Hybrid Space Vector Pulse Width Modulation
Based Direct Torque Controlled Induction Motor
Drive
Udayar Senthil & B. G. Femandes
Department of Electrical Engineering,
Indian Institute of Technology Bombay,
Powai, Mumhai 400 076, INDIA.
A b w m - l l ~ emajor dbadbantage of lhr nmcotional DTC drite is
the steady slate ripples in tnrqur and nux. The implicntions HIT, iocmase
in acoustical noire, hnmiinir locna and i n c o m l sped atimalioo. Using spare \wIor modulalion tSVPWMl technique il is possible io reduce
ihc
square flu ripple uplo base spwd. In I h b paper a ICH h! brid
SVP\VM b a w l adjuslablcspwd DTC dritc is pmpored. 'Ibis h)brid modulator ullliias the zcm vollllgc vffior redundancy that lead\ 10 clamping
sequence. Wis improtes Ihe periomocu of Ihe drive compared lo that
using con%entionalwyuencr ucrd in SVPWLl technique ni higher r p d s .
Simulaltm muILc shon lhal Ihe rippler in flux, toque and current am reduced w e r lhe entire s p e d ranp.
Key,,rd$-Dimt toque conlrol, Space \mior PWhl
the ripples in flux, torque and cuirent are reduced over the entire
speed range. Since, the switching frequency is held constant the
proposed drive does not have continuos harmonic specturm as
in the case of conventional DTC.
11. THEORY
A. Dynamic model of Znduction Machine :
The voltage and flux linkage equations of induction motor
in the stator reference frame are given by:
Fs = R,;,
1. 1NTKOI)I:CTION
+pvs
(1)
+
Variahls-speed induction motor drives are increasingly being
0 = R,:;
plJr: - jarvJ
(2)
used in most of the industrail applications. The development of
= L,I;
L"?$
(3)
high performancecontrol strategies for AC drives. driien by the
requirement of industry, has resulted in a rapid evolution during
= L,i,. L&
(4)
ihelast twodecades. Oliheiwo high performancec~~ntrolstratc:Mi
Lr =: L,f :Mi
L,,, = :Mi
pies vi7. Field Oriuntcd Control(F0CJ 1 I I and Direct lorque where, L, =
ConLrolkDTC) 121. 131 the relatively newer 1)TC has drawn a lot
The electromagnetic torque is given by
o l attention due to its bimplicity. quick rcsponse, and reduced
machine parameter dependence. The conventional DTC uses
3P
a switching table and two hysteresis controllen for torque and
Z = 52 ( w i S q- vsqisd)
(5)
flux. The prohlems associated with DTC include. performance
deterioration due t o viiriaiion in stator resistance with temper- B. Conventional Direct Torque IContml
ature and frequency (particularly at Ion, specds), steady slate
The electromagnetic torque can also be written as :
torque and flux ripple. and variation in switching frequeny. The
pulsations in flux and torque aiieets the accuracy of speed csiiamtion. It 3 k O results in higher acoustical noise and in harmonic
losses. Also, the hamionic spectrum is cuntiunous due to variation in switching frequency. In DTC, ths switching frequency where,
2
L: = L $ L- L,,,
depends on rotor speed, hysteresis hand of flux and torque con(7)
troller~,and load. The major issue of >toady \late torque, flux
Since rotor time constant of squirrel cage induction machine
and current ripples-where I-OC clearly has an edgc over UI'C- is high, rotor flux linkage changes slowly compared to stator
waq treated hy Cnuinn I.ascu ci al. 141. Conventional S V P W flux linkage. So assuming both to he constant, it follows from
technique 151, 161, 171 using the sequcnce 0127-7210 WIS u w J (6) that
torque can he rapidly changed by changing 'y in the
to switch thc inverter devices upto hase speed.
required direction. At the same time, flux control can also he
achieved by selecting appropriate voltage space vectors.
I n this pnpcr a new hyhnd SVPWM hased adjustahle-speed
Neglecting stator ohmic drop, pqs = Us. This implies that
DTC drive is propuscd. 'lhic hyhrid modulator utilixs the zero the stator flux is determined by the input voltage. A forward
voltage vector redundoncy that leads to clamping rcquences. switching of the active voltage vector causes quick movement
This improvesthe performanceofthe dnvccompnred toconvcn- of
and, hence torque increases with '7.However, when the
tional sequence 31 higher spccds. Simulation results \how that zein voltage vector is applied,
becomes stationary. Since
continues
to
move
forward,
'y
and
torque decreases (although
Cc,rrcrp,nAn& Au1hort)r. H G remind:\. Telzphonc. -91 -22-25167421.
by
slightly). Therefore it is possible to change the speed of
t;,~: -91 -22-251227U1. F-mxl.hgf@cc.ttlb.a:.in
v;
+
+
+
vs
+
vr
ir.?
vs
0-7803-7754-0/03/$17.00 02003 IEEE
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changing the ratio of time duration between the zero and nonzero vectors.
