Electrimacs 2002, August 18-21, Session)

Multimachine Multiconverter Systems

(Invited

1

Control Structures for Multi-machine Multiconverter Systems with Upstream Coupling A. Bouscayrol, B. Davat, B. de Fornel, B. François, J. P. Hautier, F. Meibody-Tabar, E. Monmasson, M. Pietrzak-David, H. Razik, E. Semail, M. F. Benkhoris

Abstract-- A multi-machine multi-converter system formalism has been proposed to describe systems composed of several electrical machines and converters. This description points out coupling elements, which have to distribute energy. Control structures have already been proposed for systems with downstream coupling. This paper is focused on control structures for systems with upstream coupling. Several solutions can be found by moving control blocks. Index Terms-- Drives, Power conversion, Power engineering, Power system control, Power system modeling.

I. NOMENCLATURE Abbreviations EC: Electrical Converter EM: Electrical Machine ES: Electrical Source MC: Mechanical Converter MS: Mechanical Source MMS: Multi-machine Multi-converter Systems Subscripts Xec : variable of an electrical converter Xem: variable of an electrical machine Xes: variable of an electrical source Xmc: variable of a mechanical converter Xms: variable of a mechanical source This work was supported in part by the GdR (Groupement de Recherche) SDSE of the French CNRS (Centre National de Recherche Scientifique) and in part by the laboratories of the MMS (Multi-machine Multiconverter Systems) project of this GdR (http://www.univlille1.fr/l2ep/web-mms.htm). A. Bouscayrol, B. François, J. P. Hautier and E. Semail are with L2EP Lille, University of Lille, F59655 Villeneuve d'Ascq, France ([email protected]). B. Davat, F. Meibody-Tabar and H. Razik are with GREEN, ENSEM, 2 avenue de la Forêt de Haye, 54 600 Vandoeuvre les Nancy, France, ([email protected]). B. de Fornel and M. Pietrzak-David are with LEEI, ENSEEIHT, 2 rue Camichel, 31 071 Toulouse, France ([email protected]). E. Momasson is with LESiR-SATIE, IUP GEII de Cergy, 95031 Cergy-Pontoise Cedex, France ([email protected]). M. Benkhoris is with GE44, Boulevard de l'Université, BP 406, 44602 Saint-Nazaire, France ([email protected] nantes.fr).

Xest: Xmes: Xref: Xw:

estimated value of the variable X measured value of the variable X reference value of the variable X weighted value of the variable X II. INTRODUCTION

M

ULTI- machine multi-converter systems can be considered as extensions of classical drives. They are used either to extend the field of the power applications or to increase their flexibility and their operating safety. Thus, for some high power applications as the railway traction [1], the manufacturers have developed these kinds of drives for several years. These systems allow energy repartitions along the conversion chains through the coupling of power structures. But, these common physical devices induce some perturbations: over-voltages, instabilities, lower performances… A specific formalism has been defined to make easier the multi-converter multi-machine system (MMS) analysis [2]. This study is made according to the Multi-machine Multi-converter System project of a national French GdR (Groupement de Recherche). Different coupling sections can be defined in these systems: electrical [3], magnetic [4], [5] and mechanical couplings [6]. Their analysis point out some conditions in order to ensure optimum behaviours [7]. In some applications a classical coupling can be replaced by another one in order to propose alternative solutions (as electrical differentials [8]). For the design of the control, two kinds of coupling structures can be considered: upstream and downstream coupling. Control structures of such systems can be built thanks to an inversion principle of the power functions. For downstream coupling structure, specific energy repartition criterions are needed [9]. This paper is devoted to control structures for systems with upstream coupling elements. Other criteria have to be defined. In the first part, the MMS formalism and the coupling devices are presented. Then, the control building of MMS is deduced by inversion rules and a general solution is suggested for upstream coupling devices. In the last section, a railway traction system is chosen to illustrate the methodology.

Electrimacs 2002, August 18-21, Multimachine Multiconverter Systems Session) III. M ULTI-M ACHINE M ULTI-CONVERTER SYSTEM FORMALISM

(Invited

2

IV. CONTROL OF UPSTREAM COUPLING DEVICES A. Mono-machine Mono-converter System A mono-machine mono-converter system is a physical device set, which ensures an energy transfer between an electrical source (ES) and a mechanical one (MS) [2]. In a general case (Fig. 1), it is composed of three conversion structures: electrical converter (EC) electrical machine (EM) and mechanical converter (MC). These conversion structures can own a tuning input, which adjusts their energy conversion. Power busses, called connection busses, which induce the action - reaction principle, link these devices. This description is based on systemic and energetic considerations. All blocks have inputs and outputs according to their own causality. Moreover, the product of two variables exchanged (voltage v and current i for example) between two elements leads to the instantaneous power exchanged by these elements (p= v i for example).

