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Control structures for Multi-machine Multi-converter Systems with several couplings by criteria merging A. Bouscayrol1, B. Davat3, P. Delarue2, B. de Fornel4, J. P. Hautier2, J. P. Louis5, F. Meibody-Tabar3, E. Monmasson5, S. Pierfederici3, M. Pietrzak-David4, H. Razik3, E. Semail2, M. F. Benkhoris1 1
L2EP Lille, bât. P2, USTL, 59 655 Villeneuve d'Ascq cedex, France, GREEN, UPRESA n°7037, ENSEM, 2 av. de la Forêt de Haye, 54 600 Vandoeuvre les Nancy, France, 3 LEEI, UMR n°5828, ENSEEIHT, 2 rue Camichel, 31 071 Toulouse cedex, France 4 LESiR, UPRESA n°8029, LESiR-SATIE - IUP de Cergy, rue d'Eragny, Neuville sur Oise, 95031 Cergy-Pontoise Cedex, France, 5 GE44, Boulevard de l'Université, BP 406, 44602 Saint-Nazaire, France 2
1,2,3,4,5
MMS Project of the GDR-ME2MS of the French CNRS
[email protected], URL: http://www.univ-lille1.fr/l2ep/web-mms.htm
Abstract A multi-machine multi-converter system formalism has been proposed in order to describe systems composed of several electrical machines and converters. The keys of such systems are coupling devices, which have to distribute energy. Control structures have also been suggested according to an inversion principle. The inversions of coupling devices have been made using repartition and weighting criteria. In this paper, the case of systems with several coupling is studied. Several control structures can be found. One of them leads to move some control blocks and to merge the repartition and weighting blocks. An example of a railway traction system is given in order to illustrate this control methodology.
I. Introduction Multi-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. So, for some high power applications [Kur-99], the manufacturers have developed such drives since several years. These systems enable energy repartitions through coupling power structures. But, these common physical devices induce some perturbations: over-voltages, instabilities, lower performances… A specific formalism has been defined to analyse Multi-converter Multi-machine System (MMS) [EPJ-00]. This study is made according to the MMS System project of a national GDR (Groupement de Recherche) of the French CNRS. Different coupling sections can be defined in these systems: electrical, magnetic and mechanical couplings. Their analysis point out some conditions in order to ensure optimum behaviours. For the control, two kinds of coupling structures can be considered: upstream and downstream one's. Previous papers have been devoted to control structures for systems with downstream coupling [EPE-01] or upstream coupling [MCS04]. This paper deals with systems with both kinds of coupling. In this case, a merging of coupling blocks is suggested in order to reduce the computation time.
II. Multi-machine Multi-converter System Formalism II.1. MMS formalism 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) [EPJ-00]. 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 have a tuning input, which adjusts their energy conversion. Exchange variables are based on the action reaction principle.
ES
EC ectun
EM emtun
MC
MS
mctun
Fig. 1: Mono-machine mono-converter system A multi-machine multi-converter system is composed of several mono-machine mono-converter systems, which share one or more power devices. Thus, it owns coupled conversion chains, which can yield interactions (perturbations) between power structures.
- Synopsis for EPE 2005, Dresde The energy distribution is obtained by specific conversion structures, which link several upstream and downstream elements (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 converters (MC).
emtun
ectun
mctun
Fig. 2: Examples of coupling structures II.2. MMS control The control structure of a mono-machine mono-converter system can be decomposed into different control blocks (Fig. 3). Each control block has to inverse the power function of its conversion structure [EPE-01]. But, for MMS, inversions of the coupling devices yield some problems, because such structures have different numbers of inputs and outputs. xse
x2-ec
ES
x2-em
EC x1-ec
EM
x1-em
x1-mc mes ?
ectun C-EC
C-EM
x2-ec-ref
x2-mc MS
MC
xms mes ?
