Proceedings of the 2008 International Conference on Electrical Machines Paper ID 1350

978-1-4244-1736-0/08/$25.00 ©2008 IEEE 1

A Novel Compensation Method Based on Fuzzy Logic Control for Matrix Converter under Distorted

Input Voltage Conditions 1Hulusi Karaca, Student Member, IEEE, 2Ramazan Akkaya, 3Hüseyin Doğan

1,2,3Elec. Eng. Dept., University of Selcuk, 42075, Konya, Turkey Tel: (+90)-332-2233715, fax: (+90)-332-2410635

1hulusikaraca@ieee.org, 2akkaya@selcuk.edu.tr, 3huseyindogan@selcuk.edu.tr

Abstract -- Matrix converter (MC) is a direct energy conversation device without dc-link components. Therefore, the output of the converter is directly affected by the disturbances in the input voltages. Many researchers have made an effort to overcome this problem.

In this paper, the behaviors of the MC have been investigated under the distorted input voltage conditions. A fuzzy logic control (FLC) based novel compensation method is proposed, which performs close loop control of the output current to improve the output performance of the MC. Some results are presented to prove the effectiveness of the proposed compensation technique.

Index terms -- matrix converter, distorted input voltage, compensation.

I. INTRODUCTION

One of the most interesting members of the power converter family is the matrix converter providing directly ac-ac power conversion. Matrix converters firstly introduced in 1976 started to improve after Venturini and Alesina proposed a generalized high-frequency switching strategy in 1980 [1,2].

Matrix converters have received considerable attention in recent years because they may become a good alternative to the traditional PWM-VSI [1]-[4]. They can produce the output voltages with the desirable amplitude and/or frequency. Energy regeneration can be done to the mains. Sinusoidal input currents can be drawn from mains and input displacement factor can be controlled. Furthermore, the matrix converter allows a compact design due to the lack of dc-link capacitors for energy storage [5].

These attractive properties have prompted researchers to study about the matrix converter [6].

However, the simultaneous commutation of controlled bidirectional switches used in matrix converter is very difficult to achieve without generating over-current or over-voltage spikes that can destroy the power semiconductors. This fact limited the practical implementation and negatively affected the interest in matrix converters, until the new commutation strategies that allow safe operation of the switches are developed by researchers [5].

Also, the load side of the MC is directly affected by the distorted and/or unbalanced input voltages due to the lack of dc intermediate circuit in the MC. The distorted and/or non-sinusoidal input voltages may cause the undesirable harmonic currents. The working performance of the load has deteriorated, when it is exposed to the harmonic and non-sinusoidal currents. If unfavorable effects of the distorted input voltages are eliminated in the MC, the popularity of the MC will more increase. Some papers have been presented to reduce the influences of the distorted input voltages [4], [7]-[10].

In this paper, a fuzzy logic control (FLC) based novel compensation technique is proposed, which performs close loop control of the output current to improve the output performance of the MC. Since this method is based on close loop control of the output current, three-phase currents must be measured. The proposed method not only reduces the output harmonic contents but also ensures over-current protection and control for the load current. Some numerical and simulation results are presented to prove the effectiveness of the proposed compensation technique.

Fig. 1. Three-phase matrix converter

L

C

Input Filter

SAa SAb SAc SBa SBb SBc

SCa SCb SCc

IA

IB

IC

Ia

Ib

Ic

N

Matrix Converter Fixed 3-Phase Supply

Load

Variable V-f Output

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The rest of paper is organized as follows. The section 2 gives

the control strategy of matrix converter. In the section 3, the proposed compensation scheme for matrix converter is explained. The section 4 gives the simulation results of the proposed system. The remarking conclusions are presented in the Section 5.

II. CONTROL STRATEGY OF MATRIX CONVERTER

The matrix converter is a single-stage converter which has an array of m x n bidirectional power switches to connect, directly, an m-phase voltage source to an n-phase load. The matrix converter of 3x3 switches, shown in Fig. 1, is the most important converter from a practical point of view, because it connects a three-phase voltage source with a three-phase load, typically a motor. [5].

The input terminals should never be short-circuited, because the MC is fed by a voltage source. Furthermore, an output phase must never be open-circuited, owing to the fact that the absence of a path for the inductive load current leads to the over-voltages. These constraints discussed can be expressed by Eq. (1).

