IN most inverter fed electrical drives, asynchronous

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1 Comparison of Different Designs of ynchronous Reluctance Machines with High-Anisotropy Rotors Erich chmit, Member, IEEE Abstract In terms of torue capability, power factor an efficiency, synchronous reluctance machines with high-anisotropy rotors represent an alternative to conventional inuction machines. In particular, they have very robust rotors an can therefore operate at constant power in a wier fielweakening range. The paper iscusses a comparison of the various machine concepts using an ientical machine geometry by using finite element analyses. Experimental results obtaine from two machine esigns confirm the results of the numerical analyses. Keywors Two-axes inuctances, Reluctance machine, Permanent magnet synchronous machine, ynchronous machine, Finite element analysis I. Introuction I most inverter fe electrical rives, asynchronous inuction machines, synchronous reluctance machines or permanent magnet excite synchronous machines are utilize. For an application in highperformance rives in particular with a wie fielweakening range, both types of synchronous machines are more favourable against inuction machines. This is base on their inherent suitability for a positionsensorless control scheme an aitionally their more robust rotor [] [7]. In orer to achieve a comparable performance, synchronous reluctance machines shoul be euippe with a high-anisotropy rotor esign with internal flux barriers [], [3] [5], [8]. In comparison to conventional synchronous reluctance machines, the effective saliency of such rotor esigns can be increase by permanent magnets inserte into the flux barriers [9] [2]. On the other han, the permanent magnet excite synchronous machine can be realize with such a high-anisotropy rotor esign an two ifferent arrangements of the permanent magnets resulting in a complete ifferent behaviour in particular within the fiel-weakening range. Conseuently, there are four ifferent machine concepts which utilize ientical stator an rotor geometries as well as ientical wining ata. The paper compares these four machine esigns in terms of the op- Erich chmit is with the Institute of Energy ystems an Electric Drives, Vienna University of Technology, Vienna, Austria ( erich.schmit@tuwien.ac.at). erating behaviour in particular in the fiel-weakening region. In orer to confirm the numerical results from various finite element analyses, measurement ata from two rotor esigns are presente aitionally. II. pace Vector Calculus In the rotor fixe reference frame, the normalize stator current an stator flux space vectors are given by i, = i e jβ = i ji, () ψ, = ψ e jϑ = ψ jψ. (2) Therein, i,ψ represent the magnitues of stator current an stator flux, β,ϑ enote stator current angle an stator flux angle, respectively. By using irect an uarature axis stator inuctances l,l as well as the linkage flux of the permanent magnets ψ M,the components of the stator linkage flux can be written as ψ = l i ψ M, (3a) ψ = l i ψ M. (3b) Conseuently, the normalize electromagnetic torue is obtaine from t i = 3 ( ) 2 Im i, ψ, = 3 ) (ψ i ψ i (4) 2 = 3 ( ψm 2 i2 sin β ψ M cos β l l ) sin 2β. i i 2 The conventional reluctance machine can be escribe with a vanishing linkage flux ψ M =. With the permanent magnet assiste reluctance machine, ψ M < represents the linkage flux of the permanent magnet which counteracts to any uarature axis stator current i >. On the other han, the permanent magnet excite reluctance machine with ψ M > can be esigne as either a normal-saliency machine l >l or an inverse-saliency machine with l <l. III. Machine Designs Fig. epicts the various arrangements of highanisotropy rotors with internal rotor flux barriers: a. conventional reluctance machine without any permanent magnets, normal-saliency l >l,

2 a. b. c.. Fig. : Comparison of the machine esigns: a. conventional reluctance machine, normal-saliency l >l, b. permanent magnet assiste reluctance machine with ψ M <, normal-saliency l >l, c. permanent magnet excite reluctance machine with ψ M >, normal-saliency l >l,. permanent magnet excite reluctance machine with ψ M >, inverse-saliency l <l b. permanent magnet assiste reluctance machine with ψ M <, normal-saliency l >l, c. permanent magnet excite reluctance machine with ψ M >, normal-saliency l >l,. permanent magnet excite reluctance machine with ψ M >, inverse-saliency l <l. Fig. 2 epicts the finite element moel of stator an high-saliency rotor of the ifferent machine esigns concerne. With