Analysis of Torque Pulsations of Inverter Fed Five-Phase Induction Machines

M. Chomat1, L. Schreier1, J. Bendl1

1 Department of Electrical Engineering and Electrophysics Institute of Thermomechanics CAS, v.v.i.

Dolejskova 5 (Czech Republic) phone:+420 660 531 46, e-mail: chomat@it.cas.cz, schreier@it.cas.cz, bendl@it.cas.cz

Abstract The analysis of torque pulsations in five-phase induction machines is presented. The pulsations arise from the mutual interaction of certain spatial harmonics present in the air gap of the machine. Simulation results are validated by experimental measurements for various voltage supply methods. A voltage supply method that significantly reduces the unfavorable effects of the third space harmonic in five-phase machines is described in the paper. Key words: Five-phase induction machines, space harmonics, torque pulsations.

1. Introduction

The multi-phase induction machines are becoming increasingly popular due to the advantages they have compared to the classical three-phase induction machines. The better waveform of the magneto-motive force (MMF), the reduced voltage at the output of the feeding converter, an improved fault tolerance are among the most important advantages mentioned in the literature [1, 2]. The investigation is based on the analysis of a five-phase induction machine fed from a ten-pulse voltage source inverter, [3-7].

An important difference in modelling the five-phase induction machine lies in the need to consider the third spatial harmonic of the MMF in the air gap of the machine even if the neutral node of the stator winding is insulated. This must be reflected in the mathematical model of the machine.

2. Investigated System

The simplifying assumptions used in the theory of electrical machines, such as the linear characteristic of iron, were used to derive the equations of the five-phase induction machine [8]. The mathematical model is based on the following equations [9-12]

1 1

1 1 1 1S R S

S S S S Md d

R L Ldt dt

λ= + +i i

u i (1)

( )1 11 1 1 1 1 1 1 10 R S S

RS R S RS M m RS R S M Sd d

R L L jp L Ldt dt

λλ λω= + + − +

i ii i i

(2)

3 3

3 3 3 3S R S

S S S S Md d

R L Ldt dt

λ= + +i i

u i (3)

( )3 33 3 3 3 3 3 3 30 3R S S

RS R S RS M m RS R S M Sd d

R L L j p L Ldt dt

λλ λω= + + − +

i ii i i

(4)

5 5

5 5 5 5 ReS R SS S S S M

di du R i L L

dt dtλ = + +

i

(5)

( )5 55 5 5 5 5 5 5 50 5R S S

RS R S RS M m RS R S M Sd di

R L L j p L L idt dt

λλ λω= + + − +

ii i

(6)

The symbols u and i represent vectors of voltage and current components and ωm is the mechanical speed, p is the number of pole-pairs, R is the resistance, and L is the inductance. Subscripts 1, 3, and 5 denote the first, the third, and the fifth symmetrical components. The stator quantities are marked by subscript S, subscript M denotes the main inductance. The rotor parameters and current components are rated to the effective number of stator conductors, subscript RS, and rotor current components are transformed into the stator coordinate system, subscript λ. The torques produced particularly by the first, third and fifth components are

1 1 1 110 ReM S R ST pL j λ∗ = i i (7)

3 3 3 330 ReM S R ST pL j λ∗ = i i (8)

5 5 5 525 ReM S R ST pL j λ∗ = i i (9)

The overall torque T is the sum of these torque components. The equation of motion is

( )m

ld 1d

T Tt Jω

= + (10)

where Tl is the load torque and J is the moment of inertia. A numerical model of a five-phase induction machine has been set up based on these equations.

An experimental five-phase induction machine with the nominal power of 1.5 kW was developed and manufactured. The experimental machine was fed from an experimental multi-phase voltage-source inverter. The scheme of the experimental system is shown in Fig. 1. There are three different ways of connecting the stator winding to the converter, Fig. 2. The connection according to Fig. 2a is denoted as star, connection according to Fig. 2b as pentagon and connection according to Fig. 2c as pentacle [4].

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Fig. 1. Five-phase inverter feeding five-phase IM.

a b c

Fig. 2. Star, pentagon, and pentacle connections of stator winding to converter.

