Energy and Power Engineering, 2011, 3, 253-261
doi:10.4236/epe.2011.33032 Published Online July 2011 (http://www.SciRP.org/journal/epe)
High Efficiency Double-Fed Induction Generator Applied
to Wind Power Generator Technical Analyses
Deng-Chern Sue
Pacific Engineers & Constructors, Ltd., Taipei, China
Received December 3, 2010; revised January 30, 2011; accepted Febr u ary 28, 2011
Abstract
High efficiency Double-Fed Induction Generator applies new power electronic technology, and utilizes vec-
tor control to fix the magnetic direction of the stator to the vertical axis. Adjusting the input current of rotor
via an inverter can separately control the cross axis and vertical axis current of real power and reactive power
of a generator. Traditionally, rotating speed affects frequency and the output is unstable. This study concen-
trates on high efficiency Double-Fed Induction Generators and Traditional Generators from mathematic
model to derive and control the characteristics simulation and comparison than get an output of high effi-
ciency Double-Fed Industrial Generators. This study utilizes the simulation software MATLAB/Simulink to
simulate the response characteristics of vector control of a Double-Fed Industrial Generator. The operating
and control functions are better than those of a traditional generator.
Keywords: Double-Fed Induction Generator, Cut-in Speed, Pushover Torque, Stall Regulator, Pitch
Regulator, Inverter
1. Introduction
Taiwan is an island; with most of its energy imported.
Because of the shortage of an indigenous energy supply
in Taiwan, the international energy market has a strong
effect on the local economy. Utilizing fossil fuels may
cause global warming and temperature variation. The
International Kyoto meeting requested to decrease the
fossil fuel consumption and minimize the CO2 emission
to control the global warming effect. Therefore, Ameri-
can and European countries are concentrating on the
study of renewable sources of energy, such as wind
power, solar energy, ocean tides, hydro power biomass,
etc., wherein the wind has a significant possibility of
producing electric power.
The Taiwanese Government has set up “Sources of re-
newable energy policy” to increase the clean energy con-
sumption and promote the renewable sources of energy.
This stable incentive policy creates the renewable
sources of energy from the surrounding environment. It
supports relative industrial development and promotes
the renewable sources of energy for all applications.
Wind comes from the effects of solar and earth rota-
tion. It causes airflow with kinetic energy. It is called
wind power. Humanity has utilized wind-powered de-
vices, such as sailboats, wind-powered water wheels,
windmills, etc. In the late nineteenth century, a wind-
powered machine was connected with a generator to
produce power. Wind power becomes a main application
for wind energy [1].
On Taiwan, the annual northeast monsoon produces
strong winds along the coast, mountain and remote is-
land areas. According to a recent investigation, over
2000 km2 of land area has an annual average wind speed
higher than 5 m/s. Wind energy has an excellent poten-
tial and the minimum recoverable wind energy is esti-
mated at around 1000 MW. Taiwan has abundant wind
energy.
Currently, the Peng-Hu Chung Tun Power Station and
Taiwan Formosa Plastic Mai-Liao Power Station have
installed wind-powered generators, which have operated
successfully. However, Taiwan has a limited experience
and few studies have been made on wind power. This
study concentrates on the analysis and comparison of
output characteristics for high efficiency Double-Fed
Induction Generator and Traditional Generator.
2. Wind Power Efficiency
Rotation of the earth and solar radiation induce tempera-

D.-C. SUE 254
ture differences at the earth’s surface cause air circula-
tion. Airflow in the horizontal direction produces wind.
The wind velocity has the following units: m/s, km/hr,
mph knots (nautical mile/hr), with the relationships as
1 ms3.6 kmhr2.24 mph1.94 knots
In addition, the Beaufort scale can be used to identify
the wind strength. The wind strength has 0 up to 17
grade (wind velocity from 0.3 m/s to 61.2 m/s). Wind
pressure (F) is produced from airflow that is directly
proportional to the cube (per formula) of its velocity.
2
1
2P
F
CAU   (kW) (1)
where
A
: cross-sectional area of wind stream (m2)

