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Space Vector Modulated Three-phase

to Two-phase Matrix Converter

Yongli Fang

Guojun Tan

member, IEEE,and Hao Liu

Abstract-- In this paper, the topologies of three-phase to two-

phase ac-ac matrix converter are analyzed and based on the

three-leg topology, indirect space vector modulation technique

has been developed which can get sinusoidal input with unity

power factor and two-phase sinusoidal output waveforms with

90 angle shift. Numerical simulation and experiment have been

carried out. The results verify the correctness and feasibility of

the proposed control scheme.

Index Terms--three-phase to two-phase matrix converter;

space vector modulation; simulation; dSPACE

I. INTRODUCTION

The matrix converter (MC) is a direct power conversion

device that generates variable magnitude variable frequency

output voltage from the ac utility grid. It has sinusoidal

input/output currents with unity power factor and fully

regeneration capability [1][2].

Recently there has been considerable interest in the use of

matrix converter technology for motor drive applications,

however, mostly in three-phase output systems. Little

attention has been paid to derive matrix converter topologies

and control schemes for alternative structures, such as single-phase and two -phase output systems. In [3], the structure and

control algorithm of the two-leg and three-leg two-phase MC

were proposed.

Inverter is the main source to the two-phase load[4].

Compared to conventional two-stage ac/dc/ac conversion with

bulky reactive components for intermediate dc-link, three-

phase to two-phase matrix converter (3-2 MC) directly

link input ac lines to output ac systems through bi-directional

switches. This leads to advantages over the conventional

inverter based power converters, such as low-volume and size,

high reliability, long lifetime and high power density due to no

electrolytic capacitors.

In the paper, an indirect space vector modulation (ISVM) is

proposed for 3-2MC, which can be seen as a combination

This work was supported in part by the technology fund of China

University of Mining and Technology E200427.

Yongli Fang is with School of Information and Electrical

Engineering ,China University of Mining and Technology. Xuzhou, Jiangsu

Province,China, 221008 (e-mail: yonglifang@126.com).

Guojun Tan is with School of Information and Electrical Engineering,

China University of Mining and Technology, Xuzhou, Jiangsu

Province,China,221008 (e-mail: gjtan@cumt.edu.cn).

of rectifier and inverter. The main study is focused on the

inverter part, while the rectifier part is just the same with the

ISVM of 3-3 MC. The effectiveness of the proposed

modulation has been verified by simulation and experiments.

II. ISVMFOR 3-2MC

The output voltages of 3-2 MC are symmetrical two-

phase voltages with 90angle shift. Usually there has three

types of 3-2MC topologies, four-leg, three-leg and two-

leg based structures which have been introduced in [2]. In

four-leg topology, MC is formed by two single-phase outputs

and the two output circuit is independent, which means the

structure has more control freedom but it requires 12 switches

which will bring more switch conduction losses. And in two-

leg topology, it just needs 6 switches but the load common

joint is connected directly to the neutral point of the source

which will causeinteraction between each other. The three-leg

topology has less switches compared to four-leg topology and

be more flexible compared to two-leg topology. It is adopted

in the paper.

Fig.1. shows a 3-2MC with nine bi-directional switches.

The voltage and current at the input side of the converter isdenoted by A,B,C while the output side is denoted by r,s,t and

t is the common terminal. v ,rt st v indicate the two-phase

output voltages whose angle shift are 90.The basic idea of

indirect modulation is to decouple the control of the input

current and the output voltage and regards the matrix

converter as a back-to-back PWM converter without DC-link

Fig.1. The topology of 3-2MC with three-leg

S11

rS12

S13

S21

S22S23

S31

S32

S33

fL

fC

Ae

Ce

s

t

ZB

e

Z

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Fig.2. The equivalent AC-DC-AC structure of 3-2MC

energy storage such as in Fig.2. And the well-known space

vector modulation is applied to rectifying stage (VSR) and

inverting stage(VSI) and duty cycles are calculated as follows.

A. Output Voltage SVM

In the VSI part, terminal t is common. The voltage andrtv

stv are sinusoidal with the angle shift 90and can be

expressed as follows.

