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Maximising the saliency ratio of the synchronous reluctance motor
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  Maximising the saliency ratio of the synchronous reluctance motor D.A. taton T.J.E. Miller S.E. ood Indexing terms: Saliency ratio, Synchronous reluctance motor Abstract: Recent interest in the synchronous reluctance motor has increased in the context of possible applications in field oriented AC drives. The absence of rotor slip losses, and the apparent simplicity of the control, suggest the possibility of performance and cost advantages over the induc- tion motor. With field oriented control, and con- tinuous shaft-position feedback, the synchronous reluctance motor does not need a starting cage and can be designed for maximum saliency ratio (LJL, ratio). This ratio is by far the most import- ant parameter for achieving high power factor, torque/ampere, and constant-power speed range. This paper analyses the various known forms of the synchronous reluctance motor, to determine the maximum achievable saliency ratio and iden- tify the parameters on which it depends. The main srcinality is the analysis of the effect of the number of flux guides/barriers. It is shown that a minimum number is required for the performance to surpass that of the induction motor. The analysis also reveals the optimum ratio of flux guide/flux barrier thicknesses and the effects of the tooth/slot geometry and stator saturation. Test results are included from three motors ranging from 50 W at 2000 rpm to 7.5 kW at 1500 rpm, covering both axially laminated and transversely laminated types. 1 Introduction 1. A revival of interest in the synchronous reluctance motor This paper explores the performance limits of the syn- chronous reluctance motor when operated from a current controlled PWM inverter (i.e. with ‘field oriented’ control), and focuses on the saliency ratio (Ld/Lq) s the key design parameter. Line start synchronous reluctance motors have been used for many years, but their design is compromised by the need for a cage winding for starting and stable operation. The vector controlled motor needs no starting cage, and its electromagnetic design can be optimised for maximum saliency ratio. EE, 1993 Paper 9344B (Pl), received 1st September 1992 D.A. Staton and T.J.E. Miller are with the Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 SLT, United Kingdom S.E. Wood is at 3 Bowling Green Court, Stainland, Halifax, West York- shire HX4 9QQ, United Kingdom IEE PROCEEDINGS-B, Vol. 140, NO. 4, JULY 1993 The synchronous reluctance motor is seen as a pos- sible replacement for ‘vector controlled’ induction motors, or at least as an extension to a range of induc- tion motors, in which the controller could be simplified by taking advantage of the absence of slip. While the induction motor is gaining in popularity for adjustable speed drives, it has inherent limitations (e.g. limited torque at low speed and complex control algorithms). At low speed, the losses in the synchronous reluctance motor might be low enough to relieve the need for an external fan. For certain applications (e.g. high tem- perature applications) the absence of magnets may be an advantage. Recent work has established the feasibility of field oriented control, with a certain flexibility in control char- acteristics [19, 203 covering a wide speed range. Imple- mentation in a PWM inverter has been shown to be relatively straightforward. The synchronous reluctance motor shares many of the advantages claimed for switched reluctance motors [2], but it uses a standard AC induction motor stator and a standard PWM inverter circuit. Like the induction motor, it is robust and brushless, and since it operates with a rotating magnetic field it is inherently smooth and quiet in operation. Its inertia is lower than that of the equivalent induction motor. 1.2 Development history Almost all of the important performance parameters of the synchronous reluctance motor depend on the syn- chronous inductance ratio or saliency ratio, 5 = L,/L,. The main classes of rotor design aimed at maximising 5 are shown in Fig.  1.  