Download High-Power-Factor Vernier Permanent

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014
High-Power-Factor Vernier
Permanent-Magnet Machines
Dawei Li, Student Member, IEEE, Ronghai Qu, Senior Member, IEEE, and
Thomas A. Lipo, Life Fellow, IEEE
Abstract—Vernier permanent-magnet (VPM) machines are well
known for high torque density but low power factor. This paper
deals with the low power factor of VPM machines. The goal is not
obtained by reducing the electrical loading or adjusting current
advance angle but by proposing a novel vernier topology, i.e., a
dual-stator spoke-array (DSSA) VPM topology. In this paper, the
characteristics of the DSSA VPM topology, such as active part,
auxiliary mechanical structure, and rotor anisotropy, are analyzed
in detail. Performances are evaluated based on finite-element analysis, including power factor, torque density, and cogging torque.
The results show that the DSSA VPM topology exhibits high power
factor, viz., ∼0.9, and significantly high torque capability. The
verification of the mechanical structure scheme is also done in this
paper. Finally, theoretical analyses are validated by the experimental results by a 44-rotor pole 24-slot DSSA VPM prototype.
Index Terms—Dual-stator spoke-array vernier permanentmagnet (DSSA VPM) machine, high power factor.
I. I NTRODUCTION
I
N recent years, due to the booming direct-drive applications,
such as wind power, electric propulsion, etc., low-speed
high-power electrical machines are attracting more and more attention. However, the low speed and high power demand makes
direct-drive machines suffer from bulky size and large material
consumption. Therefore, researchers have mostly concentrated
on high-torque-density electrical machines, and many novel
high machine topologies with high torque density are proposed
during the past couple of years.
Transverse flux permanent-magnet machines have become
very popular recently due to their high torque density, [1], [2].
Nevertheless, their power factor is really low (sometimes even
close to 0.3), which means that the larger capability converter
is required for the fixed output power [3].
Manuscript received October 15, 2013; revised February 14, 2014; accepted
March 19, 2014. Date of publication April 3, 2014; date of current version
November 18, 2014. Paper 2013-EMC-812.R1, presented at the 2013 IEEE
Energy Conversion Congress and Exposition, Denver, CO, USA, September
16–20, and approved for publication in the IEEE T RANSACTIONS ON I NDUS TRY A PPLICATIONS by the Electric Machines Committee of the IEEE Industry
Applications Society. This work was supported by the National Natural Science
Foundation of China under Project 51337004.
D. Li and R. Qu are with the School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
(e-mail: [email protected]; [email protected]).
T. A. Lipo is with the University of Wisconsin-Madison, Madison, WI 53706
USA (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/TIA.2014.2315443
Atallah et al. [4] proposed a so-called pseudo permanentmagnet (PM) machine. This machine can be regarded as the
masterly combination of a magnet gear and an electrical machine in one frame, and its excellent performances are reported.
As illustrated in [4], the torque density of the air-cooled pseudo
PM machine can be larger than 60 (kN · m)/m3 with less
than 2 A/mm2 current density, whereas its power factor can
reach as high as 0.9. However, the two air-gap structures and
low magnet usage ratio lead to large magnet consumption. In
addition, there are two rotors (one is low speed and the other
one is high speed), and the low-speed rotor is combined with
output shaft to export torque, whereas the high-speed rotor
is encircled by the low-speed rotor. Hence, its mechanical
structure is relatively complex, particularly for the low-speed
high-power applications.
Vernier permanent-magnet (VPM) machines have simple
structure and high torque density due to the so-called magnetic gear effect [5]–[8]. In addition, the VPM machine has
low pulsing torque due to its more sinusoidal electromotive
force (EMF) waveform, as compared to that of a regular PM
machine [9]; thus, it is very attractive for low-speed direct-drive
applications. VPM machines have attracted more and more
attention, and many novel VPM topologies have been proposed.
A vernier machine with a concentrated winding was presented
in [10]. Dual-rotor and dual-stator vernier topologies have been
proposed in [11], in which higher torque density of these
topologies is reported. These papers focus on the performances
such as torque density, core losses, etc., and these analysis
results show the advantages of VPM machine on torque density
and efficiency over that of the traditional PM machine.
