Abstract--Multi-phase Permanent Magnet Synchronous Motors (M-PMSM) have the many advantages over conventional 3-phases PM ones. Their feasibilities and performances are described and proven in many literatures. M-PMSM is useful for large systems such as electrical ship propulsion, locomotive traction or electrical vehicles applications. Characteristics of Independent Multi-phase Permanent Magnet Synchronous Motor (IM-PMSM) are similar to M-PMSM, but the control concept is considerably different. IM-PMSM has basic problems that multiple three harmonics are generated at each phase due to the structure of the separated windings. The main goal of this paper is developing the drive system of IM-PMSM, proving the cause of harmonics and proposing a new method to eliminate harmonics.

Index Terms-- independent multi-phase motor (IM-PMSM), multiple d-q-n space concept, third harmonic, dead-time, current distortion

I. INTRODUCTION

Multi-phase (more than 3-phases) Permanent Magnet Synchronous Motors (M-PMSM) have been studied for a long time. But it is only recently that they have attracted a considerable amount of interest in the research community and industry worldwide [1]. M-PMSM is useful for large systems such as ship of electrical propulsion, locomotive traction or electrical vehicles applications, because it has the many advantages over conventional 3-phases such as reducing the amplitude of torque pulsation, lowering the DC link current harmonics, higher reliability and decreasing the current stress of switching devices [2]-[8]. Likewise, when one of the power switches or windings is faulted, the average torque loss is less than conventional motors [3]. In case of high-capacity M-PMSM, composition of inverter system is possible by switching devices of small capacity, since the controlled power is divided on several inverter legs [9][10].

Characteristics of Independent Multi-phase Permanent Magnet Synchronous Motors (IM-PMSM) are similar to M-PMSM, but the control concept is considerably different. IM-PMSM's utility factor of voltage is higher than M-PMSM. Although failure of any one phase-drive unit does degrade motor performance somewhat, the urgency of immediate repairs is reduced since system shutdown is not required [11].

Voltage Source Inverter (VSI) to control motors generate harmonics due to dead-time and nonlinear characteristics of the switching devices and etc. The dead-time problem of the conventional 3-phases machine

has already been investigated in the several technical literatures, and various solutions have been tried [23].

Therefore, in this paper, not only vector control method based on a multiple d-q-n spaces concept but also a new dead-time compensation method are proposed to reduce the harmonics due to the dead time and nonlinear characteristics of the switching devices. The simulation and experimental results are presented to verify the proposed methods.

II. INDEPENDENT SIX-PHASE PMSM Independent Six-phase Permanent Magnet

Synchronous Motor (IS-PMSM) has six stator windings spatially shifted by 60 electrical degrees with virtual separated neutral points as shown in Fig. 1. Moreover, inverter is composed by separated six H-bridge inverters as shown in Fig. 2. The IS-PMSM's back-EMFs are sinusoidal waveforms as shown in Fig. 3.

Fig. 1. Stator equivalent circuit of IS-PMSM

0 Vdc

+

a-phase b-phase f-phase

A B F

Sa1

Sa2

Sa3

Sa4

Sb1

Sb2

Sb3

Sb4

Sf1

Sf2

Sf3

Sf4

VAH VAL VBH VBL VFH VFL

Fig. 2. Independent Six-phase Inverter

Vector Control and Harmonic Ripple Reduction with Independent Multi-phase PMSM

Chae-Bong Bae*, Young-Gook Kim*, Jang-Mok Kim*, Hyun-Cheol Kim** * Pusan National University, Busan, Korea

** Agency for Defense Development, Chin hae, South Korea

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978-1-4244-5393-1/10/$26.00 ©2010 IEEE

e a

0 π31 π 3

2 π 34 π 3

5 π π2

0

e b e c e d e e e f

Fig. 3. Back-EMF of IS-PMSM

A. Mathematical modeling of IS-PMSM IS-PMSM's voltage equation and matrix A and B can

be represented in (1) and (2) where the sum of self-inductance and mutual-inductance are assumed to be synchronous inductance L.

x x x xdv Ai B i edt

= + + (1)

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

R LR L

R LA B

R LR L

R L

= =

Where x means specific phase, ex, ix and R are each phase's back-EMF, current and stator winding's resistance, respectively. The electrical torque is equal to mechanical torque if the stator losses are neglected in this analysis. So, output torque equation can be expressed as in (3).

