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A Multi-Frequency PWM Scheme for Multi-LevelFive-Phase Open-End Winding Drives

Wahyu Satiawan, Martin JonesLiverpool John Moores University, School of Engineering, Liverpool, UK

Email: [email protected]

Abstract – This paper presents a multi-frequency pulse widthmodulation (PWM) scheme for a multi-level five-phase open-endwinding drive using the unified modulation technique. The open-end winding machine is supplied via a two-level voltage sourceinverter from each side of the windings. One inverter operates inten-step mode while the other is operated under PWM. Themulti-frequency PWM scheme is aimed to control the magnitudeof the fundamental output and to cancel low-order harmonicsproduced by the inverter operating in ten-step mode. Simulationresults show excellent performance resulting in multi-leveloutput voltages with a low THD. Implementation of the schemeis straightforward, compared with the space-vector modulation

based approach, since space vector transformation, sectoridentification, and look up tables are not required.

Index Terms – dual-inverter supply, open-end windingmachine, multi-frequency pulse width modulation, unifiedmodulation technique.

I. I NTRODUCTION

Multi-level and multi-phase voltage source inverters (VSI)have been attracting increasing research interest recently dueto their ability to overcome voltage and current limitations of

power semiconductors and their inherent ability to toleratefaults [1]-[2]. There are several configurations of multi-level

converters, the main ones being the neutral point clamped(NPC), the flying capacitor (FC) and cascaded converters [2-5].

Among the cascaded converters, the dual two-level inverterconfiguration has received growing attention due to its simplestructure. The additional diodes used in the diode-clamped(NPC) VSI are not needed, leading to a saving in the overallnumber of components. Furthermore, the issue of propercapacitor voltage balancing does not exist if the supply istwo-level at each winding side. Typically, three-phase VSIsare utilised. Application of such a dual-inverter supplyenables drive operation with voltage waveform equivalent tothe one obtainable with a three-level VSI in single-sidedsupply mode [5]. Such drives are being considered asalternative supply solutions in EVs/HEVs [6]-[7] and electricship propulsion [8].

Due to their well known advantages [1], multi-phase driveshave also been considered for similar applications as themulti-level drives. The only known examples where multi-

phase drive systems in open-end winding configuration have been developed are [9-11] where an asymmetrical six-phaseinduction motor drive was considered in [9]-[10].

This paper proposes a new, and relatively simple, PWMalgorithm for the five-phase open-end winding three-level

drive supplied by two two-level five-phase inverters. ThePWM algorithm is based on the decomposition of the there-level space vector decagon into a number of two-leveldecagons. A similar idea has been proposed in [12] for athree-phase NPC inverter and in [13] for a three-phase open-end winding drive. In the case of the five-phase open-endwinding drive the situation is significantly more complicatedsince both 2-D planes have to be considered. It is shown thatthe proposed modulation strategy is capable of achieving thetarget fundamental while eliminating any low-order harmonic

content in the output load phase voltage.The paper begins with a review of the five-phase two-leveldrive characteristics, which is followed by a generaldescription and mathematical model of the open-end windingtopology, along with mapping of the space vectors into the 2-D planes. Next, the proposed modulation method is described.It is shown that due to the nature of the five-phase topologyone of the inverters needs to operate with so called multi-frequency PWM. Finally, the performance of the proposedmodulation method is verified via simulation.

II. G ENERAL PROPERTIES OF TWO -LEVEL FIVE-PHASEDRIVES

Although the proposed modulation technique can beconsidered a carrier based PWM method the space-vectorapproach is an extremely useful tool when trying tounderstand the relationships which govern the performance offive-phase drives and the corresponding VSI modulationtechniques. A five-phase machine can be modelled in two 2-D sub-spaces, so-called - and x-y sub-spaces [14]. It can beshown that only current harmonic components which mapinto the - sub-space develop useful torque and torqueripple, whereas those that map into the x-y sub-space do notcontribute to the torque at all. A multi-phase machine withnear-sinusoidal magneto-motive force distribution presentsextremely low impedance to all non-flux/torque producingsupply harmonics and it is therefore mandatory that thesupply does not generate such harmonics. What this means isthat the design of a five-phase PWM strategy must considersimultaneously both 2-D sub-spaces, where the referencevoltage, assuming pure sinusoidal references, is in the first

plane while reference in the other plane is zero. Two-levelfive-phase inverters can generate up to 2 5=32 voltage spacevectors with corresponding components in the - and x-ysub-spaces. Active (non-zero) space vectors belong to threegroups in accordance with their magnitudes - small, mediumand large space vector groups. The magnitudes are identified

