[doi 10.1109_iemdc.1999.769200] jun-koo kang, ; dae-woong chung, ; seung-ki sul, -- [ieee electric...
TRANSCRIPT
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8/18/2019 [doi 10.1109_IEMDC.1999.769200] Jun-Koo Kang, ; Dae-Woong Chung, ; Seung-Ki Sul, -- [IEEE Electric Machines a…
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Direct Torque Control
of
Induction Machine with Variable Am plitude
Control
of
Flux and Torqu e Hysteresis Bands
Jun-Koo Kang Dae-Woong Chung and Seung-Ki
SUI
School o f Elec t r ica l Engineering
Seoul Nat ional Univers i ty
S a n 56-1, Shi l l im-Dong, Kwanak-Ku, Seoul , Korea , 151-742
Ph o n e : 82-2-880-7243, Fa x :+82-2-878-1452 e-mail : [email protected],
httD://eeDel.snu.ac.kr
Ab s t ra c t
-
In th i s paper, e ffec ts o f the hysteresi s bands on the
Di re c t To rq u e C o n t ro l (DTC ) o f a n i n d u c t i o n ma c h i n e a re
invest iga ted , and a method to cont ro l the swi tch ing frequenc y of
inverter by a variab le ampl i tude of the hysteresi s band i s
proposed for D TC of an induct ion machine.
A
m a j o r d r a w b a c k
of thc convent ional DTC is an unpred ic tab le inverter swi tch ing
frequency which varies due to opera t ing speed , load condi t ion
a n d p a ra me t e r s of t h e i n d u ct i o n ma c hi n e . Th e re fo re t h e
amp l i tude of the hysteresi s band should be la rge enough to avoid
excessive inverter swi tch ing a t any opera t ing reg ion , which
inev itab ly causes re la t ive ly la rge to rq ue r ipp le especial ly in the
low speed reg ion . This paper p roposes an effec t ive swi tch ing
frequency regula t ion method which consis t s o f hysteresi s band
c o n t ro l l e r a n d swi t c h i n g f re q u e n c y c o mma n d g e n e ra t o r . Th e
effec t iveness o f the proposed s t ra tegy i s analyzed and compared
wi th the convent ional method .
1. INTRODUCTION
Since the innovative studies in the mid-1980’s [I]-[2],
application fields of the Direct Torque Control (DTC)
strategy have been increased including paper machines,
traction and mill drives. DTC provides a fast dynamic
response of torque and a robustness to machine parameter
variations without current regulators. Among several DTC
strategies [3
1
the voltage vector selection strategy using
switching table has been widely used because it is easy in
concept and simple in implementation, only using torque and
flux hysteresis comparato rs. The amplitude of hysteresis band
strongly influences the inverter performances such as flux and
torque ripples, current harmonics and switching frequency of
power device. A major drawback of the conventional DTC is
unpredictable variation of switching frequency according to
machine parameters and operating speed conditions even
though the amplitude of hysteresis band set to constant value.
Therefore the hysteresis band has to be set large enough to
limit the inverter switching frequency below a certain level
that is usually determined by thermal restriction of power
devices. Since the hysteresis bands are set to cope with the
worst case, the system performance is inevitably degraded in
a certain operating range, especially in a
low
speed region.
In this paper, a new DTC control strategy with variable
hysteresis bands is presented. The proposed strategy modifies
the hysteresis bands
so
that the inverter switching frequency
can follow a given command frequency. The switching
frequency variation characteristic of the flux hysteresis
controller is different from that of torque hysteresis controller.
This phenomenon makes flux and torq ue hysteresis controller
to
have different contributions to the total switching
frequency. It means that the amplitude of flux and torque
hysteresis controller should be regulated separately for
effective utilization of given total switching frequency
comman d. In this paper, total switching frequency command
f, is divided into
two
components, i.e., f s i and j,:, and
then each command frequency is separately regulated by
switching frequency controller which modifies the amplitude
of flux and torque hysteresis comparators.
11. SWITCHING FREQUENCY VARIATION IN DTC
An induction machine can be modeled with stator and
rotor fluxes as state variables by the following equation.
0-7803-5293-9199 10.00 1999 IEEE
640
where os nd or are stator and rotor flux complex vectors,
v, is stator voltage complex vector, R ,
and
R, are stator and
rotor resistances,
L ,
and
L~
are stator and rotor self
inductances,
L
is a mutual inductance, c is leakage
coefficient with CT =
- L:
/
L L
and 0 is rotor angular
velocity. The electromagnetic torque can be expressed in
te rn s of stator and rotor flux as
where P is the number of poles of the machine and “ t ”
denotes the complex conjugate. Using (1) and (2), variations
of torque and flux during control sam pling time t s p t (k+l)‘h
sampling instant can be expressed as follow :
[4]
4)
As can be seen from (3), the variation of torque
A<
during
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8/18/2019 [doi 10.1109_IEMDC.1999.769200] Jun-Koo Kang, ; Dae-Woong Chung, ; Seung-Ki Sul, -- [IEEE Electric Machines a…
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t s p
i.e., torque slope is a function of stator voltage, stator and
rotor fluxes, and motor speed. Therefore, in a torque
hysteresis controller, an elapsing time to move from lower to
upper limit, and vice versa can be changed according to
operating conditions. This characteristic makes the variation
of the switching frequency according to various load and
speed operating conditions. In case of stator flux, as can be
seen from 4), the angle between stator voltage vector and
flux vector determines the rate of flux variation. As this angle
varies with a rotating stator flux in the space vector plane,
flux slope is changed. Therefore the rotating speed o f stator
flux proportion ally affects the variation cycle of flux slope.
