Investigation on Vector control of three-phase synchronous machines under fault supply conditions Y. Crévits, X. Kestelyn, E. Semail Laboratory of Electrical Engineering and Power Electronics L2EP, École Nationale Supérieure d’Arts et Métiers Boulevard Louis XIV 59040 Lille France (+33)3 20 62 22 38. e-mail: [email protected]. Abstract-- This paper deals with modeling and control of a three-phase permanent magnet synchronous machine (PMSM) with sinusoidal back electromotive forces (emf) under fault supply condition. The overall system is modeled thanks to the Energetic Macroscopic Representation (EMR) formalism considering that a fusible element opens the phase circuit. Using systematic inversion rules of the EMR, a Maximum Control Structure (MCS) is deduced. Based on the analysis of degrees of freedom of the drive, two control strategies for constant-torque under fault supply conditions are inferred. One method balances generated perturbations caused by fault supply and the other one consists in modifying current controller’s structure. These methods are validated through simulations with Matlab software. Index Terms—Permanent magnet synchronous machine, fault supply condition, Energetic Macroscopic Representation, Maximum Control Structure, degree of freedom, resonant controller.

This paper uses the extra degree of freedom offered by a three-phase PMSM with independent windings to investigate a strategy allowing to keep a constant torque under fault supply conditions. The overall system is first model using the Energetic Macroscopic Representation and a Maximal Control Structure is deduced. The simulations permit to show the effectiveness of the two proposed solutions. II. MODELING OF THE MACHINE AND ITS SUPPLY The permanent magnet synchronous machine with p pole pairs is supplied by a 6-leg inverter [2] as shown in fig. 1. Its back electromotive forces are sinusoidal. As the three currents can be independently controlled, this structure permits to use the three DOF of the system compared to wye-connected windings. sw11

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I. INTRODUCTION Fully electrical configurations are more and more used in place of classical mechanical or hybrid ones. Problems of reliability are often solved using redundancy [1]. In many applications, drives are composed of three phase permanent magnet synchronous machines (PMSM) fed by voltage source inverter (VSI). The reliability of this kind of variable speed drive suffers mostly from the failure of semiconductor devices in the inverter. In this case, the failure results in the complete switch off of the system. In some applications, continuous operation is necessary or critical, such as in aircraft, nuclear power stations, submarines or electrical vehicles. The break down of the entire drive system is unacceptable. A safety mode, even with faded performances, must take effect. As presented in [2], large numbers of defaults can lead to the fuse of the serial protection element of a phase. As a consequence, when a default appears, a phase opens. In this condition, to be able to produce a rotating field in the machine, currents in the two remaining supplied phases must be independent. To keep a constant torque, one method considers recalculating references for the two safe-phases and a new model of the machine must be found [3].

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Fig. 1: Six-leg inverter.

The modeling of the overall system is based on a vector formalism [4] that uses 3-dimensional space. This method gives an appropriate depicting where DOF can receive geometrical and graphical representations. The EMR is a synthetic graphical tool based on the principle of action and reaction between connected elements [5]. The EMR of the machine supplied by a 6-leg inverter is shown in Fig. 2. The three 2-level VSI are represented by three parallel lanes which show the three DOF offered by independent supplies. A classical abc stationary reference frame to 0dq synchronous reference frame transformation permits to represent the three-phase machine by two magnetically independent fictitious machines: one one-phase zerosequence machine (M0), with v0-i0 associated voltagecurrent, and one 2-phase main machine (Mm) with r r v m = [vd v q ]t - im = [id iq ]t . In the case of sinusoidal back-emf, its components on the zero-axis and the d-axis are null. As a consequence M0 do not produce torque and Mm produces torque only with q-axis components. Finally, the both machines are mechanically coupled on the shaft.

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VI. CONCLUSION Different ways to obtain a constant torque with a permanent magnet synchronous machine under singlephase open supply condition have been presented in this paper. A unique causal model of the system is first presented allowing then to simulate the behavior of the overall system under normal or fault conditions. Related equations permit to deduce the harmonic contents of the induced disturbances. Using a systematic inversion of the model and analyzing the remaining system’s degrees of freedom, a maximal control structure has been deduced and two strategies have been suggested. The first one consists in compensating the disturbances induced by an open phase. Although this technique permits to obtain instantly a constant torque, this technique needs three voltage sensors and a special conditioning of the signals. The second one needs to modify the controller’s structure but does not need any additional sensors. Only the frequencies of the disturbances are to be known. As all these strategies are based on the transformation of the real machine to a set a fictitious one or two-phase machines, it can be easily extended to machine with an arbitrary number of phases (multi-phase machines).

[1] BENNETT J.W., JACK A.G., MECROW B.C., ATKINSON D.J., SEWELL C., MASON G., Faulttolerant control architecture for an electrical actuator, 2004 35th Annual IEEE Power Electronics Specialists Conference, June 20-25, 2004, Aachen, Germany. [2] WELCHKO B. A., LIPO T. A., JAHNS T. M. and SCHULTZ S. E., Fault tolerant three-phase AC motor drive topologies : a comparison of features, cost, and limitation, IEEE Transaction on power electronics, Volume 19, Nr 4, july 2004. [3] WELCHKO B. A., JAHNS T. M. and HITI S., IPM synchronous machine drive response to a single-phase open circuit fault, IEEE Transaction on power electronics, September 2002, Volume 17, issue 5. [4] SEMAIL E., BOUSCAYROL A., HAUTIER J.P., Vectorial formalism for analysis and design of poly phase synchronous machines, European Physical Journal-Applied Physics, Vol 22, no3, 2003, pp 207-221. [5] BOUSCAYROL, A.; DAVAT, B.; DE FORNEL, B.; FRANCOIS, B.; HAUTIER, J.P.; MEIBODY-TABAR, F.; PIETRZAK-DAVID, M.; Multi-machine multi-converter system for drives: analysis of coupling by a global modeling, Industry Applications Conference, 2000, volume 3, 8-12 Oct. 2000, Page(s): 1474 - 1481 vol.3. [6] RUBIN Z., MUNNS S., MOSKOWA J., The development of vehicular powertrain system modeling methodologies: philosophy and implementation, System Automotive Engineering, paper 971089, 1997. [7] LOVETT T. E., SOLODOVNIK E. V., Resistive Companion Modeling and Simulation for the Virtual Test Bed, Virtual Test Bed – Department of Electrical Engineering, University of South Carolina. Undefined publication date. [8] UMLAND, J.W.; SAFIUDDIN, M., Magnitude and Symmetric Optimum Criterion for the Design of Linear Control Systems What is it and how does it compare with the others?, Industry Applications Society Annual Meeting, 1988, Conference Record of the 1988 IEEE, 2-7 Oct. 1988 Page(s):1796 - 1802 vol.2. [9] ZHENG J, Ph. DEGOBERT, D. LORIOL, J.P. HAUTIER. Robust Design of the Self-tuning Resonant Controller for AC current control systems. IEEE-ICIT 2005 Hong Kong.