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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 6, NOVEMBER 1998 1089

Vector Control of a Permanent-Magnet SynchronousMotor Using ACAC Matrix Converter

Saıd Bouchiker, Gerard-Andre Capolino, Senior Member, IEEE , and Michel Poloujadoff, Fellow, IEEE

Abstract— This paper uses a recently proposed dqo transfor-mation to analyze a permanent-magnet synchronous machine(PMSM) driven by a nine-switch matrix converter. The matrixtransformation used leads to a new equivalent circuit where itsparameters are independent of the frequency of the other sideto which the circuit is referred. From this equivalent circuit, aset of command algorithms is deduced in order to control in anindependent way the flux and torque of the machine. It is shownthat the control of the gain and the displacement power factorat either set of terminals is dependent only on the choice of thephase angle in the matrix transformation. In order to verify thevalidity of the proposed algorithms, a full PMSM drive has beensimulated with the assumption of perfect switch behavior for the

matrix converter. Index Terms— Matrix converter, synchronous machine, vector

control.

I. INTRODUCTION

ATHREE-PHASE direct converter, with its numerous mer-

its such as sinusoidal input-current power factor adjust-

ment capability and instantaneous power flow change, has

recently received increasing interest [1][16] ever since its

appearance in 1976. Power electronics designers are looking

into ways of replacing the conventional rectifiers and inverters,

and this will lead into compacting the acac conversion since

direct conversion technique does not require inductive orcapacitive elements and also permits accurate control of the

phase and waveform of input currents [1][4]. To perform

these tasks, a high number of bidirectional fully controlled

switches are required, and this will lead to complex circuit

since single power semiconductors with these characteristics

do not exist. Various methods to control the matrix converter

have been proposed [1][9], [14], [16], and most of them are

programmable and work in open loop as, for example, the

indirect frequency conversion [7], [8] based on the conven-

tional rectifier and inverter. The signals for the control of the

rectifier and inverter are generated separately, and the signals

for the control of the acac converter are built back from

the combination of the two. Another method is based on adirect frequency conversion as a coordinate transformation

[3]. The patterns for acac conversion are generated directly,

and sinusoidal input- and output-current waveforms with unity

Manuscript received October 16, 1996; revised February 11, 1998. Recom-mended by Associate Editor, D. Torrey.

S. Bouchiker is with Electroship Consultant, Marseille, France.G.-A. Capolino is with the Department of Electrical Engineering, University

of Picardie Jules Verne, 80039 Amiens Cedex 1, France.M. Poloujadoff is with the University Paris VI, Paris, France.Publisher Item Identifier S 0885-8993(98)06488-6.

Fig. 1. General topology of the matrix converter.

input displacement power factor are obtained. However, this

method needs significant amount of additional calculations to

increase the gain by injecting a third harmonic of the input and

the output frequency into the desired output-phase voltages.

In this paper, a feedback control method based on using

the input and output voltages [14] to generate the switching

functions needed to drive a permanent magnet synchronous

motor is proposed. By transforming the matrix converter in dqo

rotating reference frames as proposed in [16], the equations of

the input or output are greatly simplified, and the important

parameters that permit the control of the input displacement

power factor and gain are deduced. By using the dqo trans-formation, the rotationary circuits are now transformed to

stationary ones and the time-varying nature of the switching

system is eliminated. Previous work [9] that uses a different

topology and a different matrix transformation has shown that

the total reactance seen from the secondary terminals still

depends on the frequency of the primary circuit of the matrix

converter. With the proposed approach, it will be shown that by

using another topology and a different matrix transformation,

the total reactance seen either at the primary or the secondary

does not depend on the frequency of the other side and that

the gain and reactive compensation depend only on the choice

of the phase angle control in the transformation matrices. This

new method will simplify greatly the control algorithms usingterms that do not depend on the frequencies at both the input

and output terminals of the nine-switch matrix converter.

II. MATRIX CONVERTER TRANSFER FUNCTION

The theory of the switching function and the transfer matrix

is given as an overview since it has been developed in

[14]. Nevertheless, as the final transfer function implies, line

voltages at the input and output terminals, the development of

new formulas has been necessary. The simplified three-phase

08858993/98$10.00 © 1998 IEEE

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1090 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 6, NOVEMBER 1998

Fig. 2. Simple switching function and isolated switch of a matrix converter.

