ΦAbstract – A magnetic gear is presented that is capable of continuously varying the gear ratio in order to enable constant magnified output speed to be generated from variable input speed. A flux focusing (spoke type) inner rotor is utilized and the performance of the device is assessed when using three different stator winding configurations. In order to study the harmonics a harmonic analysis approach is outlined.

Index Terms—Gearboxes, gears, magnetic gears, permanent magnet motors, variable speed drives, variable transmission.

I. INTRODUCTION It is typically more cost and weight effective to utilize a gearbox together with a high-speed electrical machine to convert speed and torque [1-2] because of this most wind turbines today utilize a doubly-fed induction generator (DFIG) with a mechanical gearbox [3]. This type of architecture is shown in Fig. 1. The DFIG material costs are relatively low and because only the slip power must be controlled the power electronic converter typically only needs to be rated at around 30% of the total generating power [3]. Unfortunately, the mechanical gearbox requires lubrication and cooling is often required [4-5]. In addition, wind turbine gearboxes have been one of the main causes of turbine failure [5] and the failure rates increase with power level [6], this has resulted in the wind-turbine gearbox not achieving its 20 year design life [5]. Furthermore, the DFIG requires brushes and these must be regularly maintained.

Direct drive generation systems, such as shown in Fig. 2, are considered the primary solution to the reliability issues encountered when using a gearbox and DFIG [7]. However permanent magnet synchronous generators (PMSG) have much lower torque densities [8-10] when compared to gearboxes and therefore direct drive generators are both large and costly [8-10]. Massive quantities of highly expensive rare-earth magnet material is required in order to create sufficient torque at the low operating speeds [11]

Fig. 1. Doubly fed induction generation, where only the slip power s*Pgen, flows through the converter

II. MAGNETIC GEARS

Magnetic gears (MG) use a contactless mechanism for speed amplification. Martin [12] proposed the coaxial MG, as shown in Fig 3, that can achieve a high torque density. In this design there is an inner rotor, consisting of ph pole-pair permanent magnets (PM) rotating at ωh, a middle rotor with nl individual ferromagnetic steel poles that can rotate at ωl

This material is based upon work supported by the North Carolina Coastal Studies Institute.

The authors are affiliated with the Laboratory for Electromechanical Energy Conversion and Control, Department of Electrical and Computer Engineering, University of North Carolina at Charlotte, Charlotte, NC, 28223 USA (e-mail: ppadmana@uncc.edu, j.bird@uncc.edu).

and an outer rotor with ps pole-pair PMs rotating at ωs. The inner and outer rotors that contain PMs interact with the middle steel poles to create space harmonics. If the relationship between the steel poles is chosen to be [13]

h l sp n p= − (1)

then the rotors will interact via a common space harmonic [12-14] and the angular velocities for each rotor is then related by

l sh l s

h h

n p

p pω ω ω= − (2)

A MG does not require gear lubrication and has the potential for high conversion efficiency [12-15]. A MG also has inherent overload protection, since if excessive torque is applied the MGs will simply slip. In contrast, a mechanical gearbox would catastrophically fail. Therefore, the sizing of a MG can be based around a rated torque rather than extreme torque conditions. This overload protection is particularly beneficial for wind power generation where sudden load changes are common.

Fig. 2. Direct drive generation with synchronous generator (SG) , all power flows through converter

Fig. 3. A Magnetic gear using surface PMs. ph=4 pole-pairs, nl=17 steel poles and ps=13 pole-pairs on the outer rotor.

III. CONTINUOUSLY VARIABLE MAGNETIC GEAR

It can be noted from (2) that if the low input speed ωl is varying then by controlling the rotor speed ωs the high output speed ωh can be made constant. Shah experimentally demonstrated how a continuously variable magnetic gear (CVMG) can be created in this way by mechanically control the rotor speed ωs in order to keep ωh constant under varying input speeds [16]. Shah relied on a separate motor/generator to control ωs. In contrast, Atallah [17], Wang [18] and Jian [19] incorporated an additional stator and rotor within the MG structure in order to control the speed ωs thereby enabling a constant output speed to be created. Using this

ωh

ωl

ωs

IlT

A Continuously Variable Magnetic Gear

Pavithra Padmanathan, Student Member, IEEE, Jonathan Z. Bird, Member, IEEE

978-1-4673-4974-1/13/$31.00 ©2013 IEEE367

approach three rotating members are then required and additionally a large quantity of magnets is necessary.