: air density (1.225 kg/m3)
P
C
U: wind power coefficient : wind velocity (m/s)
The kinetic of wind pressure is called wind power (P),
which is wind pressure (F) produced work per unit time,
3
1
2P
PCAU   (2)
For stall regulator,
P
C is a

function and

is a
ratio of the velocity at wind tip of regulator vs. wind ve-
locity, i.e. rV

  and is the rotor radius of wind
machine,
r

(rad/s) is angle velocity, Figure 1 is the
P
C-

curve of various angles.
The power produced by a wind machine is directly
proportional to its cross-sectional area, and the cube of
the wind’s velocity [2-4]. Therefore, the wind machine’s
location is the key factor of power production and power
generating cost.
The wind machine operating at a pre-set range of wind
velocities has to ensure the generator operates at rated
speed. Means must be provided to shutdown the genera-
tor operating to protect the equipment if the wind veloc-
Figure 1. CP-λ curve of various angles.
ity becomes excessive. But, the theoretical kinetic energy
of the wind can only be partially utilized considering the
overall efficiency of machine; only a part of wind power
can be actually utilized.
3. Characteristics of Wind Machine
The kinetic energy of the moving air (wind) rotates the
blades of the wind machine. The blades convert the wind
energy to mechanical energy, which in turn, is converted
to electrical energy by the generator. The power output
of wind machine is affected by wind velocity, machine
efficiency, blade design, blade pitch, cross-sectional area,
etc. [1,2].
The wind machines type can be categorized into hori-
zontal shaft and vertical shaft depends on shape and ro-
tating shaft. The vertical shaft machine has a higher axial
retardation factor, lower rotating speed, lower efficiency
and requires more blade material, making it unsuitable
for power generating use. The horizontal shaft machine
can be categorized as facing upwind or downwind. The
upwind machine uses a rear rudder (small machine) or
universal mechanism to sense the wind direction and
position the blades to produce maximum power. The
downwind type uses the cone shape to minimize of the
rotor to follow wind direction so the blades are facing the
downwind side. Because the wind acts on the supporting
structure of the wind machine and then on the blades, the
resulting periodic fatigue loadings affects the machine
operating life. In general, horizontal shaft wind machines
are the upwind type, i.e., blades are facing the wind.
Figure 2 shows horizontal shaft wind machine type.
The blade selection significantly affects the rotating
speed and power output of machine. Currently, the major
blades type is three-blades type. The three-blades has
less loading variation more stable operation, decreased
fatigue loadings, increased blade operating life compared
to two blade and single blade units. In additional, the
(a) (b)
Figure 2. Horizontal shaft wind machine type. (a) Upwide;
(b) Downwind.

D.-C. SUE 255
operation of three-blade is smooth and comfortable of
vision, the two-blade units have an unstable rotation and
single blade units are unbalance and uncomfortable.
Therefore, the horizontal three-blades are selected for the
current study of wind machines. Accordingly, the hori-
zontal shaft, upwind and three-blade wind machines are
evaluated as the best approach for an operating wind
machine [1].
The power output is related to wind velocity or wind
speed. When the wind speed matches the cut-in speed,
the wind machine begins to produce power. From cut-in
speed to the rated speed, the wind machine power output
is directly proportional to the cube of the wind velocity.
From the rated speed to cut-out speed, the power output
remains at rated power. When the cut-out speed ex-
ceeded, the wind machine is shut down without power
output to avoid any damage. The blades must be feath-
ered to have no significant rotational velocity. Figure 3
shows wind velocity and power output of Vestas
V47-660 Type Wind Power Generator at rated power
660 kW, the cut-in speed, rated speed, and cut-out speed
are 4, 15 and 25 m/s respectively.
To maintain the rated power output for wind machine
and without damaging the gearbox and/or generator, the
power output of the wind machine has to be controlled.
Control is separated into a stall regulator and a pitch
regulator to control the amount of wind energy being
absorbed and transferred to produce power [1,2]. Ta b l e 1
is the comparison of stall regulator and pitch regulator.
4. Traditional Wind Machine Output
Characteristics
Currently, the major types of wind-powered generators
are permanent magnet generator, synchronous generator,
induction generator, and high efficiency double-fed gen-
erator [2,5]. The theory and output characteristics of the
different types of wind-powered generators are explained
as follows:
4.1. Permanent Magnet Generator
The rotor of the generator is made of permanently mag-
netic material and the rotor shaft is driven by the blades
of the unit. When the rotating blades drive the magnetic
rotor, a rotating magnetic field that interacts with the
multiple windings of the stator. These rotating lines of
magnetic force induce an alternating voltage in the
windings. The alternating current induction voltage is
A
EK