Fig. 3. Average value of a switching function.

Fig. 4. Simplified matrix converter topology.

nine-switch matrix converter topology is shown in Fig. 1 in

which the voltage source that supplies the inductive load must

never be shorted and the output phases that carry the currentflowing in the load must not be left open. The switching

function for a switch , is

defined as (Fig. 2)

when switch is on

when switch is off.

Fig. 5. Single-phase equivalent circuit of the matrix converter.

Because one and only one switch in each output phase must

be conducting at any moment, the following relations are

satisfied:

(1)

The use of switching functions to derive dependent quantities

and internal converter stresses is very simple. Let us consider

an isolated switch in a converter matrix connected to , the

th of a set of -defined voltages, and to , the th of a

set of -defined currents. Its switching function is , a

train of unit-value pulses separated by zero-value intervals

as previously described. If the defined voltage sources are

expressed as the -element column vector (called the

defined voltage vector) and all the switching functions are

expressed as the matrix , then the dependent output-

voltage vector, consisting of all the voltages impressed on the

defined current sources, can be expressed as

(2)

Similarly, if is the -element defined current vector, then

the set of -input currents can be defined as the -element

vector

(3)

The superscript denotes a transpose and is the

instantaneous input-phase to output-phase transfer matrix of

the three-phase matrix converter. and are the input and

output-voltage vectors, and and represent the input- and

output-current vectors. Alternatively, from (2) the output-line

voltages can be expressed as shown in (4), given at the bottom

of the page. The switching frequency must be much higher

than the frequencies of the input voltages and output currents,

which are assumed to be continuous low-frequency functions,

and then the high-frequency components of the transfer matrix

(4)

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BOUCHIKER et al.: VECTOR CONTROL OF A PERMANENT-MAGNET SYNCHRONOUS MOTOR 1091

can be neglected. The local-averaged value of a switching

function (Fig. 3) is the duty cycle of the switch , and

it is denoted as . The low-frequency equivalents of (1) are

(5)

represents the ON time of the switch

in the period , and it can be noted that has the

limit when becomes smaller and smaller. The new

output-line voltages can be expressed as shown in (6), given

at the bottom of the page. Since

(7)

then the output-line voltages and the input-line currents can

be expressed as

(8)

and

(9)

Fig. 4 shows the matrix converter with its switching func-

tions for each pair of switches that performs the frequency

transformation. The different cycles can be expressed as

(10)

Reference [11] shows how these modulation functions are

derived from reference input- and output-line voltages. A

simple geometric representation in complex plane of the

modulation process is shown in [14], and the resulting output-

line-voltage space vector can be constructed out of six input-

line voltage vectors ( , , , , , ) and three

zero-voltage vectors ( , , ). The control functions that

use all the three line-to-line voltages are formulated, and the

(a)

(b) (c)

Fig. 6. Simplified equivalent circuit and phasor diagram of the PMSM drive.(a) Equivalent circuit referred to the primary side, (b) voltage and currentphasor diagram for

i

= 0 and lagging displacement power factor, and (c)voltage and current phasor diagram for

i

= 0 and unity displacement powerfactor.

control can be reduced by eliminating one line voltage, since

, and two zero voltages, since

. The improvement of the control functions permits torealize lower switching frequency.

III. EQUIVALENT CIRCUIT

A. Topology

We have chosen as an example for the application of

the theory a permanent-magnet synchronous motor (PMSM)

because of its numerous advantages over other machines that

are used for ac servo drives (absence of magnetizing current

in the stator and its higher torque-to-inertia ratio and power

density). The stator equations of the PMSM in the rotor

reference frame are derived with the following assumptionswhen neither saturation nor eddy currents and hysteresis losses

are present:

(11)

(12)

where

(13)

and

(14)

where

and , axis voltages;

and , axis stator currents;

and , axis inductances;

and , axis stator flux linkages;

and stator resistance and frequency.

