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Research of six-phase induction motor windings.

I. INTRODUCTION

In early 1990s, study on multiphase machines accelerated until the beginning of recent century, it became practical in industries.

Multiphase motor drives have been proposed for different applications. Some of the most suitable applications are electric, hybrid electric vehicles and locomotive traction [1], [2], the concept of ,,more--electric" aircraft [3], ship propulsion [4]. Other suitable applications are aerospace and high power applications (including nuclear power plants) [5].

Multi-phase machines drive has many advantages over conventional three-phase drive such as increased torque per ampere for the same volume machine, reduced stator copper losses, reduced rotor harmonic currents, high power handling capability by dividing the required power between multiple phases, reduced torque pulsations and higher reliability [6], [7]. In particular, unlike in a three phase drive, the loss of stator phase does not prevent the machine from starting and running [8].

A comprehensive survey of the state-of-the-art in development and investigation of multiphase induction motors is presented in [9]. Advantages of those motors raise some specific problems to be solved and investigations of the motors continued including numerous cases of control modes. As multiphase motor for a while cannot be purchased in the store, usually it is made by rewinding of three phase motors with greater number of slots. Therefore multiphase motor has smaller number of slots per phase than three-phase motor; this causes a great number of spatial harmonics, increasing heat loss in the motor. Suitable choice of winding type allows increasing the fundamental harmonic and reducing spatial harmonics, which are able to cause torque pulsations.

This paper presents investigation of two types windings for six-phase induction motor, shows elaborated connection of winding sections and comparison of two types concentrated double layer windings: short pitch coil six-phase winding and full pitch coil six-phase winding, calculation and analysis of developed magnetomotive forces and spatial harmonics.

II. WINDINGS OF SIX-PHASE INDUCTION MOTOR

Double layer windings have many advantages over single layer windings: easier to manufacture and lower cost of coils, fractional-slot can be used, chorded-winding is possible, lower leakage reactance and therefore, better performance of the machine [10], [11]. Parameters of stator winding are: total number of slots S = 48, number of poles 2P = 8, number of phase m = 6, pole pitch [tau] = 6, slot angular pitch [gamma] = 30[degrees], number of slots per pole per phase q = 1, coil pitch y = 5, phase spread [sigma] = 60[degrees], angle between stator current phasors is 60[degrees]. Elaborated connection scheme of winding sections is presented in Fig 1.

Concentrated double layer short pitch coil six-phase winding and magnetomotive force is presented in Fig. 2.

In the case of concentrated double layer short pitch coil six-phase winding, instantaneous current values, at the pole pitch margins, are the same in upper and lower levels of five slots and only once the values of instantaneous current in upper and lower levels are different.

The other type stator winding parameters are: total number of slots S = 48, number of poles 2P = 8, number of phase m=6, pole pitch [tau] = 6, slot angular pitch [gamma] = 30[degrees], number of slots per pole per phase q = 1, coil pitch y = 6, phase spread [sigma] = 60[degrees], angle between stator current phasors is 60[degrees]. Connection of winding sections is presented in Fig. 3. Concentrated double layer full pitch coil six-phase winding and its magnetomotive force is presented in Fig. 4.

In case of concentrated double layer full pitch coil six-phase winding, instantaneous current values, at the pole pitch margins, are the same in all upper and lower levels of slots.

Analysis of the considered short pitch coil winding indicates, that during one pole pitch the relative magnetomotive force [F.sub.1]([phi]) has the shape, shown in Fig. 5.

Space harmonic spectrum of each winding magnetomotive force can be obtained on the base of Fourier series [12]. The Fourier transform coefficients of the function [F.sub.1]([phi]), shown in Fig. 5 are calculated in this way [13], [14]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

where [A.sub.1] = 1/3 and [A.sub.2] = 2/3 are amplitudes of relative magnetomotive force components.

The Fourier series coefficients were calculated according to (1).

The Fourier series is expressed as [12]

[F.sub.1, [summation]K] = [K.summation over (k = 0)] [b.sub.1, k] sin k[phi] (2)

Fourier series of function [F.sub.1]([phi]) at k = 0, 1,..., 50 is presented in Fig. 5 and denoted as [F.sub.1, [summation]50]([phi]).