UPEC 2011 · 46th International Universities' Power Engineering Conference · 5-8th September 2011 · Soest · Germany

ISBN 978-3-8007-3402-3 © VDE VERLAG GMBH · Berlin · Offenbach

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)*(** ivvv (4)

In other words, when the magnitude of the referencevoltage exceeds the maximum value obtainable with oneinverter, one inverter is operated in six-step mode while thesecond inverter is modulated in the standard way.

It is well known that operation of a five-phase inverter inten-step mode without a controllable dc link leads to

uncontrollable fundamental output voltage magnitude andunwanted low order harmonics, which for the leg voltage can be expressed as a Fourier series as follows:

...]7sin71

5sin51

3sin31

[sin1

t t t t V t v dc

(5)

In a five-phase system, harmonics of the order 10 k ±1 ( k =0, 1, 2, 3...) map into the torque/flux producing subspace, - ,while harmonics of the order 10 k ±3 map into the x-ysubspace. They do not produce any useful torque/flux andsimply lead to large unwanted loss-producing currents. Thelarge currents are a consequence of the relatively smallimpedance presented in x-y plane. 10 k ±5 are zero-sequencecomponents. This leads to the requirement that the secondinverter must be able to not only control the fundamental butalso eliminate the unwanted low order harmonics, which are

produced by applying only the large vector in from oneinverter. This causes unwanted harmonics in both planessince a large vector has a corresponding non-zero value in thesecond, x-y plane [14]. In order to achieve this objective, thesecond inverter modulation scheme will need to operate in

both the - and the x-y planes. Such PWM modulators areknown as multi-frequency PWM modulators and were firstdeveloped in order to control multiphase multi-motor drivesystems [15].

The proposed scheme is realised by utilizing two separatetwo-level modulators. Fig. 3 shows the voltage vectors thatare used by the modulators. Inverter 1, which operates in ten-step mode, applies a single vector in one switching period.The vectors are mapped in the points of the outer ring ofdecagon (labelled as A, B, C , D, E , F , G, H , I , J in Fig. 2);these correspond to the large vectors in a two-level modulator(Fig. 3(a)). The modulator for inverter 2, which operates inPWM mode, is able to choose from all 32 voltage vectors(small, large, medium and zero) and select suitable 4 activeand one zero vectors in-order to control the fundamental andcancel unwanted harmonics in the output. The multi-frequency PWM is employed for the higher modulation

indices (0.525 < M 1.05). In the lower modulation indexregion ( M 0.525) only one inverter operates, which revertsthe system into single-sided two-level SVM operation mode.Fig. 4 shows the voltage reference waveform (trace (c)) of themulti-frequency modulator for modulation index of 1.05. It isobtained by subtracting the ten-step mode inverter phasevoltage output (trace (b)) from the total voltage reference(trace (a)) and inverting the signal. It can be noticed that theresulting reference of the PWM modulator is multi-frequency.The non-sinusoidal reference is difficult to achieve using thespace-vector modulation technique. The control methoddeveloped in the paper adapts the unified PWM technique

5cos2

5

21

dcV

5cos2

52

2

dcV

Fig. 3. The voltage space vectors employed for ten-step modulator (a) and themulti-frequency modulator (b).

Fig. 4. Generation of the voltage references for multi-frequency modulator.

[16] to function as a multi-frequency PWM modulator, whichis capable of controlling the fundamental, eliminatingunwanted low-order harmonics and maintaining themaximum dc link utilisation. The technique is well-established for three-phase systems and has been recentlyextended to the single sided two-level five-phase system, asreported in [17]. Implementation of the unified method isadvantageous as the computational load is greatly reducedowing to the removal of the space vector transformation,sector identification and switching state look-up table.