However, different with the traditional PM machine, the
VPM machine suffers from low power factor. Spooner and
Hardock [12] showed that the power factor of the vernier hybrid
machine may be lower than 0.4. As well known, the low-powerfactor electrical machine requires a large-capacity converter,
which results in high cost in the converter. Therefore, the
improvement of power factor of the VPM machine is eagerly
required.
High power factor was reported to be obtained by the
Halbach VPM (HAVPM) machine in [13]. However, for the
HAVPM machine, the rotor iron is still the main flux path due to
the specified slot–pole structure of VPM machines. Therefore,
the absence of rotor iron heavily reduces the output torque, and
this feature is different from traditional HAVPM machines [14].
The object of this paper is to propose a new VPM topology
with advantages of high torque density and low torque ripple,
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LI et al.: HIGH-POWER-FACTOR VPM MACHINES
Fig. 1.
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Fig. 3. VPM machine stator teeth effect on the flux density distribution.
DSSA VPM machine.
TABLE I
M AIN S PECIFICATIONS OF A S INGLE -S IDED VPM M ACHINE
Fig. 2.
Phasor diagram of VPM machines.
which overcomes the low power factor of the state-of-the-art
VPM machine. The novel topology, i.e., the dual-stator spokearray (DSSA) VPM machine, is shown in Fig. 1. The power
factor of the VPM machine is analyzed in Section II. The
topology of DSSA VPM is introduced in Section III. Based
on the finite-element analysis (FEA), the DSSA machine’s
feature on power factor is highlighted in Section IV, and the
other performance indexes, such as torque waveform and torque
density, are investigated in Section V. The auxiliary mechanical
structures are proposed in Section VI. The prototype specifications and mechanical stress checking process are shown in
Section VII. Finally, the conclusion is drawn in Section VII.
II. P OWER FACTOR OF VPM M ACHINES
Although the operation principle of the VPM machine is
different from the PM machine, the relationship among the
electrical parameters can be also derived by the classical
synchronous machine phasor diagram. Therefore, the phasor
diagram is employed to study power factor.
The surface-mounted VPM machine is often driven by the
zero d-axis current Id = 0. If the resistance is neglected, as
shown in Fig. 2, the power factor can be given by
PF = 1
1 + LψsmI
(1)
where Ψm is the magnet flux linkage, I is the RMS phase current, and Ls is the synchronous inductance. Therefore, power
factor is determined by Ls I/Ψm .
Due to the special stator slot and rotor pole combination
of the VPM machine, the armature field pole pitch is much
Fig. 4. Flux plot excited by the stator windings. (a) Forty-four-rotor pole fourarmature pole VPM machine. (b) Four-pole PM machine.
larger than the rotor pole pitch. There are only half magnets
contributing to the flux per armature field pole pitch during
one armature field pole, as shown in Fig. 3, and the other half
magnets mainly produce flux leakage. All these reasons reduce
the fundamental flux density Bg and the power factor of VPM
machines.
In order to quantitatively investigate the power factor of VPM
machines, two FEA models have been built, with one 44-rotor
pole four-armature pole VPM machine and one regular fourpole PM machine, and the VPM machine’s size data are listed
in Table I. These two machines have the same stator structure,
winding configuration, and magnet thickness. Assuming that
the permeance of magnet is same as air and the steel saturation
is neglected, it is shown in Fig. 4 that the VPM and PM
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Fig. 5. Flux plot excited by magnets. (a) Forty-four-rotor pole four-armature
pole VPM machine. (b) Four-pole PM machine.
Fig. 8. Relative position of the two stators. (a) Proposed relative position.
(b) Variation of the back EMF with the relative position.
Fig. 9.
Fig. 6. Flux density distribution of the PM and VPM machines.
Main flux path of the DSSA VPM machines.
For the current-controlled voltage source inverter (VSI)-fed
PM machine, it is possible to improve power factor by the
current phase advance for regular PM machines. However, the
state-of-the-art VPM machine power factor is so low that this
control strategy leads to heavy reduction of output power.
III. T OPOLOGY AND O PERATION P RINCIPLE
OF THE DSSA VPM M ACHINE
Fig. 7. Flux linkage of the PM and VPM machines.
