![Fig. 5. IEEE recommended equivalent circuit of the induction machine and the applied Γ-type equivalent circuit [15].](/figures/fig-5-ieee-recommended-equivalent-circuit-of-the-induction-3kn1363z.webp)
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 3, SEPTEMBER 2006 725
Comparison of Direct-Drive and Geared Generator
Concepts for Wind Turbines
Henk Polinder, Member, IEEE, Frank F. A. van der Pijl, Gert-Jan de Vilder, and Peter J. Tavner
Abstract—The objective of this paper is to compare five differ-
ent generator systems for wind turbines, namely the doubly-fed in-
duction generator with three-stage gearbox (DFIG3G), the direct-
drive synchronous generator with electrical excitation (DDSG),
the direct-drive permanent-megnet generator (DDPMG), the
permanent-magnet generator with single stage gearbox (PMG1G),
and the doubly-fed induction generator with single-stage gearbox
(DFIG1G). The comparison is based on cost and annual energy
yield for a given wind climate. The DFIG3G is a cheap solution
using standard components. The DFIG1G seems the most attrac-
tive in terms of energy yield divided by cost. The DDPMG has the
highest energy yield, but although it is cheaper than the DDSG, it
is more expensive than the generator systems with gearbox.
Index Terms—Direct-drive, doubly fed induction generator
(DFIG), permanent-magnet generator, single-stage gearbox, syn-
chronous generator, wind turbine.
I. INTRODUCTION
T
HE objective of this paper is to compare five different
generator systems for wind turbines, namely the doubly-
fed induction generator with three-stage gearbox (DFIG3G),
the direct-drive synchronous generator with electrical exci-
tation (DDSG), the direct-drive permanent-magnet generator
(DDPMG), the permanet-magnet generator with single stage
gearbox (PMG1G) and the doubly-fed induction generator with
single-stage gearbox (DFIG1G).
The three most commonly used generator systems for wind
turbines are as follows [1], [2].
1) Until the late 1990s, most wind turbine manufacturers
built constant-speed wind turbines with power levels be-
low 1.5 MW using a multistage gearbox and a standard
squirrel-cage induction generator, directly connected to
the grid.
2) Since the late 1990s, most wind turbine manufacturers
have changed to variable speed wind turbines for power
levels from roughly 1.5 MW, mainly to enable a more flex-
ible match with requirements considering audible noise,
power quality, and energy yield. They have used a multi-
stage gearbox, a relatively low-cost s tandard DFIG and a
Manuscript received May 25, 2005; revised January 30, 2006. This work was
supported in part by Zephyros BV, Hilversum, The Netherlands and in part by
ATO Maritiem Platform, Den Helder, The Netherlands. Paper no. TEC-00176-
2005.
H. Polinder and F. F. A. van der Pijl are with the Electrical Power Processing
Group of Delft University of Technology, 2628CD Delft, The Netherlands.
They are also with DUWIND, the Interfaculty Delft University Wind Energy
Research Institute (e-mail: h.polinder@tudelft.nl; f.vanderpijl@tudelft.nl).
G.-J. de Vilder is with Harakosan Europe BV, 1213 NS Hilversum, The
Netherlands (e-mail: g.de.vilder@harakosan.nl).
P. J. Tavner is with the School of Engineering, Durham University, Durham
DH1 3LE, U.K. (e-mail: peter.tavner@durham.ac.uk).
Digital Object Identifier 10.1109/TEC.2006.875476
Fig. 1. Photo of a 1.5-MW direct-drive wind turbine with permanent-magnet
generator of Zephyros. Source: Zephyros BV.
power electronic converter feeding the rotor winding with
a power rating of approximately 30% of the rated power
of the turbine.
3) Since 1991, there have also been wind turbine manufac-
turers proposing gearless generator systems with the so-
called direct-drive generators, mainly to reduce failures in
gearboxes and to lower maintenance problems. A power
electronic converter for the full-rated power is then neces-
sary for the grid connection. The low-speed high-torque
generators and the fully rated converters for these wind
turbines are rather expensive.
Most direct-drive turbines being sold at the moment have syn-
chronous generators with electrical excitation. However, [3]–[7]
claim benefits for permanent magnet excitation, which elim-
inates the excitation losses. In this paper, this difference is
quantified. Fig. 1 depicts an example of a wind turbine with
a permanent-magnet direct-drive generator [8].
For the increasing power levels and decreasing speeds, these
direct-drive generators are becoming larger and even more ex-
pensive. Therefore, it has been proposed to use a single-stage
gearbox (with a gear ratio in the order of 6 or higher) and a
permanent-magnet generator [7]. This system, called the multi-
brid system, is illustrated in Fig. 2.