Depending on the position of qsit is possible to switch the
appropriate vectors to control both flux and torque. An optimum
switching table is constructed for picking up appropriate voltage
vectors to increasddecrease torque and flux. At every sampling
period, the switching vectors are selected so that the stator fluxlinkage error and torque error are controlled within the hysteresis hands. The self-explanatory block diagram of conventional
DTC is shown in Fig. I .
In conventional DTC, Only one vector is applied for the
entire sampling period. So for small ermrs, the motor torque
may exceed the upperilower torque limit. Instead by using more
than one vector with in the sampling period torque ripple can
be reduced. The slip frequency can he controlled precisely by
inserting zero vectors.
The electromagnetic torque is given by:
(11)
Hence, torque and flux can he controlled by controlling vSq
and Vsd respectively. The reference torque generated by the
speed controller is compared with the estimated torque. This
error i s processed by the torque controller, whose output is the
magnitude of q-axis stator voltage in stator flux reference frame.
The d-axis voltage component is obtained from the flux controller. Finally, these components are transformed to stator reference frame and the resulting voltage vector is fed to the hybrid
SVPWM block which generates inverter switching signals.
C.1 Hybrid SVPWM
The time period distribution for the two active vectors, and
the total zero voltage vector time in a sampling period are given
by:
1 .
To, =MT,(cosa---ma)
d3
(12)
2MT, .
=
J5
a
r; = Ts - T,, - To2
Fig. 1. Conventional DTC block diagram
C. Proposed Hybrid SVPWM Based Adjustable-Speed DTC
Drive
The block diagram of the proposed drive is shown in Fig. 2.
(14)
where, Tal and To, are the durations of two active vectors V,.
and Vo2which form the boundaries of the sector, T; is the duration of the zero voltage vectors, T$ is the sampling period, M
is the modulation index given by
and alpha is the angle
which varies between 0 and 60 degrees.
The conventional SVPWM uses 0127-7210 sequence in
sector-I, 0327-7230 sequence in sector-I1 and so on (refer
Fig. 3). There are 3 switchings within a suhcycle. The total
zero voltage vector time is distributed equally hetween the two
vectors viz, V, and V7. However, for higher reference voltages in
the linear range, it is possible to do away with one zero voltage
vector [PI. This results in two clamping sequences. The word
'clamping' is used because one of the phases remains clamped
to either positive or negative DC bus of the inverter. In both
the clamping sequences it is possible to use either Vo or V7 for
zero voltage vector. Hence, in all there are 4 sets of switching
sequences. They are:
012-210(S1)and 721-127(S2) in sector-I
0121-1210(S3)and 7212-2127(S4) in sector-I
2,
..
Fig. 2. Pmposed Hybrid SVPWM Based Adjustable-Speed DTC Drive
The stator voltage components of the machine in stator flux
reference frame (where = \ysd) can be written as:
It is to he noted that, all the switching sequences including the conventional sequence result in same average voltage
space vector as long as equations (12),(13) and (14) are satisfied. However, mean square flux ripple is not the same for all
the sequences. Because zero voltage vector does not affect the
average voltage hut its placement directly affects the harmonic
performance. At higher modulation index the ripple content is
minimum for the clamping sequences. This is explained as follows:
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i
, p..
...Vrip1
0
I
1
7 ' 7
-,---*~rip0,7
1 : l : o '
*~~~~~~
.............~~~~~~*
T*
(a)
''-.4
VO,V7
v1
(b)
Fig. 4. Voltage ripple vector Ibr different applied vectols
Fig. 3. (a) Voltage space vectors (b)Conventional sequence
Fig. 4 shows the voltage ripple vectors due to VO,VI,VZ,V~
in the reference frame fixed to the reference fundamental vector. The stator flux ripple vector moves in the direction of the
voltage ripple vector. The flux ripple variation over a subcycle for the conventional SVPWM sequence is plotted in Fig. 5
for both high and low values of M. It can be seen that d-axis
component of flux ripple dominates over the q-axis component
at lower M and vice versa. Application of zero voltage vector
does not affect the q-axis component of flux ripple. However,
this component increases for VI vector and decreases for V2 vector. For higher values of M, in order to keep the peak value of
q-axis component within a tolerable limit, VI and Vz must be
switched frequently. This is true for other sequences also. In
other words, the ratio of the switchings ofthe devices connected
to the phase that cannot be clamped( phase B for sector-I), to
the switchings of the devices connected to phase which can he
clamped( phases A and C for sector-1) should be high. For the
conventional SVPWM this ratio is 0.5, for SI & Sz it is 1, and
for S3 & S4 it is 2. Hence, S3 and S4 perform better at higher
values of M.
