1
Modeling and Slip Control of A Doubly Fed
Induction Wind Turbine Generator
Lingling Fan, Subbaraya Yuvarajan
Abstract—Doubly Fed Induction Generators (DFIGs) are
widely used in wind generation. The possibility of getting a
constant frequency AC output from a DFIG while driven by
a variable speed prime mover improves the efficacy of energy
harvest from wind. In the power lab at North Dakota State
University (NDSU), the wind turbine is substituted by a variablespeed DC motor which dives a DFIG. A wound rotor induction
motor is converted to a DFIG by injecting a three-phase voltage
to the rotor at various frequencies. The stator is connected to
a three-phase resistance load. Both computer simulation and
experiments are performed to demonstrate the frequency, voltage
and power relationships between the rotor and the stator. Using
the relationship between the stator and rotor voltages, a PWM
based slip control scheme together with volts/Hz control for the
rotor side converter is developed and the performance verified
in PSIM. The DFIG with the proposed control scheme generates
a constant voltage with constant frequency at the stator. The
experiments, simulation and analysis help students understand
DFIG operation and PWM control.
Index Terms—Wind Generation, Doubly Fed Induction Generator, Inverter, PWM, Slip Control
I. I NTRODUCTION
D
OUBLY Fed Induction Generators (DFIGs) are widely
used in wind generation. The possibility of getting a
constant frequency AC output from a DFIG while driven
by a variable speed prime mover improves the efficacy of
energy harvest from wind [1]. A series of experiments and
simulations are developed in the power lab in North Dakota
State University (NDSU) to help students understand how
DFIGs work and how to control DFIGs for high efficiency.
Unlike a squirrel-cage induction generator, which has its
rotor short circuited, a DFIG has its rotor terminals accessible. The rotor is fed by a variable-frequency (ωr ), variable
magnitude three-phase voltage generated by a PWM converter.
This AC voltage in the rotor circuit will generate a flux with
a frequency ωr if the rotor is standing still. When the rotor
is rotating at a speed of ωm , the net flux linkage of the rotor
with the injected rotor voltage will have a frequency ωr + ωm.
When the wind speed changes, the rotor speed ωm will change
and in order to have the net flux linkage of frequency 60 Hz,
the rotor injection frequency should also be changed.
The conventional DFIG configuration shown in Fig. 1 has
a similar structure of a wound-rotor induction motor with
Kramer drive [2], [3] except that the converters in DFIGs are
able of four-quadrant operation.
L. Fan and S. Yuvarajan are with Dept. of Electrical & Computer Engineering, North Dakota State University, Fargo, ND 58105. Email: Lingling.Fan@ndsu.edu, Subbaraya.Yuvarajan@ndsu.edu.
is
P g +jQ g
DFIG
vs
vr
Wind Turbine
To Grid
ir
Crow bar
C2
C1
C
PWM Converters
Fig. 1.
The conventional configuration of a DFIG.
The injected rotor voltage could come from other renewable
energy sources such as solar panels. In this paper, the dc input
to the inverter is assumed to be from a group of solar panels
and a maximum power point tracking (MPPT) converter [4].
The output from the solar panels is buffered through a set of
batteries which absorb the excess power from the solar panels
or from the rotor when the speed goes above its synchronous
speed. In the latter case, the power converter operates as a
rectifier. The configuration of the DFIG system is shown in
Fig. 2.
Fig. 2.
The alternative configuration of a DFIG.
To emulate the proposed system, the wind turbine is substituted by a variable-speed DC motor . A wound rotor induction
motor is converted to a DFIG by applying a variable-frequency
three-phase sinusoidal voltage to the rotor. The sinusoidal
voltage is generated from a sine-wave power source. The stator
is connected to a three-phase resistance load. Both computer
2
simulation and experiments are performed to demonstrate the
frequency, voltage and power relationships between the rotor
and the stator of the DFIG.
Further, the sine source is replaced by a bridge inverter with
sine PWM. A feedback control scheme - slip plus volts/Hz
control - is developed based on the voltage relationship.
The control scheme, which helps to maintain a constantmagnitude, constant-frequency stator voltage is verified using
the simulation software PSIM [5].
The paper is organized as follows. Section II gives the characteristics of the DFIG under steady state. Section III presents
the DFIG simulation and lab experiments using sine source
injection. Section IV presents the slip and volts/Hz control
scheme with sine PWM and verifies the control effectiveness.
Section V concludes the paper.
