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Abstract— The study of Flux Switching Generator with
Permanent Magnets in the Stator has gain relevance due to new
developments made in permanent magnets, giving this type of
machine high power density. However this is correlated with
increases Ripple Torque. In order to attenuate this ripple torque it was studied the use of
two rotors so that the forces applied to each individually would
cancel each other out. The 3D geometry resulted in around 60%
decrease in ripple torque, when no load applied and over 95%
decrease for the loaded case.
To simulate its behaviour with load, it was used an AC/AC
converter connected to a simplified version of a boing 767
electrical load. The currents generated by this resulted in the
appearance of back-EMF, which decreased total EMF output.
The current also influenced the magnetic energy distribution
resulting in increased ripple torque for each individual rotor, but
decreased the total ripple torque of the model. Keywords—Flux-Switching generator, FEM, Magnetic Field,
Permanent Magnets, Ripple Torque.
I. INTRODUCTION
HIS paper proposes a method to reduce the ripple torque of
FSPM (Flux-Switched Permanents-Magnet) generator by
not only adopting a 3D approach for the magnetic flux path but
also, by keeping a the magnetic energy in the rotor constant.
The design represented in Fig.1, is the proposed configuration.
With the new developments in PM (Permanent-Magnets) this
type of machines jumped to the spotlight due to their high
power density and performance. However placing the PM in the
rotor limited the rotation speed of the machine, mainly due to
centrifugal forces that could damage or demagnetize them. The
. *Email: joselopesdasilva@ist.utl.pt
alternative reached was placing them in the stator, solving the
mechanical stress in the PM but resulting in a strong ripple
torque component, as referred in [2].
The ripple torque could compromise the structural integrity
mainly during acceleration, since at high speeds the inertia
would filter this ripple torque, as stated in [3], the biggest issue
would be at low speeds. Considering the proposed usage of the
studied generator is directly coupled with a turbines, such as the
one in a Boeing 767, same method used in dissertation [4],
which was considered as load for the electrical study in this
paper, it will be subdued to constant velocity.
The adopted 3D solution will grant the model the ability to
duplicate the fluxes variation rate, while keeping the rotor’s
speed constant, increasing however the magnetic reluctance,
since in a path there is now 2 air-gaps.
Fig 1. FSPM generator, with 3D magnetic flux path. Components: coils
(brown); stator body (dark grey); stator saliences (green); rotor (yellow); magnets, pushing down (blue), pushing up (red).
Other methods already studied to reduce ripple torque are
Attenuation of Cogging Torque in Flux
Switching Electrical Generators with Permanent
Magnets in the Stator
José L. Silva *ª, Paulo J. C. Brancoª
ª Instituto Superior Técnico, University of Lisbon 1049-001 Lisbon, Portugal
T
2
either injecting controlled current in the windings, as mention
in studies [5] and [6], or filleting the stator and rotors salience,
smoothing the difference in magnetic reluctance throughout
each cycle [7]. In this study the main focus was utilizing the
magnetic forces applied to the rotors to counteract each other.
This method allied with the current injection will be the main
contributors for reducing ripple torque. The disposition of the
stator salience will show significant reduces in the variation of
the magnetic energy, in the rotor, while maintaining sufficient
levels of EMF.
Utilising a FEM software it is possible to understand the
behaviour of the magnetic flied throughout the model, and
retrieve the EMF wave in each coil. Afterwards the model was
tested with an AC/AC converter with the respective load
presented in dissertation [4], so that the effect of currents on the
model can be studied via a FEM software.
II. FSPM GENERATOR AND RESPECTIVE LOAD
CHARACTERISTICS
The FEM software used will be connected to a block
simulation tool. This will allow a better prediction on the
behaviour of the machine when subdued to a load. The FEM
analysis will study the internal aspects of the machine;
Magnetic field, EMF, Magnetic energy and Torque; while the
block simulation will provide with inputs such as power losses
and current in windings.
A. FSPM Generator
In order to reduce power loss and ripple torque, the design
was thought so that the magnetic reluctance between the PM
and the rotor stays constant. With it, the system is expected to
always be balanced, resulting in no force applied to the rotor,
since magnetic energy does not change with the rotor position.