The variation of flux ripple in a subcycle for SI and S2 in
sector-I is shown in Fig. 6. It is assumed that the reference voltage space vector is in the first half of this sector. For this case,
the mean square value of q-axis flux ripple is same for both the
sequences. However for Sz, the value of the d-axis flux ripple is high and remains approximately constant for T2/2 duration. So, application of SI in the first 30 degrees will result in
minimum d-axis flux ripple, while Sz in the next 30 degrees.
Similarly S, should be used for the first 30 degrees and Sq for
the next 30 degrees at highest M. The boundary region for the
different sequences are shown in Fig. 8 &. Fig. 9. Finally in
hybrid SVPWM, each sector is divided into 5 parts as shown in
Fig. I. The boundaries can be obtained from analytical expressions [8]. The flux mean square ripple at different modulation
indices within a sector are shown in Fig. IO-Fig. 13 . The proper
selection of sequences in a sector gives reduced torque and flux
ripples as compared to the conventional DTC.
(b) SLator nux ripple recIur wver s subcyde et lox 'm*
Rg. 5. Variation of stator flux ripple with modulation index
,,,i*-m
Fig. 6. Stator flux ripple over a subcycle -clamping sequences
1.0
*It
V I I Y P I sre
rn"dYl"llon lndlra
Fig. 7. Hybrid SVPWM showing five parts of a sector
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zm:LqA
-.__
........
.wdlrla
10.0
0.7
.......
........
...:::
j
oe
.........
.........
<
.-..
0x21
......
:. . . . . . . . . .
...
.
OII
....
.......
0s
s-*,w.
(0
(W9"",
&~"'----------,{;..&&;
.........
........
.........
........
I..,
.."
1. = . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
05
a
a
M
-I.w*,d-,
Fig. 8. Boundary condition for0127-012 & 0127-721
10
-...b,--,
30
10
a
Y
ca
Fig. 12. Flux mean square ripple plot withm a sector for M 3 . 7 3
Fig. 9. Boundary condition for012-0121 & 721-7212
Fig. 13. Flux mean square ripple plot within a sector for M 3 . 8 6 6
7-.,-,
C-.-,_,*.--.,
Fig. 10. Flux mean square ripple plot within a sector for M3.525
4
M
9
19
a
I'ig. 14. Conventional DTC: No-load steady state plots, 45 Hz (1350 rpm),
1 Vh, I = I m.
I
ma
TI..<.r>
SXmw.cdalll
Fig. 1 I . Flux mean square npple plat within a sector for M=0.534
Fig. 15. Conventional DTC No load starting transients, 1 V,,,,
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1 = 1 Wb.
,.y
:
-
- - ,II-- .
,::./
.:.:
. ..........
......
..................
.......
.........
. . . . . .
E-
1,
0s
I.
...
....
..........
,
.......
......
. . ........ .. .. .. .
. . .
. . ....... . .
.........
............
...........
............
...........................
**a
0-
0 2
..
0.
1
ca
a
E=
.........
tm
.......
.=
Fig. 16. Conventional DTC Speed & Torque hansients during no load acceleration from 5 4 5 HI,I vsm,
1 = 1 wh.
Fig.20. Locus of stator flux in Hybrid SVPWM based DTC
.-
:
i5,e :L.
om
07
0,s
om
0.
....................
.....
.......
. . .
om
07
5-
07,
os
.
-K;!
1
om
0.
.
08
~
d
;
-
_ e
8..o m
14 --:
o._
0.
01
036
........
~
0-
0.
............
.
.
.........
. .
.......
D m
0.-
.....................
om
0.
07
0.
'
q---,,
.....
...
0
3
'
!
.
,
-.3,
-I_
1-......
8-
..
"..... . .
....... :.
+
"~
........i...
.
:
..........
.
..........
m
P._
......
....
....................
.
.
.
j
0%
.
I"
!
.
.
I
...... :.
.
.......:.;
....
.........
.......................
~
~
,L)
.
.
0.
0-
...........
.........
.........
..........
.........
:
.........
........
......
.............
.............
..........
..........
...........
.............
..~
. . . . . . . ". .. ~ ..
"
. I " ..
. . " I" ._
" . _ ..
i..
M
g-,
.:.*
-.
0.Q
- "y*b:
'
.............
.... ..... .",:
. ..........
..
.
. . . . . .. . . . . ..
o m -
.
.
.......................
r
.
........
. ...........
.
o
. . . . . . . . . . . . . . . . . .
0.17
0.7s
DlBI
0,s
-,I.