Rather than doing the above Fu and Wang considered replacing the inner rotor with a stator and keeping the modulation poles stationary (ωl=0) [20-21]. The objective was to utilizing magnetic gearing to create a low speed high torque traction motor. However, Fu showed that there was little benefit gained in doing this.

In this paper the object is to demonstrate that a constant and magnified output speed can be created from a variable low-speed input when the outer magnetic gear rotor is replaced by a stator, as shown in Fig. 4. As the stator electrical frequency, ωe, and mechanical angular velocity, ωs, are related by ωs=ωe/ps, (1) will be

1lh l e

h h

n

p pω ω ω= − (3)

Using the parameters ph = 4, ps =13, and nl = 17 the speed relationship becomes

4.25 0.25h l eω ω ω= − (4)

A variable input speed, ωl, can then be amplified and made into a constant mechanical output speed, ωh, by continuously controlling the stator electrical frequency, ωe.

The difficulty with this approach is that a high number of stator poles is required. Zaini recently investigated the same concept but utilized a Vernier stator structure in order to create the necessary high number of stator pole while using only a small number of coils [22]. In this paper the performance when using an integer slot winding with a flux focusing high speed rotor is investigated. A spoke type inner rotor with ferrite magnets is used in order to minimize the material cost. In order to accommodate the large number of poles the machine diameter must be large. However, large diameter rotors are typical for wind generation applications and therefore this is not necessarily an negative characteristic. The operational principal of this CVMG is illustrated in Fig. 5. The results were confirmed using finite element analysis. Fig. 5 shows that if the input speeds, ωl is varied from 50 to 170RPM, the frequency, ωe can then be changed, by using (4), so as to ensure that the output speed is kept constant at ωh = 425RPM. The corresponding average torque on the input and output rotors of the CVMG is shown in Fig. 5b. The fact that the calculated average input torque and output torque does not change with control frequency is important as it shows that the control frequency will only influence the output speed and not the input torque or speed. The power flow is shown in Fig. 5c for speed changes from

50-170RPM. The negative control power means that power is flowing out of the converter. The current phase angle must also be considered. The torque magnitude and therefore power flow can also be varied by varying the converter voltage level and phase angle.

If the CVMG is combined with a PMSG and MG, as shown in Fig. 6, the resultant system can act like a gearbox and DFIG. Like with the DFIG two sets of windings will be needed however both are stationary and therefore no brushes are required. The overall system level torque density could be high and unlike with the direct drive scheme the PMSG can be sized to be relatively small because the input speed into the generator would be high.

Inpu

t spe

ed ω

l [R

PM]

Out

put s

peed

ωh [R

PM]

Control frequency, fe [Hz] (a)

Torq

ue [N

m]

Control frequency, fe [Hz] (b)

Pow

er [W

]

Control frequency, fe [Hz] (c)

Fig. 5(a) Input and output speeds when the control frequency fe (ωe/2π) is usedto hold the output speed constant. (b) Input and output torque, the torque is not affected by changes in control frequency. (c) Input, output and control power flow. When the control power is negative the power is flowing out of the converter.

IV. TORQUE CHARACTERISTICS Using the parameter shown in Table 1 and Fig. 7 the

torque on the individual rotors and stator, when only one field is rotating at a time, was calculated. The results are shown in Fig. 8. The torque on the central cage rotor is the summation of the torque in the inner air-gap and stator air-gap. The torque and torque ripple as a function of angular position when operating at a torque angle of δ=7o is shown in Fig. 9 and Fig. 10. The stator has 78 slots. The full pitch stator winding has 1 slot/pole/phase (spp). It can be seen that significant torque ripple exists and is composed of high frequency and low frequency components.

420

425

430

435

440

445

450

020406080

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OOutput torque

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0200400600800

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Output power

Control power

Fig. 4. A continuously variable magnetic gear with integral slot winding.ph=4 pole-pair on inner rotor, nl=17 steel poles on cage rotor and the statorwinding creates ps=13 pole pairs.

ωl ωh

ω3

Three phase integral slot stator winding

High speed rotor magnets

Steel poles on cage rotorSteel teeth

ωs

368

A two layer winding with 1 slot chording and three layer winding with two slot chording was also studied. Torque and torque ripple for both such winding layouts are shown in Fig. 11 to Fig. 14. Both such winding layouts also exhibit significant harmonic components. However the three layer winding mitigates the dominate torque ripple components but at the expense of lower peak torque (due to chording).

