Multiphase operation of switched reluctance motor drives

Transcription

1 Multiphase operation of switched reluctance motor drives P. Pillay, Y. Liu, W. Cai and T. Sebastian' Electrical & Computer Engineering Dept. Clarkson University, Box 5720, Potsdam, NY Abstract: Previous work on switched reluctance motors (SRMb) have dealt largely with singly excited phases. mere doubly excited phases have been used, either for torque production or position detection, the mutual coupling and effects of mutual saturation have been neglected.!phis paper demonstrates that ignoring these effects can produce erroneous results. some fundamental relationships or torque production during multiphase operation are determined, and applied to an 8-6 smf. I. INTRODUCTION Switched reluctance motors are enjoying considerable attention from machine designers, drives engineers and researchers interest,ed in control [l-101. They have several advantages over the induction motor which include the following: 1. No windings on the rotor, thus allowing easier manufacture and higher speeds; 2. No winding-related heat source on the rotor, thus confining the majority of heat generation to the stator, from where the heat is more easily removed- this leads to a more robust thermal design; 3. Since the rotor has only laminated iron, differential heating and cooling does not occur as it does for example between the rotor bars and the iron in induction motors- this leads to improved reliability /97/$ IEEE. 'Delphi Saginaw Steering Systems 3900 Holland Road Saginaw, Michigan A unidirectional current is sufficient, thus leading to improved reliability and creativity in converter design. Two serious problems facing the SFW are its acoustic noise, which is larger than that produced from an induction motor of similar size and torque ripple. The conventional mode of operation of the machine is for one phase only to conduct. If two phases conduct (either by design or lack of control) the mutual interaction between the phases is neglected or ignored: Indeed the operation of some position detection algorithms depend heavily on an absence of mutual coupling. In this paper, the operation of the motor when two phases are conducting simultaneously are considered. The paper is organized as follows: section I1 explains the multiphase operation. Section 111 has multiphase operation results. Section IV concentrates on torque calculations while section V has the conclusions. I1 MULTIPHASE OPERATION An 8-6 SFW is shown in figure 2.1. The two extreme positions of unalignment (fig 2.la) and alignment (fig 2.lb) are also shown. Eigure 2.2 illustrates the multiphase operation being considered here. In figure 2.2a, only one phase is conducting, labeled as phase 2 and referred to as the "working phase". 310

2 U (a) Unaligned position (8=Oo) (a) Single phase conducting Aligned position ( = 300) Fig 2.1 Two extreme positions for the SRM working phase Phase 3 is called the "leading phase", while phase 1 is the "trailing phase", for anti-clock wise rotation and clockwise excitation. In conventional operation, only phase 2 conducts for 15' for an 8-6 machine, after which phase 1 conducts. In multiphase operation, both phases 2 and 3 will conduct and the overlap can extend for up to 15' with both phases contributing positive torque during the overlap. Operation beyond 15' overlap between any 2 phases will result in negative torque produced in at least one of the phases. During multiphase excitations, both phases contribute flux to the machine, with flux paths shown in figure 2.2b. Except for the back of core between the two phases, where the flux contribution from each (c) Negative curremit in leading phase Fig.2.2 Leading phase influence on flux phase opposes each other, the individual phase fluxes add in the rest of the back of core. In a conventional machine, the back of core experiences some saturation at certain rotor angles even with just one phase conducting particularly in the aligned position. It is 31 1

3 therefore clear from figure 2.2b that multiphase operation in such a machine will enhance the saturation effects if the same levels of excitation are used. Care of course must be taken not to exceed the thermal ratings of the machine during such an operation. A finite element plot of the flux density during single phase excitation is given in fig. 2.3a for a 15"position of the working phase. Both halves of the back of core that is symmetrical about the working phase experiences similar levels of flux density during single phase excitation. However a finite element plot of multiphase excitation reveals the enhanced saturation in the back of core as shown in fig. 2.3b. In fig. 2.3b, the leading phase is at the aligned position, while the working phase is at the 15" position. This corresponds to the point in time just before turn-off of the leading phase. The enhancement of the back of core saturation immediately raises the question of whether an alternative excitation strategy may be used to reduce the excitation, rather than enhance it. This can be done, and is shown in figure 2.2~ where an opposite excitation in phase 3 is used from that used in figure 2.2b. An imp or t an t consequence of this is that the flux contribution of each phase is additive only in the section of the back of core between the excited poles. The resultant flux in the back of core in the rest of the machine is actually reduced. A finite element plot shown in figure 2.3~ confirms this result, where saturation is high only in that section of core between the two excited poles. In essence, the machine is forced to adopt short flux paths. The net effect will be to reduce saturation effects and core losses when compared with multiphase excitation with the same polarity. The serious penalty to be paid is the ability to be able to excite the winding with any desired polarity, since the leading phase must always be excited opposite to the working phase. Fig 2.3 Finite element plots 31 2

