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New Bearingless Generator with Buoyant Rotor

for Large Direct-Drive Wind Turbines

D. Bang1,*, G.W. Jang2, S.H. Hwang3, P.W. Han1, J.W. Kim1, D.H. Koo1, H. Polinder4, J.A. Ferreira4

1

Electric Motor Research Center, Korea Electrotechnology Research Institute

2

Faculty of Mechanical and Aerospace Engineering, Sejong University

3

Department of Electrical Engineering, Kyungnam University

4

Electrical Power Processing Group, DUWIND, Delft University of Technology

*

E-mail: djbang@keri.re.kr / deokje.bang@gmail.com

Abstract:

The aim of this paper is to verify a new concept of bearingless machine with a buoyant rotor. Large direct-drive wind generators have disadvantages of large mass and high cost compared to geared generators. In wind turbines, bearing failures have been a continuing problem and a significant proportion of all failures. It is thus required to significantly reduce both the mass and bearing failures of large direct-drive wind generators. In this paper, a new bearingless permanent magnet machine with a buoyant rotor is discussed as a solution to fulfill the requirements for large direct-drive wind generators. The proposed machine concept is verified by the experimental setups built to realize two new concepts: a buoyant rotor concept guided by magnetic bearings and a new bearingless machine concept. The electromagnetic and structural parts of the proposed generator for 10 MW wind turbines are designed by the three-dimensional finite element analysis (3D FEA). In order to identify the mass competitiveness, the total mass of the proposed generator is compared with the mass of a geared generator and a high temperature superconducting generator (HTSG). The total mass of the proposed generator for 10 MW wind turbines is estimated at about 235 tonnes, which is 75 tonnes and 5 tonnes heavier than a geared generator and a HTSG at the same torque rating, respectively.

Keywords: Bearingless, Buoyant rotor, Generator, Direct-drive, Wind turbines

1. Introduction

Direct-drive wind generators have been discussed as the generator type with higher energy yield than the geared generators. However, large direct-drive wind generators have disadvantages such as large diameter, large mass and high cost in order to get high torque rating compared to geared generators. Scaling up the power of direct-drive wind generators, the structural part becomes a dominant part of the total mass of the generators. [1][2] In wind turbines, bearing failures have been a continuing problem and a significant proportion of all failures. Bearing-related downtime is among the highest of all components of wind turbines [3]. Therefore, it is necessary to significantly reduce both the structural mass and bearing failures of large direct-drive wind generators in order to make those generators more attractive for industry use.

Different configurations of the generators such as an

ironless permanent magnet (PM) generator with a spoke structure, a PM generator with the bearings close to the air gap, and a high temperature superconducting generator (HTSG) have been discussed to reduce the mass of large direct-drive wind generators [4][5][6]. If a large direct-drive wind generator needs very small tolerance in constructing and guiding, the generator will not be attractive as far as cost is concerned even despite a lightweight structure. In order to make a generator construction which does not require very small tolerance and to reduce bearing failures of the generator, it was discussed to use magnetic bearings or bearingless drives instead of mechanical bearings for large direct-drive wind generators [7]. In previous researches [2][8] by the author, a new generator concept, ring-shaped bearingless PM wind generator with a buoyant rotor, has been proposed as a solution to reduce the structural mass and bearing failures and has been roughly designed. In this paper, the construction and features of the new generator concept are described firstly. Secondly, the new concept is verified by the experimental setups, which are built to realize both the concept of buoyant rotor integrated with seals and magnetic bearings, and the concept of new bearingless PM machine. Next, the electromagnetic and structural parts of the new generator are designed by the 3D-FEA for 10MW direct-drive wind turbines in order to address the mass competitiveness of the generator. The total mass of the generator is compared with the mass of geared generator [9] and HTSG [6] systems.

2. Ring-shaped bearingless PM

generator with a buoyant rotor

A ring-shaped bearingless PM generator concept is discussed as a concept to significantly reduce structural mass and bearing failures of large direct-drive wind turbines. The rotor of the proposed generator is supported by the buoyancy force without a shaft, torque arms and bearings. The air gap between the rotor and the stator of the proposed generator is maintained and controlled by a new concept of bearingless drives. To describe the features of the proposed generator, the following issues are covered in this section.

