vector weighting approach and vector space decoupling

Research ArticleVector Weighting Approach and Vector SpaceDecoupling Transform in a Novel SVPWM Algorithm forSix-Phase Voltage Source Inverter

PengWu1 Lei Yuan 2 Zhen Zuo1 and JunyuWei3

1College of Artificial Intelligence National University of Defense Technology Changsha 410073 China2Institute of Communications Engineering The Army Engineering University of PLA Nanjing 210007 China3College of Electric and Information Engineering Hunan University of Technology Zhuzhou 412007 China

Correspondence should be addressed to Lei Yuan leiyuanvqqcom

Received 12 February 2019 Revised 13 April 2019 Accepted 6 May 2019 Published 13 June 2019

Academic Editor Zhixiang Zou

Copyright copy 2019 PengWu et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

For six-phase permanent-magnet synchronous motor (PMSM) which has two sets of Y-connected three-phase windings spatiallyphase shifted by 30 electrical degrees to increase the utilization ratio of the DC bus voltage a novel space vector pulse widthmodulation (SVPWM) algorithm in full modulation range capability based on vector weighted method is proposed in this paperThe basic vector action time of SVPWM method is derived in detail employing vector space decomposition transformationapproach Compared with the previous algorithm this strategy is able to overcome the inherent shortcomings of the four-vector SVPWM and it achieves smooth transitions from linear to overmodulation region Simulation and experimental analysesdemonstrate the effectiveness and feasibility of the proposed strategy

1 Introduction

Compared with the pulse width modulation (PWM) controlalgorithm for conventional three-phase motors the PWMmethod for six-phase motors is more flexible [1ndash6] Atpresent carrier-type PWM algorithm permanent-magnetsynchronousmotor SVPWMalgorithm and current hystere-sis PWM algorithm are three of the PWM algorithms thatare commonly used for multiphase two-level voltage sourceinverter (VSI) [7 8] However the current hysteresis PWMalgorithm is unsuitable for high power algorithms In recentyears carrier-type PWMalgorithms and SVPWMalgorithmsthat can be applied to multiphase motor systems have beenextensively studied

The PWM algorithm for multiphase inverters aims toeliminate low-order harmonic components as much as pos-sible which is different from that for the three-phase motorsystem [9ndash11] As these low-order harmonic componentscould result in the loss of the motor by leading to a largeamount of stator harmonic current components in the x-ysubspace In order to increase the utilization ratio of the DC

bus voltage multiphase carrier-type PWM algorithm basedon zero-sequence signal injection is applied for multiphaseinverter system which is composed of several three-phasewindings In particular the reference voltage vector can bedecomposed into two three-phase inverters sharing a com-mon DC bus voltage when used in practice After that thecarrier-type PWM algorithm based on dual zero-sequenceinjection can be used [12 13] Although this method is easyfor digital realization it is not an optimal PWM algorithmformultiphase motors as there are fifth and seventh harmoniccomponents in the stator current

As the multiphase AC motors have been widely usedthe conventional inverter control algorithm is expected to beoptimized for them At present many researches are devotedto the implementation of the SVPWM algorithm One of themultiphase SVPWM algorithms is based on the maximumadjacent two vectors in which the voltage of the subspace issinus without considering the influence of the x-y subspacevoltage [14] In this connection there are more harmonicvoltages in the output and a larger fundamental voltagemodulation factor can be gotten in this way [15] While for

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 8729125 12 pageshttpsdoiorg10115520198729125

2 Mathematical Problems in Engineering

M

Vdc

A UB VC W

30∘

Figure 1 Six-phase converter drive system

multiphase AC motors the SVPWM algorithm will becomeincredibly complex And with the increase of the numberof motor phases the complexity of this direct calculationSVPWM algorithm will be greatly increased sector judg-ment vector duration calculation vector action sequencearrangement vector duration conversion into switchingaction time and other complex issues and the difficulty willbe greatly increased and the performance requirements ofthe controller will undoubtedly be greatly improved

In order to further improve the DC bus utilization rate atwo-vector and improved four-vector algorithm can be usedto increase the modulation factor by injecting the 5th and7th harmonics of the vector in the x-y subspaceThis methodonly increases the system loss and does not generate torqueripple But it only reached the maximum linear modulationrange When it is necessary to continue to improve the busvoltage utilization rate it can be said that the commonly usedthree-phase overmodulation technology [16 17] is extendedto the six-phase system and the 11th and 13th harmonicsare injected in the 120572-120573 subspace so that the maximum busvoltage utilization can be obtained However the torqueripple will be poor

In order to increase the utilization ratio of the DC busvoltage numerous studies have been done on improving thePWM algorithm for three-phase motor when overmodula-tion occurs As for the PWM overmodulation strategies formultiphase motors the fundamental amplitude of the outputreference voltage will rise by using vector space decom-position (VSD) in [10] transform matrix decomposition toget fundamental component of the x-y subspace [18] whilethe harmonic content of the reference voltage in the linearmodulation region also increases in that way

To solve above problems and to increase the utilizationratio of the DC bus voltage a novel SVPWM algorithmfor six-phase VSI with wide modulation range capabilitybased on vector weighted method is proposed in this paperThe concept of mid-vector presented in [18] is employed toobtain the expression for the time of algorithm of the activespace voltage vectors and using vector weighted method theovermodulation region is divided into three sections and theproposed SVPWM algorithm can also allow smooth transi-tion from a linear modulation region to an overmodulationregion The control strategy is verified through simulationanalysis