C-MC
x2-em-ref
x2-mc-ref
Fig. 3: Decomposed control of a mono-machine mono-converter system An upstream coupling device has to distribute energy (from a single action input to several action outputs). To solve its inversion, a weighting criterion is inserted in its control [MCS-04] (Fig. 4a). A downstream coupling device has to collect energy (from several action inputs to a single action output). To solve its inversion, a repartition criterion is inserted in its control [EPE’01] (Fig. 4b). x1-ref=kwx2-ref+(1-kw)x3-ref
x4-ref =krx6-ref x5-ref =(1-kr)x6-ref x4-ref
x2-ref x1-ref (a)
x6-ref
x5-ref
kw
x3-ref
(b)
kr
Fig. 4: Example of control for: upstream (a) and downstream (b) coupling devices II.3. Criteria merging of coupling control blocks One can notice that the inversion principle leads to a great number of control blocks. This increases the computation time, the number of sensors and the global cost of the control. Controls blocks can be moved in the control architecture according some assumptions. This modification enables a reduction of the control operation number for systems with upstream devices [MCS’04]. For systems with upstream and downstream coupling devices, we suggest to move control blocks in order to have the coupling control blocks side by side. Thus both control algorithms can be merged (Fig. 5). x1-ref=(1-kw-kr+2krkw)x6-ref
x7-ref x1-ref
x6-ref
x8-ref kw
kr
x6-ref
x1-ref kr, kw
Fig. 5: Example of coupling block fusion
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III. Application to a railway traction system III.1. MMS description A railway traction system is studied. It is ensured by DC machines with permanent magnets supplied by a single chopper, like for the automatic subway VAL 206 [Mer-04] (Fig. 6). The mechanical parts are assumed to be ideal in order to give a comprehensive illustration of the criteria fusion: right line operating, no lateral forces, no slip between the wheels and the road [Arn-97] [Hor-98]. The connections between the chopper and the machines can be assumed to be a coupling upstream device. Of course, the vehicle chassis ensures a downstream coupling device: from two traction forces to a single train velocity. The MMS representation of the system is depicted in Fig. 7. The relationships of each component will be given in the final paper. train s11
s21
e1 L1 R1
1 VDC uchop 2 s ichop 12
s22
imach
R2 L2 e2
vtrain
Ωshaft1
Ωshaft2
Fig. 6: Supply of the railway traction systems III.2. Maximum control structure of the railway traction systems A maximum control structure is deduced from the MMS modelling of the system using inversion rules (Fig. 7). It is composed of three controllers (parallelogram with oblique bar) and several measurements. This control structure will be described in the final paper. A weighting criterion is used to invert the series connection:
i mach _ ref = k w i mach _ ref 1 + ( 1 − kW )imach _ ref 1
with 0 ≤ k R ≤ 1
Moreover a repartition criterion is used to invert the mechanical coupling:
vbog 1 _ ref = k R vtrain _ ref v bog 1 _ ref = ( 1 − k R )vtrain _ ref
with 0 ≤ k R ≤ 1
In a previous paper, it has been shown that kw = 1/2 is an efficient solution for disturbance rejection as slip phenomena, in comparison with the classical master-slave control (kw = 1) [IEMDC-03]. III.2. Control with criteria merging of the railway traction systems The weighting criterion is moved from the series connection to the mechanical coupling and to the measurements. Thus, the control structure can be simplified (Fig. 8). More details will be given in the final paper. As the criterion blocks are directly connected, the can be merged:
vbog 1 _ ref = ( 1 − kW − k R + 2 kW k r )vtrain _ ref
- Synopsis for EPE 2005, Dresde shafts
chopper windings in series machines
supply
VDC ES
uchop ichop
sij
imach
emach1
imach
imach
etot
Ωshaft1
Tmach1
imach
emach2
bogies
Ω shaft
train
environment
vbog1
Tbog1
Fcont1
vtrain MS
Ω shaft
Tmach2 Ω shaft2
vbog2
Tbog2
Fres
Fcont2 vbog2-ref
imach2-ref Tmach2-ref Ωshaft2-ref
VDC-mes
uchop-ref
imach-ref
vtrain-ref
kW
Tmach1-ref Ωshaft1-ref
imach1-ref
vbog1-ref
kR
Fig. 7: Maximum control structure of the traction system supply
chopper windings in series machines Tmach1
imach VDC
uchop
imach
ES ichop
sij
imach
etot
emach1 imach
emach2
bogies
shafts
Ωshaft1
Ω shaft
train
environment
vbog1
Tbog1
Fcont1
vtrain MS
Ω shaft
Tmach2 Ω shaft2
vbog2
Tbog2
Fres
Fcont2
kW
VDC-mes
uchop-ref
imach-ref
Tmach1-ref
Ωshaft1-ref
vtrain-ref vbog1-ref
kR
Fig. 8: Simplified control structure of the traction system
III. Validation of the control with criteria merging The system model and the control with criteria merging are directly transposed into a Matlab-SimulinkTM model (Fig. 9). A test trajectory is imposed to the train: a trapezoidal set point for the train velocity. A slip phenomenon is imposed on the bogie no. 1 at t = 4 s during 2s, and on the bogie no. 2 at t = 8.5 s during 2s (Fig. 10). As shown previously [IEMDC-03], the classical master-slave control (kW = 1) yields poor performances (Fig. 11). By imposing kW = 1/2 the train velocity is not affected by slip phenomena (Fig. 12). The same test trajectory is imposed to the simplified control with criteria merging. All results are identical than results obtained without criteria merging. This second control leads to the same dynamic performances but with less control blocks and thus enable an experimental implementation with a shorter computation time. First experimental results are provided on a reduced power experimental set-up (5 kW), which will be described in the final paper. The control with criteria merging confirm that kW = 1/2 is the better solution for disturbance rejections.
