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Notes on

Matrix Converters

+

- LOADLOADLOAD

VB

VA

VC

Va Vb Vc

VI

CECA – Convertidors Estàtics de Corrent Altern

Dr. Antoni Arias

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Matrix Concept

• AC / AC direct electrical power conversion• M X N , inputs & outputs. Figure corresponds to the 3 X 3• Variable frequency and variable voltage

Bi-directional switch

SAc

T2

D2

T1

D1

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Fundamentals

• 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

Ua U U

UC

UB

UA

b c

icibia

SAa SAb SAc

SBa SBb SBc

SCa SCb SCc

iA

iB

iC

)()()(

)()()(

)()()(

tStStS

tStStS

tStStS

T

CcBcAc

CbBbAb

CaBaAa

cbao

CBAi

closed

opentSio

,,

,,

,0

,1)(

1)()()( tStStS CoBoAo

• Switching function:

• Transfer Matrix:

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Model

Ua U U

UC

UB

UA

b c

icibia

SAa SAb SAc

SBa SBb SBc

SCa SCb SCc

iA

iB

iC

)(

)(

)(

)()()(

)()()(

)()()(

)(

)(

)(

)(

)(

)(

)()()(

)()()(

)()()(

)(

)(

)(

ti

ti

ti

tStStS

tStStS

tStStS

ti

ti

ti

tU

tU

tU

tStStS

tStStS

tStStS

tU

tU

tU

c

b

a

CcCbCa

BcBbBa

AcAbAa

C

B

A

CN

BN

AN

CcBcAc

CbBbAb

CaBaAa

cN

bN

aN

)(

)(

)(

)(

)(

)(

)(

)(

ti

ti

ti

ti

ti

ti

ti

ti

C

B

A

i

c

b

a

o

)()()()( tiTtitUTtU oT

iiNoN

)(

)(

)(

)(

)(

)(

)(

)(

tU

tU

tU

tU

tU

tU

tU

tU

CN

BN

AN

iN

cN

bN

aN

oN

cbaoCBAi ,,,,

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Features

• 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

• Sinusoidal input and output

currents waveforms

• 9 bidirectional switches.

(18 IGBT + 18 Diodes)

• Output voltage limited to 86.6%

(cos30º) of input voltage

inpu

t vol

tage

s (

V )

UCUBUA

UAC UBC UBA UCA UCB UAB

1 12 3 4 5 6input sector

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Applications

• 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

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Industrial Products

• 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.

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• Yaskawa Low voltage Matrix Converter (Varispeed AC)

• V/f and vector control

Industrial Products

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Waveforms

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0.99 0.991 0.992 0.993 0.994 0.995 0.996 0.997 0.998 0.999 1

-300

-200

-100

0

100

200

300

• UAN , UBN , UCN input voltages and UaN output voltage

Waveforms

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0.99 0.9901 0.9902

-300

-200

-100

0

100

200

300

• UAN , UBN , UCN input voltages and UaN output voltage

Waveforms

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Waveforms

• Uan = 2/3 UaN -1/3 UbN -1/3 UcN = UaN + UNn

• UNn = -1/3 (UaN + UbN + UcN )

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Waveforms

0.994 0.995 0.996 0.997 0.998 0.999 1-400

-300

-200

-100

0

100

200

300

400

• Uan output voltage

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Waveforms

• Uab = f ( UAB ,UAC ,UBC ,UBA ,UCA ,UCB )

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0.98 0.982 0.984 0.986 0.988 0.99 0.992 0.994 0.996 0.998 1-600

-400

-200

0

200

400

600

• UAB , UAC , UBC , UBA , UCA , UCB input line voltages

versus Uab output line voltage

Waveforms

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0.982 0.9821 0.9822-600

-400

-200

0

200

400

600

• It uses the two largest voltages

Waveforms

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Waveforms

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0.994 0.995 0.996 0.997 0.998 0.999 1-400

-300

-200

-100

0

100

200

300

400

Uan ia inductive current (small dephase or delay)

Waveforms

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Waveforms

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0.98 0.982 0.984 0.986 0.988 0.99 0.992 0.994 0.996 0.998 1

-10

-5

0

5

10

Different frequencies isA ia

Waveforms

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WaveformsWaveforms

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0.98 0.982 0.984 0.986 0.988 0.99 0.992 0.994 0.996 0.998 1