In all cases, the objective is to achieve a high Ld by providing, essentially, flux guides for d-axis flux; and a low L, by providing flux barriers to q-axis flux. Since attention is restricted to inverter fed machines with field oriented control and shaft position feedback, it is assumed that a high saliency ratio can be pursued without concern for the stability problems that may arise in line start motors [SI. Several of the key papers published in the 1960s and 1970s, on line start reluctance motors, provide reviews of early work and discuss the geometry needed to achieve a high saliency ratio [7, 9, 101. Some early workers recog- nised the ultimate potential of the reluctance motor, but This work was supported by the UK Science and Engineering Research Council, the SPEED Con- sortium, Brook Crompton Parkinson (Small Industrial Motors Division), and Lucas Advanced Engineering Research Centre. 249  could not achieve it in practice because they did not have field oriented controllers [ll, 121. A brief discussion of alternative rotor geometries is helpful. It is convenient to distinguish between salient pole designs, Figs. la, b, single barrier designs, Fig. IC, d and multiple barrier designs, Figs. le,$ The so-called seg- quotes a calculated value of 25.6, concluding that the maximum torque is 80% of that of an ‘average’ induction motor (1923 vintage ) of the same size. Kostko also rec- ognised that the effect of slot leakage flux (which adds to both Ld and Lq) could be decreased by having a large number of thin barriers, and states that even with only Fig. 1 Main classes of synchronous reluctance rotor design mental rotor design [lo] is of the multiple barrier type, but with a small number of ‘barriers’ (typically 2-3). The rotor in Fig. la is obtained by removal of material from a conventional induction motor rotor, either by a milling operation after casting the cage, or by punching before casting the cage. Rotors of this type (‘synchronous induction motors’) have simple construction, but the saliency ratio is too small to give competitive per- formance. Fig. lb shows the salient pole construction, like a con- ventional salient pole synchronous motor with the wind- ings removed. This geometry was used by Lee [3] in a low-speed sealed rotor motor, but he used a hermetic can around the rotor, increasing the airgap and decreasing the d-axis inductance. More recently, Chiba and Fukao [4] described a two-pole rotor, of similar type, using amorphous iron laminations in a high speed application. They reported an unsaturated inductance ratio of about 3, decreasing to about 2.5 under load. Hassan and Osheiba [5] considered several variants of this geometry, but reported no value of saliency ratio higher than 3.8. The development of more specialised rotors seems to have followed two distinct routes. As early as 1923, Kostko [6] analysed a rotor of the form of Fig. le embodying several features of both the main schools of later development, including the use of multiple flux bar- riers, ‘segmental’ geometry, and a q-axis channel. Kostko points out the essential limitation of the salient pole design, namely, that if the interpolar cutout is widened to decrease the q-axis inductance, the pole arc is thereby narrowed, producing an unwanted reduction in Ld. He concludes, in effect, that the multiple barrier or seg- mented arrangement is the natural way to make a synchronous reluctance motor because it involves no sac- rifice of pole arc in the d-axis. He calculates the unsatu- rated saliency ratio for a rotor with ‘four segments’, and ‘four segments’ the saliency ratio is ‘several times as great’ as with the salient pole design. Subsequent workers, generally aware of Kostko’s work, developed the geometry along two main lines: the segmental geometry [ 03 and the axially laminated geometry. In line start motors, the segmental rotor reached a high state of development in the work of Law- renson [lo]. (See also Honsinger [13, 141.) The highest value quoted for 5 is that of Fong [7], who reported a value of 10.7 at no load and 5.3 under load. Lawrenson [lo] and Honsinger [13, 141 reported saturated values only slightly lower than Fong’s, all of the reported motors being in the range 1-10 hp. The power factors of these motors were generally in the range 0.55-0.7, but it is difficult to make a meaningful summary of the effi- ciencies because of the variety of sizes and designs. All these workers recognised the improvements in per- formance with increasing size, but very little has been published on larger motors. The literature consistently shows that, in its line start form, the axially laminated rotor produces a saliency ratio no higher than that of the segmental type. For example, Cruickshank er al. reported a value of 5.2 for a 2.25 hp four pole motor. Rao [16] reported a full load value of 6.8, but his motor was larger than the others discussed here. His 15 hp, four-pole line start motor achieved a power factor of 0.8 and an