ES

EC

EM

MC

ec

em

mc

MS

Fig. 1. Mono-machine mono-converter system

B. Multi-machine multi-converter system A MMS is composed of several mono-machine monoconverter systems, which share one or more power devices. Consequently, it owns coupled conversion chains, which can yield interactions (perturbations) between power structures [2]. The energy distribution is obtained by specific conversion structures. These power components are common to several conversion chains. They are called coupling structures and link an upstream device with many downstream elements, or vice versa (Fig. 2). Such structures are drawn by forms with intersections. The electrical coupling is associated with electrical converters (EC). It corresponds to a common electrical device of several converters (power switch, capacitor...). It leads to a common electrical variable (voltage, current...). The electromagnetic coupling is associated with electric machines (EM), and the mechanical coupling with mechanical converter (MC)

A. Control of a Mono-machine Mono-converter System The control structure of a mono-machine mono-converter system can be deduced from its MMS representation. Indeed the control of a system can be considered as an inversion of its modeling [9]. 1) Modeling inversion In order to impose a mechanical variable on the MS, a tuning input must be defined. The action chain is a succession of variables, which link the wished mechanical variable to the control one. On the example depicted in Fig. 3, the action chain leads to impose x2-mc to the mechanical source MS from the electrical source ES, through x2-ec and x2-em. The control structure has to define the adapted control variable (ecreg in the Fig. 3) in order to impose the wished effect (x2-mc-ref in the Fig. 3). Thus, control blocks are connected by reference variables, which constitute the control chain. This chain corresponds to the inversion of the action chain. In the example, the control chain has to define the ecreg for the electrical converter from the reference variable to impose on MS, x2-mc-ref through x2-em-ref and x2-ec-ref. The function of each conversion device has to be inverted by specific operations, which are controllers and perturbation rejections through measurements. In a first step, all variables are assumed to be measurable. 2) Representation of control structures In the MMS formalism all control blocks are drawn with the same pictogram (a rhombus) because they handle only information. The continuous lines are associated to inversion operations and the dashed line to perturbation rejections. A little oval on a power variable indicates its measurement.

xes

x2-ec

x2-em

EC

ES x1-ec

EM

MC x1-mc xms mes ? mes ?

x1-em ecreg C-EC

x2-mc

C-EM

x2-ec-ref

MS

C-MC

x2-em-ref

x2-mc-ref

Fig. 3. Control example of a mono-machine system

B. Control of an Upstream Coupling Device 1) Different coupling devices

ec

em

Fig. 2. Examples of coupling structures

mc

For each conversion structure, two coupling devices can be found. An upstream device owns a single upstream power bus for several downstream elements: it has to distribute the

Electrimacs 2002, August 18-21, Session)

Multimachine Multiconverter Systems

energy from the upstream device to the downstream elements (Fig. 4). A downstream device owns several upstream power busses for a single downstream one: it has to collect energy from several equivalent upstream sources to the downstream one (Fig. 4).

(Invited

be realized.

x2-ec-ref

x2-em-mes x2-em-ref

x1-es-ref x3-ec-ref

2) Control of downstream coupling

x1-es x1-ec (a)

x2-ec

x1-em

x2-em

x1-mc

x3-ec ec

x3-em

x3-mc x3-ms

x2-em (b)

x3-mc

mc

Fig. 4. Upstream (a) and downstream (b) coupling structures

3) Control of upstream coupling An upstream coupling structure owns only one action input (x1-se in Fig. 4.a) which involves the evolution of several action outputs (x2-ec and x3-ec ). The associated control block has to define the reference input to impose (x1-es-ref) from several references induced by downstream control blocks (x2-ec-ref and x3-ec-ref). In order to solve this problem, a weighting criterion is introduced for this control block structure. It defines the part of each input reference to produce the global output reference. A weighting parameter k w is then used. A coupling control block (or weighting block) is inserted in the control structure. An example is given in the Fig. 5, with only two downstream outputs:

x 1−es− ref = kw x 2 −ec−ref + ( 1 − k w )x 3 −ec−ref

x3-em-ref x3-em-mes

kw

For the downstream coupling structure, the inversion is a problem because it owns several action inputs (x1-em and x2-em in Fig. 4.b) which involve the evolution of the single action output (x3-mc). Thus there are many solutions to obtain the wished action output: acting on a single action input, acting on several one’s with equal repartition… Thus, a supplementary input for the control is necessary: it defines the wished repartition between the action inputs. It can be considered as a repartition criterion [9].

