eighteen-sided polygonal voltage space-vector-based pwm control for an induction motor drive

Eighteen-sided polygonal voltage space-vector-basedPWM control for an induction motor drive

S. Lakshminarayanan, K. Gopakumar, G. Mondal, S. Figarado and N.S. Dinesh

Abstract: An inverter scheme with 18-sided polygonal voltage space-vector structure is proposedfor induction motor drive applications. An open-end winding configuration is used for the drivescheme. The motor is fed from one end with a conventional two-level inverter and from theother end with a three-level inverter, realised by cascading two conventional two-level inverters.The inverters are fed with asymmetrical DC-link voltages. A simple linear PWM controlscheme up to 18-step mode is proposed, based only on the motor reference phase amplitudes.The proposed scheme gives an increased modulation range with the elimination of the 5th, 7th,11th and 13th-order harmonics, for the entire modulation range, when compared with anyconventional schemes. The absence of low-order harmonics gives nearly sinusoidal currentsthroughout the modulation range, and makes PWM control of voltage very simple, with lowinverter switching frequencies, especially in the extreme modulation range.

1 Introduction

Conventional two-level inverter-fed drives are wellestablished for low-voltage drive applications. In thetwo-level inverter, pole voltages can attain two distinctvoltages (þVdc or zero), if the switches in the inverter legare switched in a complementary fashion. Interest in amultilevel inverter started with the three-level topologyproposed by Nabae et al. [1]. In this topology, a thirdlevel is formed by the neutral point of the DC bus andhence the terminology neutral point clamped. The polevoltage can be Vdc=2, 0 or �Vdc=2 with respect to theneutral point. It can be seen that the voltage rating ofthe switches needs to be half the DC-link voltage for thethree-level neutral point clamped (NPC) structure. Theadvantage of multilevel inverters is that the voltage ratingof the switches is lesser and also they can be operated atlower switching frequency with lower switching losses.But multilevel inverters are preferred for medium-voltagehigh-power applications [2–10]. The NPC inverter can beextended to a higher number of levels, but more thanthree levels are not highly preferred in variable speeddrive applications. Other popular multilevel inverter topol-ogies such as the cascaded H-bridge and flying capacitorare also considered for high-power applications [11, 12].The conventional multilevel and two-level inverters havea hexagonal honeycomb-like voltage space-vector structure[6, 7, 13–16]. In extreme modulation ranges (above thelinear range, in order to utilise the full DC-link capability),there will be substantial fifth and seventh harmonics [13].So, different modulation strategies are needed for PWMcontrol in the linear region and in the over-modulationregions, with hexagonal voltage space-vector structure[13–16]. Active harmonic elimination schemes work well

# The Institution of Engineering and Technology 2008

doi:10.1049/iet-epa:20070269

Paper first received 16th June and in revised form 8th August 2007

The authors are with CEDT, Indian Institute of Science, Bangalore 560012,India

E-mail: [email protected]

56

in the linear modulation range, but it requires extensiveoffline computations [4]. In harmonic eliminationtechniques, the low-order harmonics are eliminated byintroducing notches in the pole voltages and can result ina saturation in linear modulation range (because of narrownotches), depending on the scheme used. A detailedaccount of different modulation techniques for a cascadedH-bridge multilevel topology is given in [16]. The presenceof low-order harmonics needs a different approach forPWM control, in the over-modulation range, for multilevelinverters with a hexagonal honeycomb-like voltagespace-vector structure. The very popular scheme introducedfor a conventional two-level structure [13] can be extendedto the multilevel structure, but the complexity of theimplementation increases with a large number of inverterswitching states [16–18]. Moreover, the presence of thefifth and seventh harmonic currents will also restrict thebandwidth of the current controllers in the over-modulationregion, with synchronous PI controllers in high-dynamicschemes such as vector control. A simple and veryelegant compensating current control scheme to overcomethis, for two-level inverter-fed drives, is proposed in [18]and can be extended to multilevel inverter-fed drives also.All these show that, for drive applications, the con-

ventional multilevel structure, with hexagonal honeycomb-like voltage space-vector structure, needs a different PWMcontrol approach, in linear and in extreme modulationrange, with the complexity of the implementation varyingwith the number of levels [16–18]. Also, the schemesbased on H-bridge topology will need more number ofDC-link voltages, separately for individual phases, whichincrease with increase in the number of levels. This willalso make the power circuit very complex and expensive.So, for motor drive applications, especially in the low-voltage and medium-voltage high-power ranges, it is desir-able to have polygonal voltage space-vector structure withmore than six sides (with a simple power circuit), so thatsome of the lower harmonics can be suppressed (resultingin reduced PWM inverter switching frequency) for theentire modulation range which is increased. It has beenshown that in a 12-sided polygonal voltage space-vector

