IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 1, JANUARY 2014
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Design Assessments of a Magnetic-Geared Double-Rotor Permanent Magnet Generator Cheng-Tsung Liu , He-Yu Chung , and Chang-Chou Hwang Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan Department of Electrical Engineering, Feng Chia University, Taichung 40724, Taiwan By adopting the double-rotor structure and the coaxial magnetic gear concept, a permanent magnet (PM) generator is proposed for harvesting the wind energy directly without mechanical conversions. In addition to the physical model realizations, this paper will present the detailed design and implementation concerns of the magnetic-geared double-rotor PM generator along with thorough loss assessments. The comparisons of PM magnetization directions and arrangements, the selections of proper windings, and the operational efficiencies of this machine along with the terminal voltage phase shifts due to different loading conditions will all be summarized. The realization process of a portable 2.5-kVA generator that can be directly coupled to the mechanical driven source without additional mechanical gears will be demonstrated, and the feasibility of such a machine structure can certainly be confirmed from the satisfactory performance results. Index Terms—Direct coupling, magnetic gear, permanent magnet (PM), voltage regulation.
I. INTRODUCTION
T
HE ever-increasing global warming concerns have drawn escalating focus on the utilizations of renewable energies, and the efficient and cost-effective harvest of these energies are certainly the main concerns [1]. Alternatively, at reasonable costs and operational efficiencies, small and compact energy conversion devices that can pick up those diversified energies more conveniently might be the better choices for rural or undeveloped areas [2]. To fulfill the desired energy harvesting objective, some mechanical gearing systems are usually introduced to raise the rotor operational speeds of conventional rotary generator systems. With the additional mechanical parts, these gear systems will inevitably increase both the installation volumes and the costs of the entire generating units [3]. Consequently, the desired mass applications of such systems will be limited. By adopting the design idea of planetary gear with its planet carrier being fixed, the large input torque operated at low speed can be applied to the outer ring gear, and a high-speed small torque can then be supplied from the inner sun gear [4]. In addition, since there is no physical coupling, the rotary magnetic gear concepts have been introduced in many applications to reduce the possible mechanical maintenance costs [5], [6]. Nevertheless, for conveying the mechanical energy coaxially, the axial length of the entire composition that integrates the turbine, the gear sets, and the generator altogether will still be relatively long and thus affect the overall compactness for desired system applications. As the operational magnetic fields are mainly in the radial direction, with the addition of an inner stator, the magnetic-geared outer-rotor permanent magnet (PM) machines have been proposed to extract the electromagnetic energy directly [7], [8]. With their relatively compact structures, the design concept of such a machine is adapted for con-
Manuscript received April 27, 2013; revised August 11, 2013; accepted August 19, 2013. Date of current version December 23, 2013. Corresponding author: C.-T. Liu (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2013.2279260
structing the integrated generator to meet the desired application specifications. Since the entire generating unit must be sufficiently compact for easy implementation and its overall cost must also be lower enough for mass applications, detailed design and construction assessments of such a machine system that is capable for wind and tidal energy extractions will be performed. With the radii of turbine blades being selected at relatively small sizes in the range from 1.0 to 2.0 m, based on the fluid (air or sea water) densities and the reasonable operational speeds, it can be roughly estimated from common kinetic energy theory that the maximum generating capacity is around 2.5 kW. Therefore, different from the common machine design concerns, the analyses of inner and outer PM magnetization arrangements, the stator winding selections, and the possible operational characteristics of the proposed small magnetic-geared double-rotor permanent magnet generator (MDPMG) will be thoroughly performed to confirm its application competences. Also, from these systematic assessments, the comprehensive design and implementation references of MDPMG for its mass implementations and effective energy extractions can then be supplied. II. MAGNETIC-GEARED DOUBLE-ROTOR PERMANENT MAGNET GENERATOR The conceptual arrangements of a magnetic-geared double-rotor permanent magnet generator are illustrated in Fig. 1. Though detailed structural and parameter designs must be conducted before the construction of the machine system, some parameters of the generator prototype are determined based on the feasible and available mechanical arrangements for cost and manufacture concerns. The corresponding physical specifications for this prototype machine are provided in Table I, and the operational principle of this MDPMG is governed by the general speed relation [6] (1 in which , , and are, respectively, the mechanical angular speeds of the inner PM rotor, the outer PM rotor, and the iron pole yokes. The pole pairs of inner rotor PMs can be
0018-9464 © 2013 IEEE
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 1, JANUARY 2014
Fig. 1. Conceptual illustration of a magnetic-geared double-rotor permanent magnet generator.
