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A six-phase transverse-flux-reversal linear machine for lowspeed reciprocating power generation
Li, WL; Chau, KT; Ching, TW
The 2015 IEEE International Electric Machines and Drives
Conference (IEMDC), Coeur d'Alene, ID., 10-13 May 2015., p. 618
- 623
2015
http://hdl.handle.net/10722/217330
IEEE International Conference on Electric Machines and Drives
(IEMDC). Copyright © IEEE.
A Six-Phase Transverse-Flux-Reversal Linear
Machine for Low-Speed Reciprocating Power
Generation
Wenlong Li, K. T. Chau, Fellow, IEEE, and T. W. Ching, Senior Member, IEEE
favorable since both the PMs and armature winding are
accommodated in the stator and the mover only consists of
iron cores, therefore, the robust structure and system
reliability can be achieved [7]-[10]. This machine originates
from a combination of PMs into a switched reluctance
machines for solving the problem of one excitation source
[11]. According to the PM location in the stator, it can be
classified into three major categories, namely doublysalient PM (DSPM) machine [11]-[14], flux-reversal PM
(FRPM) machine [15]-[17], and flux-switching PM (FSPM)
machine [18]-[22].
PMs of the FRPM machine are mounted on surface of
stator teeth. Each stator tooth has several pairs of magnets
with different polarity mounted at its surface. For
generating operation, the flux-linkage of each coil reverse
polarity as the mover translates. Thus, a voltage is induced
in the coil. For motoring operation, when a coil is excited,
the magnetic field under one magnet reduced while another
one increases, and the mover translates towards the stronger
magnetic field. The flux-linkage variation in FRPM is
bipolar. Thus, its thrust density is greater than that of a
DSPM machine. Since the magnets are more vulnerable to
partial irreversible demagnetization, the phase inductance
should be large enough for limiting short-circuit current.
Compared to the FSPM machine that also has a bi-polar
flux linkage variation, the structure of FRPM machine is
much simpler to fabricate.
This paper presents a 6-phase transverse-flux-reversal
linear machine for low-speed linear reciprocating power
generation [23]. The proposed machine has the following
distinct features: firstly, PMs are mounted on surface of
stator teeth and the mover has no excitation sources but iron
core; secondly, by borrowing the transverse-flux concept
[24], the electric loading and magnetic loading can be
totally decoupled. The thrust density can be improved by
increasing the electric loading. In addition, the phase
inductance is also increased for avoiding PM
demagnetization; thirdly, by using the multiphase design
concept [25]-[26], the phase current can be reduced and
while the phase voltage is kept unchanged which can
further minimizes the associated copper losses; lastly but
not the least, by using the modular design for stator, each
Abstract--In this paper, a 6-phase permanent-magnet fluxreversal linear machine for low-speed reciprocating power
generation is presented. By increasing the phase number, the
phase current is reduced for the same rated power which
results in a lower ohmic loss. In addition, the thrust force
ripple can be reduced accordingly. By borrowing the
transverse-flux concept, the electric loading and the magnetic
loading is decoupled and the thrust density can be improved
accordingly. The stator of the proposed machine adopts the
modular design, and each phase is magnetically decoupled
with each other which gives more flexibility and controllability
of the generator. Based on the same topology, the proposed
machine can be extended to a machine with an arbitrary
number of phase to suit different applications.
Index Terms--Multiphase, permanent magnet, transverse
flux, flux reversal, linear machine
I. INTRODUCTION
E
LECTRO-mechanical power conversion based on the
linear reciprocating motion attracts more and more
attention recently, such as free-piston engine based power
generation for hybrid vehicle [1]-[2] and oceanic wave
power generation [3]-[5]. By utilizing the linear machine to
directly harness linear reciprocating motion, the bulky
linear-to-rotary transmission mechanism and the associated
power losses are eliminated accordingly. Among various
machine topologies, the permanent-magnet (PM) linear
machine is predominant to other machines in terms of
power density, torque/force density, efficiency and power
factor [6]. Especially, the stator-PM machine is more
This work is supported in part by a grant (Project No.