-10

-5

0

5

10

• iA input current and , ia , ib , ic load currents

Waveforms

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WaveformsWaveforms

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Waveforms

0.98 0.982 0.984 0.986 0.988 0.99 0.992 0.994 0.996 0.998 1

-10

-5

0

5

10

• isA filtered input current and iA non filtered input current

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WaveformsWaveforms

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0.98 0.982 0.984 0.986 0.988 0.99 0.992 0.994 0.996 0.998 1

-300

-200

-100

0

100

200

300

• isA filtered input current and usA source voltage. Power Factor = 1

Waveforms

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Waveforms

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• UsAN source and UAN input phase voltages

Waveforms

0.98 0.982 0.984 0.986 0.988 0.99 0.992 0.994 0.996 0.998 1

-300

-200

-100

0

100

200

300

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Alternatives

• 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)

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Alternatives

• Bi directional power flow• 4 quadrant• DC link capacitor and input inductors• Sinusoidal input currents. Input Power Factor 1• Matrix Converter real alternative

N

San

Sap

Sbn

Sbp Scp

Scn

ia

ic

ib

a

b

c

SBp SCp

A

BC

SAp

SBn SCnSAn

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MC versus back to back

• 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

Ua U U

UC

UB

UA

b c

icibia

SAa SAb SAc

SBa SBb SBc

SCa SCb SCc

iA

iB

iC

T2

D2

T1

D1

N

San

Sap

Sbn

Sbp Scp

Scn

ia

ic

ib

a

b

c

SBp SCp

A

BC

SAp

SBn SCnSAn

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D1

T1

D2

D3D4

Bi Directional Switch

• 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

• Back to back switch with common emitter– Switch: 2 IGBT + 2 diodes– Diode required for reverse blocking capability – Conducting losses: 1 diode +1 IGBT

T2

D2

T1

D1

T2

D2

T1

D1

• Must be able to conduct positive and negative current and block positive and negative voltage

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Bi Directional Switch

SUMMARY IGBTs DiodesIsolated Power

SuppliesConducting

DevicesDiode bridge 9 36 9 3

Common Emitter 18 18 9 2

Common Collector 18 18 6 2

T2

T1

• Reverse Blocking IGBT, RBIGBT– Two reverse blocking IGBTs– Lower conducting losses: one switching device– Still under research– Switch control will remain the same

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Bi Directional Switch Device Packaging

• Dynex 200 (A) Bi directional Module– From standard one leg conventional VSI – 9 for a 3x3MC– Large Converters > 200 (A)– Common collector

LOAD

Va Vb Vc

T2

D2

T1

D1

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…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…

….announced the release of two bi-directional IGBT modules for use in matrix converter power stages…

…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

Bi Directional Switch Device Packaging

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Bi Directional Switch Device Packaging

• SEMELAB 200 (A) Bi directional Module– 3 for a 3x3MC– Large Converters

LOAD

Va Vb Vc

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A Matrix Converter IGBT Bi-Directional switching moduleA 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.

Bi Directional Switch Device Packaging

http://www.semelab.co.uk/power/

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Full Matrix Converter Device Packaging

• EUPEC 35A Matrix Converter Module– 1 for a 3x3MC– Small Powers Converters. 7.5 kW

LOAD

Va Vb Vc

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Full Matrix Converter Device Packaging

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Full Matrix Converter Device Packaging

• Fuji Electric Device Technology Co.,Ltd.– 1 for a 3x3MC– Four options (Price 390 € Nov 2009) :

• 1200V 50A 1200V 100A• 600V 100A 600V 200A

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Full Matrix Converter Device Packaging

• 600V 200A

• 1200V 100A

• 1200V 50A

• 600V 100A

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Commutation

• Current commutation– Needs the sign of the output current per phase

• Add two anti parallel diodes and measure its voltage drops

• Measure the device voltage drops

– Most widely used

• Voltage commutation– Needs the input voltage values per phase

T2

D2

T1

D1

T2

D2

T1

D1

VA

Va

D6

D5

T2

D2

T1

D1

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4 Step Current Commutation

T4

T3

D3

T2

D2

T1

D1

VB

VA

Va

D4

T2

T3

Va

t d1

VA

T1

T4

Va

t d2t c

ideal

T2

T3

Va

T1

T4

Va

ideal

t d1

VB

t d2t c

t rt f

VB VAVA VB

I a > 0

VA VB>

realreal

• No short circuits at the input• No open circuit at the output

(inductive loads)