The induced stator voltage and the rotor voltage are related
by
Vr
Vs =
a.
(4)
s
From the above equation, we can tell that the faster the shaft
rotates, the higher will be the magnitude of the stator voltage.
The equivalent circuit of Fig. 3 can be simplified by moving
XM to the stator terminal as in Fig. 4 [3]. Since the currents
in the rotor circuit and the stator circuit are the same from
Fig. 4, the stator power and the rotor injected power have the
following relationship after neglecting the power loss in the
stator and rotor:
Pr /s = real(
The per-phase steady state equivalent circuit model of a
DFIG is given in Fig. 3 [6].
j( ωe / ωb )x' lr
Ias
j( ωe / ωb )x M
I' ar
Llr
Rr/s
Vr/s
V'ar/s
Fig. 4. The simplified steady state induction machine circuit representation.
-
Fig. 3.
Vs
r' r/s
Lls
+
+
Vas
Rs
Lm
j( ωe / ωb )x ls
(5)
where Pr is the power injected into the rotor which is also
called the slip power [3].
II. D OUBLY F ED I NDUCTION G ENERATOR
C HARACTERISTICS
rs
Vr′ ′
I ) ≈ real(Vs Is ) = Ps
s r
Steady state induction machine circuit representation.
In the case of a squirrel-cage induction machine, the rotor
is short circuited or Vr′ = 0. In the case of a would-rotor
induction machine, the rotor is not short circuited or Vr′ 6= 0.
The frequency relationship for the DFIG is as follows:
fs = fm + fr
(1)
where fs is the frequency of the stator voltage, fm is the
frequency of the rotating shaft and fr is the frequency of the
injected rotor voltage. The stator voltage and rotor voltage
relationship, neglecting the voltage drops in the series elements
can be expressed as
|V ′ |
(2)
|Vs | = r
s
where s = fr /fs . Note Vr′ is the rotor voltage seen at the
stator side.
When the shaft is not rotating, s = 1 and the DFIG acts
like a transformer. The injected rotor voltage and the stator
voltage has a ratio a = ns /nr , where ns and nr are the turns
of the stator windings and the rotor windings. We can express
the relation of Vr′ (rotor voltage seen at the stator side) and
Vr (rotor voltage) as simple as
Vr′
= a.
Vr
When the rotor speed is less than the synchronous speed,
the slip will be positive and the injected rotor voltages have
a positive frequency sωs where ωs = 2π × 60 rad/s. The
slip power is also greater than zero, i.e., the converter will
inject power into the rotor circuit. When the rotor speed is
less than the synchronous speed, the slip will be negative and
the converter will absorb the slip power from the rotor circuit.
The resulting rotor frequency will be negative which means
that the phase sequence is reversed.
(3)
III. E MULATING WIND
TURBINE DRIVEN
DFIG
IN
PSIM
AND PHYSICAL LAB
In the power lab at North Dakota State University, the
simulation software PSIM [5] is available to simulate a DFIG.
In both the physical lab and the simulation software PSIM,
the wind turbine is emulated by a DC motor whose speed
can easily be varied by varying the armature voltage to the
DC motor. In the case of a wind generation system, the shaft
speed varies with the the wind speed.
A 5 HP wound rotor motor is used in the physical experiments as the DFIG generator which has six pole and a
synchronous speed of 1200 rpm. The stator feeds a 3-phase,
wye-connected resistance load with 21 Ω per phase.
In the first step of the test, 3-phase sinusoidal voltages are
injected into the rotor circuit of the wound rotor induction
machine. The configuration of the system in PSIM is shown
in Fig. 5 and the photograph of the machine set up is shown
in Fig. 6.
3
Fig. 7. (a) Rotor voltage in volt (b) Stator voltage in volt and (c) Motor
speed in rpm.
Fig. 5.
Configuration in PSIM.
Fig. 6.
Photograph of the physical system.
be ACB). The resulting stator frequency should be fr − fm =
10 Hz. In Fig. 8, we can observe the rotor voltage is still
maintained constant at 35 Hz yet the stator voltage is now
10 Hz. What is more, the magnitude of the stator voltage is
much lower. This is because |Vs | ≈ |Vr |/s. In the first test,
s = 35/60 and |Vs | = 1.7|Vr |. In the second case, s = 35/10
and |Vs | = 0.29|Vr |.
A. PSIM Simulation
In PSIM, a typical wound-rotor induction machine with a
synchronous speed of six poles and synchronous speed 1200
rpm is chosen as DFIG . The frequency of the rotor injection
voltage is set to 35 Hz and the rotor speed is set at 500 rpm.