(6)

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Fig. 7. Block diagram of the PMSM drive.

is the flux linkage due to the rotor magnet linking the

stator. The electromagnetic torque is

(15)

The equation of the rotor dynamics is

(16)

is the number of pole pairs, is the load torque,

is the damping coefficient, is the rotor speed, and is

the moment of inertia. During the steady-state operation, the

matrix converter frequency is related to the rotor speed as

follows:

(17)

To adapt the equations of the PMSM to the topology of the

variable-frequency converter, (11) and (12) are reorganized in

the following manner by substituting and from (13)

and (14):

(18)

(19)

with

From this new representation, the equations of the three-phase

voltages of the machine are given by the following:

(20)

with

and

where is the inverse Park transform.

Then, a single phase of the input-voltage vector and

the output-current vector can be represented in steady

state by an equivalent circuit (Fig. 5). On the secondary

side, the PMSM is reduced to the induced voltage , itsarmature resistance , and its leakage reactance . On

the primary side, the voltage supply is represented by the

electromagnetic force (emf) , the resistance , and the

reactance . The main circuit of the matrix converter uses

nine bidirectional switches that are capable of conducting

current in both directions to connect the three-phase source

to the three-phase load. , , and denote the input source

voltages after the input ac filters , , and denote the input

currents. , , and denote the output voltages viewed

from the neutral point , and , , and denote the output

currents. , , and represent the resistance, inductance, and

capacitance of the filter used to eliminate the switching ripples.

B. Circuit Equations

All circuit elements are linear and time invariant, and the

nine switches and source voltages are ideal. Now, the switched

linear time-varying system can be changed to an equivalent

linear time-invariant system by the dqo transformation in two

rotating reference frames. The equations of the source at the

primary side of the matrix converter can be written as

(21)

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TABLE ICONTROL SIGNALS g

1

–g

6

OF THE NINE SWITCHES

If represents the angle between the source emf and the

axis at the input of the converter, then

(22)

If the motor emf coincides with the axis at the output of

the converter, (18) and (19) of the PMSM at the secondary

can be rewritten as

(23)

where

(24)

The dqo rotating reference frames at the input and the output

of the converter are not identical, but both sides can have

a common reference frame using the voltage and currentequations. Then, (2) and (3) that describe the phase voltages

and phase currents are rewritten as

(25)

with

(26)

This transformation illustrates that the multiplication of a set

of three balanced sinusoidal quantities by a second similar set

yields a third set of balanced quantities, whose frequency can

change by varying the frequency of the second set. Practicalconverter switches, however, operate in the ON/OFF mode,

yielding pulsed switching patterns, and, consequently, the

converter switching functions have the following forms:

(27)

(28)

where is a time function defined as

(29)

The frequency changing capability of is very well

known from previous works [1], [3]. and represent

the maximum amplitude of the input and output voltages of

the converter. is the gain control, and are the

frequency control, and and represent the phase anglecontrol. denotes the modulation function of the nine

switches, and if the dqo transformation is applied to both

voltages and currents, the following equations are obtained:

(30)

where

(31)

is deduced from (31) by replacing by . If (25)

and (30) are reported into (21), the input voltages are written as

(32)

with

(33)

is the output-to-input-voltage ratio which is equal to .

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(a)

(b)

(c)

(d)

Fig. 8. Startup from standstill to a speed of 100 rd/s with vector control at constant load torque ( T

r

= 5 nm). (a) Reference and rotor speed (rd/s),(b) electromagnetic torque (nm), (c) i

d

current (A), and (d) i

q

current (A).

and ( and are the phase angle

control of the transfer function matrix). We can see from (33)

that does not contain parameters that are dependent on

the secondary frequency. It can be shown that if the circuit

is referred to the secondary side, the elements of would

depend only on the secondary frequency.

C. Control Functions

In (33), has the same effect as the turn ratio in a

transformer, the emf is proportional to , the im-

pedances are proportional to , and is equal to zero.

displaces the PMSM emf with respect to the axis reference.The input current is tied directly to the phase voltage when

is equal to zero, and it is independent of load characteristics.

So, in a balanced operation, the input current remains in phase

with the phase voltage as long as is maintained equal to zero.

equals zero means that the secondary reactance does

not influence the total input reactance, and the choice of the

pair determines the reactive power at the input of the

matrix converter. When contains sinusoidal functions of

either or , the control method is called

unrestricted frequency changers (UFC) [7]. As a result, low-

frequency harmonics exist in both output voltage and input

current, and the input displacement power factor is restricted to

the positive or negative value of the output displacement power

factor, whereas this control method uses a modulation function

which is composed of two matrices and in

which contains sinusoidal functions of that

produce reactive power and contains sinusoidal

functions of that produce reactive power.