 Ring-shaped generator with a buoyant rotor

 New sealing mechanism (Magneto-mechanical seal)  New bearingless PM machine

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Figure 1: Sketch of a bearingless PM generator with a buoyant rotor

Figure 2: Conventional seal concepts

Figure 3: New sealing concept

2.1 Ring-shaped buoyant rotor concept

Using the buoyancy force, a very heavy structure floats easily in fluid. Therefore, the use of the buoyancy force for supporting the heavy rotating structure of large direct-drive wind generator has been introduced in [2][8]. The advantages of a buoyant rotating structure could be summarized as follows.

 Easily support a heavy structure without consuming energy

 Reduce structural material required for support  Provide flexibility in supporting a heavy structure The construction of the buoyant rotating part and the stationary part is sketched as shown in Figure 1. The generator is a double-sided air gap and axial flux configuration. The buoyant rotor consists of the iron cores, the PMs and the structural part with hollow space to make the rotor afloat. The iron cores and copper windings are set on the stationary part. Fluid fills the gaps between the buoyant rotor and the stationary part. In order to connect the generator rotor with the blade adapters, the flexible joints that are flexible to the radial and axial directions but rigid to the circumferential direction can be used through the protruding parts on the left side of the rotor. In this buoyant rotor concept, some sealing systems must be included between the rotor and the stationary part of the generator in order to prevent leakage of fluid. A new sealing mechanism for the proposed generator is discussed in the next subsection in detail.

2.2 New sealing concept

Seals can be classified into static seals and dynamic seals. Static seals perform the sealing function between surfaces which do not move relatively to each other. Dynamic seals perform the sealing function between surfaces in relative motion. [10] The seals for the proposed generator are included in a type of dynamic seals. They can be subdivided into dynamic clearance seals and dynamic contact seals. In dynamic clearance seals the sealing surface is separated by a hydrodynamic fluid film while the surface is separated by a very small gap. Dynamic clearance seals thus are limited to use for the rotating machine with a large diameter whose surfaces are wary. In dynamic contact seals the sealing surface is in contact with the opposite

surface. Figure 2 depicts conventional dynamic contact seals, rotary lip-seals and V-ring seals. Conventional dynamic contact seals use elastic force of seal material or spring to produce the sealing pressure on the seal surfaces, and require plane and smooth surfaces to contact. Therefore, conventional dynamic clearance seals and contact seals are difficult to use for the proposed large ring-shaped generator which is segment structure and wary.

In this paper, a new sealing mechanism is proposed to apply for the bearingless generator with a buoyant rotor as shown in Figure 3. The flexible material and the seal tube are set on the stationary part. The tube guide, the PMs and the yoke (iron core) are set on the rotating part. The ferromagnetic material is filled in the seal tube, thus the sealing pressure is occurred on the contact surface between the seal tube of the stationary part and the guide on the magnets of the rotating part. The flexible material is flexible to the X-axis direction, but rigid to the Y-axis direction. Therefore, the sealing pressure on the contact surface can be maintained at a constant pressure, even though the distance between the stationary part and the rotating part is changed. Considering friction and life of the seals, Teflon material (PTFE: polytetrafluoroethylene) has been chosen for the seal tube and the guide. The roughness of the Teflon is 0.001524 mm that is 3.3% of the roughness of commercial steel, 0.04572. Applying this new sealing mechanism to the large PM generator with a buoyant rotor, the magnets set on the rotor can be used to produce the sealing pressure without additional magnets.