Therefore, the corresponding speed of the rotor in Hz is
500
fm =
60 = 25Hz
1200
. With a 35 Hz injected voltage, the induced stator voltage
should have a frequency
fs = 35 + 25 = 60Hz
.
Fig. 7 shows the simulated waveforms of the injected
voltage, stator voltage for phase A and the rotor speed and
they confirm the frequency relationship. It is seen that the
frequency of the stator voltage is 60 Hz.
To emulate the voltage injection at a negative frequency, the
phase sequence is reversed (ABC sequence is now changed to
Fig. 8. (a) Rotor voltage in volt (b) Stator voltage in volt and (c) Motor
speed in rpm.
B. Physical Lab Tests
In the lab, we use a sine wave generator with adjustable
voltage magnitude and frequency as the motor voltage source.
In the test, we vary the speed of the DC motor and at the
same time vary the frequency of the injected rotor voltage.
The purpose is to get a constant 60 Hz frequency in the stator
circuit. Fig. 9 shows the stator voltage versus slip relationship
which is expressed in Eqn. 4.
In the DC motor-DFIG set, the power drawn by the DC motor consists of the mechanical power loss and the mechanical
power transferred to the rotor of the DFIG. The mechanical
power loss is measured at various rotating speed when DC
motor runs without any load (DFIG not excited). Fig. 10
shows the mechanical power loss of the DC motor versus
4
Stator voltage versus slip characteristic.
Fig. 11.
Mechanical power, slip power and stator power relationship.
X
1- ωm
ωm
Fig. 12.
Fig. 10.
Mechanical power loss of the DC motor versus the rotating speed.
The mechanical power input to the DFIG can be calculated
by subtracting the mechanical power loss from the power
drawn by the DC motor. Fig. 11 shows the relationship
among the mechanical power Pm , injected rotor power Pr
and stator power Ps . It is observed that the test results follow
the power relationship Ps = Pr + Pm . Thus, the PSIM
and physical lab tests demonstrate the frequency relationship,
voltage relationship and power relationship of a DFIG.
IV. F EEDBACK
CONTROL VIA
PWM
OF THE INVERTER
Slip and constant volts/Hz control scheme is widely used adjustable frequency induction machine [3]. The control scheme
is shown in Fig. 12. The objective of the control scheme is
to generate a voltage with constant magnitude and constant
frequency. The rotor speed is fed back and the desired slip
frequency is computed in the control unit. In order to keep the
stator voltage magnitude constant, the rotor voltage magnitude
is adjusted according to the desired slip: Vr = sVs /a, where
a is the stator/rotor winding turn ratio.
|Vr|
Vs /a
rotating speed. The greater the rotating speed, the greater is
the mechanical power loss.
slip
120π
Fig. 9.
ang(Vr)
R
Stator voltage versus slip.
The control scheme can be realized in the PSIM model using
PWM. With PWM, both the magnitude and the frequency of
the inverter output voltage can be adjusted. The PSIM IGBT
bridge along with the DFIG system is shown in Fig. 13. The
PWM control scheme is shown in Fig. 14. The triangle carrier
frequency is 1500 Hz. The rotor voltage frequency will be
same as the control signal frequency which is generated from
DQ0-ABC block as in Fig. 14. In the test, the DC motor
excitation current is set to 2A and the armature voltage is
set to 100 V. The speed of the motor is 825 rpm, equivalent to
41.25 Hz. A DQ0-ABC block is used to generate three-phase
sinusoidal voltage. The two inputs to the block are angle and
DC voltage magnitude. The transformation from a DC voltage
to AC voltages is expressed as
Vabc

cos θ
=  cos(θ − 2π
3 )
cos(θ + 2π
3 )


sin θ
1
Vdc
  0  . (6)
sin(θ − 2π
3 ) 1
sin(θ + 2π
)
1
0
3
The angular displacement θ is the integral of the desired slip
frequency, where the slip frequency is derived from the rotor
speed.
The DC voltage input to the DQ-abc block Vdc is controlled
by the slip frequency. Based on the constant volts/Hz control
scheme, Vdc = 100(1 − N/1200) where N is the rotor speed
in rpm and Vdc = 100 volts when the slip equals zero. When
the speed is 830 rpm, Vdc = 30 V. The AC voltages will have
magnitudes of 30.8 V. The amplitude of the triangle carrier
waveform (V̂tri ) is 100 V. The magnitude of the phase to
neutral voltage is linearly proportional to the DC voltage input
5
Fig. 15. Stator phase-neutral voltage vs an (volts), rotor voltage phase-phase
voltage vr ab (volts), speed in rpm and rotor current waveforms.