Equations (32) and (33) show that the reactive power may be

directly controlled by and , and by choosing a positive

or negative phase angle , it is possible to shift the input

current with respect to the input voltage, therefore altering the

input displacement power factor. So, the input displacementpower factor is totally controllable by proper adjustment of

the phase angle , regardless of the load characteristic. It is

also possible to alter the input displacement power factor by

the phase angle , but some limitation to the available voltage

transfer ratio results. The voltage transfer ratio is proportional

to , therefore, for small values of the voltage transfer

ratio reduction is in the order of few percents. In conclusion,

the system is completely defined by two important parameters

which are the angle which controls the input displacement

power factor and the angle which changes the transfer ratio

of the matrix converter.

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(a)

(b)

(c)

(d)

Fig. 9. Startup from standstill to a speed of 200 rd/s in field-weakening mode at constant load torque ( T

r

= 5 nm). (a) Reference and rotor speed(rd/s), (b) electromagnetic torque (nm), (c) i

d

current (A), and (d) i

q

current (A).

D. Equivalent Circuit

During the steady-state operation, speed, currents, voltages,

and fluxes are constant and the previous equivalent circuit can

be simplified with the fact that the origin phase shift of the

reference frame can be set to any arbitrary value. Then, (32)

can be written as

(34)

where is expressed in polar form as

(35)

with

(36)

The equivalent circuit of the system referred to the primary

side of the matrix converter can be represented as the vector

diagram given by (34), where is the primary current (Fig. 6).

From the circuit phasor, it can be seen that the system works

with a current in phase lag or lead depending on the choice

of the angle , and, therefore, the displacement power factor

at the input can be set to any value.

E. Displacement Power Factor

For the sake of simplification, let us consider the case where

, then is in phase with when the imaginary part

is equal to zero which means that the following equation

has to be satisfied:

(37)

with .

If we consider that , this means that is approx-

imately equal to , then has to be set to

in order to obtain a unity displacement power factor at the

input [Fig. 6(c)]. In this case, the input current is given

approximately by the following equation:

(38)

where stands for the equivalent reactance presented by the

converter at the input terminals. The angles and may be

set to any desired value, and the system can work either as a

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(a)

(b)

(c)

(d)

Fig. 10. Phase current of the PMSM at startup with a constant load torque (T

r

= 5 Nm). (a) Rated speed !

r e f

= 1 0 0 rd/s, (b) field-weakening mode!

r e f

= 2 0 0 rd/s, (c) low-speed operation !

r e f

= 2 0 rd/s, and (d) very low-speed operation !

r e f

= 2 rd/s.

capacitive load or as a reactive load. has a great influence

on the gain and therefore on the transfer of power, and it is

maximum when is the greatest, and this occurs when

the angle is equal to zero.

IV. SIMULATION OF THE DRIVE

A. Description

The machine, speed, position feedback speed, voltage con-

trollers, and matrix converter constitute the PMSM drive as

shown in Fig. 7. The error between the reference and actualspeeds is operated upon by the speed controller to generate the

torque reference. In the constant airgap flux mode of operation,

the torque reference is divided by the motor torque constant

to give the reference quadrature axis current . From

(23) and (24), the dq reference output voltages are derived

to go through the Park transformation in order to generate

the , , stator reference output voltages. The source

input reference voltages are measured, and then from both

input and output reference voltages, the switching functions

for each pair of switches are generated. These functions are

sampled and passed through a zero-order holder block that

translates them into time functions needed to drive each switch

of the matrix converter. Both position and speed feedback

can be obtained from a resolver/signal processor combination.

When the reference speed is greater than the rated speed, the

PMSM operates in flux-weakening mode and the airgap flux is

weakened by applying a direct axis current in opposition

to the rotor magnet flux. The torque-speed profile of the drive

is as shown in the block named FW with the output unity up to

rated speed and decreases hyperbolically with speed between

the rated and the maximum speeds to ensure constant output

power. The first step in organizing the matrix converter controllogic requirements is to consider that the respective output-

voltage waveforms are identical to the ones obtained with

standard three-phase pulsewidth modulation (PWM) inverters.