6a a b b c c d d e e f fe s se

m m m

e i e i e i e i e i e iP E ITω ω ω

+ + + + += = = (3)

Where Pe , Es Is , and m are the electrical power, RMS of back-EMF, RMS of current and mechanical angular velocity of motor, respectively. The torque equation of the rotational motion can be expressed as in (4).

me m m m L

dT J B Tdtω ω= + + (4)

Where Jm , Bm and TL are the inertia of the rotor, static coefficient of friction and load torque, respectively. Fig. 4 shows IS-PMSM's block diagram that execute Laplace-Transform using the equations from (1) to (4).

Fig. 4. Block diagram of IS-PMSM

B. Transformation of IS-PMSM Six-phase space vector can be equivalently represented

by the following three-dimensional (3-D) complex space vector as shown in (5) and (6). d-axis is real axis, q-axis is a imaginary axis. d-q axes are related to output torque, but n-axis which is at right angle to both ds axis and qs

axis is loss element in the motor.

0 1 2 3 4 5

3

1 ( )3

n a b c d e f

s s sd q dq

j

f a f a f a f a f a f a f

f jf f

where a eπ

= − + − + −

= + =

=

(5)

1 ( )6n a b c d e ff f f f f f f= − + − + − (6)

Because Y-connected motors do not have (6n ± 3)thharmonics which in-phase at the each phase [12][13], not only sum of each phase variable, but also n-axis is always zero. However, independent-connected motor has (6n ± 3)th harmonics which in-phase at the each phase. Therefore, sum of each phase variable is not always zero, and then n-axis is not always zero. From (5), the space vector on the synchronously rotating reference frame can be defined as follows:

eje sdqs dqsf f e θ−≡ (7)

sdf

sfsq

f

saxisd

edf

eaxisd

eqf

θ

eaxisq

saxis

q

Fig. 5. Stationary reference frame and Synchronous reference frame

C. Switching method Space Vector PWM (SVPWM) technique is widely

used to control three-phase motors [24][25]. SVPWM can apply to IS-PMSM. Switching equation given to (8) because two switches in one pole between poles of H-bridge are alternately operated as (9). Moreover, the number of output voltage vectors is 729(36) as shown in TABLE I and Fig. 6 because there are 24 switches in the inverter as shown in Fig. 2.

3 21 41 32 2

{1,0, 1)

HB

HB

S SS SS S S

S

−−= − = −

∈ −

1 4

2 3

S S

S S

=

=

(2)

(8)

(9)

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TABLE I. PHASE VOLTAGES AND VOLTAGE VECTORS OF IS_PMSM

Fig. 6. Switching Vectors of IS-PMSM

However, because IS-PMSM's back-EMFs are continuous, if voltage vectors which are discontinuous and smaller than maximum magnitude (4/3)Vdc are removed, voltage vectors can be rearranged for 6 active voltage vectors and 2 zero voltage vectors as shown in TABLE II and Fig. 7.

TABLE II. PHASE VOLTAGES AND VOLTAGE VECTORS OF IS_PMSM

0.5

1

1.5

30

210

60

240

90

270

120

300

50

330

Sector1

Sector2

Sector4

Secto

r3

Sector5

Secto

r6

V1

V2V3

V4

V5 V6

V*

Fig.7. Six active voltage vectors

For example, a d-q axes reference voltage vector(V*)is located in sector 1, as shown in Fig. 7, switching signals can be expressed like Fig. 8.

Sa1

Sa2

Sc1

Sc2

Se1

Se2V0 V1 V2 V7 V7 V2 V1 V0

T2 T1T02

T02

T02

T02 T1 T2

Ts

Sd1

Sd2

Sf1

Sf2

Sb1

Sb2V0 V1 V2 V7 V7 V2 V1 V0

T2 T1T02

T02

T02

T02 T1 T2

Ts

(a) a, c, e phase (b) b, d, f, phase

Fig. 8. Switching signals when d-q axes reference voltage vector is located in sector 1

There is a problem that switching signals are necessarily discontinued during one sampling period in all sectors as shown in Fig. 8. So in this paper, unipolar SPWM is used to control IS-PMSM. In case of M-PMSM, utility factor of voltage of SPWM approach 61.2% of the DC link voltage (compared to SVPWM’s 70.7%) in the linear modulation range [24], because maximum phase voltage is (k-1/k)Vdc (but only under the condition of that k is phase-number and Vdc is DC link voltage). But in case of IS-PMSM, utility factor of voltage of SPWM approach 70.7% because maximum phase voltage is Vdc.So SPWM is more suitable for IS-PMSM. Output voltage (Vout) frequency of a unipolar SPWM becomes double when compared to fundamental frequency because Vout is twice a period of the carrier waveform as shown in Fig. 9. Therefore, THD (Total Harmonic Distortion), iron loss and current pulsation are lower than bipolar SPWM [16].