Fig. 13.
An FFT analysis gives the harmonic components in the
waveforms as which are shown in Fig. 16.
The IGBT bridge and DFIG system.
to the inverter Vd [2]:
V̂an = M
Vd
2
(7)
where M is the modulation index and M = V̂control
,
V̂tri
vcontrol (t) is the control signal voltage and vtri is the triangular carrier voltage.
830
Given Vd = 100V , when s = 1 − 1200
= 0.3083, we
can estimate the magnitude of the ac control voltage to be
100 × 0.3083 = 30.83 V. Hence, the injected rotor per-phase
voltage magnitude will be V̂r an = 30.83
100 × 50 =
√ 15.4 V and
the line to line rotor voltage magnitude to be 3 × 15.4 =
26.7 V. The stator voltage magnitude can be estimated from
|Vs | ≈ |Vr |/s. When s = 0.308, |Vs | = 48V . The estimation
coincides with the PSIM simulation results shown in Fig. 15.
Fig. 16.
FFT analysis.
To test the effectiveness of the control algorithm, the DC
motor armature voltage is adjusted to 80V and the speed of
the DC motor now reduces to 658 rpm. To get a 60 Hz stator
voltage, the slip frequency should be 60(1−658/1200) = 27.1
Hz. The control scheme measures the rotating speed and automatically increases the slip frequency to 27 Hz. Meanwhile the
injected rotor voltage is also adjusted based on the slip. The
control voltage magnitude becomes Vdc = s × 100 = 45.17
and the rotor voltage per-phase magnitude becomes V̂r an =
45.17
100 ×50 = 22.585 V. The stator per-phase voltage magnitude
is estimated to be 22.58/s = 50V. The waveforms of the stator
voltage, rotor voltage are shown in Fig. 17.
Fig. 14.
PWM control scheme.
It is found that the proposed slip control scheme together
with constant volts/Hz control can well keep the stator voltage
constant within a range.
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Fig. 17. Stator phase-neutral voltage vs an (volts), rotor voltage phase-phase
voltage vr ab (volts), speed in rpm and rotor current waveforms.
V. C ONCLUSION
This paper presents the simulation and experimental test
showing the performance of a DFIG wind generation system.
The steady state voltage and frequency relationships of DFIG
are verified in PSIM and the physical lab. Further more, a
PWM based slip control scheme is proposed and tested in
the simulation software package. The control scheme helps to
maintain the frequency and magnitude of the stator voltage
constant.
R EFERENCES
[1] S. Muller, M. Deicke, and R. W. D. Doncker, “Doubly fed induction
generator systems for wind turbine,” IEEE Ind. Appl. Mag., pp. 26–33,
May/June 2002.
[2] J. Murphy and F. Turnbull, Power Electronics Control of AC Motors.
Pergamon Press, 1988.
[3] B. K. Bose, Modern Power Electronics and AC Drives. Prentice Hall,
2001.
[4] S. Yuvarajan, D. Yu, and S. Xu, “A novel power converter for photovoltaic
applications,” Journal of Power Sources, vol. 135, no. 1-2, pp. 327–331,
Sep 2004.
[5] PSIM, A software by Powersim Technologies. Professional Version 6.05,
2004.
[6] P. Krause, Analysis of Electric Machinery. New York: McGraw-Hill,
1986.
Lingling Fan is an assistant professor in Dept. of Electrical & Computer
Engineering, North Dakota State University. She received the BS, MS degrees
in electrical engineering from Southeast University, Nanjing, China, in 1994
and 1997, respectively. She received Ph.D. degree in electrical engineering
from West Virginia University in 2001. Before joining NDSU, Dr. Fan
was with Midwest ISO, St. Paul, Minnesota. Her research interests include
modeling and control of renewable energy systems, power system reliability
and economics.
Subbaraya Yuvarajan received his Ph.D. degree in Electrical Engineering
from Indian Institute of Technology, Chennai, India in 1981. He received his
M. Tech degree from Indian Institute of Technology in 1969 and B.E (Hons)
degree from University of Madras in 1966. Dr. Yuvarajan has been a Professor
of Electrical and Computer Engineering at NDSU from 1995. His research
areas are Electronics, Power Electronics and Electrical Machines.