424 1
Analysis of a Novel Transverse Flux Generator in
Direct-driven Wind Turbines
Dmitry Svechkarenko, Juliette Soulard, and Chandur Sadarangani
Abstract This paper presents analysis of a novel transverse An interest in gearless energy systems is likely to continue
flux direct-driven wind generator. The analytical model for the
growing in the near future, as larger power converters become
calculation of different parts of the inductance is developed and
available.
applied for the evaluation of machine performance with respect
A direct-driven low-speed generator with a large number of
to its geometry. Generators rated for 3, 5, 7, and 10 MW output
poles and larger than conventional generator output diameter
power are investigated. The possible ranges of design parameters
are discussed and conclusions are drawn. is used in the gearless energy system. Electrically excited
direct-driven synchronous and induction generators are uti-
Index Terms Direct-driven wind turbine, inductance model,
lized by a number of wind turbines manufacturers (Enercon,
permanent magnet, transverse flux machine.
Made) [1]. In the last few years, a reduced magnet price made
a synchronous generator with a permanent magnet excitation
I. INTRODUCTION
(PMSG) an attractive alternative. This topology, for example,
is utilized by Harakosan in their 2 MW wind turbine. In
ITH the further development of wind energy and
comparison to the electrical excitation, the permanent magnet
increased wind power penetration level in power sys-
W
excitation favors a reduced active weight, decreased copper
tems, the issues of availability and reliability of generating
losses, yet the energy yield is somewhat higher [2].
units become of great importance. This particularly applies
A number of studies have been conducted to investigate
for stand-alone and offshore applications due to their often
different topologies of PMSG suited for direct-driven low-
hard-to-reach locations. The overall reliability of wind turbine
speed wind generators. A possibility of utilizing a transverse
is somewhat reduced by using a gearbox, which is applied for
flux permanent magnet (TFPM) topology in the gearless wind
adjustment of a low-speed turbine shaft to a higher rotational
energy system was discussed by Weh in [3]. An attractive
speed of a conventional generator. In addition, a gearbox is
feature of the TFPM is that with increasing number of poles,
subject to mechanical wear, vibrations, requires lubrication
unlike in the radial flux machine, the current loading can be
and more frequent maintenance at considerable cost. As a
increased and as a result a higher value of specific torque
result, a gearless wind energy system has drawn attention of
density can be achieved [4].
wind turbine manufacturers (Enercon, Made, Harakosan). An
This paper concentrates on the analysis of a novel TFPM
overview of gearless system, as well as the components it
topology and investigates its possible utilization in wind
comprises, is presented in Fig. 1.
generators from 3 to 10 MW.
As can be noticed, for the connection of a generator to
the network, a converter scaled for the full output power is
required. This would increase a system cost and introduce
A. General Overview of a Novel TFPM Generator
additional losses. On the other hand, a full-scaled converter has
The novel machine can be referred to as a rotational multi-
an opportunity of a variable speed control with a large range.
phase single-sided transverse flux machine without return
This allows a better utilization of the available mechanical
paths [4], [5]. The cross-section of the TFPM generator
power and therefore has a potentially higher energy yield.
geometry is presented in Fig. 2. As can be observed, the
generator consists of a hollow toroidal rotor with surface-
mounted permanent magnets embraced by the laminated stacks
Generator Full-scaled converter Transformer
with the windings placed in the slots. The main machine radius
Rm and the tube radius Rs are shown in Fig. 2. The cut
Grid
required for the mechanical assembling of the rotor on the
ac/dc dc/ac
shaft is presented by angle 2 �.
The TFPM topology allows to use a stator winding of a
simple mechanical structure, which facilitates high voltage
insulation. This could be an attractive feature in the future
Fig. 1. A gearless wind energy system.
since the voltage of wind generators has been continuously
Manuscript received July 6, 2006. increasing in the voltage levels up to 5 kV can reasonably be
D. Svechkarenko, J. Soulard, and C. Sadarangani are with the Electrical
expected in the forthcoming generators [6].
Machines and Power Electronics Laboratory, School of Electrical Engineering,
The arrangement presented in Fig. 3 was selected for
Royal Institute of Technology, Teknikringen 33, 10044 Stockholm, Sweden
(tel: [phone], fax: [phone], email: [e-mail]). the further analysis, as it has a shorter end-winding and is
424 2
3 4
Set the predefined parameters
Rrmax as in Table I

Rs
2 5



Vary the parameters

as in Table II


Rm

Calculate the main dimensions
1 6
of magnetic circuit
R
rmin
�
Calculate the induced emf
by integrating the flux in the teeth
Set the power factor cos Ć
and the efficiency �
�m