2 Dwell Time Calculation for Six-Phase VSI

The six-phase motor system fed by six-phase VSI is shownin Figure 1 There are two sets of Y-coupled three-phasestator windings which are spatially separated by 30∘ electricaldegrees Since there are two switch states for each bridge armthe six-phase inverter has 26 switch states According to theVSD transformation approach all of the space vectors can bemapped to the 120572-120573 x-y and o1-o2 three mutually orthogonalsubspaces The fundamental component and harmonics withthe order 12nplusmn1 (n=1 2 3 ) are mapped into the 120572-120573 subspace The harmonics with the order 6nplusmn1 (n=1 35 ) and the harmonics with the order 6nplusmn3 (n=1 3 5 )are mapped into the x-y subspace and the o1-o2 subspacerespectively The subspaces are divided into 12 sectors

To suppress the harmonic current component of statorcurrent a good four-vector SVPWM method should satisfythat the amplitude of the reference voltage vector in the 120572-120573subspace is maximum and in the x-y subspace is minimum

Mathematical Problems in Engineering 3

2

4

3b

r

a2

1

Figure 2 SVPWMmethod based mid-vector

In the 120572-120573 subspace any three adjacent voltage vectors canbe synthesized into a new vector called mid-vector and themid-vector has a same direction as the vector in the middleposition As shown in Figure 2 three adjacent basic vectorsv1 v2 and v3 are employed to synthesize into a mid-vector vaSupposing the dwell time of vector v2 is aTs the vectors v1 andv3 will be 05(1-a)TsThe amplitude of va in 120572-120573 subspace andx-y subspace respectively are as follows

10038161003816100381610038161003816Vmax101584010038161003816100381610038161003816 =

radic2 (radic3 + 1)6 119881119889119888 (119886 + radic32 (1 minus 119886)) (1)

10038161003816100381610038161003816Vmin101584010038161003816100381610038161003816 =

radic2 (radic3 minus 1)6 119881119889119888 (119886 minus radic32 (1 minus 119886)) (2)

where a is a positive constantSimilarly the three adjacent basic vectors v2 v3 and v4

are employed to synthesize into a mid-vector vb In this waywe can synthesize 12 voltage vectors which have the samedistribution as the traditional two vector SVPWMalgorithmbut the magnitude is different So the reference voltage vectorvr in 120572-120573 subspace can be synthesized by using 12 mid-vectors and the basic principle is the same as the traditionaltwo vector SVPWM algorithm the dwell time of mid-vectorsTa and Tb can be calculated according to (5) and |Vmax|mustbe replaced by the variable |Vmax

1015840| and the dwell time ofvectors v1 v2 v3 and v4 can be obtained by

1199051 = 05 (1 minus 119886) 1198791198861199052 = 119886119879119886 + 05 (1 minus 119886) 1198791198871199053 = 05 (1 minus 119886) 119879119886 + 1198861198791198871199054 = 05 (1 minus 119886) 119879119887

(3)

Moreover the relationship between 120579 and 120575 is obtained by120579 = 120575 + 12058712 minus 119896 minus 16 120587 (4)

where k is the sector with k=12 3 12According to the traditional three-phase SVPWM

method the dwell time of mid-vector can be used by

119879119886 =1003816100381610038161003816V11990310038161003816100381610038161003816100381610038161003816Vmax1003816100381610038161003816 sin (1205876) sin(

2119896 minus 112 120587 minus 120575)119879119904

linear

over-modulation I

over-modulation IIover-modulation III

Figure 3 Linear and overmodulation range

119879119887 =1003816100381610038161003816V11990310038161003816100381610038161003816100381610038161003816Vmax1003816100381610038161003816 sin (1205876) sin(120575 minus

2119896 minus 312 120587)119879119904(5)

where Ts is the switch period and |V119903| is the amplitude of thereference voltage vector

In the linear modulation range the control objectiveof four-vector SVPWM based on mid-vector method is toreduce the current harmonic component ie the amplitudeof reference is maximum in the 120572-120573 subspace and minimumin the x-y subspace For this purpose (1) is only to be satisfiedwith |Vmin

1015840| = 0 ie 119886 = 2radic3 minus 3 Equation (2) will changeinto |Vmax

1015840| = (3radic2minusradic6)3sdot119881119889119888The dwell time ofmid-vectorcan be obtained by replacing |Vmax| with |Vmax

1015840| and then theexpression of dwell time can be achieved by (3)

3 A Novel SVPWM Technology withWide Modulation Range

31 Overmodulation Region Division To facilitate the analy-sis the modulating index is defined by

119898 = 120587 1003816100381610038161003816V1199031003816100381610038161003816(2119881119889119888) (6)

when the reference voltage vector is more than this limitingvalue of |V119903| = 2119881119889119888radic3 and the inverter moves into theovermodulation region for 2119881119889119888radic3 lt |V119903| lt 2119881119889119888120587 Whenthe voltage vector is |V119903| = 2119881119889119888120587 the inverter operates in thetwelve-step mode as shown in Figure 3

