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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

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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.

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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

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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)

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(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.

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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;

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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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