Calculate the required copper area
Fig. 2. Cross-section of the novel TFPM generator in the stack plane with
the main dimensions, where wm is the direction of rotation.
Calculate the synchronous inductance
and evaluate the machine performance
a a2 a2 a c c2 c2 c b b2 b2 b
Calculate the active weight, iron losses,
recalculate power factor and efficiency
�m

Check NO
cos Ć and �
N S
N S
OK
N S
S N Further analysis
S N
S N
Fig. 4. Flowchart showing the design procedure of the TFPM generator.
N S
N S
N S
�m
Fig. 3. Arrangement of winding in case of separated flux paths.
The subject to changes design parameters are varied in ranges
as shown in Table II. After that, the dimensions of the magnetic
circuit and the induced emf can be calculated. To obtain
relatively easier to analyze. The main magnet flux path is the required copper area, the power factor cos Ć = 0.92
shown with a dashed line. As the winding has a three-time
and the efficiency � = 0.97 are being assumed. Once the
single phase structure it is referred to as a separated winding. equivalent parameters and the performance are evaluated, the
The stator slots have a rectangular shape, as well as the active weight and the iron losses can be obtained. The new
conductors in the windings.
values for the power factor and the machine overall efficiency
A more detailed description of the novel TFPM topology, as can finally be obtained. However, if the differences between
well as the design procedure applied for the parametric study the initially guessed and recalculated cos Ć and � are large
of 5 MW wind turbines can be found in [7]. (i.e. more then 5%), the corrected values should be used and
the calculations be repeated.
II. ANALYSIS OF THE NOVEL TFPM
The procedure with the equations used for analysis has
The calculation procedure used in the analysis of the TFPM been described in more details in [7]. The evaluation of
generator is presented as a flowchart in Fig. 4. At first, the the equivalent parameters has however not been presented
predefined parameters are set into the program as in Table I. previously and therefore is described below.
424 3
TABLE I
where the airgap reluctance Rg and the permanent magnet
PREDEFINED PARAMETERS FOR 5 MW WIND TURBINE
reluctance Rpm are given by
g g
Property Value
Rg = = , (3)
�0Ag �0bts1 lst,r
Output power Pout (MW) 5
Number of teeth per stator stack Qs 36
hm hm
Rpm = = . (4)
Copper losses Pcu (W) 0.02Pout
�0�pmApm �0�pmlm,s lm,r
Turbine speed nm (rpm) 13.2
2) Airgap Leakage Inductance: The analysis for the airgap
Fill factor kf ill 0.55
leakage inductance is similar to the previous case. The currents
Number of conductors in series per coil per slot ns 1
in the coils produce the magnetic field in the airgap, without
Maximum flux density in the teeth Bts (T) 1.4
entering the rotor iron, as illustrated in Fig. 6. Considering the
Airgap flux density Bg (T) 0.9
ć%
Magnet remanent flux density Br,pm (T) at 100 C 1.1 new magnetic circuit, the airgap leakage inductance Lag per
Magnet relative permeability �pm 1.05 phase can be found
4n2 Qs p
s
Lag = , (5)
TABLE II
2
2Rg + Rgpm 6 2
DESIGN PARAMETERS FOR 5 MW WIND TURBINE
2
where the reluctances Rg and Rgpm can be calculated as
Variable Value
g + hm g + hm
2
Rg = = , (6)
Main machine radius Rm (m) 1.5..2
2�0Ag 2�0bts1 lst,r
Radii ratio kR = Rs/Rm 0..1
�p,s �p,s
Cut angle � (rad) 0..Ą
Rgpm = = . (7)
�0Agpm �0hm lm,r
Number of poles p 400..700
2Ni
(a) (b)
+ -
A. Equivalent Parameters of the TFPM Generator
1) Main Inductance: The inductance of a coil is defined
i i
as the ratio of the flux linkage  of this coil to the current i ""
drawing it
2 2
Rg Rg
 nsŚ n2
s
L = = = , (1)
i i R Rgpm
where Ś is the flux in the magnetic circuit with the sum
reluctance R and ns is the number of conductors in series
Fig. 6. Airgap leakage inductance geometry (a) and the equivalent magnetic
per coil. The magnetic field caused by the armature reaction
circuit (b).
and the magnetic circuit are depicted in Fig. 5. By analyzing
the magnetomotive force in the airgap and taking into account 3) Slot Leakage Inductance: The current flowing in the
the mutual effect of two other phases, the main inductance La winding creates a magnetic field not only in the airgap, but also
per each phase can be calculated as follows in the slot, as depicted in Fig. 7. This magnetic field results
in the so-called slot leakage inductance. By applying the
4n2 Qs p
coenergy equation and integrating the magnetic field intensity
s
La = , (2)
in the slot volume occupied by the winding [8], the slot
2(Rg + Rpm) 6 2
leakage inductance can be calculated as follows
2Ni
(a) (b)
+ -
i i
i i
Rg Rg H
""
""
hss
g
bss
hm Rpm Rpm
Fig. 5. Main inductance geometry (a) and the equivalent magnetic circuit
(b). Fig. 7. Slot leakage geometry.
424 4

