8.urmila bandaru 86-97

Innovative Systems Design and Engineering www.iiste.org

ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)

Vol 2, No 6, 2011

86

Design of Multilevel Inverter Driven Induction Machine

Urmila Bandaru

G.. Pulla Reddy Engineering College, Kurnool

A.P., India

E-mail: [email protected]

Subbarayudu

Brindavan Institute of Technology, Kurnool

A.P., India

E-mail: [email protected]

The research is financed by Asian Development Bank. No. 2006-A171(Sponsoring information)

Abstract

Multilevel inverters have gained interest in recent years in high-power medium-voltage industry. This

paper considered the most popular structure among the transformer-less voltage source multilevel inverters,

the diode-clamped inverter based on the neutral point converter. This paper proposes a single carrier multi-

modulation SVPWM technique with conventional space vector switching sequence. Simulation results

presents comparison of single and multicarrier conventional space vector switching sequence with general

switching sequence of nine-level diode-clamped inverter for stator currents, electromagnetic torque and

speed for constant modulation index and for constant V/f control method. Simulation is carried out in

MATLAB-Simulink software.

Keywords- Multilevel inverter, APODC, SVPWM, total harmonic distortion, Diode-clamped inverter,

SCMMOS, MCMMOS, Induction machine, synchronously rotating reference frame

1. Introduction

Multilevel inverters have drawn tremendous interest in high-power medium-voltage industry. In literature,

inverters with voltage levels three or more referred as multilevel inverters. The inherent multilevel structure

increase the power rating in which device voltage stresses are controlled without requiring higher ratings on

individual devices. They present a new set of features that suits well for use in static reactive power

compensation, drives and active power filters. Multilevel voltage source inverter allows reaching high

voltages with low harmonics without use of series connected synchronized switching devices or

transformers. As the number of voltage levels increases, the harmonic content of output voltage waveform

decreases significantly. The advantages of multilevel inverter are good power quality, low switching losses,

reduced output dv/dt and high voltage capability. Increasing the number of voltage levels in the inverter

increases the power rating. The three main topologies of multilevel inverters are the Diode clamped

inverter, Flying capacitor inverter, and the Cascaded H-bridge inverter by Nabae et al. (1981).

The PWM schemes of multilevel inverters are Multilevel Sine-Triangle Carrier Pulse Width Modulation-

SPWM and Space Vector Pulse Width Modulation-SVPWM. Multilevel SPWM involves comparison of

reference signal with a number of level shifted carriers to generate the PWM signal. Due to its simplicity

and its well defined harmonic spectrum which is concentrated at the carrier frequency, its sidebands, and its

multiples with their sidebands, the SPWM method has been utilized in a wide range of AC drive

applications. However, the method has a poor voltage linearity range, which is at most 78.5 % of the six-

step voltage fundamental component value, hence poor voltage utilization. Therefore, the zero sequence

signal injection techniques that extend the SPWM linearity range have been introduced for isolated neutral

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load applications which comprise the large majority of AC loads. The carrier based PWM methods can

operate with high switching frequency and offer high waveform quality and implementation advantages.

Carrier based PWM methods employ the per carrier cycle volt-second balancing principle to program a

desirable inverter output voltage waveform. The programmed PWM technique, SVPWM involves

synthesizing the reference voltage space vector by switching among the nearest voltage space vectors.

SVPWM is considered a better technique of PWM owing to its advantages (i) improved fundamental

output voltage (ii) reduced harmonic distortion (iii) easier implementation in microcontrollers and Digital

Signal Processor. This paper considered the most popular structure among the transformer-less voltage

source multilevel inverters, the diode-clamped converter based on the neutral point converter with

SVPWM technique by Carrara et al. (1992). This paper proposes a single carrier multi-modulation

technique for multilevel inverter driven induction machine, modeled in synchronously rotating reference

frame. Simulation results present comparison of single and multicarrier SVPWM of nine-level diode-

clamped inverter. Improved fundamental component of voltage is observed with SCMM method. Reduced

total harmonic distortion and current ripple can be observed with Alternate Phase Opposition Disposition

Carrier (APODC) SVPWM technique by Leon et al. (1999). Simulation is carried out in MATLAB-

Simulink software.

2. Diode-Clamped Multilevel Inverter

A three-phase nine-level diode-clamped inverter is shown in Fig.1. Each phase is constituted by 16

switches. The complementary switch pairs for phase ‘A’ are (Sa1, Sa1’), (Sa2, Sa2

’), (Sa3, Sa3

’), (Sa4, Sa4

’), (Sa5,

Sa5’), (Sa6, Sa6

’), (Sa7, Sa7

’), (Sa8, Sa8

’) and similarly for B and C phases. Clamping diodes carry the full load

current by Jose Rodriguez (2002).