TABLE II
P ERFORMANCE OF S INGLE -S IDED VPM M ACHINE
machines have the same armature field. Therefore, the inductances of the two machines should be the same.
The magnet flux of the VPM machine is much smaller than
that of the PM machine, as shown in Figs. 5 and 6, respectively.
It is shown in Fig. 7 that the flux linkage of the PM machine is
almost 3 times that of the VPM machine. Therefore, the power
factor of the VPM machine is low. Table II shows that the power
factor of the VPM machine is lower than 0.66, although the
ratio of magnet thickness to air-gap length reaches almost 9.5.
The proposed DSSA VPM machine has two stators and one
rotor that is sandwiched by the two stators, as shown in Fig. 1.
The relative position angle of the two stators is defined as
zero, when the inner teeth axis is coincident with the outer stator
teeth axis. The relative position that the inner stator tooth has
half teeth pitch displacement compared to the outer stator tooth
is proposed, as shown in Fig. 8(a). The special relative position
of the two stators is the optimal design to get the maximum
back-EMF amplitude, as shown in Fig. 8(b).
The rotor adopts the spoke-array magnets with flux across
the outside/inside air gap, whereas the adjacent rotor pole
drives flux across the inside/outside air gap. After the flux
goes through the outside/inside air gap, the flux travels in the
outside/inside stator iron, back across the air gap into the rotor,
as shown in Fig. 9. Briefly, the specified relative position of the
two stators and magnet array combine the two stators together
from the view of magnetic field. Fig. 10 shows the 3-D configuration of the DSSA VPM machine active part. In addition,
there is also another stator configuration whose inner stator is
nonwinding and only works as a flux guide, as shown in Fig. 11.
The magnet can be also trapezoidal, as shown in Fig. 12, which
can make the pole shoe rectangular, and the rotor pole iron near
the two air gaps has a similar saturation level. However, this
trapezoidal-magnet rotor structure does not significantly affect
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Fig. 10. Configuration of the DSSA VPM machine. (a) Outside stator.
(b) Rotor. (c) Inside stator. (d) Global model.
Fig. 11. One of the stator configurations.
Fig. 12. Magnet topologies. (a) Rectangular magnet. (b) Trapezoidal magnet.
(c) Back-EMF comparison of the two DSSA VPM machine models.
the back EMF, as illustrated in Fig. 12, whereas the magnet
shape is more complex than that of the rectangular magnet.
Hence, the rectangle-magnet rotor is preferred.
Fig. 13 shows the magnet flux density distributions of the
DSSA VPM machine. It can be seen that the PMs excite a
44-pole field density, as shown in Fig. 13(a) and (c), in both air
gaps. The space harmonics with four poles in both side stator
yokes, as depicted in Fig. 13(b) and (d), become the highest
flight due to the modulation effect of the stator teeth on the
magnetic field, and then, the four-pole space harmonics interact
with the four-pole armature field to produce steady torque. It
is clear that the stator teeth of VPM machines work as a “pole
number transformer.”
IV. P OWER FACTOR OF DSSA VPM M ACHINES
A. Open-Circuit Field Distribution
The DSSA VPM topology is not just a double-sided VPM
machine but a novel topology, which employs the inside/outside
stator teeth flux paths to replace the outside/inside slot paths, as
shown in Fig. 14(b), and then all magnets produce the main flux
at the same time. Therefore, the magnet leakage flux is much
reduced, and the main flux is boosted.
Fig. 13. Magnet flux density distribution. (a) Inner air gap. (b) Inner stator
yoke. (c) Outer air gap. (d) Outer stator yoke.
Moreover, since the flux focusing effect can be obtained
by the spoke-array rotor structure, the air-gap flux density is
greatly improved.
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014
Fig. 15.
Flux density distribution of the DSSA VPM machine.
TABLE IV
P ERFORMANCE OF A DSSA VPM M ACHINE
Fig. 14. Flux plot at the no-load condition. (a) Single-sided, (b) dual-sided,
and (c) DSSA VPM machines.
TABLE III
M AIN S PECIFICATIONS OF A DSSA VPM M ACHINE
Fig. 16.
Variation of torque and power factor versus gamma angle.
The FEA results are summarized in Table IV. It is clear that
the power factor of the proposed machine is 0.91, although the
magnet thickness is only 3 times the air-gap length.