1=== ∑∑∑

=== C,B,AKKc

C,B,AKKb

C,B,AKKa )t(m)t(m)t(m (1)

In this paper, CB, A, i ,vsi = , are the source voltages,

CB, A, i ,isi = , are the source currents, c b, a, j ,v jn = , are the load voltages with respect to the neutral point of the load n, and c b, a, j ,i j = , are the load currents. Additionally, other auxiliary variables have been defined to be used as a basis of the modulation and control strategies: CB,A, i ,vi = , are the MC input voltages, CB,A, i ,ii = , are the MC input currents, and c b, a, j ,v jN = , are the load voltages with respect to the neutral point N of the grid.

Each switch c b, a, j C,B, A, K ,S Kj == , can connect or disconnect phase K of the input stage to phase j of the load and, with a proper combination of the conduction states of these switches, arbitrary output voltages jNv can be synthesized. Each switch is characterized by a switching function, defined as follows [11].

⎪⎩

⎪⎨⎧

=closedisSswitchif

openisSswitchif(t)S

Kj

Kjij 1

0 (2)

The appropriate firing pulses to each of the nine bi-

directional switches must be calculated to generate variable frequency and/or variable amplitude sinusoidal output voltages from the fixed frequency and the fixed amplitude input voltages.

If it is defined as :tKj the time during which switch KjS is

on, Ts: the sampling interval, sKjKj Tt)t(m = : duty cycle of

switch KjS , modulation matrix is given in Eq. (3).

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

)t(m)t(m)t(m)t(m)t(m)t(m)t(m)t(m)t(m

)t(M

CcBcAc

CbBbAb

CaBaAa (3)

Under normal conditions, the input three phase voltages of

the MC can be given as,

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

π+ωπ+ω

ω=

)/tcos()/tcos(

)tcos(V)t(v

i

i

i

imsi3432 (4)

In accordance with this, each output phase voltages can be

expressed by Eq. (5).

[ ] [ ][ ])t(v)t(M)t(v ijN = (5) In the same way, the input currents are also shown by

expression in Eq. (6).

[ ] [ ] [ ])t(i)t(M)t(i oT

i = (6)

Where, [M(t)]T is the transpose matrix of [M(t)]. To obtain a maximum voltage transfer ratio is added common-mode voltages to the target outputs voltages as shown in Eq. (7).

[ ]

( ) ( )

( ) ( )

( ) ( )⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

ω+ω−π+ω

ω+ω−π+ω

ω+ω−ω

=

tcostcos)tcos(

tcostcos)tcos(

tcostcos)tcos(

qV)t(v

ioo

ioo

ioo

imjN

332

1361

34

332

1361

32

332

1361

(7)

Where, q is the voltage gain. The common-mode voltages

have no effect on the output line-to-line voltages, but allow the target outputs to fit within the input voltage envelope with a value of q up to 86,6%. It should be noted that a voltage ratio of 86,6% is the intrinsic maximum for any modulation method where the target output voltage equals the mean output voltage during each switching sequence [5].

The formal statement of the algorithm, including displacement factor control, in Venturini’s paper [2] is rather complex and appears unsuited for real time implementation. In fact, if unity input displacement factor is required, then the algorithm can be more simple in the form of (8) [5].

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( ) ( )

3

43

20

3322

131

2

ππ=β==

⎥⎥⎦

⎤

⎢⎢⎣

⎡ωβ+ω++=

,,,c,b,aj,C,B,AK

tsintsinqq

V

vvm

K

iKimim

jKKj

(8)

In the modeled system, firstly, the power circuit, including

nine bidirectional-switches was designed. Then, an input filter and a clamp circuit were modeled to smooth distortion of the input current and to prevent damaging of the power switches due to over-voltages or over-currents possibly occurring during commutation, respectively. Then, duty cycles of bidirectional switches were calculated according to (9).

( ) ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡ωβ+ω++= tsintsin

qq

V

vvTt iKi

mim

jKsKj 3

92

3

231

2 (9)

The switching functions (SKj(t)), determining turn-on-time

of the switches were obtained according to the logic statements in equation (10) by using duty cycles. These functions are gate-drive signals of the power switches [11].

)Y(notand)X(notS

c,b,aj)Y(and)X(notS

)X(S

Cj

Bj

Aj

=

==

=

(10)

III. THE PROPOSED COMPENSATION SCHEME

Modulation algorithms used in the MC have employed fixed switching patterns under the normal input voltage conditions. For certain frequency and/or amplitude values, duty cycles of the power switches are pre-calculated and placed into the table. But, since the disturbance reflects the output of the converter under the distorted input voltage conditions, using the fixed switching patterns are not appropriate. Therefore, duty cycles for switching patterns must be calculated instantaneously by measuring the output currents at each sampling period [12].