4 During maximal overlap of 15" between phases, the trailing phase will be excited just as the leading phase is deenergized. Thus each phase can actually produce torque over a 30" angle as shown in figure 2.1. I11 Multiphase Operation Results The results presented are centered around a 5.5 hp, commercial drive rated at 10A rms. Figure 3.1 shows the flux linkage vs current curve of the SRM under single excitation. Also shown are the effects of a constant (16A) current flowing in Phase Current ( A ) Fig 3.1 Flux linkage vs current the leading phase on the fluxlinkage of the working phase. This effect is shown from the unaligned position of the working phase to its 15" position. When the working phase is in the unaligned position, its flux linkage is low. At the same time, the leading phase flux linkage is not at its peak value, since it is not aligned. Thus the effect of the leading phase on the working phase in the unaligned position is small. However at the 15" position of the working phase, its flux is higher than its value at the unaligned position; in addition, the leading phase is in its aligned position so that it is experiencing its maximum flux linkage. The effect on the flux linkage of the working phase is therefore large at this point; this is also the region at which maximum torque is produced by the working phase. From the position of 15" to 30, when the working phase reaches alignment, it is under the influence of the trailing phase. When the trailing phase is first excited, it is in its unaligned position and the leading phase, -which was in its aligned position is turned off. The effect on the back of core is to produce a transition in the flux from the large contribution by the leading phase to the much smaller contribution by the trailing phase. This is shown in figure 3.1 where the effects of the trailing phase at 15" are negligible, compared to the effects of the leading phase. The effects of the trailing phase on the working phase is enhanced as the latter approaches alignment and the trailing phase approaches its peak torque production, since the flux linkage of both phases are increasing. Overall, there is a marked impact on the flux linkage results of the working phase, particularly in the aligned position and any calculation neglecting this effect will be in error, particularly as it relates to torque ripple. From Fig 3.1 it i.s also evident that at 15" when the leading phase is turned off and the trailing phase turned on, that there is a jump in the flux linkage. This occurs because the leading phase at this angle is fully aligned and experiencing its maximum flux linkage. This i:; switched off and the trailing phas8e switched on which is experiencing its minimum flux linkage because it is in the unaligned position. Thus the flux linkage jumps from a maximum effect on the working phase (when the leading phase is on) to essentially no effect when thie trailing phase is on at this position. The results in fig 3.1 shows the effect of a constant 16A current in the leading or trailing phase. Fig 3.2 demonstrates the effects of different current: magnitudes in the leading-phase on the flux linkage of the working phase at the particular 31 3

5 in this particular machine, the overall saturation is still higher with two phases excited than with only one excited (regardless of current polarity). The fact that certain portions of the teeth are under heavy saturation at the 15' angle accounts for this phenomenon. IV Torque Calculations 0 1 " ' " I Phase Current ( A ) Fig. 3.2 Flux linkage in the working phase with 0,4,12,16 A flowing in the leading phase (0 A is the top curve and 16A is the bottom curve) The torque is calculated by measuring the flux-linkage vs current curve for a particular phase, with an overlap of 15' with the leading and trailing phases respectively. Cubic splines are fitted to the measured data and the curves integrated with respect to current to obtain the co-energy. This is subsequently differentiated with respect to angle to calculate the torque. During conventional operation of an 8-6 SRM, only phase 1 would be on. However the zero torques produced at alignment and in the unaligned position, points to overlap (perhaps over the entire conduction period of a phase) as a means to reduce torque ripple Phase Current ( A ) Fig 3.3 Flux linkage vs current in the working phase with 0 A(top), -16A (middle) and +16A (bottom) in the leading phase. angle of 15'. Thus a substantial reduction in the working phase flux linkage occurs with increasing current in the leading phase. It is ihstructive at this point to examine the equations governing the calculation of torque. The torque produced when two phases conduct needs further consideration because of the mutual coupling and saturation effects. The co-energy at position 8, when two phases are excited is given by: The effect of the direction of the At position the cocurrent in the leading phase is energy is shown in figure 3.3, where it is clear that an opposite current to wc2 = l: Jr y1 di/ i- y that flowing in the working phase e+ae causes a smaller effect on the overall saturation than a current The torque is, flowing in the same direction as that in the working phase. However 2 di/ il=conm (4 2 A8 Ae 314