B. Reluctance Torque of DSSA VPM Machines
The FEA model of the DSSA VPM machine has been built,
and its size data are listed in Table III. Fig. 14 shows the
comparison of the open-circuit field distribution of regular,
dual-sided, and DSSA VPM machines that were investigated by
FEA. It is clearly demonstrated that the DSSA VPM machine
can greatly improve the flux density. Specifically, the flux
density of the machine can reach almost 1.8 T in both sides
of the air gap, as shown in Fig. 15. If the DSSA VPM machine
was regarded as the proposed two separated VPM machines,
the relative position of the two stators boosts the performances
for both of them.
The spoke-array magnets introduce rotor anisotropy for the
DSSA VPM topology. Therefore, the DSSA VPM machine has
two torque components, i.e., a reluctance torque component and
a magnet torque component.
As shown in Table IV, the d- and q-axis inductances are
5.6 and 5.2 mH, respectively, and in other words, the ratio of
q-to-d inductance is small, viz., 1.08. This rotor anisotropic
feature can be explained that the stator slot opening can even
be larger than the rotor pole pitch, and the stator tooth works as
an “anisotropic filter” to smooth the rotor anisotropic; thus, the
saliency ratio is heavily reduced. Fig. 16 shows the variations
of torque and power factor with gamma angle, which is the
electrical angle between open-circuit EMF E 0 and input phase
current I, and the gamma angle is positive when the current
phase leads the EMF phase. It can be seen that the optimal
LI et al.: HIGH-POWER-FACTOR VPM MACHINES
Fig. 17. Variation of reluctance torque/magnet torque versus gamma angle.
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Fig. 19. Torque waveform of the DSSA VPM machine.
TABLE V
E LECTROMAGNET P ERFORMANCE C OMPARISON
OF S INGLE -S IDED AND DSSA VPM M ACHINES
Fig. 18. Back-EMF waveform of the DSSA VPM machine.
gamma angle for maximum torque is at ∼18◦ , whereas the
power factor is larger than 0.86. If the gamma angle varies from
0◦ to 30◦ , the power factor would increase from 0.76 to 0.91
with almost 2% torque improvement, and the reluctance torque
component contributes from 0 to 13% of the total torque, as
shown in Fig. 17.
The inside/outside stator teeth cooperate with the outside/inside stator teeth to provide the main flux path, which
replaces the flux leakage paths introduced by stator slots. The
specified structure heavily reduces magnet flux leakage and
increases air-gap flux density. In addition, although the saliency
ratio of the DSSA VPM machine is small, the reluctance torque
of the DSSA VPM machine also contributes the output torque.
As a result of all the aforementioned reasons, the power factor
of the DSSA VPM topology is boosted to a higher level.
V. E LECTROMAGNETIC P ERFORMANCE
OF DSSA VPM M ACHINES
This section analyzes other important electromagnetic performance indexes of the DSSA VPM machine, including the
back-EMF waveform, cogging torque, and torque density.
A. Back-EMF Waveform and Cogging Torque
Benefited from the large rotor poles, few slots, and harmonic
couple effect, the back-EMF waveform of the regular VPM
machine is more sinusoidal than that of the regular PM machine
[9], and it is also true for the DSSA VPM topology, as shown
in Fig. 18.
Cogging torque results from the interaction of rotor magnets
and stator teeth, and many methods have been presented to
reduce its value, such as skewing slot or pole, using fractionalslot concentrated winding, and so on.
In terms of the interaction of rotor magnets and stator teeth,
the DSSA machine can be regarded as a PM machine with a
small number of slots per phase per pole, and its “goodness
factor” CT [15] is small. Therefore, it is an inherent feature that
the DSSA VPM topology has a small cogging torque.
Fig. 19 shows the FEA results of torque ripple and cogging
torque. It can be seen that the torque ripple percentage, i.e., the
ratio of peak-to-peak value to average value, of the DSSA VPM
machine is ∼3.5%, and the cogging torque is 42 N · m.
In summary, the DSSA VPM machine has more sinusoidal
back-EMF waveform than that of the regular PM machine,
while the pulsing torque of the DSSA VPM machine is small
due to the more sinusoidal back-EMF waveform and the specified slot–pole combination.
