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ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
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86
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 (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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(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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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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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.
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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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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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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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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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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.