3

Fig. 5. Example of an upstream coupling control

4) Moving of the control blocks The inversion rules and coupling criteria leads to a theoretical control structure of MMS. The coupling control blocks are the key of the energy management. In the case of upstream coupling devices, the control structure owns a lot of control blocks (except for the masterslave criterion). The practical implementation can lead to a great computing time. In order to reduce the control operation number, the coupling control can be moved (Fig. 6). In this case, the weighting criterion is imposed to the inputs of the upstream control block. For this block, the references have to be weighted, but also the measurements:

x w −em−ref = k w x 2 −em−ref + ( 1 − k w ) x3 −em−ref

(2)

x w −em −mes = k w x 2 −em − mes + ( 1 − k w ) x3 −em −mes

(3)

Several control blocks are replaced by a weighted control block, which has to inverse an equivalent and weighted model of the real power structures. x2-em-mes

x1-es-ref

xw-ec-ref

x3-em-mes kw xw-em-mes xw-em-ref

x2-em-ref x3-em-ref kw

Fig. 6. Example of a coupling control moving

(1) V. A PPLICATION TO A MMS WITH AN UPSTREAM COUPLING

If k w=1 (or k w=0), a master-slave control is obtained: only the first input reference is taken into account. In this case, the control blocks of the slave part (discontinuous lines in Fig. 5) and the coupling control block have not to be realized. Even if the control structure is so simplified, one has not to forget that an implicit master-slave criterion is used. This choice has necessarily an impact on the system behavior. If k w=1/2, a mean control is obtained. Of course other weighting criteria can be defined, and the weighting parameter can evolve with time. In this case, all the control blocks have to

A. MMS Description of the System 1) System description The system studied is composed of a three-leg inverter supplying two induction machines for a railway traction application (Fig. 7) [10]. Both motors move the same bogie of the train. The dc voltage source is generated by a rectifier followed by a RLC filter.

Electrimacs 2002, August 18-21, Session)

V

Multimachine Multiconverter Systems

IM1

Rect. + V RLC dc filter

mech. transm.

Fig. 7. Three-leg inverter for two induction motors

In the chosen representation, the electrical source (ES) is assumed to be the generation system of the dc voltage Vdc (Fig. 8). It is connected to the inverter, which generates an absorbed current ivsi (reaction variable). The classical three-leg voltage source inverter (VSI) yields an electrical coupling, because it generates two ac three-phase voltages vvsi1 and vvsi2 to supply the machines. The power switches are crossed by the machine currents iim, which are the reactions to the supply voltages of the machines. Each induction machine (IM) produces an electromagnetic torque Tim. The mechanical part imposes a rotation speed Ω mc on the machine shafts. The common bogie yields a mechanical coupling. It induces a linear speed of the train vtrain from the interaction between the traction forces (induced by the torques) and the resistive force Fres. It can be viewed as two mechanical converters with common devices. This drive ensures a local energy repartition, which allows a reduction of the torque produced by each motor. The mechanical source (MS) is assumed to be the environment of the train. It yields the resistive force.

machines

vvsi ES

VSI

ivsi

iim1

Ωmc1 Tim2

IM2

iim2

(4)

The upstream electrical coupling is more restricting. It is solved by a weighting criterion:

v vsi −ref = kw v vsi1−ref + ( 1 − kw )v vsi2 −ref

VDC-mes vsitun

iim1-mes Ωmc1-mes Tim1-ref = Tim2-ref

kw

vvsi1-ref

FOC1

Tim1-ref

PWM

vvsi-ref

vvsi2-ref

PWM: Pulse Width Modulation FOC: Field Oriented Control

vvsi2-ref

123

dq vvsdq2-ref

FOC2

Ωmc2

CC: Current Controller ΦC: Flux Controller VE: Variable Estimations

Tim2-ref

T-ref

iim2-mes Ω mc2-mes

CC2

isdq2-mes

isdq2-ref esdq2-est

dq

vtrain Fres

(5)

A master-slave control (k w=0) is a natural choice as weighting criterion. But it has been shown that this strategy leads to problems in the case of an adhesion loss on the slave wheel [10].