2.3 New bearingless PM machine drive

concept

A significant feature of the bearingless machine compared to the electric machine with the magnetic bearing is that the bearing winding is integrated into

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Figure 4: 4-pole and 2-pole winding arrangements of a primitive bearingless drive [11]

θY X Y Z θZ θX moving direction Stator 2 Stator 1 Rotor air gap 1 air gap 2

(a) Longitudinal flux PM machine configuration

θY X Y Z θZ θX moving direction Stator 2 Stator 1 Rotor air gap 1 air gap 2

(b) Transverse flux PM machine configuration Figure 5: Double-sided bearingless PM machine

configurations Stator_1 Stator_2 Current controller Rotor gap sensor g1–g2>0

+

_

i + ig1-g2 i – ig1-g2 2i Current controller Rotor (moving direction) air gap 1 (g1) air gap 2 (g2) Z X Y

Figure 6: Simplified control diagram of new bearingless machine in the case of airgap 1>airgap 2 the electric machine.

Conventional bearingless machine drives need to control both the bearing force with bearing winding and the torque with torque winding. In order to achieve extensive decoupling between the generations of the bearing forces and the torque, those windings are designed with different numbers of poles. Figure 4 depicts a winding arrangement of a primitive bearingless drive, where the windings for four-poles are 4a and 4b and the windings for two-poles are 2a and 2b [11]. Bearingless drives are thus more complicated than the conventional electric machine drives.

In the case of the large direct-drive machines, the mass of the rotating part is large. Thus it is expected that the power consumption of producing the bearing force, for supporting the rotating part against the gravity, will be large for large direct-drive wind generators. However, the new bearingless machine drive discussed in this paper does not need the power consumption to support the rotating part against the gravity because the part is supported by the buoyancy force. Additionally the new bearingless drive concept needs only one winding to produce both the bearing

force to control the air gap length and the torque. The proposed bearingless machine is a type of bearingless PM machine and the machine is constructed with the double-sided air-gap configuration with a buoyant rotor. The bearingless machine could be constructed with the longitudinal flux (LF) configuration or the transverse flux (TF) configuration. Figure 5 (a) and (b) depict a cross-section of linearized bearingless PM machines with the LF configuration and the TF configuration, respectively. The rotor of the bearingless PM machines consists of the PMs and the iron cores. The stator consists of the slotted iron cores and the windings. Figure 6 depicts an air gap control diagram of the new bearingless PM machine with current controllers in the case of air gap 1 is larger than air gap 2. The moving direction of the rotor is the Y-axis that is represented with a “ ” mark. The flux paths of the machine are represented with dotted lines and arrows. The mark “ ” under the rotor means the rotor is supported against gravity, thus there is no bearing force necessary to maintain the position of the rotor to Z-axis direction. The bearing force is only used to control the air gap length in the X-axis direction. When the air gap 1 is larger than the air gap 2, the difference can be relayed to the current controllers by the gap sensors. The air gap 1 can be reduced by increasing the attractive force in the air gap 1 and by reducing the force in the air gap 2 by controlling the currents of stators.

3. Verification of the bearingless

machine with a buoyant rotor

To verify the new concept of bearingless machine with a buoyant rotor, two sets of experimental setups are built to realize two concepts:

 concept of buoyant rotor integrated with new seals and magnetic bearings

 concept of new double-sided bearingless PM machine

3.1 Buoyant rotor integrated with seals

and magnetic bearings

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Figure 7: Sketch of the setup of buoyant rotor integrated with seals and magnetic bearings

Figure 8: Photograph of the setup of buoyant rotor integrated with seals and magnetic bearings

U-core Winding

I-core Buoyant Rotor Stator structure

Table 1: Dimensions and mass of the setup of buoyant rotor system

Stationary part Outer diameter [mm] 836 Inner diameter [mm] 140 Axial length [mm] 278 Rotating part Outer diameter [mm] 796 Inner diameter [mm] 180 Axial length [mm] 220 Mass [kg] 92 (including coupling and I-cores) Magnetic bearings Coil d=1mm * 200 turn * 4 layer (series & 2-parallel winding) U-core width [mm] 80 (core thickness: 20) U-core length [mm] 150 Air gap [mm] (in controlled) 5 I-core thickness [mm] 10 I-core width [mm] 80 Fluid mass [kg] 28