V. U NIFIED VOLTAGE MODULATION TECHNIQUE FORMULTI -FREQUENCY OUTPUT GENERATION

In the conventional SVM scheme, calculation of dwelltime is based on the magnitude of the voltage reference spacevector and its relative angle with respect to the reference axis.Space vector transformation, sector identification andinformation regarding the selected vectors are required to

perform the task. In the unified PWM technique the dwelltime is determined directly from instantaneous values of the

phase voltage reference. This is so since the effective timeevaluated in the conventional SVM is just the differencevalue between two application times corresponding to the

phase voltage [16], [17]. The basic principle of the method isshown in Figs. 5 and 6.

In what follows it is assumed that the inverter 2 output ismodulated. Regardless of the sector where the referencevector is, the application time for each phase voltage can bedefined using:

0

0**********

esdscsbsas

esdscsbsas

T T T T T

vvvvv (6)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-400

-300

-200

-100

0

100

200

300

400References for modulation index, M = 1.05

( V )

Time (s)

(a)

(c)

(b)



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**

2

**

2

**

2

**

2

**

2

,

, , ,

esdc

sesds

dc

sds

csdc

scsbs

dc

sbsas

dc

sas

vV T

T vV T

T

vV T

T vV T

T vV T

T

(7)

where T s is the switching period. The application times, T as ,T bs , T cs , T ds and T es which are then named as “imaginaryswitching times” are proportional to the instantaneous phasevoltage reference magnitude. The effective time, T eff isdefined as the difference between the maximum andminimum values among T as , T bs , T cs , T ds and T es. The effectivetimes are the time durations of the active vector application.The time duration of zero vector, T zero is obtained bysubtracting from T s the effective time [16]:

},,,,min{

},,,,max{

min

max

minmax

eff s zero

esdscsbsas

esdscsbsas

eff

T T T

T T T T T T

T T T T T T

T T T

(8)

In order to obtain a symmetrical switching pattern overswitching period, the zero voltage has to be distributedequally. The offset time T offset is required:

min)2/( T T T zerooffset (9)

The actual switching times for each inverter leg can beobtained by the time shifting operation as follows:

offset es ge

offset ds gd offset cs gc

offset bs gboffset as ga

T T T

T T T T T T

T T T T T T

,

,

(10)

VI. S IMULATION VERIFICATION

In order to verify the drive’s performance a series ofsimulations were performed. The dc link voltage of eachinverter is 300 V ( 2/21 dcdcdc V V V ), giving an effectivedc link voltage of 600 V when M > 0.525. The switchingfrequency of the modulated inverter is 2 kHz. Ideal operationof the inverters is assumed, meaning that effects due to thedead-time and semiconductor voltage drops were neglected.Fig. 7 shows the load phase voltage and the inverter’s legvoltage waveforms and spectra at the boundary betweenregions where the PWM modulated inverter reduces thefundamental voltage, created by the ten-step inverter, or addsto it (this takes place when M = 0.6366). The converterachieves the reference fundamental with minimum low orderharmonics. The leg voltages of each inverter show that theharmonics created by the ten step inverter are counter

balanced by the modulated inverter and the fundamental isoverwhelmingly provided by the ten step modulator. Thismeans that the modulated inverter is only compensating theunwanted harmonics. In order to examine the drives

performance over the complete linear operating rangesimulations were performed with modulation index of 0.1 –1.05 in 0.05 increments. The THD of the phase output voltageand the respective and x-component is shown in Fig. 8. Itcan be seen that the THD remains low for the entire linear

Ts

Phase a

Tas

t1

Phase b

Tbs

t2

Phase c Vdc/2Tcs

t3

Phase d

Tds

t4

Phase e

TesTeff

Tmin Tmax

Fig. 5. Illustration of the imaginary switching times.

Fig. 6. Actual switching pulse pattern.

operating region. The performance is significantly improvedwhen compared to the single-sided two-level drive in linewith the higher number of phase voltage levels available

particularly in the higher modulation index.