Fig. 6. A wind turbine magnetically geared power take off system. Thecontinuously variable MG converts the variable speed input to constantspeed output suitable for power conversion by a small surface mounted PMgenerator. No brushes or mechanical gears are required.

TABLE I SIMULATION PARAMETERS

Description Value Units

Inner rotor

Pole pairs, ph 4 - Inner radius, ri1 80 mm Outer radius, ro1 184.5 mm Magnet radial thickness, Lh 95.1 mm Magnet width, Wh 36.2 mm Steel pole span, θs1 π/8 rad. Air gap, g 0.5 mm

Cage rotor

Steel poles, nl 17 - Inner radius, ri2 185 mm Outer radius, ro2 199.5 mm Radial thickness of steel pole, Lc 14.5 mm Steel pole span, θs2 π/15 rad.

Stator

Pole pairs, ps 13 - Slots, Q 78 - Inner radius , ri3 200 mm Outer radius, ro3 235 mm Slot opening width, Ws 4 mm Coil Length, Ll 23.5 mm Back Iron Length, Li 10 mm Air gap, g 0.5 mm

Material Magnet, Hitachi NMF-5G, Br 0.38 T

Winding Turns of coil 30 - Current density, J 3 A/mm2

Model Stack length, d 100 mm

Fig. 7. Definition of geometric parameters.

Torq

ue

[Nm

]

Torque angle, δ [degrees] Fig. 8. Static torque with respect angular position for full pitch stator winding with 1spp. Only one rotor is rotating at a time.

Torq

ue

[Nm

]

Rotational angle [mechanical degrees] Fig. 9. Torque as a function of angular position when the high speed (inner) rotor speed is ωh= 42.5 RPM, low speed (cage) rotor speed is ωl= 6 RPM and stator frequency is fe = -1.133 Hz

To

rque

ripp

le o

n ca

ge ro

tor

[Nm

]

Torq

ue ri

pple

on

inne

r rot

or

[Nm

]

Rotational angle [mechanical degrees] Fig. 10. Predicted torque ripple on low speed (cage) rotor and high speed (inner) rotor

Torq

ue [N

m]

Torque angle, δ [degrees] Fig. 11. Static torque with respect angular position for two layer windingwith 5/6 fractional pitch winding.

Torq

ue ri

pple

- ca

ge r

otor

[N

m]

Torq

ue ri

pple

- in

ner r

otor

[Nm

]

Rotational angle [degrees] Fig. 12. Predicted torque ripple on low speed (cage) rotor and high speed (inner) rotor when using two layer winding

cω

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100

200

0 1 2 3 4 5 6 7-200

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0

100

200

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0

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369

Torq

ue

[Nm

]

Torque angle, δ [degrees] Fig. 13. Static torque with respect angular position for three layer windingwith 2/3 fractional pitch winding.

Torq

ue ri

pple

on

cage

rot

or

[Nm

]

Torq

ue ri

pple

on

inne

r rot

or

[Nm

]

Rotational angle [degrees] Fig. 14. Predicted torque ripple on low speed (cage) rotor and high speed (inner) rotor when using three layer winding

V. SPATIAL HARMONIC ANALYSIS In order to learn more about the harmonic characteristics a

spatial harmonic analysis was conducted. The torque production by the CVMG can be decomposed into the torque created within the inner and outer air-gaps. A low current density has been used in this paper in order to minimize non-linear effects thereby allowing superposition to be utilized when calculating the magnetic field coupling effects on torque.

The mechanism for torque production can be explained by examining the field harmonic analysis shown in Fig. 15 the radial flux density, Br, in the stator air-gap is shown along with the corresponding spatial harmonic component for the case when the stator field is not excited. In this case the 13th harmonic is still significant and this is due to the high speed magnetic rotor harmonics being modulated by the 17 steel pole pieces. Thus, without the central steel poles there would not be a connection between the outer and inner rotors.

