IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 2, JUNE 2012
403
A Combined Wye-Delta Connection to Increase the
Performance of Axial-Flux PM Machines With
Concentrated Windings
Hendrik Vansompel, Peter Sergeant, Luc Dupré, and Alex Van den Bossche
Abstract—In this paper, a combined wye-delta connection is introduced and compared with a conventional wye-connection of a
concentrated winding. Because the combined wye-delta connection has a higher fundamental winding factor, the output torque is
higher for the same current density when a sinusoidal current is
imposed. As the combined wye-delta connection has only a minor
influence on the losses in the machine, the efficiency of the machine
is also increased. The combined wye-delta connection is illustrated
in detail for an axial-flux permanent-magnet synchronous machine
with a rated power of 4 kW at a fixed speed of 2500 r/min, using finite element computation and measurements on a prototype
machine.
Index Terms—Axial-flux machine, combined wye-delta connection, concentrated winding, permanent-magnet machines, winding
factor.
Fig. 1. Considered AFPMSM topology: the YASA or SAT topology, which
consists of two rotor disks within a stator.
I. INTRODUCTION
OMPARED to distributed windings, concentrated windings have the advantage of shortened end windings, higher
torque density and efficiency, ease in winding process and
mounting and some configurations enable a low torque ripple.
However, a general disadvantage of the concentrated windings
is a lower winding factor [1], resulting in a lower output torque,
and high magnetomotive force (MMF) harmonic content, which
has a major impact on the rotor losses [2].
In [3]–[5], a combined wye-delta connection is used to increase the winding factor, and, thus, the output torque, and decrease the MMF harmonic content for machines with distributed
windings. In this paper, the use of such a combined wye-delta
connection is investigated for machines with concentrated windings. As the electromotive force (EMF) of such a concentrated
C
Manuscript received August 9, 2011; revised November 22, 2011; accepted
January 9, 2012. Date of publication February 13, 2012; date of current version
May 18, 2012. This work was supported by the Research Fund of the Ghent
University Project BOF-associatieonderzoeksproject 05V00609, Fund of Scientific Research Flanders Projects G.0082.06 and G.0665.06, the Geconcerteerde
Onderzoeksacties Project BOF 07/GOA/006, and the Interuniversity Attraction
Poles Project P6/21. Paper no. TEC-00386-2011.
H. Vansompel, L. Dupre´, and A. Van den Bossche are with the
Department of Electrical Energy, Systems and Automation, Ghent University, B-9000 Ghent, Belgium (e-mail: Hendrik.Vansompel@UGent.be;
Luc.Dupre@UGent.be; Alex.VandenBossche@UGent.be).
P. Sergeant is with the Department of Electrical Energy, Systems and Automation, Ghent University, B-9000 Ghent, Belgium, and also with the Department
of Electrotechnology, Faculty of Applied Engineering Sciences, University College Ghent, B-9000 Ghent, Belgium (email: Peter.Sergeant@UGent.be).
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/TEC.2012.2184114
winding has a zero-sequence component, circulating currents in
the delta-connected windings will cause additional losses. On
the other hand, the zero-sequence flux in the delta-connected
windings is suppressed, which will have an influence on the
flux density pattern in the teeth and consequently on the iron
losses. Therefore, this paper focuses on the aspects which may
limit the use of the combined wye-delta connection for a concentrated winding.
It will be shown that the rate of improvement of the winding factor strongly depends on the combination of pole and slot
numbers. An overview of the winding factors for some commonly used combinations is given. Finally a 16-pole–15-slot
combination is chosen and examined extensively. To illustrate
the benefits of the combined wye-delta connection, a wye connection is compared with the combined wye-delta connection
for an axial-flux permanent-magnet synchronous machine (AFPMSM) with concentrated windings. Although an axial-flux
machine is used, the same theory applies to radial machines.
A simplified overview of the used AFPMSM is given in Fig. 1.
This topology, a yokeless and segmented armature (YASA)
or segmented armature torus (SAT) topology discussed in [6]
and [7], and like AFPMSM’s, in general, is very suitable, for
e.g., wheel motors and direct drive wind energy applications
[8]–[11].