B. Torque Density
The FEA results show that the DSSA VPM machine can
produce 1.73 times torque compared to that of a single-sided
VPM machine; thus, the machine has larger torque density. As
shown in Table V, the DSSA VPM machine has impressive
torque density and magnet-saving capability.
This high torque density of the proposed machine is attributed to three reasons.
1) Special structure significantly improves magnet usage
ratio and greatly reduces magnet flux leakage.
2) Spoke-array magnet structure can be used to improve airgap flux density.
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Fig. 21.
End leakage flux of the proposed machine configuration.
TABLE VI
S PECIFICATION AND D ESIGN PARAMETERS OF THE P ROTOTYPE
Fig. 20. Proposed machine configuration. (a) Front view. (b) Subdivision
graph.
3) Output torque components include magnet torque and
reluctance torque.
TABLE VII
M ATERIAL OF DSSA VPM M ACHINE PARTS
VI. AUXILIARY M ECHANICAL S TRUCTURE
OF DSSA VPM M ACHINES
The frame and outer stator are assembled together by the
shrinkage fit process as the traditional PM machine does. As
shown in Fig. 20, the support structure of the rotor and inner
stator uses a cantilever structural model. The rotor active part
combines with the output shaft by the rotor support, and the
inner stator support is fixed on the frame by bolts. In order
to reduce the deformation of the inner stator support shaft, a
reinforcing ring is employed in this paper.
Rotor support is used to transfer torque from the rotor active
part to the output shaft; thus, the rotor support should have
enough mechanical strength. In addition, since the spoke-array
magnets produce heavy-end magnet flux leakage, as shown in
Fig. 21, the rotor support should be manufactured by nonmagnetic material.
VII. P ROTOTYPE AND E XPERIMENTAL M EASUREMENTS
A three-phase DSSA VPM prototype has been designed,
built, and tested here.
The design parameters and size data of the prototype are
listed in Table VI, and Table VII gives out the materials of
mechanical parts. The stator uses the traditional distributed
winding configuration and short-pitched, viz., 5/6, to reduce the
stator MMF harmonics. As a principle verification prototype,
the machine is designed to be flat shaped, which simplifies the
processing difficulty but makes the machine tend to have large
end-winding length. For the specific design cases of DSSA
VPM machines, the end-winding length can be reduced by
optimizing the ratio of diameter to stack length and that of
rotor and armature pole number. As illustrated in the foregoing
section, the DSSA VPM machine has high torque density and
smooth torque waveform. Therefore, it is suitable to the directdrive applications. However, the direct-drive machine always
means large mass and volume, and the inner stator has to use
a cantilever structural model, due to the sandwich structure of
dual stators and rotor.
A. Mechanical Checking
As a result, the stiffness of the inner stator support shaft must
be checked. As shown in Fig. 22, the maximum mechanical
stress of inner stator support due to gravity is almost 59 MPa,
which is smaller than the yield strength of carbon steel, viz.,
100–200 MPa. The maximum vertical deformation due to
LI et al.: HIGH-POWER-FACTOR VPM MACHINES
Fig. 22. Mechanical stress distribution plot. (a) Inner stator support and
Reinforcing ring. (b) Rotor support.
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Fig. 25. Flux route excited only by armature winding.
TABLE VIII
FEA C ALCULATION R ESULTS OF L OSSES
Fig. 23. Deformation plot. (a) Inner stator support and reinforcing ring.
(b) Rotor support.
Fig. 26. No-load three-phase short-circuit current.
gravity of inner stator and rotor support are 0.0025 and
0.12 mm, respectively, as shown in Fig. 23. If there is a 1/5 airgap length dynamic eccentricity, the mechanical stress will be
significantly increased, and the maximum stress reaches almost
125 MPa, as shown in Fig. 24, and the maximum deformation
is almost 0.1 mm. Therefore, the dynamic eccentricity should
be made as small as possible.
Fig. 25 shows the armature flux route, and it can be seen
that the magnet is not exposed to the armature flux. Therefore,
the low magnet losses can be predicted. Table VIII summarizes
the results of FEA loss calculation at the rated load. It can be
obtained that the magnet loss is really small.
