Multi-Machine Modelling of Two Series Connected 5-phase Synchronous Machines: Effect of Harmonics on Control E. Semail1, E. Levi2, A. Bouscayrol1, X. Kestelyn1 1
L2EP LILLE ENSAM, 8 Bd Louis XIV,
59 046 Lille, France E-Mail:
[email protected] URL: http://www.univ-lille1.fr/l2ep
2
LIVERPOOL JOHN MOORES UNIVERSITY
School of Engineering, Byrom St Liverpool L3 3AF, UK E-Mail:
[email protected] URL: http://www.eng.livjm.ac.uk/Research/Gr oups/EMAD/home.html
Keywords Multiphase drive, Multi-machine system, Converter machine interactions, Harmonics, Modelling
Abstract This paper deals with the series connection of two 5-phase synchronous machines supplied by a single 5-leg voltage source inverter. Using a specific modelling tool, design constraints on both machines are defined in order to control them independently. The effects of harmonics of back-electromotive force are then examined and improved control is deduced.
Introduction Industrial economic constraints lead to systems where one supply is used for several machines. In traction systems, two DC motors are connected in series in order to use only one chopper. Independent torque control can be achieved using field current control [1]. Parallel connections of AC machines are often used in railway traction applications [1]. For 3-phase AC machines supplied by a 3-leg inverter, series connection cannot yield such independent control. Independent control with series connection however becomes possible for n-phase induction or synchronous machines with n≥5. In [3]-[5], under the assumption of sinusoidal magneto-motive force and back-electromotive force (back-EMF) waveforms, concept of independent control of (n-1)/2 series connected induction machines supplied by an n-leg voltage source inverter (VSI) has been described. In [6] series connections of synchronous and induction machines are also examined. This paper deals with a series connection of two 5-phase permanent magnet synchronous machines (PMSM) supplied by a single 5-leg VSI (Fig. 1). Using a Multi-Machine vectorial characterization developed for a 5-phase synchronous machine [7], the influence of back-EMF harmonics on the PWM vector control is examined. The rules for design of a PMSM, suitable for application in this type of series connection, are deduced from this analysis. First, the Multi-Machine modelling of the drive is performed. The studied two-motor drive is equivalent to four fictitious 2-phase machines that are mechanically and electrically coupled. Each fictitious machine is characterised by a family of harmonics. It is thus possible to deduce conditions that enable carrying out independent control for series connected double-motor drives. Next, rotor flux oriented control is implemented in order to examine effects of harmonics. Simulation results are provided for two types of machines, namely with sinusoidal and trapezoidal back-EMF. Results confirm predicted disturbances induced by harmonics. Finally, an improved control scheme, deduced from Multi-Machine modelling, is proposed to smooth the effects of harmonics.
30
5 4.5
Torque of Machine n°1 with improved Torquel of Machine n°1 without improved
25
Torque of machine Reference °1 torque of MM1 fictitious hi
4 3.5
20
3 T (Nm) 2.5
T 15 (Nm)
2
10
1.5
5
1 0
0.5 0 0.4
0.42 0.44 0.46 0.48
0.5
0.52 0.54 0.56 0.58
-5 0
0.6
Fig. 15: Zoom of torque of machine n°1 for the two controls.
0.1
0.2
0.3
0.4 0.5 time s
0.6
0.7
0.8
0.9
Fig. 16: Torque of machine n°1 and reference torque of MM1 with improved control.
Conclusion Using Multi-Machine modelling, it is shown that the two series-connected 5-phase machines, supplied by a single 5-leg VSI, can be considered as a set of four fictitious 2-phase machines. Independent control of these four machines is not possible, as there are not enough degrees of freedom from the 5-leg VSI. One solution is to impose the requirement that two of these four machines do not produce torque. As the Multi-Machine modelling gives a harmonic characterisation of the four machines, it is easy to deduce that if the back-EMFs of the actual machines are sinusoidal then the machines SM1 and SM2 do not have back-EMF. Only the inductances of these machines remain and these appear in series with the two controlled machines MM1 and MM2.
35 MM1 Torque SM1 Torque
30 25
T (Nm)
20 15 10 5 0 -5 -10
0
0.1
0.2
0.3
0.4 0.5 time s
0.6
0.7
0.8
0.9
Fig. 17: Torques of fictitious machines MM1 and SM1 with improved control.
In the second part, we examine at first the effect of a third harmonic component in the back-EMF of machine no. 1. Then, the modelling is used to achieve logically an improved control scheme.
References [1] J. N. Verhille, A. Bouscayrol, P. J. Barre, J.C. Mercieca, J. P. Hautier, E. Semail, “Torque tracking strategy for anti-slip control in railway traction systems with common supplies”, IEEE-IAS’04, Seattle (Washington), October 2004, vol. 4. pp. 2738-2745. [2] Y. Matsumoto, S. Ozaki, A. Kawamura “A novel vector control of single-inverter multiple-induction-motor drive for Shinkansen traction system", in Proceedings of APEC'01, March 2001, Anaheim (USA). [3] S. Gataric, “A polyphase cartesian Vector Approach To control of Polyphase AC Machines”, IEEE-IAS’00, Rome (Italy), October 2000. [4] E. Levi, M. Jones, S.N. Vukosavic, H.A. Toliyat, “A Novel Concept of a Multiphase, Multimotor Vector Controlled Drive System Supplied From a Single Voltage Source Inverter”, IEEE Transactions on Power Electronics, vol. 19, no. 2, March 2004, pp. 320-335. [5] E. Levi, M. Jones, S.N. Vukosavic, H.A. Toliyat, “A Five-Phase Two-Machine Vector Controlled Induction Motor Drive Supplied from a Single Inverter”, EPE Journal, vol. 14, no. 12, August 2004, pp 38-48.
[6] M. Jones, E. Levi, “Combining Induction and Synchronous Machines in a Seven-Phase Series Connected Three-Motor Drive”, EPE-PEMC'04, Riga (Latvia), September 2004, CD-ROM. [7] E. Semail, X. Kestelyn, A. Bouscayrol, “Sensitivity of a 5-phase Brushless DC machine to the 7th harmonic of the back-electromotive force”, IEEE-PESC’04, Aachen (Germany), June 2004, vol. 6, pp. 4564 – 4570. [8] E. Semail, X. Kestelyn, A. Bouscayrol, “Right Harmonic Spectrum for the back-electromotive force of a nphase synchronous motor”, IEEE-IAS’04, Seattle (Washington), October 2004, vol. 1, pp. 71-78.
Appendix: Synoptic of Energetic Macroscopic Representation
Electrical converter (without energy accumulation)
Electromechanical converter (without energy accumulation) Mechanical Converter (without energy accumulation)
Control block without controller Control block with controller
Element with energy accumulation
Coupling device (distribution of energy)
Control block with coupling criterion
Source of energy
MM1
series connection
mechanical coupling
load 1
shaft1 DC bus
SM1 5-leg VSI
transformation [E1]
[TSM1]
[i1]
[Fres1]
SM2
series connection.
[W1]
mechanical coupling1
shaft2
load 2
MM2
1/2
W2_ref
1 [E1]
[Fres1]
[I1]
[W1]
1/2
W1_ref 1
[TSM1]
Fig. 18: EMR modelling of the system and of the control in Matlab/Simulink environment.