6 is the leading phase torque without the influence of the working phase (using the flux linkage vs. current curves shown in fig 2.1, with no influence from leading phase to calculate co-energy). '12 = + Ae is the working phase torque calculated by using the flux linkage curves in fig 2.1 under the influence of the leading phase. Hence the total torque when two phases conduct is the sum of the leading phase torque without considering the influence of the working phase and the working phase torque calculated under the influence of leading phase. Using this method, torque can be calculated more precisely during the two phase conducting period and it is possible to find the optimal turn-on and turn-off angles to reduce the torque ripple. A plot of the torque curves, for a single phase excitation is given in fig This is calculated by using the flux linkage data of fig 2.1, integrating with respect to current to obtain co-energy and differentiating with respect to angle to obtain torque. The instantaneous torque, under conventional operation, with single phase excitation is given in fig Also shown are the torque contribution waveforms of the individual phases and how they contribute individually to make up the total torque output and ripple. A 5' overlap between the leading and working phases produces a torque contribution as shown in fig 4.3. The upper dashed curve shows the effects of simply adding the total torque contributions of individual phases, without regard to the mutual effects between the phases. The solid curve shows a more precise calculation of the torque using the theory developed here and the dotted curve is the contribution of an individual phase under single excitation. Appr0:Kimately one Nm of torque difference exists between the two calculations, which is a significant error in torque ripple calculations , Rda Posibim (Msh me8) Fig 4.1 Torque CUI. rve s Fig 4.2 Torque with single phase excitation

7 Toial torque not considering leading phase influence b5r Toial iorqus noi considering leading phasa inhence - Toial torque considering leading phase infiuams 'I-one phardtorque a m m 80 Rotor Position (hiech Dgrse).Fig 4.3 Torque with multiphase excitation with So overlap Rotw Position (hiech Dgree) Fig. 4.4 Torque with lso overlap I Position I 0.0 I 3.0 I 6.0 I 9.0 I 12.0 I 15.0 I T1,Tle T ) I Table 4.1 Torque errors Fig. 4.4 shows the torque ripple results for full 15" overlap. Torque ripple can be reduced, but again care must be taken to use to correct theory for calculation to avoid the errors shown in fig 4.4. Table 4.1 shows T1 and Tle, the torque developed by the leading phase assuming no influence of the working phase as well as T2, the torque developed by the working phase, under the influence of the leading phase. T2e is the torque developed by the the working phase under multiphase excitation, neglecting the effects of the leading phase. Te is the sum of Tle and T2e. T is the sum of T1 and T2, using the theory developed here to calculate the total torque. Errors of up to 16% can be made in the torque calculation at particular angles by simply adding the individual phase torque contributions instead of accounting for their mutual effects. V Conclusions This paper has examined the operation of SFWs with multiphase excitation. Experimental results from a 8-6 commercial machine were presented as well as relevant equations for the calculation of the torque. Multiphase excitation can enhance saturation in large sections of the back of core with unipolar excitation, while bipolar excitation increases saturation only in the back of core between the excited poles. Indeed, saturation in the rest of the back of core is reduced relative to single phase excitation. The influence of the leading phase excitation on torque was also presented. The mathematics and results presented here can form the basis of improved techniques for torque ripple reduction and perhaps even core loss control. 31 6

8 References [l] P.J. Lawrenson, J.M. Stephenson, P.T. Blenkisnsop, J. Corda, and N. N. Fulton, "Variablespeed switched reluctance motors," in Proc. Inst. Elec. Eng. (England), ~01.127, pt.b, no. 4, pp , July [2] M.R. Harris, J.W. Finch, and T.J. Miller, "A review of the integral horsepowerswitched reluctance drive", IEEE Trans. Industry Appl., IAS-22, no.4, pp , July [31 T. J.E.Miller, "Brushles s permanent magnet and reluctance motor drives", Oxford Science Publications, [41 T. J. E. Mill er, '\ Switched reluctance motors and their con t r o 1 ", Oxford Science Publlcations, [5] B.C.Mecrow, "New winding configurations for doubly salient reluctance machines", IEEE Trans. on Industry Applications, vol 32, no. 6, Nov/Dec 1996, pp [6] R.C.Colby, F.M.Mottier and T. J.E.Miller, Vibration modes and acoustic noise in a four-phase switched reluctance motor", IEEE Trans. on Industry Applications, vol 32, no. 6, Nov/Dec 1996, pp I71 J. Faiz, R. Iranpour and P.Pillay, "Thermal Model for a Switched Reluctance Motor of TEFC Design During Steady and Transient Operation", Electric Machines and Power Systems, vol 26, No 1, [ 81 P. Pillay, R. Samudio, M.Ahmed and R. Patel, "A chopper-controlled SRM Drive with Reduced Acoustic Noise and Improved Ride-through Capability Using Supercapacitors", IEEE Transactions on Industry Applications, Sept/Oct 1995, V O ~ 31, NO 5, pp [ 91 A.M.Michaelides and C. Pollock, "Modeling and design of switched reluctance motors with two phases simultaneously excited", Proc IEE, Pt.B, vol 143, no 5, pp [ 10lA.M.Michaelides and C. Pollock, "The effect of end core flux on the performance of the switched reluctance motor", Proc IEE, Pt. B, NOV 1994, pp