Grid Connection of Doubly-Fed Induction Generators
in Wind Energy Conversion System
*
**
Ahmed G. Abo-Khalil , and Dong-Choon Lee , and Se-Hyun Lee
*,**
***
***
Dept. of Electrical. Eng. Yeungnam Univ., 214-1, Daedong, Gyeongsan, Gyeongbuk, Korea
Electro-Mechanical Research Institute, Hyundai Heavy Industry Co., Ltd, Gyeongki, Korea
E-mail ** : dclee@yu.ac.kr
Abstract—This paper presents a new synchronization
algorithm for grid connection of a doubly fed induction
generator (DFIG) in wind generation system. A stator fluxoriented vector control is used for the variable speed DFIG
operation. By controlling the generator excitation current
the amplitude of the stator EMF is adjusted equal to the
amplitude of the grid voltage. To set the generator
frequency equal to the grid one, the turbine pitch angle
controller accelerates the turbine/generator until it reaches
the synchronous speed. A slight difference of stator and grid
frequencies may cause the large phase difference between
the two voltages. To compensate for this phase difference, a
PLL algorithm is used. After the synchronization is
achieved, the generator is connected to the grid and is
controlled to extract the maximum power. The effectiveness
of the proposed synchronization algorithm is verified by
simulation results using PSCAD.
Keyword- Wind energy, synchronization, DFIG, PSCAD.
I.
INTRODUCTION
Wind energy is one of the most important and
promising sources of renewable energy all over the world,
mainly because it is considered to be nonpolluting and
economically viable. At the same time, there has been a
rapid development of related wind turbine technology [1].
A doubly-fed induction generator is based on a wound
rotor induction machine. The three-phase rotor windings
are supplied with a voltage of controllable amplitude and
frequency using an ac/ac converter. Consequently, the
speed can be varied while the operating frequency on the
stator side remains constant. Depending on the required
speed range, the rotor converter rating is usually low
compared with the machine rating. Therefore, a DFIG is
preferable for variable-speed wind turbine applications
[2].
The choice of control strategy incorporated can vary
depending on wind turbine generators, but the most
popular control scheme for the DFIG of wind turbine
generators is a field-oriented control (FOC). This control
strategy is well established in the field of variable-speed
drives and, when applied to the DFIG control, allows
independent control of the electromagnetic torque and
stator reactive power [3]. The DFIG using back-to-back
PWM converters for the rotor-side control has been
well established in wind power system. When used with a
1-4244-0449-5/06/$20.00 ©2006 IEEE
wind turbine it offers several advantages over the fixed
speed generator systems. These advantages, including
speed control and reduced flickers, are primarily achieved
by controlling the voltage source converter, with its
inherent bi-directional active and reactive power flow [4].
Before connecting the stator of the DFIG to the grid
terminals, the stator voltage has to be adjusted to be
synchronized with the line voltage. There are only a few
papers which handled the DFIG control for the
synchronization process. There are some control schemes
for DFIG synchronization [5], [6]. In these papers, the
transition state for synchronizing duration was not
investigated in detail.
This paper describes a smooth and fast synchronization
scheme of the DFIG to the grid as well as independent
control of active and reactive power of the generator using
the stator flux-oriented control at normal operation.
During the synchronization process, the blade pitch angle
controller adjusts the speed closely to the synchronous
speed to make it sure that the stator frequency is the same
as that of the grid. The magnitude of stator induced
voltage is controlled by adjusting the rotor flux and the
phase difference between the stator and grid voltages is
compensated by PLL algorithm. The wind turbine control
systems are developed using PSCAD software.
II.
WIND TURBINE ODEL
A simplified aerodynamic model can be used when the
electrical behavior of the wind turbine is the main interest.
The relation between the wind speed and aerodynamic
torque may be described by the following equation [10]:
Tt =
C (λ , β )
1
ρπ R 3υ 2 p
2
λ
(1)
where
Tt : turbine aerodynamic torque [Nm]
ρ : specific density of air [kg/m3];
υ : wind speed [m/s];
R : radius of the turbine blade[m];
C p : coefficient of power conversion;
β
: pitch angle.
