3 Phase WindingDistribution

True 6 PhaseWinding

Distribution

1 2

3

4

5

6Quasi 6 Phase

WindingDistribution

made from two3-phasewindings 30 deg phase

shift betweentwo 3-phase

sets

Analysis and Performance Assessment of 6-pulse Inverter-Fed 3-Phase and 6-phase Induction machines

David G Dorrell Dept of Electronics and Electrical Engineering

The University of Glasgow Glasgow, G12 8LT, UK d.dorrell@elec.gla.ac.uk

C. Y. Leong and R. A McMahon Dept of Engineering

The University of Cambridge Cambridge, CB2 1PZ, UK

cyl28@eng.cam.ac.uk and ram1@eng.cam.ac.uk

Abstract— The paper describes a model for a 6-phase induction motor driven by an inverter operating in a 6-pulse (square wave) mode. The model is implemented and performance, in terms of torque, current, efficiency and pulsating torque, compared to the performance of a 3-phase motor (both sine and 6-pulse supplied). The models are verified experimentally, in particular the efficiency performance, and it is illustrated that the improvement in inverter efficiency when in 6-pulse operating mode may improve the performance of the overall system.

Keywords 6-phase induction motor,inverter, 6-pulse operation

I. INTRODUCTION Six phase induction motors have received some attention in

the past [1-7] and they can offer the opportunity to spread the load across more half bridge sections so that the device ratings can be decreased; in terms of motor magnetics they can increase the winding factor slightly. They have some interesting characteristics when compared to standard induction motors; the two most notable are the fact that the phases have to be distributed around 180 degrees to avoid phases being opposite each other (where they are then essentially the same phase) and that if the voltage supply contains time harmonics then the 5th , 7th, 15th 17th, etc, time harmonics have a short-circuited magnetizing reactance in the fundamental per-phase equivalent circuit. The former point is illustrated in Fig 1 for clarity while the latter point (which was first reported by Jahns [2] and recently used in another paper [8]) is illustrated by the equivalent circuits shown in Figs. 2 and 3. The latter point is relevant if the motor is supplied from an inverter which is operating in square wave (180 degree conduction period) mode which produces 6-pulse operation across the phase winding in a star-connected induction motor and a quasi square-wave across the windings of a delta-connected machine. While the efficiency of an induction motor (either 3 or 6 phase) decreases when moving from sine wave to square wave operation it is shown in this paper that this is not a large decrease and that moving from a PWM strategy to a square wave control strategy can reduce inverter switching losses and, in fact, may lead to a higher overall system efficiency. The increase in inverter efficiency, using simple square-wave operation rather than sine-wave PWM, was reported in [9]; and further discussion of this will be offered in the full paper. This was verified using calorimetric measurements [10].

Fig. 1 Three phase and six phase spatial representation

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Fig. 2 Three-phase and quasi six-phase equivalent circuit for voltage harmonics but neglecting higher space harmonics

Fig 3 Quasi 6-phase connection when k = 5, 7, 17, 19, etc. when

neglecting space harmonics

II. MOTOR ANALYSIS

The paper will give a description of the motor in terms of a mathematical model. A modeling technique is put forward that includes both voltage time harmonics due to the use of 6 pulse (square wave) excitation and motor space harmonics due to MMF harmonics in the windings. This is a development on the work in [8] where only the fundamental MMF waves for each voltage time harmonics was included.

A. Voltage Harmonics There are two options for connecting the quasi 6-phase

winding – either double star or double delta. If a double star is used then the phase windings will experience a six-pulse voltage waveform if the conduction period of the inverter is 180 degrees, whereas if the winding is a double delta connection then the phase windings will experience a quasi square-wave voltage, with 120 degree conduction period, when the inverter conduction period is again 180 degrees. For the delta connection, the Fourier decomposition of the voltage across one motor phase and centred on the reference axis is

( ) ( )( )Set 1Phase A 2 3

( ) cos 6 11 6

DCk S

VV t n t

nω

π= ±

± (1)

where n = 0, 1, 2, 3, etc., k = 6n ± 1 when n > 0 and k = 1 when n = 0 . This gives k = 1, 5, 7, 11, 13, etc. For the star connection

( ) ( )( )( )

Set 1Phase A 2

( ) cos 6 11 1 6

DCk Sn

VV t n t

nω

π= ±

− ± (2)

