UPC
Notes on
Matrix Converters
VA
VB
VC
+
I
V
-
CECA – Convertidors Estàtics de Corrent Altern
Va
Vb
LOAD
Dr. Antoni Arias
1
Matrix Concept
UPC
Bi-directional
switch
SAc
D1
T2
T1
D2
• AC / AC direct electrical power conversion
• M X N , inputs & outputs. Figure corresponds to the 3 X 3
• Variable frequency and variable voltage
2
Vc
Fundamentals
UPC
UA
 1, open
Switching function: Sio (t )  
0, closed
i  A, B, C
•
iA
SAb
S Ac
UC
SBa
SBb
S Bc
SCa
SCb
SCc
iC
Transfer Matrix:  S (t )
Aa
•
•
•
SAa
iB
o  a, b, c
•
UB
S Ba (t ) SCa (t )
T   S Ab (t ) S Bb (t ) SCb (t )
 S Ac (t ) S Bc (t ) SCc (t ) 
ia
Ua
ic
ib
Ub
Uc
There are 2^9 (512) possible combinations
Each output phase can be connected to any input phase
There are several constraints:
– Avoid line to line input short circuit
– Avoid open circuits with inductive currents
S Ao (t )  S Bo (t )  SCo (t )  1
3
Model
UPC
U aN (t )
U oN (t )  U bN (t )
U cN (t ) 
U AN (t )
U iN (t )  U BN (t ) 
U CN (t ) 
ia (t )
io (t )  ib (t )
ic (t ) 
i A (t ) 
ii (t )  iB (t )
iC (t )
i  A, B, C
o  a, b, c
UA
iA
UB
SAa
SAb
S Ac
UC
SBa
SBb
S Bc
SCa
SCb
SCc
iB
iC
ia
Ua
ic
ib
Ub
Uc
U oN (t )  T  U iN (t )
ii (t )  T T  io (t )
U aN (t )  S Aa (t ) S Ba (t ) SCa (t ) U AN (t )
U (t )    S (t ) S (t ) S (t )  U (t ) 
Bb
Cb
 bN   Ab
  BN 
U cN (t )   S Ac (t ) S Bc (t ) SCc (t )  U CN (t ) 
i A (t )   S Aa (t ) S Ab (t ) S Ac (t ) ia (t )
i (t )    S (t ) S (t ) S (t )   i (t ) 
Bb
Bc
 B   Ba
 b 
iC (t )  S Ca (t ) S Cb (t ) SCc (t )  ic (t ) 
4
Features
UPC
• Direct AC / AC Conversion. No DC Link: all silicon solution
– Less bulky (compact motor drives)
– Safer (hostile environments: aircraft, submarine…)
• Bidirectional power flow. 4 quadrant converter
• No restriction on input and output frequency within limits
imposed by switching frequency
U
U
U
U
U
• Sinusoidal input and output
U
U
U
currents waveforms
• 9 bidirectional switches.
(18 IGBT + 18 Diodes)
• Output voltage limited to 86.6%
(cos30º) of input voltage
input voltages ( V )
AC
input sector
BA
BC
A
1
CA
CB
B
2
3
UAB
C
4
5
6
5
Applications
UPC
• Standard:
– Wind/Water Force Machines (blowers, boilers, incinerators),
pumps, and general Industrial Machines.
• Specific Applications:
– Compact or Integrated Motor Drives
– Motor Drives for hostile environments (aircrafts,
submarines)
– AC/AC Power Conversions: wind energy, variable speed
drives...
• Still a topic of research
6
1
Industrial Products
UPC
• Yaskawa Medium voltage FSDrive-MX1S.
• Launched in 2004
• World’s first matrix converter Drive
• Super energy –saving medium-voltage Matrix
Converter with Power regeneration
• 3kV 200 to 3000kVA
• 6kV 400 to 6000kVA
• Applications:
– Wind/Water Force Machines (blowers, boilers, incinerators),
pumps, and general Industrial Machines.
7
Industrial Products
UPC
• Yaskawa Low voltage Matrix Converter
(Varispeed AC)
• V/f and vector control
8
Waveforms
UPC
9
Waveforms
UPC
300
200
100
0
-100
-200
-300
0.99
0.991 0.992 0.993 0.994 0.995 0.996 0.997 0.998 0.999
1
• UAN , UBN , UCN input voltages and UaN output voltage
10
Waveforms
UPC
300
200
100
0
-100
-200
-300
0.99
0.9901
0.9902
• UAN , UBN , UCN input voltages and UaN output voltage
11
Waveforms
UPC
• Uan = 2/3 UaN -1/3 UbN -1/3 UcN = UaN + UNn
• UNn = -1/3 (UaN + UbN + UcN )
12
Waveforms
UPC
400
300
200
100
0
-100
-200
-300
-400
0.994
0.995
0.996
0.997
0.998
0.999
1
• Uan output voltage
13
Waveforms
UPC
• Uab = f ( UAB ,UAC ,UBC ,UBA ,UCA ,UCB )
14
Waveforms
UPC
600
400
200
0
-200
-400
-600
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
• UAB , UAC , UBC , UBA , UCA , UCB input line voltages
versus Uab output line voltage
15
Waveforms
UPC
600
400
200
0
-200
-400
-600
0.982
0.9821
• It uses the two largest voltages
0.9822
16
Waveforms
UPC
17
Waveforms
UPC
400
300
200
100
0
-100
-200
-300
-400
0.994
0.995
0.996
0.997
0.998
0.999
Uan ia inductive current (small dephase or delay)
1
18
Waveforms
UPC
19
Waveforms
UPC
10
5
0
-5
-10
0.98
0.982
0.984
0.986
0.988
0.99
0.992
Different frequencies
0.994
0.996
0.998
1
isA ia
20
Waveforms
UPC
21
Waveforms
UPC
10
5
0
-5
-10
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
• iA input current and , ia , ib , ic load currents
22
Waveforms
UPC
23
Waveforms
UPC
10
5
0
-5
-10
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
• isA filtered input current and iA non filtered input current
24
Waveforms
UPC
25
Waveforms
UPC
300
200
100
0
-100
-200
-300
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
• isA filtered input current and usA source voltage. Power Factor = 1
26
Waveforms
UPC
27
Waveforms
UPC
300
200
100
0
-100
-200
-300
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
• UsAN source and UAN input phase voltages
28
Alternatives
UPC
•
•
•
Industry “workhorse” from less than kW to MW
Unidirectional power flow
2 quadrant
– When the current changes its sign, the power must be
burn in the DC link
•
•
DC link capacitor (30% -50% of the power circuit
volume)
Input currents very poor. (awful THD)
29
Alternatives
UPC
SAp
SBp
SCp
Sap
A
Sbp
ia
a
N
B
SBn
•
•
•
•
•
SCn
ib
b
C
SAn
Scp
c
San
Sbn
ic
Scn
Bi directional power flow
4 quadrant
DC link capacitor and input inductors
Sinusoidal input currents. Input Power Factor 1
Matrix Converter real alternative
30
MC versus back to back
UPC
UA
iA
SAp
SBp
SCp
Sap
A
Sbp
N
C
SBn
ib
b
c
San
SCn
Sbn
UB
SAa
SAb
S Ac
UC
SBa
SBb
S Bc
SCa