IET Electr. Power Appl., 2008, 2, (1), pp. 56–63

scheme, there is complete elimination of the 6n+ 1, n ¼ 1,3, 5, . . . , harmonics with significant suppression of the 11thand 13th harmonics [19, 20]. In [19], the 12-sided polygonalvoltage space-vector structure is realised for an open-endwinding induction motor drive, using only the conventionaltwo-level inverter structure. More recently, an inverter with12-sided polygonal voltage space vectors has been realisedby an inverter structure with asymmetrical DC links feedingan induction motor from one side [20]. Here also, theinverter structure is realised by cascading the conventionaltwo-level inverter topology with simple power-busstructure.On the basis of the above approaches, in the present work,

an inverter with 18-sided polygonal voltage space-vectorlocations is proposed for an induction motor drive. Themotor is fed from both the ends (motor with open-endwindings). One side is connected to a two-level inverter,whereas the other side is connected to a three-level inverterstructure realised by cascading two conventional two-levelinverters. This will also make the power circuit easy tofabricate with simple power-bus structure. The inverters arefed with asymmetrical DC-link voltages. A simple 18-sidedpolygonal voltage space-vector PWM scheme is proposedfor the entire modulation region, with linear control up tothe final 18-step mode. In the proposed drive scheme, the5th, 7th, 11th and 13th harmonics are removed from themotor phase voltage for the complete modulation range, upto the 18-step operation. So, high PWM switching frequencyis not needed for inverter control, especially in the lowermodulation range. Mostly, sinusoidal currents are possiblefor the entire modulation range. Also, different PWMcontrol ranges with different implementation techniques, asin the case of conventional inverter-fed drives (hexagonalvoltage space-vector structure), are not needed for the pro-posed scheme in the extreme modulation range. Themaximum phase peak fundamental for the proposed18-step motor phase voltage profile is 0.663Vdc (with theabsence of the 5th, 7th, 11th and 13th harmonics) comparedwith 0.658Vdc in the case of 12-sided polygonal space-vectorapproach (12-step waveformwith the absence of the fifth andseventh) and 0.637Vdc in an inverter with hexagonal voltagespace-vector structure (6-step waveform with the presenceof the fifth and seventh harmonics). The proposed schemeis experimentally verified on a low-power laboratoryprototype.

2 Proposed power circuit

The power circuit to achieve the 18-sided polygonal voltagespace vectors is shown in Fig. 1. The power circuit consistsof a two-level inverter on one side and a three-level inverteron the other side of the open-end windings of the inductionmotor. The three-level inverter is made by cascading twoconventional two-level inverters. The asymmetrical DC-link voltage is used for the power circuit. Each pole A, Bor C in INV1 can be independently connected to theupper DC-link voltage of 0.742Vdc or to the bottom DClink. The three-level inverter makes it possible to connecta pole A0, B0 or C0 to any of the three levels: 0, 0.258Vdcor 0.395Vdc independently (where Vdc is equivalent toDC-link voltage of a conventional two-level inverter). Itwill be shown that this feature can be used to generate18-sided polygonal voltage space vectors. It is to be notedthat in the three inverters INV1, INV2 and INV3, the topand bottom switches in each leg are operated complemen-tary to each other. The state of the upper switch definesthe state of the lower switch.