On the one hand, the resulting system combines some of
the disadvantages of both the geared and direct-drive systems:
the system has a gearbox and it has a special and therefore
expensive generator and a fully rated converter. On the other
hand, compared to direct-drive systems, a significant decrease
0885-8969/$20.00 © 2006 IEEE
726 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 3, SEPTEMBER 2006
Fig. 2. Sketch of the system with a single-stage gearbox. Source: WinWinD.
in the generator cost and an increase in the generator efficiency
can be obtained.
Further, the question arises whether this system with a single-
stage gearbox could be used in combination with a DFIG. Be-
cause the generator torque is still rather high and the speed rather
low, the generator can be expected to have a large diameter
and air gap, and therefore a high magnetizing current and high
losses. However, the rating of the converter could be reduced to
roughly 30%, giving an important benefit in cost and efficiency.
This new system is introduced and further investigated in this
paper.
For both systems with a single-stage gearbox, the use of a
gearbox leads to a significant reduction of the external dimen-
sions, enabling the installation of such a 3-MW wind turbine on
locations that are currently limited from a logistic point of view
to 1.5-MW turbines.
The objective of this paper, therefore, is to compare five wind
turbine generator systems, namely:
1) the DFIG3G as currently used;
2) the DDSG as currently used;
3) the DDPMG;
4) the PMG1G;
5) the DFIG1G.
To compare the five generator systems, a 3-MW, 15-r/min
wind turbine is used. For this turbine, an approximate design
of the generators is made to get indications of weight and cost.
The differences in annual energy yield are calculated for a given
wind climate. This comparison and the proposal to use a DFIG
in combination with a single-stage gearbox are the original con-
tributions of this paper.
An early comparison of the efficiency of three wind turbine
generator systems is given in [9]. In [6] and [7], more genera-
tor systems were compared and more criteria were taken into
account. The contribution of this paper is that it introduces the
TABLE I
M
ODELING CHARACTERISTICS
DFIG1G, and compares it with four other generator systems.
It also quantifies the difference between the electrical-excited
direct-drive generator and the PM direct-drive generator.
The paper starts with a section about modeling of the wind
turbine, the gearbox, the converter, and the generator. Next the
five generator designs are briefly described and the resulting
performance is given. The paper concludes with a comparison
of the five generator concepts.
II. M
ODELING THE GENERATOR CONCEPTS
A. Wind Turbine Modeling
Table I gives t he characteristics of the wind turbine that was
used to compare the different generator systems. Using these
characteristics, the available s haft power P can be calculated as
a function of the wind speed as [2], [10]
P =
1
2
ρ
air
C
p
(λ, θ)πr
2
v
3
w
(1)
where ρ
air
is the mass density of air, r is the wind turbine
rotor radius, v
w
is the wind speed, and C
p
(λ, θ) is the power
coefficient or the aerodynamic efficiency, which is a function of
the tip speed ratio λ (tip speed divided by wind speed) and the
pitch angle θ.
Fig. 3 illustrates the rotor speed, which is assumed to be pro-
portional to the wind speed at maximum aerodynamic efficiency
at low wind speeds and equal to the rated rotor speed at higher
wind speeds (above 9 m/s). At wind speeds above the rated
POLINDER et al.: COMPARISON OF DIRECT-DRIVE AND GEARED GENERATOR CONCEPTS FOR WIND TURBINES 727
Fig. 3. Rotor speed and Weibull distribution of the wind as a function of wind
speed.
wind speed, the blades are pitched to reduce the aerodynamic
efficiency and so the power.
For energy yield calculations, an average wind speed of 7 m/s
with a Weibull distribution [10] is used as illustrated in Fig. 3.
Integrating the area below the curve gives a value of 1.
Table I also gives some approximate numbers for the cost of
the rest of the wind turbine. Because the paper concentrates on
the generator system, these numbers are not extensively vali-
dated and must be seen only as indicators.
B. Gearbox Modeling
The gear ratio of the single-stage gearbox is chosen as 6.
Some references suggest higher gear ratios [7]. However, at the
moment, this is not seen as proven technology with a guaranteed
lifetime. From the commercially available gearboxes, it appears
to be cheaper to use gearboxes with more stages for higher gear
ratios. A cost estimate of the gearbox is given in Table I.
According to [11], a viscous loss of 1% of the rated power
per gearbox stage is a reasonable model. This means that the
losses are proportional to the speed
P
gear
= P
gearm
n
n
rated
(2)
where P
gearm
is the loss in the gearbox at rated speed (3%
of rated power for a three-stage gearbox [11] and 1.5% for a
single-stage gearbox, see Table I), n is the rotor speed (r/min),
and n
rated
is the rated rotor speed (r/min).
C. Converter Modeling
A back-to-back voltage source inverter is used to ensure that
the generator currents and the grid currents are sinusoidal. A
cost estimate is given in Table I.