Fig. 18. Hybrid SVPWM based D T C No-load steady stale plots, 45 Hz (1350
rpm), I
,-,
o*
0,s7.".
0.as
D l l
011,
Fig.22. Hybrid SVPWM based D T C Speed & Torque transients during no
load acceleration from 545 Hz, I vImI
1 = 1 wb.
vsmf
I = 1 Wb.
.....
+a6
0s
8 Obr,
0:e
-0-
0.1.
.........
........
.,
-1
a
-6
-.-"".-
00
Fig. 19. Locus of stator flux in eanventionrll DTC
0.-
U
o:,
.....
0,s
*&
vas
9s
0,;s
018
0.83
os
. . . . . . . . . .
. . . .
.....
........
......
......
T",.,_,
Fig.23. Hybrid SVPWM based D T C :Stepchange in torque from 0 to 30 N-m,
I vk., I = 1 wb.
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111. SIMULATION RESULTS
REFERENCES
MAI'LAB/Simulink based simulation studies are canied
out to predict the performance of the proposed and Conventional
DTC drives. Various conditions such as starting, step change in
load are simulated. The parameters and the rating of the machine used for the study are given in Appendix. The simulated
results are shown in Fig.14-Fig.23. It can be observed that in
the proposed drive there is a significant reduction in the torque
and flux ripples. This has resulted in the reduction in the speed
pulsation.
[I] F.Blaschke,"The principle of field orientation as applied to the new
bansvector closed Imp contml of rotating machines:'Siemens Review,
~01.30,"0.5, pp.27-220, 1972.
[Z] I. Takahashi and N. Noguchi,"A new quick response and high efficiency
conml strategy of an induction motor,"IEEE Trans. on Indusuy Applications, ~01.22,"0.5. Sept./Oct. 1986,pp.820-827.
[3] M. Depenbrok'Direct Self-Conml(DSC) of inverter-fed induction machine:'IEEE Trans. on Power Electmnics, vol.PE-3, 110.4, Oct.1998,
pp.420-429.
Modified Direct
~ 4 1Cnstian Lascu. Ion Baldea, and Frede Blanbjerg.'X
Toque Canml for Induction Motor Sensorless Drive:'IEEE Trans. Ind.
Applications vo1.36, pp.122-130,lan./Feb. 2OOO.
rsi. H.W. van der Broeck H.C. Skudenly and G.V. SIanke,"Analysis and red.
imtion of a pulse width modulator based on voltage space vecIan,"lEEE
Trans. Ind App. ~01.24,pp.142-lSOk.Feb.1988.
[SI Handley P.G. and Boys J.T.,"Space vector modulation : an engineering
review:'IEE 4th International Conf. on Power Electronics and VSDs,
Conf.Puh.324. 1990.00.87-91.
[7l Handley P.G. and BO;bI.T.~Practicd Real-Time PWM modulalm : An
assessmenL'7EE hoc. pan B, ~01.39,1992, pp.96-102.
[SI G. Narayanan," Synchronised Pulsewidth Modulation Strategies based on
Space Vector approach for Induction motor drives:Phd. Thesis, Indian Institute of Science, Bangalore, Aug.1999.
Appendix
Rated output power
Rated Voltage
Rated Torque
Ploes
4kW
400 v
30 N-m
RS
1.57 Q
1.21 n
0.17H
0.17H
0.165H
4
R,
LS
L,
L"
IV. CONCLUSIONS
The ripples in torque, flux and current for conventional DTC
are very high. The harmonic spectrum is continuous due to variable switching frequency. Also the inverter has to be designed
for the maximum switching frequency,though it mostly operates
at lesser switching frequencies.
A new hybrid SVPWM based adjustable-speedDTC drive for
induction motor is developed. In hybrid SVPWM, each sector is
divided into five parts to reduce the torque and flux ripples over
the entire speed range. The simulation results for the drive show
that ripples in torque and flux are significantly reduced. This
has resulted in the reduction in speed pulsatation. The switching
frequency is also constant allowing the inverter to be used to its
full capacity. Also the hybrid SVPWM based DTC does no1
1 e continuous harmonic spectrum as in conventional DTC.
I
List of Symbols
:
2phase variables in stator ref. frame
2phase variables in synch. ref. frame
Voltage space Vector
Stator c m n t space vector
Stator Rm linltage space vector
Resistance parameten
Inductance parameten
Single phase magnetizing inductance
Leakage inductance
Stator tmmient inductance
Differential operator
Electromagnetic toque
No. of poles
Angle between Txand @:
Position of stator flux vector
Voltage ve~torsin VSI
Voltageripplevectorsdueto Vo,K, ...,V,
Time duration of VI,V2
Reference voltage vector
DC link voltage
Modulation index
Speed of stator flux vector
Electrical rotor frequency
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