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T2

T3

Va

t d1

VA

T1

T4

t d2t c

ideal

T2

T3

Va

T1

T4

ideal

t d1

VB

t d2t c

t ft r

VB VAVA VB

I a < 0

Va V

a

VA VB>

realreal

T4

T3

D3

T2

D2

T1

D1

VB

VA

Va

D4

4 Step Current Commutation

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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 / 1.5F

4 Step Current Commutation

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Input Filter

• 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

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 / 1.5F

LOAD

VB

VA

VC

Va Vb Vc

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Clamp circuit

LOAD

VB

VA

VC

Va Vb Vc

• Diode bridge like a standard rectifier• Protection against

– open circuits with inductive currents– over voltage caused by transients in power up and voltage sags

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MC Output Voltage vectors

• Space Vector Concept: 34

32

32 j

cj

bao etUetUtUtU

State +1Ua=UA Ub=UB Uc=UB

Ua=ÛA cos (30º)Ub=ÛB cos (-90º)Uc=ÛB cos (-90º)

Ua=ÛA cos(0º)Ub=ÛB cos(-120º)Uc=ÛB cos(-120º)

Ua=ÛA cos(-30º)Ub=ÛB cos(-150º)Uc=ÛB cos(-150º)

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inpu

t vol

tage

s (

V )

MC Output Voltage vectors

• Variable amplitude

• Same angle

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MC Input Current vectors

cos(30º) = sqr(3)/22/3·2·cos(30º) = 2/sqr(3)

• Space Vector Concept: 34

32

32 j

Cj

BAi etietititi

State +1iA = ia iB=ib+ic iC=0

aA

B

C

b c a

a -30º

• Amplitude dependant on the load• Same angle

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oV

ii

a b c o i

+1 A B B 2/3UAB 0 2/sqr(3) ia 11/6

+2 B C C 2/3UBC 0 2/sqr(3) ia /2

+3 C A A 2/3UCA 0 2/sqr(3) ia /6

+4 B A B 2/3UAB 2/3 2/sqr(3) ib 11/6

+5 C B C 2/3UBC 2/3 2/sqr(3) ib /2

+6 A C A 2/3UCA 2/3 2/sqr(3) ib /6

+7 B B A 2/3UAB 4/3 2/sqr(3) ic /6

+8 C C B 2/3UBC 4/3 2/sqr(3) ic /2

+9 A A C 2/3UCA 4/3 2/sqr(3) ic /6

+R1 A B C U [U] io MAX [io MAX]

+R2 C A B U [U +2/3] io MAX [io MAX+2/3]

+R3 B C A U [U +4/3] io MAX [io MAX+4/3]

0A A A A 0 …. 0 ….

0B B B B 0 …. 0 ….

0C C C C 0 …. 0 ….

a b c o i

-1 B A A -2/3UAB 0 -2/sqr(3) ia 11/6

-2 C B B -2/3UBC 0 -2/sqr(3) ia /2

-3 A C C -2/3UCA 0 -2/sqr(3) ia /6

-4 A B A -2/3UAB 2/3 -2/sqr(3) ib 11/6

-5 B C B -2/3UBC 2/3 -2/sqr(3) ib /2

-6 C A C -2/3UCA 2/3 -2/sqr(3) ib /6

-7 A A B -2/3UAB 4/3 -2/sqr(3) ic /6

-8 B B C -2/3UBC 4/3 -2/sqr(3) ic /2

-9 C C A -2/3UCA 4/3 -2/sqr(3) ic /6

-R1 A C B U [- U] io MAX [-io MAX]

-R2 B A C U [- U +2/3] io MAX [-io MAX+2/3]

-R3 C B A U [- U +4/3] io MAX [-io MAX+4/3]

oV

ii

27 vectors: 18 constant in direction + 3 nulls + 6 rotating

MC Output Voltage & Input Current vectors

Where, U equals to 2/3·cos(30º)· ÛL

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MC Output Voltage & Input Current vectors