Figure 9: Block diagram of the magnetic bearing system for a buoyant rotor

integrated with seals and magnetic bearings, the experimental setup is constructed with a buoyant rotor and a stator structure integrated with a new sealing system and magnetic bearings as shown in Figure 7. In the experimental setup, three U-cores and windings are equipped on each side of the stator, and I-cores are circumferentially equipped on the both sides of the buoyant rotor. These U-cores, windings and I-cores are used as magnetic bearings to control the air gaps of both sides. To measure and control the air gaps between the rotor and the stator, displacement sensors are equipped in the stationary part. The rotor of the experimental setup is rotated by the driving motor, and the rotor speed is controlled by the inverter. The experimental setup has been built as shown in Figure 8. The dimensions and the mass of the rotor and stationary part are given in Table 1. Figure 9 depicts the overall block diagram of the magnetic bearing system to control the air gaps. For each magnetic bearing set, a single-phase bi-directional AC/DC/AC converter module is used. The control algorithm is performed by a digital signal processor (DSP) control system. Figure 10 represents the experimental results of the air gap controls of the buoyant rotor system by

six-sets of magnetic bearings. Figure 10 (a) and (b) represent the results of air gap controls in the two cases of the buoyant rotor not rotating and rotating, respectively. Three lines in the figure are the air gap displacement wave forms measured from the gap sensors equipped close by the magnetic bearings. The maximum displacement of the air gap in the axial direction is 0.3 mm, which is 6 % of the air gap length, 5 mm, at 2 m/s speed (48 rpm).

3.2 New double-sided bearingless PM

machine

In order to verify the concept of bearingless PM machine drive, a double-sided PM linear machine is constructed as shown in Figure 11. The stator consists of two-sets of three-modules of the iron cores and windings. Each phase of the stator is constructed as an independent module. The mover consists of the PMs and the iron cores for two sides. In this paper, a transverse flux machine configuration is used for the verification, but longitudinal flux machine configurations can be also used to realize the double-sided bearingless machine concept. Moving direction of the

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(a) Case of the rotor not rotating

(b) Case of the rotor rotating

Figure 10: Experimental results of air gaps controls between the buoyant rotor and stator at 2m/s( speed

(5V/div = 1mm/div)

(a) Front view (b) Top view

Figure 11: Sketch of the double-sided PM linear machine

Figure 12: Photograph of the double-sided transverse flux PM linear machine

mover for the thrust-position control is the Y-axis. Linear motion (LM) guides are set on between the moving part and the stationary part. In order to test and verify the air gap control integrated with the thrust-position control, it requires making free movement of the mover in the X-axis direction. Thus LM guides are additionally set on between the moving part and the LM guides on the bottom. Figure 12 depicts the double-sided transverse flux PM linear machine built to verify the new concept of bearingless machine drives. The specifications of the machines are given in Table 2. The significant feature of this bearingless machine compared to the conventional bearingless machine is that the coil windings in the stators are used to simultaneously control both the air gap length and the thrust-position without additional winding to produce

the bearing force. In this paper, this machine is driven as a linear motor to verify the new concept of bearingless drives. Driving for the generator mode will be considered in further researches. The control block diagram of the air gap control and the thrust-position control is represented as shown in Figure 13. The air gap length reference is produced by the proportional-integral-derivative (PID) controllers. In this paper, a phase angle shift algorithm is developed and applied for the proposed double-sided bearingless machine in order to control the air gap length by controlling the normal forces between the mover and the stator. After operating the gap controller, the currents to control the air gap length are generated by shifting the phase angles. These signals are added to the outputs of the PI speed controller. The final three-phase current commands are given to the PI current controller. Figure 14 depicts the overall block diagram of the experimental setup of the bearingless machine. Figure 15 represents the experimental results of both the thrust-position control and the air gap length control. The position command variation is between 5 mm and

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Table 2: Specifications of the double-sided transverse flux PM linear machine

Air gap length [mm] 3

Pole pitch [mm] 20 MMF [AT] 3,000 Stator Pole width [mm] 16 Slot width [mm] 50 Slot height [mm] 50 Pole length [mm] 30 Yoke height [mm] 30 Height [mm] 80

Core S20C(Solid core)

Coil

d=1mm*165turn*8layer (4-series & 2-parallel winding) Rotor Pole width [mm] 796 Height [mm] 180 Width [mm] 220 Core 92 (including coupling and I-cores)

Magnet Ferrite

(Br=0.4T)

Magnet thickness

[mm] 8

Figure 14: Block diagram of the experimental setup

Figure 15: Experimental results of the position and air gap controls of the double-sided bearingless machine

Figure 13: Control block diagram of the double-sided bearingless machine 200 mm, and the air gap length command is 3.2 mm.