The overmodulation region is further divided into threesubmodes the overmodulation region I (0907 lt 119898 le 0977)the overmodulation region II (0977 lt 119898 le 0988) and theovermodulation region III (0988 lt 119898 le 1)32 SVPWM Based on Vector Weighted Method When thesystem is running in different overmodulation region as


shown in Figure 3 the basic idea of vector weighting methodis to obtain a new integrated reference voltage vector byweighting the voltage vectors in different overmodulationregions with using the concept ofmodulation coefficient anduse the reference voltage vector to calculate the duty cycle ofPWM In order to facilitate calculation four voltage vectorsare defined in this paper such as 119881sin1 119881sin2 119881119889119900119889 and 119881119905119908119890119881sin1 is the voltage vector of the maximum linear modulationratio when the four vector SVPWM algorithm is used andthe trajectory is a circle with a radius of 119881119889119888radic3 119881sin2 isthe voltage vector corresponding to the two-vector SVPWMalgorithm and the trajectory is a dodecagon inscribed circlewith a radius of radic2(radic3 + 1)6 sdot 119881119889119888 sdot cos(12058712) 119881119889119900119889 isthe voltage vector that rotates on the contour line of regulardodecagon119881119905119908119890 is the voltage vector of twelve-step waveTheexpression of the four voltage vectorswill be shown as follows

119881sin1 = 119881119889119888radic3119890119895120575 asymp 0577119881119889119888 sdot 119890119895120575 (7)

119881sin2 = radic2 (radic3 + 1)1198811198891198886 cos 12058712119890119895120575 asymp 0622119881119889119888 sdot 119890119895120575 (8)

119881119889119900119889 = radic2 (radic3 + 1)1198811198891198886 cos (((2 (119896 minus 1) + 1) 12) 120587 minus 120579) cos 12058712119890119895120575

asymp 0622119881119889119888cos (((2 (119896 minus 1) + 1) 12) 120587 minus 120579)119890119895120575

(9)

119881119905119908119890 = radic2 (radic3 + 1)1198811198891198886 119890119895119896(12058712)asymp 0644119881119889119888 sdot 119890119895119896(12058712) 119896 minus 16 120587 le 120575 le 1198966120587

(10)

where 120575 is the angle between reference voltage vector Vr and120572 axis the relationship between 119881sin1 119881sin2 119881119889119900119889 and Vr isphase equality and the amplitude of four-vector is 0577Vdc0622Vdc 0629Vdc and 06366Vdc

321 Overmodulation Region I (0907 lt m le 0977) It canbe seen from (1) and (2) that the amplitude |Vmax

1015840| of funda-mental voltage vector will gradually become larger with anincrease of 119886 but the amplitude of harmonic subspace voltagevector will also gradually increase The modulation methodespecially will become two-vector SVPWM algorithm Toobtain the reference voltage vector Vr the amplitude need tobe satisfied with |V119903| = |Vmax

1015840| cos(12058712) it can be obtained asfollows

119886 = 12 1003816100381610038161003816Vlowast1003816100381610038161003816119881119889119888 minus 2radic3 minus 3 (11)

The unitary expression of dwell time can be achievedwhen (11) is substituted into (1) with considering function(3) When the reference voltage vector Vr is in the modulationregion I the amplitude of Vr will gradually increase to0622Vdc and the value of 119886 will also gradually increasefrom 2radic3 minus 3 to 1 Thus the smooth transition from linearmodulation region to overmodulation region I is realized

o

ok1VＭＣＨ2

B

lowast

(1 minus k1)VＭＣＨ1

A

B

Figure 4 The principle diagram reference voltage vector in over-modulation section

According to the principle of vector weighting methodthe overmodulation coefficient of overmodulation I is definedas

1198961 = 119898 minus 11989811198982 minus 1198981 (0 le 1198961 le 1) (12)

where m1=0907 and m2=0977 The value 1198961 will be set to 0when the vector Vr is in linear modulation region and thevalue 1198961 is set to 1 when Vr rotates along the inner-circle ofthe regular dodecagon

Like overmodulation I region to illustrate the processof adjusting the reference voltage vector sector 2 shown inFigure 4 will be taken as an example and 119881sin1 and 119881sin2 willbe used to reconstruct the reference voltage vector Vlowast ie

Vlowast = (1 minus 1198961)119881sin1 + 1198961119881sin2 (13)

According to (7) and (8) the expression of Vlowast in sector 2can be obtained by

1003816100381610038161003816Vlowast1003816100381610038161003816 = 119881119889119888radic3 (1 minus 1198961)

+ 2 (radic3 + 1)2 11988111988911988824 (119886 + radic32 (1 minus 119886)) sdot 1198961

(14)

The function (14) is substituted into (5) with considering(3) so the dell time of nonzero vector of each sector canbe calculated and then get the PWM waveform of theovermodulation I

Figure 5 shows the A phase voltage curve in whichVdc=1V and modulation ratio m increased from 0907 to0977 As can be seen from the figure with the gradualincrease of modulation ratio m the output voltage of the Aphase voltage has a certain distortion When m is close to0977 the reference voltage vector rotates along the inner-circle of the regular dodecagon

322 Overmodulation Region II (0977 lt m le 0988)When the vector Vr is in overmodulation II the outside ofthe regular dodecagon cannot be synthesized by the switch


Out

put p

hase

volta

ge (V

)

08

06

04

02

0

minus02

minus04

minus06

minus08

Modulation ratio (M)09709609509409309209109

Figure 5 The relationship between fundamental amplitude of output phase voltage and m in mode I

Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1

Modulation ratio (M)

0988098609840982098097809760974

Figure 6 The relationship between fundamental amplitude of output phase voltage and m in mode II

vector the amplitude or phase of Vr must be adjusted so thatthe average value of output voltage for the entire period isequal to the reference voltageTheovermodulation coefficientof over modulation II is defined as