0 0

0 0

cos( )

sin( )

rt om

st om

v U t

v U t

= +

= + (1)

so the expected output voltage space vector can be defined

by

rt st V v jv= + (2)

TABLEThe space vectors of the equivalent VSI

Terminal state

r s tspace vectors

n n n 0 0V =

p n n 1 pnV U=

p p n4

2 2 j /

pnV U e

=

n p n2

3

j /

pnV U e =

n p p 4j

pnV U e

=

n n p5 4

5 2 j /

pnV U e =

p n p3 2

6

j /

pnV U e

=

p p p 7 0=V

The VSI has three bridges and all the switch states will have

eight space vectors, which are called voltage switching state

vectors. All the vectors are listed in Tableand six of themare nonzero space vectors, the other two are zero space

vectors. The amplitudes of the six nonzero vectors are not the

same, the amplitudes of vectors are1 3 4 V V V V 6 pnU and

that of vectors are2V V

5 2 pnU .And the angle between two

adjacent switching state vectors are not the same, as shown in

Fig.3(a).

The space vector of the desired output voltages can be

approximately synthesized by two adjacent switching state

vectors, andV

V , and the zero voltage vector, or , using

PWM as shown in Fig.3.(b).

0V 7Vp Srp Ssp StpSCpSBpSAp

rA

0 7 0V V V V (V = + +d d )d (3)sBtC

1( , , )V p n n

6( , , )V p n p

5( , , )V n n p

4( , , )V n p p

3( , , )V n p n2( , , )V p p n

0 7( , , ), ( , , )V n n n V p p p

Srn StnSsnSBnSAn SCn

n

(a) Space vectors of VSI

(b) Space vector addition in different sectors

Fig.3. The space vector modulation of voltage source inverter

In sectors and , the angle between the adjacent

switching state vectors is 90, and the duty cycles of the

switching state vectors are

0 0

/ cos(

/ sin(/ 1

)

)

s v sv

s v s

v v s

d T T m

d T T md T T d d

v

= =

= = = =

(4)

where is the VSI modulation index, its value is

between 0 and 1,and

vm

sT is the switching period.

In sectors , ,and , the angle between the adjacent

switching state vectors is 45. In sectors and, the duty

cycles of the switching state vectors are

0 0

/ sin(45

/ sin( ) /

/ 1

)

2

s v s

s v sv

v v s

d T T m

d T T m

d T T d d

v

= =

= =

= =

(5)

And in sectorsand, the duty cycles of the switching

state vectors are

0 0

/ sin(45 ) /

/ sin( )

/ 1

s v sv

s v sv

v v s

d T T m

d T T m

d T T d d

= =

= =

= =

2

(6)

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B. Input current SVM

In the VSR part, due to the utility grid is the same with the

3-2MC, the method is exactly the same with it. The space

vector of the desired input current is defined

120 1202 (3

j j

A B CI i i e i e

= + +

)

(7)

The input current switching vector hexagon is shown in

Fig.4. The reference input current space vector I can be

synthesized by the adjacent switching vector uI and vI . Theduty cycles of the switching state vectors are

0 0

/ sin(60

/ sin( )

/ 1

)s c s

s c sc

c c s

d T T m

d T T m

d T T d d

c

= =

= = = =

(8)

where , the current modulation index.1cm =

5( , )I c b

1( , )I a c

6( , )I a b

2( , )I b c

3( , )I b a

4( , )I c a

d I

d I

sc

I

I

Fig.4. The space vector modulation of

voltage source rectifier

C. Entire matrix converter modulation

To assure proper operation of the converter, the two

modulation strategies must now be combined to generate the

switching pattern for the entire converter by a product of the

corresponding duty cycles.

0 0 / 1s

d d d d d d

d d d d d d

d T T d d d d

= = = =

= =

(9)

In order to minimize the switching numbers in a sampling

period, the optimized double-sided vector sequence is adopted

and it changes the output voltage vector sequence according to

whether the sum of the input and output space vector sector is

even or odd [5].

For example, when the desired output voltage vector is in

sector and the desired input current vector is in sector ,

the vector sequence will be 0

,and the corresponding switch-state sequence will

be ABB ABA ACA ACC CCC ACC ACA ABA ABB

In each switching period ,the switching number is eight and

the zero vector is put in the middle.

III. SIMULATIONRESULTS

In order to verify the proposed control strategy, the

numerical simulation of the 3-2MC has been carried out

using MATLAB. The MC is considered as a 33 ideal switch

matrix and the parameters of the two phase balanced R-L load

are 10 and 5mH. The parameters of the input filter are

L=5mH , C=6uF and R=15. The MC is supplied by a 220V,

50Hz voltage source and the desired output frequency is 30Hz.

