A MODULATION STRATEGY TO REDUCE COMMON-MODE VOLTAGE FOR CURRENT-CONTROLLED MATRIX CONVERTERS

Lin Hua He Bi, Zhang Xiaofeng College of Electric and Electronic Engineering College of Electric Engineering

Huazhong University of Science and Technology Naval University of Engineering 1037#, Luoyu load, Wuhan 430074 717#, Jiefang Avenue, Wuhan 430033

CHINA CHINA Lhua@mail.hust.edu.cn 9744103@163.com

Abstract –In this paper, a basic hysteresis control strategy for current-controlled matrix converter (MC) is introduced and discussed. Based on the rectifier-inverter equivalent circuit, a novel primary modulation strategy for improving the input current quality of MC is presented. That is, space vector modulation is used for control input current, and hysteresis current strategy with zero vectors is used for control output current. Furthermore, an optimal modulation strategy that reduces common-mode voltage at the output is proposed. This optimal strategy maintains subdivision of 6 input current sectors and proper selection of zero vectors and switching sequences. Therefore, by using this optimal strategy, peak value of common-mode voltage is reduced by 33.3% and RMS value is reduced by over 50% compared to the unoptimizable modulation strategy. Finally, simulation and experimental results are provided to verify the validity and feasibility of modulation strategy proposed in this paper.

I. INTRODUCTION

The matrix converter was first introduced by Venturini [1]. It has evolved into a direct ac-ac converter which converts the ac line voltage to a variable-voltage variable-frequency source without an intermediate DC-link circuit and has the following advantages: sinusoidal input and output waveforms; bidirectional power flow; controllable input power factor; high reliability; and more compact design.

The common-mode voltage produced by a modern power converter has been reported as a main source of early motor winding failure and bearing deterioration. Furthermore, the presence of high frequency and large magnitude of common-mode voltage at the motor neutral point have been shown to generate high frequency leakage current to ground path as well as induced shaft voltage [2]. Although, several methods to reduce common-mode voltage have been proposed in [3][4], these methods are based on voltage-controlled matrix converter system. The research on common-mode voltage for current-controlled matrix converter has not been reported in published documents.

In this paper, a basic hysteresis control strategy for current-controlled matrix converter (MC) is introduced and discussed. In order to improve the input current quality, a novel primary modulation strategy is proposed. That is, space vector modulation is used for control input current, and hysteresis current strategy with zero vectors is used for control output current. Furthermore, an optimal modulation strategy to reduce common-mode voltage at the output is

proposed. The advantages of the optimal modulation strategy are as follows.

1) Peak value of common-mode voltage is reduced by 33.3% and rms value is reduced by over 50%.

2) It reduces the switching loss compared to the primary current-controlled modulation

II. COMMON-MODE VOLTAGE IN MATRIX CONVERTER

Fig. 1 shows a matrix converter with nine bidirectional

switches. The voltage and current at the input side of the converter is noted by a, b, c while the output side is denoted by A, B, C, and common-mode voltage ucm indicates the potential between the motor neutral point and ground. The presence of common-mode voltage contributes to high-frequency leakage current icm generation. The common-mode voltage ucm is derived as follows:

AA cm A

BB cm B

CC cm C

diu u ri L

dtdi

u u ri Ldtdi

u u ri Ldt

− = +

− = +

− = +

(1)

Where, uA, uB, uC are output phase voltage with respect to ground. r and L are per-phase equivalent resistance and inductance of the induction motor respectively. Assuming iA+ iB+iC ≈ 0 , then from equation (1)

Motor

a

b

c

A B C

LZcmu

cmi Leakage Current

Common-mode Voltage

aAS

bAS

cAS

bBS

aBS

cBS

aCS

cCS

bCS

Fig. 1 Common-mode voltage circuit of MC

27751-4244-0136-4/06/$20.00 '2006 IEEE

3A B C

cmu u uu + += (2)

The output phases of MC are directly connected to the input phases via switching matrix. There are 27 allowed switching state combinations, such as acb, acc, bbb. The three letters are described as the connection state of input phase and output phase. For example, switching state acc is represented as turning on SaA, ScB and ScC. The output voltage vectors based on 27 allowed switching state combinations can be classified into rotating vectors, stationary vectors and zero vectors [5]. When every output phase is connected to different input phase, the rotating vector is obtained, such as acb. When two of output phase are connected to the same input phase, the stationary vector is obtained, such as abb. When three of output phase are connected to the same input phase, the zero vector is obtained, such as bbb.