Fig. shows the switching frequencies of the torque and
flux hysteresis controllers versus motor speed with different
hysteresis band amplitude, where p 7 denotes the size of
hysteresis band of torque controller in per unit and p
denotes that of flux controller. As can be seen,
fi has
maximum value in a medium speed range while switching
frequency of the flux hysteresis controller fa s proportional
to the rotating speed
con .
Thus, for a regulation of switching
frequency, two variable amplitude hysteresis controllers are
required.
8
( r l l i 4 0 0 3 ib) i 4 U l ( r l P-aOZ
id1 p U O 7 i d g -OO5 in
8 A O i
a8
I v
0
(a) Torque hysteresis control.
0
M
m
lcel
1440 llD0
Motor spccd
o
dmin)
k x o r
spccd
mm
dn i in )
(b) Flux hysteresis control.
Fig. I . Simulated switching frequency o f hysteresis controllers versus
motor speed with different hysteresis bands of pa, and
PT
111.
THE PROPOSED SWITCHING FREQUENCY REGULATION
The basic implementation of the proposed
DTC
system is
presented in Fig.
2
The goal is to maintain the switching
frequency at a commanded value equal tot:. Fig 2 is a
diagram
of
flux hysteresis controller, but a torque controller
also has a same structure. The basic technique to achieve the
constant switching frequency is not quite different from the
case of hysteresis current controller which also modifies the
amplitude of hysteresis comparator
[5].
The proposed
switching frequency regulation strategy can be briefly
described as; pulse counter counts the output pulse of
hysteresis comparator S and the counter output is used as a
feedback to the
PI
controller. Frequency command, J,:, is
integrated to obtain a switching count command. Then PI
controller modifies the amplitude of hysteresis band in order
to drive feedback-switching count,
N
of flux controller to
commanded values, N ; . The dotted line indicates the
optional amplitude predictor which can be used as
a
feedforward compensation signal. But for an accuate
prediction, electical parameters and rotor speed are required
as can be seen from (3) and
4).
Fig. 3 shows a DTC control block diagram with the
proposed variable hysteresis band controller. Like hysteresis
bands setting procedure in the conventional DTC, the ratio
of
f ; and
f ;
should be determined depending on the
application requirement. A frequency command divider
calculates two frequency commands based on the ratio. Stator
voltage vector v, is selected by S
S ,
nd stator flux sector
.
A
voltage selection rule is same as the conventional DTC.
IV. SIMULATION RESULTS
Simulations have been carried out for the evaluation of a
proposed algorithm. Simulation parameters are as follows ;
Motor ra t ing
:
3 phase,
4
ole,
220V,
7.5kW,
40
N-m
Pa ra me t e r : Rs= 0 . 1 5 8 , Rr
=
0 .1 7 8 , Ls=3 5 mH, Lm= 3 3 .8mH,
Lr=35mH
load
inertia
=0.4 kg-m2.
PI
Control ler
Fig. 2. Flux hysteresis controller with switching frequency regulation.
641
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8/18/2019 [doi 10.1109_IEMDC.1999.769200] Jun-Koo Kang, ; Dae-Woong Chung, ; Seung-Ki Sul, -- [IEEE Electric Machines a…
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vol tage
vector
Selection
Switching
Frequency
I 1 tmledor
I I I I
Fig. 3. Control block diagram of the Proposed DTC
Fig. 4 shows the torque control characteristic of the proposed
DTC method. At I = 0.02
s,
torque command is set to 50N-m,
120% of the rated value, and at motor speed U = 1750 r/min,
120
load torque is applied. As can be seen, the amplitudes
of torque and flux ripple vary according to operating speed .
For comparison igures of torque and flux are also presented
with constant hysteresis band. Fig. 5 shows the variation
of
hysteresis band under the same operating condition as Fig. 4.
As can be seen, both torque and flux controllers maintain
their frequencies at command values (dotted lines)
whilep,. and pg are varied according to operating speed.
The fkequency errors of flux in low speed region and error
of
torque in high speed region come from the limitation
of
control cycle time (here 2 5 ~ s ) .
s
I
-
'i
5
e
0
.- I
I
0 0 0 4
0 8 1 2 1 6
2 0
time
s)
machine drive. (upper two; conventional DTC for comparison.)
Fig. 4.
Step torque characteristic of the proposed
DTC
induction
I I
ci
0
9
- -
0
.
0 0 0 4 0 8 1 2 1 6
2.0
time
(s)
Fig. 5 Switching frequency control characteristic of system
V.
CONCLUSION
In this paper, the switching frequency of DTC inverter is
controlled for the improvement
of
drive performance. The
main advantages of the proposed DTC method are
;
efficient
and s table utilization
of
power devices by regulating inverter
switching frequency, and improvement
of
torque ripple
characteristic in a low and high speed regions. The
differences between conventional and proposed DTC have
been investigated. The simulation results verify the feasibility
of the proposed control.
REFERENCES
[ l ]
I.Takahashi,T.Noguchi,
A
new quick-response and high-efficiency
control strategy of an induction motor, IEEE Trans. on
Ind.
M. Depenbrock, Direct self-control DSC )of inverter-fed induction
machine, IEEE
Trans.
on Power Elcr.,Vol.3, N o.4, pp.420-429,1988
G. Buja, D. Casadei, DTC-based strategies for induction motor
drives I, in Con
Rec.
IEEE-IECON, pp1506-1516,1997
J.K. Kang, S.K. SUI, Torque Ripple Minimization Strategy for
Direct Torque Control of Induction Motor, in Con Rec. IEEE-IAS,
pp. 438-443, 1998.
L.Males ani, P. Mattavelli, High-performance hysteresis modulation
technique for active filters, in Proc. IEEE-APEC, pp. 939-946, 1996
Appl V01.22
O.5 p.820-827,1986.
[2]
[3]
[4]
[5]
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