The total voltage is then

Set 1Phase A

1( ) Re sjk t

kk

V t V e ω∞

=

= ∑ (3)

For the voltages in the same 3-phase set 2

Set 1 3Phase B

1

1

( ) Re

Re

s

s

jkjk tk

k

jk t kk

k

V t V e e

V e a

πω

ω

∞ −

=

∞−

=

=

=

∑

∑ (4)

and 2

Set 1 3Phase C

1

1

( ) Re

Re

s

s

jkjk tk

k

jk t kk

k

V t V e e

V e a

πω

ω

∞

=

∞

=

=

=

∑

∑ (5)

We are using the operator a where2

3ja eπ

= . For a 3-phase balanced set we find that the forwards and backwards rotating sets are defined by

1

1

Forwards rotating set= Backwards rotating set

a 1 Zero order (no current harmonic)

k

k

k

a aa a−

=

=

When we look at the 3-phase harmonic sets defined by (3), (4) and (5) we find that we have forwards-rotating sets when k = 1, 7, 13, 19, etc., and backwards-rotating sets when k = 5, 11, 17, etc.

For Set 2 (when we are using a 6-phase arrangement) the voltages are rotated through 30 electrical degrees (as can be seen in Fig. 1) so that

Set 2 6Phase A

1

1

( ) Re

Re

s

s

jkjk tk

k

jk t kk

k

V t V e e

V e b

πω

ω

∞ −

=

∞−

=

=

=

∑

∑ (6)

where we introduce the operator 6jb eπ

= . If the supply frequency is fS then the harmonic frequency fk = kfS. Similar equations exist for Phases B and C for Set 2:

B. Winding Harmonics Phase A of a 3-phase harmonic winding can be denoted as

( )Phase ASet 1m ( ) cos( )

2jm jmm

mN

n N m e eθ θθ θ −= = + (7)

where θ is electrical angle. Phases B and C are:

( )

Phase BSet 1m

2 23 3

2'' '3

''

2( ) cos3

2

2 2

m

jm jmm

jmm jmm m

m mm m

n N m

Ne e

N Ne a e

π πθ θ

πθθ

πθ θ

− − −

− =−

=±=±

= −

= +

= =

(8)

and

Rc

Vk

jkωsL1R1I1 k I'2k

Im kIc kR'2sk

jkωsLm

jkωsL2

Vk

jkωsL1R1I1 k

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( )

Phase CSet 1m

2 23 3

2'' '3

''

2( ) cos3

2

2 2

m

jm jmm

jmm jmm m

m mm m

n N m

Ne e

N Ne a e

π πθ θ

πθθ

πθ θ

+ − +

+ − −

=±=±

= +

= +

= =

(9)

These equations are valid for the 3 phase machine and Set 1 of the 6 phase machine. For Set 2 in the 6 phase machine

Phase A' 'Set 2

m'

( ) cos12 2

m jmmm

m m

Nn N m b e θπθ θ −

=±

= − =

(10)

( )Phase B

' ' 'Set 2m

'

( )2

m m jmm

m m

Nn b a e θθ −

=±

= (11)

( )Phase C

' ' 'Set 2m

'

( )2

m m jmm

m m

Nn b a e θθ − −

=±

= (12)

Fig 4 Per-phase equivalent circuit for fundamental time harmonic but including higher harmonics

C. MMF generation If we assume that there are currents of suitable frequency

then the MMF for the 3-phase machine is:

( ) ( )

3Phase Phase

1

'' '

' 1

( , ) ( ) ( )

Re 12

s

Ph

j kw t mm k m kmk

m k

MMF t n i t

Na a a a I e θ

θ θ=

∞ ∞−− −

=−∞ =

=

= + +

∑

∑ ∑ (13)

When this is analyzed we obtain the usual spatial relationships for sinusoidal excitation (m’ harmonics for k = 1) with the harmonics existing for m’ = 1, -5, 7, -11, 13, etc. This is illustrated in Fig 4 which gives the equivalent circuit including the 5th and 7th spatial MMF harmonics. If the rotor equivalent

resistance blocks the circuit at a slip greater than 1 then it is a backwards rotating field whereas if it is less than 1 then it is a forwards rotating field. However, for the higher time harmonics (k > 1) then there exists other sets of spatial MMF harmonics and this leads to quite a complex double series to analyze. For example, for k = 5 spatial MMF waves exist for m’ = -1, 5, -7, 11, -13, etc. It is more straightforward to state the synchronous speeds in Table 1. If the synchronous speed is negative then the torque is negative in the first quadrant; if the synchronous speed is positive then the torque contribution is positive when sub-synchronous and negative super-synchronous.

