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IMPROVING IMPROVING DIRECT TORQUE CONTROL DIRECT TORQUE CONTROL
USING MATRIX CONVERTERSUSING MATRIX CONVERTERS
Technical University of Catalonia. Electronics Engineering Department. Colom 1, Terrassa 08222, Catalonia, Spain
University of Malta.Department of Electrical Power and Control Engineering.
Msida MSD 06, Malta
Research Student:
Carlos Ortega García
Home Supervisor:
Dr. Antoni Arias Pujol
Malta Supervisor:
Dr. Cedric Caruana
2
IndexIndex
Introduction
Matrix Converters.
Direct Torque Control.
Classical
Using Matrix Converters.
Sensorless Control of a DTC drive using hf injection
Conclusions.
3
IntroductionIntroduction
Matrix Converters (MC) Advanced circuit topology capable of generating AC-AC.
Load voltage with arbitrary amplitude and frequency, and
sinusoidal input/output waveforms.
Power Factor Correction (PFC).
No inductive or capacitive elements
are required, thus allowing a very
compact design.
A very good alternative to Voltage Source Inverters (VSI).
4
Direct Torque Control (DTC).
Simple and robust signal processing scheme. No coordinate transformation and no PWM generation are
needed. Quick and precise torque response. The torque and flux modulus values and sector of the flux are
needed. High torque ripple.
IntroductionIntroduction
5
High Frequency Signal Injection.
Non Model-Based method. Avoids problems at low and zero speed due to the lack of
back-EMF. No dependence of machine parameters. Saliency required.
IntroductionIntroduction
6
Main objectives:
Improve the Direct Torque Control, regarding torque ripple,
using small vectors of Matrix Converters.
Analysis of different High Frequency signal Injection
methods for sensorless Direct Torque Control.
IntroductionIntroduction
7
A switch, Sij, i={A,B,C}, j={a,b,c} can
connect phase i of the input to phase j of the load.
Switches states characterized by:
closed is switch if 1
open is switch if 0
ij
ijij S
SS
A mathematical model of the MC can be derived:
Voltage equations: Current equations:
)(
)(
)(
)()()(
)()()(
)()()(
)(
)(
)(
tv
tv
tv
tStStS
tStStS
tStStS
tv
tv
tv
C
B
A
CcBcAc
CbBbAb
CaBaAa
cN
bN
aN
)(
)(
)(
)()()(
)()()(
)()()(
)(
)(
)(
ti
ti
ti
tStStS
tStStS
tStStS
ti
ti
ti
c
b
a
CcCbCa
BcBbBa
AcAbAa
C
B
A
V SBS Ab
S Ac
V SA
V SC
M
Lf
Lf
Lf
R f
Rf
Rf
S Aa
S Ba S Bb S Bc
S Cb S CcS Ca
Cf
Cf
Cf
Matrix ConverterInput Filter
ISB
ISA
I SC
I a I b I c
IB
IA
I C
VaN
VbN V cN
State of the ArtState of the Art
Matrix Converters
8
Since any output phase can be connected to any input phase, there are 27 possible switching configurations.
Applying Clark’s transformation to all switching states, it can be found that MC can generate:
18 active vectors, 6 rotating vectors, and 3 zero vectors.
Output line-to-neutral voltage vectors Input line current vectors
Matrix Converters
Sector
1
23
4
56
±1,±2,±3
±4,±5,±6
±7,±8,±9
a )
Sector
1
23
4
5 6
±2,±5,±8
±1,±4,±7±3,±6,±9
b)
State of the ArtState of the Art
9
Direct Torque ControlDirect Torque Control
Stator flux *s and torque T*
e
references are compared with the corresponding estimated values.
Both stator flux and torque errors, E and ETe, are processed by means
of hysteresis band comparators.
A proper VSI voltage vector is selected.
The flux vector reference and the hysteresis band tracks a circular trajectory, thus, the actual flux follows its reference within the hysteresis band in a zigzag path.
Look-up table
Flux and Torque Estimator
S
H
T e
T e*
S*
T e
S
E
H Te
E Te
Voltage Source Inverter
IA
IB
V o
S A
S B
S C
S(n)
M
S(1)
S(2)S(3)
S(4)
S(5) S(6)
V 3t1
V 4t2
V 3t3V 4t4
S
V 1
V 2V 3
V 4
V 5 V 6
1
23
4
5 6
a) b)
sin||||'2
3sr
sr
me LL
LpT
10
Direct Torque Control using Direct Torque Control using Matrix ConvertersMatrix Converters
Matrix converter generates a higher
number of output voltage vectors with
respect to a VSI.
Another variable, <sin >, is
introduced to control the input power
factor.
Keeping this variable close to zero,
unity power factor operation is
possible.
A new hysteresis comparator is introduced which controls this variable.