efficiency of 86% at full load. When the starting cage is removed, higher values of 5 are encountered. For example, Fratta er al. [17] report a saturated value of 9.2 in a 20 kW motor. Lip0 [18] quotes performance figures for a six-pole motor which imply a saliency ratio of about 7. The cageless rotor in Fig. Id is distantly related to the segmental rotor. It is derived from the so-called interior magnet PM synchronous motor [lZ, 151 by removing the 250 IEE PROCEEDINGS-B, Vol. 140, NO. 4, JULY 1993  magnets. The highest value oft reported for this design is 4.7 in a 6 kW motor [l]. A figure of 4 was also achieved in a very small (50 W) motor [12]. What is surprising about all the reported saliency ratios is how far they fall short of Kostko's prediction of 25, even for cageless designs. In the following Sections, this theoretical figure is redeveloped from a slightly dif- ferent (but equally simple) basis, and it will be shown by finite element analysis why it cannot be achieved in prac- tice with a fully loaded motor. 2 Basictheory 2. Torque per ampere The electromagnetic torque is the classical reluctance torque of the conventional synchronous machine, eqn. 1, where Id and I are components of the RMS phase current I resolved along the d- and q-axes of the phasor diagram, Fig. 2; they correspond to the space q-axis I,% I PH IPH d-axis Fig. 2 Synchronous reluctance motor phasor diagram vector components of stator MMF along the d- and q-axes of the rotor. The torque is given by rn 2 = rnplJI,(LJ - L,) = lgH sin 2y(Ld - L,) (1) Here, rn is the number of phases, p is the number of pole pairs, and Ld and L, are the direct and quadrature axis synchronous inductances, respectively. Note that Xd = hfLd and X, = 2nfL,, where f is the frequency. The convention adopted here, in which the d-axis is the high inductance axis, is the same as that used in the literature on the line start reluctance motor'. For maximum torque per ampere, the inductance difference (Ld - L,) should be maximised within constraints set by manufacturability, and the current angle y made equal to 45 . Saturation in the d-axis causes the maximum torque per ampere to occur at a value of y greater than 45 , and this value increases with increasing phase current (Section 6). The inductance difference (Ld - L,) takes no account of the voltage requirements of the motor. The saliency ratio (5 = L,,/L,) provides a more general guide to the overall performance, because the power factor, the speed range at constant power, and several aspects of the dynamic response, are all directly related to [19, 203. In In References 1 and 12, the opposite convention was used, with the q-axis the high inductance axis, because the particular motors in those papers were related to the interior magnet hybrid motor in which the magnet axis is the low inductance direct axis. general, the performance is improved as t is increased. In this paper, attention is focused on power factor: the effect of on the other parameters is discussed in References 19 and 20. 2.2 Power factor The synchronous reluctance motor is intended to operate with sinewave currents, and therefore the fundamental (or 'displacement') power factor cos 4 is used. It is related to the saliency ratio by the equation in 2y 2(tan y + 5 cot y) cos 4 = (5 - 1) in which y is the phase angle between the current and the d-axis (Fig. 2). The inverter rating is closely related to the power factor and to the fundamental kVA requirement of the motor. Eqn. 2 assumes zero phase resistance (RPH). While this simplification is valid for motors with integral horsepower and larger rating, it is not valid when the resistance is comparable with X, , as is the case in smaller motors. Neglecting R,,, the power factor has a maximum value of 5-1 cos ( J = - with tan y = ,,/ ) (3) Fig. 3 shows the variation in power factor with for y = 45 , and with y = tan-',,/((). To achieve a power factor greater than 0.8, must exceed 9, and y will have a value in excess of 71.6'. Even with = 9, a power factor of only 0.625 is achievable when y = 45 . r B 6 01 t; Bt .5 L i3 1 y=450 1.5 t 01   I I I I I 2 Ld/Lq x 1.0el Fig.  3 Variation in powerfactor with saliency ratio 3.1 Physical factors For a four-pole motor with sinusoidally distributed wind- ings, if the rotor is removed, the rotating magnetic field has the form of Fig. 4a. By suitable choice of time srcin, the d-axis can be aligned with the reference axis of the flux, so that all the flux is d-axis flux, and the q-axis flux is zero. The saliency implied by this flux pattern is infin- ite. The ideal