TABLE I. 3-PHASE SYNCHRONOUS SPEEDS FOR TIME AND SPACE HARMONICS

Spatial harmonic m’

(ωs = supply frequency (rad/sec and p = pole pair number) Time Har

k ±1 ±5 ±7 ±11 ±13 ±17 ±19 ±23 ±25

1 s

pω

5s

pω−

7s

pω

11s

pω−

13s

pω

17s

pω−

19s

pω

23s

pω−

25s

pω

5 5 s

pω− s

pω 5

7s

pω− 5

11s

pω 5

13s

pω− 5

17s

pω 5

19s

pω− 5

23s

pω

5s

pω−

7 7 s

pω 7

5s

pω− s

pω 7

11s

pω− 7

13s

pω 7

17s

pω− 7

19s

pω 7

23s

pω− 7

25s

pω

11 11 s

pω− 11

5s

pω 11

7s

pω− s

pω 11

13s

pω− 11

17s

pω 11

19s

pω− 11

23s

pω 11

25s

pω−

13 13 s

pω 13

5s

pω− 13

7s

pω 13

11s

pω− s

pω 13

17s

pω− 13

19s

pω 13

23s

pω− 13

25s

pω

17 17 s

pω−

175

s

pω 17

7s

pω−

1711

s

pω

1713

s

pω−

s

pω

1719

s

pω−

1723

s

pω 17

25s

pω−

19 19 s

pω 19

5s

pω−

197

s

pω 19

11s

pω−

1913

s

pω

1917

s

pω−

s

pω

1923

s

pω−

1925

s

pω

23 23 s

pω− 23

5s

pω 23

7s

pω− 23

11s

pω 23

13s

pω− 23

17s

pω 23

19s

pω− s

pω 23

25s

pω−

25 25 s

pω 5 s

pω− 25

7s

pω 25

11s

pω−

2513

s

pω−

2517

s

pω−

2519

s

pω 25

23s

pω−

s

pω

If a 6 phase winding is used then the MMF breaks down into

( )( )( )

( )

Phase Phase2 3Set Set

1 1

'

'' '

' 1' '

( , ) ( ) ( )

1

Re 12

1

s

Set Ph

m k

j kw t mm k m kmk

m km k m k

MMF t n i t

b bN

a a b b I e

a a b b

θ

θ θ= =

−

∞ ∞−− −

=−∞ =− −

=

+ = + + + +

∑ ∑

∑ ∑ (14)

This time if m’- k = ± 6n (where n is an integer) then

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(1 + bm’b-k) = 0 or 2 (15)

depending on whether n is odd or even. In essence, if n is odd then the MMF from Set 2 cancels the MMF from Set 1. If n is even or zero then the MMF from the two sets add. Addressing the non-zero MMFs seen in the 3-phase analysis and applying the extra 6-phase MMF cancellation criterion; if k = 1, 13, 25 etc then m’ = 1, -5, 7, -11, 13, -23, 25, etc, in which case the zero criterion is met when m’ = -5, 7, -17, 19, etc. If k = 7, 19, etc. then the same series for m’ exists but this time the zero criterion is met when m’ = 1, -11, 13, -23, 25, etc. In addition, with k = 11, 23 etc then m’ = -1, 5, -7, 11, -13, 23, -25, etc, which gives zero results for all m’ = 5, -7, 17, -19, etc and k = 5, 17, etc then the zero criterion is met when m’ = -1, 11, -13, 23, -25, etc. If a zero result is returned in (15) then the magnetizing reactance for that space-time harmonic is short-circuited. Table II illustrates the time and space harmonics. In the introduction it was discussed that the previous literature assumes that the MMF was sinusoidal so that the higher MMF space harmonics, as illustrated in Fig. 4, could be neglected. From this analysis we can glean that the per-phase equivalent circuit in Figs. 2 and 3 are not quite correct. In Fig. 2, we can add in space harmonics for m = 11, 13, 23, 25, etc. and in Fig. 3 there will be space harmonics for m = 5, 7, 17, 19, etc. In effect, there will be additional blocking capacity in the rotor circuit for the cases where k = 5, 7, 17, 19, etc due to the space harmonics. This is a development from the theory put forward by the authors in [8].