Next, the phase variable model of the five-phase machineis used and the drive is operated in open-loop V/f mode. Thevoltage reference profile is such that the supply frequency ofthe machine is ramped from zero to 50 Hz in 0.5s. At theoperating frequency of 50 Hz the maximum modulation indexis reached ( M = 1.05). Voltage boost is not applied. Theacceleration transient is presented in Figs. 9 and 10 for 25 Hz( M = 0.525) and 50 Hz ( M = 1.05), respectively along withthe steady-state load phase voltage waveform and spectrum. Itcan be seen in Fig. 9 that no voltage reference is applied toinverter 2 when M = 0.525 and so the drive operates in two-level mode. For this reason the steady-state phase voltagecontains only nine levels. However, the spectrum is muchimproved when compared with its single sided two-levelequivalent due to the 50% reduction in the effective dc linkvoltage. Fig. 10 shows that, as soon as M > 0.525 (at t = 0.25s) inverter 1 operates in ten-step mode, while inverter 2operates in multi-frequency PWM mode. At t = 0.5 s thereference frequency is reached and the modulation index ismaximum, M = 1.05. The drive is operating in multi-levelmode and the steady-state phase voltage now comprises 15levels. The torque ripple is mininal and the stator current issinusiodal without any low order harmonics. The load phasevoltage spectra indicate absence of unwanted low-order

Ts Ts

A+gating

Tga

B+gating

Tgb

C+gating

Tgc

D+ gating

Tgd

E+ gating

Tge Teff t31 /2 to/2



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harmonics and the target fundamental voltages have been metin both cases.

VII. C ONCLUSION

A multi-frequency PWM scheme for multi-level dual-inverter fed open-end winding drives has been successfully

Fig. 7. Stator phase and inverter leg voltage waveforms and spectra for M =0.636, f = 30.31Hz.

Fig. 8. Total harmonic distortion (THD) of the stator phase voltage and the -axis and x-axis components.

developed based on the unified PWM technique. When M <0.525, the converter operates in two-level mode utilising asingle inverter. When the reference fundamental exceeds thecapabilities of a single inverter ( M> 0.525), one inverter is inten-step mode and the other is multi-frequency modulated. As

Fig. 9. Motor acceleration under V/f control (ref. 25 Hz, M = 0.525): invertermodulation signals, speed, torque, stator current and steady-state stator phase

voltage waveform with spectrum.

0.74 0.75 0.76 0.77 0.78 0.79 0.8-400

-200

0

200

400fund = 190.6587(pk) THD = 0.58257 levels = 13

( V )

Time (s)

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

( V r m s )

0.74 0.75 0.76 0.77 0.78 0.79 0.8-200

-100

0

100

200Inverter 1 leg "A", Mod index =0.63659

( V )

Time (s)

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

( V r m s

)

0.74 0.75 0.76 0.77 0.78 0.79 0.8-200

-100

0

100

200Inverter 2 leg "A" , Mod index =0.63659

( V )

Time (s)

0 100 200 300 400 500 600 700 800 900 10000

20

40

60

( V r m s )

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

Modulation index

T H D

Phase voltage

-axisx-axis

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

I n v .

1 .

l e g

" a " m o

d .

s i g n a

l ( p

. u . )

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

I n v .

2 .

l e g

" a " m o

d .

s i g n a

l ( p

. u . )

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-5

0

5

10

15

T o r q u e

( N m

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

200

400

600

800

S p e e

d ( r p m

)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-8

-6

-4

-2

0

2

4

6

8

Time (s)

S t a t o r p

h a s e

" a " c u r r e n

t ( A )

0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8-300

-200

-100

0

100

200


( V )

Time (s)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

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( V r m s )



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a result the converter is operated in multilevel mode. Themulti-frequency modulated inverter is used to control thefundamental voltage and eliminate any low order harmonicscreated by the ten-step mode inverter. The method has beenverified by simulation.

Fig. 10. Motor acceleration under V/f control (ref. 50Hz, M = 1.05): invertermodulation signals, speed, torque, stator current and steady-state stator phase

voltage waveform with spectrum.

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[3] S. Kouro, M. Malinowski, K. Gopakumar, J. Pou, L. G. Franquelo, B.Wu, J. Rodriguez, M. A. Perez and J. I. Leon, “Recent advances andindustrial applications of multilevel converters,” IEEE Trans. on Ind.