SCb
SCc
iB
ia
a
B
SAn
Scp
iC
ic
Scn
ib
ia
D1
T2
Ua
Ub
T1
D2
•
•
•
12 IGBTs + 12 Diodes
1 large electrolytic capacitor (DC link)
Input filter (1st order)
– 3 large inductors
•
•
18 IGBTs + 18 Diodes
Input filter (2nd order)
– 3 inductors
– 3 capacitors
•
Clamp circuit
31
Bi Directional Switch
UPC
•
Must be able to conduct positive and negative current and block positive
and negative voltage
D1
•
•
T1
Diode embedded switch
– Switch: 1 IGBT + 4 diodes
– Conducting losses: 2 diodes +1 IGBT
Back to back switch with common collector
– Switch: 2 IGBT + 2 diodes
– Diode required for reverse blocking capability
– Conducting losses: 1 diode +1 IGBT
D2
D4
D3
D1
T2
T1
D2
•
Back to back switch with common emitter
– Switch: 2 IGBT + 2 diodes
– Diode required for reverse blocking capability
– Conducting losses: 1 diode +1 IGBT
D1
T2
T1
D2
32
ic
Uc
Bi Directional Switch
UPC
•
Reverse Blocking IGBT, RBIGBT
–
–
–
–
T2
Two reverse blocking IGBTs
Lower conducting losses: one switching device
Still under research
Switch control will remain the same
T1
36
Isolated Power
Supplies
9
Conducting
Devices
3
18
18
9
6
2
2
SUMMARY
IGBTs
Diodes
Diode bridge
9
Common Emitter
Common Collector
18
18
33
Bi Directional Switch Device Packaging
UPC
•
Dynex 200 (A) Bi directional Module
–
–
–
–
From standard one leg conventional VSI
9 for a 3x3MC
Large Converters > 200 (A)
Common collector
D1
T2
T1
D2
Va
Vb
Vc
LOAD
34
Bi Directional Switch Device Packaging
UPC
….announced the release of two bi-directional IGBT modules for use in matrix
converter power stages…
…Dynex Semiconductor is working closely with researchers at Nottingham
University. Through this collaboration and in response to commercial
requirements, Dynex has created the DIM400PBM17-A000 for use in a 60Hz to
400Hz fixed frequency converter and the GP200MBS12 for use in a high
efficiency brushless dc motor drive.
The DIM400PBM17-A000 module is a 400A 1700V bi-directional switch mounted
on a 140mm x 73mm metal matrix baseplate. Long-term reliability and enhanced
thermal performance are achieved through the use of aluminium nitride
substrates mounted on a metal matrix compound baseplate. The package has a
6 kV isolation rating…
…The DIM200MBS12-A000 module is a 200A 1200V bi-directional switch
mounted on a 106mm x 62mm copper baseplate. The package has a 4 kV
isolation rating…
http://www.dynexsemi.com/corporate/news/items/20020514-prod-b.htm
35
Bi Directional Switch Device Packaging
UPC
•
SEMELAB 200 (A) Bi directional Module
– 3 for a 3x3MC
– Large Converters
Va
Vb
Vc
LOAD
36
Bi Directional Switch Device Packaging
UPC
A Matrix Converter IGBT Bi-Directional
switching module
A 360kVA (600V max line-line at up to 300A)