0 π π2

Vdc

-Vdc

Carrier waveformVH

*-VL

*

Vdc

-Vdc

VoutLVout VH V

1γ 7γ

tω

tω

Fig.9 . Unipolar SPWM waveform

III. ANALYSIS OF VOLTAGE DISTORTION OF PWM INVERTER

In PWM VSI, there is voltage distortion caused by dead-time and nonlinear characteristics of the switching devices. Also the clamping phenomenon of current around zero crossing point, called Zero-Current-Clamping (ZCC), affects voltage distortion because the phase current flows through the bottom/top diode during the dead-time [25]. It is convenient to analyze the dead-time effects from one phase leg of the inverter and extend the results to the other phase legs [21]. In case of Y-connection, Fig. 10 shows the average voltage distortion based on dead-time, turn-on/off delay time of switching devices and sampling period. Independent-connection of IS-PMSM is shown in Fig. 11.

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(Ideal)

(Real)

(Real)

(Ideal)

Sa

(Real)Van

Van

Van

Sa

Sa

Sa

Td + Ton Toff

T d + TonT off

T s T s

T d Td

ias 0

i as 0

Fig. 10. Switching patterns and output voltages of inverter of the conventional 3phase motor (Y-connected)

S4

S1

VH

S3

S2

VL

Vo

Td + TonToff

Td Td

Td + Ton Toff

Td + Ton

ToffToff

Td + Ton

Ts Ts

Td Td

ias 0

Fig. 11. Switching patterns and output voltages of inverter of IS-PMSM (Independent-Connected)

In case of Y-connection, the average distorted voltage (� V3y) according to the direction of the phase current (ias) can be represented in (10)[23].

3

3

, 02

, 02

d on offy dc

s

d on offy dc

s

T T TV V i

TT T T

V V iT

− − +Δ = >

+ −Δ = <

(10)

In case of independent-connection, average distorted voltage (� V1) is (11).

, 0

, 0

d on offI dc

s

d on offI dc

s

T T TV V i

TT T T

V V iT

− − +Δ = >

+ −Δ = <

(11)

Where, Ts, Td, Ton, Toff are sampling period, dead-time, turn-on and turn-off delay time. In case of Y-connection, the average voltage distortions may be expressed according to the direction of the respective phase currents as shown in (12).

3_

3_

3_

2 ( ) ( ) ( )2 3

2 ( ) ( ) ( )2 3

2 ( ) ( ) ( )2 3

d on offy as bs csas err dc

s

d on offy bs cs asas err dc

s

d on offy cs as bsas err dc

s

T T T sign i sign i sign iV VT

T T T sign i sign i sign iV VT

T T T sign i sign i sign iV VT

+ − − −=

+ − − −=

+ − − −=

IS-PMSM can be expressed like (13). From this equations, the average of the distorted voltage is large than the average of the distorted voltage of the Y-connected motor as shown in (12).

{ }

{ }

{ }

_

_

_

( )

( )

( )

d on offas err dc as

s

d on offbs err dc bs

s

d on offfs err dc fs

s

T T TV V sign i

TT T T

V V sign iT

T T TV V sign i

T

− − +=

− − +=

− − +=

(13)

Fig. 12 and Fig. 13 express waveforms of the (12) and (13), respectively.

vas_err

ias

vbs_err

vcs_err

ibs

ics

3 Δ V2

3 Δ V4 3 Δ V2

3 Δ V43 π2

3 π4

tω

tω

tω

Fig. 12. Phase current and distorted phase voltage waveforms in Three- phase (Y-Connected)

vas_err

vbs_err

vfs_err

ias

ibs

ΔV

ΔV

ΔV

ΔV

ΔV

ΔV

6 π2

6 π10

ifs

tω

tω

tω

Fig. 13. Phase current and distorted phase voltage waveforms in Six- phase. (Independent-Connected)

The distorted voltages of each phase of IS-PMSM using the FFT can be represented in (14). Each phase doesn’t affect.