There are various ways of modeling converter losses [12].
The model used here divides them into three parts [13]:
1) a small part that is constant and consists of power dis-
sipated in power supplies, gate drivers, control, cooling
systems and so on [9];
2) a large part that is proportional to the current and consists
of switching losses and conduction losses;
3) a part that is proportional to the current squared and con-
sists of conduction losses because the on-state voltage of
a semiconductor increases with the current.
Therefore, the losses in the converter P
conv
are modeled as
P
conv
=
P
convm
31
1+10
I
s
I
sm
+5
I
2
s
I
2
sm
+10
I
g
I
gm
+5
I
2
g
I
2
gm
(3)
where P
convm
is the dissipation in the converter at rated power
(3% of the rated power of the converter, see Table I), I
s
is the
generator side converter current ,I
sm
is the maximum generator
side converter current, I
g
is the grid side converter current, and
I
gm
is the maximum grid side converter current.
D. Generator Modeling
The different generators are modeled using equivalent circuit
models. This section describes the equations used to determine
the parameters of the equivalent circuit. The machine parameters
are calculated in conventional ways [9].
The following assumptions are used in the calculations.
1) Space harmonics of the magnetic flux density distribu-
tion in the air gap are negligible; only the fundamental is
considered.
2) The magnetic flux density crosses the air-gap perpendic-
ularly.
Slot, air-gap, and end-winding leakage inductances are cal-
culated as given in [14]. The magnetizing inductance of an AC
machine is given by [14], [15]
L
sm
=
6µ
0
l
s
r
s
(k
w
N
s
)
2
p
2
g
eff
π
(4)
where l
s
is the stack length in axial direction, r
s
is the stator
radius, N
s
is the number of turns of the phase winding, k
w
is
the winding factor [14], [15], p is the number of pole pairs, and
g
eff
is the effective air gap.
The effective air gap of the machine depends on the t ype of
machine. For all machine types, it can be written as
g
eff
= k
sat
k
Cs
k
Cr
g +
l
m
µ
rm
(5)
where k
sat
is a factor representing the reluctance of the iron in
the magnetic circuit, k
Cs
is the Carter factor for the stator slots
[14], k
Cr
is the Carter factor for the rotor slots (if present) [14], g
is the mechanical air gap, µ
rm
is the relative recoil permeability
of the magnets, and l
m
is the magnet length in the direction of the
magnetization (which is zero in a machine without permanent
magnets).
The Carter factor is given by [14], [16]
k
C
=
τ
s
τ
s
− g
1
γ
g
1
= g +
l
m
µ
rm
γ =
4
π
b
so
2g
1
arctan
b
so
2g
1
− log
1+
b
so
2g
1
2
(6)
where τ
s
is the slot pitch and b
so
is the slot opening width.
The factor representing the reluctance of the iron of the mag-
netic circuit is calculated as [17]
k
sat
=1+
1
H
g
g
eff
l
Fe
0
H
Fe
dl
Fe
(7)
where H
Fe
is the magnetic field intensity in the iron, estimated
from the BH curve.
728 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 3, SEPTEMBER 2006
Fig. 4. Sketch of a cross section of four poles of a permanent magnet syn-
chronous machine with full pitch winding.
In permanent-magnet machines, this factor representing sat-
uration is much smaller than in the other machines because the
effective air gap is much larger due to the low permeability of
the magnets.
Using Ampere’s circuital law, the BH characteristic of a rare-
earth permanent magnet and the magnetic flux continuity, the
flux density above a magnet in the air gap of a permanent-magnet
machine (Fig. 4) can be calculated as [15]
ˆ
B
g
=
l
m
µ
rm
g
eff
B
rm
(8)
where B
rm
is the remanent flux density of the magnets (1.2 T).
Using Fourier analysis, the fundamental space harmonic of
this flux density can be calculated as [15], [16]
ˆ
B
g
=
l
m
µ
rm
g
eff
B
rm
4
π
sin
πb
p
2τ
p
(9)
where τ
p
is the pole pitch and b
p
is the width of the magnet.
The no-load (motional) voltage induced by this flux density
in a stator winding can be calculated as [15], [16]
E
p
=
√
2k
w
N
s
ω
m
r
s
l
s
ˆ
B
g
(10)
where ω
m
is the mechanical angular speed of the rotor.
The copper losses are calculated from the currents and the
resistances. The phase resistance is calculated as
R
s
=
ρ
Cu
l
Cus
A
Cus
(11)
where ρ
Cu
is the resistivity of copper, A
Cus
is the cross-sectional
area of the conductor, and l
Cus
is the length of the conductor of
the phase winding.