matrix converter module designed by Semelab.
•IGBT Packaging Available in 300V to 1800V
•Aerospace
•Customised to fit your needs.
•Good CTE match, from Silicon to the metal
matrix base plate.
•Excellent reliability module, temp cycling,
humidity tested, elevated pressure.
•Low power losses.
•Plastic package / Hermitic packaging
•Power connection,
•Mounting holes
•Void free die attach, X-ray capability.
http://www.semelab.co.uk/power/
37
Full Matrix Converter Device Packaging
UPC
•
EUPEC 35A Matrix Converter Module
– 1 for a 3x3MC
– Small Powers Converters. 7.5 kW
Va
Vb
Vc
LOAD
38
Full Matrix Converter Device Packaging
UPC
39
Full Matrix Converter Device Packaging
UPC
• Fuji Electric Device Technology Co.,Ltd.
– 1 for a 3x3MC
– Four options (Price 390 € Nov 2009) :
• 1200V 50A
• 600V 100A
1200V 100A
600V 200A
40
Full Matrix Converter Device Packaging
UPC
•
600V 200A
•
1200V 100A
•
1200V
•
600V 100A
50A
41
Commutation
UPC
•
Current commutation
– Needs the sign of the output current per phase
• Add two anti parallel diodes and measure its voltage drops
D5
D1
T2
VA
Va
T1
D2
D6
• Measure the device voltage drops
D1
D1
T2
T1
T2
T1
D2
D2
– Most widely used
•
Voltage commutation
– Needs the input voltage values per phase
42
4 Step Current Commutation
UPC
D1
T2
VA
•
•
T1
No short circuits at the input
No open circuit at the output
(inductive loads)
D2
Va
D3
VB
T4
T3
D4
t d1
tc
t d1
t d2
tc
t d2
T2
T2
T3
T3
T1
T1
tf
tr
T4
T4
Va ideal
Va ideal
VB
VA
Va real
VA
VB
Va real
VB
VA
Ia >0
VA > V B
43
4 Step Current Commutation
UPC
D1
T2
VA
T1
D2
Va
D3
VB
T4
T3
D4
t d1
tc
t d1
t d2
tc
t d2
T2
T2
T3
T3
T1
T1
T4
tr
tf
Va ideal
Va real
T4
Va ideal
VB
VA
VA
VB
VB
Va real
VA
Ia <0
VA > V B
44
4 Step Current Commutation
UPC
Matrix Converter
EUPEC FM35R12KE3ENG module
Switching device
1200V, 35 A, IGBT
td1 / tc / td2
1 / 0.2 / 0.5 s
tf / tr
65-90 ns / 30-45 ns
Power
7.5 kW
AC Input voltage
3 x 415V
Input filter (L/C) values
1mH / 1.5F
45
Input Filter
UPC
•
2nd Order Input L-C filter
– Typical cut off frequency 1-3 kHz
• between the fundamental 50Hz
• and the PWM frequency 10-20 kHz
– R in parallel with L in order to have an adequate damping
– L impedance at 50Hz should be negligible
• 2*pi*f*L = 2*3.14*50*10-3 = 0.314 ohms
VA
VB
Matrix Converter
EUPEC FM35R12KE3ENG module
Switching device
1200V, 35 A, IGBT
Power
7.5 kW
AC Input voltage
3 x 415V
Input filter (L/C) values
1mH / 1.5F
VC
Va
Vb
LOAD
46
Vc
Clamp circuit
UPC
•
•
Diode bridge like a standard rectifier
Protection against
– open circuits with inductive currents
– over voltage caused by transients in power up and voltage sags
VA
VB
VC
Va
Vb
Vc
LOAD
47
MC Output Voltage vectors
UPC
•

