7/30/2019 1 Matrix Lecture

1/11

1

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

7/30/2019 1 Matrix Lecture

2/11

2

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

7/30/2019 1 Matrix Lecture

3/11

3

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.

7/30/2019 1 Matrix Lecture

4/11

4

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

7/30/2019 1 Matrix Lecture

5/11

5

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

7/30/2019 1 Matrix Lecture

6/11

6

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.

7/30/2019 1 Matrix Lecture

7/11

7

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.

7/30/2019 1 Matrix Lecture

8/11

8

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

7/30/2019 1 Matrix Lecture

9/11

9

]//)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.

7/30/2019 1 Matrix Lecture

10/11

10

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

7/30/2019 1 Matrix Lecture

11/11

11

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.