all four esigns, the stator is ientical an consists of 24 slots carrying a conventional star-connecte three-phase full-pitch wining. lot weges with a magnetic anisotropy are utilize to minimize the cogging torue of the unskewe machine. With regar to the circumferential symmetry, only one pole pitch is inclue in the finite element moel. The various angular rotor positions are moelle with a concentric sliing surface insie the air-gap. This approach facilitates fully inepenent stator an rotor moel parts without any remeshing of the air-gap regions when consiering ifferent angular rotor isplacements [3] [5]. insie the air-gap [3], [6], [7]. On the other han, the inuctances presente in the following are always apparent inuctances obtaine by utilizing the frozen permeabilities metho [6] [8]. IV. Analysis Results A. Comparison with Measurements Fig. 3 an Fig. 4 epict a comparison of measurement ata an numerical results for the electromagnetic torue from two esigns, the permanent magnet assiste reluctance machine with ψ M =.3 an Torue ti () i =.25 i =.5 i = Fig. 3: Torue versus stator current angle β, comparison of numerical results (ashe line) an measurement ata (symbols), PM assiste reluctance machine.5 Torue ti () Fig. 2: Finite element moel of stator an high-saliency rotor with a sliing surface insie the air-gap The results iscusse further on are evaluate from various finite element analyses. Thereby, the electromagnetic torue is obtaine from the Maxwell stresses - i =.25 i =.5 i = Fig. 4: Torue versus stator current angle β, comparison of numerical results (ashe line) an measurement ata (symbols), inverse-saliency PM reluctance machine

3 the inverse-saliency permanent magnet excite reluctance machine with ψ M =.66. Obviously, there is a goo agreement between the measurement ata an the results obtaine numerically. B. Reluctance Machines As from (4), for any given stator current i the maximum torue of the conventional reluctance machine is achieve with a current angle of cos 2β =. On the other han, for any given stator current i the maximum torue of the permanent magnet assiste reluctance machine is achieve with a current angle of ψ ( M ψ ) 2 M sin β = 4(l l ) i 4(l l ) i 2. (5) Fig. 5 shows the ratio l /l in epenence on the stator current magnitue i with various current angles. On the other han, Fig. 6 epicts the absolute valueofthepowerfactorcosϕ sin(β ϑ) in epenence on the stator current magnitue i with various current angles. Ratio l/l () β = ±π/4, ±3π/4 β =π/4, 3π/4 β = π/4, 3π/ tator Current i () Fig. 5: Ratio l /l versus stator current magnitue i, current angles of β = ±π/4, ±3π/4, conventional reluctance machine (ashe line), PM assiste reluctance machine (straight line) Power Factor cos ϕ () β = ±π/4, ±3π/4 β =π/4, 3π/4 β = π/4, 3π/ tator Current i () Fig. 6: Power factor cos ϕ versus stator current magnitue i, current angles of β = ±π/4, ±3π/4, conventional reluctance machine (ashe line), PM assiste reluctance machine (straight line) In comparison of both esigns of the reluctance machine, the permanent magnet assiste reluctance machine yiels the best performance at current angles as given by (5) nearby β = π/4 orβ =3π/4. Conseuently, the permanent magnets with ψ M =.3 significantly increase the ratio l /l of the apparent inuctances yieling a wier spee range with constant power. Aitionally, they result in an increase power factor with current angles of β >. With higher stator current magnitues on the other han, the saturation level increases which results in ecreasing saliency-ratio an power factor. Further, Fig. 7 an Fig. 8 epict the torue t i with various stator current magnitues. Finally, Fig. 9 an Fig. show current trajectories resulting in a contour map of the torue t i. Torue ti () Torue ti () i =.25,.5,.75 i = i =.25, Fig. 7: Torue t i versus stator current angle β, current magnitues of i = , conventional reluctance machine i =.25,.5, i = i =.25, Fig. 8: Torue t i versus stator current angle β, current magnitues of i = , PM assiste reluctance machine Obviously, the compensation of the uarature axis current accomplishe by the permanent magnets significantly increases the evolve torue in the range of β π. In particular, the contour map Fig. confirms the best performance of the permanent magnet assiste reluctance machine at current angles nearby β = π/4 orβ =3π/4. C. Permanent Magnet Machines As from (4), for any given stator current i in case of the normal-saliency machine the maximum torue