HKU710711E) from the Hong Kong Research Grants
Council, Hong Kong Special Administrative Region, China
and a grant (Project No. MYRG067(Y1-L2)-FST13-CTW)
from Research Council of University of Macau, Macao.
W. Li and K. T. Chau are with the Department of
Electrical and Electronic Engineering, The University of
Hong Kong, Hong Kong, China (e-mail: wlli@eee.hku.hk,
ktchau@eee.hku.hk).
T. W. Ching is with the Faculty of Science and
Technology, University of Macau, Macao, China (e-mail:
twching@umac.mo).
l-)))
phase can be decoupled entirely which results in an easy
control strategy for machine control and drives.
flux leakage. Fig. 2 shows the flux distribution under
different PM pole-pair numbers. It is observed that when
the pole-pair number is small there are a lot of flux flowing
in the main flux to link the phase winding, and when the
pole-pair number is large, less flux can flow in the main
flux path and more flux leakage occurs. Fig. 3 shows the
phase flux linkage and induced voltage amplitude when the
PM pole-pair number increases gradually. The amplitude of
induced voltage varies non-linearly with the flux linkage. It
is due to that a long pole-pitch can avoid the flux leakage
but with a very low flux changing velocity. The optimum
pole-pair number of PMs is 7 according to Fig. 3.
Another key parameter is the number of turns of the
phase winding. For low-speed generator, it is necessary to
achieve a large induced voltage by increasing the number of
turns of the phase winding. However, since the phase
inductance is proportional to the square of the number of
turns of the phase winding, a large self-inductance of the
phase is usually resulted. Although a large inductance is
useful for limiting the short-circuit current [29], it also has a
great influence on the capability to drive the loads due to a
large voltage drop on the reactance. Fig. 4 shows the phase
inductance and the amplitude of the induced voltage versus
the number of turns of the phase winding.
II. MACHINE DESIGN
A. Operating Principle
The FRPM machine exhibits a bi-polar flux linkage
variation pattern when the air-gap permeance varies as the
mover translates. The stator accommodates the armature
winding and PMs. Several pairs of PMs in different
polarities are mounted onto each stator tooth surface. The
mover consists of iron lamination only with poles and slots
interleaving each other. In order to develop a steady thrust
force, the PM pole-pair number, the stator tooth number
and the mover pole number should satisfy the following
equations [27]:
Nr 1
­
°°n = N ± m
s
(1)
®
N
° N s = pm
°¯
p0
where n is an integer number greater than one, Nr is the
mover tooth number, Ns is the stator tooth number, m is the
phase number, Npm is the total PM pole-pair number, and p0
is the PM pole-pair number of each stator tooth.
For the longitudinal-flux PM linear machine, the thrust
density is determined by the product of the electrical
loading and the magnetic loading. However, the two
variables cannot be increased simultaneously since the
tooth width and the slot area affects each other. To solve
this problem, a new class of electric machine named
transverse-flux permanent magnet (TFPM) machine was
proposed [28]. In this kind of electric machines, the flux
path plane is orthogonal to the mover movement plane, the
magnetic loading and electric loading which related to the
stator tooth width and the slot area can be adjusted
independently. Therefore, the thrust density is higher
compared to their longitudinal-flux counterparts.
B. Proposed Linear Machine
Fig. 1 shows a single phase module of the proposed
linear machine. The proposed machine consists of a stator
and a mover. The stator accommodates the PMs and the
phase winding. The mover only consists of iron lamination
with slotted structure. The main flux path is perpendicular
to the motion direction of the mover. By combining the
flux-reversal topology with the transverse-flux topology,
the proposed linear machine attains advantages of both
machines. By utilizing the modular stator design each phase
is decoupled to each other, therefore, it is convenient to
design one phase and then extend it into a 6-phase machine.
For low-speed operation, an appropriate pole-pair number
of PMs is desirable for generating a voltage with an
acceptable frequency. However, when the stator length is
given, a larger PM pole-pair number results in a shorter
pole-pitch which may leads to a server magnet-to-magnet
Fig. 1. A single phase module of proposed linear machine.