As a concentrated double layer winding is used for this topology, each individual winding is wound around one tooth. In this
way, a modular stator construction is introduced: individual stator teeth are made in advance, and are then combined to form a
solid stator as shown in Fig. 2. This way allows easy comparison
because measurements take place on the same machine; just by
0885-8969/$31.00 © 2012 IEEE
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 2, JUNE 2012
Fig. 2. YASA or SAT topology allows to make an AFPMSM topology with
a modular stator construction: individual stator teeth are made in advance, and
are then combined to form a solid stator. Each module can be easily replaced
which makes this topology very suitable for this research topic.
TABLE I
CHARACTERISTICS AND PARAMETERS OF THE CONSIDERED
AFPMSG-PROTOTYPE
Fig. 3. Phasorial diagram of one phase for the conventional wye connection
for the example with 15 slots and 16 magnets. The EMF of one coil is indicated
by E c , and the resulting EMF by E.
the EMFs of the different coils E c exist, the total phase EMF
E has an amplitude which is only a fraction kz 1 of the sum of
the amplitudes of the contributing coil EMFs. This fraction, the
so-called zone factor, is given by
sin q α2
kz 1 = (1)
q sin α2
rearranging and replacement of the stator modules, a change
from wye connection to combined wye-delta connection is
performed.
This construction method is not only advantageous for easy
manufacturing, but has general advantages quoting [12]: 1)
shortened end windings leading to higher torque density and
efficiency, 2) ease of winding process and high winding fill factor, 3) reduced mutual inductance between the machine phases
resulting in improved phase independence and fault tolerance,
and 4) reduced stator core weight due to the absence of the stator
yoke.
The comparison between a wye connection and a combined
wye-delta connection is performed by finite element computation as well as by measurements on a prototype YASA AFPMSM [13], of which the main characteristics are summarized
in Table I.
II. COMBINED WYE-DELTA CONNECTION
In [1]–[14], the winding factor kw Y 1 for a conventional wye
connection for different combinations of slots and poles, which
allow the realization of a balanced winding, is determined and
summarized in Table II. The phasorial diagram for a conventional wye connection is represented in Fig. 3 for the example
with 15 slots and 16 magnets. As phase differences between
where q is the number of neighboring slots assigned to one
phase, and α is the electric angle between two slots.
As each coil consists of two wires lying in two neighboring slots, a phase difference between these neighboring EMFs
exists, which reduces the coil EMF with a factor kp , the pitch
factor, given by
α
.
(2)
kp = cos
2
The winding factor kw Y 1 , which is calculated in Table II for
different slot and pole numbers can then be calculated by
kw Y 1 = kz 1 kp .
(3)
In the considered example of 15 slots and 16 magnets, the
zone factor kz 1 equals 0.9567 and the pitch factor kp equals
0.9945 leading to a winding factor kw Y 1 of 0.9514.
As for easy construction, the individual winding is wound
around one tooth, the pitch factor cannot be changed. However,
by using the combined wye-delta connection, the zone factor
can be increased and thus the winding factor. The phasorial
diagram for a combined wye-delta connection is represented in
Figs. 4 and 5 for the example with 15 slots and 16 magnets. By
assigning the coils to the wye or the delta connection, depending
on whether the phase of the coil best suits with the phase of the
wye or delta connection, a higher zone factor can be obtained. In
the 15-slots–16-magnets configuration, the zone factor increases
from
kz 1 =
1 + 2 cos (12◦ ) + 2 cos (24◦ )
= 0.9567
5
(4)
VANSOMPEL et al.: COMBINED WYE-DELTA CONNECTION TO INCREASE THE PERFORMANCE OF AXIAL-FLUX PM MACHINES
405
TABLE II
WINDING FACTORS FOR DIFFERENT SLOT–POLE COMBINATIONS WHICH REALIZE A BALANCED THREE-PHASE SYSTEM1
Fig. 4. Phasorial diagram of one phase for the combined wye-delta connection
for the example with 15 slots and 16 magnets. The EMF of one coil is indicated
by E c . The resulting EMFs of the wye- and delta-connected coils are indicated
by E Y and E Δ , respectively.
to
1 + 2 cos (12◦ ) + 2 cos (6◦ )
= 0.9891
(5)
5
which is an increase of 3.4%. The corresponding winding diagram and actual connections between the individual coils are
given in Fig. 6. The same can be done for all combinations of
slot and pole numbers. The obtained winding factors are summarized in Table II.