The rotational system may therefore be modeled by a
equation of motion [11]:
dω g
(2)
J
= T − T − Bω
dt
g
t
where J is the system inertia,
g
ω g is the rotor speed, Tg
IPEMC 2006
Fig. 1. Basic configuration of DFIG wind turbine
θe
θ sl
θr
Fig. 3. Control block diagram of DFIG system
Lr : rotor self-inductance;
λds , λqs : stator d-q flux linkage;
λdr , λqr : rotor d -q flux linkage;
Fig. 2. Vector diagram for stator flux-oriented control
is the generator torque, Tt is the turbine torque and B is
the damping coefficient.
III.
CONTROL OF DFIG
A schematic diagram of the overall system is shown in
Fig. 1. Back-to-back PWM converters are connected
between the rotor of 2[MW] DFIG and the grid utility.
The DFIG is controlled in a rotating d-q reference frame,
with the d-axis aligned along the stator-flux vector as
shown in Fig. 2. For the stable control of the active and
reactive power, it is necessary to independently control
them. The stator active and reactive power of the DFIG is
controlled by regulating the current and voltage of the
rotor windings. Therefore the current and voltage of the
rotor windings need to be decomposed into components
related to the stator active and reactive power.
A. Stator-Flux Oriented Control of DFIG
For the stator active and reactive power control, a d-q
reference frame synchronized with the stator flux is
chosen. The stator flux vector is adjusted to be aligned
with the d-axis. The flux linkages of the stator and rotor
are expressed as [7]:
λs = λds = Lmims = Lsids + Lmidr
λdr =
2
m
L
ims + σLr idr
Ls
(3)
(4)
λqr = σLr idr
(5)
L 2m
Lr Ls
(6)
σ =1−
ims , i ds , idr : magnetizing, stator and rotor d-axis
currents.
Rotor voltages in d-q reference frame can be expressed as
a function of rotor and magnetizing currents
vdr = Rr idr + σLr
vqr = Rr iqr + σLr
diqr
dt
didr
− ωslσLr iqr
dt
+ ωsl (σLr idr +
L2m
ims )
Ls
(7)
(8)
where
vdr , vqr : rotor d-q voltages;
Rr : rotor resistance;
ωsl : slip angular frequency.
The stator flux angle is calculated as follows:
λsds = ∫ (vdss − Rs idss )dt
λsqs = ∫ (vqss − Rs iqss )dt
(9)
(10)
λ
(11)
λ
where a superscript “s” represents quantities in stationary
reference frame and
Rs : stator resistance;
θ e = tan −1
s
qs
s
ds
θ e : synchronous frame angle.
B. Power control
Adjustment of the q-axis component of the rotor
current controls either the generator developed-torque or
the stator-side active power of the DFIG.
where
Lm : magnetizing inductance;
Ls : stator self-inductance;
Ps =
3
3 L
(vqs iqs + vds ids ) = − ⋅ m ⋅ vqs iqr
2
2 Ls
(12)
Fig. 4. Wind turbine characteristics
Fig. 6. Sequence of synchronization
Fig. 5. Phase difference compensation for synchronization
On the other hand, regulating the rotor d-axis current
component controls directly the stator-side reactive
power.
3
3 L
(13)
Qs = (vqsids − vdsiqs ) = ⋅ m ⋅ vqs (ims − idr )
2
2 Ls
It is noticeable that the stator active and reactive power
components are proportional to the iqr, and idr, respectively.
Fig. 3 shows the schematic configuration of the DFIG
wind turbine system and its simplified control scheme.
The stator of the DFIG is connected to the utility grid. The
back-to-back PWM converters provide a bidirectional
power-flow control thereby enabling the DFIG to operate
either in subsynchronous ( ω r < ωe ) or in
supersynchronous modes ( ω r > ωe ). In both modes the
stator active power is generated from the DFIG and
delivered to the grid. On the other hand, the rotor active
power is either supplied to the machine in the
subsynchronous mode or delivered to the grid in the
supersynchronous mode. The stator active power is
controlled directly assuming that a maximum generator
developed power is known from the optimum generator
speed value.
The operating curve of the studied wind turbine, which
is applied to most modern wind turbines [8], is illustrated
in Fig. 4. This curve is characterized by four sections as
follows; A~B for minimum rotor speed which is less
than that for optimal operation, B~C for an optimal
characteristic curve given by P * = K optυ 3 (where υ is the
wind speed) between the cut-in speed and the rated speed,
C~D for a constant speed characteristic up to the rated
power, and D~ E for a constant power characteristic for
higher wind speed than the rated value followed by a
blade pitch control.