  (3)
where
K
: electrical coefficient of the generator
Figure 3. Wind velocity and power output of vestas V47-660
type wind power gener a tor.
Table 1. Comparison of stall regulator and pitch regulator.
Item Stall Regulator Pitch Regulator
Output Characteristics
Has small range of
output characteristic
curve
Has large range of
output characteristics
curve
Constant Speed
Control
Can meet control
requirements
Has difficulty at high
wind speed
Variable Speed
Control Can’t meet
Has better power
quality and lower
transmission load
compare to stall
regulator
Start Wind VelocityHigher wind velocity Lower wind velocity
Safety Needs breaker system
to protect over speed
Without over speed
problem
Structure
Structure and
maintenance
are easier
Structure and
maintenance more
complicated
Cost Lower cost Higher cost

: rotor magnetic flux (Wb)

: angle velocity of rotor speed (rad/sec)
Because the rotating magnetic field is fixed and the
rotor rotating speed varies with wind velocity, the output
voltage and frequency are variable and cannot provide a
stable power supply. The produced power must be run
through a rectifier and an inverter to be compatible with
a 60 Hz power system. Due to the small capacity and
higher cost per kilowatt of output, this type is not suit-
able for commercial applications. It is only suitable for
remote areas without a grid power supply.
4.2. Synchronous Generator
A synchronous generator operates at the synchronous

D.-C. SUE 256
syn
rotating speed of an alternating current system to which
it is connected. A synchronous generator requires direct
current to be supplied to the rotor winding via slipping to
produce the rotor’s magnetic flux. The prime mover
(wind) drives the generator rotor forming a rotating
magnetic field that induces a voltage in the stator wind-
ings of the unit. The windings of the stator are arranged
so that a three-phase voltage is produced. Interactions of
rotating magnetic field of synchronize rotation, which
inducts a three-blades voltage. The induction voltage of
alternating current is
A
EK

