1. Direct Torque Control of Five-phase Permanent Magnet Synchronous Machine  
Professor Mukhtar ahmad Senior Member IEEE
Aligarh Muslim University
Aligarh
INDIA

2. Introduction
Permanent magnet synchronous machines are becoming attractive in many industrial applications due to their high torque to inertia ratio, higher efficiency , and power density .
Interest in Multi-phase motor drives has considerably increased during last few years. The main applications of multi-phase machines are in electric traction, electric vehicles, and hybrid vehicles. Multi-phase motor drives have many advantages including higher reliability and power density, and lower torque pulsations at higher frequencies

3. Direct torque control
The DTC method provides a powerful control of stator flux and torque instead of controlling the current used in vector controlled drives.
In this paper a modified DTC scheme for five phase PMSM based on look up table is described .
The conventional DTC of five-phase PM only controls locus of the flux space vector. Thus, large number of harmonics are present in stator current waveform. In order to overcome this problem DTC based on Space Vector Modulation (SVC) has been proposed .

4. Dynamic model of five phase PMSM
The stator voltage equation can be written as -
The air gap flux linkages are represented as

5. The stator currents are –

6. The self and mutual inductances are assumed to have same value for all the phases.
That is

7. To simplify the machine model an arbitrary transformation is introduced which transforms the phase variables of five phase motor into a reference frame rotating at an arbitrary angular velocity. The transformation matrix for this system is given by the following matrix. A=

8. By applying this transformation to the stator voltages and flux the following equations are obtained

9. The torque T can be expressed as –

10. Five-phase voltage source inverter

11. A five phase voltage source inverter is shown in Fig
A five phase voltage source inverter is shown in Fig.1 The input dc voltage to the inverter is assumed to be constant. The model of five phase VSI is developed in space vector form, assuming an ideal commutation and zero forward voltage drop.
Since a five phase VSI is considered here , the analysis requires five-dimensional space. Two space vectors are therefore defined, each of which will describe space vectors in a two dimensional subspace (d-q) and (x-y). The third subspace is single dimensional ( zero sequence) which has zero value in star connected system.

12. Space vectors of phase voltages in stationary reference frame are expressed as the Equations shown below-

13. In general an n-phase two level VSI has a total of space vectors
In general an n-phase two level VSI has a total of space vectors. In five phase VSI therefore , there are 32 space vectors, thirty non-zero vectors and two zero vectors. The thirty non-zero vectors form three decagons in both d-q (Fig.2)) and x-y plane ( Fig.3) and can be easily calculated using Equations shown earlier.

14. Five-phase VSI phase voltage space vectors in the: d-q plane,
Fig.2

15. Five-phase VSI Space vector in x-y plane
Fig.3

16. ). As can be seen from Figures 2 and 3, the outer decagon of space vectors of d-q plane map into inner decagon of the x-y plane. The innermost decagon of d-q plane forms the outer decagon of x-y plane. Thus application of large vectors only can not yield the sinusoidal voltage. The principle of selecting a voltage space vector in a conventional DTC method in five phase PMSM is similar to the method used in three–phase PMSM.

17. Torque Equation
For five phase PMSM , the equation for electromagnetic torque can be written as –
It can be seen from Eq.(12) that only the interaction between stator flux space vector in d-q subspace and permanent magnet flux produces the torque. In order to control the torque therefore, the voltage space vectors are selected to control the stator flux . The stator flux can be obtained from the equation

18. In the five-phase inverter shown in Fig
In the five-phase inverter shown in Fig.1, each leg switching function called can take either 1, or 0 value based on the state of upper or lower switch .If the upper switch is on the switching function is ‘1’ else it is’ 0’.In order to control the stator flux proper voltage space vector is to be selected out of 30 possible non-zero space vectors and two zero vectors

19. Application of large and medium vectors
Although only one switching is necessary from one vector to near by vectors for large decagon. However if only large vectors are used to create the desired d-q voltages, x-y voltages will be invariably created. Thus low order voltage harmonics such as 3rd and 7th are generated.
The application of only large space vectors does not produce satisfactory result in terms of harmonic contents, because only two active voltage vectors are always applied. In [4] it has been emphasized that the number of applied active space vectors for multi-phase VSI with odd phase number should be one less than the number of inverter phases. This means that for better operation four active vectors must be applied instead of two

20. n this paper four active vectors combining the medium and large vectors is used to get almost sinusoidal voltage from the inverter, thereby improving the performance of motor. The scheme has been described in [5] and used here. To apply large and medium vectors two schemes are used so that as far as possible the output of the inverter is sinusoidal.

21. In first scheme uses proportional to their length sub division of time of application of large and medium space vectors. This SVPWM will provide sinusoidal input but can provide output which is only 85.41% of maximum achievable from the inverter. From 85.42% to 100% only large vectors are applied. Thus it will result in appearance of low order harmonics but their magnitude is small. The time of application of different vectors are variable and depend on the magnitude of reference voltage.

22. Conclusions
n this paper SVPWM technique for five-phase voltage source inverter is used to control the speed of five-phase Permanent magnet motor drives. The scheme used has been simulated and found to have considerable lower harmonics in stator currents. The response of the motor in terms of speed and torque is superior to simple scheme of DTC.

23. References
[1] Parsa L, On advantages of Multiphase Machines, Industrial Electronis society IECON nd annual conference of IEEE 2005 pp
[2] Parsa L. and Toliyat H.A. , Five-phase Permanent magnet Motor Drives , IEEE Transactions on Industry Applications vol.41, no1, 2005 pp30-37
[3] Gao Yuan and Parsa L., Modified Direct Torque Control of Fie-phase Permanent Magnet Synchronous motor Drives, Applied Power Electronics Conference APEC 2007 pp
[4] Kelly J.W., Strangas E.G., and Miller J.M.,”Multiphase Space Vector Pulse Width Modulation” IEEE Transaction on Energy Conversion vol18, no pp
[5] Iqbal A, and Levi E. “Space vector modulation schemes for a five-phase voltage source inverter” European conference on Power Electronics and Applications 2005.pp12.