The optimum power P * of the DFIG is used as the
reference value for the power control loop. In the inner
current control loop, the stator-flux vector position is
used to establish a reference frame that allows q-axis
components of the rotor current to be controlled. As the
rotor current reference is expressed in stator-flux
coordinates, these must be transformed into the same
reference frame. This is achieved by rotating the rotor
current reference vector by an angular position θ sl . Due
to the rotor speed variation, θ sl is updated at every
sample interval. Once the reference frames for both the
reference and measured current vectors are conformed,
simple proportional plus integral (PI) regulators can be
used to control the d-q components of the rotor current.
C. Synchronization control
The process of connecting the DFIG to the grid
consists of two stages, that is, synchronization stage and
running stage. At standstill, rotor blades are in a
feathering position and the generator is disconnected
from the grid. From a complete stop, the first step is to
charge the dc link voltage by closing SW1 as shown in
Fig. 1. The anemometer measures the wind speed and if
the wind speed is higher than the cut-in value, the switch
SW2 is closed and the pitch controller changes the blade
pitch angle so that the turbine begins to rotate. The
controller of the generator rotor side is activated so an
excitation current is sent through the rotor.
The excitation current generates the generator flux and
then the stator EMF. The turbine accelerates until it
reaches near the rated speed. At this point the frequency
of the stator EMF is about the same as that of the grid
voltage. The amplitude of the stator EMF is about the
same as that of the grid. Even slightly different
frequencies may cause the phase difference between the
two voltages. To compensate for the phase difference
between the stator EMF and grid voltage, the phase
difference compensation component δθ sl is added to the
calculated slip angle as shown in Fig. 5. The
compensation component δθ sl is calculated by
controlling the stator d-axis voltage component to be zero,
equally to the grid d-axis voltage.
The synchronization process is summarized in the flow
chart shown in Fig. 6. After the synchronization
conditions are achieved, the stator-side contactor is
closed, and the generator is connected to the grid.
Synchronization
4.0
∫
Grid angle
Stator angle
Ea
Vas
y
2.0
0.0
-2.0
-4.0
y
Fig. 7. Block diagram of pitch angle control
The pitch angle controller sets the blade pitch at the
optimum point if the blades are not yet at this point. The
generator power reference is set to the maximum value
which is determined by the wind speed and the pitch
angle. Usually the reactive power reference between the
grid and the generator is set according to the grid
requirements.
800
600
400
200
0
-200
-400
-600
-800
0.475
0.500
0.525
0.550
0.575
0.600
0.625
0.650
0.675
Fig. 8. Stator and grid
(a) Phase angle (b) Voltage
Stator current
3.0k
Ias
Ibs
Ics
Iar
Ibr
Icr
2.0k
IV.
SIMULATION RESULTS
The proposed model is implemented using PSCAD
software and simulated to investigate the DFIG operation
during starting and normal running. From a complete stop,
the dc link capacitor is connected to the grid utility
through the back-to-back PWM converters at t=0[s].
Speed, torque, rotor and stator currents are all zero
initially since the rotor and stator are open-circuited.
The pitch angle is controlled from the feathering
position to the turbine rated speed position. At t=0.5[s],
the rotor terminals are connected to the dc link capacitor
through SW2. The stator voltage amplitude increases
with the rotor flux current and the phase angle is adjusted
using the PLL algorithm. It is noticeable that the
synchronization process takes almost two cycles, which
means that the synchronization control is fast as shown in
Fig. 8. After satisfying the synchronization conditions,
the stator contactor is closed and the generator supplies
the grid with the power corresponding to the wind speed.
From that time, the control algorithm for normal
condition replaces the starting algorithm. The rotor d, qaxis currents are adjusted according to the active and
reactive power reference. The stator and rotor currents
and generator speed are shown in Fig. 9.
During fault condition, the stator terminals are
disconnected from the grid while the rotor terminals are
kept connected. The pitch angle controller adjusts the
pitch angle to the position which reduces the effect of the
abnormal condition.
y
1.0k
0.0
-1.0k
-2.0k
-3.0k
2.0k
y
1.0k
0.0
-1.0k
-2.0k
Wrpm
2.4k
2.2k
y
D. Pitch angle control
The aerodynamic model of the wind turbine has shown
that the aerodynamic efficiency is strongly influenced by
variation of the blade pitch angle with respect to the
direction of the wind or to the plane of rotation. Small
changes in the pitch angle may have a dramatic effect on
the power output. In low to moderate wind speeds, the
pitch angle should only be at its optimum value to
produce the maximum power. In high wind speeds, the
pitch angle control provides a very effective means of
regulating the aerodynamic power and loads produced by
the rotor so that design limits are not exceeded. The
relationship between pitch angle and wind speed is shown
in Fig. 7.