Constant magnetic reluctance, means constant flux, therefore
no EMF. By dividing the stator salience, as seen in Fig 2, the
flux can be directed via a path, imposing the needed variation
of flux. On Fig 2 there are codes composed of a number [1, 2]
and 2 letters, the first letter [a, b, c] and the second A to F. The
converter in Fig 8 has two rectifiers, the number determines the
rectifier. The first letter corresponds to the phase of a rectifier,
the second letter is associated with the stator leg. The arrows
determine if the rotation is clockwise or counter-clockwise.
(a)
(b)
Fig 2. Top view of the machine model, with magnetic distribution
and direction and windings connections: (a) bottom stator and rotor
piece; (b) top stator and rotor piece
1) Magnetic flux path/coil placement
The proposed geometry forces the magnetic flux to follow
one of the stators salience, as seen in Fig 3. This method
increases the number of coils and, while keeping the total
magnetic flux in the magnet constant, increase the discrepancy
between the maximum and minimum magnetic flux.
In Fig 3 the arrows represent the magnetic flux’s x and y
components. Aligning a rotor salience with stator’s salience
will direct the magnetic flux through that path, this
configuration increases the total magnetic reluctance and
magnetic field density. When the rotor’s salience is biding both
stator saliences flux divides between the two and afterwards
starts aligning with the other stator salience. This transition,
considering the winding placement shown in Fig 3, allied with
the direction of the windings, counter or clock wise, facilitates
the appearance of a seemly ideal harmonic wave form for the
EMF, supported by the results ahead.
(a)
(b)
(c)
Fig 3. Top view of a stator leg, with the flux behaviour in a x, y
plane, for different rotor positions: (a) aligned with the right salience,
(b) equal interaction with both salience, (c) aligned with the left
salience.
Fig 4. EMF of each stator leg’s arm.
3
By analysing Fig 4, it can be assumed the best series
connection possible is as shown in Fig 5.
Fig 5. Illustrative linear representation of the electrical connections
between windings
The resulting EMF, for each leg, is the result of connecting
all windings in series. The variation of flux affecting each
winding will result in the waveform observed in Fig 6.
Fig 6. Wave form of the EMF for each stator’s leg
The connections established in Fig 5, give the model 6
phases. Those allow utilizing either a system with six-phases or
two three-phases. To make two three phase systens the
connections would be as stated in Fig 5.
Fig 7. EMF phases arranged in two 3 phase systems.
2) General dimensions of the model
As the model is now, the necessary dimensions to withstand
a 90kVA load are presented in Tab 1. This result in the volumes
of each component seen in Tab 2.
Tab 1. 3D model, 6 legged common stator
Stator’s outer radios 324 mm
Stator’s inner radios 172 mm
Rotor’s outer radios 170 mm
Rotor’s inner radios 130 mm
Rotor’s and stators depth 80 mm
Magnets outer radios 324 mm
Magnets inner radios 270 mm
Magnets surface 3200 mm2
Magnets depth 4 mm
Tab 2. Volume of material needed
Material (dm3)
Iron NdFeB Copper
laminated composite
12.759 24.266 0.168 13.476
B. Chosen load, specifications
Assuming a constant rotation speed of 3000 rpm, the
resulting generated frequency is 400 Hz. In order to simulate
the one of the uses of the machine, the equivalent 6 phase
generator will be followed by an AC/AC converter and a
simplified version of a Boing 767 plane.
1) AC/AC converter
The chosen rectifier is a 12 pulse rectifying bridge found in
book [8]. This rectifier provides a smother DC level, and due to
the transformers, one can increase the voltage output of the
machine, decreasing current in windings, consequently joule
losses. The DC level is composed by a capacitor, and is
followed by a inverter. With this connection even with an
unbalanced load the current in the machine stays evenly
distributed. After the oscillator a low pass filter is crucial in
order to remove the high frequency harmonics.
Fig 8. AC/AC converter proposed for each phase of the generator, with the
output of 115 V, 400Hz
2) Load specifications
The full use of this machine will be at high velocities,
therefore, in order to simulate its behaviour and establish a
comparison with the machines design for the same purpose,
such as in dissertation [4], it will be used the load and turbine
of a Boeing 767, described in [9]. This 90kVA load can be
divided into 3 parallel three-phase RL loads, 1 single-phase RL
4
load and one 12 pulse converter connected to a couple of R
loads, as specified.
Fig 9. Simplified electric load of a Boing 767 plane.