IET Electr. Power Appl., Vol. 2, No. 1, January 2008

2.1 Generation of 18-sided polygonal voltagespace vectors

The 18-sided voltage space vectors are shown in Fig. 2a.The angle between two adjacent vectors is 20º. In Fig. 2a,vector 1 is the resultant of the sum of vectors OA and AB.OA is produced by INV1 connecting pole A to level0.742Vdc and B and C to zero voltage levels. AB has a mag-nitude of 0.258Vdc and is generated by the following methodshown in the vector diagram (Fig. 2b). Pole voltages of A0,B0 and C0 are subtracted from the pole voltages of A, B andC; hence, when B 0 is connected to 0.258Vdc, it is along thenegative B-axis and C0 is connected to 0.258Vdc, which isalong the negative C-axis. So their resultant is AB with amagnitude 0.258Vdc along the A-axis (Fig. 2b). The vectorAB together with OA from INV1 gives vector 1 of magni-tude Vdc (Fig. 2a). Vector 2 is generated by the followingmethod. In INV1, pole A is connected to 0.742Vdc andpoles B and C are at zero as before. This yields vectorOA. AC (dotted line in Fig. 2c) is the contribution of thethree-level inverter (INV2 and INV3) in which pole C0 isconnected to 0.395Vdc, and A0 and B0 poles are connectedto zero voltage. Once again, the negative of the spacevector is added to make up the overall vector OC. Similarly,vector 3 is generated and explained as follows. In INV1,levels along A and B are maintained at 0.742Vdc, whereasC is at 0Vdc. This results in a vector along the negativeC-axis with magnitude 0.742Vdc. In INV2, the pole A0 ismaintained at zero with B 0 and C0 at the level 0.395Vdc,which is added to give 0.395Vdc along the negative A-axisdirection. Once again, by subtracting the three-level invertervector, this yields 0.395Vdc (dotted line in Fig. 2a) along the

Fig. 1 Power circuit of the proposed inverter-fed IM drive gen-erating 18-sided polygonal voltage space vector

Fig. 2 Generation of 18-sided polygonal voltage space vectors

a Eighteen-sided polygonal voltage vectorsb Vector addition for obtaining vector ABc Realising vector OC

57

58

Table 1: Generation of 18-sided polygonal vectors

Vector number Pole A Pole B Pole C Pole A0 Pole B0 Pole C0

1 0.742Vdc 0 0 0 0.258Vdc 0.258Vdc

2 0.742Vdc 0 0 0 0 0.395Vdc

3 0.742Vdc 0.742Vdc 0 0 0.395Vdc 0.395Vdc

4 0.742Vdc 0.742Vdc 0 0 0 0.258Vdc

5 0.742Vdc 0.742Vdc 0 0.395Vdc 0 0.395Vdc

6 0 0.742Vdc 0 0 0 0.395Vdc

7 0 0.742Vdc 0 0.258Vdc 0 0.258Vdc

8 0 0.742Vdc 0 0.395Vdc 0 0

9 0 0.742Vdc 0.742Vdc 0.395Vdc 0 0.395Vdc

10 0 0.742Vdc 0.742Vdc 0.258Vdc 0 0

11 0 0.742Vdc 0.742Vdc 0.395Vdc 0.395Vdc 0

12 0 0 0.742Vdc 0.395Vdc 0 0

13 0 0 0.742Vdc 0.258Vdc 0.258Vdc 0

14 0 0 0.742Vdc 0 0.395Vdc 0

15 0.742Vdc 0 0.742Vdc 0.395Vdc 0.395Vdc 0

16 0.742Vdc 0 0.742Vdc 0 0.258Vdc 0

17 0.742Vdc 0 0.742Vdc 0 0.395Vdc 0.395Vdc

18 0.742Vdc 0 0 0 0.395Vdc 0

positive A-axis. The resultant of this gives vector 3 as shownin Fig. 2a with magnitude equal to Vdc. Table 1 shows thelevels required by the pole voltages in order to generatevectors 1–18 (Figs. 2a and 4a). Figs. 3a–c show theswitch transition diagrams for generating vectors 18, 1and 2, respectively.

3 Space-vector PWM with 18-sided polygon

A reference vector Vr in a sector (Fig. 4a), as it rotates, issampled at (Ts sampling period) certain number of timesin each sector. In Fig. 4a, vector Vr is in sector 2. Thisvector can be generated by time averaging the vectors OEand OF. OE is kept on for a time interval T1 and OF fora time interval T2. For the time interval T0 ¼ TS–T1–T2,zero voltage level is maintained. T0 is split into twohalves of T0/2; one half is applied at the beginning of thetime interval TS and the other half at the end of TS. Let Vbe the magnitude of vectors OD, OE and so on and ‘m’be the sector number in which Vr lies. The volt-secondbalance equation in any sector is shown as

T1V/(m� 1)208þ T2V/m208 ¼ TS(Va þ jVb) (1)

Va and Vb are the components of the reference voltagealong the a- and b-axes (Fig. 3a). On separating the realand imaginary parts, we have the following matrixequations

T1T2

� �¼

TSV

cos (m� 1)208 cos (m208)sin (m� 1)208 sin (m208)

� ��1Va

Vb

� �(2)

Taking the inverse of the matrix, we obtain

T1T2

� �¼

2:924 � TSV

sin (m208) � cos (m208)� sin (m� 1)208 cos (m� 1)208

� �

�Va

Vb

� �(3)

(Note that 2.9238044. . . ¼ 1/sin 208.)