In order to have the same output voltage in the wye connection as well as in the combined wye-delta connection, the
kz 1 =
Fig. 5. Three-phase phasorial diagram for the combined wye-delta connection
for the example with 15 slots and 16 magnets. The EMF of one coil is indicated
by E c . The resulting EMFs of the wye- and delta-connected coils are indicated
by E Y and E Δ , respectively.
√
delta-connected coils should have 3 times the numbers of the
wye-connected coils. As the slot width is the same for wyeand√delta-connected coils, the wire section should be reduced
by 3. In this way, Joule’s losses in both the wye- and deltaconnected coil windings are equal. In the prototype machine,
the winding consists of two coils per tooth, one on each side
of the tooth (see Fig. 1), and are put in parallel. For the wyeconnected teeth, on each coil 72 turns are placed in four layers
of 18 turns, while on the delta-connected coils 125 turns are
placed in five layers of 25 turns. The wire diameter of the wyeand delta-connected teeth is 1.05 and 0.8 mm, respectively. This
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 2, JUNE 2012
Fig. 6. Winding diagram and actual connections between the individual coils
in the combined wye-delta connection for the example with 15 slots and 16
magnets.
combination of turn number and wire diameter results in the
same output voltage and Joule’s losses in the windings. Finding
the number of turns per layer, the number of layers and winding diameters in order to have a good copper filling factor for
both wye- and delta-connected coils becomes more complicated
as for the wye-connected machine. However, enameled copper
wires are offered in many diameters. Moreover, the modular
stator concept simplifies the winding process as each tooth can
be wound outside the machine. Therefore, it is still possible to
obtain good copper filling factors.
The combined wye-delta connection will also have an influence on the losses in the machine. Due to the zero-sequence flux
in the delta-connected coils, circulating currents are present and
will result in additional Joule’s losses in the copper windings.
As will be shown in the following paragraphs, the losses corresponding to the circulating currents in the copper windings
are minor compared to global losses. As the circulating current in the delta-connected coils mitigates the zero-sequence
flux, the iron losses in these teeth are smaller comparing to the
wye-connected teeth and result in global lower iron losses.
Next to the Joule losses in the copper windings and the iron
losses in the teeth, the combined wye-delta connection also has
an impact on the eddy current losses in the permanent NdFeB
magnets as the airgap magnetic field harmonic content is changing. The magnitude of the eddy current losses is limited to ±3
and ±9 W for no-load and load, respectively. The increase in
magnet eddy current loss due to the wye-delta connection for
the examined prototype is only 3.5%, i.e., ±0.3 W, which is
negligible to the global losses and is, therefore, not taken into
account in the comparison.
III. FINITE ELEMENT MODEL (FEM)
The theory explained in previous paragraph is evaluated using
an FEM. The FEM is the same for both wye and combined wyedelta connections, but differs in the way in which the currents
are imposed.
Because AFPMSM’s have an inherent 3-D structure, 3-D
FEMs should be used in simulations. As these 3-D FEMs are
very time consuming, “quasi-3-D” [15], [16] approximations
using multiple 2-D FEMs at different radii are often used (see
Fig. 7). The global solution is found as a weighted summation
over the different 2-D FEM solutions. In this way, the computation time can be reduced. In such a 2-D FEM, the whole
circumference of the machine is modeled, i.e., 15 teeth and 16
magnets. As the magnets are in an North-South (NS) topology [17], only half of the machine needs to be modeled by
Fig. 7. Part of one of the six 2-D FEM solutions in which the circumference
of the AFPMSM is modeled at a given radius. Left boundary is the symmetry
axis of the vector-potential problem. Flux density levels are in Tesla.
applying the Neumann boundary condition at the center part
of the teeth. In circumferential direction, obtaining the right
solution requires the use of periodic boundary conditions. An
example of such a 2-D FEM is shown in Fig. 7.