The radial and azimuthal magnetic flux density due to the high speed inner rotor can be expressed in terms of their harmonic components as

,1

( , , ) ( )cos[ ( ) ]h hr r m h h h h

m

B r t b r mp t mpθ θ ω δ∞

=

= − +∑ (5)

θ θ,1

( , , ) ( )cos[ ( ) ]h hm h h h h

m

B r t b r mp t mpθ θ ω δ∞

=

= − +∑ (6)

where superscript, h denotes the high-speed rotor and δh is an initial phase angle at time t=0. The field components created by the outer stator are defined as:

,1

( , , ) ( )cos[ ( ) ]s sr r k s s s s

k

B r t b r kp t kpθ θ ω δ∞

=

= − +∑ (7)

θ, θ,1

( , ) ( )cos[ ( ) ]s sm k s s s s

k

B t b r kp t kpθ θ ω δ∞

=

= − +∑ (8)

where superscript s denotes the stator field contribution and δs is an initial phase angle.

Rad

ial f

lux

dens

ity, B

r [T]

Angle [degrees] (a)

Har

mon

ic a

mpl

itude

[T]

Spatial harmonic (b)

Fig. 15(a) The radial flux density in the stator air-gap when no stator field is present and (b) the corresponding spatial harmonics.

The segmented iron poles contained on the low speed rotor modulate the flux and their influence on the fields can be expressed as [13]

,0 ,1

( , , ) ( ) ( )cos[ ( ) ]l l lr r r j l l l l

j

B r t r r jn t jnθ λ λ θ ω δ∞

=

= + − +∑ (9)

,0 ,1

( , , ) ( ) ( )cos[ ( ) ]l l lj l l l l

j

B r t r r jn t jnθ θ θθ λ λ θ ω δ∞

=

= + − +∑ (10)

where superscript l denotes low speed rotor and δl is an initial phase angle.

The radial modulating field interacts with the stator field to create a net field in the inner rotor air-gap (r=rh) given by:

,0 ,1

( , , ) { ( ) ( )cos[ ( ) ]}sl l lr h r h r j h l l l l

j

B r t r r jn t jnθ λ λ θ ω δ∞

=

= + − +∑

,1

( )cos[ ( ) ]sr k h s s s s

k

b r kp t kpθ ω δ∞

=

× − +∑ (11)

Utilizing trigonometric identity

1 1cos( )cos( ) cos( ) cos( )

2 2a b a b a b= + + − (12)

and rearranging (11) the radial harmonics terms within the inner rotor due to the stator and modulation rotor is

, , ,0 ,( , , ) ( ) ( )cos[ ( ) ]sl l sr k j h r h r k h s s s sB r t r b r kp t kpθ λ θ ω δ= − +

(, ,( ) ( )cos[( )( ) ]

2

l sr j h r k h

s l h s s l l

r b rkp jn t kp jn

λθ ω δ δ++ + − + +

)cos[( )( ) ]s l h s s l lkp jn t kp jnθ ω δ δ−+ − − + − (13)

where s s l lh

s l

kp jn

kp jn

ω ωω+ +

=+

(14)

s s l lh

s l

kp jn

kp jn

ω ωω− −

=−

(15)

Similarly, the azimuthal field within the inner rotor air-gap due to the stator and modulating flux is given by

1 2 3 4 5 6 7 8 9 10 11 12 13 14

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-50

0

50

100

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-3

-1

1

3

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-5

0

5

10

0 60 120 180 240 300 360-1.5

-1

-0.5

0

0.5

1

1.5

0 5 10 15 20 25 30 35 40 45 500

0.1

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370

θ θ,, , ,0( , , ) ( ) ( )cos[ ( ) ]sl l sk j h h k h s s s sB r t r b r kp t kpθθ λ θ ω δ= − +

(θ,, ( ) ( )cos[ ( ) ]

2

l sj h k h

h h l l s s

r b rmp t jn kpθλ θ ω δ δ++ − + +

)cos[ ( ) ]h h l l s smp t jn kpθ ω δ δ−+ − + − (16)

The torque harmonic components created within the inner rotor air-gap can be computed by using

, , , , , , , , ,I II

h j k m h j k m h j k mT T T= + (17)

where

θ, θ22

, , , , ,0

( , , ) ( , , )I h slh j k m m h r k j h

o

wrT B r t B r t d

π

θ θμ

= ∫ (18)

θ22

, , , , , ,0

( , , ) ( , , )II h slh j k m r m h k j h

o

wrT B r t B r t d

π

θθ θμ

= ∫ (19)

where w is the stack length. By comparing (13) with (6) it can be observed that in order to create non-zero torque using (18) the following condition must be met [13] h l smp jn kp= ± (20) This condition also applies to (19). Substituting, (20) into (14) and only considering the first harmonic term (j=k=m=1) one obtains (2). Looking at the magnetostatic case (t=0). The field component of (18), when applying (20) is given by