The actual air gap length and thrust-position are tracking well the reference values. The maximum displacement of the air gap is 0.1 mm, which is 3 % of the air gap length, at 0.2 m/s speed.

4. Design of the proposed generator

for 10MW direct-drive wind turbines

In [2], the electromagnetic and structural parts of the generator with a buoyant rotor have been roughly designed to estimate the mass of the generators for large direct-drive wind turbines with the power ratings from 5 MW to 20 MW. In this section, the generator

with a buoyant rotor is designed in detail by the three-dimensional finite element analysis (3D FEA) for 10 MW direct-drive wind turbines. The parameters of the turbine and the requirements of the generator are given in Table 3.

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Table 3: Wind turbine parameters and generator requirements

Wind turbine parameters

Rated grid power, P 10 [MW]

Rotor blades diameter, Dr 178 [m]

Rotor blades tip speed, vtip 80 [m/s]

Rated rotor speed, N 8.6 [rpm]

Generator requirements

Nominal power, Pgennom 10.6 [MW]

Nominal torque, Tgennom 11.8 [MNm]

b'

a

c'

b

a'

c

X Y Z s

b

m

l

p

b

h

ry sy

h

s

h

t

b

g

l

p

s

(a) Dimensional parameters

(b) 3D-FEA model

Figure 16: Dimensional parameters and 3D-FEA model for the proposed generator

Table 4: Electromagnetic dimensions and parameters of the proposed generator

Generator mean diameter, Dg [m] 8.91 Stack length, ls(= Ro-Ri) [m]

1.183 (5.047-3.864)

Air gap length, lg[mm] 8.91

Magnet height, lm[mm] 22.3

Number of phases, m [-] 3

Stator slot pitch, τs [mm] 33.3 Number of slots per pole per phase,

q [-] 1

Pole pitch, τp [mm] 100

Number of pole pairs, p [-] 140

Rotor pole width, bp [mm] 80

Stator slot width, bs [mm] 15

Stator tooth width, bt [mm] 18.3

Stator slot height, hs [mm] 80

Stator yoke height, hsy [mm] 40

Rotor yoke height, hry [mm] 40

N u m b e r o f c o n d u c t o r s of phase winding, Ns [turns]

560

Table 5: Electromagnetic design results by theoretical design and 3D-FEA for one-side of the generator

Theoretical design 3D-FEA No-load induced

voltage [kV] 3.485 3.375

Output current [A] 563 588

Total inductance [mH] 25.45 23.18 Torque [kNm] 5,890 5,332 Force density [kN/m2] 40 36.1 Mass [ton] Rotor iron 20.2 PMs 8.9 Stator iron 43.3 Copper 17.3 Total 89.7

4.1 Electromagnetic part

A longitudinal flux surface-mounted PM generator with double-sided air gap, full pitch winding and axial flux configuration represented in Figure 5(a) is considered for the proposed generator configuration in this paper. Dimensional parameters and the 3D-FEA model for the generator are represented in Figure 16. One-pole of one-side of the generator is modelled for the 3D FEA. Considering the dimensional parameters and relevant equations in [1][2][12][13][14] and the material characteristics in [14], the electromagnetic dimensions and parameters of the generator for 10 MW direct-drive wind turbines are determined as Table 4. The design

results of the generator by the theoretical design [2] and the 3D-FEA are given in Table 5. Figure 17 (a), (b) and (c) depict the results of the no-load induced voltages, the phase currents and the torque of one-side of the generator by the 3D-FEA, respectively.