n2�0hsslst,r Qs p
s
Ls = . (8) bsshss
Rc = Rew = ,
3bss 3 2
2Ą
�p,s
4) Between-stack Inductance: The between-stack induc- r = rew = ,
2
Ą�p,s
tance is created by the magnetic field H that surrounds a
le = lew = .
2
conductor in the space between two neighboring stacks. If the
The end-winding inductance per each phase is calculated as
infinitely long conductor carrying a surface current i as shown

in Fig. 8a is assumed for simplicity, then the inductance for
"
�0�p,sn2 � Ą 2Qs
s
a conductor of length le and the conductor radius Rc < r is
Lew = ln "p,s , (11)
4 3
2bsshss
given by [8]

Finally, the magnetization reactance Xsm and leakage reac-
�0len2 r
s
tance Xs� can be calculated
L = ln . (9)
2Ą Rc
Xsm = 2ĄfeLa, (12)
(a) (b)
Rc
Xs� = 2Ąfe(Lag + Ls + Lbs + Lew), (13)
i
i i
"" where fe = nmp/120 is the electrical frequency with nm =
�m 30/Ą the speed of turbine in rpm.
r
H
B. Performance of the TFPM Generator
The equivalent circuit and the applied phasor diagram are
presented in Fig. 10. The winding current is placed between
the induced emf and the terminal voltage, so the angles are
Fig. 8. Magnetic field about a cylindrical conductor (a) and a coil while it
equal � = Ć. This positioning of the current would likely
is between two neighboring stacks (b).
reduce saturation and find a reasonable compromise between
For the conductor geometry and the magnetic field distri- the generator rating and converter rating.
bution shown in Fig. 8b, the effective radii and the length can When the copper area is known, the inductance of the
be calculated as follows winding can be evaluated and the new value of the power
factor cos Ć can finally be obtained, as


�p,s(hss+bts1)
2
Rc = Rbs = ,
2
Ą
Eph - (Xsm + Xs�)Iph/2

cos Ć = . (14)
hssbss
r = rbs = , Eph
Ą
le = lbs = 2 �p,r - lst,r.
Lsm Ls� Iph j(Xsm + Xs�)Iph
Finally, the between-stack inductance per phase is
Eph Ut