Three kinds of voltage vectors generate different common-mode voltages magnitude.

Assuming that the magnitude of input phase voltage is Um, then from equation (2), the magnitude of common-mode voltage generated by the rotating vectors is expressed as follows.

03

a b ccm

u u uu

+ += = (3)

The magnitude of common-mode voltage generated by the stationary vectors is

1 33 3 3

( , , , )

i i jcm ij m

u u uu u U

i j i j a b c

+ += = ≤

≠ = (4)

The magnitude of common-mode voltage generated by the zero vectors is

( , , )3

i i icm i m

u u uu u U i a b c

+ += = ≤ = (5)

III. A NOVEL PRIMARY CURRENT CONTROL

STRATEGIES A. Basic Control Strategy of Hysteresis Current

The MC is modelled as an imaginary rectifier and an imaginary inverter as shown in Fig. 2. The two parts are connected via an imaginary DC-link.

As basic control, phase-controlled mode is adopted in the imaginary rectifier to make the voltage of imaginary DC-link

reach its maximum, and the control strategy of hysteresis current is used in the imaginary inverter to track command current [6]. Each period of input voltage can be divided into 6 sections according to the phase-controlled mode. Fig. 3 shows the sections of input voltage.

Assuming the upper limit and the lower limit of output current are expressed as subscript of “up” and “low” respectively, the error range of hysteresis current of phase A is shown in Fig. 4. The control strategies of hysteresis output current are: 1 If iA > 0 and iA > iAup, or iA < 0 and iA < iAlow, then turn

on SAn; 2 If iA > 0 and iA < iAup, or iA < 0 and iA > iAlow, then turn

on SAp; 3 If iB > 0 and iB > iBup, or iB < 0 and iB < iBlow, then turn

on SBn; 4 If iB > 0 and iB < iBup, or iB < 0 and iB > iBlow, then turn

on SBp; 5 If iC > 0 and iC > iCup, or iC < 0 and iC < iClow, then turn

on SCn; 6 If iC > 0 and iC < iCup, or iC < 0 and iC > iClow, then turn

on SCp; Then the switching rules of hysteresis current control for

MC can be obtained which is shown in Table I, according to combination of above error range of hysteresis current and input voltage sections. The combination method is mentioned in [6][7].

a

b

c

A B C

aAS aBS aCS

bAS bBS bCS

cAS cBS cCS

p

n

abc

ABC

apS

cnSbnSanS

CpSBpSApSbpS cpS

CnSBnSAnS

pI

Fig.2 Fundamental circuit and equivalent circuit of MC

au bu cu

Fig. 3 Input voltage sections

Ai

Aupi

Alowi

h

refAi

Fig.4 Error range of hysteresis current

TABLE I

THE SWITCHING RULES OF HYSTERESIS CURRENT CONTROL FOR MC U-1 U-2 U-3 U-4 U-5 U-6

I-1 1 4 6 caa cbb abb acc bcc baa I-2 1 3 6 cca ccb aab aac bbc bba I-3 2 3 6 aca bcb bab cac cbc aba I-4 2 3 5 acc bcc baa caa cbb abb I-5 2 4 5 aac bbc bba cca ccb aab I-6 1 4 5 cac cbc aba aca bcb bab

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The basic control strategy of hysteresis current is studied by computer simulation. A fixed step Ts is selected in simulation. The simulation waveform of input current ia and output voltage UAB are shown in Fig. 5. Apparently, the input current is non-sine wave and has plenty of harmonic components. In each cycle, the magnitude of input current is zero during the two periods, and the input current is high frequency oscillatory from positive magnitude to negative during the other part of the cycle.