Electr ., vol. 57, no. 8, 2010, pp. 2553-2580.[4] S. Lu, S. Mariethoz and K. A. Corzine, “Asymmetrical cascade multi-

level converters with noninteger or dynamically changing DC voltageratios: Concepts and modulation techniques,” IEEE Trans. on Ind.

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motor drive topologies for low-voltage, high-power EV/HEV propulsion systems, ” IEEE Proc. Int. Symp. on Ind. Electronics. ISIE ,Rio de Janerio, Brazil, 2003, pp. 379-384.

[6] C. Rossi, G. Grandi, P. Corbelli and D. Casadei, “Generation system forseries hybrid powertrain based on dual two-level inverter,” Proc. Eur.

Power Elec. and Appl. Conf. EPE, Barcelona, Spain, 2009, CD-ROM paper 0978-13043073.

[7] Y. Kawabata, M. Nasu, T. Nomoto, E. C. Ejiogu and T. Kawabata,“High-efficiency and low acoustic noise drive system using open-winding AC motor and two space-vector-modulated inverters,” IEEETrans. on Ind. Electr., vol. 49, no. 4, 2002, pp. 783-789.

[8] L. Shuai and K. Corzine, "Multilevel multi-phase propulsion drives," in IEEE Electric Ship Technologies Symposium , Philadelphia, PA, USA,2005, pp. 363-370.

[9] G. Grandi, A. Tani, P. Sanjeevikumar and D. Ostojic, “Multi-phasemulti-level AC motor drive based on four three-phase two-levelinverters,” in Proc. Int. Symposium on Power Electronics., Electrical.

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[10] K. K. Mohapatra and K. Gopakumar, “A novel split phase inductionmotor drive without harmonic filters and with linear voltage control forthe full modulation range,” EPE Journal, vol. 16, no. 4, 2006, pp. 20-28.

[11] E. Levi, M. Jones, and W. Satiawan, “A multiphase dual-inverter

supplied drive structure for electric and hybrid electric vehicles,” in Proc. IEEE Vehicle Power and Propulsion Conf., VPPC, Lille, France,2010, CD-ROM paper 95-45603.

[12] G.Shiny and M.R.Baiju, “Space vector PWM scheme without sectoridentification for an open-end winding induction motor based 3-levelinverter,” Proc. IEEE Ind. Electronics. Soc. Annual Meeting IECON,Porto, Portugal, 2009, pp. 1310-1315.

[13] E.G. Shivakumar, K. Gopakumar, S.K. Sinha, A. Pittet and V.T.Ranganathan, “ Space vector PWM control of dual inverter fed open-end winding induction motor drive”, EPE Journal, vol. 12, no. 1, 2002,

pp. 9-18.[14] D. Dujic, M. Jones and E. Levi, “Generalized space vector PWM for

sinusoidal output voltage generation with multi-phase voltage sourceinverters,” Int. J. Ind. Electronics. and Drives, vol. 1, no. 1, 2009, pp. 1-13.

[15] D. Dujic, G. Grandi, M. Jones and E. Levi, “ A space vector PWM

scheme for multi-frequency output voltage generation with multi-phaseVoltage Source Inverter,” IEEE Trans. on Ind. Electr., vol. 55, no. 5,2008, pp. 1943 – 1955.

[16] D.W. Chung, J.S. Kim and S.K. Sul, “Unified voltage modulationtechnique for real-time three-phase power conversion,” IEEE Trans. on

Ind. Appl., Vol. 34, no. 2, 1998, pp. 374 – 380.[17] A. Iqbal, and M.A. Khan, “A simple approach to space vector PWM

signal generation for a five-phase voltage source inverter,” Proc. IEEE- INDICON ., Kanpur, India, 2008, vol.2, pp. 418 – 424.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

I n v .

1 .

l e g

" a " m o

d .

s i g n a

l ( p

. u . )

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I n v .

2 .

l e g

" a " m o

d .

s i g n a

l ( p

. u . )

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-10

0

10

20

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( N m

)

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500

1000

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d ( r p m

)

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h a s e

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0


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