Tab 3. Loads value for the simplified model of a Boeing 767 in [9],
with a 90kVA power demand
Load Phase R(Ω) L(mH)
A A 0.84 0.304
B 2.41 1.065
C 2.49 1.129
B A 14.28 2.752
B 14.28 2.752
C 14.28 2.752
C A 2.15 0.597
B 1.91 0.712
C 1.91 0.712
D A 4.34 0.504
B - -
C - -
E - 0.068 -
F - 0.076 -
III. RESULTS
A. Electromotive Force
The influences of the magnetic field created by the current
circulating in the coils influences the magnetic flux, resulting in
a significant change in the EMF. This influence can be seen in
Fig 10.
Fig 10. Magnetic flux change due to application of a load in a stator
leg’s arm.
The contribution of the winding’s current in the magnetic
flux is responsible for the appearance of back-EMF. This will
contradict the 1º harmonic and increase the 3º influence. The
difference in EMF output between the two is evident in Fig 11
and Tab 4.
(a)
(b)
Fig 11. Comparison between having and not a load of 90kVA on the
EMF: (a) FFT, (b) waveform.
Using a Simulink model it was possible to reach the
interaction between the load and the generator, the results are
presented in Tab 4.
Tab 4. Electrical characteristics of the generator when connected to
the specified load, at 3000rpm.
No Load Load
EMF1º h,RMS (V) 9.13 5.51 (−40%)
EMF3º h,RMS (V) 0.48 1.55 (+223%)
EMFRMS (V) 9.14 5.73(−37.3%)
The EMF decreased, due to applying the load. The
configuration used for the study of the generator was as
established by Tab 5. The total power output surpasses the load
requirements due to losses within the generator and converter.
Tab 5. Electrical characteristics of the model with electric load
application.
Turn per coil EMFRMS (V) CurrentRMS (V) S (kVA)
80 731 24.02 105.38
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B. Ripple torque
1) No load
By coupling the rotors, their ripple torques will contradict
each other, greatly reducing their influence. The result of each
rotor can be seen in Fig 12, Fig 13 and in Fig 14 their combined
contribution. In Fig 15 it is seen the reconstructed signals the
FFTs
Fig 12. FFT of the Ripple Torque signals generated by the machine
without electrical load, at 3000 rpm, top stator.
Fig 13. FFT of the Ripple Torque signals generated by the machine
without electrical load, at 3000 rpm, bot stator.
Fig 14. FFT of the Ripple Torque signals generated by the machine
without electrical load, at 3000 rpm, complete machine.
Fig 15. Ripple Torque behaviour with no electrical load at 3000rpm,
nominal torque 286 Nm.
2) With load
The current alters the behaviour of the magnetic energy of
the model. The presence of current in the windings significantly
reduces the magnetic energy in each rotor salience since the
magnetic flux produced by the coils opposes the one produced
by the magnets resulting in the difference notices in Fig 16.
Fig 16. Response of the magnetic energy on a rotor, at 3000rpm with
and without a load of 90kVA.
Since the ripple torque is obtain from the magnetic energy
variation, it is easy to assume, even though the variation rate in
the no load case is higher, its harmonic components, apart from
the 1º harmonic, is more significant. This will result in, as seen
in Fig 17, a much strong harmonic component for the ripple
torque in the load case.
(a)
6
(b)
Fig 17. Ripple torque in a rotor salience, at 3000rpm with and
without a load of 90kVA: (a) FFT signal; (b) obtained signal.
The effect of all saliences in a rotor results in the behaviour
examined in Fig 18. In both cases only the 3rd and 8th of each
salience remain.
(a)
(b)
Fig 18. Ripple torque of the top rotor at 3000rpm with and without a
load of 90kVA: (a) FFT signal; (b) obtained signal.
The top and bottom rotors are 60º apart, considering the 1st
harmonic stands at 400 Hz. This means since, as seen in Fig 18,
the 3rd harmonic, at 1.2 kHz is the most significant, the ripple
torque discrepancy between them is 180º, as evidence in Fig 18.
By adding the effect on the two rotors, the ripple torque value
is significantly reduced.
Fig 19. Ripple torque in each rotor and the complete model, at 3000
rpm with a 90kVA electric load.