θs2-est

MS vvsi

vsireg

environment

Tim1 IM1

Vdc

train

and the weighting block (for the voltage references). One can notice that the reference is generally a torque reference instead of a train reference, in railway applications.

1 Tim1−ref = Tim2 −ref = Tref 2

2) MMS Representation

inverter

4

The global traction force is generally decomposed into identical traction forces on the bogies. Thus, the mechanical coupling is solved by an equal-repartition criterion of the torque references:

IM2

dc supply

(Invited

123

iim2-mes

θs-est

ΦC2

Φ r2-ref

Tim2-ref Φr2-est VE2

Ω mc2-mes

Fig. 9. Theoretical control structure of the railway traction system Fig. 8. MMS representation for the railway traction system

2) Practical control structure of the MMS studied B. Global Control of the MMS 1) Theoretical control structure of the MMS studied The global control structure is deduced from the MMS description through the inversion rules and coupling criteria. This theoretical control structure (Fig. 9) leads to a PWM (Pulse Width Modulation) block, two FOC (Field Oriented Control) blocks, a repartition block (for the torque reference)

The most of the computing time is imposed by both FOC blocks. Indeed, they include flux observers, frame changing, flux and current controllers, and several other operations (see Fig. 9). In order to reduce the computing time, the weighting block is moved upstream the machine controls. Thus, a weighting FOC is defined, and the weighting criterion is applied to the torque references and to the current and speed measurements:

Electrimacs 2002, August 18-21, Session)

Multimachine Multiconverter Systems

Tw−ref = k wTim1− ref + ( 1 − kw )Tim2 −ref

(6)

i w− ref = k w iim1−ref + ( 1 − k w )i im2 −ref

(7)

For k w=1, only the first induction machine is controlled. The voltage references of the inverter are so defined from the first torque reference. All control blocks of the second machine can be suppressed. As the same three-phase voltages are imp osed to both motors, the second one is supplied by the voltage defined for the first one. This control is called master-slave control [10]. For k w=1/2, the voltage references are defined as the mean of the voltage references of both control chains. A weighted FOC is defined through the weighting references and measurements. Thus, the control has to inverse an equivalent mean motor. This control is called mean control [10]. One can notice that, the weighting criterion has also been applied to observer structures in order to improve the flux estimation of the weighted machine [11]. Moreover, weighted behavior model control has also been applied to solve the adhesion loss by reducing the global reference torque [12]. All these control strategies have been validated by SABER simulations taking into account the dynamics of the train with a fourth order model [10].

VDC-mes

iim1-mes iim2-mes Ωmc1-mes Ωmc2-mes

vsitun

Tim1-ref = Tim2-ref

kw I w-im-est PWM

Ωw-mc-est

Tim1-ref

FOCW

vvsi-ref

Tim2-ref

T w-im-ref

PWM: Pulse Width Modulation FOCW: weighted Field Oriented Control

T ref

kw

Fig. 10. Practical control structure of the railway traction system

VI. CONCLUSION A specific formalism has been defined to describe and analyze Multi-machine Multi-converter Systems [2]. First, inversion rules have been previously suggested in order to define control structures for such systems. It has been shown that MMS with downstream coupling need repartition criteria in their control structure [9]. This paper is focused on control structures for upstream coupling device. In order to solve the coupling inversion, a weighting criterion has to define the part of each downstream control reference. Now, with inversion rules and coupling criteria, a control structure of a MMS can be directly deduced from the MMS representation. Even if other control solutions can be found, this methodology leads quickly to one control solution.

(Invited

5

A railway traction system [10] has been studied in order to illustrate the control structure construction. This methodology has been already successfully applied to an electric vehicle [13], a five-phase synchronous machine [14], a wind Generation system [15].

VII. A CKNOWLEDGMENT The authors gratefully acknowledge the contributions of P. Escané and R. Peña-Equiluz for their works on the application of the railway traction, which has been chosen to illustrate the MMS methodology.

