1 matrix lecture
TRANSCRIPT
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Direct AC/AC Matrix Converters
Direct AC/AC Matrix ConvertersDirect AC/AC Matrix Converters
Dipartimento di Ingegneria Elettrica
Alma Mater Studiorum - Universit di Bologna
Viale Risorgimento, 2 - 40136 Bologna
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Matrix Converters
3ii
0
3oi
2ii
3iv
1oi 2oi
1ii
3ov
2iv
33S
1ov 2ov
1iv 11S
12S
13S
21S
22S
23S
31S
32S
Basic schemeof matrix converters.
have received considerable attention in recent years
may become a good alternative to PWM-VSI topology
Bi-directional power flow
Sinusoidal input/output waveforms
Controllable input power factor Compact design, due to the lack of
dc-link capacitors for energy storage
Topology complexity of the matrix
converter makes study a hard task
Topology complexity of the matrix
converter makes study a hard task
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Space Vector Modulation (SVM) algorithm
SVM completely exploit the possibility of matrix converters to
control the input power factor regardless the output power factor
fully utilize the input voltages
reduce the number of switch commutations in each cycle period.
SVM allows an immediate comprehension of the modulation
process
without the need for a fictitious DC link
avoiding the addition of the third harmonic components.
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29 = 512 Available
27 Possible
21 = 18+3 usefully employed
Active Configurations
Determine an output voltage
vector , and an input current
vector , having fixed
directions
ov
ii
Switching Configurations
Zero Configurations
Determine zero input current
and zero output voltage vectors
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Switching Configurations Employed
Switching
configurationlist
Switches On vo o ii i
+1 S11 S22 S32 2/3 v12i 0 2/3io1 -/6
1 S12 S21 S31 -2/3 v12i 0 -2/3 io1 -/6
+2 S12 S23 S33 2/3 v23i 0 2/3 io1 /22 S13 S22 S32 -2/3v23i 0 -2/3 io1 /2+3 S13 S21 S31 2/3v31i 0 2/3io1 7/6
3 S11 S23 S33 -2/3v31i 0 -2/3 io1 7/6+4 S12 S21 S32 2/3v12i 2/3 2/3io2 -/6
4 S11 S22 S31 -2/3v12i 2/3 -2/3io2 -/6+5 S13 S22 S33 2/3v23i 2/3 2/3 io2 /2
5 S12 S23 S32 -2/3v23i 2/3 -2/3 io2 /2+6 S11 S23 S31 2/3v31i 2/3 2/3io2 7/6
6 S13 S21 S33 -2/3v31i 2/3 -2/3 io2 7/6+7 S12 S22 S31 2/3v12i 4/3 2/3io3 -/6
7 S11 S21 S32 -2/3v12i 4/3 -2/3 io3 -/6+8 S13 S23 S32 2/3v23i 4/3 2/3 io3 /2
8 S12 S22 S33 -2/3v23i 4/3 -2/3 io3 /2+9 S11 S21 S33 2/3v31i 4/3 2/3io3 7/6
9 S13 S23 S31 -2/3v31i 4/3 -2/3 io3 7/601 S11 S21 S31 0 - 0 -02 S12 S22 S32 0 - 0 -
03 S13 S23 S33 0 - 0 -
Active configurationsActive configurations18
Zero configurationsZero configurations3
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Output Voltage and Input Current Space Vectors
ov
1,2,3
4,5,6
7,8,9
o
vo
sector d
h
g
f
e cov
Sectors and directions
of the outputline-to-neutral
voltage vectors.
2,5,8
3,6,9 1,4,7
iii
sector
h
c
de
f
g
Sectors and directions
of the input current vectors.
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At any sampling instantand i are known (reference quantities)
is imposed by the source (known by measurements)
ov
iv
SVM Algorithm
SVM Algorithm is based on the selection of 4 activeconfigurations that are applied for suitable time intervals
within each cycle period Tc.Thezero configurations are applied to complete Tc.
The control ofi can be achieved by controlling the phase
angle i of the input current vector.
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SVM algorithm
Selection of the active switching configurationsfor each combination of
output voltage sector
input current sector
Sector of the output voltage vector (Kv)
1 or 4 2 or 5 3 or 6
1 or 4 +9 +7 +3 +1 +6 +4 +9 +7 +3 +1 +6 +4
2 or 5 +8 +9 +2 +3 +5 +6 +8 +9 +2 +3 +5 +6
Sectorofthe
inputcurren
t
3 or 6 +7 +8 +1 +2 +4 +5 +7 +8 +1 +2 +4 +5
I II III IV I II III IV I II III IV
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]//)K[(joo
IIIIo
IIo
'o
ve)~cos(vvvv331
33
2 +=+=
]/)K[(joo
IVIVo
IIIIIIo
"o
ve)~cos(vvvv31
33
2 +=+=
( ) ( ) 031 =+ ii Kj~
jIIIIi
IIi eejii
( ) ( ) 031 =+ ii Kj~
jIVIVi
IIIIIIi eejii
SVM Algorithm
Basic equations of the SVM algorithm
To satisfy to the requirements of the
reference output voltage vector
input current displacement angle.
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i
ioKKI
cos
)/~
cos()/~cos(q)( iv
= +
33
3
21
i
ioKKII
cos
)/~cos()/~cos(q)( iv
+= ++
33
3
21
1
i
ioKKIII
cos
)/~
cos()/~cos(q)( iv
+= ++
33
3
21
1
i
ioKKIV
cos
)/~
cos()/~cos(q)( iv
++= +
33
3
21
SVM Algorithm
Solutions of the Basic Equations
Applied for any combination of
output voltage sectorKvinput current sectorKi
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SVM Algorithm
1+++ IVIIIIII
For the feasibility of the control strategy.
Otherwise: the instantaneous values of the input
voltages do not allow to satisfy the requirementsof output voltage and input power factor.