Fig 5 One phase of a distributed 3-phase winding

Fig 6 One phase of a concentrated 3-phase winding to represent the

quasi 6-phase machine

TABLE II. 6-PHASE SYNCHRONOUS SPEEDS FOR TIME AND SPACE HARMONICS

Spatial harmonic m’

(ωs = supply frequency (rad/sec and p = pole pair number) Time Har

k ±1 ±5 ±7 ±11 ±13 ±17 ±19 ±23 ±25

1 s

pω s/c s/c

11s

pω−

13s

pω s/c s/c

23s

pω−

25s

pω

5 s/c s

pω 5

7s

pω− s/c s/c

517

s

pω 5

19s

pω− s/c s/c

7 s/c 75

s

pω− s

pω s/c s/c

717

s

pω− 7

19s

pω s/c s/c

11 11 s

pω− s/c s/c s

pω 11

13s

pω− s/c s/c 11

23s

pω 11

25s

pω−

13 13 s

pω s/c s/c

1311

s

pω− s

pω s/c s/c

1323

s

pω− 13

25s

pω

17 s/c 175

s

pω 17

7s

pω−

s/c s/c s

pω

1719

s

pω−

s/c s/c

19 s/c 195

s

pω−

197

s

pω s/c s/c

1917

s

pω−

s

pω s/c s/c

23 23 s

pω− s/c s/c

2311

s

pω 23

13s

pω− s/c s/c s

pω 23

25s

pω−

25 25 s

pω s/c s/c

2511

s

pω−

2513

s

pω−

s/c s/c

2523

s

pω−

s

pω

III. SIMULATION In this simulation we will assume that the only space

harmonics of any significance are the 5th, 7th, 11th, 13th, 23rd and 25th. We can consider that for each voltage harmonic there is a “shaft machine” which allows us to split the analysis up so that each harmonic is treated in a standard fashion, we will simulate the operation of both the 3-phase and 6-phase machine. We can then extract the current as a set of harmonics with magnitude and phase and then reconstruct the current waveform for comparison to the measured.

By inspection of (14) and comparison of Tables I and II it can be seen that we can actually use a 3-phase simulation package to obtain results, or at least to obtain the equivalent circuit parameters, and short-circuit the space harmonics. For a standard package, a simulation has to be run for each time harmonic where the voltage and frequency is set for each. Here, we will use PC-IMD from the SPEED laboratory, University of Glasgow, UK. In the case of the machine we are using here, it is a 4 pole machine with 24 slots and a single layer winding so that for 3-phase connection there are 2 coils per pole-pair per phase as shown in Fig. 5. For 6-phase winding this is 1 coil per pole-pair per phase However, (14)

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illustrates that Set 2 has the same MMF alignment as Set 1, which are concentrated windings. Therefore we can represent the 6 coils of Set 2 in the 6 phase machine as a parallel set of coils to the 6 coils in Set 1. We then end up with only 12 slots being used; this is shown in Fig 6. However adjustments must be made here to correct the phase resistance, phase leakage reactance and shorted harmonic winding reactances. The resistance of the phases in the 6 phase arrangement has to be doubled to that of the 3-phase “pseudo” arrangement and the slot leakage is incorrect. If we assume slot leakage is a square of the turns then there is no change here because of the parallel paths. The simulation assumes separate coils so that no change in end winding reactance is required. However, in terms of the pseudo calculation, the slot permeance should be halved to remove the mutual inductance in the simulation; the slot reactance should then be doubled when extracting the values.

If we assumed that the MMF harmonic content is minimal then we can simply sum the results from the simulation of each “shaft machine” and that is what the Authors carried out in [8] with fair results in terms of the current waveform correlation. A full set of tests and machine data were not available however these have now been carried out and the machines disassembled to get a more complete specification. To include the space harmonics, the equivalent circuit parameters have to be extracted and then a simulation conducted with the correct shorted harmonic reactances. The results from the simulations are put forward in the results section for comparison to the measurements.