Space Vector Concept: U o t   2 U a t  U b t  e j
3
Ua=ÛA cos (30º)
Ub=ÛB cos (-90º)
Uc=ÛB cos (-90º)
2
3
 U c t  e j
4
3

State +1
Ua=UA Ub=UB Uc=UB
Ua=ÛA cos(0º)
Ub=ÛB cos(-120º)
Uc=ÛB cos(-120º)
Ua=ÛA cos(-30º)
Ub=ÛB cos(-150º)
Uc=ÛB cos(-150º)
48
MC Output Voltage vectors
input voltages ( V )
UPC
• Variable
amplitude
• Same angle
49
MC Input Current vectors
UPC
•

j 2
j 4
Space Vector Concept: ii t   2 3 i A t  i B t  e 3  iC t  e 3

State +1
B
A
iA = ia iB=ib+ic iC=0
a
C
b
c
a
a
-30º
cos(30º) = sqr(3)/2
2/3·2·cos(30º) = 2/sqr(3)
• Amplitude dependant on the load
• Same angle
50
MC Output Voltage & Input Current vectors
UPC
abc

Vo
o

ii
i

ii
abc

Vo
BAA
-2/3UAB
0
-2/sqr(3) ia
o
i
+1
ABB
2/3UAB
0
2/sqr(3) ia
11/6
+2
BCC
2/3UBC
0
2/sqr(3) ia
/2
-2
CBB
-2/3UBC
0
-2/sqr(3) ia
/2
+3
CAA
2/3UCA
0
2/sqr(3) ia
/6
-3
ACC
-2/3UCA
0
-2/sqr(3) ia
/6
+4
BAB
2/3UAB
2/3
2/sqr(3) ib
11/6
-4
ABA
-2/3UAB
2/3
-2/sqr(3) ib
11/6
/2
-1
11/6
+5
CBC
2/3UBC
2/3
2/sqr(3) ib
/2
-5
BCB
-2/3UBC
2/3
-2/sqr(3) ib
+6
ACA
2/3UCA
2/3
2/sqr(3) ib
/6
-6
CAC
-2/3UCA
2/3
-2/sqr(3) ib
/6
+7
BBA
2/3UAB
4/3
2/sqr(3) ic
/6
-7
AAB
-2/3UAB
4/3
-2/sqr(3) ic
/6
+8
CCB
2/3UBC
4/3
2/sqr(3) ic
/2
-8
BBC
-2/3UBC
4/3
-2/sqr(3) ic
/2
+9
AAC
2/3UCA
4/3
2/sqr(3) ic
/6
-9
CCA
-2/3UCA
4/3
-2/sqr(3) ic
/6
+R1
ABC
U
[U]
io MAX
[io MAX]
-R1
ACB
U
[- U]
io MAX
[-io MAX]
BAC
U
[- U +2/3]
io MAX
[-io MAX+2/3]
CBA
U
[- U +4/3]
io MAX
[-io MAX+4/3]
+R2
CAB
U
[U +2/3]
io MAX
[io MAX+2/3]
-R2
+R3
BCA
U
[U +4/3]
io MAX
[io MAX+4/3]
-R3
0A
AAA
0
….
0
….
0B
BBB
0
….
0
….
0C
CCC
0
….
0
….
Where, U equals to 2/3·cos(30º)· ÛL
27 vectors: 18 constant in direction + 3 nulls + 6 rotating
51
MC Output Voltage & Input Current vectors
UPC
 4,  5,  6
 7,  8,  9
Kv=2
vo’
vo
~
0
Kv=3
 1,  2,  3
 1,  2,  3
vo’’
Kv=4
Kv=5
 7,  8,  9
 2,  5,  8
Kv=6
 1,  4,  7
 4,  5,  6
Ki=3
Ki=2
 3,  6,  9
ii’
~
0
Ki=4
ii
ii’’
 3,  6,  9
Ki=5
Ki=6
 1,  4,  7
 2,  5,  8
52
Modulation
UPC
• PWM Modulation technique is applied in order to:
– follow a reference at the output, which on average will be a
sinusoidal
– get sinusoidal input currents on phase with the input voltage
(power factor 1)
• Several modulation techniques:
– Venturini, Scalar…
• Direct & Indirect Space Vector Modulation
– Based on the Space Vector Modulation for Standard PWM
Inverters
– There are two references:
• Output voltage vector
• Input current angle
53
Direct Space Vector Modulation
UPC
Kv=2
vo ’
Kv=3
~0
vo’’
Kv=4
Reference 1
vo
Kv=6
•
Output voltage vector:
•
The voltage reference
vector will be synthesized
using adjacent vectors :

v0
'
0
v0  v  v
''
0
Kv=5
54
Direct Space Vector Modulation
UPC
Reference 2
Ki=2
Ki=3
vi
•
~
0
ii
i  0
where usually:
•
ii’’
Ki=6
Ki=5
~
0
ii’
i
Ki=4
Input current angle:
The input current angle will
be obtained distributing the
load current among
adjacent vectors in the right
proportions:
'
i
ii  i  i
''
i
55
Direct Space Vector Modulation
UPC
Reference 1, output voltage vector:
'
0
v0  v  v