The torque of the generator is calculated by evaluating the
Maxwell stress tensor along a line in the center part of the airgap.
As the Maxwell stress tensor is very sensitive to numerical noise,
a very fine mesh around the tooth tip and the airgap is required
to obtain the right torque values.
As this paper focuses on the stator teeth, an anisotropic material model based on the magnetic energy (variant on [18]) is
applied. The anisotropic material model calculates the magnetization vector M as a function of the induction vector B. The
equation for the magnetic potential A equals
1
∇ × A − ∇ × M (∇ × A) = Je
(6)
∇×
μ0
where Je is the external current density.
The magnetic potential equation is solved statically for different rotor positions using ±170.000 second-order elements.
The voltage waveform is calculated a posteriori based on the
calculated flux waveforms of the individual coils. The current
waveforms, that are imposed by specifying Je , are calculated
iteratively based on the voltage waveform in case of a resistive
load. The circulating current in the delta-connected coils, for
no load as well as full load, is done by iteration: for each static
simulation, the current is modified until the zero-sequence flux
is mitigated.
The iron losses are calculated a posteriori, based on the simulated flux density patterns. The used model for the iron losses
is based on loss separation [19], [20] and is explained in detail
in [21].
The parameters in the anisotropic material model and the
loss model are fitted from data retrieved by measurements on
an Epstein frame. As the used material is grain oriented (GO),
magnetic properties vary with respect to the direction in which
VANSOMPEL et al.: COMBINED WYE-DELTA CONNECTION TO INCREASE THE PERFORMANCE OF AXIAL-FLUX PM MACHINES
Fig. 8.
Prototype AFPMSM: stator view without rotors.
407
Fig. 9. Simulated and measured back EMF waveforms of two consecutive
teeth. For the 15-slot–16-pole combination, a shift of 12◦ exists between adjacent
coil back EMFs.
the field is applied. Therefore, strips in seven different directions, i.e., 0◦ , 15◦ , 30◦ , 45◦ , 60◦ , 75◦ , and 90◦ , were cut out
of a insulated GO steel sheet. The complete determination of
the material required measurements for various magnetic field
amplitudes and different frequencies.
IV. SIMULATION RESULTS AND EXPERIMENTAL VERIFICATION
To check the validity of the simulations, a prototype AFPMSG
shown in Fig. 8 was built. In Table I, the main characteristics of
the suggested AFPMSM are listed.
As only an increase of 3.4% in winding factor is expected,
simulations and especially measurements should be done with
great accuracy. However, when both wye and combined wyedelta-connected generators are connected to the same resistive
load at the same speed, the power is equal to the square of
the terminal voltage. This means that the output power of the
combined wye-delta connected generator will be 1.069 times the
output power of the wye-connected generator when connected to
an equal resistive load at the same speed. This increase of 6.9%
should be detectable in simulations as well as in measurements
on a prototype.
For simulations as well as for the measurements, a three-phase
resistive load with a phase resistance of 30 Ω is chosen, and the
reference speed is set to the nominal speed of 2500 r/min. The
corresponding current delivered by the generator will in both
cases not exceed the nominal current.
To perform measurements on the suggested prototype AFPMSG, an experimental setup was built. In this setup, the AFPMSG is connected to a two-pole 7.5-kW induction motor via a
torque sensor. This induction motor is fed by a 11-kW inverter
that is controlled by laboratory virtual instrumentation engineering workbench. An optical position sensor is used to obtain
the shaft speed, and a voltage measurement on the terminals of
the AFPMSG is performed. Although each phase consists of
five teeth, the winding of each individual tooth is accessible.
The data retrieved from voltage, torque and speed measurement
are sampled by a National Instruments data-acquisition system
with a sampling speed up to 250 ksamples/s.
Fig. 10. Simulated and measured back EMF waveforms of three wyeconnected teeth and two delta-connected coils. Circulating currents in the deltaconnected teeth mitigate zero-sequence components in the back EMF of the
delta-connnected coils.
In all subsequent figures, simulated and experimental data
will be represented in the same axes to allow easy comparison.