Experience suggests that the correct harmonics to include are the 5th, 7th, 11th, 13th and also the harmonics either side of stator slot number, i.e., the 23rd and 25th harmonics [12]. In [8], space harmonics were not included in the 6-phase square-wave machine with only the fundamental MMF wave being considered. While fair agreement was found this was only obtained when a 9mH line inductance was included to cover stray and inverter inductance. In reality, the inverters were voltage fed and these inductances could not be traced. With the inclusion of the MMF space harmonics, the additional inductance was not needed since the stray inductance was in fact the inductance due to the MMF space harmonics.

The simulation of the 6-phase and 3-phase machines with 6-pulse operation required the writing of a special MATLAB script which broke the voltage down into the correct harmonic components and called, using Active-X, PC-IMD for each “shaft machine”. The correct input powers, output powers, torque were extracted (remembering that some harmonic voltages rotate forwards and some backwards) and summed. The current waveform was then reconstructed so that it could be compared to the measured waveform. The 3-phase simulation was carried out directly using PC-IMD.

One point that had to be address is that the core loss resistance was only present in the fundamental frequency “shaft machine” as shown in Fig. 4. It was set to a very high value in the higher harmonic voltage “shaft machines” in PC-IMD to negate the effect. Obviously the effect of the harmonic currents on iron losses needs further work but it is envisaged

that this is a stray loss of small magnitude, and this is verified in the experimental results.

IV. EXPERIMENTAL MACHINE Two identical 4-pole machines were used in the

experimental work however one was rewound as illustrated in Fig. 7. The 3-phase machine (on the left) has a distributed 3-phase winding with 57 turns per coil and 12 coils. There are 4 series-connected coils per phase with a wire diameter of 0.6 mm. The 6-phase winding also has 12 coils with 2 series-connected coils per phase. Each coil has 110 turns formed from two parallel strands each with a diameter of 0.4 mm. The rated full load torque was nominally 2 Nm which gives an approximate rating of 300 W. More parameters for the machines are in Table III. However it should be emphasized that these machines were purchased and the parameter table for use in PC-IMD was drawn up by measurement, lamination drawing and a manufacturer specification sheet. One of the main problems that the Authors have found with small machines such as these is the difficulty with parameter variation in manufacture. The issues here include steel lamination variation, stray losses due to surface losses in the rotor and stator, variation of resistivity and incorrect casting of the rotor cage aluminum, etc.

The 6-phase machine was fed from two 3-phase inverters with 180º conduction period. The line voltage under these conditions is a quasi square wave with a peak equal to the DC link voltage. The phase voltage is a 6 pulse wave shape. The 3-phase machine is also studied under similar 6-pulse inverter control conditions and with sinusoidal PWM control.

The inverters were rated 1.5 kW (which is somewhat larger than required) which used IGBTs type IRG4BC20F (fast switching) with 600V and 10 A ratings.

The DC link voltage could be varied and the efficiency of the drive system was analyzed by measurement of the DC link voltage and current, the input power (via a 3-phase power analyzer – the values from this had to be doubled for the 6-phase machine) and the output mechanical power, torque and speed via a torque transducer. The motors were loaded via a MAGTROL load unit.

Fig 7 3-phase (left) and 6-phase test motors

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TABLE III. MOTOR PARAMETERS

Pole number 4 Stator OD 90 mm Axial length 90 mm Stator Slots 24 Slot opening 1.9 mm Rotor diameter 55 mm Rotor bars 22 Rotor Fabrication Aluminum, closed slots Skew 1 stator slot Air-gap length 0.35 mm

V. RESULTS The 6-phase and 3-phase machines were simulated using the

software and compared to the measured values in terms of current and voltage waveforms and also the power and efficiency values to illustrate that the there can be an improvement in overall efficiency on some circumstances. The results in [8] used only the fundamental MMF (but with added line inductances) so a comparison is made under these conditions but without the added line inductance. There is obviously numerous load conditions that could be tested however it was decided to test the machines at no load, nominal half-load (1 Nm) and full load (2 Nm) for a DC link voltage of 110 volts for the 6-phase machine. The 6-phase and 3-phase machines had different windings; however it is worth comparing the results directly since the required line voltages are similar. For the 3-phase sine and square wave operation, it was attempted to maintain the half load and full load speeds constant and to adjust the line voltage to obtain the correct torques. However, this is not easy and in fact the full load speed for square wave operation was at a higher speed and voltage to prevent stalling of the system.