Fig. 2. Illustrations of possible outer rotor PM arrangements. (a) With radially magnetized pole pair and back iron. (b) With laterally magnetized pole pair and iron poles. (c) With two-segment Halbach array.
TABLE I PHYSICAL SPECIFICATIONS OF MDPMG PROTOTYPE Fig. 3. Possible inner rotor PM magnetizations and arrangements. (a) With one radial magnetized PM. (b) With three diametrically magnetized PMs.
with large arcs are more expensive, as shown in Fig. 3, three diametrically (parallel) magnetized PMs with equal pole arcs will thus be assessed for implementations. Since the system design objective is to provide maximum flux that can couple the stator windings, the general objective function for selecting the rotor PM arrangements can then be conceptually expressed as Maximize: expressed by , with fixed iron pole yokes ( ) and the given parameters as indicated in Table I, it can be seen that a machine with speed ratio of 8.5 and opposite rotating rotors to alleviate the axial mechanical stress will be developed. III. MAGNETIZATION ARRANGEMENTS OF INNER/OUTER ROTOR PERMANENT MAGNETS By either increasing the outer rotor pole pairs or reducing the inner rotor pole pairs, a higher gear ratio can be achieved on the generating unit. However, the corresponding smaller PM pieces for the outer rotor or larger PM pieces for the inner rotor will introduce both the operational flux harmonics and the higher installation cost concerns. Hence the detailed analyses of these rotor magnetization arrangements must be performed in advance to provide better design references. Because every set of PM pole pairs and yoke composition on the outer rotor must supply a return path for the magnetic field, three possible arrangements are conceptually illustrated in Fig. 2. For supplying the maximum magnetizations, only the outer rotor PM arrangement as shown in Fig. 2(a) will be adopted for construction. Thus, by expanding the electrical pole arc of the outer rotor PM to and integrating with the radial magnetized inner rotor PMs, the air-gap fluxes that will couple the stator poles can then be investigated. In addition, since the total pole-pair number is relatively larger, with smaller mechanical pole arcs, the outer rotor PM poles can be composed by rectangular PM pieces for cost-down concerns. However, for the inner PM rotor, since its operational objective is mainly to convey the electromagnetic energies, field paths are designed to pass through it. With fewer pole pairs, apparently the rectangular PM pieces are not suitable for composing the inner rotor. Since the costs of radially magnetized PM poles
(2
where is the flux passing through the stator pole surface, is the flux density inside the generator, and is the individual stator pole surface. As the magnetic fluxes are dependent on the corresponding rotor positions, with stable operational speeds of the inner and outer rotor, the exhibited magnetic fluxes and the total harmonic distortion (THD) can be expressed as (3 and THD
(4
where is the magnitude of the corresponding th order harmonic flux passing through the stator pole surface, and is the phase shift of the th order flux component. Based on the selected outer and inner rotor PM arrangements, by 3-D finite element analyses (FEA) [9], Fig. 4 shows the air-gap fluxes that will couple the stator poles and their corresponding spectra. The summarized fundamental components and THD information of these two air-gap fluxes are provided in Table II. It can be clearly observed that the pole assembly with three diametrically magnetized PMs can provide almost the same fundamental flux as that from the single radially magnetized one with even smaller THD. Certainly the desired inner rotor PM structure can be more conveniently achieved with less cost. By driving the selected inner PM rotor assembly and holding the outer PM rotor, with the stator windings opened, the torqueangle relations for the two rotors can be obtained [10]. As shown
LIU et al.: DESIGN ASSESSMENTS OF MAGNETIC-GEARED DOUBLE-ROTOR PERMANENT MAGNET GENERATOR
Fig. 4. Air-gap fluxes that are coupling the stator poles with different inner rotor PM magnetizations and arrangements (a: with radial magnetizations, b: with three pieces of diametrical magnetizations). (a) Magnetic fluxes. (b) Spectra of the magnetic fluxes.