4 Current i () Current i () Fig. 9: Contour map of torue t i versus stator current components i,i, conventional reluctance machine Current i () Current i () Fig. : Contour map of torue t i versus stator current components i,i, PM assiste reluctance machine of the is achieve with a current angle of ψ ( M ψ ) 2 M cos β = 4(l l ) i 4(l l ) i 2 (6) an in case of the inverse-saliency machine ψ ( M ψ ) 2 M cos β = 4(l l ) i 4(l l ) i 2.(7) Fig. shows the ratio l /l of the normal-saliency machineantheratiol /l of the inverse-saliency machine with ψ M =.66inepenence on the stator current magnitue i with various current angles. On the other han, Fig. 2 epicts the absolute value of the power factor cos ϕ sin(β ϑ) in epenence on the stator current magnitue i with various current angles. In comparison of both esigns of the permanent magnet excite machine, the inverse-saliency permanent machine yiels a significantly increase power factor in particular with current angles of π/2 β 3π/4 representing the regular operational moe with a Ratio l/l, l/l () β = ±π/4 β = ±π/2 β = ±3π/ tator Current i () Fig. : Ratio l /l or l /l versus stator current magnitue i, current angles of β = ±π/4, ±π/2, ±3π/4, normalsaliency PM reluctancemachine (ashe lines), inversesaliency PM reluctance machine (straight lines) Power Factor cos ϕ () β = ±π/4 β = ±π/2 β = ±3π/ tator Current i () Fig. 2: Power factor cos ϕ versus stator current magnitue i, current angles of β = ±π/4, ±π/2, ±3π/4, normalsaliency PM reluctancemachine (ashe lines), inversesaliency PM reluctance machine (straight lines) uarature current only as well as the fiel-weakening region. On the other han, the inverse-saliency permanent magnet machine shows the highest saliencyratio of the apparent inuctances yieling the wiest spee range with constant power. In particular, an operation at current angles nearby β = π/4 resultsin a high saliency-ratio but simultaneously a poor power factor. Again with higher stator current magnitues, the saturation level increases which results in ecreasing saliency-ratio an power factor. Further, Fig. 3 an Fig. 4 epict the torue t i with various stator current magnitues. Finally, Fig. 5 an Fig. 6 show current trajectories resulting in a contour map of the torue t i. Obviously, the normal-saliency machine acts rather like a reluctance machine ue to the high saturation occurring from the flux concentration in the irect axis. The contour map Fig. 5 confirms this behaviour uite well. Therefore, this arrangement oes not present a significant improvement against the arrangement without permanent magnets. On the other han, the contour map Fig. 6 confirms the behaviour of the inverse-saliency permanent magnet machine where a given torue value can be obtaine with only a uarature current but eually

5 Torue ti () Torue ti () i =.25,.5,.75 i = i =.25, Fig. 3: Torue t i versus stator current angle β, current magnitues of i = , normal-saliency PM reluctance machine i =.25,.5, i = i =.25, Fig. 4: Torue t i versus stator current angle β, current magnitues of i = , inverse-saliency PM reluctance machine with a smaller current within the fiel-weakening region yieling an increase efficiency ue to the reuce power losses. Further, the inverse-saliency permanent magnet machine can operate on the current limit in a wie spee range. Due to the rather small apparent inuctance in irect axis, such a machine can prouce much higher torue values without emagnetizing the permanent magnets in case of an increase current limit of the inverter. Conseuently, the inverse-saliency machine shows an inherent suitability for electrical rives where short overloa operational conitions reuire high torue values. V. Conclusion ynchronous reluctance machines with internal rotor flux barriers are well suite for an application in position-sensorless rives with a wie fiel-weakening range ue to their high effective saliency. By using an ientical machine geometry, the conventional reluctance machine an the permanent magnet assiste reluctance machine as well as the normal-saliency permanent magnet machine an the inverse-saliency permanent magnet machine are compare against their operational behaviour in particular in the fielweakening range. Current i () Current i () Fig. 5: Contour map of torue t i versus stator current components i,i, normal-saliency PM reluctance machine Current i () Current i () Fig. 6: Contour map of torue t i versus stator current components i,i, inverse-saliency PM reluctance machine The comparison is one in terms of current trajectories with respect to the reference frame accoring to current an voltage limits of the inverter. These iagrams obviously show