  (4)
where
K
: electrical coefficiency of generator

: rotor magnetic flux (Wb)
s
yn

: angular velocity of rotor rotating at synchronous
speed
2π
syn
f

 (rad/sec)
f
: stator frequency, 120
m
fnP
m
P
n: rotor synchronize speed (rpm)
: number of rotor poles
Output power (neglecting stator resistance) is
3sin δ
TA
out s
VE
PX  (5)
where,
T
V: voltage across generator terminals (volts)
s
X
: synchronous reactance () 
δ: phase angle difference between and (de-
gree).
A
ET V
In general, the large power supply system needs to use
two sets or more synchronous generators to combine into
system for supply power. It has the advantages of in-
creased system efficiency, decreased spare capacity, ease
of unit maintenance, increased power supply reliability
and meeting optimal dispatch, etc. Figure 4 shows out-
put power and torque angle for raised pole and cylindri-
cal rotor of synchronous generator.
Synchronous generator applies to wind-powered units
when the rotating blades directly drive the rotor without
any gearbox, avoiding the noise and wear of meshing
drive gears. When the actual wind speed exceeds the
design wind speed and the unit is operating at full load, a
pitch control system is installed to adjust the blade angle
to reduce the power extracted from the wind. Pitch con-
trol limits rotor speed and power output to eliminate
overload/overspeed damage.
The synchronous generator is same as the permanent
magnet generator. The output voltage and frequency
varies with the wind velocity. The wind machine nor-
mally rotates at 20 - 30 rpm compared to the maximum
synchronous speed of 3600 rpm for a 60 Hz grid system.
Figure 4. Output power characteristics of synchronous
generator.
In order to make the wind machine’s output compatible
with the 60 Hz grid, the machine’s output must pass
through a rectifier to become a DC and then through an
inverter to match the system frequency before being
stepped-up via a transformer to feed into the power grid.
4.3. Induction Generator
The three-phase induction generator uses magnetic in-
duction theory to transfer the electrical energy in the
form of magnetic flux from stator to rotor, without any
wire connection. Power from an external source ener-
gizes the stator, causing the rotor to turn, just like an in-
duction motor. The rotating speed of the rotor is slightly
lower than the rotating magnetic flux in the stator. This
type generator is also called an asynchronous machine.
When the rotor speed of an induction generator exceeds
the speed rotating magnetic field in the stator, and the
rotor direction is consistent with rotating magnetic field,
the rotor will tend to pull the stator field faster. This ac-
tion causes a reverse torque in the rotating direction, thus
causing the induction generator to operate as a generator
at the frequency and voltage of the initial power supply
to the stator. In a properly designed machine, the mag-
netic link between the rotor and stator is strong enough
to prevent the rotor going into over speed, regardless of
the energy input from the blades. The definition of rotat-
ing difference ratio for an induction generator is
100%
syn m
syn
nn
sn

 (6)
where,
s
yn
n
n: synchronous speed of magnetic field (rpm)
m: rotor speed of rotor (rpm)

D.-C. SUE 257
Figure 5 follows Kirchhoff’s voltage law, the voltage
loop equation for single-phase effective circuit of an in-
duction generator is

s
ssmSm
VRjXXIjXI

 

r
(7)

0r
msrm r
R
jXIj XXI
s
 (8)
In Equations (7) and (8), only the magnetic reactance,
jXm, is considered and the flux branch resistance of the
core, Rc, is neglected. The conversion power and torque
of an induction generator are represented as
21
3
convr r
s
PIR
s






(9)
conv
ind m
P


 (10)
Figure 6 shows the torque-speed characteristics cur-
ves of induction generators with differing rotor resistance
values. The produced power is directly proportional to
the torque applied to the stator by the blades and thus
rotor, but if the input torque developed by the wind on
the blades, is larger than pushover torque, the induction
Figure 5. Effective circuit of a single phase of an induction
generator.
Figure 6. Torque-speed char acteristic curve of an induction
generator with diff erent rotor resistanc e va lues.
generator will over speed. Therefore, when applied to a
wind-powered generator an adequate breaker, rotor re-
sistance control, blade pitch control or similar devices to
prevent high wind speed and/or excessive torque from
inducing over speed of the blades and rotor [1].
The induction generator rotor is without a magnetic
field circuit, to change the magnetic field to control the
output voltage and is not self-exciting. The required re-
active power for excitation needs is supplied by a con-
nection from an external capacitor or from grid system.
The excitation power controls the voltage at the genera-
tor terminals, which supply the power to grid system [5].
The advantages of induction generator are structural
simplification; exciting field system is not required, un-
necessary to synchronize operation, easy for operation
and maintenance. When induction generator derives power
from wind, the self-exciting type is used. A capacitor is
installed across the terminals to provide the required re-
active power for startup and improve the power factor
during operation.
4.4. Comparison Synchronous Generator and
Induction Generator
The stator construction is identical for a synchronous
generator and an induction generator. The major differ-
ence is rotor design and construction. The winding of
rotor of a synchronous generator need to have direct cur-
rent (DC) for excitation to produce the rotor’s magnetic
field but the damper windings of the rotor of the induc-
tion generator need to be short-circuited to produce rotor
magnetic field. Table 2 shows the comparison of syn-
chronous and induction generators.
Table 2. Performance comparisons of synchronous and
induction generators.
Items Synchronous Generator Induction Generator
Stator structureThree-phase winding Three-phase
winding
Rotor structure
Has evidenced and
controlled pole rotor
winding need to
connect to DC source
Has cage rotor, winding
doesn’t need to connect
DC
Speed Operating at
synchronize speed
Operating at
over-synchronous speed
Reactive power
compensation Not needed From system or connect to capacitor
End voltage
control
Cause exciting system
control Can’t control
Converter deviceNeeded Not needed
Maintenance Complicate and difficult Simple and easy
Cost Expensive Cheap