Therefore, the matrix converter can be viewed as a standard

six-switch inverter supplied sequentially from input voltages

, , , , , and . The exact correspondence

between input voltages and groups of switches, comprising

the six-switch equivalent inverter, is shown in Table I. This

table establishes the relationship between the gating signals

( to ) of the equivalent six-switch converter and the real

nine-switch ( ) circuit as a function of the input voltages.

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(a)

(b)

(c)

(d)

Fig. 11. Steady-state input and output characteristics for rated speed ! = 1 0 0 rd/s. (a) Input-line voltage (V), (b) input-line current (A) (filtered), (c)input-line current (A) (unfiltered), and (d) output-line current (A).

B. Vector Control Transients

Digital computer simulations of the drive system are pre-

sented in this section. The state-space models of the PMSM,

speed controller, and switching logic of the voltage controllers

are included in the simulation with the semiconductor devices

considered as simple switches. To study the speed control

system presented, a startup from standstill to a speed of 100

rd/s has been simulated. The parameters of the PI controller

are chosen to be , , and s,

a time constant associated to the PI controller that defines the

bandwidth. The PI parameters are calculated to beJ/ and for a critical damping. The simulation

results in Fig. 8 show the performances of the controller with

a speed response without an overshoot and with a fast time

response (25 ms) for a maximum torque limited at 15 Nm.

At startup, the electromagnetic torque reaches the limit value

and then stabilizes to a value of 5 Nm at steady state which

corresponds to half the rated torque. The response of the two

stator currents shows the decoupling introduced by the vector

control command to the machine ( around a constant value)

with the torque shape depending only on the component.

The case of startup with a speed reference greater than rated

speed is also examined (Fig. 9), and the machine then operates

in the constant-power mode. Since the PMSM is entirely

controlled by the stator, the airgap flux is weakened by the

introduction of a negative current which creates a flux in

opposition to the flux due to the magnets. The system, as

shown in Fig. 9, responds without an overshoot and a greater

time response (65 ms) than in the rated speed response.

An other simulation has been performed in order to compare

the starting currents of the PMSM at different reference speeds

(Fig. 10). For all the presented cases, the load torque has

been set to the same constant value (5 Nm) and the torque

limitation has remained constant (15 Nm). For the previouscases with speed references of 100 rd/s [Fig. 10(a)] and 200

rd/s [Fig. 10(b)], the starting period with torque limitation

is very short with a transient for the stator current of two

periods and a maximum peak current of 40 A. For a low-

speed reference of 20 rd/s [Fig. 10(c)], the torque limitation

has not been reached and the maximum peak current remains

lower than 15 A. In this case, the regular shape of the

current can be observed with a one and a half period during

0.16-s simulation. A very low-speed reference of 2 rd/s has

been simulated [Fig. 10(d)] with the same conditions as for

low-speed reference. This last simulation permits to see a

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(a)

(b)

(c)

(d)

Fig. 12. Steady-state input and output characteristics for rated speed! = 2 0 0

rd/s. (a) Input-line voltage (V), (b) Input-line current (A) (filtered), (c)input-line current (A) (unfiltered), and (d) output-line current (A).

magnification of the current oscillations at 5-kHz switching

frequency.

C. Steady-State Investigation

The steady-state performances of the matrix converter have

been examined from the inputoutput characteristic point

of view. In this way, the input-phase voltage, line current

after and before the filter, and the output current have been

simulated. This filter is a low-pass second-order structure with, mH, and F which corresponds

with a cutoff frequency of 3.6 kHz. For a machine of a rated

output power of 1 kW, the capacitor gives a leading power

factor because of the addition of 450 VAR as an input balance.

For a speed reference of 100 rd/s (Fig. 11), the filtered input-

line current [Fig. 11(b)] leads the line voltage [Fig. 11(a)]

while the unfiltered line current [Fig. 11(c)] is in phase with

this voltage. The peak input current is around 6 A while the

peak output current [Fig. 11(d)] is around 11 A. For a speed

reference of 200 rd/s (Fig. 12), the filtered input-line current

[Fig. 12(b)] has more oscillations than in the former case while

the output current has the same shape as for the 100 rd/s speed

reference, but with a peak magnitude around 13 A.