1198962 = 119898 minus 11989821198983 minus 1198982 (15)

wherem3=0988 In addition the value of k2 is set to 0 whenvoltage vector is located in overmodulation I and the valueof value of k2 is set to 1 when voltage vector rotates along theregular dodecagon


1003816100381610038161003816Vlowast1003816100381610038161003816 = 2 (radic3 + 1)2 11988111988911988824 (1 minus 1198962) + 2 (radic3 + 1)

2 11988111988911988824 cos (1205876 minus 120593)1198962 (16)

In addition when the reference voltage vector is locatedoutside the regular dodecagon an unreasonable situation thatthe dwell time of the zero vector is less than 0 will happen So(3) is modified by

119905119894 = 1199051198941199051 + 1199052 + 1199053 + 1199054 119894 = 1 2 3 41199050 = 0

(17)

Figure 6 shows the A phase voltage curve in whichVdc=1V and modulation ratio m increased from 0974 to0988 As can be seen from the diagram with the gradualincrease of the modulation ratio m the distortion of theoutput phase voltage is more and more obvious when m isclose to 0988 the output voltage vector will rotate along thetrack of the regular dodecagon

323 Overmodulation Region III (0988 lt m le 1) Theovermodulation coefficient of overmodulation III is definedas

1198963 = 119898 minus 11989831 minus 1198983 (18)

where the value of k3 is set to 0 when voltage vector is locatedin overmodulation II and the value of k3 is set to 1 whenvoltage vector rotates along the twelve-step wave

Like overmodulation II region to illustrate the processof adjusting the reference voltage vector sector 2 shown inFigure 7 will be taken as an example and 119881119889119900119889 and 119881119905119908119890 willbe used to reconstruct the reference voltage vector Vlowast ie

Vlowast = 119881119889119900119889 (1 minus 1198963) + 1198811199051199081198901198963 (19)

Although the introduced 119881119905119908119890 vector makes the phaseof reconstructed voltage vector different from the reference


o

o

B

lowast

A

B

k3Vtwe

(1 minus k3)Vdod

r

Figure 7 The principle diagram reference voltage vector in overmodulation section III

Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1


Figure 8 The relationship between fundamental amplitude of output phase voltage and m in mode III

voltage vector it increases the output amplitude of voltagevector According to (9) and (10) the magnitude of thereconstructed voltage vector on the 120572-120573 axis can be obtainedas

1003816100381610038161003816Vlowast1205721003816100381610038161003816 = 2 (radic3 + 1)2cos120593 sdot 11988111988911988824 cos (1205876 minus 120593) (1 minus 1198963)

+ radic2 (radic3 + 1) cos (1205874) sdot 1198811198891198886 1198963(20)

10038161003816100381610038161003816Vlowast12057310038161003816100381610038161003816 = 2 (radic3 + 1)2 sin 120593 sdot 11988111988911988824 cos (1205876 minus 120593) (1 minus 1198963)

+ radic2 (radic3 + 1) sin (1205874) sdot 1198811198891198886 1198963(21)

The amplitude and phase of the reconstructed voltagevector can be obtained by

1003816100381610038161003816Vlowast1003816100381610038161003816 = radic1003816100381610038161003816Vlowast12057210038161003816100381610038162 + 10038161003816100381610038161003816Vlowast120573100381610038161003816100381610038162

120574 = arctan(10038161003816100381610038161003816Vlowast120573100381610038161003816100381610038161003816100381610038161003816Vlowast1205721003816100381610038161003816)

(22)

Figure 8 shows the A phase voltage curve in whichVdc=1V and modulation ratio m increased from 0987 to 1As can be seen from the diagram with the gradual increaseof the modulation ratio m the distortion of the output phasevoltage is more and more obvious when m is close to 1 theoutput voltage vector will rotate along the track of the regulardodecagon vertex

4 Simulation Results Analysis

To verify the validity of the proposed SVPWM algorithm ofsix-phase VSI with wide modulation range the simulationmodel is built in MatlabSimulink environment Figure 9shows the phase voltage and phase voltage harmonic spectrain different modulation regions The voltage is per unitvalue When m=0906 the harmonic voltages vx and vyare zero in x-y subspaces and the phase voltage is sinewave THD=0 As the modulation ratio increases the THDof phase voltage gradually increases and the low-orderharmonic components are mainly from 120572-120573 subspace and x-ysubspace

Figure 10 shows the voltage vector of the different mod-ulation ratios in the 120572-120573 and x-y subspaces Among themthe left side of Figures 9(a) 9(b) and 9(c) is 120572-120573 subspaceand the right side is x-y subspace It can be seen from


Phas

e vol

tage

(pu

)A

mpl

itude

(pu

) Fundamental (5Hz) = 0577 THD= 000

05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

1 2 3 4 5 6 7 8 9 10 110 1312Harmonic order

(a) m=0906

Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

Harmonic order43210 98765 13121110

5

(b) m=095

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p

u) Fundamental (5Hz) = 06288 THD= 1640

1

06

08

04

02

0

Harmonic order43210 98765 13121110

(c) m=098

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p

u)

Fundamental (5Hz) = 0637 THD= 3138

1

06

08

04

02

0

Harmonic order43210 98765 13121110

(d) m=1

Figure 9 Phase voltage and phase voltage harmonic spectra in different modulation regions

Figure 9 with the increase of the modulation ratio m thefundamental amplitude of voltage vector on 120572-120573 subspaceincreases gradually and the modulation ratio ism=0988 theoutput voltage vector tracks along the regular dodecagon andthe output voltage vector trajectory rotates along the trackof the regular dodecagon vertex with the modulation ratioof m=1 which verify the correctness of the above theoryanalysis