D.-C. SUE 258
5. High Efficiency Double-Fed Induction
Generator
The disadvantages and limitations of the self-exciting
induction generator include the difficulty to adjust the
output voltage and frequency, the need to be operated at
over-synchronous speed, the small range of output power,
etc. Currently, new developments in the windings of the
induction generator and vector control theory as applied
to controlling the rotor input voltage and frequency can
modulate the power input and output characteristics of
the generator rotor. With the advantages of operating in
an aubsynchronous speed range, output can exceed rated
power; closer control of output voltage and frequency is
obtained. Figure 7 shows a double-fed induction gen-
erator structure [2].
5.1. Model of Double-Fed Induction Generator
After transformation and d-q transformation of a three-
phase dynamic model for a double-fed induction genera-
tor [3,4], the equations of dynamic model can be written
as:
d
d
d
d
ds
dss dssqs
qs
qss qssds
VRI t
VRI t






(11)
d
d
d
d
dr
drr drrqr
qr
qrr qrrdr
VRI t
VRI t






(12)

d
d
r
me r
eqsdr dsqr
s
Jf
t
M
I
I
L

 

 

where
Figure 7. Structure of double-fed induc tion ge nerator.
r

: angle speed of rotor

,radsec
rs
s  
dss dsdr
qss qsqr
drdsrdr
qrqsrqr
LI MI
LI MI
M
ILI
M
ILI









(13)
Due to generator operating at steady condition, there-
fore, with further analysis, the term d
dt

can be ne-
glected, allowing the voltage of stator and rotor to be
re-written as:





dssdsssqsqr
qssqss sdsdr
drrdrr rqrqs
qrrqrr rdrds
VRI LIMI
VRI LIMI
VRI LIMI
VRILIMI




 
 
 
 
(14)
5.2. Related Equations of Vector Control
The output of double-fed induction generator is con-
nected to power system; therefore, the voltage of shaft
end is equal to the voltage of system. The vector control
theory is to fix magnetic direction of stator to the vertical
axis.
and 0
ds qs
edsqr
s
MI
L
 



 (15)
The magnetic torque is only related with rotor current
of cross-axis. Neglect wire resistance of stator,
s
R the
voltage of stator end and voltage of vertical axis-cross
axis for double-fed induction generator can be written as:
d; ,,
d
0 and
sn
sn
dsqs s
Vna
t
VV
bc
V



(16)
Use vertical axis-cross axis as reference base, rewrite
the voltage, current and magnetic of stator end, as fol-
low:
0
ds
qsss ds
V
VV



 (17)
0
dss dsdrs
qss qsqr
drdsrdr
qrqsrqr
LI MI
LI MI
MIL I
MIL I











(18)

1
dss dr
s
qs qr
I
MI
L
M
II
L
 

(19)

