Chapter 2The Six Phase Motor Magnetic Field

In conventional induction motors, sinusoidal flux density distribution around themachine air gap periphery is generally assumed to simplify machine analysis. .However, this generic assumption does not hold in all cases but depends mainly onthe winding layout. As mentioned before, one of the most important merits ofmultiphase windings is their ability to produce a high quality flux distribution withless harmonic contents, which in turn minimizes induced torque ripple.

In this chapter, the magneto motive force MMF of a six-phase winding isillustrated and compared with that of a conventional three-phase winding layout. Thiscomparison is made for both symmetrical and asymmetrical six-phase winding. Theharmonic spectrum is also used to investigate the effect of increasing the number ofphase on the quality of the air-gap flux distribution.

2.1 MMF of Distributed Winding2.2.1 MMF of a Distributed Three-phase Winding

The MMF distribution along the airgap periphery depends on the windinglayout and the exciting current. The effect of winding distribution has changed theshape of the MMF wave, from normal sinusoidal to stepped sinusoidal. The followingfigure represent the MMF produced by single N turns coil carrying current i Spans180o elec.

Figure 2.1

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The MMF of the distributed winding is the summation of coils placed in several slotswhich produce MMF closer to sinusoidal with less harmonic contents.

Figure 2.2In order to obtain a truly sinusoidal MMF in the airgap, the number of slots

has to infinitely large and conductors are sinusoidally distributed in the slots.Practically, the numbers of slots are limited & it is a lot easier to place the samenumber of conductors in a slot so, Sinusoidal flux density distribution around theairgap is difficult to achieve. As a result to field harmonics, the principal torquecomponent developed with torque harmonics components in additions and thatproduce speed disturbance and mechanical vibrations.

2.2.2 MMF Distribution of Six-Phase WindingThe six phase induction motor winding consist of two three phase groups

which can be separated by 60 electrical degree -symmetry six phase machine- or 30electrical degree which called asymmetry six phase machine as the angular distancebetween adjacent phases are not the same . And the main Reason of that is to reducethe fifth and the seventh harmonic.

Figure 2.3

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To verify that asymmetry winding in six phase motor improving the MMFdistribution around the air gap a MATLAB script, given in the appendix, was used tosimulate the magnetic field of 6 pole machine with 36 slots. Comparison was madebetween three phase, symmetrical six phases and asymmetrical six phase winding byapplying FFT analysis in each case.

The MMF distributions for the three cases are shown in Figure (2.4). Among differentcases, it is clear that the asymmetrical six-phase case gives the best MMF distribution.To highlight this improvement, the Fourier components of the MMF distributions forthe three cases are given in. Table (2.1) summarizes the simulation results for thethree cases. the results declare that the MMF distribution around the air gap in boththree phase winding and six phase symmetry winding are almost the same Figure(2.5),but it is a massive reduction in the 5th and 7th harmonics -almost quarter- withimproving the THD of the field in case of asymmetry winding Figure(2.6) Whichimproving the motor performance with higher principal torque component, lessvibrations, lower core losses and protecting the motor from suffering crawling at lowspeed due to the high ratio of 5th and 7th harmonics.

Figure(2.4) The produced MMF in the three cases of winding three phase winding, sixphase symmetry winding and six phase asymmetry winding.

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Figure(2.5) The FFT analysis of threephase winding and six phase symmetry

winding

Figure(2.5) The FFT analysis of six phaseasymmetry winding

Table (2.1) shows Comparison between three phase winding, six phase symmetrywinding and six phase asymmetry winding:

Harmonic order Three phase winding Symmetry winding Asymmetrywinding

Fundamental peak 208.8 208.6 201.53 0.11 % 0.0 % 0.06 %5 5.42 % 5.45 % 1.46 % (Lowest)7 3.76 % 3.73 % 0.99 % (Lowest)9 0.11 % 0.0 % 0.06 %11 9.1 % 9.03 % 9.09 %13 7.61 % 7.68 % 7.62 %

THD 16.26 % 16.24 % 14.68 %

2.2 ConclusionThe asymmetry six phase winding produce MMF with lower harmonic

content especially the 5th and 7th harmonics which improve the motor performancewith lower speed disturbance and mechanical vibrations.