Table1 shows phase to fictitious midpoint ‘o’ of capacitor string voltage (VAO) and line-to-line voltage

(VAB) for various switching’s.

Table 1 Nine-Level Inverter Voltage States

Sa1 Sa2 Sa3 Sa4 Sa5 Sa6 Sa7 Sa8 VAO VAB 1 1 1 1 1 1 1 1 +Vdc/2 Vdc 0 1 1 1 1 1 1 1 +3Vdc/8 7Vdc/8 0 0 1 1 1 1 1 1 +Vdc/4 6Vdc/8 0 0 0 1 1 1 1 1 +Vdc/8 5Vdc/8 0 0 0 0 1 1 1 1 0 5Vdc/8

0 0 0 0 0 1 1 1 -Vdc/8 3Vdc/8 0 0 0 0 0 0 1 1 -Vdc/4 2Vdc/8 0 0 0 0 0 0 0 1 -3Vdc/8 Vdc/8 0 0 0 0 0 0 0 0 -Vdc/2 0




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Figure 1 Circuit Diagram of 3 Phase Nine Level Diode Clamped Inverter




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3. SVPWM Implementation

Implementation of SVPWM involves (i) Sector identification-where the tip of the reference voltage vector

lies (ii) Nearest three voltage space vectors (NTV) identification (ii) Determination of the dwelling time of

each of these NTVs (iv) Choosing an optimized switching sequence.

Space vector diagram of nine-level inverter with its 729 (=39) vectors are shown in Fig 2. Each sector takes

60 degrees. Sector1 diagram is shown in Figure 3. Each sector consists of 64 regions 177 vectors.

3.1 Sector and Region identification

Three phase instantaneous reference voltages (1) are transformed to two phase (2). Every 60 degrees, from

zero to 360 degrees constitute a sector. Identification of the sector in which the tip of the reference vector

lies is obtained by (3).

(1)

