3216 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011
Electromagnetic Performance Analysis of Hybrid-Excited Flux-SwitchingMachines by a Nonlinear Magnetic Network Model
Wei Hua, Gan Zhang, Ming Cheng, and Jianning Dong
School of Electrical Engineering, Southeast University, Nanjing 210096, China
In this paper, a nonlinear magnetic network model (NMNM) is proposed to predict the electromagnetic performance of a hybrid-ex-citation flux-switching (HEFS) machine, in which the modeling of the magnetic motive forces (MMF) due to field windings is specifi-cally investigated. The proposed NMNM enables the predictions of air-gap flux-density distributions, flux linkage, back-electromotiveforce (back-EMF), and inductances of both armature and field windings under different excitation conditions, including pure magnets,pure field currents, and hybrid excitations. The predicted results from the NMNM model are validated by 2-D finite element analysis.
Index Terms—Brushless machine, finite element analysis, flux-switching, hybrid excitation, magnetic network model, nonlinear.
I. INTRODUCTION
F LUX-SWITCHING permanent magnet (FSPM) machineshave attracted considerable attention in recent years due to
the large torque capability, essentially sinusoidal back-electro-motive force (EMF) waveforms, high torque (power) density, aswell as compact and robust structure since both the locations ofmagnets and armature windings are located in stator instead ofrotor as those in the conventional rotor-PM machines [1]–[9].However, for solely permanent-magnets excited machines, it isa traditional contradiction between the requests of high torquecapability under the base speed (constant torque region) andwide speed operation above the base speed (constant powerregion). Hence, hybrid-excitation flux-switching (HEFS) ma-chines are proposed in which the magnet dimensions were re-duced to save room for the introduced field windings as shownin Fig. 1(b) [10], and corresponding flux-regulation capabilitywas investigated [11].
Although nonlinear magnetic circuit models and Fourieranalysis for the performance prediction of FSPM machineshave been introduced in [3], [12], and [13], the analysis ofHEFS machines has not been reported, especially for themodel of magneto-motive-force (MMF) due to field windingexcitation. Hence, in this paper a nonlinear magnetic networkmodel (NMNM) is proposed to predict the electromagneticperformance of a prototyped HEFS machine having 12 statorslots and 10 rotor poles as shown in Fig. 2(a). Moreover, thedesign dimensions are shown in Fig. 2(b), and the key designspecifications are listed in Table I. The detailed topology andoperation principle can be found in [10].
II. NONLINEAR MAGNETIC NETWORK MODEL
The following NMNM modeling procedure for the HEFS ma-chines is organized by three steps.
1) The field distributions of the prototyped three-phase12/10-pole HEFS machine is investigated under both purepermanent magnet and hybrid excitations.
2) Based on the field distributions, the modeling principle ofNMNM for HEFS machine is proposed.
Manuscript received February 20, 2011; accepted May 02, 2011. Date ofcurrent version September 23, 2011. Corresponding author: W. Hua (e-mail:[email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMAG.2011.2154377
Fig. 1. Topology of the 12/10-pole FSPM and HEFS machines. (a) FSPMmachine. (b) HEFS machine.
Fig. 2. Configuration and design dimensions of a 12-stator-slots/10-rotor-polesHEFS machine. (a) Cross section. (b) Design dimensions.
TABLE IKEY DESIGN SPECIFICATIONS OF THE HEFS MACHINE
3) The NMNM is obtained, and the electromagnetic perfor-mance of the HEFS machines is predicted by the model.
HUA et al.: ELECTROMAGNETIC PERFORMANCE ANALYSIS OF HYBRID-EXCITED FLUX-SWITCHING MACHINES 3217
Fig. 3. Field distributions when � � � . (a) � � ��� T and � � �.(b) � � ��� T and � � � A/mm .
Fig. 4. Flux direction configuration. (a) � � ��� T and � � �. (b) � �
��� T and � � � A/mm .
A. Field Distributions
Fig. 3 shows the partial field distributions obtained by 2-Dfinite element (FE) analysis under two typical excitations (purepermanent magnet excitation and hybrid excitation), respec-tively. Obviously, the fluxes enclosed all through the magnetunder pure permanent magnets excitation ( T and
). However, in the case of hybrid excitations ( Tand A/mm ), some of the combined fluxes enclosedpartially through the magnet, while the others enclosed directlyin the area of field winding.
B. Modeling Principle
Fig. 4 shows the magnetic circuit and flux direction config-urations corresponding to Fig. 3. Since the field windings areintroduced to regulate the air-gap flux-density, the model of theMMF due to field current is specifically built according to thelocal magnetic field distributions and the corresponding flux di-rections. It should be noted that as illustrated in Fig. 4, the MMFof field excitations is located in closed-circuit branches com-posed of two series magnetic sources, which is not directly con-nected with the MMF due to magnets. Overall, the proposedMMF locations due to field excitations and branch connectionsenable the fluxes to be enclosed adaptively under different exci-tation conditions.
C. NMNM Model
Hence, the NMNM can be obtained as illustrated in Fig. 5with the locations of three kinds of MMF sources. Additionally,the MMF due to armature current is located in the stator yokebranches combined of two series ones. Moreover, the armatureMMF , field MMF , and magnet MMF can begiven by
(1)
Fig. 5. Nonlinear magnetic network model of the prototyped 12/10 poles HEFSmachines.