'
y  v0  cos
v0' 
''
0
 

 v0  cos    ~0 
6
6 6

3


 v0  cos   ~0 
2
3


2
2



v0' 
v0  cos   ~0  
v0  cos  ~0  
3
3
3

3


~0

 ~0 
6
6

 0  ~0 
6


 
'
2
 ~   j   K v 1 3  3 
v0 
v0  cos   0    e
3
3

56
Direct Space Vector Modulation
UPC
'
0
v0  v  v
x  v0''  cos
v0'' 
''
0
~0


 
 v0  cos    ~0 
6

6 6
3


 v0  cos   ~0 
2
3


 ~0 
6
6

 0  ~0 
6

2

v 
v0  cos  ~0  
3
3


''
0


 ''
2
 ~   j   K v 1 3 
v0 
v0  cos   0    e
3
3


57
Direct Space Vector Modulation
UPC
 4,  5,  6
 2,  5,  8
 7,  8,  9
Kv=2
 1,  4,  7
vo
vo’
~0
Kv=3
 1,  2,  3
Kv=6
 3,  6,  9
UCA
UB
Ki=6
Ki=5
 1,  4,  7
 4,  5,  6
 7,  8,  9
UA
ii
ii’’
Kv=5
UBC
~
0
Ki=4
vo’’
Kv=4
UAC
 3,  6,  9
ii’
 1,  2,  3
UBA
Ki=2
Ki=3
UAB
UCB
 2,  5,  8
•
UC
What vectors can be used?
– Maximum input voltages at Ki=1 : UAB, UAC.
– Common vectors For Kv=1 & Ki=1:
• ±1 (± 2/3 UAB) ±3 (± 2/3 UCA)
• ±7 (± 2/3 UAB) ±9 (± 2/3 UCA)
input sector
1
2
3
4
5
6
1
– Using just 2 vectors, both references can not
be fulfilled => 4 active vectors will be used
58
Direct Space Vector Modulation
UPC
o
~0
y
o
voII·
vo’
voI ·
vo’’
voIII·
x
o
voIV·
III
'
II
''
v0  v0  v0
'
I
'
III
II
v 0  v o · I  v o · II
I
IV
v 0  v o · III  v o · IV
IV
 

I
II
'
2
 ~   j   K v 1 3  3 
I
v0 
v0  cos   0    e
 v o ·  v o · II
3
3



III
IV
 ''
2
 ~   j   K v 1 3 
III
v0 
v0  cos   0    e
 v o ·  v o · IV
3
3

59
Direct Space Vector Modulation
UPC
Reference 2, input current angle
i
i
ii  i  i
ii
ii’
~
'
i
'
~
i
i
iiIII·
ii’’
iiII ·
iiI ·
II
iiIV·
III
''
i
I
III
II
IV
i i  i i · I  i i · III
'
i i  i i · II  i i · IV
I
IV

 i iI · I  i iII · II · je j~i  e j  K i 1 3  0




 i iIII · III  i iIV · IV



· je j~i  e j  K i 1 3  0


60
Direct Space Vector Modulation
UPC
 

I
II

  j   K v 1 3  3 
2

v0' 
v0  cos  ~0    e 
 v o · I  v o · II
3
3



IV
III
 ''
2
 ~   j   K v 1 3 
v0 
v0  cos   0    e
 v o · III  v o · IV
3
3


 i iI · I  i iII · II · je j~i  e j  K i 1 3  0





 i iIII · III  i iIV · IV · je j~i  e j  K i 1 3  0




•
•
Solving the 4 equations, the
four duty cycles are found
The remaining duty is for
the zero vectors
 I   1K
v
 II   1K
 III   1K
 K i 1
v
 Ki
v  Ki
 0  1   I   II   III   IV 
 IV   1K
v
 K i 1
 ~ 

cos  ~0   cos   i  
2 vo
3
3


 
cos  i
3 vi
2 vo
 
3 vi
2 vo
 
3 vi
 ~ 

cos  ~0   cos   i  
3
3


cos  i
 ~ 

cos  ~0   cos   i  
3
3


cos  i
 ~ 

cos  ~0   cos   i  
2 vo
3
3


 
cos  i
3 vi
61
Indirect Space Vector Modulation
UPC
Rectification stage
Inversion stage
Ref. input
current


d  mI  sin    *in 
3

•
 
d  mI  sin  *in
Ref. output
voltage


d  mU  sin    *out 

3

d   mU  sin  *out
To obtain a correct balance of the input currents and the output voltages,
the modulation pattern should be a combination of all 4 duty-cycles
d  d  d 
d  d  d
d   d   d
d   d   d 
•
And the zero vector is calculated as follows
•
The typical modulation pattern is as shown in next slide
d 0  1  d  d  d   d  
62