_4 1 1 1sin sin 3 sin5 sin 7

3 5 7xs errV V t t t tω ω ω ωπ

= Δ + + + + (14)

(12)

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From (14), distorted current based on load impedance ZL(n mm) and load impedance angle n can be acquired like (15).

( ) ( )

( ) ( )

1 3

_

5 7

1 1sin sin3( ) 3 (3 )41 1sin5 sin7

5 (5 ) 7 (7 )

L Lxs err

L L

t tZ Z

I Vt t

Z Z

ω φ ω φω ω

π ω φ ω φω ω

− + −= Δ

+ − + − +

2 2

1

( ) ( )

tan

L e e

en

Z n R jnw L R jnw Lnw L

R

where ω

ψ −

= + = +

=

IV. DETECTION AND COMPENSATION OF DISTORTED CURRENT

A. Selection of control signal for compensation Assuming that 3th, 9th, 15th harmonics that low

harmonics at (6n ± 3)th harmonics are generated since dead-time and nonlinear characteristics of the switching devices exist at each phase current, total current equations as followings.

3 9 15

3 9

15

3 9

15

sin sin3 sin9 sin15

sin sin3 sin93 3 3

sin153

5 5 5sin sin3 sin93 3 3

sin15

as m a a a

bs m b b

b

fs m c c

c

i I t I t I t I t

i I t I t I t

I t

i I t I t I t

I

ω ω ω ωπ π πω ω ω

πω

π π πω ω ω

= − + + +

= − − + − + −

+ −

= − − + − + −

+ 53

t πω −

Where Ih3, Ih9, Ih15 are magnitude of 3th, 9th, 15thharmonics. If (16) is transformed into ds-qs-ns axes, the current of stationary reference frame ds-qs axes don't have harmonics, but the current of ns axis has the harmonics equal to the sum of harmonics in current of each phase like (17).

{ }

{ }

{ }3 9 15

1 2 26

sin

1 cos2 3

16

sin 3 sin 9 sin15

sds as bs cs ds es fs

m

sqs bs cs es fs m

sns as bs cs ds es fs

h h h

i I I I I I I

I t

i I I I I I t

i I I I I I I

I t I t I t

ω

ω

ω ω ω

= + − − − +

= −

= + − − =

= − + − + −

= + +

(17)

Likewise, synchronous reference frame de-qe axes are ideal as well as stationary reference frame like (18).

( ) ( )( ) ( )

cos sin 0

sin cos

e s sds e ds e qs

e s sqs e ds e qs m

e sns ns

I t i t i

I t i t i I

i i

ω ω

ω ω

= + =

= − + =

=

(18)

Therefore, sum of the (6n ± 3)th harmonics in each phase is easily detected by d-q-n reference frame transformation.

B. The proposed compensation method Fig. 14 shows the proposed compensation method to

detect and compensate the distorted real currents. The detected (6n ± 3)th harmonics through the d-q-n reference frame transformation are controlled to zero by the proposed compensator.

Stator current & Electrical angle

a b c d e f eθ

dqs*

xspK

Synchronous DQ-axis Current Regulators

nsi

dqsi

dqs_ffv

nsi *

SPWM

Independent Multi-PhasePMSM

xsie

e

nsie

e

dqsie

dqsie*

e*

v e*ev

ns*v e

sKi

eθ

eθ

Encoder

Proposed Current Pulsation Compensator

pK

2462

2

22

2

2ns_ffv e* =0

dsi e

qsi e

nsi e

Synchronous Frame

eθ(6n 3)=

2

Independent Multi-PhaseInverter

3 6

d-q-nTransform

A

B

C

D

E

F

sN

VDC

6

3 6

d-q-nTransform

Dead time TΔ

Fig. 14. Block diagram of applied current pulsation compensation algorithm.

The compensation voltage (vns)* generated by

compensator is added to each phase reference voltage like (19).