805 740 634 523

012

768 657 506 045 430 324

213

868 757 606 545 030 424

313

781

681

581

881

851

861

871

801

841

831

821

081

481

381

281

181

182

183

184

180

185

186

187

832

721

842

731

802

741

852

701

862

751

872 761

882

771

782

671

682

571

582 071

082

471

482

371

382 271

282 171

283

172

284

173

280

174

285

170

286

175

287

176

387 276

165

386 275 160

385 270

164

380 274

163

803 742

631

853 702

641

863 752 601

873 762

651

883 772

661

783 672 561

683 572

061

583 072

461

083 472 361

483 372

261

383 272

161

384 273

162

487 376 265

150

486 375 260

154

485 370 264 153

480 374 263

152

484 373 262 151

084 473 362

251

860 754 603 542

031

870 764 653 502

041

086 475 360 254

103

085 470 364 253

102

080 474 363 252

101

580 074 463 352

201

680 574 063 452

301

780 674 563 052401

865 750 604 543 032

421

875 760 654 503 042 431

885 770 664 553 002

441

785 670 564 053 402

341

685 570 064 453 302

241

585 070 464 353 202 141

876 765 650 504 043 432 321

886 775 660 554 003 442 331

786 675 560 054 403 342 231

686 575 060 454 303 242

131

687 576 065 450 304 243 132

887 776 665 550 004 443 332

221

787 676 565 050 404 343 232

121

587 076 465 350 204

143

586 075 460 354 203

142

087 476 365

250

104

880 774 663 552

001

850 704 643 532

021

854 703 642 531

864 753 602 541

874 763 652

501

884 773 662

551

784 673 562

051

684 573 062

451

584 073 462

351

804 743 632

521

843

732

621

811

812

813

814

810

815

816

817

818

718

618

518

018

418

318

328

217

428 317

028 417

528 017

628 517

728

617

828

717

827

716

826

715

825

710

820

714

824 713

823

712

822

711

438 327

216

038 427

316

538 027 416

638 527 016

738 627 516

838 727 616

837 726

615

836 725 610

835 720

614

830 724

613

834 723

612

833 722 611

848 737 626 515

748 637 526 015

648 537 026

415

548 037 426

315

048 437 326

215

847 736 625 510

846 735 620

514

845 730 624

513

840 734 623

512

844 733 622

511

800 744 633 522 011

806 745 630 524

013

808

747 636 525

010

708

647 536 025

410

608 547 036 425 310

508

047 436 325

210

658 507 046 435 320

214

758 607 546 435 420 314

858 707 646 535 020

414

758 607 546 035 420

314

658 507 046 435 320

214

855 700 644 533 022

411

867 756 605 540 034 423 312

866 755 600 544 033 422

311

878 767 656 505 040 434 323 212

807 746 635 205

014

877 766 655 500 044 433 322

211

218

288

117

238

127

248

137

208

157

258

107

268

157

278

167

288 177

478 367 256

105

468 357 206 145

458 307 246

135

408

347 236 125

448 337 226

115

488 377 266

155

008

447 336 225

110

058 407 346 235

120

068 457 306 245

130

078 467 356 205

140

088 477 366 255

100

558 007 446 335 220

114

568 057 406 345 230 124

578 067 456 305 240

134

668 557 006 445 330 224

113

678 567 056 405 340 234

123

778 667 556 005 440 334 223

112

588 077 466 355 200

144

688 577 066 455 300 244

133

788 677 566 055 400 344 233

122

888 777 666 555 000 444 333 222

111

188

178

168

158

108

148

138

128

118

378 267 156

388 277 166

368 257

106

358 207

146

308

247

136

348 237 126

338 227

116

Figure 2 Nine-Level Inverter State Space Vector Diagram




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90

(2)

; (3)

Where θ is the angle varies from 0 to 2π.

Amplitude and angle of the reference vector are obtained from (3).

From Park’s transformation the di-phase, α-β components are:

(4)

(5)

Region is obtained by normalizing the di-phase components of the space vector (4)-(5) of an n-level

inverter through division by Vdc/n-1, where Vdc is the dc link voltage.

3.2 Determination of the duration of nearest three voltage space vectors

Switch dwelling duration is obtained from (6)-(7).

(6)

(7)

3.3 Determination of optimized switching sequence

Consider reference vector is lying in sector1 region 35 of Figure 3. The nearest three space vectors for

switching sequence are , , .

The space redundant vectors for sector1-region 35, are, for 4 0 8, 3 5 7, 2 3 6, 1 2 5 (4 redundant

vectors), for 4 4 8, 3 3 7, 2 2 6, 1 1 5 (4 redundant vectors), and for 3 4 8, 2 3 7, 1 2 6 (3 redundant

vectors).

An optimized switching sequence starts with virtual zero vector’s state. A virtual zero vector is with

minimum offset from zero vector of two-level inverter. Based on the principles derived in literature for

two-level inverter, for Region 35, the switching sequence is 4 0 8→4 4 8→ 3 4 8→ 3 4 7→ 3 3 7→ 2 3 7→

2 3 6→ 2 2 6→ 1 2 6→ 1 2 5→ 1 1 5 during a sampling interval and 1 1 5→ 1 2 5→ 1 2 6→ 2 2 6→ 2 3

6→ 2 3 7 → 3 3 7→ 3 4 7→ 3 4 8 → 4 4 8 → 4 0 8 during the subsequent sampling interval. This sequence

uses all the space redundant vectors of each state by Anish Gopinath et al.(2007), (2009).

4. Mathematical Modeling of Induction Machine

Three-phase asynchronous or induction machines which contain a cage, are very popular motors in many

industrial variable speed drive applications and all this is due to its simple construction, robustness,

inexpensive, reliability, good efficiency and good self-starting capability and available at all power ratings.

Progress in the field of power electronics and microelectronics enables the application of induction motors

for high-performance drives, where traditionally only DC motors were applied. During starting up and

other severe transient operations induction motor draws large currents, produces voltage dips, oscillatory

torques and can even generate harmonics in the power systems by Vivek Pahwa et al.(2009), Ogubuka et

al.(2009). It is important to predict these phenomena. A transient free operation of the induction machine is




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91

achieved only if the stator flux linkages are maintained constant in magnitude and its phase is stationary

with respect to the current by Krishnan (2003) and Leon et al. (1999). Various models have been developed

and the qd0 or two axis model for the study of transient behaviors has been tested and proved to be very

reliable and accurate.