Based on the above discussions, the proposed 6-phase
linear machine is designed with 12 modules. The PM polepair number of each stator teeth is selected as 6, and the
mover pole number is 3, based on (1). The key design data
is shown in Table I. Compared with conventional PM
machines, the proposed linear machine has several
advantages:
• By using the flux-reversal configuration, bi-polar
operation is resulted which can fully utilized and thrust force
density is improved.
• The mover consists of iron core only without any
excitation sources. Thus, the structure is robust and reliable
for operating in a harsh environment.
• By using transverse-flux topology, the electric loading
and the magnetic loading is totally decoupled. Therefore, the
force density can further be enhanced by increasing the
electrical loading.
• Since the electric loading can be improved
independently, the phase inductance can be designed for
avoiding the PM magnetization. In addition, the armature
adopts the concentrated winding which reduces the endwinding and the associated copper loss.
• By using modular design, this machine can be extended
in to a machine with any arbitrary phase. Also, it is easier
for fabrication.
• Using multi-phase and phase-isolation design, the faulttolerance capability is improved. The complexity for control
is reduced.
Fig. 4. Self-inductance and induced voltage amplitude of a single phase
module.
TABLE I
Key Design Data
Rated power
Phase number
Rated phase voltage (RMS)
Rated phase current (RMS)
Rated speed
No. of turns per armature coil
Stator width
Air-gap length
Main slot area
Stack length
Machine length (active)
PM pole-pair number
PM dimension
PM material
PM coercivity
PM remanence
(a)
3600 VA
6
100 V
6A
1 m/s
100
318 mm
1 mm
7280 mm2
72 mm
2200 mm
72
80 mm × 12 mm × 6 mm
NdFeB
940 kA/m
1.2 T
III. ANALYSIS
Since the flux path of the proposed machine is
perpendicular to the plane of the mover translation, 2-D
finite element method (FEM) is incapable for calculating
the magnetic field for the proposed linear machine.
Therefore, 3-D FEM is applied for machine analysis and
evaluation where the governing Maxwell equation is as
following [30]:
1
∇ × ( ∇ × A) = −( J + J pm )
(3)
(b)
Fig. 2. Flux distribution under different PM pole-pairs. (a) 2 pole-pairs. (b)
9 pole-pairs
μ
where P is the permeability of the material in calculated the
region, A is the magnetic vector potential used in the 3-D
analysis, J is the current density, and Jpm the equivalent
surface current density of PMs.
The developed thrust force is expressed based on the
Maxwell stress tensor [30]-[31]:
F =³
S
G
1
( BT B − B2 E) ⋅ ndS
μ
2
1
(4)
where B is the flux density, E is the identity matrix, S is a
G
surface enclosing the calculated body, n is a unit vector
perpendicular to the surface S.
Then, as shown in Fig. 5, the circuit diagram of the
Fig. 3. Flux linkage and induced voltage amplitude.
proposed generator can be coupled to the FEM model for
evaluating the generating performance.
1
∂A
di
(5)
dΩ = ( r0 + R )i + ( L0 + L)
³³
S0 Ω ∂t
dt
where S0 is the conductor area of a single turn of the phase
winding, : is the total conductor area of each phase
winding, r0 is the phase internal resistance, R is the load
resistance, L0 is the phase inductance, and L is the load
inductance.
When the proposed linear machine operates with an
electric load, its on-load performance can be evaluated. The
efficiency can be determined at the rated condition. Since
the wave speed is variable, so for different speeds, the
induced voltage is different. For calculating its efficiency at
different speeds, a variable resistance is connected to the
phase terminal which ensures that the load current is in the
rated condition. Then by calculating the output power and
the losses, the efficiency can be obtained shown in Fig. 9. It
can be observed that the efficiency is very low under 1 m/s,
at the rated speed efficiency is 84.7%, and the efficiency
increases along with the increasing of speed. The efficiency
up to 92.5% can be resulted when the speed is 2 m/s. When
two phases, Phase A and Phase C is in short-circuit, and the
other phases are in healthy states. The current and voltage
waveforms are shown in Fig. 10. It is found that the
amplitude of the short-circuit current is about 10 A which is
19% higher of the rated current. It shows that the current is
limited due to the large phase inductance. The voltage
waveforms of the healthy phases are also similar to that
under the no-load condition which verifies that each phase
is magnetically isolated. Therefore, a high fault-tolerant
capability can be achieved.