Electrimacs 2002, August 18-21, Session)

Multimachine Multiconverter Systems

VIII. REFERENCES [1] H. Kurtz, “Rolling across Europe's vanishing frontiers”, IEEE Spectrum , pp. 44-49, February 1999. [2] A. Bouscayrol, B. Davat, B. de Fornel, B. François, J.P. Hautier, F. Meibody-Tabar and M. Pietrzak David, “Multi-machine Multiconverter System: application for the electromechanical conversion”, EPJ Applied Physics, Vol. 10, no. 2, pp-131-147, May 2000 (common paper of GREEN, L2EP and LEEI, according to the MMS project of GdR-SDSE). [3] B. François and A. Bouscayrol, "Decoupled control of two induction motors fed by a five-phase voltage source inverter", in Proc. ElectrIMACS'99, vol. 3, pp. 313-318, Lisbon, September 1999. [4] N. Moubayed, F. Meibody-Tabar and B. Davat, "Study and simulation of magnetically coupled multi-stator induction machine supplied by independent three phase voltage -source inverters", in Proc. ElectrIMACS'99, vol. 1, pp. 59-64, Lisbon, September 1999. [5] D. Hadiouche, H. Razik and A. Rezzoug, "On the design of dualstator winding for safe VSI fed AC machine drives", in Proc. IEEEIAS Annual meeting, Chicago, September 2001. [6] P. Escané, C. Lochot, M. Pietrzak-David and B. de Fornel, "Electromechanical interactions in a high speed railway traction system", in Proc. ElectrIMACS'99, Lisbon, September 1999. [7] A. Bouscayrol, B. Davat, B. de Fornel, B. François, J.P. Hautier, F. Meibody-Tabar and M. Pietrzak-David, "Multi-machine multiconverter systems for drives: analysis of couplings by a global modeling", in Proc. IEEE-IAS annual meeting, Rome, October 2000 (common paper of GREEN, L2EP and LEEI, according to the MMS project of GdR-SDSE). [8] V. de Olivera, E. Monmasson and J. P. Louis, “Analysis of an electrical differential realized by two connected induction motors”, in Proc. ICEM’2000, pp. 1862-1865, Espoo (Finland), August 2000. [9] A. Bouscayrol, B. Davat, B. de Fornel, B. François, J.P. Hautier, F. Meibody-Tabar, E. Monmasson, M. Pietrzak-David and H. Razik, "Control structures for multimachine multiconverter system with downstream coupling", in Proc. EPE’2001, Graz (Austria), September 2001 (common paper of GREEN, L2EP, LEEI and LESiR, according to the MMS project of GdR-SDSE). [10] P. Escané, C. Lochot, M. Pietrzak-David, B. de Fornel, "Electromechanical interactions in a high speed railway traction system - Comparison between two drive control structures" in Proc. EPE'99, Lausanne (Switzerland), September 1999.1 [11] R. Peña-Eguiluz, M. Pietrzak-David and B. de Fornel, “Observation strategy in a mean control structure for parallel connected dual induction motors in a railway traction drive system”, in Proc. EPE’2001, Graz (Austria), August 2001. [12] J. Pierquin, P. Escané, A. Bouscayrol, M. Pietrzak-David, J. P. Hautier and B. de Fornel, "Behavior model control of a high speed railway traction system", in Proc. EPE-PEMC'2000 , Kosice (Slovak Republic), vol.6, pp. 197-202, September 2000 (common paper of L2EP and LEEI, according to the MMS project of GdRSDSE). [13] J. Pierquin, B. Vulturescu, A. Bouscayrol and J.P. Hautier, "Behavior Model Control Structures for an Electric Vehicle", in Proc. EPE'01, Graz (Austria), August 2001. [14] J-P. Martin, E. Semail, S. Pierfederici, A. Bouscayrol, F. Meibody Tabar and B. Davat, " Space Vector Control of 5-phase PMSM supplied by 5 H-bridge VSIs ", Proc. In ElectrIMACS'02, Montreal, August 2002 (common paper of GREEN and L2EP, according to the MMS project of GdR-SDSE).. [15] A. Tounzi, A. Bouscayrol, Ph. Delarue, C. Brocart and J. B. Tritsch, "Simulation of an induction machine wind generation

(Invited

6

system based on an Energetic Macroscopic Representation", in Proc. ICEM'2002, Brugges (Belgium), August 2002.

Electrimacs 2002, August 18-21, Session)