Fig. 2. FLC based compensation scheme for matrix converter

In the MC, which is shown schematically in Fig. 2, the measured output currents are used to calculate the magnitude of the output current space vector (Ido) according to Eq. (11). If the input voltages of the MC are sinusoidal and balanced, the output currents will be sinusoidal, too. Under this condition, Ido is constant. However, if the input voltages of the MC are non-sinusoidal and unbalanced, Ido will be not constant due to the output harmonic currents.

∑=

=c,b,ajjdo )t(iI 2

32 (11)

Receiving inspiration from this idea, if Ido is kept constant,

the output of the converter is not affected by disturbances in the input voltages. The proposed compensation technique is based on this principle and a fuzzy logic controller is employed for this purpose.

Accordingly, the fuzzy logic control system shown in Fig. 3 is fed by the instantaneous error of Ido ( e(k) ) in Eq. (12) and the change of error ( )k(eΔ ) in Eq. (13) and produces a variable voltage-gain (q) according to the disturbance of the input voltage. In these equations, α and β is normalization coefficients. Duty cycles of the power switches are calculated, substituting the variable-voltage-gain-value produced by the FLC in Eq. (14).

( ) ( )[ ]α−= .)k(IkIke refdo (12)

( ) ( ) ( )[ ]β−−=Δ .kekeke 1 (13)

( ) ( )⎥⎥⎦

⎤

⎢⎢⎣

⎡ωβ+ω++= tsintsin

qq

V

vvTt iKi

mim

jKsKj 3

92

3

231

2 (14)

Block diagram of the FLC based feedback system is clearly

given in Fig. 4. The instantaneous value of the error can be calculated by subtracting Iref from the current space vector obtained by the measured three-phase output current. The change of error is the difference between present and previous values of the error.

Fig. 3. The proposed fuzzy logic control scheme

Error (e)

Change of error (∆e)

FLC

Output

q

Load

3-Phase AC Source

3-Phase Current

Measurement

Controller and

Driver 3

3

3

9 Iref q

Ido

-+

FLC Control System

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Fig. 4. Simulink diagram of FLC based feedback system

The output of the FLC system is the change of voltage gain

(∆q) and its value is between -1 and +1 according to rule base in Table I. Actual voltage gain is calculated by adding the previous value and the change of the voltage gain, as seen in Eq. (15) . A saturation block has been supplemented, due to the magnitude of q can not exceed 0.866 and can not be negative.

)k(q)k(q)k(q Δ+−= 1 (15)

TABLE I

RULE BASE OF PROPOSED COMPENSATION METHOD

∆e/e NB NS Z PS PB N PB PS PS Z NB Z PB PS Z NS NB P PB Z NS NS NB

IV. SIMULATION RESULTS

Some simulation studies have been done using the following parameters: source voltage amplitude Vi = 311V, input frequency fi = 50 Hz, load resistance R = 10 Ω, load inductance L = 30 mH. The parameters of the input filter are Lf = 3 mH, Rf =0.1 Ω and Cf = 25 µF. Switching frequency fs = 5 kHz and simulation step = 10 µs.

The simulations have been performed under the input voltage conditions which has 20% third harmonic as shown Fig. 5.

Under the abnormal input voltage conditions, thanks to the proposed compensation method, duty cycles of the power switches aren’t fixed anymore, are variable according to the disturbance in the output currents. The variation of q is illustrated in Fig. 6.

The waveforms of the output currents and line voltages for 25 Hz are shown in Fig. 7 and Fig. 8, respectively. In Fig 7(a) and 8(a), the output currents and line voltages under the normal input voltage conditions, in Fig. 7(b) and 8(b), the output currents and line voltages under the input voltage conditions with 20% third harmonic distortion, in Fig. 7(c) and 8(c), the output currents and line voltages compensated with the proposed method under the input voltage conditions with 20% third harmonic distortion.

Fig. 5. Distorted input voltages

Fig. 6. Variation of the voltage gain

Total harmonic distortion of the output current is 1.54% for

the sinusoidal input voltages, 8.27% for the distorted input voltages (uncompensated), and 2.5% for the distorted input voltages (compensated). As it is shown, if the input voltage of the MC is distorted, the low order harmonics occur on the output current and voltage. But, under the same conditions, the proposed fuzzy logic control based compensation method has satisfactorily eliminated this harmonics.