All the tests and simulations were conducted with delta connection. While star connection is possible, and this was simulated in [8], space constraints prevents reporting of operation under these conditions, but it was found to follow similar trends and returned similar results.

A. Direct comparision for Power, Torque and Speed Table IV shows a comparison of the performances of the

machines under full load operation. There are three sets simulations and tests: 6-phase 6-pulse (square wave operation), 3-phase 6-pulse and 3-phase sine wave (via a PWM inverter control). The inverter was not simulated although the efficiency of the inverter (or inverters in the case of 6-phase operation) was measured. There is a degree or variation between the simulated and measured due to parameter variation in these small motors as discussed above. However it can be seen that there is improved inverter efficiency when using the 6 pulse strategy of 3 to 4 %. It was found that the 6 phase machine had a much lower efficiency that than predicted although the 3 phase machine, under both 6 pulse and sinusoidal control, gave close results.

TABLE IV. COMPARISION BETWEEN SIMULATED AND MEASURED OPERATION AT FULL LOAD (T = 2 NM)

Motor operation (2 Nm) nominal) 6-phase Square 3-phase Square 3-phase Sine Variable Sim Test Sim Test Sim Test

Vdc link [V] 110 109 121 121 --- 133

Idc link [I] --- 4.62 --- 3.90 --- 3.91

Vrms line motor [V] 89.5 88.5 98.6 96.4 74.3 74.3

Irms motor [A] 2.34 2.26 3.43 3.81 4.07 4.39

Qin motor [VAr] 539.7 558 367 506.4 311 303

Frequency [Hz] 50 50 51.6 51.6 51.6 51.6

Torque [Nm] 2.4 2 1.97 1.96 1.86 2.01

Speed [rpm] 1343 1343 1427 1451 1337 1338

Inverter P [W] --- 503.6 --- 471.9 --- 520.0

Pin motor [W] 484.8 486.4 456.2 449.5 421 481.2

Pout motor [W] 335.9 281.3 295.1 297.6 261 281.0

Inverter Efficiency

[%] --- 96.6 --- 95.3 --- 92.5

Motor Efficiency

[%] 69.3 57.8 64.7 66.2 61.2 58.4

Overall Efficiency

[%] --- 55.9 --- 63.1 --- 54.0

It is difficult to compare the results for full load therefore a

half load set of tests were conducted and these are tabulated in Table V. The efficiencies between the simulation and test motors are now closer. Again, the inverter (or inverters) in 6 pulse operation is shown to be 3 or 4 % more efficient than the sinusoidal PWM operation.

The main problem with the results put forward here is that the two motors are different. To compare like with like then the simulations were run using the same motor and windings which are connected and controlled in either 6-pulse or sinusoidal operation. This is shown in Table VI where we take the 6-phase machine model and reconnect the windings for 3-phase operation then attempt to simulate the machine operation for different control strategies but the same loading.

Table VI more clearly illustrates two points. Firstly that the 6-phase machine, under 6-pulse operation, appears to absorb more reactive power and secondly that the 6-pulse system appears to deliver improved overall performance only under high loading conditions.

To address the first point, the 6-pulse 6-phase operation has high harmonic current content which will lead to an increased reactive power requirement. This is illustrated in the next section that compares the simulated and experimental

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waveforms. The second point is a little more complex however most machines are rated such that their rated operation is beyond the peak efficiency point (when increasing the load from zero. This is seen in Table VI when comparing the half load and full load. Also, the input power due the time harmonics tends to be electrical dissipation rather than torque production and also they are more constant with respect to load. Therefore as the motor is loaded up then the harmonic power becomes a smaller proportion of the loss and hence has less effect on the efficiency. This is illustrated in Table VII. Note that only the 5th and 7th space harmonics have input powers that can be considered as more than negligible. This illustrates that the harmonic currents generate reactive rather than active power.