Kv=3

Kv=4

Kv=5

Kv=2

Kv=6vo’’

vo’0

~

vo

9,8,7

9,8,7

3,2,1 3,2,1

6,5,4

6,5,4 Ki=3

Ki=4

Ki=5

Ki=2

Ki=6

ii’’

ii’

0

~ii

7,4,1

7,4,1

9,6,3

9,6,3

8,5,2

8,5,2

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Modulation

• 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

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Kv=3

Kv=4

Kv=5

Kv=2

Kv=6vo’’

vo’0

~

vo

• Output voltage vector:

0v

''

0

'

00 vvv

• The voltage reference vector will be synthesized using adjacent vectors :

Direct Space Vector Modulation

Reference 1

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• Input current angle:

where usually:

0

~

• The input current angle will be obtained distributing the load current among adjacent vectors in the right proportions:

Direct Space Vector Modulation

Reference 2

Ki=3

Ki=4

Ki=5

Ki=2

Ki=6

ii’’

ii’

0

~ii

vi

i

0i

'''

iii iii

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Direct Space Vector Modulation

3~cos

3

2~3

cos3

2

~3

cos2

3

~66

cos6

cos

0000'0

00'0

00'0

vvv

vv

vvy

6~

6 0

6~

00

33

1

00'0 3

~cos3

2

vKj

evv

''

0

'

00 vvv 0

~

Reference 1, output voltage vector:

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3~cos

3

2

~3

cos2

3

~66

cos6

cos

00''

0

00''

0

00''

0

vv

vv

vvx

3

1

00''

0 3~cos

3

2

vKj

evv

6~

6 0

6~

00

0~

''

0

'

00 vvv

Direct Space Vector Modulation

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Kv=3

Kv=4

Kv=5

Kv=2

Kv=6vo’’

vo’0

~

vo

9,8,7

9,8,7

3,2,1 3,2,1

6,5,4

6,5,4

• 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)

– Using just 2 vectors, both references can not be fulfilled => 4 active vectors will be used

Ki=3

Ki=4

Ki=5

Ki=2

Ki=6

ii’’

ii’

0

~ii

7,4,1

7,4,1

9,6,3

9,6,3

8,5,2

8,5,2

UCUBUA

UAC UBC UBA UCA UCB UAB

1 12 3 4 5 6input sector

Direct Space Vector Modulation

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vo’

voI · I

voII· II

vo’’

voIII· III vo

IV· IV

''

0

'

00 vvv II

II

oI

I

o vvv ··'

0 IV

IV

oIII

III

o vvv ··'

0

II

II

oI

I

o

Kj

vvevvv

··3

~cos3

2 331

00'0

IV

IV

oIII

III

o

Kj

vvevvv

··3

~cos3

2 31

00''

0

o

o

y

x

0~

o

Direct Space Vector Modulation

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60

'''

iii iii

IIIIII

iI

I

ii iii ··'

IVIV

iII

II

ii iii ··'

ii’

iiI · I

iiIII· IIIii’’

iiII · II

iiIV· IV

i~

ii

i~

i

i

0··· 3

1~

ii

KjjIIII

iI

I

i ejeii

0··· 3

1~

ii

KjjIVIV

iIII

III

i ejeii

Direct Space Vector Modulation

Reference 2, input current angle

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II

II

oI

I

o

Kj

vvevvv

··3

~cos3

2 331

00'0

IV

IV

oIII

III

o

Kj

vvevvv

··3

~cos3

2 31

00''

0

0··· 3

1~

ii

KjjIIII

iI

I

i ejeii

0··· 3

1~

ii

KjjIVIV

iIII

III

i ejeii

i

i

i

oKKIV

i

i

i

oKKIII

v

v

v

v

iv

iv

cos3

~cos

3~cos

3

21

cos3

~cos

3~cos

3

21

01

0

i

i

i

oKKII

i

i

i

oKKI

v

v

v

v

iv

iv

cos3

~cos

3~cos

3

21

cos3

~cos

3~cos

3

21

0

01

IVIIIIII 10

• Solving the 4 equations, the four duty cycles are found

• The remaining duty is for the zero vectors

Direct Space Vector Modulation

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• 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

• And the zero vector is calculated as follows

• The typical modulation pattern is as shown in next slide

ddd ddd ddd ddd

ddddd 10

inImd *

3sin

inImd *sin

outUmd *

3sin

outUmd *sin

Rectification stage Inversion stage

Ref. inputcurrent

Ref. outputvoltage

Indirect Space Vector Modulation

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Modulation switching pattern