Because phase-controlled mode is adopted in the imaginary rectifier, one phase input current always equals to zero during two input voltage sections, which can be explained. What reason causes high frequency oscillation in the other time?

Suppose the section of input voltage is unchanged, according to hysteresis current control strategy, when the output current exceeds a prescribed upper limit band, the upper switching in imaginary inverter is turned off and the lower switching is turned on. As a result, the output line voltage transitions from positive value to negative value, and the output current starts to decay, therefore, the polarity of input current changes. As the output current crosses the lower band limit, the lower switching is turned off and the upper switching is turned on, the polarity of input current changes again. B. Control Strategy of Hysteresis Current With Zero Vectors

It is obvious that the high frequency oscillation of input current will occur inevitably, if only 18 stationary vectors are used to decrease the absolute value of output currents. Then, zero vectors are adopted to solve this problem. When zero vectors are used, the absolute value of output currents decreases, and the input currents equal to zero. The control strategy of hysteresis current with zero vectors can be summarized as follows:

1) When the output current exceeds upper limit band, zero vectors are used;

2) When the output current is between the upper band and lower band or crosses the lower band limit, 18 stationary vectors are used. Switching states of MC are selected based on Table I;

Simulation results show that the input current waveform is improved by using zero vectors, which is shown in Fig. 6. C. Control Strategy of Hysteresis Current With Input Current Vector Control

When phase-controlled mode is adopted in the imaginary rectifier, the input currents equal to zero during two input voltage sections. Vector control strategy of imaginary rectifier can be used to improve further the quality of input current. The input current vector hexagon and synthetic input current vector are shown in Fig. 7.

PWM is used to obtain uniform rotational current vector Ii by impressing the adjacent vector IM and IN with the duty cycles dM, dN and d0 which is expressed as:

0 0

0 0

/ sin(60 )/ sin

/ 1

i M M N N

M M s i i

N N s i i

s M N

I d I d I d Id T T md T T md T T d d

θθ

= + += = −= == = − −

(6)

Where, mi is the input current modulation index. The novel primary control strategy is proposed, that is,

space vector control modulation is used for control input current, and hysteresis current control with zero vectors is used for control output current. The combinatorial switching rules of novel current control strategy are shown in Table II. The control strategy of hysteresis current with input current vector control can be summarized as follows:

1) When the output current exceeds upper limit band, the whole switching state will choose zero vectors;

2) When the output current is between the upper band and lower band or crosses the lower band limit, switching states of MC are selected based on Table II;

Simulation and experimental waveform of current and voltage by using the novel current control strategy is shown in Fig. 8. Apparently, the input current quality is further improved.

aiABu

Fig. 5 Simulation waveform of input current and output voltage using basic control Strategy of Hysteresis Current

aiABu

Fig. 6 Simulation waveform of input current and output voltage using control Strategy of Hysteresis Current with zero vectors

3( )I ba

2 ( )I bc

1( )I ac

6( )I ab

5 ( )I cb

4 ( )I ca

aI

cI

bI

iθ

MI

iINI

M Md I

N Nd I

(a) Input current hexagon (b) Synthetic input current vector Fig. 7 Space vector modulation of input current vector

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IV. A OPTIMAL CONTROL STRATEGIES TO REDUCE

COMMON-MODE VOLTAGE A. Selection of Zero Vectors

According to the equation (3)∼(5), the magnitude range of common-mode voltage ucm generated by stationary vectors is (0∼0.577)Um, and range of ucm generated by zero vectors is (0∼1)Um. Therefore, by using zero vectors, the magnitude range of common-mode voltage may be higher compared with the basic modulation strategy. Since the matrix converter is able to use three different kinds of zero vectors such as aaa, bbb, ccc, a proper selection of zero will decrease the magnitude of ucm