In Fig. 9, the no-load EMFs of two consecutive teeth are presented. Very good correspondence between simulated and measured data is found. As illustrated in the example in Section II,
a shift of 12◦ exists between adjacent coil EMFs. Furthermore,
it can be noticed that apart from fundamental harmonics, the
coil EMFs contain additional harmonics. In the delta-connected
teeth, the triple-harmonics in the flux will give rise to circulating currents. These currents strongly mitigate zero-sequence
components in the coil EMFs (see Fig. 10).
Simulation results of the wye and combined wye-delta connection are given in Table III. As predicted by the theory, a
higher average torque output is achieved by the combined wyedelta connection: an increase of 7.8% and 7.2% for simulations
and measurements, respectively, which is slightly above the expected 6.9%.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 2, JUNE 2012
Fig. 11. Simulated and measured waveform of the circulating current in the
delta-connected coils. Corresponding Joule’s losses are limited due to the small
resistance of the delta-connected coils.
TABLE III
COMPARISON SIMULATED DATA FOR WYE AND COMBINED WYE-DELTA
CONNECTION: MACHINES CONNECTED TO A RESISTIVE LOAD OF 30 Ω
Fig. 12. Simulated and measured phase voltage and phase current for the wye
connection of the coils.
In Fig. 11, the circulating current present in the deltaconnected coils is shown. Due to the relatively high inductance
of the winding, the amplitude of the circulating current is limited. As the multilayer 2-D FEM does not take into account
the effects of the end windings on the inductance, the simulated circulating current is higher than the measured one. As
the resistance of a delta-connected winding is calculated to be
0.2 Ω, the Joule losses in the copper losses are very limited.
Table III also shows that the no-load iron losses are slightly reduced. This small decrease can be explained by the absence of
the zero-sequence components in the flux-density distribution
in the delta-connected teeth.
The full-load phase voltage and current waveforms of the
wye and combined wye-delta connection are shown in Figs. 12
and 13, respectively. Good correspondence between simulations
and measurements is found. Note that the full-load phase voltage waveforms are deformed due to the armature reaction. As
can be seen in the current waveform of the delta-connected teeth
in Fig. 13, the waveform is a superposition of the fundamental
sinusoidal component and the circulation current. However, the
effect of these circulation currents in the total Joule’s losses in
the copper windings are limited and the losses in both connections are nearly equal.
For both wye and combined wye-delta connection, the electric
power output was measured using a three-phase power analyzer.
Power outputs of 3776 and 4048 W were measured, which are
in good correspondence with the simulated ones in Table III.
Fig. 13. Simulated and measured phase voltage and phase current for the
combined wye-delta connection of the coils. Values for the wye- and deltaconnected coils are indicated separately. Note that the current in the deltaconnected coils is a superposition of the load current and the circulating current.
Moreover, the power ratio of the combined wye-delta connection
is 7.2% higher than those of the wye connected, which means
that the fundamental winding factor is increased with 3.5%.
VANSOMPEL et al.: COMBINED WYE-DELTA CONNECTION TO INCREASE THE PERFORMANCE OF AXIAL-FLUX PM MACHINES
409
TABLE IV
COMPARISON SIMULATED DATA FOR WYE- AND COMBINED WYE-DELTA
CONNECTION: FUNDAMENTAL SINUSOIDAL CURRENT WITH AN RMS VALUE
OF 6.67 A IS IMPOSED IN PHASE WITH THE BACK EMF
Fig. 14. Simulated phase voltage and phase current for the combined wyedelta connection of the coils. Values for the wye- and delta-connected coils
are indicated separately. Note that the current in the delta-connected coils is a
superposition of the load current and the circulating current.
Subtraction of the input mechanical power of the prime mover
and the electrical power is used to estimate the losses in the machine. Losses at no and full load are significantly higher than
the simulated ones: ±132 and ±250 W, respectively for both
machines. However, next to the Joule losses in the copper and
the losses in the iron of the stator teeth that are evaluated in
the simulations, also bearing, windage and Joule’s losses due to
eddy currents in the magnets are present when performing measurements on the prototype. Therefore, the measured efficiency
of both machines is only 94%. As the output power increases for
the same active mass, i.e., mass of copper windings, stator teeth
iron, magnets, and rotor back iron, the power density increases.