The voltage transfer ratio is 0.83 , the desired input power

factor is 1 and the switching frequency is 5 kHz. Fig.5 shows

the output currents and current harmonic spectrum, and the

THD of output current is 2.27%. Fig.6 shows the input voltage,

current and the current harmonic spectrum. The input current

is sinusoidal with unity power factor, in accordance with the

results of the theoretical analysis.

Fig.5. Output current and harmonic spectrum

Fig.6. Input voltage, current and the current harmonic spectrum

IV. EXPERIMENTALRESULTS

The prototype was developed using a dSPACE +CPLD

structure system. The Block diagram of the realization wasshown in Fig7.

The proposed control method is implemented on the

dSPACE system, whose kernel is DS1005 board, and some

other I/O boards including a Multi-channel A/D board

DS2003, and a high-speed PWM generating board DS5101.

To ensure the PWM signals synchronous, the DWO unit is

used. The four-step commutation strategy is implemented in

CPLD.

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Fig.7 The whole implementation scheme of MC prototype

The dSPACE+CPLD structure system is applied to control

an IGBT-based matrix converter driving a passive R-L load.

The experimental parameters are shown in Table . Fig.8

shows waveforms of output two-phase currents with

90angle shift. Fig.9 shows waveforms of input voltage and

current with unity power factor.

Table Specifications for experiments

Source line voltage 120V,50Hz

Input filter 5mH, 6uF,15

Load RL,LL 11, 5mH

Output-to input voltage ratio 0.86

Output voltage frequency 30Hz

Carrier frequency 5kHz

Fig.8.Output current waveforms

Fig.9.Input voltage and current waveforms

V. CONCLUSIONS

An indirect space vector modulation is proposed for a three-

leg based three-phase to two-phase matrix converter in this

paper. The SVM in the inverter stage is analyzed in detail, the

concrete modulation algorithm is given and a duty cycle

formula is gained by integrating virtual rectifying process and

inverting process. The ISVM can provide the sinusoidal two-

phase output currents with 90 angle shift and sinusoidal input

currents with unity power factor. Simulation and experiment

are carried out and the results show the correctness of the

control method.

VI. REFERENCES

[1] L. Huber and D. Borojevic. Space vector modulated three-phase to

three-phase matrix converter with input power factor correction, IEEE

Transactions and Industry Applications, vol.31, No.6, pp. 1234-1246,

Nov./Dec. 1995.

[2] Yongli Fang, Study on the control strategies of matrix converter and itscontrol method for doubly-fed adjusting speed system. The ph.D.

dissertion, China University of Mining and Technology, 2006.[3] Sangshin Kwak and H.A.Toliyat, Development of modulation strategy for

two-phase AC-AC matrix converters. IEEE Transactions on Energy

Conversion, vol.20,No.2 ,pp. 493- 494, June,2005.[4] F.Blaabjerg, F.Lungeanu and K.Skaug, Two-phase induction motor

drives. IEEE Industry Applications Magazine, vol.10, No.4, pp.24-32,

July-Aug.2004

[5] P. Nielsen, F. Blaabjerg, and J. K. Pedersen. Space vector modulated

matrix converter with minimized number of switching and feed-forward

compensation of input voltage unbalance. Proc. PEDES96, vol. 2, pp.

833-839,1996.

VII. BIOGRAPHIES

Yongli Fangwas born in Heilongjiang Province ,

china, on Feb. 17, 1972. She received the ph.D.

degree from China University of Mining and

Technology, Jiangsu Province, chinain 2006.

She joined the School of Information andElectrical Engineering, China University of

Mining and Technology, in 2007. Her fields of

interest cover power converters and power

quality.

Guojun Tan (M08) received the B.Sc. and

M.Sc. degrees from China University of Mining

and Technology, Xuzhou, Jiangsu Province,

China, in 1984 and 1988, respectively, and the

Ph.D. degree from China University of Mining

and Technology, in 1992, all in electrical

engineering.

Since 1995, he has been an Associate

Professor in the Electrical and Automation

Department, China University of Mining and

Technology, Xuzhou, Jiangsu Province, China.His research interests include electric machinery, motor drives, power

electronics, renewable energy source power systems, and power quality.

Hao Liu was born in Jiangsu Province, China,

on Mar. 15, 1981. He received the B.Sc. degree

from China University of Mining and

Technology, Jiangsu Province, China, in 2003.

And now he is pursuing his Ph.D. degree in

China University of Mining and Technology. His

fields of interest cover new type power

converters and power quality.