+
�0lbs n2 rbs Qs p
s
Iph
Lbs = ln . (10)
2Ą Rbs 3 2
Eph Ut
Ć
�
5) End-winding Inductance: The end-winding inductance
-
is created by the magnetic field about a coil when it makes
a turn between two slots, as shown in Fig. 9. The same as
Fig. 10. The equivalent circuit and applied phaser diagram.
previously Eq. 9 is applied for derivation of the end-winding
inductance. Recognize that
III. SIMULATION RESULTS
rew
A. Analyzed Characteristics
end-winding
A number of characteristics have been selected in order to
compare machines with different geometries and various out-
put power. The induced emf is obtained by integrating the flux
stack
in the stator teeth produced by the magnets. This parameter is
a machine size related and therefore for analysis, the induced
voltage per total active weight Eph/Gtotal is chosen. This
characteristic would show how well the active weight of the
generator is utilized. The other analyzed characteristic is the
Fig. 9. End-winding geometry.
generator overall efficiency �.
424 5
TABLE III
3
(a)
Maximum curve
DATA FOR ANALYSIS
2.5
3
Property 1 2 3
Radii coefficient kR 0.4082 0.5102 1.0000
2
Tube radius Rm (m) 0.6735 0.8418 1.6500
Cut angle � (rad) 0.5077 1.2693 2.3483
1.5
Total active weight Gtotal (kg) 36 360 34 400 36 440
Magnet weight Gpm (kg) 2 680 3 590 7 840
30
2
1
25 Efficiency � 0.97 0.97 0.97
Power factor cos Ć 0.99 0.99 0.99
0.5
Induced emf Eph (V) 975 1053 1275
1
0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
kR
for more detailed analysis. The most important characteristics
of these machines are summarized in Table III. The machines
3
(b)
have different geometries, as kR and � are varying, yet the
Maximum curve
machine overall efficiency � is almost the same. As can be
2.5
observed, machine 2 has somewhat less total active weight
3
and the weight of permanent magnets in machine 3 is almost
2 twice as much as in machine 2. As the permanent magnet is
one of the most expensive active materials, it makes it more
advantageous to keep kR and � reasonably low.
1.5
Theoretically, any of machines along this maximum line
could possibly be selected for further analysis. However, there
2
1
is a number of constraints that should be taken into account.
For example, at low values kR and high values �, the machine
0.5
would quite likely suffer from the increased leakage fluxes.
1
On the other hand, the value kR should not be too high and �
0
not too low, in order to allow the mechanical attachment of the
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
kR
generator to the turbine shaft. There might be several machines
that have the same active weight for different Rm. However,
Fig. 11. Distributions of the ratio Eph/Gtotal in (10-3V/kg) (a) and � (b)
the large machine radius requires a larger nacelle and a more
with respect to kR and �. The maximum curves for both characteristics and
three possible machine geometries denoted by circles are presented as well. massive construction. Therefore, the ranges of kR = 0.4 - 0.8
Ą Ą
The figure is plotted for machine with the following parameters: Pout =
and � = - can reasonably be selected.
4 2
5 MW, Rm = 1.65 m, p = 660, Qs = 36.
B. Various Output Power
The distribution of the ratio Eph/Gtotal with respect to kR This study is conducted in order to investigate how the
output power of the TFPM generator is related to the main
and � is presented in Fig. 11a. Once the radii ratio kR and
machine radius. The chosen values for the output power,
the cut angle � reach certain level, the characteristic attains its
number of teeth per stator stack, and the nominal mechanical
maximum value and drops if the active weight continues to
speed are summarized in Table IV.
increase (i.e. when kR increases and � decreases). In this case,
To be able to analyze the generators with various output
the machine becomes somewhat oversized and, as a result, the
power, the magnetic circuit dimensions in the rotational di-
TFPM machine looses one of its main advantageous features,
rection should be nearly the same for all studied machines.
i.e. high torque density. A gray stripe in Fig. 11a represents
It would help to keep the flux leakage at approximately the
the maximum line, along which the machines have nearly the
same level. This could be done by varying the main machine
same total weight.
radius and the number of poles in such a way that the pole
Fig. 11b shows the variation of �. As can be observed, the
pitch in the rotational direction �p,r is nearly constant, i.e.
maximum line is similar to the one in Fig. 11a. The amount
2ĄRm(1 + kR)
of copper in the machine is nearly constant for specified
�p,r max = = constant. (15)
p
output power, as the copper losses are assumed to be constant
(2% of the output power). As a result, after a certain point,
The main machine radius is assumed to vary in the range
the machine active weight is increasing mainly due to the
Rm = (1..3) m, while the radii ratio kR and the cut angle �
increasing iron weight. The increased iron weight results
remain constant, and the ratio Rm/p = 0.0025. The results of
in additional losses and reduced overall efficiency � of the
the simulations are demonstrated in Fig. 12.
machine.
As can be observed, the characteristic slope increases until
Three machines denoted by circles in Fig. 11 were selected it reaches its maximum, at which the generators have the
�
(rad)
�
(rad)
0
2
5
2
0
3
2
3
0
5
2
2
3