θ, , ,( , , 0) ( , , 0)h slm h r k j hB r B rθ θ =

0, , cos[ ( )]cos[ ( )]Ik m s s h hB kp mpθ δ θ δ+ +

, ,cos[ ]cos[ ( )]

2

Ij k m

h s s l l h h

Bmp kp jn mpθ δ δ θ δ+ + + +

, ,cos[ ]cos[ ( )]

2

Ij k m

h s s l l h h

Bmp kp jn mpθ δ δ θ δ+ + − + (21)

where θ,, , , ,( ) ( ) ( )I l s h

j k m r j h r k h m hB r b r b rλ= (22) Utilizing trigonometric identity (12), (21) can be written as

θ, , ,( , , ) ( , , )h slm h r k j hB r t B r tθ θ =

0, , cos[( ) ]Ik m s h s s h hB kp mp kp mpθ δ δ+ + +

0, , cos[( ) ]Ik m s h s s h hB kp mp kp mpθ δ δ+ − + −

, ,

, ,

cos[2 ]4

cos[ ]4

Ij k m

h h h s s l l

Ij k m

s s l l h h

Bmp mp kp jn

Bkp jn mp

θ δ δ δ

δ δ δ

+ + + +

+ + −

, ,cos[2 ]

4

Ij k m

h s s l l h h

Bmp kp jn mpθ δ θ δ+ + − +

, ,cos[ ]

4

Ij k m

s s l l h h

Bkp jn mpδ δ δ+ − − (23)

The torque is obtained by integrating (23) and rearranging to yield

2

, , , , , cos( )cos( )I Ih j k m j k m s s h h l l

o

wrT B kp mp jn

πδ δ δ

μ= − (24)

This gives the torque expression for all potential harmonic components. Similarly the second torque term, (19), within the inner rotor evaluated at t=0 is composed of

, , ,( , , 0) ( , , 0)h slr m h k j hB r B rθθ θ =

(

0, ,

, ,

cos[ ]cos[ ]

cos[ ]cos[ ( )]2

Ik m s s s h h hIj k m

h l l s s h h

B kp kp mp mp

Bmp jn kp mp

θ δ θ δ

θ δ δ θ δ

+ +

+ + + +

)cos[ ]cos[ ( )]h l l s s h hmp jn kp mpθ δ δ θ δ+ + − + (25)

where θ,, , , ,( ) ( ) ( )II l s h

j k m j h k h r m hB r b r b rθλ= (26) Utilizing trigonometric identity (12), (25) can be written as

, , ,

0, ,

, ,

, ,

, ,

( , , 0) ( , , 0)

cos[ ]cos[ ]

cos[2 )]4

cos[2 ]4

cos[ ]4

h slr m h k j hIIk m s s s h h hIIj k m

h l l s s h h

IIj k m

h l l s s h h

IIj k m

l l s s h h

B r B r

B kp kp mp mp

Bmp jn kp mp

Bmp jn kp mp

Bjn kp mp

θθ θ

θ δ θ δ

θ δ δ δ

θ δ δ δ

δ δ δ

=

+ +

+ + + +

+ + − +

+ + −

, , cos[ ]4

IIj k m

l l s s h h

Bjn kp mpδ δ δ+ − − (27)

Integrating (27) the first three terms become zero and this leads to the torque equation

2

, ,, , ,

2cos[ ]

4

IIj k mII

h j k m l l s s h ho

BwrT jn kp mp

πδ δ δ

μ= + −

2

, ,2cos[ ]

4

IIj k m

l l s s h ho

Bwrjn kp mp

πδ δ δ

μ+ − − (28)

or

2

, , , , , cos[ ]cos[ ]II IIh j k m j k m l l h h s s

o

wrT B jn mp kp

πδ δ δ

μ= −

Utilizing finite element analysis the inner rotor field components present in the inner rotor (when stator field is zero) and also the stator field contribution in the inner rotor air-gap when the inner rotor field was turned off were determined separately. The resultant torque was then computed for each harmonic component utilizing the harmonic approach described by (17). The torque components from (18) are shown in Fig. 16 while the torque contributions from (19) are shown in Fig. 17. The analysis was conducted on the two-layer winding design. The main harmonic components and the associated, harmonic indices are shown in Table 2 and Table 3. The harmonic, j and k values given in the Tables were computed using

l sharmonic jn kp= + (29) where k=0,±1, ±2, ±3,…., ∞ , j=0,1,2,3,…., ∞ It can be noted that additional harmonic terms not associated with multiples of mph are present and these terms are understood to be associated with the additional harmonic terms introduced by utilizing the flux focusing rotor.

