Study of a 5-phases synchronous machine fed by PWM inverters under fault conditions E.Robert-Dehault*, M.F Benkhoris*, E.Semail** *CRTT, bd de l’université BP 406 44602 St Nazaire cedex Tel: 02 40 17 26 04 Fax: 02 40 17 26 18 E-mail:[email protected]

Abstract – This paper deals with a five-phase permanent magnet synchronous machine supplied with a five leg PWM inverter both in normal and fault condition due to the open circuit of one stator phase. The machine model is developed in the abcde frame both in α,β,z1,z2,z3. This second modeling approach is a powerful tool to analyze the current and the torque waveforms in this electrical drive. It is based in the use of bijective transformation. Hence it is a good tool for the control of the electrical drive in the d-q frame.

1.

Introduction

In the field of high power systems, especially in the naval industry, it is often interesting to use machines with more than three phases. The most common solution is to use double-star machines [6], but machines with any number of phases can be founded. In this paper, a methodology for the study of a 5-phases synchronous machine supplied by PWM inverters as shown in figure 1 will be investigated. In this particular case, we will consider a linear permanent magnet machine. This methodology can be used both in normal condition than in fault conditions due to the loss of one or two stator phases. Hence a new state space α,β,z1,z2,z3 is defined. It is possible to generalize this methodology for machines having more phases. This new space allows, obtaining new models, both for simulation and control. In case of the loss of stator phases, we will suggest a new control strategy, that will reduce the torque ripple. inverter

machine

Einv

1 2 3 4 5

Fig.1):studied structure

**L2EP 8 bd Louis XIV 59046 Lille cedex tel: 03 20 62 15 61 E-mail:[email protected]

Notations Ls: stator phase inductance Rs: stator winding resistance lf : stator leakage inductance M=Ls-lf: mutual inductance Φr: rotor flux Lcs: cyclic inductance. His value is: 5 Lcs= lf + M 2 Hypothesis: the permanent magnet machine has a sinusoidal repartition of the magneto-motive forces, is not saturated and the rotor is not salient. 2.

Model under normal conditions

A. Model in the abcde frame In the abcde plane, the model is simply: d [V]=[e]+[L] [I]+[R][I] dt were [L] is a classical inductance matrix:   lf + M    2π M cos  5   4π  [L] = M cos  5  M cos 4π    5  M cos 2π   5 

           

 2π   4π M cos  M cos  5   5  2π lf + M M cos  5  2π  M cos lf + M   5   2π  4π  M cos  M cos  5  5   4π   4π M cos  M cos  5   5

  4π   M cos    5    4π   M cos    5   2π  M cos   5   lf + M     2π   M cos    5 

            lf + M   

 2π M cos  5  4π M cos  5  4π M cos  5  2π M cos  5

The resistance matrix is: [R]=Rs[Id]5 in our case, the FEM vector is considered as a fivedimension, balanced, voltage vector:  cos(ωt − ψ )    2π   cos ωt − ψ − 5      4π  cos ωt − ψ −   [e]=Eo   5  6π    cos ωt − ψ − 5     cos ωt − ψ − 8π     5  

phase currents are increasing (fig.9b). Figure 9c shows the effect of the PWM inverter. Those results show that, if the internal angle is constant, the machine is naturally reacting in order to try to minimize the unbalance resulting from the loss of one stator phase. This is easy to explain : when a phase is lost, the flux in the

of simulation, and control, both in normal or fault conditions. The zero sequence subspace is a good tool to interpret the simulation results with PWM inverter. It helps us do define a torque control strategy under fault condition.

Fig.9a):torque waveform in normal and fault conditions

References [1] Y.Zhao and A.Lipo, ‘modelling and control of a multi-phase induction machine with structural unbalance’ , IEEE transactions on energy conversion, September 1996 p 570 à 577

Fig.9b): current waveform in sinusoidal case

[2] C.L.Fortescue, ‘method of symmetrical coordinates applied to the solution of polyphase networks’ annual convention of the American institute of electrical engineers, June 1918 , p 629 to 715 [3] E.Semail, ‘outils et méthodologie d’étude des systèmes électriques polyphasés. Généralisation de la méthode des vecteurs d’espace’ thèse préparée au L2EP de Lille, soutenue le 30 juin 2000

Fig.9c):current waveform with the PWM inverter

[4] T.Elch-Heb,Y.Fan and J.P.Hautier, ’reliability improvement of field-oriented controlled threephase AC drives by means of two-phases remedial operation’ , ICEM 1994 ,volume 2 [5] E.E. Ward et H.Härer, ‘preliminary investigation of an inverter-fed 5-phases induction motor’ proceedings of the institution of electrical engineers, June 1969 [6] F.Terrien, M.F.Benkhoris ‘analysis of doublestar motors for electrical propulsion’ IEE : 9th international conference on electrical machines and drives, EMD 99, Canterbury, UK;1-3september 1999; pp 90-95

phase’s direction decreases, and so do the voltage. So, the remaining phases absorb more current to compensate this loss. Some other simulations prove that the torque ripple is decreasing when the stator resistance is lowered. Unfortunately, it is impossible to simulate when the stator resistance is equal to zero, because the state model is getting unstable. 4.

conclusion

General model in α,β,z1,z2,z3 5-phases synchronous machine fed by PWM inverter is developed. The introduction of bijective transformation, allows obtaining a model, in view

[7] K.H.Kettler,’mutisystem propulsion concept on the bases of the double star circuit’, EPE 95,2:pp159-166,1995,Sevilla,Spain [8]L.Werren, ’synchronous machine with 2 threephase windings, spacially displaced by 30° el. commutation reactance and model for converterperformance simulation’,ICEM 1984, 2:pp781-794, september 1984, Lausanne, Switzerland.