The end result is a clear reduction in the ripple torque when
applying the electric load. Considering the nominal torque
provided by the turbine, in order to generate enough power for
the 90 kVA electric load is over 286 Nm, the value reached for
the ripple torque is insignificant.
(a)
(b)
Fig 20. Ripple torque of the model at 3000rpm, with and without a load
of 90kVA: (a) FFT signal; (b) obtained signal.
7
C. Thermal
By increasing the EMF output, the current can will be reduce
since the power output is the same. That process reduces the
power losses in the coils due to joule heating. However both
magnets and the soft-iron are susceptible to losses due to
induced currents in the iron fragments.
Using a natural convection heat transfer coefficient
estimation calculator, downloaded from [12], it is possible to
discover the natural convection heat transfer. The obtained
value is seen in Tab 7. As for the power losses, those have to be
divided into several categories: windings, rotor saliences, stator
saliences, magnets and stator body. The winding losses are
given by the joule heating formula while the others are from the
manufactures power loss per kg per magnetic field variation in
[13]. The power losses reached are presented in Tab 6.
Tab 6. Power losses in the different components of the model, while
connected to the specified electric load.
Windings
(𝐖)
Rotor
saliences (𝐖)
Stator
saliences (𝐖)
Stator
body (𝐖)
Magnets
(𝐖)
399.2 585.1 677.4 658.8 115.6
The components with the loads thermal limit are the
windings insulation which are around 100ºC. This is not
possible with a natural convection heat transfer, since a thermal
simulation situates the overall temperature over 239ºC.
Tab 7. Convection heat transfer ratio related to the maximum
temperature present in the model while connected to the specified
electric load
h(𝐖 (𝐦𝟐 ∗ 𝐊⁄ )) 5.77(natural) 15(forced)
MAX temp(ºC) 241 66.2
(a)
(b)
Fig 21. Heat distribution in the model while connected to the
specified electric load: (a) natural convection, (b) forced convection
The purpose of the machine is to operate coupled to a turbine
rotating axis, this will result in a constant flux of air passing
through the generator. If the heat transfer resulting from that
environment is sufficient then no other form of cooling is
needed.
IV. CONCLUSION
A. Final analysis of the study
Electric machines with permanent magnets and
concentrated windings in the stator are commonly known for
their high torque ripple. However the model reached shows
significant improvements in that regard specially while
carrying and electric load. While normally the effects of the
load increases the torque ripple, with the design presented the
torque ripple is insignificant when compared with the nominal
torque provided by the planes turbine.
Reducing the magnetic energy variation limited the
production of EMF, which resulted in an increased number of
turn per coil to reduce the injected current. This current,
simulates the application of the load and reduced the EMF
RMS by 37% reviling a high contribution of the back-EMF,
created by the currents in the windings.
The initial thermal analysis supports the idea of a need
to have force cooling the system. However, since the machine
is design to integrate a turbine axis, the model will have a
stream of cold air passing through its gaps, potentially
abolishing the need for additional cooling systems.
Overall the model reached its main objective, but the
size of the model could turn out to be problematic. There are
some improvements required for it to be considered a viable
machine, nevertheless the results support the possibility for
this design to be a plausible solution for the torque ripple
problem in Permanent Magnets flux switching Generated.
B. Future work
As mentioned before the size of the model and its high
dependence on the injected currents are easily the issues that
need to be addressed. To do so only one aspect needs to be
improved, the variation of magnetic flux. The main focus
should be them:
Optimising the length of the magnets;
8
Change the rotors configuration;
Increase the number of legs in the stator.
By increasing the length of the magnets, one can increase
their contribution on the magnetic flux flow, however in doing
so, one must take into consideration the magnetic saturation
and the path chosen by the magnetic flux.
Changing the rotor configuration can increase the
magnetic flux variation, however the major setback is the
increased torque ripple. The proposed rotor would be as seen
in Fig 22 (b), opposed to the minimal torque ripple solution
reached in Fig 22 (a). One would have to outweigh their
differences to see if the change is valid.
(a)
(b)
Fig 22. Rotor configuration: (a) used to minimize ripple torque; (b)
proposed to maximize EMF.
The studied model was developed to minimize ripple torque,
therefore, in its complexity, the design was always taught with
a minimalistic perspective. Based on the study made and the
results obtained, it is expected that by keeping the number of
legs as multiples of 6 the ripple torque should stay at the same
level as it is right now.
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