V. CONCLUSION

The matrix converter has been completely analyzed through-

out this paper in a closed-loop system driving a PMSM.

By transforming both the primary and the secondary of the

converter to dqo rotating reference frames, the system has

been simplified and the important parameters that control the

input displacement power factor and the gain are deduced. Infact, two phase angles ( , ) of the switching functions

determine the reactive power at the unfiltered input and

the gain of the converter. This new method of control for

the matrix converter permits obtaining results at the output

similar to the conventional rectifier-inverter converter, whereas

at the input, with this simple control method, the system

proposed shows numerous merits such as sinusoidal input

current and power factor adjustment plus reverse power-flow

capability. From the output point of view, the proposed control

method is similar to a classical vector-controlled drive with

decoupling capabilities.

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APPENDIX

MOTOR PARAMETERS

kW, V, , mH,

mH, mH, mH,

kg m , Nm/rd/s, , and

Wb.

REFERENCES

[1] M. Venturini, “A new sine wave in, sine wave out, conversion techniqueeliminates reactive elements,” in Proc. Powercon 7 , San Diego, CA,1980, pp. E3E15.

[2] A. Alesina and M. Venturini, “Solid state power conversion: A Fourieranalysis approach to generalized transformer synthesis,” IEEE Trans.Circuits Syst., vol. CAS-28, no. 4, pp. 319330, 1981.

[3] , “Intrinsic amplitude limits and optimum design of 9 switch directPWM acac converters,” in Proc. IEEE PESC Conf., Kyoto, Japan,1988, pp. 12841291.

[4] D. G. Holmes and T. A. Lipo, “Implementation of a controlled rectifierusing acac matrix converter theory,” in Proc. IEEE-PESC Conf.,Milwaukee, WI, 1989, pp. 353359.

[5] J. Oyama et al., “Novel control strategy for matrix converter,” in Proc. IEEE-PESC Conf., Milwaukee, WI, 1989, pp. 360367.

[6] G. Roy and G. E. April, “Cycloconverter operation under a new scalar

control algorithm,” in Proc. IEEE-PESC Conf., Milwaukee, WI, 1989,pp. 368375.

[7] P. D. Ziogas et al., “Analysis and design of forced commutated cyclo-converter structures with improved transfer characteristics,” IEEE Trans.

Ind. Electron., vol. IE-33, no. 3, pp. 271280, 1986.

[8] , “Some improved forced commutated cycloconverter structures,” IEEE Trans. Ind. Applicat., vol. IA-21, pp. 12421254, 1985.

[9] M. Kazerani and B. T. Ooi, “Feasibility of both vector control anddisplacement factor correction by voltage source type acac matrixconverter,” IEEE Trans. Ind. Electron., vol. 42, no. 5, pp. 524530,1995.

[10] S. Bouchiker and G. A. Capolino, “ATP simulation of a flexible acacand dcac converter using the matrix converter control system,” inProc. First Europ. Conf. Power Systems Transients (EPST’93), Lisbon,Portugal, 1993, pp. 119124.

[11] S. Bouchiker, G. A. Capolino, and M. Poloujadoff, “A control methodfor generalized converter using instantaneous values of input line-to-

line voltages,” in Proc. IEEE IECON’94, Bologna, Italy, Sept. 1994,pp. 388393.

[12] , “A control method for generalized converter using instantaneousphase voltages,” in Proc. European Power Electronics Conf. (EPE’95),Sevilla, Spain, Sept. 1995, pp. 3.7043.709.

[13] P. Tenti, L. Malesani, and L. Rosseto, “Optimum control of N -inputK -output matrix converters,” IEEE Trans. Power Electron., vol. 7, no.4, pp. 707713, 1992.

[14] L. Huber and D. Borojevic, “Space vector modulated three-phase tothree-phase matrix converter with input power factor correction,” IEEE Trans. Ind. Applicat., vol. 31, no. 6, pp. 12341246, 1995.

[15] S. Bouchiker, “Contribution to a design of control laws for a matrixconverter,” Ph.D. dissertation, Univ. Paris VI, 1996 (in French).