Classical DTC using Matrix Converters
Voltage VectorTable
MatrixConverter
Flux and TorqueEstimator
S
H
T e
T e*
S*
T e
S
IA
IB
V o
S(n)
S A
S B
S C
H
H Te
<sin >
E T e
E
< sin >estimator
M
Direct Torque Control for Induction Motors Using Matrix Converters (CPE-05)
11
A new torque hysteresis comparator will provide
four different levels instead of three to distinguish
between small and large positive and negative
torque errors.
E Te
H Te
H TeE Te
Large vectors will be used when large
torque error is detected.
When torque error is small, the small
voltage vector will be applied.
Zero vectors will be applied if small
torque error is detected and back EMF
imposes a variation in torque towards
its reference value.
The use of small vectors of Matrix Converters
Zero vector applied Low torque slope
Small vector applied Medium torque slope
±Upper torque band
±Lower torque band
Large vector applied High torque slope
±Upper torque band
±Lower torque band
a) b)
Direct Torque Control using Direct Torque Control using Matrix ConvertersMatrix Converters
12
Torque ripple performance.Comparison between the classical use of MC in DTC and the proposed method.
Classical DTC using MC Proposed method
0.85 0.9 0.95 14
4.5
5
5.5
6
6.5
7
7.5
8
Time (s)
Tor
que
(Nm
)
0.85 0.9 0.95 14
4.5
5
5.5
6
6.5
7
7.5
8
Time (s)
Tor
que
(Nm
)
The use of small vectors of Matrix Converters
ref=100% rated speed and TL=100% rated torque.
Direct Torque Control using Direct Torque Control using Matrix ConvertersMatrix Converters
13
Torque ripple performance.Comparison between the classical use of MC in DTC and the proposed method.
The use of small vectors of Matrix Converters
0 250 500 750 1000 1250 15000.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Speed (rpm)
rms
valu
e of
Te
ER
RO
R (
Nm
)
Classcal DTC using MCProposed method
The use of zero and large vectors in the classical method leads into an over/undershoot, more pronounced as the speed increases.
Small vectors are more effective keeping the torque within the its reference bands.
Direct Torque Control using Direct Torque Control using Matrix ConvertersMatrix Converters
14
Sensorless ControlSensorless Control
Saliency
gmax
gmin
r
(a)
(b)
gmaxgmin
Lm
r(elec)
Asymmetry in the machine. Magnetizing inductance variation. Asymmetry in the rotor Rotor Position.
t
tV
v
v
i
ii
si
si
cos
sin
tLtL
tLtL
LL
Vi
i
irsis
irsis
qsdsi
i
si
si
2sinsin
2coscos
15
Sensorless ControlSensorless Control
frame rotating injection. Straightforward in vector
controlled drives. The carrier can be
superimposed to the voltage reference.
v ds*
iqs*
ids*
VoltageSourceInverter
iabc
i
PMSM
flux positionestimate
+
-
-
+
abc
e
++
+
+
dq
dq
PI
PI
ids
iqs
v qs*
vs*
vs*
vsi
vsi
i
i
i
tan -1e j2 ite -jiti i i i ipos
Synchronous filter
Band-pass filter
High-pass filter
2r
16
Sensorless ControlSensorless Control
injection in a DTC drive. Flux and Torque processed errors, Hs and
HTe, converted directly to switching signals.
No voltage command => Difficult to inject. Injection directly modifying the vector
pattern imposed by the DTC switching table.
V 4 V 5 V 4 V 6Vn
Vn
Vn+
1
Vn+
1
x K x K
T z
T i
Voltage VectorTable
Stator Fluxand
TorqueEstimator
S
H
T e
T e*
S* E
H Te
E Te
VoltageSourceInverter
iabc
i
S A
S B
S C
S(n)
PMSMInjectionalgorithm
VSI+
PMSM hf Model
abc/
i i
VSI+
FundamentalEstimator
Synchronousfilter
i f
+
-
-
-
-
+
+
+
High bandwidth of hysteresis controllers. Difficult to inject outside of this bandwidth. Decoupling of fundamental and hf currents is necessary
17
Sensorless ControlSensorless Control
injection in a DTC drive.
Steady state at 375 rpm Speed reversal.
Comparison between real and estimated position
0 0.05 0.1 0.15 0.2-4
-2
0
2
4
Time (s)
Mod
el b
ased
an
gle
esti
mat
e (r
ad)
0 0.05 0.1 0.15 0.2-4
-2
0
2
4
Time (s)
Inje
ctio
n m
etho
d
angl
e es
tim
ate
(rad
)
0 0.1 0.2 0.3 0.4 0.5 0.6-4
-2
0
2
4
Time (s)
Mod
el b
ased
an
gle
esti
mat
e (r
ad)
0 0.1 0.2 0.3 0.4 0.5 0.6-4
-2
0
2
4
Time (s)
Inje
ctio
n m
etho
d
angl
e es
tim
ate
(rad
)
18
Conclusions Conclusions
Advantages of Matrix Converters over the traditional VSI has
been combined with the advantages of the DTC scheme.
The use of small vectors of the MC has been investigated.
High frequency injection in a DTC drive has been presented.
19
Thank you.