Modulation switching pattern
UPC
63
Modulation switching pattern
UPC
64
Modulation switching pattern
UPC
UAC
600
UBA
UBC
UCA
UAB
UCB
400
UA
UB
UC
200
0
- 200
- 400
input
sector
2
1
3
4
5
6
1
65
Modulation switching pattern
UPC
Input sector 1. Input angle +30º Output sector 1. Output angle +30º
UC
UA
U C -3
+9
δ O3 /2 δ 1 /2
UA
UA
δ 3 /2 δ O1 /2
-7
δ 2 /2
UB
+1
UB UB
UB
UA
+1
-7
δ4 /2 δO2 /2 δO2 /2 δ4 /2
UA
UA
UC
+9
-3
δ2 /2 δ O1 /2 δ 3 /2
UC
δ 1 /2 δ O3 /2
0.87
U aN
-0.87
0.87
U bN
-0.87
0.87
U cN
-0.87
0.87
1/3·0.87
-1/3·0.87
-2/3·0.87
-0.87
4/3·0.87
2/3·0.87
1/3·0.87
2/3·0.87
1/3·0.87
-1/3·0.87
-2/3·0.87
-1/3·0.87
-2/3·0.87
-4/3·0.87
U Nn
U an
U bn
U cn
66
Matrix Converter linearization
UPC
Matrix Converter linearization

General scheme
VA
D1
T2
VA
VB
T1
D2
VC
Va
+
D3
I
V
VB
Va
-

Vb
Vc
T4
T3
D4
LOAD
Voltage Drop effect
Ii
D1
VA
T2
Va
VDi
T1
D2
67
Matrix Converter linearization
UPC
Matrix Converter linearization
D1

T2
VA

T1
Four step commutation
(td1 + tc + td2 = 1µs+0.2µs+0.5µs)
D2
Va
t d1
tc
t d1
t d2
tc
t d2
D3
VB
T4
T3
T2
T2
T3
T3
D4
T1
T1
tf
tr
T4
T4
Va ideal
Va real
Va ideal
VB
VA
VA
VB
Va real
VB
VA
Ia >0
VA > V B

Voltage Edge Uncertainty effect
68
Matrix Converter linearization
UPC
Matrix Converter linearization


SECTOR 1
VC
VA
VA
δ1/2
δO1/2
δ3/2
=
VB
VA
VC
δO3/2
I
Model for Voltage Edge Uncertainty effect
SVM
δ2/2
δ4/2
+VEU
VB
VB
VB
δO2/2
δO2/2
VA
VA
VC
VA
δ4/2
δ2/2
δO1/2
VC
δ3/2
δ1/2
V
-VEU
δO3/2
Va ideal
t d1 + t c + t f
t d1 + t r
Ia >0
t d1 + t c + t f
t d1 + t r
Va real
Vb ideal
t d1 + t c + t f
Ib <0
t d1 + t c + t f
t d1 + t r
t d1 + t r
Vb real
V c ideal
t d1 + t r
t d1 + t c + t f
Ic <0
t d1 + t c + t f
t d1 + t r
V c real
TPWM
69
Matrix Converter linearization
UPC
DUAL COMPENSATION

Voltage Drop effect
I

Dual Compensation
I
V
input: phase
current

Voltage Edge Uncertainty effect
I
-V EU
+VEU
-VEU
+ Ic
+V EU
-Ic
V
output:
compensating
phase voltage
V
70
Matrix Converter linearization
UPC
Dual Compensation in Matrix Converters FOC Scheme Grid
Ia
6
Dual
Compensation
Vdcomp
4
Va, Vb, Vc (V)
VA
Ib
Ic
8
Vdcomp
a
Vdcomp
b
VB
VC
c
LC filter
3/2
2
Vdcomp
0
Id* +
d-axis current
controller
-2
Iq*
-4
+
dq
V

q-axis current
controller
-6

V +
+
Vdcomp
+
+
Ia

Ib
Matrix
Converter
SVM
PMSM
Ic
-8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9

1
time (s)
3
2
dq
0.1
10
0.1
0
8
0
4
-0.2
2
Id (A)
Va, Vb, Vc (V)
Id (A)
6
-0.1
0
-0.1
-2
-4
-0.2
-0.3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-6
time (s)
-8
-10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-0.3
0
time (s)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
time (s)
71
Summary
UPC
• Matrix Converter topology
– 9 Bidirectional switch
•
•
•
•
•
•
4 step commutation
Space Vector Modulation
Input Filter
Clamp Circuit
Matrix Converter linearization
Advantages of Matrix Converters:
–
–
–
–
Size. Compactness.
Sinusoidal input/output
Hostile environments
4 quadrant
• Applications
72
1