In addition although the harmonic component in the x-y subspace is gradually increasing the utilization ratio of DCvoltage is increased to a certain extent and the distortion rateand harmonic content of phase voltage increase graduallywith the increase of modulation ratio According to theabove analysis when the modulation ratio is higher thanthe linearmodulation region (mgt0907)modulation strategycompletely degenerates into two-vector SVPWM algorithmthe distortion rate of harmonic distribution is applicable to

all the two-largest-vector synthesis and only the harmonicamplitude is different

Figure 11 shows the modulation curve of SVPWMmethod with different modulation ratio it can be seen thatwhen the modulation ratio is m=1 the modulation wavebecomes a square wave signal

To verify the validity of the proposed SVPWM algorithmachieves the smooth transitions from linear to overmodula-tion region Figure 12 shows the curve of phase voltage whenthe modulation ratio is m increased from 0907 to 1 It canbe seen that as the modulation ratio increases stepwise thephase voltage waveform achieves a smooth transition fromlinear modulation region to overmodulation region

In order to illustrate the superiority of the control algo-rithmproposed in this paper Figure 13 shows the comparisonwith the traditional two-vector SVPWM algorithm and thesimulation results As can be seen from Figure 13 the THD


06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015

0604020minus02minus04minus06 015010050minus005minus01minus015

(a) Overmodulation region I (m=0974)

06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015


(b) Overmodulation region II(m=0988)

06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015


(c) Overmodulation region III(m=1)

Figure 10 The voltage vector of 120572-120573 and x-y subspaces in different modulation regions


1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020

Figure 11 The modulated wave with different modulation ratio

08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)

Figure 12 The modulated wave in different modulation regions

091 092 093 094 095 096 097 098 099 1modulation ratio m

0

10

20

30

40

50

THD

The method in the paperTwo-vector methodThe method in Ref[1]

Figure 13The comparisonwith the traditional two-vector SVPWMalgorithm

content of the proposed control strategy is relatively smallThus it is verified that the proposed algorithm has bettercontrol performance

5 Experimental Results Analysis

To demonstrate the effectiveness of the proposed a novelSVPWM algorithm in full modulation region for six-phase

3MWConverter system

2MW IPMSM system

Figure 14 The overall experiment setup

voltage source inverter the drive operation is examined atexperiment platform shown in [19] Figures 14 and 15 illus-trate a 2MW IPMSMdriving system and detailed experimentsetup a high-power back-to-back converter system is used tofeed the IPMSM system and the parameters of IPMSM arepresent in Table 1 All three-phase currents and voltages aremeasured using magnetic current and voltage transducers

The system control algorithms are developed in Mat-labSimulink followed by implementation on an OPAL RT-Lab (Real-time Digital Simulator) controller board In thispaper the method of changing the amplitude of a given signalis used to change the modulation ratio m value The motor iscontrolled byVF and the dead time is 10usThe phase voltagewaveforms under different modulation degrees are observed


High-power inverter

Communication Circuit board

RT-Lab system

Figure 15 The detailed experiment setup

500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1

Figure 16 Phase A voltage experimental waveforms in different modulation index

Table 1 Parameters of IPMSM prototype

Rate power [kW] 2180Rate speed [rmin] 17Rate frequency [Hz] 85Rotor inertia [kgsdotm2] 16000Rate phase to phase voltage [V(rms)] 690Rate current [A] 1960Number of pole pairs 30Stator resistance per phase(R) [Ω] 00192d-axis inductance (Ld) [mH] 4q-axis inductance (Lq) [mH] 5Permanent magnet flux (Ψ119891) [Wb] 10228

by an oscilloscope as shown in Figure 16 It can be seen thatwith different modulation ratios along with the increasing

modulation the modulated wave in the PWM also graduallychanges from a sine wave to a square wave signal This isthe same as the simulation result shown in Figure 9 andthe phase voltage also transitions from the linear modulationregion to the overmodulation region119880A and 119880U phase voltage reconstruction waveforms areshown in Figure 17 It can be seen that the experimentalwaveform is consistent with the simulation waveform shownin Figure 10 Phase voltage UU lags UA 30 electrical anglesAs the modulation index m increases the voltage utilizationrate increases gradually and the phase voltage graduallytransitions from a sine wave to a twelve-step wave

6 Conclusion

To improve the utilization ratio ofDCbus voltage and restrainthe stator current harmonics and torque ripple a novel


200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1

Figure 17 Phases A and U voltage experimental waveforms in different modulation index

SVPWM modulation strategy based on vector space decou-pling transform approach and vector weighting method isproposed in this paper The overmodulation of the six-phaseinverter is divided into 3 regions such as overmodulation Iovermodulation II and overmodulation III and the dwelltime of the SVPWM algorithm based on vector weightingmethod is deduced Simulation and experimental analysesdemonstrate the effectiveness and feasibility of the proposedstrategy

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare no conflict of interest

Authorsrsquo Contributions

All authors contributed to this article Peng Wu and Lei Yuandesigned the study and put forward the articlersquos methodsThey also participated in programming Zhen Zuo collected agreat deal of materials to form the articlersquos structure as well asreviewing the manuscript Junyu Wei carried out the simula-tions for the proposedmethods and handled the experimentsAll authors read and approved the final manuscript

Acknowledgments

This work is supported by National Nature ScienceFoundation of China (under Grant 51507188) and Nature