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Modulation switching pattern

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65

-400

-200

0

600

400

200UCUBUA

UAC UBC UBA UCA UCB UAB

1 12 3 4 5 6

input sector

Modulation switching pattern

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Modulation switching pattern

UC UAUA UB

δO3 /2 δ 1 /2 δ 3 /2 δO1 /2

UAUC

U aN

δ 2 /2 δ4 /2 δO2 /2

UB

δO2 /2

UB

δ4 /2 δ2 /2 δO1 /2

UA

δ 3 /2 δ 1 /2

UC

δ O3 /2

UB UAUA UC

Input sector 1. Input angle +30º

UNn

Uan

U

U

U bN

U cN

bn

cn

2/3·0.87

-0.87

0.87-0.87

0.87-0.87

0.87

1/3·0.87-1/3·0.87-2/3·0.87

0.871/3·0.87-1/3·0.87-2/3·0.87

-0.87

-1/3·0.87-2/3·0.87-4/3·0.87

4/3·0.872/3·0.871/3·0.87

Output sector 1. Output angle +30º

-3 +9 -7 +1 +1 -7 +9 -3

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+

- LOADLOADLOAD

VB

VA

VC

Va Vb Vc

VI T4

T3

D3

T2

D2

T1

D1

VB

VA

Va

D4

T2

D2

T1

D1VA

Va

Ii

VDi

Voltage Drop effect

General scheme

Matrix Converter linearization

Matrix Converter linearization

UPC

68

Four step commutation

(td1 + tc + td2 = 1µs+0.2µs+0.5µs)

T2

T3

Va

t d1

VA

T1

T4

Va

t d2t c

ideal

T2

T3

Va

T1

T4

Va

ideal

t d1

VB

t d2t c

t rt f

VB VAVA VB

I a > 0

VA VB>

realreal

T4

T3

D3

T2

D2

T1

D1

VB

VA

Va

D4

Voltage Edge Uncertainty effect

Matrix Converter linearization

Matrix Converter linearization

UPC

69

I a

I b

VC VA

I c

VA VB

δO3/2 δ1/2 δ3/2 δO1/2

VAVC

Va ideal

Va

> 0

Vb ideal

Vb

< 0t ft d1+ tc +

Vc ideal

Vc

< 0t ft d1+ tc +

δ2/2 δ4/2 δO2/2

VB

t ft d1+ tc +t rt d1 +

t rt d1+

t rt d1 +

δO2/2

VB

δ4/2 δ2/2 δO1/2

VA

δ3/2 δ1/2

VC

δO3/2

=VB VA

VA VC

t rt d1+ t ft d1+ tc +

t ft d1+ tc + t rt d1+

t ft d1+ tc + t rt d1+

SECTOR 1

TPWM

real

real

real

Model for Voltage Edge Uncertainty effect

SVM

V

I

-VEU

+VEU

Matrix Converter linearization

Matrix Converter linearization

UPC

70

V

I

V

I

-VEU

+VEU

V

I

-VEU

+V EU+Ic

-Ic

input: phasecurrent

output:compensatingphase voltage

Voltage Drop effect

Voltage Edge Uncertainty effect

Dual Compensation

DUAL COMPENSATION

Matrix Converter linearization

UPC

71

SVMMatrix

Converter

DualCompensation

Grid

LC filter

Ia

Ib

Ic

VA

VB

VC

V

V

3 / 2

+

++

+

PMSM

32d q

Iq* +

d-axis currentcontroller

q-axis currentcontroller

+Id*

-

-d q

Ia

Ib

Ic

VdcompaVdcompc

Vdcompb

VdcompVdcomp

Dual Compensation in Matrix Converters FOC Scheme

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-8

-6

-4

-2

0

2

4

6

8

time (s)

Va,

Vb

, Vc

(V)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10

-8

-6

-4

-2

0

2

4

6

8

10

time (s)

Va,

Vb,

Vc

(V)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.3

-0.2

-0.1

0

0.1

time (s)

Id (

A)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.3

-0.2

-0.1

0

0.1

time (s)

Id (

A)

Matrix Converter linearization

UPC

72

Summary

• 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