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Fig. 6. Illustrations of flux densities inside the generator system at one operational condition.
TABLE II COMPARISONS OF AIR-GAP FLUXES WITH DIFFERENT INNER ROTOR PM ARRANGEMENTS (OUTER ROTOR POLE ARC: )
Fig. 7. Three-phase terminal voltages of the MDPMG at certain wire and loading specifications.
Fig. 5. Calculated torque-angle curves of the proposed MDPMG.
in Fig. 5, with the pullout torques of the outer and inner rotors being, respectively, at 170.54 N-m and 20.30 N-m, from Table I, the expected geared up ratio of 8.5 (17/2) can certainly be confirmed. IV. DETERMINATIONS OF STATOR WINDINGS The selections of wires will affect both the voltage regulations and the efficiencies of the designed MDPMG, by assuming rated outer and inner rotor speeds, thorough assessments of the generator operational characteristics at various loading conditions are required. From the conceptual machine structure as depicted in Fig. 1, because thicker wires generally have smaller slot filling factors, the required outslot stator windings are realized by a flyer type winding machine. By setting a reasonable filling factor of 0.65 and an expected operational voltage level of about 208 V at the rated inner rotor speed of 1800 r/min, performance of the three-phase concentrated stator windings are systematically investigated. The detailed 3-D flux densities of the MDPMG at one operational condition are shown in Fig. 6, and the corresponding induced voltages are depicted in Fig. 7. To further explore the operational characteristics of the MDPMG due to winding selections, three different wires with diameters of 1.6, 1.7, and 1.8 mm will be evaluated. Based on the feasible filling factor, it is found that the corresponding winding turns will be 138, 123, and 110, respectively. The output power capabilities of the generator at various winding and terminal voltage conditions are illustrated in Fig. 8. By checking these indices at the objective output power range of 2.0-2.5 kW, the windings with diameters of 1.6 and 1.7 mm will have voltage regulations at about 9% and higher, while
Fig. 8. Generator output power-voltage characteristics with different stator windings and fixed inner rotor speed of 1800 r/min (1.6 mm/138 turns; 1.7 mm/123 turns; 1.8 mm/110 turns).
these values are only between 4% to 7% for the 1.8 mm one. Therefore, as long as the thicker (1.8 mm) wires can fulfill the desired operational voltages with feasible and acceptable construction overheads, it is selected for the MDPMG system manufacturing processes. V. OPERATIONAL ASSESSMENTS Since the aim is to seek the feasible integration of magnetic gear and synchronous generator, the conversion efficiencies of such a structure at various operational conditions are the key concerns. Though the best physical compositions of related component dimensions and arrangements can be determined by adopting Taguchi’s method [11], the entire system operations must be analyzed in advance. As the stator induced voltages will be proportional to the inner rotor speeds, from Fig. 9(a), the voltage of the single-phase equivalent circuit can be expressed as (5 where subscript indicates the th loading condition, and are the induced voltage and its phase angle, is the terminal voltage, and are the generator supplied current and the load angle, and is the stator winding impedance. If the MDPMG is driven at fixed operational speed, the phase shifts between induced and terminal voltages will be accordingly changed to meet the load requirements. By setting the same load angles for simple illustrations, Fig. 9(b) shows
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 1, JANUARY 2014
ILLUSTRATIONS
OF
TABLE III COMPONENT LOSSES OF MDPMG OPERATIONAL CONDITIONS
AT
DIFFERENT
Fig. 9. Illustrations of steady-state terminal voltage relationships of the MDPMG. (a) Single-phase equivalent circuit. (b) Phasor diagram at different loadings with same power factor.
VI. CONCLUSION
Fig. 10. Terminal output voltage-power relationships of the MDPMG at different inner rotor operational speeds.