4.2 Structural part

A lightweight design of the generator with a buoyant rotor is presented by the optimization methods based on a finite element analysis. The cross-section of the stator and the rotor for the optimization is initially modeled as Figure 18. The electromagnetic part of the generator is not illustrated in the figure. For the design optimization, the objective is set as a mass, and the maximum deformation by the magnetic attractive force between the stator and the rotor is constrained below 5 % of the air gap length. Normal pressure acting on the vertical plates of the stator and the rotor due to the flux density in the air gap is 320 kPa obtained by Bg

2/2μ

0. Here, Bg is the air gap flux density and μ0 is

the permeability of free space.

For the design of the stator structural part, a rib construction is introduced as a method stiffening the plates, and the layout of the mass-minimized rib is

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(a) No-load induced voltage at the rated speed

(b) Phase currents

(c) Torque

Figure 17: Results of the 3D-FEA

(a) Stator structure (b) Rotor structure Figure 18: Cross-section of the generator in tangential view

(a) Stator structure

(b) Rotor structure

Figure 19: Lightweight design results of the stator and the rotor structure

Table 6: Dimensions of the structural part of the generator Stator parameter Dimension [mm] Rotor parameter Dimension [mm] i

st

3757.3

R

i 3846.1 o

st

5122.7

R

o 5033.9 h

st

1365.4

l

rh 1596.0 w

st

1978.1

l

rb 1187.8 1 h

r

1600

t

rh1 3.8 2 h

r

1500

t

rh2

~

t

rh8 2.7 1 s

r

550

t

rh9 3.8 2 s

r

550

Table 7: Structural mass of the generator for 10 MW wind turbine

Rotor structure [ton] 16 Stator structure [ton] 118

Fluid (Water) [ton] 11

Total [ton] 145

designed by solving an optimization problem. For the design of the rotor structural part, the dimensions of the rotor is determined by using CAE-based structural optimization methods. Figure 19 and Table 6 represent the design results of dimensions of the stator and the

rotor. Table 7 gives the mass of the structural part by the optimization.

4.3 Mass comparison

In order to address the mass competitiveness of the proposed generator, the total mass of the generator is compared with the masses of a geared generator and a high temperature superconducting generator (HTSG) at the same torque rating. The geared generator consists of a three-stage gearbox and a high speed generator. In this paper, the mass of a three-stage gearbox (m3G) and the mass of a high speed generator

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(mhs.Gen) are estimated using equations (1) and (2)

[9][15]. As represented in the equations, the masses of a three-stage gearbox and a high speed generator are scaled based on the low speed shaft torque (TL) and

the generator power rating (PGen), respectively. The

mass of the geared generator for 10 MW wind turbines rated at 8.6 rpm is thus estimated at about 160 tonnes by (1) and (2).

𝑚ℎ𝑠.𝑔𝑒𝑛 = 6.47 × 𝑃𝑔𝑒𝑛0.9223 (1)

𝑚3𝐺= 10.35 × 𝑇𝐿+ 1950 (2)

In [6], the mass of a 10 MW HTSG was estimated at 180 tonnes at 11 rpm. Considering the rated speed of the HTSG from 11 rpm to 8.6 rpm, the torque of the HTSG increases from 9,202 kNm to 11,770 kNm. For the HTSG, the mass to torque rating ratio is 19.56 kg/kNm. Thus the mass of the HTSG rated at 8.6 rpm can be estimated at about 230 tonnes by multiplying the ratio by the torque. Therefore, it is expected that the total mass of the proposed 10MW generator with a buoyant rotor, estimated at 235 tonnes, is 75 tonnes and 5 tonnes heavier than a geared generator with three-stage gearbox and a HTSG rated at 8.6 rpm.

5. Conclusions

This paper discussed a new concept of ring-shaped bearingless permanent magnet generator with a buoyant rotor, which enables to significantly reduce the structural mass and bearing failures of large direct-drive wind generators. In the new concept, the rotor of the generator was supported by the buoyancy force, and the air gaps between the rotor and the stator were maintained and controlled by a new simplified bearingless drive concept. A new sealing mechanism was proposed for the new generator.