*

*

*

*

* * *

* * *

* * *

* * *

* * *

* * *

1 32 21 32 2

1 32 21 32 2

s sa d n

s s sb q nd

s s sc q nd

s sd d n

s s se q nd

s s sf q nd

v v v

v v v v

v v v v

v v v

v v v v

v v v v

= +

= + −

= + +

= −

= − +

= − −

V. SIMULATION RESULT

The proposed compensation method is simulated when distortion element is inserted into IS-PMSM at the rotor speed is 100[rpm]. Fig. 15 shows simulation waveform. Distortion of phase current is improved after start of compensation and maximum value of phase current is reduced. As known from Fig. 15 (b) and (c), the currents of the synchronous reference frame have no ripple component. The A phase current harmonics spectrum by FFT are shown in Fig. 16. After compensation, THD decreases from 26.1% to 0.1% because (6n ± 3)thharmonics are dispersed.

(15)

(16)

(19)

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(a) Phase currents (b) qes-axis current,

(c) des-axis current (d) ne

s-axis current. Fig. 15. Simulation results

(a) Before compensation, (b) After compensation. Fig. 16. FFT waveform of a-phase

VI. EXPERIMENTAL

In this paper, inverter set and IS-PMSM were made-up as Fig. 17 and 18 to verify the proposed compensation method.

Because voltage distortion at a low speed range is severer than that at a high speed range [21], the experimental tests have been performed at 100[rpm]. IS-PMSM's pole number is 48, so fundamental electrical frequency is 40Hz. The dead time is configured at 2[us], and turn-on/off delay time of the used switching devices in the inverter are 35[ns] and 2.0~2.9[ns], respectively.

24

Power Unit

Diode Rectifier DC_link

3φ 220V

Contrrol Unit

A/D

Independent Six-phase System Controller Board

Computer

DSP

FLEX10K100PWM pulse generator

M/Tprotectdecoder

TMS320VC33A/D AD7864

D/A DAC8420

Phase Conversion Signal

Gating Signal

C . T

Encoder

A

B

C

D

E

F

s N

E-phase

A-phaseB-phase

C-ph

ase

D-phase

6

Vdc

F-ph

ase

Fig. 17. Configuration of the system

As known from Fig. 19, phase current is the perfect sinusoidal waveform and maximum value of phase current is reduced after start of compensation. Fig. 21 shows the A-phase current harmonics spectrum by FFT. After compensation, (6n ± 3)th harmonics disappear. This means that the distorted current and voltage waveforms are completely compensated by using the proposed compensation algorithm.

Fig. 18. Configuration of the experimental system

VII. CONCLUSIONS

In this paper, vector control method based on a multiple d-q-n spaces concept for IS-PMSM (Independent Six-phase Permanent Magnet Synchronous Motor) and compensation algorithm for current distortion caused by dead-time and nonlinear characteristics of the switching devices were proposed. The proposed compensation algorithm uses the zero sequence component of d-q-n reference frame transformation as the input signal of the compensator.

This algorithm doesn’t require any additional hardware, the other information except magnitude of the phase current and position of rotor for reference frame transformation, complicated mathematical calculation and off-line experimental measurements. Moreover, this

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algorithm can be easily implemented, and applied to not only the steady state but also transient state.

All these are verified through the several simulation and experiments.

2

-2

0 [A ]

P h a se C u rre n t

1

-1

0 [A ]

D -a x is C u r re n t

2

0

1 [A ]

Q -a x is C u r re n t

0 .5

-0 .5

0 [A ]

0 [m s] 6 0 [m s]S ta r t o f C o m p e n sa tio n

N -a x is C u r re n t

a b c

(a )

(b )

(c )

(d )

(a) Phase currents (b) qes-axis current

(c) des -axis current (d) ne

s -axis current

Fig. 19. Experimental result

(a) Waveforms of ds-qs-ns axes currents (b) Lissajous circle and ds-qs-ns axes current (2-D) (c) Lissajous circle and ds-qs-ns axes current (3-D) (100 r/min)

Fig. 20. Waveforms of Lissajous circle after compensation

1

0

[A]

100Hz/Div

1

-0.5

[A]

1th

3th

1th

3th

(a)

(b)

(a) Before compensation (b) After compensation.

Fig. 21. FFT of a-phase current

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[19] Takashi Sukegawa, Katsuhiro Mizuno, Takayuki Matsui, Toshiaki Okuyama,"Fully Digital, Vector Controlled PWM VSI-Fed ac Drives with an Inverter Dead-Time Compensation Strategy",IEEE Trans. on Industrial Applications. Vol.27, No.3, pp.552-559, 1991.

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