This paper reported the detailed design and implementation concerns of an integrated magnetic-geared double-rotor PM generator along with loss evaluations. The rotor PM magnetization directions and compositions, the stator winding selections, and the terminal operational characteristics have all been systematically assessed. Based on the evaluated results, a compact 2.5-kVA generator prototype that can be directly coupled to the mechanical driven source without additional mechanical gears is proposed with thorough design and operational references. From such assessments, we are confident that an applicable standalone generation system structure for renewable energy extractions can thus be developed. ACKNOWLEDGMENT
Fig. 11. Illustrations of the speed-dependent efficiency ( ) and induced voltage phase shift ( ) characteristics of the proposed MDPMG at different 1, 2, 3 with 1: 1600 r/min, 2: 1800 r/min, 3: 1900 r/min). loading conditions (
the phasor diagram at three different loading conditions and the phase advanced effects can be evidently observed. For the efficiency concerns, the system losses resulting from all the individual parts must be evaluated at various operational conditions. Table III shows the component losses of this machine operated at two different inner rotor speeds and loading conditions for illustrations. As can be seen, the system iron losses will be almost maintained at the same speed, and the stator winding copper losses will be proportional to the square of line currents. For the rotational parts, since the inner rotor is designed to convey the input energy, its rotational losses will almost be proportional to the speeds. While for the outer rotor ones, with input energy applied, not only the speeds but also the loading conditions will all be contributed to the rotational losses. Nevertheless, from these assessments, for operations of such a standalone MDPMG, it is typical to output the maximum allowable real power as long as the terminal voltage is within the acceptable range. Such constraints are defined by the voltage-power curves as shown in Fig. 10, and the summarized terminal characteristics of the MDPMG are depicted in Fig. 11. It is clear that the generator can meet wider power output variations within the specified voltage range if the inner rotor is operated at 1800 r/min. The output voltage and operational efficiency can also be properly controlled by implementing adequate driver control schemes to adjust the corresponding - and -axes currents.
This work was supported in part by the National Science Council of Taiwan under Grant NSC 102-2221-E-110-031MY3. The authors are grateful to S. Kumagai, formerly with the Nidec Corporation, Japan, for suggestions on the machine design. REFERENCES [1] S. R. Weart, The Discovery of Global Warming. Cambridge, MA, USA: Harvard Univ. Press, 2008. [2] J. Chen, C. V. Nayar, and L. Xu, “Design and finite-element analysis of an outer-rotor permanent-magnet generator for directly coupled wind turbines,” IEEE Trans. Magn., vol. 36, no. 5, pp. 3802–3809, Sep. 2000. [3] S. Huang, J. Luo, F. Leonardi, and T. A. Lipo, “A general approach to sizing and power density equations for comparison of electrical machines,” IEEE Trans. Ind. Appl., vol. 34, no. 1, pp. 92–97, Jan./Feb. 1998. [4] E. Gouda, “Comparative study between mechanical and magnetic planetary gears,” IEEE Trans. Magn., vol. 47, no. 2, pp. 439–450, Feb. 2011. [5] K. Atallah and D. Howe, “A novel high performance magnetic gear,” IEEE Trans. Magn., vol. 37, no. 4, pp. 2844–2846, Jul. 2001. [6] L. Shah, A. Cruden, and B. W. Williams, “A variable speed magnetic gear box using contra-rotating input shafts,” IEEE Trans. Magn., vol. 47, no. 2, pp. 431–438, Feb. 2011. [7] L. Jian, K. T. Chua, and J. Z. Jiang, “A magnetic-geared outer-rotor permanent-magnet brushless machine for wind power generation,” IEEE Trans. Ind. Appl., vol. 45, no. 3, pp. 954–962, May/Jun. 2009. [8] S. Niu, S. L. Ho, and W. N. Fu, “Performance analysis of a novel magnetic-geared tubular linear permanent magnet machine,” IEEE Trans. Magn., vol. 47, no. 10, pp. 3598–3601, Oct. 2011. [9] The Magsoft Corporation, Flux3D User’s Guide ver. 11.1. Clifton Park, NY, USA, 2012. [10] L. Jian, K. T. Chau, Y. Gong, J. Z. Jiang, C. Yu, and W. Li, “Comparison of coaxial magnetic gears with different topologies,” IEEE Trans. Magn., vol. 45, no. 10, pp. 4526–4529, Oct. 2009. [11] H. V. Khang, A. Arkkio, and J. Saari, “Loss minimization for formwound stator winding of a high-speed induction motor,” IEEE Trans. Magn., vol. 48, no. 12, pp. 4874–4879, Dec. 2012.