the avantages of a high saliency ratio l /l in case of normal-saliency machines or l /l in case of inverse-saliency machines in particular in the fiel-weakening region. Thereby, the results from the finite element analyses are successfully compare with measurement ata obtaine from two machine esigns. References [] Vagati A., Fratta A., Franceschini G.: AC Motors for High-Performance Drives: A Design-Base Comparison. IEEE Transactions on Inustry Applications, Vol. 32, o. 5, eptember 996. [2] Miller J.M., McClear P.J., Lang J.H.: tarter-alternator for Hybri Electric Vehicle: Comparison of Inuction an Variable Reluctance Machines an Drives. Proceeings of the IEEE Inustry Applications ociety 33th Annual Meeting, t.louis (MO, UA), 998. [3] Lovelace E.C., Jahns T.M., Lang J.H.: Impact of aturation an Inverter Cost on Interior PM ynchronous Machines Drive Optimization. IEEE Transactions on Inustry Applications, Vol. 36, o. 3, May

6 [4] Vagati A., Pastorelli M., capino F., Franceschini G.: Impact of Cross aturation in ynchronous Reluctance Motors of the Transverse-Laminate Type. IEEE Transactions on Inustry Applications, Vol. 36, o. 4, July 2. [5] Vagati A., Canova A., Chiampi M., Pastorelli M., Repetto M.: Design Refinement of ynchronous Reluctance Motors Through Finite Element Analysis. IEEE Transactions on Inustry Applications, Vol. 36, o. 4, July 2. [6] Haataja J., Pyrhönen J.: ynchronous Reluctance Motor: An Alternative to Inuction Motor. Proceeings of the 4th International Conference on Electrical Machines, ICEM, Espoo (Finlan), 2. [7] De Kock H.W., Kamper M.J., Kennel R.M.: Anisotropy Comparison of Reluctance an Permanent Magnet ynchronous Machines for Low pee Position ensorless Applications. Proceeings of the 3th Power Electronics an Motion Control Conference, EPE-PEMC, Poznan (Polan), 28. [8] Bianchi., Bolognani., Chalmers B.J.: Comparison of Different ynchronous Motors Drives for Flux-Weakening Applications. Proceeings of the 3th International Conference on Electric Machines, ICEM, Instanbul (Turkey), 998. [9] Weinmeier P.: Lagegeberlose hochynamische Regelung eines Hybri-Reluktanzmotors im unteren Drehzahlbereich bis zum tillstan. Doctoral Thesis (in German), Vienna University of Technology, 998. [] Lee J.H., Kim J.C., Hyun D..: Effect Analysis of Magnet on L an L Inuctance of Permanent Magnet Assiste ynchronous Reluctance Motor using Finite Element Metho. IEEE Transactions on Magnetics, Vol. 35, o. 3, May 999. [] chmit E., Branl W., Grabner C.: Design Improvement of ynchronous Reluctance Machines with Internal Rotor Flux Barriers for High-pee Drives. Proceeings of the 33r IEEE Power Electronics pecialists Conference, PEC, Cairns (QLD, Australia), 22. [2] Bianchi., Bolognani., Bon D., Dai Pré M.: Rotor Flux-Barrier Design for Torue Ripple Reuction in ynchronous Reluctance an Permanent Magnet Assiste ynchronous Reluctance Motors. IEEE Transactions on Inustry Applications, Vol. 45, o. 3, May 29. [3] Hameyer K., Belmans R.: umerical Moelling an Design of Electrical Machines an Devices. WIT Press, outhampton (UK), 999. [4] De Gersem H., Gyselinck J., Dular P., Hameyer K., Weilan T.: Comparison of liing urface an Moving Ban Techniues in Freuency-Domain Finite Element Moels of Rotating Machines. Proceeings of the 6th International Workshop on Electric an Magnetic Fiels (EMF), Aachen (Germany), 23. [5] De Gersem H., Weilan T.: Harmonic Weighting Functions at the liing urface Interface of a Finite Element Machine Moel Incorporating Angular Displacement. IEEE Transactions on Magnetics, Vol. 4, o. 2, March 24. [6] Bastos J.P.A., aowski.: Electromagnetic Moeling by Finite Element Methos. Marcel Dekker Lt, ew York (UA), 23. [7] Bianchi.: Electrical Machine Analysis Using Finite Elements. CRC Press, Boca Raton (UA), 25. [8] Walker J.A., Dorrell D.G., Cossar C.: Flux Linkage Calculation in Permanent Magnet Motors Using the Frozen Permeabilities Metho. IEEE Transactions on Magnetics, Vol. 4, o., October 25. Erich chmit was born in Vienna, Austria, in 959. He receive his Mc an PhD egrees in Electrical Engineering from the Vienna University of Technology, Austria, in 985 an 993, respectively. Currently, he is an Associate Professor of Electrical Machines at the Institute of Energy ystems an Electric Drives of the Vienna University of Technology. His research an teaching activities are on numerical fiel computation techniues an esign optimization of electrical machines an transformers. He has authore more than technical publications mainly in the fiels of electrical machines an numerical fiel calculation.