Fig. 3 Switch transition diagrams

a Switch transitions for generating vector 18b Switch transitions for generating vector 1c Switch transitions for generating vector 2


We can replace Va and Vb in terms of the sampled refer-ence phase amplitudes vA, vB and vC

Va ¼3

2vA ¼ �

3

2(vB þ vC) (4)

Vb ¼

ffiffiffi3

p

2(vB � vC) (5)

The resulting equations are

T1 ¼ 2:924 �ffiffiffi3

p�TSV

[�vB sin(m208þ 308)

þ vC cos(m 208þ 608)] (6)

T2 ¼ 2:924 �ffiffiffi3

p�TSV

[vB sin((m� 1)208þ 308)

� vC cos((m� 1)208þ 608)] (7)

Thus, if we can calculate T1 and T2 and switch the twovectors forming the sector, for the calculated time intervals,the reference vector can be generated in every samplingperiod. From (6) and (7), it can be noted that the periodT1 and T2 can be generated only by the sampled referencephase amplitudes.

4 Sampling and sector identification

The number of samples per sector depends on the speed ofthe motor and is chosen such that the overall switching fre-quency is below ,900 Hz in order to keep switching losseslow. If ‘f ’ is the fundamental frequency of operation, thenumber of samples is selected as follows

0 , f � 15 Hz: three samples per sector15 Hz , f � 25 Hz: two samples per sector25 Hz , f � 50 Hz: one sample per sector

Fig. 4 Space-vector PWM with 18-sided polygon

a Sectors of the 18-sided polygonb Phase A 18-step voltage profile with equal step duration


With this, the PWM control will take the drive to the final18-step mode very smoothly. The 18-step voltage profile ofphase A (projection of all 18 vectors of Fig. 4a on phaseA-axis) is shown in Fig. 4b. From the Fourier analysis of this,as shownbelow, it canbe computed that all the lower-order har-monics from the 3rd to 13th are absent from the phase voltage

An ¼2

T

ðT0

f (t) sin(nvt) dt, where v ¼2p

T(8)

For ‘n’ (order of harmonics) being even, An ¼ 0 for the18-step waveform shown in Fig. 4b. For ‘n’ being odd,the expression can be found by integrating over a quartercycle

An ¼ 4 �2

T

ðT=40

f (t) sin(nvt) dt

An ¼8

T

ðT=180

cos4p

9

� �sin(nvt) dt

�

þ

ð2T=18T=18

cosp

3

� �sin(nvt) dt

þ

ð3T=182T=18

cos2p

9

� �sin(nvt) dt

þ

ð4T=183T=18

cosp

9

� �sin(nvt) dt

þ

ðT=44T=18

cos (0) sin(nvt) dt

�(9)

An ¼4

np0:1736 1� cos

np

9

� �� h

þ 0:5 cosnp

9

� �� cos

2np

9

� ��

þ 0:766 cos2np

9

� �� cos

np

3

� ��

þ 0:94 cosnp

3

� �� cos

4np

9

� ��

þ cos4np

9

� �� cos

np

2

� �� (10)

From (10), the fundamental motor phase amplitude is2/3(A1) ¼ 2/3 (0.995) ¼ 0.663Vdc, where Vdc is theamplitude of the 18-sided polygonal radii. For the18-sided multilevel inverter operation, always the extremevertices and the zero vectors are used for PWM operation.So, it is easy to show with simple Fourier analysis (10)that the 5th, 7th, 11th and 13th harmonics are absent in an18-step waveform (e.g. projection of the 18 vectors alongthe phase A-axis, Fig. 4b). In PWM operation, with zeroand the active vectors forming a sector (there are 18sectors), notches are introduced in the 18-step waveformat equal intervals (switching period), the frequency ofwhich will be a multiple of 18 (3 times, 2 times. . .). So, low-order harmonics due to PWM operation will always bearound 18 times the fundamental (17th and 19th). Thiswill ensure throughout the modulation range, that all thelow-order harmonics such as the 5th, 7th, 11th and 13thare absent. This can also be verified from the fast Fouriertransform (FFT) plots of the experimental waveforms.