The radial-field dual-stator PM machines are always troubled
by the inner stator thermal issues, and there are many papers
discussing on this topic, such as Sun and Cheng [16].
In order to make sure that the prototype can operate under
a permissible range of temperature rising, it is necessary to test
the temperature of the inner stator end-winding temperature rise
under at least 7-h continuous rated load operation and should
guarantee that the temperature rise is no more than 90◦ .
B. Loss Calculation and Thermal Checking
C. Demagnetization Investigation
Losses in electrical machines can be classified into the
following:
1) copper loss;
2) magnet loss;
3) core losses, including stator and rotor iron losses;
4) stray loss;
5) mechanical loss.
This section focuses on the copper, magnet, and core loss
calculation, and the results will be treated as the thermal source
to do the thermal dissipation process.
The fault tolerance of electrical machines is one of the
important performance indexes for the drive machines. There
are many fault tolerance indexes, such as ability to resist
short current, demagnetization, etc. Due to space limitations,
this section focuses on evaluating the risk of demagnetization
during the no-load three-phase short-circuit fault. As shown in
Fig. 26, the short-circuit current reaches its maximum value at
around 41 ms, and the flux density is given out in Fig. 27. It can
be seen that there is almost no demagnetization part during the
no-load three-phase short circuit.
Fig. 24. Dynamic eccentricity fault for 1/5 air-gap length. (a) Mechanical
stress. (b) Deformation plot.
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Fig. 27. FEA result of demagnetization.
Fig. 29.
Back-EMF waveforms of the prototype machine.
Fig. 30. Comparison of the 2-D FE predicted and measured phase amplitudes
of the fundamental back EMF.
Fig. 31.
DSSA VPM machine. (a) Air-gap flux density. (b) Winding function.
The back EMF of the DSSA VPM machines can be expressed as
e=
d
d
λ=
dt
dt
2π
N (θs )Bgm (θs , t) dθs
(2)
0
Fig. 28. Prototype. (a) Outer stator. (b) Rotor. (c) Inner stator. (d) Test bed.
D. Test
The prototype and its test setup are shown in Fig. 28. The
back-EMF waveform of inner and outer stators is measured at
33.5 r/min. The back EMF waveforms shown in Figs. 29 and
30 illustrate that the measured back EMFs match simulations
well. The discrepancy between the measured and simulated
line back-EMF amplitudes of outer and inner stators is about
0.5% and 0.2%, respectively. Moreover, the experiments show
that the total harmonic distortion (THD) of the line back-EMF
waveform is only 1.24%.
where e is the phase back EMF, λ is the magnet flux linkage,
N (θs) is the winding function of one-phase winding, and
Bgm (θs) is the air-gap flux density.
The harmonics of back EMF is dependent on the couple
effect between the flux density distribution and the winding
configuration, i.e., the winding function.
For the DSSA VPM machine, its rotor pole number is much
larger than that of the stator pole number, e.g., for the 22-rotor
pole, 12-stator teeth VPM machine, the pole number of magnet
field harmonic arrays excited by the interaction between magnet
MMF and fundamental air-gap permeance harmonics is shown
in Fig. 31. It is clearly seen that the harmonics arrays of the
two fields are staggered. Therefore, the DSSA VPM has lower
back-EMF harmonic distortion.
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compensate with each other. They can provide large permeance
and guide leakage flux for the contribution to the useful flux
from one side to the other side.
Moreover, the rotor anisotropy introduces the reluctance
torque, which could lead to high torque density and high power
factor for the proposed machine.
Furthermore, the DSSA VPM machine has inherent advantages, i.e., low cogging torque and low THD of the back-EMF
waveform. Therefore, the DSSA VPM machine is suitable for
the applications with strict requirements of high output torque
density and low torque ripple.
R EFERENCES
Fig. 32. Measured line voltage and current waveform (curve 1: line voltage;
curve 3: line current).