Analysis of the full pitch coil winding shows, that relative magnetomotive force [F.sub.2]([phi]) in the one pole pitch displacement varies in the way, shown in Fig. 6.

Fourier series coefficients of function [F.sub.2]([phi]) are calculated in the form

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)

where [A.sub.1] = 1/2 and [A.sub.2] = 1/2 are amplitudes of relative magnetomotive force components.

In accordance with (3) the series can be rewritten in the form

[F.sub.2, [summation]K] = [K.summation over (k = 0)] [b.sub.2, k] sin k[phi]. (4)

Fourier series of function [F.sub.2]([phi]) at k = 0,..., 1, 50 is presented in Fig. 6 and denoted as [F.sub.2, [summation]50]([phi]).

Analysis of magnetomotive forces gives information about higher harmonics, appearing in the air gap.

Comparing the amplitude [b.sub.2k] of k-th harmonic magnetomotive force [F.sub.2]([phi]) with amplitude [b.sub.1k] of k-th harmonic magnetomotive force [F.sub.1]([phi]), the difference between those is calculated and expressed in percent as

[[delta].sub.k] = [[absolute value of [b.sub.2, k]] - [absolute value of [b.sub.1, k]]/[b.sub.1, 1]] 100%. (5)

Figure 6 indicates, that the short pitch coil six-phase winding has significantly greater the first harmonic (by 22 %). Analysis of (1) and (2) shows, that the first harmonic of this winding approximately is equal to 0.8 and that of the full pitch coil six-phase winding is smaller - reaches 0.6 as shown in Fig. 8. So from the point of view of the first harmonic the motor with the short pitch coil six-phase winding will have higher efficiency.

Analysis shows, that even harmonics have the same amplitude. According to (1) and (3), they are equal to zero.

The spectrum of magnetomotive forces for short pitch coil six phase winding and full pitch winding is presented accordingly in Fig. 7 and Fig. 8.

From Fig. 7 and Fig. 8 can be evidently seen, that difference of higher odd harmonics [absolute value of [b.sub.2, 1]] - [absolute value of [b.sub.1, 1]] > 0. That indicates the odd higher harmonics of full pitch coil winding having greater amplitude. While the higher harmonics increase torque oscillations and heat loss, it is possible to state, that the short pitch coil winding has greater efficiency.

Dependence of harmonic amplitude difference [[delta].sub.k] against harmonic number k is shown in Fig. 9. The first harmonic of full pitch coil winding is smaller by 22 % from that of short pitch coil winding, while the third, fifth, seventh and ninth harmonics are greater, but no more than 5 %, the eleventh and thirteen are smaller about 2 %.

Research indicated that according to the harmonic spectrum, the short pith coil winding has greater efficiency than full pith coil winding.

Experimental motor was made according to concentrated double layer short pitch coil six-phase winding connection scheme.

Figure 10 shows general view of stator with concentrated double layer short pitch coil six-phase winding.

Each section of experimental induction motor winding consist of 160 turns with wire diameter of 0.4 mm. Six-phase induction motor with concentrated double layer short pitch coil winding was successfully tested.

III. CONCLUSIONS

Two types of six phases motor windings connections are proposed: concentrated double layer short pitch coil winding and concentrated double layer full pitch coil winding.

The relative magnetomotive forces are calculated. Space harmonic spectrum of each winding magnetomotive force was obtained on the base of Fourier series.

Analysis of Fourier special spectrum shows, that even harmonics for concentrated double layer short pitch coil six phase winding and concentrated double layer full pith coil six phase winding are equal to zero.

Concentrated double layer short pith coil six phase winding has the first harmonic greater by 22 % compared with concentrated double layer full pith coil six phase winding.

Research indicated that according to the harmonic spectrum, the short pith coil winding has greater efficiency than full pith coil.

Experimental six-phase induction motor with concentrated double layer short pitch coil winding was made and successfully tested.

http://dx.doi.org/ 10.5755/j01.eee.20.1.2237

Manuscript received April 16, 2013; accepted October 29, 2013.