Science Foundation of HuNan province China (under Grant2019JJ50121)

References

[1] C Zhou G Yang and J Su ldquoPWM strategy with minimumharmonic distortion for dual three-phase permanent-magnetsynchronous motor drives operating in the overmodulationregionrdquo IEEE Transactions on Power Electronics vol 31 no 2pp 1367ndash1380 2016

[2] XGuoMHe andY Yang ldquoOvermodulation strategy of powerconverters A reviewrdquo IEEE Access 2018

[3] E E M Mohamed and M A Sayed ldquoMatrix convert-ers and three-phase inverters fed linear induction motordrivesmdashPerformance comparerdquoAin Shams Engineering Journalvol 9 no 3 pp 329ndash340 2018

[4] Q Luo J Zheng Y Sun and L Yang ldquoOptimal modeled six-phase space vector pulse width modulation method for statorvoltage harmonic suppressionrdquo Energies vol 11 no 10 articleno 2598 2018

[5] X Tang C Lai Z Liu andM Zhang ldquoA SVPWM to eliminatecommon-mode voltage for multilevel invertersrdquo Energies vol10 no 5 p 715 2017

[6] M Moranchel F Huerta I Sanz E Bueno and F J RodrıguezldquoA comparison of modulation techniques for modular multi-level convertersrdquo Energies vol 9 no 12 p 1091 2016

[7] L Yuan M-L Chen J-Q Shen and F Xiao ldquoCurrent harmon-ics elimination control method for six-phase PM synchronousmotor drivesrdquo ISA Transactions vol 59 pp 443ndash449 2015

[8] L Yuan B X Hu K Y We et al ldquoA novel current vectordecomposition controller design for six-phase PMSMrdquo Journalof Central South University vol 23 pp 443ndash449 2016

[9] KHatua andVTRanganathan ldquoDirect torque control schemesfor split-phase inductionmachinerdquo IEEETransactions on Indus-try Applications vol 41 no 5 pp 1243ndash1254 2005


[10] Y Zhao and T A Lipo ldquoSpace vector PWM control of dualthree-phase induction machine using vector space decomposi-tionrdquo IEEE Transactions on Industry Applications vol 31 no 5pp 1100ndash1109 1995

[11] D Dujic M Jones and E Levi ldquoAnalysis of output currentripple rms in multiphase drives using space vector approachrdquoIEEE Transactions on Power Electronics vol 24 no 8 pp 1926ndash1938 2009

[12] D Dujic M Jones and E Levi ldquoAnalysis of output current-ripple RMS inmultiphase drives using polygon approachrdquo IEEETransactions on Power Electronics vol 25 no 7 pp 1838ndash18492010

[13] A Iqbal and S Moinuddin ldquoComprehensive relationshipbetween carrier-based PWM and space vector PWM in a five-phase VSIrdquo IEEE Transactions on Power Electronics vol 24 no10 pp 2379ndash2390 2009

[14] K Marouani L Baghli D Hadiouche A Kheloui and A Rez-zoug ldquoA new PWM strategy based on a 24-sector vector spacedecomposition for a six-phase VSI-Fed dual stator inductionmotorrdquo IEEE Transactions on Industrial Electronics vol 55 no5 pp 1910ndash1920 2008

[15] D Hadiouche L Baghli and A Rezzoug ldquoSpace-vector PWMtechniques for dual three-phase ac machine Analysis perfor-mance evaluation and DSP implementationrdquo IEEE Transac-tions on Industry Applications vol 42 no 4 pp 1112ndash1122 2006

[16] S Bolognani and M Zigliotto ldquoSpace vector Fourier analysisof SVM inverters in the overmodulation rangerdquo in Proceedingsof the International Conference on Power Electronics Drives andEnergy Systems for Industrial Growth pp 319ndash324 New DelhiIndia 1996

[17] D Yazdani S Ali Khajehoddin A Bakhshai and G Joos ldquoFullutilization of the inverter in split-phase drives by means of adual three-phase space vector classification algorithmrdquo IEEETransactions on Industrial Electronics vol 56 no 1 pp 120ndash1292009

[18] G Grandi G Serra and A Tani ldquoSpace Vector Modulationof a Six-Phase VSI based on three-phase decompositionrdquo inProceedings of the 2008 International Symposium on Power Elec-tronics Electrical Drives Automation and Motion (SPEEDAM)pp 674ndash679 Ischia Italy June 2008

[19] L Yuan F Xiao J-Q Shen M-L Chen Q-M Shi and LQuan-feng ldquoSensorless control of high-power interior perma-nentmagnet synchronous motor drives at very low speedrdquo IETElectric Power Applications vol 7 no 3 pp 199ndash206 2013

Hindawiwwwhindawicom Volume 2018

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Volume 2018

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Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


M

Vdc

A UB VC W

30∘

Figure 1 Six-phase converter drive system

multiphase AC motors the SVPWM algorithm will becomeincredibly complex And with the increase of the numberof motor phases the complexity of this direct calculationSVPWM algorithm will be greatly increased sector judg-ment vector duration calculation vector action sequencearrangement vector duration conversion into switchingaction time and other complex issues and the difficulty willbe greatly increased and the performance requirements ofthe controller will undoubtedly be greatly improved

