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

Design of Multilevel Inverter Driven Induction Machine
Urmila Bandaru
G.. Pulla Reddy Engineering College, Kurnool
A.P., India
E-mail: urmila913@gmail.com

Subbarayudu
Brindavan Institute of Technology, Kurnool
A.P., India
E-mail: dsr@gmail.com

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 (V AO) 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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Vol 2, No 6, 2011

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

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Vol 2, No 6, 2011

818 718 618 518 018 418 318 218 118

828 728 628 528 028 428 328 288
817 128
717 617 517 017 417 317 217 117

827 838 738 638 538 038 438 338 238
816 327 138
716 727 627 527 027 427 227 127
616 516 016 416 316 216 116

826 837 848 748 648 548 048 448 348 248 148
815 715 726 637 537 037 437 337 237 137
737
615 626 526 026 426 326 226 126
515 015 415 315 215 115
808 708 608 508 008
825 836 847 747 647 547 047 447 408 308 208
108
810 710 725 736 636 536 036 436 336 347 247 157
610 625 525 025 425 325 225 236 136
510 010 410 310 210 110 125
846 807 858 758 658 558 058
820 835 735 746 707 607 507 007 407 458 358 258
814 158
714 720 620 635 646 546 046 446 346 307 207 107
614 514 205 535 435 435 335 235 246 146
014 020 868 420 768 320 220 120 135
806 758 668 568 068
414 757 314 657 214 114
824 830 845 745 607 557 057 457 468 368 268
813 606 506 168
713 724 730 630 546 006 406 306 357 257 157
545 045
613 624 524 035 445 345 245 206 106
030 878 430 778
513 013 420 867 330 230 130 145
424 767 324 667 678
840 805 658 314 756 224 124 578 078
313 656 213 556 567
823 834 734 740 507 113 067 467 478 378 278
812 605 505 056 178
712 723 623 634 046 005 456 356 367 267 167
540 040 405
612 523 435 440 305 205 256 156
512 034 877 888 340
866 434 334 788 688 240 140 105
012 855 320 423 766 777 234
844 800 755 323 223 677 577 134 588 088 488
700 214 312 655 666 123
822 833 733 744 600 212 112 566 066 077 477 377 388 288
644 500 555
711 722 622 633 544 055 455 466 366 266 277 177 188
811 533 044 000
611 511 522 033 400 300 355 255 155 166
022 433 444
011 865 422 876 887 787 344 687 244 200 100
850 411 322 333 587
750 311 765 776 676 233 576 133 144 087 487
832 704 211 222 076
843 804 604 650 665 565 122 065 476 376 387 287
721 643 111 050 465 276
732 743 543 504 550 450 365 265 176 187
821 532 404 350 165
621 632 032 043 004 304 150
021 421 875 432 886 443 786 343 686 586 204
521 243 250
854 860 760 321 775 332 675 232 575 075 143 086 486
842 803 132 286
703 754 654 660 221 560 121 060 460 475 375 386
731 742 354 104 260 275 175
831 642 603 503 554 054 454 360 186
631 531 542 042 003 403 303 203 254 154 160
031 431 885 442 785 685 242 585 142 103
342
870 770 670 570 131 070 085 485
331 231
802 853 864 764 664 564 064 464 470 370 385
285
741 702 753 653 553 053 453 353 364 264 270
841 170 185
641 602 502 002 402 302 202 253 153 164
541 041 441 341 241 141 102
880 780 680 580 080 480
852 863 874 774 674 074 474 374 380 280
574
701 752 763 663 563 363 263 274 174
063 463
801 601 652 163 180
552 052 452 352 252 152
501 001 401 201 101
884 301 584
784 684 084
862 873 484 284
773 673 573 073 473 384
751 762 373 173
662 562 062 462 362 273
851 651 262 184
551 051 451 351 251 162
151

872 283
761 883 783 683 583 083 483 383
861 172
772 672 572 072 472 372 272 183
661 561 061 461 361 261 161

882 782 682 582 082 482 382 282
871 771 671 071 271 171 182
571 471 371

881 681 581 081 481 381 281 181
781

Figure 2 Nine-Level Inverter State Space Vector Diagram

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)

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Vol 2, No 6, 2011

(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 V dc/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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Vol 2, No 6, 2011

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.

64

63
49 62

48 61
0
36 47 60

35 46 59
25 P 34 45 58

24 33 44 57
16 23 32 0 43 56

15 22 31 42 55
9 14 21 30 41 54

8 13 20 29 40 53
4 7 12 0 19 28 39 52

3 6 11 18 27 38 51
1 2 5 10 17 26 37 50

Figure 3 Sector1 Regions Space Vector Representation

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.

e
 
vqds  T c vqds
(8)

e

vqds  vqs
e e
vds ,
t
vqds  vqs vds 
t
(9)

  sin  
T   cos
c
 sin cos   (11)
 

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Vol 2, No 6, 2011

Vqs   Rs  Ls p
e
s Ls Lm p s Lm  iqs 
e

 e  e
Vds     s Ls Rs  Ls p  s Lm Lm p  ids 
 (13)
Vqr  
e
Lm p (s  r ) Lm Rr  Lr p (s  r ) Lr  iqr 
e

 e   e 
Vds   (s  r ) Lm
  Lm p  (s  r ) Lr Rr  Lr p  ids 
 

The electromagnetic torque is
3P
Te  Lm (iqsidr  iqrids )
e e e e
(14)
22
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.

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Vol 2, No 6, 2011

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.

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
0 0.5 1 1.5 2

Figure 4 MCMM Stator Currents, Torque and Speed
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
0 0.5 1 1.5 2

Figure 5 SCMM Stator Currents, Torque and Speed

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Vol 2, No 6, 2011

400

300

200

100

0

-100

-200

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

Figure 6 SCMM, MCMM Stator Currents for speed reversal
from +314rad/sec to -314 rad/sec

300

200

100

0

-100

-200

-300

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

Figure 7 SCMM, MCMM Stator Currents for speed reversal
from -314rad/sec to +314 rad/sec
100

0

-100

-200

-300

-400
0.75 0.8 0.85 0.9 0.95 1 1.05 1.1

100

0

-100

-200

-300
0.75 0.8 0.85 0.9 0.95 1 1.05 1.1

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

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Vol 2, No 6, 2011

320

300

280

260

240
0.35 0.4 0.45 0.5 0.55 0.6

350

300

250

200
0.35 0.4 0.45 0.5 0.55 0.6

Figure 9 SCMM, MCMM rotor speed when torque change
from 0 to +50 N-m

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
0 0.01 0.02 0.03 0.04 0.05 0.06

Figure 10 SCMM Pole, Phase and Line Voltage

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
0 0.01 0.02 0.03 0.04 0.05 0.06

Figure 11 MCMM Pole, Phase and Line Voltage

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Vol 2, No 6, 2011

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
0 0.5 1 1.5 2 2.5 3 3.5
Figure 12 SCMM Stator Currents, Torque and Speed with V/f Control

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
0 0.5 1 1.5 2 2.5 3 3.5
Figure 13 MCMM Stator Currents, Torque and Speed with V/f Control
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
0 0.5 1 1.5 2 2.5 3 3.5

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

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Vol 2, No 6, 2011

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
0 0.5 1 1.5 2 2.5 3 3.5

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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