It is shown in Fig. 9(a) that the magnitude range of ucm is (0~0.866)Um if zero vectors are selected according to Table II. Dividing each input current space vector sector into 0<θi<π/6 and π/6<θi<π/3, if a input phase voltage with medium value within an input current vector sector is chosen as a zero vector, the maximum magnitude of common-mode voltage ucm is reduced to 0.5Um , which is shown in Fig. 9(b). For example, during rectifier I-inverter 1, ccc is selected as

zero vector, when 0<θi<π/6; and bbb is selected as zero vector, when π/6<θi<π/3. B. Adjustment of Switching Sequence

However, zero vectors are continually used in the proposed current-controlled modulation. The following guidelines are derived to make number of switching to be minimum.

1) When 0 <θi< π/6 and the sum of the rectifier section and inverter section is even, the output switching sequence must be

1 2 2 10 0

2 2 2 2N N

Md d d d

d→ → → →

2) When 0 <θi< π/6 and the sum of the rectifier section and inverter section is odd, the output switching sequence must be

2 1 1 20 0

2 2 2 2N N

Md d d d

d→ → → →

3) When π/6 <θi< π/3 and the sum of the rectifier section and inverter section is even, the output switching sequence must be

1 2 2 10 0

2 2 2 2M M

Nd dd d

d→ → → →

TABLE II SWITCHING RULES OF NOVEL CURRENT CONTROL STRATEGY

Rectifier I Rectifier II Rectifier III Rectifier IV Rectifier V Rectifier VI Sectioms

dM dN d0 dM dN d0 dM dN d0 dM dN d0 dM dN d0 dM dN d0

Inverter 1 abb acc ccc acc bcc ccc bcc baa aaa baa caa aaa caa cbb bbb cbb abb bbb

Inverter 2 aab aac aaa aac bbc bbb bbc bba bbb bba cca ccc cca ccb ccc ccb aab aaa

Inverter 3 bab cac ccc cac cbc ccc cbc aba aaa aba aca aaa aca bcb bbb bcb bab bbb

Inverter 4 baa caa aaa caa cbb bbb cbb abb bbb abb acc ccc acc bcc ccc bcc baa aaa

Inverter 5 bba cca ccc cca ccb ccc ccb aab aaa aab aac aaa aac bbc bbb bbc bba bbb

Inverter 6 aba aca aaa aca bcb bbb bcb bab bbb bab cac ccc cac cbc ccc cbc aba aaa

au bu cu

tω0 π

(a) Selection of zero vectors according to Table.II

tω0 π

au bu cu

(b) Selection of zero vectors to reduce common-mode voltage

Fig.9 Selection of zero vectors

aiABu

(c) Simulation waveform

auai

ACuBCu

(d) Experimental waveform (without input filter)

Fig.8 Simulation and experimental waveform using novel primary current control strategy

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4) When π/6 <θi< π/3 and the sum of the rectifier section and inverter section is odd, the output switching sequence must be

2 1 1 20 0

2 2 2 2M M

Nd dd d

d→ → → →

The figure over the arrow indicates switching times during state transformation. When the zero vectors are partly used in the switching period, the switching times are six. When the zero vectors are used in the whole period, the switching times are zero. Zero vectors can be chosen according to above method. V. SIMULATION AND EXPERIMENTAL RESULTS ON

COMMON-MODE VOLTAGE REDUCTION

Simulations have been built to validate proposed strategy. Simulation parameters are: Ts=0.0001s, input phase voltage 220V/50Hz, load resistance 24Ω, load inductance 50mH, simulation time 0.1s.

When output frequency is 20Hz, and under the condition of different current command, the simulation waveform of common-mode voltage and spectrum are shown in Fig. 10. It can be seen, under large current command, the high-frequency component (around 10kHz) of common-mode voltage ucm is obviously restrained and the magnitude of low-frequency component around 150Hz is decreased nearly by 50% by selecting appropriate zero vectors, and the high-frequency component of ucm is more restrained and the low-frequency component has no change by adjusting switching sequence. Under small current command, the harmonic component of ucm is centralized around low frequency

because zero vectors are continually used, and magnitude of ucm is larger than that under large current command. It is obviously that the magnitude of low-frequency component is restrained by selecting appropriate zero vectors.