In order to further improve the DC bus utilization rate atwo-vector and improved four-vector algorithm can be usedto increase the modulation factor by injecting the 5th and7th harmonics of the vector in the x-y subspaceThis methodonly increases the system loss and does not generate torqueripple But it only reached the maximum linear modulationrange When it is necessary to continue to improve the busvoltage utilization rate it can be said that the commonly usedthree-phase overmodulation technology [16 17] is extendedto the six-phase system and the 11th and 13th harmonicsare injected in the 120572-120573 subspace so that the maximum busvoltage utilization can be obtained However the torqueripple will be poor

In order to increase the utilization ratio of the DC busvoltage numerous studies have been done on improving thePWM algorithm for three-phase motor when overmodula-tion occurs As for the PWM overmodulation strategies formultiphase motors the fundamental amplitude of the outputreference voltage will rise by using vector space decom-position (VSD) in [10] transform matrix decomposition toget fundamental component of the x-y subspace [18] whilethe harmonic content of the reference voltage in the linearmodulation region also increases in that way

To solve above problems and to increase the utilizationratio of the DC bus voltage a novel SVPWM algorithmfor six-phase VSI with wide modulation range capabilitybased on vector weighted method is proposed in this paperThe concept of mid-vector presented in [18] is employed toobtain the expression for the time of algorithm of the activespace voltage vectors and using vector weighted method theovermodulation region is divided into three sections and theproposed SVPWM algorithm can also allow smooth transi-tion from a linear modulation region to an overmodulationregion The control strategy is verified through simulationanalysis

2 Dwell Time Calculation for Six-Phase VSI

The six-phase motor system fed by six-phase VSI is shownin Figure 1 There are two sets of Y-coupled three-phasestator windings which are spatially separated by 30∘ electricaldegrees Since there are two switch states for each bridge armthe six-phase inverter has 26 switch states According to theVSD transformation approach all of the space vectors can bemapped to the 120572-120573 x-y and o1-o2 three mutually orthogonalsubspaces The fundamental component and harmonics withthe order 12nplusmn1 (n=1 2 3 ) are mapped into the 120572-120573 subspace The harmonics with the order 6nplusmn1 (n=1 35 ) and the harmonics with the order 6nplusmn3 (n=1 3 5 )are mapped into the x-y subspace and the o1-o2 subspacerespectively The subspaces are divided into 12 sectors

To suppress the harmonic current component of statorcurrent a good four-vector SVPWM method should satisfythat the amplitude of the reference voltage vector in the 120572-120573subspace is maximum and in the x-y subspace is minimum


2

4

3b

r

a2

1



10038161003816100381610038161003816Vmax101584010038161003816100381610038161003816 =


10038161003816100381610038161003816Vmin101584010038161003816100381610038161003816 =






(3)




119879119886 =1003816100381610038161003816V11990310038161003816100381610038161003816100381610038161003816Vmax1003816100381610038161003816 sin (1205876) sin(

2119896 minus 112 120587 minus 120575)119879119904

linear

over-modulation I




2119896 minus 312 120587)119879119904(5)








119898 = 120587 1003816100381610038161003816V1199031003816100381610038161003816(2119881119889119888) (6)









(9)


(10)







o

ok1VＭＣＨ2

B

lowast


A

B



1198961 = 119898 minus 11989811198982 minus 1198981 (0 le 1198961 le 1) (12)







(14)





Out

put p

hase

volta

ge (V

)

08

06

04

02

0

minus02

minus04

minus06

minus08



Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1


0988098609840982098097809760974



1198962 = 119898 minus 11989821198983 minus 1198982 (15)




2 11988111988911988824 cos (1205876 minus 120593)1198962 (16)


119905119894 = 1199051198941199051 + 1199052 + 1199053 + 1199054 119894 = 1 2 3 41199050 = 0

(17)



1198963 = 119898 minus 11989831 minus 1198983 (18)



Vlowast = 119881119889119900119889 (1 minus 1198963) + 1198811199051199081198901198963 (19)



o

o

B

lowast

A

B

k3Vtwe

(1 minus k3)Vdod

r


Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1











(22)






Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

1 2 3 4 5 6 7 8 9 10 110 1312Harmonic order

(a) m=0906

Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

Harmonic order43210 98765 13121110

5

(b) m=095

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(c) m=098

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p

u)


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(d) m=1









06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015





1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020


08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)



0

10

20

30

40

50

THD






3MWConverter system

2MW IPMSM system





High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018









2

4

3b

r

a2

1



10038161003816100381610038161003816Vmax101584010038161003816100381610038161003816 =


10038161003816100381610038161003816Vmin101584010038161003816100381610038161003816 =






(3)




119879119886 =1003816100381610038161003816V11990310038161003816100381610038161003816100381610038161003816Vmax1003816100381610038161003816 sin (1205876) sin(

2119896 minus 112 120587 minus 120575)119879119904

linear

over-modulation I




2119896 minus 312 120587)119879119904(5)








119898 = 120587 1003816100381610038161003816V1199031003816100381610038161003816(2119881119889119888) (6)









(9)


(10)







o

ok1VＭＣＨ2

B

lowast


A

B



1198961 = 119898 minus 11989811198982 minus 1198981 (0 le 1198961 le 1) (12)







(14)





Out

put p

hase

volta

ge (V

)

08

06

04

02

0

minus02

minus04

minus06

minus08



Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1


0988098609840982098097809760974



1198962 = 119898 minus 11989821198983 minus 1198982 (15)




2 11988111988911988824 cos (1205876 minus 120593)1198962 (16)


119905119894 = 1199051198941199051 + 1199052 + 1199053 + 1199054 119894 = 1 2 3 41199050 = 0