3
4
4
0
3
2
4
3
3
3
0
3
2
5
2
2
0
3
0
2
3
0
5
3
2
3
0
2
5
0
2
0
2
5
2
5
2
0
2
7
9
.
0
7
9
.
0
7
9
.
0
7
9
.
0
7
9
6
.
9
.
0
0
5
6
9
.
0
5
5
9
.
0
5
9
.
7
0
6
9
.
9
.
7
0
0
9
.
5
0
6
9
5
.
4
5
0
9
5
.
9
4
0
.
9
0
.
0
424 6
160
would limit the maximum allowed size of the generator, as the
Pout = 3 MW
(a)
increased generator weight would increase the inactive portion
140
Pout = 5 MW
of the nacelle weight and as a result require a more massive
Pout = 7 MW
120 tower construction.
Pout = 10 MW
4
3
100
IV. CONCLUSIONS
2
The analytical method for the evaluation of the synchronous
80
1
inductance in the TFPM has been developed and applied for
60
the evaluation of machine performance. Different machine
geometries have been analyzed. It has been found that there
40
is a number of machines with various � and kR that have
approximately the same performances. Therefore, some new
20
constraints have been added and the optimal ranges for further
0
analysis have been suggested.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Rm (m)
Furthermore, the machine performance has also been eval-
uated for the output power 3, 5, 7, 10 MW. It was found that
the torque density turns to improve with the increasing output
Fig. 12. Torque density (Nm/kg) with respect to the main radius Rm for
power of the generator.
turbines with the output power Pout = 3, 5, 7, 10 MW. The figure is plotted
for machine with the following parameters: � = Ą/3 rad, Rs = 0.5152 m, In order to improve the analytical calculations of induc-
Rm/p = 0.0025.
tances, the three-dimensional finite element analysis is re-
quired. This study will also help to analyze more thoroughly
TABLE IV
the influence of the dimensions of magnetic circuite on the
DATA FOR ANALYSIS
flux leakage.
For the performed analysis, it was assumed that all the heat
Property 1 2 3 4
produced by losses can be extracted from the machine. This
Fixed values:
might however not be a case in reality and the thermal model
Output power Pout (MW) 3 5 7 10 should therefore be included in the calculations.
Number of teeth Qs 24 36 48 72 In order to investigate in more details the influence of the
Mech. speed nm (rpm) 18.6 13.2 10.6 8.3 machine radius Rm and the cut angle � on the mechanical
Calculated values: strength of the generator and the total weight of the system,
the analysis of the mechanical structure (i.e. shaft, bearings,
Machine radius Rm (m) 1.0 1.4 1.8 2.4
Number of poles p 400 560 720 960 fastening) should be considered as well.
Active weight Gtotal (kg) 20 040 36 065 55 380 93 735 Finally, to verify the developed model, a downscaled proto-
Magnet weight Gpm (kg) 820 2 220 4 490 11 120 type is under development, the measurements to be performed
Efficiency � 0.97 0.97 0.97 0.97 and compared with analytical results.
Power factor cos Ć 0.98 0.99 0.99 0.99
Induced emf Eph (V) 340 690 1 150 2 120 REFERENCES
Torque density (Nm/kg) 79 103 117 126
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ison of direct-drive and geared generator concepts for wind turbines , in
Proc IEEE Int. Conf. Electric Machines and Drives, San Antonio, USA,
highest torque density. It is therefore worth investigating the
2005, pp. 543-550.
geometry and performance at these points in more details. The
[3] H. Weh, H. Hoffmann, J. Landrath,  New permanent magnet excited
synchronous machine with high efficiency at low speeds , in Proc. Int.
simulation results of the four machines with the different rating
Conf. Electrical Machines, Vol. 3, Pisa, Italy, 1990, pp. 35-40.
marked with circles in Fig. 12 are summarized in Table IV.
[4] H. Weh, H. May,  Achievable force densities for permanent magnet
The obtained values for the torque density are comparable excited machines in new configurations , in Proc. Int. Conf. Electrical
Machines, Munich, Germany, 1986, pp. 1107-1111.
with those previously reported, for example in [9]. However, a
[5] G. Henneberger and M. Bork,  Development of a new transverse flux
more detailed comparison will be performed once the thermal
motor , IEE Colloquium on New Topologies for Permanent Magnet
constraints are included in the calculation procedure. Machines, Digest No. 1997/090, 1997, pp. 1/1-1/6.
[6] H. Polinder, S.W.H. de Haan, M.R. Dubois, and J.G. Slootweg,  Basic
The total active weight, as well as the permanent magnet
operation principles and electrical conversion systems of wind turbines ,
portion of the total active weight are larger for the machines
in Proc. Nordic Workshop on Power and Industrial Electronics, Trond-
heim, Norway, 2004.
with higher rating, as a result of a nonlinear dependence of
[7] D. Svechkarenko, J. Soulard, and C. Sadarangani,  A novel transverse
the volume with the main machine radius Rm. This would
flux generator in direct-driven wind turbines , in Proc. Nordic Workshop
likely increase the price per total weight, yet would favor a
on Power and Industrial Electronics, Lund, Sweden, 2006.
more compact design as the output power increases consid- [8] D. Hanselman, Brushless permanent magnet motor design, Second edi-
tion, The Writers Collective, 2003.
erably with the main machine radius (Pout is approximately
[9] A. Grauers,  Design of direct-driven permanent-magnet generators for
proportional to the cube of Rm).
wind turbines , PhD thesis, Chalmers University of Technology, Sweden,
1996.
It should also be mentioned that the mechanical constraints
total
T/G
(Nm
/
kg)