UPC

1

Notes on

Matrix Converters

+

- LOADLOADLOAD

VB

VA

VC

Va Vb Vc

VI

CECA – Convertidors Estàtics de Corrent Altern

Dr. Antoni Arias

UPC

2

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

UPC

3

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:

UPC

4

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 ,,,,

UPC

5

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

UPC

6

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