(a) In the normal input voltage conditions

(b) In the distorted input voltage conditions (uncompensated)

(c) In distorted input voltage conditions (compensated)

Fig. 7. Three-phase output currents for the MC (fo = 25 Hz)

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(a) In the normal input voltage conditions

(b) In the distorted input voltage conditions (uncompensated)

(c) In the distorted input voltage conditions (compensated)

Fig 8. Output line voltages for the MC (fo = 25 Hz) (green line is average of voltage)

V. CONCLUSIONS

A FLC based novel compensation technique is proposed, which performs close loop control of the output current to improve the output performance of the MC. The proposed method has satisfactorily got rid of harmonics in the output currents and voltages under the distorted input voltage conditions.

The method not only reduces the output harmonic contents but also allows the control of the load current. It is confirmed by simulation results that this compensation technique is an effective method to reduce harmonics of the output current and voltage in spite of undesirable effects on the input supply voltage waveforms.

ACKNOWLEDGMENT

The authors gratefully acknowledge the financial support provided by Scientific Research Project Found of Selcuk University (project number: 08701291).

REFERENCES [1] M. Venturini, A New Sine Wave in Sine Wave out, Conversion

Technique Which Eliminates Reactive Elements, Proceedings of Powercon 7, pp. E3/1-E3/15, 1980.

[2] A. Alesina, M. Venturini, “Analysis and Design of Optimum-Amplitude Nine Switch Direct AC-AC Converters”, IEEE Trans. Power Electron., vol. 4, no.1, pp. 101-112, Jan. 1989.

[3] L. Huber, D. Borojevic, “Space Vector Modulated Three-Phase to Three-Phase Matrix Converter with Input Power Factor Correction”, IEEE Trans. Ind. Applicat., vol. 31, no. 6, pp. 1234-1246, Nov./Dec. 1995.

[4] D. Casadei, G. Serra and A. Tani, “Reduction of the Input Current Harmonic Content in Matrix Converters under Input /Output Unbalance” IEEE Trans. Ind. Applicat., vol. 45, no. 3, pp. 401-409, June 1998.

[5] P.W. Wheeler, J. Rodriguez, J.C. Clare, et al., “Matrix Converters: a Technology Review”, IEEE Trans. Ind. Electron., Vol. 49, no.2, pp.276-288, April 2002.

[6] H. Karaca, R. Akkaya, “A Matrix Converter Controlled with the Optimum Amplitude-Direct Transfer Function Approach”, 6th International Conference on Electrical Engineering ICEENG 2008, May 2008.

[7] P. Nielsen, F. Blaabjerg, J. K. Pedersen, “Space Vector Modulated Matrix Converter with Minimized Number of Switchings and a Feedforward Compensation of Input Voltage Unbalance”, IEEE-PEDES’96, vol. 2, pp. 833-839, 1996.

[8] P. Nielsen, D. Casadei, G. Serra, A. Tani, “Evaluation of the Input Current Quality by Three Modulation Strategies for SVM Controlled Matrix Converters with Input Voltage Unbalance”, IEEE-PEDES’96, vol. 2, pp. 794-800, 1996.

[9] K. Sun, D. Zhou, L. Huang, K. Matsuse, “Compensation Control of Matrix Converter Fed Induction Motor Drive under Abnormal Input Voltage Conditions”, IEEE-IAS’04, pp. 623-630, 2004.

[10] M. E. O. Filho, E. R. Filho, K. E. B. Quindere, J. R. Gazoli, “A Simple Current Control for Matrix Converter”, IEEE-International Symposium on Industrial Electronics, pp. 2090-2094, 2006.

[11] J. Rodriguez, E. Silva, F. Blaabjerg, P. Wheeler, J. Clare, J. Pontt, “Matrix Converter Controlled with the Direct Transfer Function Approach: Analysis, Modelling and Simulation”, Taylor&Francis-International Journal of Electronics, vol. 92, no. 2, pp. 63–85, February 2005.

[12] S. Sünter, H. Altun, J. Clare, “A Control Technique for Compensating the Effects of Input Voltage Variations on Matrix Converter Modulation Algorithms”, Taylor&Francis-Electric Power Components and Systems, vol. 30, pp. 807-822, 2002.