[16] W. H. Kwon and G. H. Cho, “Analysis of static and dynamic charac-teristics of practical step-up nine-switch matrix converter,” Proc. Inst.

Elect. Eng., vol. 140, no. 2, pp. 139146, 1993.

Sa ıd Bouchiker was born in Tizi-Ouzou, Algeria. He received the B.Sc. andM.Sc. degrees from the University of Manchester Institute of Science andTechnology (UMIST), Manchester, U.K., in 1979 and 1981, respectively, andthe Ph.D. degree from the University Paris VI, Paris, France, in 1996.

From 1982 to 1989, he was an Electrical Engineer with the AlgerianNavigation Company (CNAN) and a Lecturer at the Military School of Engineering, Algiers, Algeria, the Electrical Engineering Institute of Tizi-Ouzou, Tizi-Ouzou, and the Naval Institute of Bousmal, Bousmal, Algeria.From 1990 to 1996, he was a Research Assistant and a Lecturer at theMediterranean Institute of Technology, Marseille, France. Since 1996, he hasbeen working as a Consultant for several naval companies in Marseille. Histeaching and research interests are in the areas of power electronics, electricmachines, power systems, and control systems.

Gerard-Andre Capolino (A’77M’83SM’89) was born in Marseille,France. He received the B.S. degree in electrical engineering from theEcole Superieure d’Ingenieurs de Marseille, Marseille, in 1974, the M.S.degree from the Ecole Superieure d’Electricite, Paris, France, in 1975, thePh.D. degree from the University Aix-Marseille I, France, in 1978, and theD.Sc. degree from the National Polytechnic Institute of Grenoble (INPG),Grenoble, France, in 1987.

In 1978, he joined the University of Yaounde, Cameroon, West Africa, asan Associate Professor and Head of the Department of Electrical Engineering.From 1981 to 1993, he was a Professor at the University of Dijon and

Mediterranean Institute of Technology, Marseille, where he was Founder andDirector of the Modeling and Control Systems Laboratory. From 1983 to1985, he was a Visiting Professor at the University of Tunis, Tunisia. From1987 to 1989, he was also the Scientific Advisor of the French companyTechnicatome. In 1994, he joined the University of Picardie Jules Verne,Amiens, France, as a Full Professor, Head of the Department of ElectricalEngineering, and Director of the Power Systems and Power ElectronicsLaboratory. In 1995, he was a Fellow of the European Community (E.C.)as a Professor at Polytechnic University of Catalunya, Barcelona, Spain. Hehas published more than 150 papers in scientific journals and conferenceproceedings since 1975. He has been the advisor of 12 Ph.D. and numerousM.S. students. In 1990, he founded the European Community Group forteaching electromagnetic transients and coauthored the book Simulation &

CAD for electrical machines, power electronics, and drives.Dr. Capolino is the Chairman of the French chapter of the IEEE Power

Electronics Society. He is the Cofounder of the IEEE International Symposiumfor Diagnostics of Electrical Machines Power Electronics and Drives

(SDEMPED), which he chaired for the first time in 1997. He is a Memberof steering committee for several international conferences, both in Europeand the United States. His research interests are electrical machines, powerelectronics, drives, diagnostic techniques in power systems, and CAD of control systems.

Michel Poloujadoff (M’65SM’77F’82) received the Diplome d’Ingenieurdegree from the Ecole Superieure d’Electricite, Paris, France, the M.S. degreefrom Harvard University, Cambridge, MA, and the D.Sc. degree from theUniversity of Paris, Paris.

He was a Professor of Electrical Power Engineering at the NationalPolytechnic Institute of Grenoble (INPG), Grenoble, France, for 25 yearsand is now with the University Paris VI, Paris. His research activities coverseveral subjects in electrical power engineering.

Dr. Poloujadoff received the Doctor Honoris Causa degrees from LiegeUniversity, Belgium, University of Budapest, Hungary, and University of Bucarest, Romania. He is a Laureat of the Academie des Sciences, Paris,a Fellow of the New York Academy of Sciences, and a Membre Emerite of the SEE (French Institute of Electrical Engineers). He is the recipient of the1991 IEEE-PES Nikola Tesla Award and 1994 IEEE Lamme Medal.

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