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4.1 Sector identification

The sector number ‘m’, in which the reference voltage lies,is required to compute the time intervals T1 and T2 and thisis done by the following simple method. First, the quadrant(Fig. 4a) in which the vector lies is found as follows:‘vA’ positive and ‘(vB � vC)’ positive: first quadrantvA negative and (vB � vC) positive: second quadrantvA negative and (vB � vC) negative: third quadrantvA positive and (vB � vC) negative: fourth quadrant

Once the quadrant is found, the sector in which the refer-ence vector lies is found as follows.

In quadrant 1:If jvB � vCj � jvAj

ffiffiffi3

ptan 208 then sector 1

Else,If jvB � vCj � jvAj

ffiffiffi3



ffiffiffi3



ffiffiffi3


Else, sector 5In quadrant 2:If jvB � vCj � jvAj

ffiffiffi3



ffiffiffi3



ffiffiffi3



ffiffiffi3


In quadrant 3:Else, sector 5If jvB � vCj � jvAj

ffiffiffi3



ffiffiffi3



ffiffiffi3



ffiffiffi3


Else, sector 14In quadrant 4:If jvB � vCj � jvAj

ffiffiffi3



ffiffiffi3



ffiffiffi3



ffiffiffi3


Else, sector 14

For one sample, only one quadrant is checked, so themethod is fast. When the quadrant is identified, amaximum of only four comparisons are needed for sectoridentification (Table 2). This makes the algorithm veryfast in digital implementation.Fig. 5 shows the sector identification in quadrant x, x ¼ 1,

2, 3 or 4.

5 Experimental verification

A vector control scheme is used for the motor drive (Fig. 6)and experimentally verified on a 1.5 kW induction motor.An IGBT-based power circuit is used for the inverterset-up along with their associated gate drives. A digitalsignal processor (DSP) platform from Texas InstrumentsTMS320LF2407A is used to generate the PWM signals.The DSP computes switching times T1 and T2 and alsogenerates the sector information. The gating signals forthe three inverters are finally generated in a PAL

60

(PALCE22V10-Programmable array logic) as shown inTable 1. The motor is initially run at different speeds andFigs. 7a–11b show the experimental results at varioussteady-state operations. Fig. 7a shows the pole voltages,phase voltages and the phase current waveforms (no loadoperation) at 15 Hz operation. Pole voltages of A and A 0

are taken with respect to their lower DC link. The resultantphase voltage is seen across A and A0 (Fig. 7a). It can beobserved that in a phase, in INV1 (high-voltage inverter),the switches are in the OFF condition for nearly 50% ofthe time, resulting in reduced switching losses. It can alsobe noted that the pole voltages of INV2 (series-connectedlow-voltage inverters) are also in the OFF state for nearly30% of the fundamental period. This will reduce the switch-ing losses with an increase in the overall efficiency of thedrive system. Fig. 7b shows the relative amplitude of theharmonic spectrum with three samples in a sector, with anoverall inverter switching frequency of ,900 Hz. It canalso be noted that from the relative harmonic amplitudespectrum, all the 5th, 7th, 11th and 13th harmonics areabsent in the motor phase voltage waveform. The corre-sponding experimental waveforms for 25, 30, 45 and50 Hz (18-step operation) are shown in Figs. 8–10, respect-ively. The number of samples in a sector up to 15 Hz isthree, and from 15 to 25 Hz only two samples are taken in

Table 2: Determining the sector number after quadrantis known

Quadrant

number x

Sector number

a b c d e

1 1 2 3 4 5

2 9 8 7 6 5

3 10 11 12 13 14

4 18 17 16 15 14

Fig. 5 Sector identification using four comparisons


a sector for PWM control. From 30 Hz onwards (up to18-step mode), only one sample (at the start of the sector)is chosen for PWM control. It should be noted that from30 Hz up to the final 50 Hz (18-step operation), the motorphase current distortion becomes reduced and the currentbecomes smoother as the modulation increases. This isbecause all the lower order harmonics (5th–13th) areabsent throughout, and hence a current ripple is only dueto the inverter switching frequency (18 times the fundamen-tal). Now, as the fundamental frequency increases, the har-monic impedance because of the inverter switchingfrequency (18 times the fundamental) increases, thecurrent ripple amplitude reduces, the current becomessmoother and will be more close to a sinusoid in the18-step mode. This will also make the PWM control forthe proposed scheme very simple in the higher modulation