This research was funded by the European Social Fund under the project ,,Microsensors, microactuators and controllers for mechatronic systems (Go-Smart)" (Agreement No. VP1-3.1-SMM-08-K-01-015).

REFERENCES

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[2] J. I. Leon, O. Lopez, L. G. Franquelo, J. Doval-Gandoy, S. Vazquez, J. Alvarez, F. D. Freijedo, "Multilevel multiphase feedforward space-vector modulation technique", Industrial Electronics, vol. 57, no. 6, pp. 2066-2075, 2010. [Online]. Available: http://dx.doi.org/10.1109/ TIE.2009.2034171

[3] R. Gregor, F. Barrero, S. Toral, M. J. Duran, "Realization of an asynchronous six-phase induction motor drive test-rig", in Int. Conf. on Renewable Energy and Power Quality, 2008.

[4] J. M. Apsley, A. Gonzalez-Villasenor, M. Barnes, A. C. Smith, S. Williamson, J. D. Schuddebeurs, P. J. Norman, C. D. Booth, G. M. Burt, J. R. McDonald, "Propulsion drive models for full electric marine propulsion systems", Industry Applications, vol. 45, no. 2, pp. 676-684, 2009. [Online]. Available: http://dx.doi.org/10.1109/TIA. 2009.2013569

[5] O. Grigore-Muler, M. Barbelian, "The simulation of a multi-phase induction motor drive", in Int. Conf. on Optimization of Electrical and Electronic Equipment, 2010, pp. 297-306.

[6] G. K. Singh, "Multi-phase induction machine drive research - a survey", Electric Power Systems Research 61, pp. 139-147, 2002. [Online]. Available: http://dx.doi.org/10.1016/S0378-7796(02) 00007-X

[7] B. Kundrotas, S. Lisauskas, R. Rinkeviciene, "Model of multiphase induction motor", Elektronika ir Elektrotechnika (Electronics and Electrical Engineering), no. 5, pp. 111-114, 2011.

[8] S. Lisauskas, B. Kundrotas, R. Rinkeviciene, A. Smilgevicius, "Investigation into six-phase induction drive dynamic characteristics", in Int. Conf. on Electrical and Control Technologies (ECT2011), pp. 218-221, 2011.

[9] J. Buksnaitis, "Electromagnetical efficiency of the six-phase winding", Elektronika ir Elektrotechnika (Electronics and Electrical Engineering), no. 3, pp. 3-6, 2012.

[10] E. Levi, R. Bojoi, F. Profumo, H. A. Toliyat, S. Williamson, "Multiphase induction drives - a technology status review", IET Electrical Power Applications, no. 1, pp. 489-516, 2007.

[11] J. Buksnaitis, "New apprroach for evaluation of electromagnetic properties of three-phase windings", Elektronika ir Elektrotechnika (Electronics and Electrical Engineering), no. 3, pp. 31-36, 2007.

[12] R. Rinkeviciene, A. Petrovas, "Harmonic analysis of inverter fed motor currents", in Int. Conf. on Electromagnetic Disturbance (EMD 2008), 2008, pp. 169-172.

[13] B. Ronald, The Fourier Transform & Its Applications, McGraw-Hill Science, 1999.

[14] J. Buksnaitis, "Research of electromagnetic parameters of single-layer three-phase and six-phase chain windings", Elektronika ir Elektrotechnika (Electronics and Electrical Engineering), no. 9, pp. 11-14, 2013.

B. Kundrotas (1), A. Petrovas (1), R. Rinkeviciene (1), A. Smilgevicius (1)

(1) Department of Automation, Vilnius Gediminas Technical University, Naugarduko St. 41, LT-03227 Vilnius, Lithuania

roma.rinkeviciene@vgtu.lt
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Author:Kundrotas, B.; Petrovas, A.; Rinkeviciene, R.; Smilgevicius, A.
Publication:Elektronika ir Elektrotechnika
Article Type:Report
Geographic Code:4EXLT
Date:Jan 1, 2014
Words:1900
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