2.0k
1.8k
1.6k
0.80
1.00
1.20
1.40
Fig. 9. Generator performance
(a) Stator current (b) Rotor current (c) Speed
After the fault clearing, the synchronization process
can be applied again for recovering the generator power.
In Fig. 10, the fault occurs after 2 [s], then the
aforementioned steps are performed to resynchronize the
generator. The stator currents during the disconnection
are zeros, while the rotor current is equal to the
magnetizing current as shown in Fig. 10(a) and (b). The
stator active power is adjusted to the optimum power
value during normal operation and is set to zero during
faults. Consequently, the generator runs at the
synchronous speed during the synchronizing process at
starting and re-synchronizing process after fault clearing.
After synchronization, the generator runs at a speed
corresponding to the optimum power as shown in Fig.
10(c) and (d).
The generator performance for step variations of wind
speed is shown in Fig. 11. At low wind speed the
controller operates at constant pitch angle and varying
rotational speed. The generator active power reference is
adjusted to extract the maximum power and the reactive
power reference is determined by the grid side
requirement. In this study, the reactive power reference is
set to zero. The active and reactive power controllers give
a fast dynamic response and good steady state
performance.
At high wind speeds, the pitch angle controller controls
the generator speed at the rated value. It is noticeable that
the generator power is limited to the rated value of
Stator current
y
2[MW] during the high wind speed operation as shown in
Fig. 11(a). It is noticeable that the system is reliable and
fast to achieve synchronization as well as excellent
control for normal operating condition.
3.0k
2.5k
2.0k
1.5k
1.0k
0.5k
0.0
-0.5k
-1.0k
-1.5k
-2.0k
-2.5k
-3.0k
Ias
Ibs
1.00
V.
1.50
2.00
Ics
2.50
3.00
3.50
4.00
4.50
3.50
4.00
4.50
3.00
3.50
4.00
4.50
3.00
3.50
4.00
4.50
Rotor currents
CONCLUSIONS
y
In this paper, a new synchronization scheme of stator
flux-oriented DFIG control systems to the utility gird has
been proposed. Compared to the existing DFIG
synchronization algorithms, the proposed method gives
fast starting and can take only 2 cycles to be performed.
The stator EMF, frequency and phase angle are adjusted
according to the grid values. The pitch angle controller
adjusts the turbine speed at the synchronous speed for
equal frequencies. The stator EMF is generated then
adjusted by controlling the generator d-axis current to be
equal to the grid voltage. The voltage phase difference is
compensated by comparing the d-axis voltage component
of both sides. The proposed synchronization algorithm
gives smooth and fast synchronization, which enables the
system to be resynchronized quickly after grid fault
clearing. The steady state and transient responses of the
power, current and pitch angle controllers show excellent
performance for the different modes and wind speed.
PSCAD simulation has verified that the proposed
synchronization and control algorithms are effective and
advantageous for 2[MW] DFIG wind power system.
3.0k
2.5k
2.0k
1.5k
1.0k
0.5k
0.0
-0.5k
-1.0k
-1.5k
-2.0k
-2.5k
-3.0k
Iar
Ibr
1.00
1.50
2.00
Icr
2.50
3.00
y
Active power control
0.2M
0.0
-0.2M
-0.4M
-0.6M
-0.8M
-1.0M
-1.2M
-1.4M
-1.6M
-1.8M
-2.0M
-2.2M
Ps_ref
Ps
1.00
1.50
2.00
2.50
speed
2.2k
Wrpm
2.1k
y
2.0k
1.9k
1.8k
1.7k
1.6k
1.00
1.50
2.00
2.50
Fig. 10 Generator performance at different control modes
Active power control
Ps_ref
Ps
Qs_ref
Qs
-0.3M
-0.6M
-0.9M
y
-1.2M
-1.5M
-1.8M
-2.1M
-2.4M
200.00k
ACKNOWLEDGMENT
150.00k
100.00k
50.00k
This work has been supported by the KEMCO (Korea
Energy Management Corporation) under project grant
(2004-N-WD12-P-06-3-010-2005).
y
0.00
-50.00k
-100.00k
-150.00k
-200.00k
15.0
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