Fig. 5. Combined circuit for generating analysis.
Induced voltage (V)
Based on the 3-D FEM, the air-gap flux density under
each stator tooth can be obtained as shown in Fig. 6. Then,
the back-EMF of the proposed generator can be obtained as
shown in Fig. 7. It can be found that the induced voltage
waveform is more sinusoidal which is more suitable for
brushless ac operation. The phase inductance also can be
calculated as shown in Fig. 8. It can be found that the phase
self-inductance is about 90 mH and the mutual inductance
is nearly zero. The phase inductances show that the mutual
inductance between each phase is negligible when
compared to the self-inductance which confirms that the
phases are magnetically decoupled to each other. Therefore,
each phase can be controlled independently and the
complexity of control algorithm can be reduced. In
addition, the faulty phases have little influences on the
other healthy phases. Furthermore, by using the 6-phase
configuration, the voltage waveform via rectifier is
smoother when compared to the 3-phase machine.
Fig. 7. No-load EMF waveforms.
Fig. 6. Air-gap flux density waveform.
Fig. 8. Phase inductance waveforms.
IV. CONCLUSION
This paper presents and analyzes a permanent magnet
linear machine dedicated for low-speed linear reciprocating
power generation. For enhancing the machine structure,
PMs are mounted on the stator teeth and the mover has no
magnets and windings. For decoupling the magnetic
loading and the electric loading, transverse-flux
configuration is adopted. For decoupling the armature
phases, each phase adopts a modular stator design,
therefore, the control flexibility can be improved and the
proposed machine can be extended to arbitrary phase
machine based on this concept. By using 3-D finite element
method, the electromagnetic performance of proposed
machine is numerically analyzed. The analytical results
verifiy the design and ensure it is suitable for proposed
application.
Fig. 9. Proposed linear machine efficiency at different operating speeds.
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Training and Public Awareness, the Award for Innovative Excellence in
Teaching, Learning and Technology, and the University Teaching Fellow
Award.
T. W. Ching (M’1993, SM’2008) received the B.Eng. and M.Sc. degrees
in Electrical Engineering from The Hong Kong Polytechnic and the Ph.D.
degree in Electrical and Electronic Engineering from The University of
Hong Kong, in 1993, 1995, and 2002, respectively.
Dr. Ching served 11 years in industry with CLP Power Ltd., Hong
Kong. He is currently an Assistant Professor of the University of Macau,
and Honorary Assistant Professor of the University of Hong Kong. His
research interests include clean energy and environment, engineering
economics, power electronic converters, variable speed drives, electric
vehicles and charging infrastructure..
Wenlong Li (S’2008, M’2012) received the B.Eng. degree from Sichuan
University in 2005, the M.Eng. degree from University of Science and
Technology of China in 2008, and Ph.D. degree from The University of
Hong Kong in 2012, respectively. Currently, he is with The University of
Hong Kong. His research interests are the areas of electric drives, electric
vehicles and renewable energy harvesting.
K .T. Chau (M’1989, SM’2004, F’2013) received his first-class honors
B.Sc.(Eng.), M.Phil., and Ph.D. degrees in electrical and electronic
engineering from The University of Hong Kong, Hong Kong, in 1988,
1991, and 1993, respectively. He is currently Professor in the Department
of Electrical and Electronic Engineering, and Director of international
research center for electric vehicles in The University of Hong Kong. His
teaching and research interests focus on electric vehicles, electric drives,
and power electronics. In these areas, he has published 4 books, 3 book
chapters, and over 150 refereed journal papers. He is a Chartered Engineer,
Fellow of the IET and Fellow of the HKIE. Prof. Chau has received many
awards: including the Chang Jiang Chair Professorship, the SAE
Environmental Excellence in Transportation Award for Education,