TABLE V. COMPARISION BETWEEN SIMULATED AND MEASURED OPERATION AT HALF LOAD (T = 1 NM)

Motor operation (1 Nm) nominal) 6-phase Square 3-phase Square 3-phase Sine Variable Sim Test Sim Test Sim Test

Vdc link [V] 110 109 86 86 --- 107

Idc link [I] --- 2.48 --- 2.78 --- 2.29

Vrms line motor [V] 89.5 89.4 70 67.9 60 60

Irms motor [A] 1.77 1.71 2.35 2.66 2.57 2.75

Qin motor [VAr] 493.7 497 176.5 243 189 172

Frequency [Hz] 50 50 51.6 51.6 51.6 51.6

Torque [Nm] 0.979 1.0 0.98 1.0 0.81 1.01

Speed [rpm] 1442 1443 1430 1445 1423 1424

Inverter P [W] --- 270.3 --- 239.1 --- 245.0

Pin motor [W] 239.6 261.3 223.7 227.7 188.0 228.7

Pout motor [W] 147.8 151.1 147.0 151.3 121.0 151.1

Inverter Efficiency

[%] --- 96.7 --- 95.2 --- 93.3

Motor Efficiency

[%] 61.7 57.8 65.7 66.4 64.6 66.1

Overall Efficiency

[%] --- 55.9 --- 63.3 --- 61.7

B. Comparision of current waveforms Fig. 8 shows a comparison between the measured and

simulated current waveforms. This shows good agreement and this should be expected since the current and input power and reactive power comparisons in Table IV are close for 6-phase full-load operation. It was discussed earlier that the

fundamental MMF wave should not only be considered since the higher MMF waves add additional line inductances which are necessary to limit harmonic currents. This is illustrated in Fig. 9 where the harmonic currents are higher for the fundamental MMF only

TABLE VI. COMPARISION BETWEEN DIFFERENT DRIIVE SIMULATIONS AT HALF AND FULL LOAD

Full Load (2 Nm) Half Load (1 Nm)

Variable 6 phase square

3 phase sine

3 phase sine

6 phase square

3 phase sine

3 phase sine

Vline [V] 89.5 78.8 78.8 89.5 78.8 78.8

Iline [A] 2.34 4.17 4.4 1.77 2.96 3.03

Speed [rpm] 1343 1343 1327 1442 1443 1435

Torque [Nm] 2.4 2.21 2.4 0.98 0.86 0.98

Pin [W] 484.8 428.2 463.4 239.6 190.8 209.6

Qin [W] 539.7 375.7 382.8 493.7 356.1 355.9

Pout [W] 335.9 310.8 333.2 147.8 130.8 146.9

Efficiency [%] 69.3 72.58 71.89 61.7 68.56 70.1

TABLE VII. INPUT AND OUTPUT HARMONIC POWERS FOR 6-PHASE MACHINE

No Load [W] Half Load [W] Full load [W] Time harmonic Pin Pout Pin Pout Pin Pout

1 82.267 5.532 233.191 147.565 477.778 335.183 5 4.358 -0.001 4.678 0.305 5.162 0.660 7 1.327 -0.047 1.329 -0.033 1.345 -0.023

11 0.206 -0.013 0.204 -0.012 0.204 -0.011 13 0.059 0.006 0.059 0.006 0.059 0.006 17 0.047 0.003 0.046 0.003 0.046 0.002 19 0.028 -0.001 0.028 -0.001 0.028 -0.001 23 0.016 -0.001 0.016 -0.001 0.016 -0.001 25 0.006 0.000 0.006 0.000 0.006 0.000

-5

-4

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-1

0

1

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4

5

0 100 200 300

Angle [Elec Deg]

Cur

rent

[A]

-150

-100

-50

0

50

100

150

Volta

ge [V

]

SimulatedMeasuredline voltage

Fig 8 Comparison between simulated and measured currents for 6 pulse

6-phase operation at full load

IAS 2005 498 0-7803-9208-6/05/$20.00 © 2005 IEEE

-5

-4

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-2

-1

0

1

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4

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0 50 100 150 200 250 300 350

Angle [Elec Deg]

Cur

rent

[A]

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0

50

100

150

Volta

ge [V

]

SimulatedSimulated with fundamental MMFline voltage

Fig 9 Comparison between simulated currents with and without higher

MMF harmonics for 6 pulse 6-phase operation at full load

The measured and simulated current with 6-pulse operation at full load for the 3-phase machine is shown in Fig.10. Again good agreement is found. It can be observed that this waveform has a little less harmonic content than the 6-phase machine when comparing Fig. 8 with Fig. 10.