371

Torq

ue [N

m]

Harmonic component Fig. 16. Harmonic torque contributions in the inner rotor air gap from I

lT calculated using harmonic analysis from FEA plots by using (18).

Torq

ue

[Nm

]

Harmonic component Fig. 17. Harmonic torque contributions in the inner rotor air gap from II

lT calculated using harmonic analysis from FEA plots by using (19).

TABLE II, HARMONIC COMPONENTS DUE TO IhT

Harmonic Magnitude j k m 4 -52.99 1 -1 1 5 -2.66 3 -2

11 0.57 7 -6 12 21.77 3 -3 3 13 15.42 0 1,-1 14 0.96 5 -3 20 6.94 5 -5 5 21 5.64 1 -2 29 -10.22 3 -4 30 -0.67 1 1 36 -1.63 8 -4 9 37 -6.24 -5 6 45 -1.47 7 -8 47 1.76 1 2 52 1.71 4 0 13 72 1.57 1 -5 18 81 0.69 1 4 92 0.65 -6 10 23

TABLE III, HARMONIC COMPONENTS DUE TO IIhT

Harmonic Magnitude j k m 4 -11.17 1 -1 1

12 -2.93 3 -3 3 13 7.71 0 1,-1 20 -1.79 5 -5 5 21 -12.70 1 -2 22 0.55 14 -12 28 0.56 7 -7 7 29 -1.50 3 -4 30 1.88 -1 -1 36 0.64 8 -4 9 38 -2.67 1 -3 46 -0.61 3 -5 52 -0.56 4 0 13 72 -1.66 1 -5 18

Within the stator air-gap the torque contribution is given by

θ22

, , , , , ,0

( , , ) ( , , )II s lhs j k m r k l m j l

o

wrT B r t B r t d

π

θθ θμ

= ∫ (30)

θ, θ22

, , , , ,0

( , , ) ( , , )I s lhs j k m k l r m j l

o

wrT B r t B r t d

π

θ θμ

= ∫ (31)

The harmonic contributions due to (30) are shown in Fig. 18 while the main harmonic contributions due to (31) is shown in Fig. 19.

Torq

ue

[Nm

]

Harmonic component Fig. 18. Harmonic torque contributions in the stator air-gap from II

sT calculated using harmonic analysis from FEA plots by using (30).

Torq

ue

[Nm

]

Harmonic component Fig. 19. Harmonic torque contributions in the stator air-gap from I

sT calculated using harmonic analysis from FEA plots by using (31)

CONCLUSIONS A novel CVMG device has been presented. When integrated with a PMSG and MG a magnetically geared power take-off system that acts analogously to a DFIG power take off system could be realized. When designing this type of CVMG great care must be taken in order to minimize torque ripple. The three layer winding design minimized torque ripple at the cost of a reduced torque magnitude.

ACKNOWLEDGMENT The authors would gratefully like to thank the JMAG

Corporation for the use of their finite element analysis software.

REFERENCES

[1] H. Polinder, F. F. A. Van der Pijl, et al., "Comparison of direct-drive and geared generator concepts for wind turbines," IEEE Trans. Energy Conv., vol. 21, pp. 725-733, 2006.

[2] J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent-Magnet Motors: Oxford University Press, 1995.

[3] S. Muller, M. Deicke, et al., "Doubly fed induction generator systems for wind turbines," IEEE Ind. Appl. Mag., vol. 8, pp. 26-33, 2002.

[4] S. Sheng and P. Veers, "Wind turbine drivetrain condition monitoring - an overview," in MFPT: Applied Systems Health Management Conference, Virginia Beach, VA 2011.

[5] W. Musial, S. Butterfield, et al., "Improving Wind Turbine Gearbox Reliability," National Renewable Energy Laboratory, NREL/CP-500-41548May 2007.

[6] J. Ribrant, "Reliability performance and maintenance - A survey of failures in wind power systems," M.S. Thesis, KTH School of

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