4.1 Synchronously Rotating Reference Frames Model

The three phase balanced voltages are transformed to di-phase components which are in stationary rotating

reference frame. These are transformed to synchronously rotating reference frames using (11). The speed of

the synchronously rotating reference frames is the stator supply angular frequency.

qds

ce

qds vTv (8)

te

ds

e

qs

e

qds vvv ,

tdsqsqds vvv (9)

cossin

sincoscT

(11)

19

16

9

15

14

12 7

13

4

8

6 11 3

10 5 2 1

62

48

0

64

49

63

46 59

45 58

57

56 43

44

0

42

41 54

55

53 40

52 39

38 51

37 50

60

61

47

25

35

34

32

33

23

24

22

21 30

29 20

0 28

18 27

17 26

31

36

P

Figure 3 Sector1 Regions Space Vector Representation




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92

e

ds

e

qr

e

ds

e

qs

rrrrsmmrs

rrsrrmrsm

mmsssss

msmssss

e

ds

e

qr

e

ds

e

qs

i

i

i

i

pLRLpLL

LpLRLpL

pLLpLRL

LpLLpLR

V

V

V

V

)()(

)()(

(13)

The electromagnetic torque is

)(22

3 e

ds

e

qr

e

dr

e

qsme iiiiLP

T (14)

4.2 V/f Control on Induction Motor

Most of the industrial loads are operated based on constant Volts/Hz control method of speed because of its

simplicity. Neglecting the stator resistance drop, the ratio of supply voltage to frequency is maintained

constant by varying these variables. When the frequency approaches to zero, the magnitude of the stator

voltage also tends to zero and the stator resistance absorbs this low voltage. The stator resistance drop is

compensated at low speed by injecting the boost voltage to maintain rated air gap flux thus full load torque

is available up to zero speed. At steady state operation, if load torque is increased, the slip increases within

stability limit and a balance will be maintained between the developed torque and the load torque. This

paper considered the V/f control on induction machine by Krishnan (2003).

5. Simulation Results and Conclusions

Simulation is carried out on nine-level diode-clamped inverter driven induction machine in synchronously

rotating reference frame for two methods of Space Vector PWM technique at switching frequency 1.5 KHz

with APODC technique.

(i) SCMM CSVPWM-Single Carrier Multi-Modulation for Conventional SVPWM

(ii) MCMM CSVPWM-Multi-Carrier Multi-Modulation for Conventional SVPWM

In MCMM the carriers are in Alternative phase opposition disposition, where each carrier band is shifted

by 1800 from the adjacent bands.

Multi-Carrier Multi-Modulation results reduced harmonic distortion with reduced fundamental component;

however Single Carrier Multi-Modulation results reduced harmonic distortion with highly improved

fundamental component of voltage.

Figure4 and Figure5 are responses of induction machine for stator currents, electromagnetic torque and

speed of MCMM and SCMM respectively.

The response is observed for speed reversal from +314 rad/sec to -314 rad/sec at time of 0.86 seconds and

from -314 rad/sec to +314 rad/sec at time of 0.85 seconds and 1.01 seconds respectively, in Figure6 and

Figure7. Transients are more in MCMM compared to SCMM. Reduced oscillatory behavior is observed in

MCMM. Settling time is less in SCMM compared to MCMM.

Figure6 shows the toque response with speed reversal at 0.86 seconds. When compared to MCMM, SCMM

results more torque.

Figure7 shows the speed response with change in toque from 0 to 50 N-m at 0.4 seconds. When compared

SCMM, dip in speed is more in MCMM.

Figure8 and Figure9 are the pole, phase and line voltages for SCMM and MCMM methods respectively.




Vol 2, No 6, 2011

93

Figure12 and Figure13 show the stator currents, torque and speed response for constant V/f control. The

load torque requirement shifts from 0 to 50 N-m at 0.4 seconds. Modulation index is 0.906 (50 Hz) at 0

seconds, 0.84 (46 Hz) at 0.8 seconds, 0.73 (40 Hz) at 1.2 seconds, 0.62 (35 Hz) at 1.6 seconds, 0.906 (-50

Hz) at 2 seconds, 0.84 (-46 Hz) at 2.4 seconds, 0.73(-40 Hz) at 2.8 seconds, and 0.62 (-35 Hz), at 3.2

seconds.

Figure14 and Figure15 are the pole, phase and line voltages for SCMM and MCMM methods respectively

for constant V/f control.

When frequency falls below 40 Hz the MCMM performance is poor compared to SCMM.

Ripple content is high with V/f control in SCMM.