D.-C. SUE 259
Derivative from the above equation, the magnetic field
and voltage of rotor is s
s
ds dsqs qsqr
s
VM
PVIVII
L
 (22)
2
2
s
dr rdr
s
ss
qr rqr
s
M
V M
LI
LL
M
LI
L



 






(20)
ss s
s
qs dsds qsdr
ss
VVM
QVI VII
LL

 (23)
2
2
d
d
d
d
dr
drr drrsrqr
ss
qr
qrr qrrsrdr
s
s
sss
I M
VRI LsLI
Lt L
I
M
VRI LsLI
Lt L
MV
sL



 
 
 
 
 
 
 
 

2
2
s
M
M
(21)
From the above derivative, the real power and reactive
power of stator for the double-fed induction generator
can be calculated. The current of vertical axis and cross
axis for rotor can be separately controlled.
5.3. Simulation Analysis
If the software MATLAB/Simulink is used to simulate
the vector control response characteristic of Double-Fed
Induction Generator, and the above theoretical derivative
is solved using the following simulation parameters with
the results shown on Figures 8 and 9:
The real power and reactive power of the stator of a
double-fed induction generator can be presented as:
Figure 8. Simulation of response results for real power and reactive power.

D.-C. SUE 260
Figure 9. Simulation of response results of control current for rotor’s vertical axis and cross axis.
0.05
s
R
s
L
, , ,
,
0.05
r
R
50 mHr L
47.3 mHM
50 mH
The generator power output is 5000 W and speed is
3600 rpm. The power control setting of Double-Fed In-
duction Generator is 5000 W for real power and 200
VAR for reactive power, speed is 3420 rpm (s = 0.05).
From the above simulation results, the vector control of a
high efficiency Double-Fed Induction Generator and the
magnetic field of the stator is fixed on the vertical axis.
The real power and reactive power components of the
output only related to the relative strengths of the current
of cross axis and the vertical axis of the rotor. The gen-
erator can operate at lower than synchronous speed,
which does not limit to operate at over the synchronous
speed. At over synchronous speeds, the stator and rotor
produce power; therefore, the output is higher than the
rated power and has an excellent characteristic of voltage
and frequency adjustment.
6. Conclusions
From the above analysis and because suitable wind
power is available in Taiwan, the following conclusions
are derived:
1) Use the vector control for the high efficiency
Double-Fed Induction Generator, to control the output
power of the wind-powered generator. Even if the wind
velocity is unstable, it can rapidly adjust the current in
the cross axis and vertical axis of the rotor to control the
ratio of real power to reactive power to obtain the desired
characteristics of the output power.
2) The generator can be operated sub-synchronous
speeds and output is higher than the rated power. It has
excellent adjustment characteristics for voltage and fre-
quency. Therefore, the high efficiency Double-Fed In-

D.-C. SUE 261
duction Generator is an optimal selection for new wind-
powered generator applications.
7. References
[1] T. Burton, D. Sharpe, N. Jenkins and E. Bossanyi, “Wind
Energy Handbook,” John Wiley & Sons, Inc., Hoboken,
2001. doi:10.1002/0470846062
[2] A. Petersson, “Analysis, Modeling and Control of Dou-
ble-Fed Induction Generator,” PhD Thesis, Chalmers
University of Technology, Gothenburg, 2003.
[3] L. Zhang and C. Watthanasarn, “A Matrix Converter
Excited Double-Fed Induction Machine as a Wind Power
Generator,” 7th International Conference on Power Elec-
tronics and Variable Speed Drives, London, 21-23 Sep-
tember 1998, pp. 532-537. doi:10.1049/cp:19980583
[4] J. G. Slootweg, H. Polinder and W. L. Kling, “Dynamic
Modelling of a Wind Turbine with Double Fed Induction
Generator,” Power Engineering Society Summer Meeting,
Vancouver, 2011, pp. 644-649.
doi:10.1109/PESS.2001.970114
[5] P. Kundur, “Power System Stability and Control,”
McGraw-Hill, Inc., New York, 1994.