(17)



1198963 = 119898 minus 11989831 minus 1198983 (18)



Vlowast = 119881119889119900119889 (1 minus 1198963) + 1198811199051199081198901198963 (19)



o

o

B

lowast

A

B

k3Vtwe

(1 minus k3)Vdod

r


Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1











(22)






Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

1 2 3 4 5 6 7 8 9 10 110 1312Harmonic order

(a) m=0906

Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

Harmonic order43210 98765 13121110

5

(b) m=095

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(c) m=098

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p

u)


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(d) m=1









06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015





1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020


08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)



0

10

20

30

40

50

THD






3MWConverter system

2MW IPMSM system





High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018














(9)


(10)







o

ok1VＭＣＨ2

B

lowast


A

B



1198961 = 119898 minus 11989811198982 minus 1198981 (0 le 1198961 le 1) (12)







(14)





Out

put p

hase

volta

ge (V

)

08

06

04

02

0

minus02

minus04

minus06

minus08



Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1


0988098609840982098097809760974



1198962 = 119898 minus 11989821198983 minus 1198982 (15)




2 11988111988911988824 cos (1205876 minus 120593)1198962 (16)


119905119894 = 1199051198941199051 + 1199052 + 1199053 + 1199054 119894 = 1 2 3 41199050 = 0

(17)



1198963 = 119898 minus 11989831 minus 1198983 (18)



Vlowast = 119881119889119900119889 (1 minus 1198963) + 1198811199051199081198901198963 (19)



o

o

B

lowast

A

B

k3Vtwe

(1 minus k3)Vdod

r


Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1











(22)






Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

1 2 3 4 5 6 7 8 9 10 110 1312Harmonic order

(a) m=0906

Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

Harmonic order43210 98765 13121110

5

(b) m=095

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(c) m=098

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p

u)


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(d) m=1









06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015





1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020


08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)



0

10

20

30

40

50

THD






3MWConverter system

2MW IPMSM system





High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018









Out

put p

hase

volta

ge (V

)

08

06

04

02

0

minus02

minus04

minus06

minus08



Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1


0988098609840982098097809760974



1198962 = 119898 minus 11989821198983 minus 1198982 (15)




2 11988111988911988824 cos (1205876 minus 120593)1198962 (16)


119905119894 = 1199051198941199051 + 1199052 + 1199053 + 1199054 119894 = 1 2 3 41199050 = 0

(17)



1198963 = 119898 minus 11989831 minus 1198983 (18)



Vlowast = 119881119889119900119889 (1 minus 1198963) + 1198811199051199081198901198963 (19)



o

o

B

lowast

A

B

k3Vtwe

(1 minus k3)Vdod

r


Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1











(22)






Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

1 2 3 4 5 6 7 8 9 10 110 1312Harmonic order

(a) m=0906

Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

Harmonic order43210 98765 13121110

5

(b) m=095

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(c) m=098

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p

u)


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(d) m=1









06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015





1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020


08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)



0

10

20

30

40

50

THD






3MWConverter system

2MW IPMSM system





High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018









o

o

B

lowast

A

B

k3Vtwe

(1 minus k3)Vdod

r


Out

put p

hase

volta

ge (V

)

1

05

0

minus05

minus1











(22)






Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

1 2 3 4 5 6 7 8 9 10 110 1312Harmonic order

(a) m=0906

Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

Harmonic order43210 98765 13121110

5

(b) m=095

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(c) m=098

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p

u)


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(d) m=1









06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015





1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020


08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)



0

10

20

30

40

50

THD






3MWConverter system

2MW IPMSM system





High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018









Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

1 2 3 4 5 6 7 8 9 10 110 1312Harmonic order

(a) m=0906

Phas

e vol

tage

(pu

)A

mpl

itude

(pu


05

0

minus05

1

06

08

04

02

0

0201501Time (s)

0050

Harmonic order43210 98765 13121110

5

(b) m=095

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(c) m=098

Phas

e vol

tage

(pu

) 05

0

minus05

0201501Time (s)

0050

Am

plitu

de (p

u)


1

06

08

04

02

0

Harmonic order43210 98765 13121110

(d) m=1









06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015





1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020


08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)



0

10

20

30

40

50

THD






3MWConverter system

2MW IPMSM system





High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018









06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015



06

04

02

0

minus02

minus04

minus06

V(V

)

V(V)

Vy(V

)

Vx(V)

015

01

005

0

minus005

minus01

minus015





1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020


08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)



0

10

20

30

40

50

THD






3MWConverter system

2MW IPMSM system





High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018









1

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Times (s)

SVPW

M w

avef

orm

02018016014012010080060040020


08

06

04

02

0

minus02

minus04

minus06

minus08

Times (s)08070605040302010

Phas

e vol

tage

(pu

)



0

10

20

30

40

50

THD






3MWConverter system

2MW IPMSM system





High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018









High-power inverter


RT-Lab system


500V

div

Times (50msdiv)

(a) m=09

500V

div

Times (50msdiv)

(b) m=098

500V

div

Times (50msdiv)

(c) m=1






6 Conclusion



200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018









200V

div

Times (50msdiv)

UU

UA

(a) m=09

200V

div

Times (50msdiv)

UU

UA

(b) m=09820

0Vd

iv

Times (50msdiv)

UU

UA

(c) m=1



Data Availability






Acknowledgments



References




























Journal of












Journal of







Volume 2018






Volume 2018


























Journal of












Journal of







Volume 2018






Volume 2018








vector weighting approach and vector space decoupling

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