The proposed generator concept was verified by the experimental setups built to realize two concepts: 1) concept of buoyant rotor integrated with seals and magnetic bearings, and 2) concept of new double-sided bearingless permanent magnet machine. In the experiments, the air gap of the buoyant rotor, and the air gap and thrust-position of the double-sided bearingless machine were tracking well the reference values. The maximum displacements of the air gap were below 6 % of the air gap length in the experiments.

The total mass of the generator was estimated at about 235 tonnes, which is comparable with the mass of a high temperature superconducting generator (230 tonnes) and 75 tonnes heavier than a geared generator with a three-stage gearbox for 10 MW wind turbines rated at 8.6 rpm.

References

[1] A.S. McDonald, M.A. Mueller and H. Polinder, “Comparison of generator topologies for direct-drive wind turbines including structural mass”, in Proc. of the International Conference on Electrical Machines(ICEM), pp. 360.1-7, September 2006. [2] D. Bang, “Design of transverse flux permanent

magnet machines for large direct-drive wind

turbines”, 2010, Ph.D. dissertation, Delft University of Technology, Delft, The Netherlands.

[3] J. Ribrant and L.M. Bertling, “Survey of Failures in Wind Power Systems with Focus on Swedish Wind Power Plants during 1997-2005”, IEEE Transactions on Energy Conversion, Vol. 22, pp.167-173, 2007.

[4] E. Spooner, P. Gordon, J.R. Bumby and C.D. French, “Lightweight, ironless-stator, PM generators for direct-drive wind turbines” , IEE Proc.-Electr. Power Appl., Vol. 152, No. 1, pp. 17-26, January 2005.

[5] S. Engström and S. Lindgren, “Design of NewGen direct-drive generator for demonstration in a 3.5 MW wind turbine”, EWEC (European Wind Energy Conference & Exhibition, Milan, Italy, May 7-10 2007.

[6] G. Snitchler, B. Gamble, C. King and P. Winn, “10MW class superconductor wind turbine generators”, IEEE Trans. on Applied Superconductivity, Vol. 21, No. 3, June 2011, pp. 1089-1092.

[7] D. Bang, H. Polinder, G. Shrestha, and J.A. Ferreira, “Review of generator systems for direct-drive wind turbines”, in Proc. EWEC (European Wind Energy Conference & Exhibition), Brussels, Belgium, March 31 - April 3 2008.

[8] D. Bang, H. Polinder, J.A. Ferreira and S.S. Hong, “Structural mass minimization of large direct-drive wind generators using a buoyant rotor structure”, in Proc. 2010 IEEE Energy Conversion Congress and Exposition, Atlanta, Georgia, September 12-16 2010.

[9] H. Li, Z. Chen and H. Polinder, “Models for numerical evaluation of variable speed different wind generator systems”, Research report, UpWind/D1B2.b.2, 2007.

[10] A. van Beek, “Advanced engineering design: Lifetime performance and reliability”, pp. 371-394, TUDelft, 2009.

[11] A. Chiba, T. Fukao, O. Ichikawa, M. Oshima, M. Takemoto, and D.G. Dorrell, “Magnetic Bearings and Bearingless Drives”, London, U.K.: Newnes, 2005.

[12] A. Grauers, “Design of direct-driven permanent-magnet generators for wind turbines”, Ph.D. dissertation, Chalmers University of Technology, Göteborg, Sweden, 1996.

[13] J.J. Cathey, “Electric machines: Analysis and design applying MATLAB”, McGraw-Hill, 2001. [14] H. Polinder, F.F.A. van der Pijl, G.J. de Vilder, P.

Tavner, “Comparison of direct-drive and geared generator concepts for wind turbines”, IEEE Trans. Energy Conversion, Vol. 21, pp. 725-733, September 2006.

[15] L. Fingersh, M. Hand and A. Laxson, “Wind turbine design cost and scaling model”, Technical Report, NREL/TP-500-40566, December 2006.

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