The length of the conductor is calculated as the number of
turns multiplied by the length of a turn, where the length of a
turn is estimated as twice stack length (in the slots) plus four
times the pole pitch (for the end windings)
l
Cus
= N
s
(2l
s
+4τ
p
). (12)
The cross-section area of the conductor is the available slot
area multiplied by the fill factor divided by the number of turns
per slot:
A
Cus
=
pqk
sfil
b
sav
h
s
N
s
(13)
where q is the number of slots per pole per phase, k
sfil
is the s lot
fill factor (60%), b
sav
is the average slot width, and h
s
is the slot
height.
The specific iron losses (the iron losses per unit mass) are
calculated using [14], [15]
P
Fe
=2P
Fe0 h
f
e
f
0
ˆ
B
Fe
ˆ
B
0
2
+2P
Fe0 e
f
e
f
0
2
ˆ
B
Fe
ˆ
B
0
2
(14)
where f
e
is the frequency of the field in the iron, P
Fe0 h
is the
hysteresis loss per unit mass at the given angular frequency f
0
and flux density B
0
(Table I), and P
Fe0 e
is the eddy current loss
per unit mass at the given angular frequency f
0
and flux density
B
0
(Table I).
The factor 2 is included in this equation because the flux den-
sities do not change sinusoidally and they are not sinusoidally
distributed, which increases the iron losses. High quality lami-
nations are used to limit the iron losses in the generators with
higher frequencies.
To calculate the total iron losses, the specific iron losses in
the different parts (teeth and yokes) are evaluated, multiplied by
the weight of these parts, and added.
To find out the cost of a generator, the masses of iron, copper,
and magnets are calculated and multiplied by the assumed cost
per kilogram of the material (see Table I).
III. G
ENERATOR DESIGN AND PERFORMANCE
A. DFIG3G
The number of pole pairs of the DFIG3G is chosen as 3.
Because the stator is directly connected to the 50-Hz grid, the
synchronous speed is 1000 r/min. With a gear ratio of 80, the
rated speed of the generator is 1200 r/min, so that at rated speed,
there is still some margin for control purposes.
The DFIG3G has an air-gap radius of 0.42 m and a stack
length of 0.75 m. Other important dimensions are given in
Table II.
Fig. 5 depicts two induction-machine equivalent circuits. The
rotor side parameters are all referred parameters. The parame-
ters of the second equivalent circuit can be calculated from the
parameters of the first in the following way [15]:
L
s
= L
sσ
+ L
sm
;
R
R
=
R
r
L
2
s
L
2
sm
L
L
=
L
sσ
L
s
L
sm
+
L
rσ
L
2
s
L
2
sm
. (15)
To simplify the calculations, the second equivalent circuit
has been used. It is further assumed that the converter controls
the rotor current in such a way that the magnetizing current is
confined to the stator and that the transformed rotor current I
R
is in phase with the voltage applied to the inductance L
s
.
Fig. 6 depicts s ome results from the model as a function of
the wind speed. Voltage, current, power, generator efficiency,
generator system efficiency (including losses in the converter
and the gearbox), and losses are depicted. The annual energy
POLINDER et al.: COMPARISON OF DIRECT-DRIVE AND GEARED GENERATOR CONCEPTS FOR WIND TURBINES 729
TABLE II
M
AIN DIMENSIONS,PARAMETERS,WEIGHTS,COST, AND ANNUAL
ENERGY OF THE FIVE GENERATOR SYSTEMS
dissipation, determined from a combination of the losses with
the Weibull distribution, is also depicted in Fig. 6. Table II gives
the annual energy yield and the annual dissipation. It also gives
cost estimates.
The losses in the gearbox dominate the losses in this generator
system: Roughly 70% of the annual energy dissipation in t he
generator system is in the gearbox.
B. DDSG
The air-gap diameter of the DDSG is chosen to be 5 m. From
the electromagnetic point of view, larger air-gap diameters are
better, but mechanical design, construction and transportation
Fig. 5. IEEE recommended equivalent circuit of the induction machine and
the applied Γ-type equivalent circuit [15].
Fig. 6. Characteristics of the DFIG3G.
Fig. 7. Sketch of a linearized cross section of two poles of an electrically
excited synchronous machine.
become more difficult. This 5-m air-gap diameter is a compro-
mise between these criteria.
Fig. 7 depicts a cross section of two poles of the machine. The
number of slots per pole per phase is two. Increasing this number
makes the machine heavier and more expensive because of the
increasing dimensions of end-windings and yokes. Decreasing
this number results in a significant increase in the excitation
losses, mainly in part load. Table II gives some other important
dimensions.
Fig. 8 depicts the equivalent circuit of the DDSG and the ap-
plied phasor diagram. The phase current leads the phase voltage
a little in order to reduce saturation and excitation losses while a
larger rating of the converter is not necessary. A more extensive
description of the model for saturation is given in [17].