0 0.5 1 1.5 2-400

-200

0

200

400

0 0.5 1 1.5 2-400

-200

0

200

400

0 0.5 1 1.5 2-400

-200

0

200

400

Figure 4 MCMM Stator Currents, Torque and Speed

0 0.5 1 1.5 2-400

-200

0

200

400

0 0.5 1 1.5 2-400

-200

0

200

400

0 0.5 1 1.5 2-400

-200

0

200

400

Figure 5 SCMM Stator Currents, Torque and Speed




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94

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1-300

-200

-100

0

100

200

300

400

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1-300

-200

-100

0

100

200

300

Figure 6 SCMM, MCMM Stator Currents for speed reversal

from +314rad/sec to -314 rad/sec

1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7-400

-300

-200

-100

0

100

200

300

1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7-300

-200

-100

0

100

200

300

Figure 7 SCMM, MCMM Stator Currents for speed reversal

from -314rad/sec to +314 rad/sec

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1-400

-300

-200

-100

0

100

0.75 0.8 0.85 0.9 0.95 1 1.05 1.1-300

-200

-100

0

100

Figure 8 SCMM, MCMM Electromagnetic torque for speed reversal at 0.86sec




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95

0.35 0.4 0.45 0.5 0.55 0.6240

260

280

300

320

0.35 0.4 0.45 0.5 0.55 0.6200

250

300

350

Figure 9 SCMM, MCMM rotor speed when torque change

from 0 to +50 N-m

0 0.01 0.02 0.03 0.04 0.05 0.06-100

-50

0

50

100

0 0.01 0.02 0.03 0.04 0.05 0.06-200

-100

0

100

200

0 0.01 0.02 0.03 0.04 0.05 0.06-200

-100

0

100

200

Figure 10 SCMM Pole, Phase and Line Voltage

0 0.01 0.02 0.03 0.04 0.05 0.06-100

-50

0

50

100

0 0.01 0.02 0.03 0.04 0.05 0.06-200

-100

0

100

200

0 0.01 0.02 0.03 0.04 0.05 0.06-200

-100

0

100

200

Figure 11 MCMM Pole, Phase and Line Voltage




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96

0 0.5 1 1.5 2 2.5 3 3.5-500

0

500

0 0.5 1 1.5 2 2.5 3 3.5-500

0

500

0 0.5 1 1.5 2 2.5 3 3.5-2

0

2

Figure 12 SCMM Stator Currents, Torque and Speed with V/f Control

0 0.5 1 1.5 2 2.5 3 3.5-500

0

500

0 0.5 1 1.5 2 2.5 3 3.5-200

0

200

0 0.5 1 1.5 2 2.5 3 3.5-2

0

2

Figure 13 MCMM Stator Currents, Torque and Speed with V/f Control

0 0.5 1 1.5 2 2.5 3 3.5-100

0

100

0 0.5 1 1.5 2 2.5 3 3.5-200

0

200

0 0.5 1 1.5 2 2.5 3 3.5-200

0

200

Figure 14 SCMM Pole, Phase and Line Voltages with V/f Control




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97

0 0.5 1 1.5 2 2.5 3 3.5-100

0

100

0 0.5 1 1.5 2 2.5 3 3.5-200

0

200

0 0.5 1 1.5 2 2.5 3 3.5-200

0

200

Figure 15 MCMM Pole, Phase and Line Voltages with V/f Control

4. References

Nabae, Takahashi, Akagi.(1981) “A Neutral-Point Clamped PWM inverter”, IEEE Transactions on

I.A., Vol. IA-17, No. 5, pp. 518-523.

Carrara, Gardella, Marchesoni, Salutari, and Sciutto, (1992) “ A New Multilevel PWM Method: A

theoretical Analysis”, IEEE Transactions on Power Electronics, Vol. 7, No. 3, July, pp.497-505.

José Rodríguez, Jih-Sheng Lai, Fang Zheng Peng (2002) “Multilevel Inverters: A Survey of

Topologies, Controls, and Applications”, IEEE Trans., VOL. 49, NO. 4, AUGUST

Anish Gopinath, Baiju, (2007) “Space Vector PWM for Multilevel Inverters- A Fractal Approach”

PEDS, Vol.56, No. 4, April, pp 1230-1237

Anish Gopinath, Aneesh Mohammed, and Baiju, (2009) “Fractal Based Space Vector PWM for

Multilevel Inverters-A Novel Approach” IEEE Transactions on Industrial Electronics, Vol.56, No. 4,

April, pp 1230-1237

Vivek pahwa, Sandhu (2009) “Transient Analysis of Three-phase Induction Machine using Different

Reference Frames” ARPN Journal of Engineering and Applied Sciences, Vol. 4, No.8.

Ogabuka, Eng (2009) “Dynamic Modelling and Simulation of a 3-HP Asynchronous Motor Driving a

Mechanical Load” The Pacific Journal of Science and Technology, Vol. 10, No. 2.

Krishnan (2003) “Electric Motor Drives” Pearson prentice Hall.

Leon Tolbert, Fang Peng, ,Thomas Habetler (1999) “Multilevel PWM Methods at Low

Modulation Indices” APEC ’99, Dallas, Texas, March 14-18, pp 1032-1039.


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