Fig. 6. Open-circuit field distributions with different materials. (a) � � ��� Tand � � � . (b) � � ��� T and � � � . (c) � � ��� T and � � � .(d) � � ��� T and � � � .
where and are the cross-section areas of armature slot andfield slot, respectively, is armature slot current density, ismagnet thickness, is the relative permeability of magnet, and
is the permeability of free space. It should be emphasizedthat the air-gap branch connection in NMNM varies adaptivelywith different rotor positions, and the permeability of each ironcore branch is determined by iterative calculation.
III. PREDICTED RESULTS FROM NMNM AND FE ANALYSIS
A. Flux-Linkage in Armature Windings
Fig. 6 shows the open-circuit PM field distributions at twotypical rotor positions where phase-A flux linkage isand peak value , respectively, due to different magnetmaterials, namely Ferrite ( T) and NdFeB (
T). Additionally, the corresponding air-gap flux distributionspredicted by NMNM and FE analysis are compared in Fig. 7. Ascan be seen, good agreements are achieved. Furthermore, due tothe doubly salient machine topology, the air-gap field distribu-tion is nonsinusoidal and exhibits significant harmonics, similar
3218 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011
Fig. 7. Open-circuit air-gap flux distributions under PM excitation only.(a) � � ��� T and � � � . (b) � � ��� T and � � � . (c) � � ��� Tand � � � . (d) � � ��� T and � � � .
to a switched reluctance machine. However, due to the simpli-fication of the air-gap flux paths in NMNM, the air-gap fielddistributions obtained from the model are smoother than thatpredicted from FE analysis. Overall, the proposed NMNM hasbeen validated to predict the air-gap flux density under magnetexcitations only employing different materials with acceptableaccuracy.
B. Flux Linkage in Armature Windings
Fig. 8 compares the phase flux linkage per turn under dif-ferent excited conditions, where promagnetized and demagne-tized field current densities are 5 and 5 A/mm , respectively.Obviously, when T, the flux-regulation capability due
Fig. 8. Comparison of phase flux-linkages per-turn. (a) � � ��� T. (b) � �
��� T.
Fig. 9. Comparison of phase flux linkages per turn with phase armature currentdensity of 5 A/mm .
to field excitation is excellent, as shown in Fig. 8(a), whereaswhen T, the phase fluxes under both pro- and de-magnetized conditions are reduced, as illustrated in Fig. 8(b),due to significant saturation effect. Overall, good agreementsare achieved by NMNM and FE analysis.
Furthermore, Fig. 9 shows the phase flux waveforms with anarmature current of phase A (current density A/mm )under pure magnet excitation, which therefore enables the ar-mature inductances to be calculated as given by
(2)
where is self-inductance of phase A, is combined flux-linkage of phase A due to permanent magnet and phase-A cur-rent, is phase-A flux linkage due to magnet only.
Hence, the proposed NMNM can predict the flux linkage ofarmature windings and consequently calculate the self- and mu-tual inductance of armature windings.
C. Flux Linkage in Field Windings
Similarly, Fig. 10 compares the flux linkages of field wind-ings obtained by NMNM and FE analysis under different
HUA et al.: ELECTROMAGNETIC PERFORMANCE ANALYSIS OF HYBRID-EXCITED FLUX-SWITCHING MACHINES 3219
Fig. 10. Comparison of coil-f1 flux linkages per turn. (a) � � ��� T.(b) � � ��� T.
Fig. 11. Comparison of coil-f1 flux linkages per turn with an armature currentdensity of 5 A/mm under magnet excitation only.
excitation conditions. Fig. 11 compares the combined flux link-ages of coil-f1 as labeled in Fig. 2(a) due to both magnets andfield current predicted by NMNM and FE analysis. Similarly,the self- and mutual inductances between armature and fieldwindings can be calculated by
(2)
(3)
where is self-inductance of field windings, is flux linkageof field windings due to magnet and field current, is fluxlinkage of field windings due to magnet only, is field current,
is mutual inductances between field windings and armaturewindings (e.g., phase A), is flux linkage of field windingsdue to magnet and armature current, and is the correspondingarmature current. Obviously, good agreements are achieved byNMNM and FE analysis.
IV. CONCLUSION
In this paper, a nonlinear magnetic network model hasbeen proposed to predict the performance of HEFS machines.
Particular attention is paid to the locations of the MMF due tomagnets and field windings. It is confirmed that the proposedNMNM can predict the air-gap flux density distribution andthe flux linkages of armature and field windings under differentexcitations with satisfied accuracy. All the results from theNMNM are validated by FE analysis.
ACKNOWLEDGMENT
This work was supported by the National Natural ScienceFoundation of China (50807007, 60974060), the SpecializedResearch Fund for the Doctoral Program of Higher Educationof China (200802861038), the Qing Lan Project of JiangsuProvince, the Fund Program of Southeast University for Ex-cellent Youth Teachers, the Southeast University Science Fundfor Distinguished Young Scholars, the Southeast UniversityKey Science Research Fund, and the Aeronautical ScienceFoundation of China (20100769004).
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