Fig. 11(a) and (b) shows rms and peak value of ucm for various output frequency respectively by using novel primary strategy and optimal strategy. By using optimal strategy, the rms value of common-mode voltage ucm is reduced by over 50% and the peak value is reduced to 0.577Um from 0.866Um.

A 5kVA 110V MC prototype was developed to validate the theoretical analysis and simulation. The prototype consists of a DSP board using TMS320LF2407, a CPLD board and analog board for commutation, gate drives, a power supply board, a power board containing IGBT modules (1MBH60D-100), voltage and current sensors, and filters.

In the experiment, a resistance-inductance load (24Ω, 50mH) is operated with constant frequency 20Hz and switching frequency is 5kHz. Fig. 12 shows the experimental waveform of common-mode voltage by using different modulation strategies. It can be seen that the common-mode voltage can been greatly reduced by using the optimal modulation method.

VI. CONCLUSION

In this paper, a basic hysteresis control strategy for current-controlled matrix converter (MC) is introduced and discussed. A novel primary modulation strategy is proposed for improving the input current quality of current controlled

(a) Primary modulation strategy under large current command (b) Primary modulation strategy under small current command

(c) Selection of zero vectors under large current command (d) Selection of zero vectors under small current command

(e) Selection of zero vectors and switching sequence (f) Selection of zero vectors and switching sequence

under large current command under small current command

Fig. 10 Common-mode voltage and spectrum simulation waveform under different current command

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MC, based on the basic hysteresis current control strategy. That is, space vector modulation is used for control input current, and hysteresis current strategy with zero vectors is used for control output current. Furthermore, an optimal modulation strategy to reduce common-mode voltage at the output is proposed. The optimal strategy has been accomplished by choosing a medium-valued phase voltage within an input current vector sector as a zero vector and adjusting switching sequence. Therefore the rms value of common-mode voltage is reduced by over 50% and peak value is reduced by 33.3% compared to the primary method. Simulation and experimental results are provided to verify the validity and feasibility of modulation strategy proposed in this paper.

VII. REFERENCE [1] M. Venturini, “A new sine wave in sine wave out,

conversion technique which eliminates reactive elements,” in Proc. POWERCON 7, 1980, pp. E3_1–E3_15.

[2] D. A. Rendusara and P. N. Enjeti, “An improved inverter output filter configuration reduces common and

differential mode dv/dt at the motor terminals in PWM drive systems,” IEEE trans. Power Electro, vol. 13, Nov. 1998, pp. 1135-1143.

[3] Liu Hongchen, Chen Xiyou, Feng Yong et al, “A research on common-mode voltage for matrix converter based on two line voltage synthesis,” Proceeding of the CSEE, vol. 24, no. 12, 2004, pp. 82-186.

[4] Han Ju Cha and Prasad N. Enjeti, “An approach to reduce common-mode voltage in matrix converter,” IEEE Trans. on Industry Applications, vol. 39, no. 4, 2003, pp. 1151-1159.

[5] Lars Helle, Kim B Larsen and Blaabjerg F. “Evaluation of modulation schemes for three-phase to three-phase matrix converters,” IEEE Trans. on Industry Electronics, vol. 51, no. 1, 2004, pp. 158-171.

[6] Zhang Zhixue, Ma Hao, “ Current control strategies for matrix converter,” Proceeding of the CSEE, vol. 24, no. 8, 2004, pp. 61-66.

[7] Peter Mutschler, Matthias Marcks, “A direct control method for matrix converters,” IEEE Trans. on Industrial Electronics, vol. 49, no. 2, pp. 362-369.

ucm

RMS/

(25V

/m)

(a) Comparison of rms value (b) Comparison of peak value

Fig.11 Comparison between primary strategy and optimal strategy

ucm

(70V

/m)

(a) Under large current command (b) Under small current command

Fig. 12 Experimental waveform of the common-mode voltage

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