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Fig. 9: Matalb-SimulinkTM model of control structure with criteria merging 1 (p u ) 0 .75
0.5
bogie torque T bog1
0.25
bogie torque T bog2 tim e (s)
0
0
0
4
8
12
16
Fig. 10: Bogie torques (simulation) 1
reference velocity
(p u ) 0 .75
train velocity
0.5
0.25
tim e ( s ) 0
0
0
4
8
12
16
Fig. 11: Train speed with a master salve control, kW=1 (simulation)
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reference velocity
(p u ) 0 .75
train velocity 0.5
0.25
tim e ( s ) 0
0
0
4
8
12
16
Fig. 12: Train speed with weighted control kW=1/2 (simulation)
reference speed Ωref (rad/s)
600
400
mean speed Ωmean (rad/s)
200
time (s)
0 0
5
10
15
Fig. 13. Train velocity for criteria merging based control with kW = 1 (experimental results) reference speed Ωref (rad/s)
600
400
mean speed Ωmean (rad/s) 200
time (s)
0 0
5
10
15
Fig. 14. Train velocity for criteria merging based control with kW = 1/2 (experimental results)
Conclusion The control structures of MMS with a single coupling device needs a control criterion in order to optimise the energy conversion. This paper is focused on MMS with several coupling devices. In such cases, the theoretical control structure obtained by inversion principle can be modified by moving control blocks and merging the criteria of coupling blocks. This methodology has been validated with a railway traction system. Simulation results indicate that there is no difference with and without merging both criteria. The simplified control structure enable a shorter computation time for an experimental implementation. Experimental results will be provided in the final paper.
References 1. H. Kurtz, “Rolling across Europe's vanishing frontiers”, IEEE Spectrum, Vol. 36, no. 2, February 1999, pp. 44-49. 2. A. Bouscayrol, B. Davat, B. de Fornel, B. François, J.P. Hautier, F. Meibody-Tabar, M. Pietrzak David, “Multi-machine Multiconverter System: application for the electromechanical conversion”, EPJ Applied Physics, Vol. 10, no. 2, May 2000, pp-131147. 3. A. Bouscayrol, M. Pietrzak-David, B. de Fornel, "Comparative studies of inverter structures for a mobile robot asynchronous motorisation", IEEE-ISIE'96, Vol. 1, Warsaw, June 1996, pp 447-452. 4. J. Pierquin, “Contribution à la commande des systèmes multimachines multiconvertisseurs. Application à la résolution de problèmes en traction électrique", PhD, University of Lille, July 2002. 5. B. Arnet, M. Jufer, "Torque control on electric vehicles with separate wheel drives", EPE’97, Trondheim, Vol. 4, September 1997, pp 659-664.
- Synopsis for EPE 2005, Dresde 6. Y. Hori, Y. Toyoda, Y. Tsuruoka, “Traction control of electric vehicle: basic experimental results using the test EV “UOT Electric March", IEEE Transactions on Industry Applications, Vol. 34, n°5, September 1998, pp 1131-1138. 7. A. Bouscayrol, B. Davat, B. de Fornel, B. François, J. P. Hautier, F. Meibody-Tabar, E. Monmasson, M. Pietrzak-David, H. Razik, "Control structures for Multi-machine Multi-converter Systems with downstream coupling", EPE’01, Graz, August 2001, CD-ROM. 8. 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, "Control Structures for Multi-machine Multi-converter Systems with upstream coupling", Mathematics and Computers in Simulation, vol. 63, no3-5, pp. 261-270, November 2003. 9. Ph. Delarue, A. Bouscayrol, B. François, "Control implementation of a five-leg voltage-source-inverter supplying two threephase induction machines", IEEE-IEMDC’03, Madison (USA), June 2003, CD-ROM, pp. 1909-1915