TABLE IX
C OMPARISON OF S IMULATION AND M EASURED P ERFORMANCE I NDEXES
Fig. 32 shows the measured line current and voltage waveform, and Table IX summarizes the comparison of the designed
and measured electromagnetic performances of the prototype. It
can be seen that the measured line current to produce the same
amount of torque as simulated is larger by 4% compared to that
of the designed value, which would lead to larger copper loss
and lower efficiency in response. The error between measured
and FEA values is attributed to the relative complex mechanical structure and immature manufacture, which introduces a
large no-load loss. In addition, a commercial converter is used
to drive the prototype machine, and it is not good enough
for the DSSA VPM machine. The measured power factor is
0.83, which is slightly lower than the foregoing prediction.
It is also shown in Table IX that the torque density can be
larger than 66 (kN · m)/m3 with less than 1.2 A/mm2 current
density.
VIII. C ONCLUSION
A high-power-factor vernier topology DSSA VPM machine
has been proposed in this paper. Both the structure and performance characteristics of the DSSA VPM topology have been
discussed in this paper.
At first, the power factor of normal VPM machines is investigated. The analysis shows that the low power factor is mainly
caused by heavy magnet flux leakage and low magnet utilization, viz., 50%. It has been proven that the proposed DSSA
VPM topology can greatly reduce the magnet flux leakage, and
all magnets contribute to the air-gap flux density at same time.
This improvement is benefited from the special structure, i.e.,
the inner stator tooth has half teeth pitch displacement relative
to the outer stator tooth. Therefore, both inner and outer teeth
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Dawei Li (S’12) was born in China. He received the
B.Eng. degree in electrical engineering from Harbin
Institute of Technology, Harbin, China, in 2010. He
is currently working toward the Ph.D. degree in
the School of Electrical and Electronic Engineering,
Huazhong University of Science and Technology,
Wuhan, China.
His research interests include design and analysis
of novel permanent-magnet brushless machines.
3674
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014
Ronghai Qu (S’01–M’02–SM’05) was born in
China. He received the B.E.E. and M.S.E.E. degrees
from Tsinghua University, Beijing, China, in 1993
and 1996, respectively, and the Ph.D. degree in electrical engineering from the University of WisconsinMadison, Madison, WI, USA, 2002.
In 1998, he joined the Wisconsin Electric Machines and Power Electronics Consortiums as a
Research Assistant. He became a Senior Electrical
Engineer with Northland, a Scott Fetzer Company,
in 2002. In 2003, he joined the General Electric
(GE) Global Research Center, Niskayuna, NY, USA, as a Senior Electrical
Engineer with the Electrical Machines and Drives Laboratory. Since 2010, he
has been the “Thousands of People Plan” Professor at Huazhong University
of Science and Technology, Wuhan, China. He has authored more than 50
published technical papers. He is the holder of more than 40 patents/patent
applications.
Prof. Qu is a Full Member of Sigma Xi. He has been the recipient of
several awards from the GE Global Research Center since 2003, including the
Technical Achievement and Management Awards. He was the recipient of the
2003 and 2005 Best Paper Awards, Third Prize, from the Electric Machines
Committee of the IEEE Industry Applications Society (IAS) at the 2002 and
2004 IEEE IAS Annual Meetings, respectively.
Thomas A. Lipo (M’64–SM’71–F’87–LF’00) was
born in Milwaukee, WI, USA.
From 1969 to 1979, he was an Electrical Engineer
with the Power Electronics Laboratory, Corporate
Research and Development, General Electric Company, Schenectady, NY, USA. He became a Professor
of electrical engineering at Purdue University, West
Lafayette, IN, USA, in 1979, and in 1981, he joined
the University of Wisconsin-Madison, Madison, WI,
USA, where he served for 28 years as the W. W.
Grainger Professor of Power Electronics and Electrical Machines. He is currently an Emeritus Professor at the University of
Wisconsin-Madison.
Dr. Lipo received the Outstanding Achievement Award from the IEEE
Industry Applications Society, the William E. Newell Award from the IEEE
Power Electronics Society, and the 1995 Nicola Tesla IEEE Field Award
from the IEEE Power Engineering Society for his work. He was elected a
member of the Royal Academy of Engineering (U.K.) in 2002, a member
of the National Academy of Engineering (USA) in 2008, and a member of
the National Academy of Inventors (USA) in 2013. In 2014, he was selected
to receive the IEEE Medal for Power Engineering. For the past 40 years, he
has served the IEEE in numerous capacities, including President of the IEEE
Industry Applications Society in 1994.