3. Simulation and Measurement Results

Simulations of various configurations and supply methods were carried out. First, the star connection of the machine supplied by a standard ten-pulse voltage was investigated. The simulated stator voltage uSA across phase A and current iSA of this phase winding at load torque 3 Nm are shown in Fig. 3 and corresponding quantities measured on the experimental machine are shown in Fig. 4. Second, in order to enable the use of common control schemes designed for three-phase IM drives in the investigated system, an individual voltage vectors were substituted by sequences of voltage vectors, which leads to near elimination of the torque produced by the third symmetrical components of stator currents. Figures 5 and 6 show the corresponding quantities to those shown in Figs. 3 and 4. From Figs. 7 and 8, it can be seen that the torque component due to the third current component was nearly eliminated, however, the total torque pulsations rose due to the bigger content of the higher time harmonics in the first component of the currents.

Fig. 3. Simulated phase voltage and current for star connection and normal voltage supply.

Fig. 4. Measured phase voltage and current for star connection and normal voltage supply.

Fig. 5. Simulated phase voltage and current for star connection and modified voltage supply.

iSB

iSA

iSC

iSE

iSD

A

B

C

D

E

iB

iA

iC

iE

iD

iSA

iSB

iSC

iSD

iSE

iB

iA

iC

iE

iD

iSA

iSE

iSB

iSD

iSC

A

B

C

D

E

A

B

C

D

E

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Fig. 6. Measured phase voltage and current for star connection and modified voltage supply.

Fig. 7. Simulated torque and torque components for star connection and normal voltage supply.

Fig. 8. Simulated torque and torque components for star connection and modified voltage supply.

Various sequence combinations have been investigated regarding the torque pulsations and harmonic content in the stator voltages and currents. The total harmonic distortion (THD) for three different voltage patterns used

in operation corresponding to ten-pulse supply are shown in Table I. The voltage vectors combinations were chosen as symmetrical and consisted of sequences of six vectors giving the required average vector over the switching period. The lower-magnitude voltage vector in the reference plane of the first symmetrical components was at the first and sixth positions in the first pattern, second and fourth in the second pattern, and third and fourth in the third pattern. Star, pentagon and pentacle connections of the stator winding were investigated and compared. The harmonic spectra of phase voltage and current for various connections and three investigated voltage-vector sequences are shown in Figs. 9 to 17.

TABLE I. THD OF STATOR PHASE CURRENT

Voltage Pattern 1 2 3

star 40.9 % 21.3 % 35.5 % pentagon 63.8 % 31.7 % 54.8 % pentacle 28.1 % 15.5 % 24.3 %

Fig. 9. Harmonic spectra of stator phase voltage and current for star connection and first investigated voltage-vector sequence.

Fig. 10. Harmonic spectra of stator phase voltage and current for star connection and second investigated voltage-vector sequence.

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Fig. 11. Harmonic spectra of stator phase voltage and current for star connection and third investigated voltage-vector sequence.

Fig. 12. Harmonic spectra of stator phase voltage and current for pentagon connection and first investigated voltage-vector sequence.

Fig. 13. Harmonic spectra of stator phase voltage and current for pentagon connection and second investigated voltage-vector sequence.

Fig. 14. Harmonic spectra of stator phase voltage and current for pentagon connection and third investigated voltage-vector sequence.

Fig. 15. Harmonic spectra of stator phase voltage and current for pentacle connection and first investigated voltage-vector sequence.

Fig. 16. Harmonic spectra of stator phase voltage and current for pentacle connection and second investigated voltage-vector sequence.

Fig. 17. Harmonic spectra of stator phase voltage and current for pentacle connection and third investigated voltage-vector sequence.

4. Conclusion

Various voltage supply schemes were investigated by simulations and the results were validated by the corresponding measurements on an experimental five-phase machine. A method of voltage supply minimizing the unfavorable effects of the third symmetrical current component on operation of a five-phase machine has been tested. The elimination of the torque component appearing due to the third current components was quite successful. However, the basic method of the modified voltage supply leads simultaneously to a significant rise in torque pulsations caused by bigger content of the higher time harmonics in the first component of stator currents. It is anticipated that this negative effect may be

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minimized by dividing the time intervals into more sections and shifting, therefore, the voltage harmonics towards higher frequencies where they would produce current harmonics of lower magnitudes. The verification of this will be the subject of further research. Space vector modulation schemes for five-phase induction machines are going to be investigated based on the obtained results.

Acknowledgement

This work was supported by the Czech Science Foundation under research grant No. 16-07795S and by the institutional support RVO 61388998. The authors would like to thank the company EMP Inc. for cooperation and manufacturing the experimental machine.

References

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