changes direction and becomes opposite to the preceding vector. As illustrated in Figure 8, the vectors 53 , 46 and 36 of D 3 , D 1 and D 4 respectively and which constitute the group G 1 have the same direction. However, in the (z 1 , z 2 ), 53 has an opposite direction to 36 and 46 as shown in Figure 8. Consequently, the use of vector of D 3 and vector of D 4 together allows controlling current in (z 1 , z 2 ) and then reducing current harmonics. For the example if 36 is chosen according to the switching table, the vector 52 must be applied with 36 to cancel its effect in (z 1 , z 2 ) subspace. The (12) relation gives the time allotted for each vector: Where is the sampling time. The calculation of the times gives: Thus, the proposed approach consists of replacing the 12 vectors of D 4 used in the conventional DTC by a combination of vectors of D 3 and D 4 as depicted in Table 2. The module of synthetic vector is given by (14).
The synthetic vector has a module slightly lower than that generated by the classical DTC.

RESULTS AND DISCUSSION
The simulations via MATLAB/Simulink environment were performed using information found in Table 3 [21]. The two studied strategies conventional and proposed ST-DTC for DTP-PMSM drives, have been tested and results are presented in Figures 9 to 15. As shown in Figure 9, using the classic DTC strategy results in a non-sinusoidal phase current, indeed, the current contains a large quantity of the 5 ℎ and 7 ℎ harmonics which are dominant (THD = 51.6%) as shown in Figure 11. These current components do not contribute to the electromechanical conversion and only generate losses. Figure 10 shows the phase current corresponding to the proposed ST-DTC strategy. It can be observed that the shape of the current is nearly sinusoidal, harmonic analysis presented in Figure 12 shows that the harmonics are significantly reduced (THD about 11%), this is due to the fact that modified DTC method allows the control of current components in the (z 1 , z 2 ) subspace, and this consequently allows the reduction of harmonic currents. The Figure 13 and Figure 14 represents the currents in (α, β) subspace, we notice that for the two approaches we have the same amplitude, low ripple and regular trajectory. In Figure  15 (a) and Figure 15 (b) the torque presents the same appearance for both strategies. The torque quality is not affected by the presence of aforementioned harmonics. We also notice that the velocity reaches its setpoint with good dynamic and zero static error.

CONCLUSION
DTC is one of the strategies used for high performance electrical drive systems. Applied to DTP-PMSM the conventional DTC leads to significant harmonic currents. To deal with this problem, a DTC with a modified switching table has been proposed to control the DTP-PMSM. The purpose of this method is to minimize the harmonics of the stator current. It is based on the use of 12 voltage vectors synthesized in a two-step process. This technique allows the elaborating of the most suitable inverter voltage vector which permits not only the control of variables in ( , ) subspace but also the reduction of currents in the (z 1 , z 2 ) subspace. Simulations have shown the effectiveness of the modified strategy to minimize harmonic current and increase system efficiency, while preserving the benefits and the merits of the classical technique.