rotor is one which is infinitely permeable along the flux lines in Fig. 4a, and completely imperme- able across them. This would require an hypothetical anisotropic material whose permeability was not only Theoretical limits to the saliency ratio IEE PROCEEDINGS-E, Vol. 140, NO. 4, JULY 1993 251  directional, but which also followed a pattern corres- ponding to the natural shape of the flux lines. The axially laminated rotor approximates this arrangement. It has d-axis / \\ q-axis /’ /’ Fig. 4 L ideal rotor (current sheet) b ideal rotor (36 slots) c single barrier rotor d IO-layer rotor e 24-layer rotor J axially laminated rotor 0132 synchronous reluctance motor.flux plots laminations shaped to follow the d-axis flux, and flux barriers which inhibit the q-axis flux. The achievable saliency ratio is limited by two factors that are immediately obvious: (i) the q-axis permeance cannot be zero; and (ii) the laminations are subject to saturation in the d-axis. A third limiting factor, less obvious, is that (iii) if the laminations are too thick they can short circuit the stator slot openings; (as recognised by Kostko), effectively increasing the stator slot leakage inductance which adds to both Ld and L,. A fourth limiting factor is (iv) end turn and other leakage inductances which add a ‘swamping term’ to both Ld and L, . 252 Two methods have been used to estimate the theoretical limits to saliency: a simple calculation based on the ideal flux paths, and a wide ranging study using finite element analysis. 3.2 Simple estimate of maximum saliency ratio Assume that the laminations and flux barriers are every- where very thin, and let t be the average ratio of flux barrier thickness to the combined thickness of lamination and flux barrier. Then 1/ 1 - ) is a measure of the flux concentration that occurs in the laminations owing to the loss of effective d-axis pole arc to the flux barriers. For a peak airgap flux density of 0.8 T and a saturation density of around 1.7 T, t must be limited to the order of 0.5. Now the synchronous reactance xd is inversely pro- portional to the airgap length g, and, by the methods of Reference 2, it can be shown that X, is inversely pro- portional to the sum of g and the combined thickness of the flux barriers, which is of the order of tR, where R is the rotor radius. Therefore the saliency ratio is given approximately by 4) =A=--- tR + 9) - R , x 9 9 With t = 0.5 and R/g typically 120, this indicates a maximum unsaturated saliency ratio of about 60, which is even larger than Kostko’s prediction of 25. This simple theory explains the limitation due to the finite q-axis per- meance (factor 1 above), but the limitations due to the other two factors are more difficult to estimate, and require finite element analysis in the context of the whole design of the motor. Nevertheless, the unsaturated figure of 60 represents a yardstick against which practical designs can be evaluated. 3.3 Finite element analysis of maximum saliency ratio Theoretical limits on L, and Ld can be defined using a fictional motor model which approximates the proper- ties of the ideal anisotropic material discussed in Section 3.1. The d-axis flux distribution is computed with a solid rotor having a normal B/H characteristic. The q-axis flux distribution is computed with the rotor removed alto- gether. The ideals of infinite permability in the d-axis and zero permeability in the q-axis are thus relaxed to what might be achievable with real materials. A further ideal- isation is to represent the stator winding as an infinitely thin current sheet located on a smooth bore. This will give a benchmark against which the effects of slotting can be assessed. The q-axis and d-axis flux plots for the ideal motor (in a D132 frame size) are shown in Fig. 4a while the saliency ratios at two levels of phase current are given in the first row of Table 1. Saturation is minimal in this ideal machine, even at the maximum current of 15 A, and the saliency ratio of about 60 corresponds quite closely to the simple estimate in Section 3.2. Table 1 : D132 motor saliency ratios (y = 45”) Design Unsaturated Saturated Ideal rotor + current sheet Ideal rotor + 36 slot stator Single barrier + 36 slots 3-layer + 36 slots 10-layer + 36 slots 24-layer + 36 slots Axial lamination + 36 slots Ideal rotor + 24 slot stator 24-laver + 24 slots I = 1 amp 61.70 30.76 1.72 6.68 10.09 11.21 11.63 26.53 9.57 I = 15 amp 57.56 20.53 4.66 5.43 8.1 6 8.73 8.69 17.50 6.89 IEE PROCEEDINGS-B, Vol. 140, No. 4, JULY 1993
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