-8

-6

-4

-2

0

2

4

6

8

0 50 100 150 200 250 300 350

Angle [Elec Deg]

Cur

rent

[A]

-150

-100

-50

0

50

100

150

Volta

ge [V

]

SimulatedMeasuredline voltage

Fig 10 Comparison between simulated and measured currents for 6

pulse 3-phase operation at full load

VI. CONCLUSIONS The work put forward here illustrates that under certain

circumstances an induction motor drive system can operate more efficiently when fed from a 6-pulse inverter system rather than a PWM inverter supplying a sinusoidal voltage (although this is marginal for the small 300 W motors tested here). While the motor may be more inefficient, the inverter has reduced switching losses so that the overall system may be more efficient. The theory of operation of the induction motor is developed when operating firstly under 6-pulse 3-phase conditions and then as a 6-phase machine. It shows that careful consideration has to be made of both the spatial and time harmonics, especially for the 6-phase machine. Once this is done, standard analysis packages and techniques can be used; with the machine broken down into different “shaft

machines” in order to account for different voltage time harmonics. The model is verified experimentally using a small 3-phase and 6-phase machine. Efficiency measurements were taken to illustrate the possibility of improved efficiency under some circumstances. However, it was found that this was really only possible at high loading. One point that should be made is that further work will investigate larger drive machines that have different characteristics; and this can easily be achieved using the inverter used here as a model and conducting simulations of known induction motors of high power. Also further work is to investigate if there are any design improvements possible for the induction motor operating under 6 pulse supply conditions and also if there is any further improvements in supply operation.

REFERENCES

[1] R. O. C Lyra and T. A. Lipo, “Torque Density Improvements in a Six-Phase Induction Motor with Third Harmonic Current Injection”, IEEE Transactions on Industry Applications, Vol 38, No 5, pp 1351-1360, Sept 2001.

[2] T. M. Jahns, “Improved Reliability in Solid State AC Drives by Means of Multiple Independent Phase-Drive Units”, IEEE Transactions on Industry Applications, Vol IA-16, No 3, pp 32-331, May 1980.

[3] K. Gopakumar, V. T. Ranganthan and S. R. Bhat, “Split Phase Induction Motor Operation from PWM voltage Source Inverter”, IEEE Transactions on Industry Applications, vol 29, No 5, pp 927-933, Sept 1993.

[4] E. A. Klingshirn, “High Phase Order induction motors Part 1, Description and theoretical considerations”, IEEE Transactions PAS, Vol 112, No 1, Jan 1983.

[5] K. Oguchi, A. Kawaguchi, T. Kubota and N. Hoshi, “A Novel Six-Phase Inverter System with 60-Step Output voltages for High-Power motor Drives”, IEEE Transactions on Industry Applications, vol 35, No 5, pp 1141-1149, Sept 1999.

[6] K. K. Mohapatra, K. Gopakumar, V. T. Somasekhar and L. Umanand, “A Novel Modulation Scheme for a Six phase Induction motor with Open-End Windings”, IEEE Industrial Electronics Society Annual Conference, pp 810-815, 5-8 Nov 2002.

[7] Y. Zhao and T. A. Lipo, “Space Vector PWM Control of Dual Three-Phase Induction Machine Using Space Vector Decomposition”, IEEE Transactions on Industry Applications, Vol 31, pp 1100-1109, Sept 1995.

[8] D G Dorrell, R A McMahon and C Y Leong, “Analysis of an Inverter-Fed 6-phase Induction machine – the Effects of Voltage Harmonics on the Operation, International Conference on Electrical Machines, Krakow, Poland, Sept 2004.

[9] N.P. van der Duijn Schouten, N. G. Damasius and R. A. McMahon, “New Drive Concepts using Single Chip Inverters”, 36th IEEE Industry Applications meeting, Vol 3 pp 1715-1720, 30th Sept-1st Oct 2001.

[10] P. D. Milliband and R. A. McMahon, “Implementation and calorimetric verification of models for wide speed range three-phase induction motors for use in washing machines”, 39th IEEE Industry Applications meeting, Vol 4 pp 2485-2492, 3rd-7st Oct 2004.

[11] A. C. Smith and D. G. Dorrell, "The calculation and measurement of unbalanced magnetic pull in cage induction motors with eccentric rotors. Part 1: Analytical model", 1996 Proc. IEE Electric Power Applications, Vol. 143, No. 3, pp 193-201.

[12] P. L. Alger, “Induction Machines, Their Behavior and Uses”, Gordon and Breach Publishers, Third Edition, 1995, ISBN 2-88449-199-6.

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