Fig. 6 Vector control scheme with 18-sided polygonal voltagespace-vector-based inverter

Fig. 7 Experimental waveforms for 15 Hz

a For 15 Hz waveforms: V/div ¼ 50 V, I/div ¼ 1 A, t/div ¼10 msFirst trace is the pole voltage of A0, second trace the pole voltage ofA, third trace the phase voltage between A and A0 and fourth tracethe motor phase currentb Relative harmonic components in phase voltage


a For 25 Hz waveforms: V/div ¼ 50 V, I/div ¼ 1 A, t/div ¼10 msFirst trace is the pole voltage of A0, second trace the pole voltage of A,third trace the phase voltage between A and A0 and fourth trace themotor phase currentb Relative harmonic spectrum of phase voltage


ranges [only the vertices forming one side of a triangularsector is switched and the points in the inner regions of asector are not sampled for PWM control resulting from 30to 50 Hz (18-step PWM operation)], unlike the case of con-ventional multilevel inverters with hexagonal honeycomb-like voltage space-vector structure. The FFT plots showthe absence of low-order harmonics such as the 5th, 7th,11th and 13th throughout the modulation range up to thefinal 18-step mode (with low inverter switching frequen-cies), unlike the case of PWM schemes with hexagonalspace-vector structure [1–18]. In conventional multilevelstructures with hexagonal voltage space-vector structure,high-frequency inverter PWM switching or harmonic elim-ination techniques are needed, when compared with thepresent scheme, to suppress the low-frequency componentsin the extreme modulation ranges. Also, the fifth andseventh harmonics will always be present in the convention-al multilevel schemes if the drive is taken to the extremeover-modulation region up to six steps, to fully utilise theDC-link capability. The harmonic amplitudes for themotor phase voltage are computed for the full modulationrange up to the 18-step operation. A comparative study ofthe conventional two- and three-level and the H-bridgeare presented in Table 3. The present scheme requiresthree DC links with asymmetrical voltages and also someof the switching devices (bottom devices of INV-3) need0.74Vdc. These are some of the drawbacks of the presentscheme compared with the popular conventional three-levelstructure. But with the increased modulation range andimproved harmonic spectrum, the present proposedscheme can be considered for low-voltage high-powerinduction motor (IM) drive applications. Figs. 12a and bpresent the fundamental and the harmonic amplitudes forthe entire modulation range. It can also be noted(Figs. 12a and b) that the fundamental voltage component


a Phase voltage and current at 30 Hz (top and bottom, respectively):V/div ¼ 50 V, I/div ¼ 1 A, t/div ¼ 10 msb Harmonic components at 30 Hz


a For 45 Hz waveforms: V/div ¼ 50 V, I/div ¼ 1 A, t/div ¼5 msFirst trace is the pole voltage of A0, second trace the pole voltage ofA, third trace the phase voltage between A and A0 and fourth tracethe motor phase currentb Relative harmonic spectrum of phase voltage

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Table 3: Comparison of 18-sided polygonal voltage space-vector method with some multilevel topologies

Criteria Two level Three-level NPC H-bridge

(three level)

18-sided polygonal

voltage

space-vector based

number of

switching

devices

6 12þ (6 clamping

diodes)