Fig. 15. Simulated full-load torque waveform of the wye- and combined wyedelta connection. Although a higher average torque output is achieved by the
combined wye-delta connection, the torque ripple is higher than that for the wye
connection.
iron losses are even lower in the combined wye-delta machine
due to the absence of triple harmonics in the delta connected
teeth. As the losses remain the same while the output power
increases, the efficiency of the machine improves.
Despite the increase in torque and efficiency, Fig. 15 shows
that the combined wye-delta connection has higher torque
ripple.
VI. CONCLUSION
V. HIGHER EFFICIENCY
In previous section, the increase in torque due to the higher
winding factor of the combined wye-delta connection was illustrated. Good comparison between simulations and measurements proved the validity of the FEM. In this section, as in [22],
the influence of load on the efficiency is studied. Therefore,
simulations in which a fundamental sinusoidal current with an
rms value of 6.7 A is imposed in phase with the back EMF are
done for both wye and combined wye-delta connection. For the
combined wye-delta connection, the voltage and current waveforms are shown in Fig. 14. However, this time the focus will
be on the efficiency of the machine during operation.
Comparison of the data in Table IV shows that the no-load
losses due to the circulating current in the wye-delta-connected
only result in small Joule’s losses. No load as well as full-load
In spite of the many advantages of concentrated windings,
an important drawback is that most configurations have a lower
winding factor. In this paper, it was illustrated theoretically that
in most configurations the winding factor can be increased by
using a combined wye-delta connection instead of a common
wye connection.
The effectiveness of such a combined wye-delta connection
was illustrated for a 16-magnet–15-slot YASA AFPMSM, by
using finite element computations and measurements on a prototype machine. The increase in output torque is comparable
with the increase in winding factor, as theoretically expected.
On the other hand, the losses in the combined wye-delta connection were the same as those for a common wye-connected
machine. As the power for the same machine was increased
without supplementary losses, the machines efficiency is
increased.
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2005, pp. 1331–1336.
Hendrik Vansompel was born in Belgium in 1986.
He received the Bachelor’s and Master’s degrees in
electromechanical engineering from Ghent University, Ghent, Belgium, in 2008 and 2009, respectively,
where he is currently working toward the Ph.D. degree at the Department of Electrical Energy, Systems
and Automation.
His research interests include electrical machines
modeling and design, particularly for sustainable energy systems.
Peter Sergeant received the M.S. and the Ph.D. degrees in electromechanical engineering from Ghent
University, Belgium, in 2001 and 2006, respectively.
He is a Postdoctoral Researcher for the Fund of
Scientific Research Flanders since 2006, and a Researcher in the University College Ghent, Ghent,
Belgium, since 2008. His current research interests include numerical methods in combination with
optimization techniques to design nonlinear electromagnetic systems, in particular, electromagnetic
actuators.
Luc Dupré was born in 1966. He graduated in electrical and mechanical engineering in 1989 and received the degree of Doctor in applied sciences in
1995, both from the University of Gent, Belgium.
Currently, he is full professor at the Faculty of
Engineering and Architecture of Ghent University,
Belgium. His research interests mainly include numerical methods for electromagnetics, modeling and
characterization of soft magnetic materials, micromagnetism, inverse problems and optimization in
(bio)electromagnetism.
Alex Van den Bossche received the M.S. and Ph.D.
degrees in electromechanical engineering from Ghent
University, Ghent, Belgium, in 1980 and 1990, respectively.
He was with Electrical Energy Laboratory, Ghent
University, where since 1993, he has been a Professor
in electromechanical engineering. He is an author of
the book Inductors and Transformers for Power Electronics (Boca Raton, FL: Taylor & Francis, 2005). He
was a starter of the spin-off companies Inverto n.v.
(1990) and recently Alenco n.v. (2009). His research
interests include electrical drives, power electronics on various converter types
and passive components and magnetic materials. He is also interested in renewable energy conversion.