Multimachine Multiconverter Systems

IX. BIOGRAPHIES Alain Bouscayrol received the Ph.D. degree from INP Toulouse, France, in 1995. Since 1996, he has been engaged as assistant Professor at University of Lille (USTL), France. In L2EP (Laboratory of Electrical Engineering of Lille), his research interests include electrical machine controls and multi-machine systems. Since 1998, he has managed the Multi-machine Multiconverter Systems project of GdR-SDSE, a national research program of the French CNRS. Bernard Davat received the Engineer degree at ENSEEIHT, Toulouse, France, in 1975, the Ph.D. degree in 1979 and the "Docteur d'Etat" degree in 1984, both from the Institut National Polytechnique (INP) de Toulouse. During 1980 1988, he was been Researcher at CNRS (Centre National de la Recherche Scientifique) at LEEI (Laboratoire d'Electrotechnique et d'Electronique Industrielle de Toulouse). Since 1988 he has been engaged as Professor at INP de Lorraine. His main research interests deal with architectures / control of static converters and interactions with electrical machines. Bernard de Fornel received the Engineer degree at ENSEEIHT, Toulouse, France in 1965, and the Doctorat of Engineer degree in 1969 and "Docteur d'Etat" degree in 1976, both from the Institut National Polytechnique de Toulouse (INPT). He is Professor in Electrical Engineering Department of ENSEEIHT. Dr. de Fornel does research and industrial contracts, in LEEI UMR/CNRS, in the area of automatic control for electrical machines. Bru no François received the Ph. D. degree from the University of Lille, France in 1996. He is Associate Professor at the department of Electrical Engineering of: Ecole Centrale de Lille. He is a member of Laboratory of Electrical Engineering (L2EP), Lille. He is currently working on the design of modulation and control systems for multilevel converters and also the development of next-generation power systems. Web site : http://www.univ-lille1.fr/l2ep/c-br-fr.htm. Jean-Paul Hautier received the PhD degree from the University of Lille (USTL), France, in 1984. He received the "Habilitation à diriger des Recherches" degree from Engineering School of Douai, France, in 1989. In 1989, he became Professor at the ENSAM Lille. Its main research interests are power electronics and electrical systems control. Since 2000, Pr. Hautier has the direction of the the L2EP Lille (Laboratory of Electrical Engineering of Lille).

(Invited

7

Farid-Meibody -Tabar Tabar received the Engineer degree at ENSEM, Nancy, France, in 1982, the Ph.D. degree in 1986 and the "Habilitation à diriger des recherches" degree in 2000, both from the Institut National Polytechnique de Lorraine (INPL). Since 2000 he has been engaged as Professor at INPL. His research activities in GREEN, UMR/CNRS, deal with architectures and control of electrical machines supplied by static converters.

Eric Monmasson received the Engineer degree at ENSEEIHT, Toulouse, France in 1989, the PhD degree from INP in 1993. Since 1994, he has been an Assistant Professor at the University of Cergy Pontoise, near Paris. His research activities in LESiR-SATIE, UPRESA/CNRS, include the Control of Electrical Machines, the Hardware Architecture of Real-time Control System and the Analysis and the Design of Multi-machine Multiconverter Systems. Maria Pietrzak-David received the Engineer degree from Technical University of Gdansk, Poland, in 1970, the Doctorat of Engin eer degree in 1979 and the "Docteur d’Etat" degree in 1988, both from the Institut National Polytechnique de Toulouse (INPT), France. She is Professor in Electrical. Engineering Department of ENSEEIHT. Her research activities in LEEI, UMR/CNRS, deal with automatic control and observation techniques for industrial electrical drives. Hubert Razik is graduated from the Ecole Normale Supérieure in 1987, Cachan, France. He received the Ph.D. degree from the Polytechnic Institute of Lorraine in Electrical Engineering, Nancy, France, in 1991. He joined the Groupe de Recherche en Electrotechnique et Electronique deNancy in 1993. He currently works as an associate Professor in the University Henri Poincaré. His research interests are the modelling, the control and the diagnostic of induction motors. Eric Semail is graduated from the Ecole Normale Supérieure, Cachan, France. He received the teaching degree "Agrégation" in 1986. From 1987 to 2001, he has been professor (holder of agrégation) in University of Lille (USTL). He received Ph.D. degree in 2000 and became associate professor at ENSAM Lille in 2001. In L2EP (Laboratory of Electrical Engineering of Lille) his fields of interest include modeling, control and design of polyphase systems (converters and AC Drives)

Electrimacs 2002, August 18-21, Multimachine Multiconverter Systems Session) Mohamed F. Benkhoris received the Engineer degree at ENPA, Alger, Algerie, in 1986, and the Ph.D. degree from INPLorraine in 1991. During 1991-1999, he was been assistant Professor at ESA IGELEC St Nazaire. Since 1999, he has been engaged as assistant Professor at EpUN (Ecole polytechnique de l'Université de Nantes). In GE44LARGE (Laboratory of Electrical Engineering of Nantes and St Nazaire), his research interests deal with modelling, simulation and control of Electrical drives particularly multi-converter systems and polyphase machine.

(Invited

8