12 18

number of

DC links

1 1 3 3

voltage rating

of the switches

Vdc Vdc/2 Vdc/2 0.742Vdc,

0.395Vdc,

0.137Vdc

peak

fundamental

voltage

0.637Vdc in the

six-step mode

0.637Vdc in the

six-step mode

0.637Vdc in the

six-step mode

0.663Vdc

in the

18-step mode

harmonics 5th, 7th, 11th and

13th predominant

in over-modulation

5th, 7th, 11th and

13th harmonics

present in

over-modulation

5th, 7th, 11th and

13th harmonics

present in

over-modulation

5th, 7th, 11th and 13th

harmonics eliminated

throughout the range of

operation

is linear for the full modulation range, and the lowerharmonic components up to the 13th is absent for theentire modulation range. This will make the closed-loopcurrent control scheme very simple and compensatedsynchronous proportional integral (PI) controllers are notneeded [18], as in the case of conventional hexagonalspace vector-based multilevel PWM control [6–8, 17], forvector control drive applications. Fig. 13a shows themotor phase voltage and current waveforms during accel-eration in the extreme modulation range. The drivescheme is accelerated from 40 Hz to the final 18-step oper-ation, and it can be noted that the transition is very smoothand the current waveform is very close to a sinusoid, withthe absence of low-order harmonics. The dynamic voltageand current waveform during acceleration are shown inFig. 13b, and the corresponding waveforms during decelera-tion are presented in Fig. 13c. The speed reversal wave-forms are shown in Fig. 13d. All the experimentalwaveforms show that the proposed multilevel inverter canbe operated with simple power circuit and low inverterswitching frequency (simple PWM control), coupled withvery good dynamic performances in the extreme modu-lation range (up to 18 steps), without the need for extrasignal processing, as in the case of any conventional multi-level schemes. But the present scheme needs asymmetrical


a For 50 Hz waveforms: V/div ¼ 50 V, I/div ¼ 1 A, t/div ¼ 5 msFirst trace is the pole voltage of A0, second trace the pole voltage A,third trace the phase voltage between A and A0 and fourth trace themotor currentb Harmonic spectrum of phase voltage

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Fig. 12 Fundamental and the harmonic amplitudes for the entiremodulation range

a, b Harmonic components at different operating frequencies

Fig. 13 Phase voltage and current waveforms during accelera-tion in the extreme modulation range

a Smooth transition to 18-step operation 40–50 Hzb Acceleration from 5 to 25 HzTop waveform, phase voltage; bottom waveform, motor current;t/div ¼ 500 ms, V/div ¼ 50 V, I/div ¼ 1 Ac Deceleration from 25 Hz to 5 HzUpper trace, phase voltage; lower trace, phase current;t/div ¼ 500 ms, V/div ¼ 50 V, I/div ¼ 1 Ad Speed reversalUpper trace, phase voltage; lower trace, motor phase current;t/div ¼ 1 s, V/div ¼ 50 v, I/div ¼ 1 A


DC-link voltages (ratio of 0.742:0.137:0.259 can be realisedwith three transformer secondaries with the above ratios andthen using diode rectifiers), and hence the three- and two-level inverter blocks need different voltage ratings.

6 Conclusions

An inverter structure with 18-sided polygonal voltage spacevectors is proposed for an induction motor drive application.An open-end winding structure is used for the drive scheme.The power circuit consists of a two-level inverter on one sideand a three-level inverter on the other side of the open-endwindings, resulting in a simple power-bus structure for theproposed scheme. The three-level structure is realised bycascading two conventional two-level inverters. But asym-metric DC-link voltages are required to feed the inverterson both the sides. A simple PWM scheme based only onsampled reference phase amplitudes is used for PWMcontrol for the entire modulation range. Different PWMcontrol ranges, as in the case of a conventional hexagonal-based multilevel inverter structure, are not needed for thepresent scheme, especially in the extreme modulationrange. The high-voltage inverter is switched only fornearly 50% of the duty cycle and the series-connected lowvoltage is not switched for nearly 30% of the duty cycle.This will reduce the switching losses considerably and willimprove the overall efficiency of the drive scheme. Also,the low-frequency components such as the 5th, 7th, 11thand 13th are eliminated for the entire modulation range,without resorting to very high-frequency PWM switching,and hence, special closed-loop current control schemeswith compensated PI current controllers are not needed inthe extreme modulation range with vector control schemes.The present drive scheme gives an increased modulationrange, when compared with any conventional multilevelinverter scheme. The proposed simple PWM controlscheme smoothly takes the drive to the extreme 18-step oper-ation, with nearly sinusoidal currents. The scheme is exper-imentally verified with a 1.5 kW induction machine withthe control platform implemented on a DSP. But, due toasymmetrical DC-link voltages, the three- and two-levelinverter blocks need different voltage-blocking capabilities.The proposed inverter scheme with the simple power circuit,simple PWM control scheme (for the entire modulationrange with nearly sinusoidal currents, especially in theextreme modulation range) and with low inverter switchinglosses can be considered as a viable alternative for low-and medium-voltage high-power applications.

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eighteen-sided polygonal voltage space-vector-based pwm control for an induction motor drive

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