ISTANBUL UNIVERSITY –
JOURNAL OF ELECTRICAL & ELECTRONICS ENGINEERING
YEAR
VOLUME
NUMBER
: 2009
:9
:2
(1057-1066)
VECTOR CONTROL
OF A DFIG BASED WIND TURBINE
1
Md. ARIFUJJAMAN, 2M.T. IQBAL, 2John E. QUAICOE
1,2
Faculty of Engineering and Applied Science
Memorial university of Newfoundland
St. John’s, NL, Canada A1B3X5
1
Email: mda04@mun.ca
ABSTRACT
Variable speed wind turbines (WT) based on the Doubly-Fed Induction Generator (DFIG) is
commercially offered and is frequently used in grid connected mode. The variable speed operation in
such wind turbines is achieved by means of a four-quadrant ac-dc-ac power converter among the
rotor winding and the grid while the stator is directly connected to the grid. Below rated wind speed,
tracking the maximum power/torque curve realized by speed/current control mode while pitch
control ensures the rated power for above rated wind speed. In this research, a maximum power
control strategy is incorporated with the DFIG whereby the produced power serves as the dynamic
active power reference for the DFIG. Stator flux oriented vector control is applied to decouple the
control of active and reactive power generated by the DFIG based WT. Details of the control strategy
and system simulation results in Simulink are presented in the paper to show the effectiveness of the
proposed control strategy.
Keywords: Variable speed wind turbine; Doubly fed induction generator; Pitch control; Vector
control; Maximum power control.
1. NOMENCLATURE
Vds ,Vqs
: d- and q- axis stator voltages
respectively
Vdr , Vqr
: d- and q- axis rotor voltages
respectively.
I ds , I qs
: d- and q- axis stator currents
respectively.
I dr , I qr
: d- and q- axis rotor currents
respectively.
ϕ ds , ϕ qs : d- and q- axis stator flux linkages
respectively.
Received Date: 05.02.2009
Accepted Date: 05.11.2009
ϕ dr , ϕ qr
: d- and q-axis rotor flux linkages
respectively.
Rs , Rr
: Stator and rotor resistances
respectively.
Ls , Lr
: Stator and rotor inductances
respectively.
Lm
: Mutual inductance of stator and
rotor.
ωm , ωs , ωr : Mechanical, synchronous and rotor
speeds respectively.
Pm , Ps , Qs : Mechanical, stator active and rotor
reactive powers respectively.
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Vector Control Of A Dfig Based Wind Turbine
Tm , Te
: Mechanical and electrical torques
respectively.
2. INTRODUCTION
A Doubly-Fed Induction Generator can realize
the variable speed operation and thus maximize
the output power from the wind turbine [1]. The
rotor windings of the DFIG are fed to the grid
via a four-quadrant ac-dc-ac power converter.
This arrangement has several advantages
including rotor speed variation from sub
synchronous to super synchronous speed based
on the wind speed, independent control of active
and reactive power and reduced flicker.
Fig. 1 A typical Grid connected WT based on
DFIG
Typically the rotor converter adapts the slip
power (usually 25% of the generator rating),
which results in reduced cost of the converter
system. A typical grid connected WT based on
DFIG is presented in Fig. 1.
Two converters namely, Rotor side converter
(RSC) and Grid side converter (GSC) are an
integral part of such configuration. Scalar or
vector control of the DFIG allows optimum
performance of the system. The vector control
literature [3-5]. The strategies are based on the
fact that below rated wind speed (BRWS), the
WT will trace the maximum power/torque curve
and above rated wind speed (ARWS), the output
power is limited to its rated power. To trace the
maximum power/torque curve, speed/current
control mode is favored, while pitch regulation
ensures the rated power for ARWS of the WT.
The scope of the present work is limited to the
development of a control strategy for operation
BRWS. The proposed maximum power
extraction control strategy for the DFIG based
grid connected wind turbine employs the
produced power as a dynamic active reference
power for the DFIG in BRWS mode. A fourth
order DFIG model is developed and stator flux
orientation vector control scheme is adopted to
decouple the control of active and reactive
power production by the DFIG. The q- axis
component of the rotor current is controlled to
achieve the control of active power production
by the DFIG while d- axis component of the
rotor current is controlled to achieve the control
of reactive power production. The control of the
grid side converter is not of primary concern for
this study as the focus of the work is the
tracking of the maximum power of the wind
turbine and the control of the active and reactive
power produced by the stator of the DFIG.
This paper is organized as follows. The second
section gives a short overview of the DFIG
based WT. In the third section, the
characteristics of the wind turbine are depicted.
The dynamic model of the DFIG and controller
analysis is presented in the fourth and fifth
sections respectively, and the sixth section
contains the simulation results. Finally, the
findings of the investigations are highlighted in
the conclusions.
3. WIND TURBINE
CHARACTERISTIC
scheme (VCS) is favored when a fast dynamic
response and accurate control is required [2].
Applying VCS allows decouple control of active
and reactive power produced by the DFIG. The
RSC can realize the decouple control of active
and reactive power by adopting the stator flux or
voltage control strategy while the GSC can
realize the control of the DC link and network
power factor by using the grid voltage oriented
vector control strategy.
A wind turbine can be characterized by the nondimensional curve of power coefficient Cp as a
function of Tip-Speed Ratio (TSR) λ, where, λ is
given in terms of rotor speed, ωm (rad/s), wind
speed, V (m/s), and rotor radius, R (m) as
Rωm
λ=
(1)
V
Based on the control of DFIG and WT, several
control strategies have been proposed in the
Wind turbine power coefficient, Cp is dependent
upon λ. If pitch angle, β is incorporated, Cp
Md. ARIFUJJAMAN M.T. IQBAL
J.E. QUAICOE
1059
Vector Control Of A Dfig Based Wind Turbine
becomes
a
function
of
and β ,
λ
i.e.
C p = f ( λ , β ) . The power coefficient as a
function of λ and β can be expressed as [6]
Pmax = k pV 3 = kopt ωm 3
−21
⎛ 116
⎞
− 0.4β − 5 ⎟ e λi
C p ( λ , β ) = 0.5176 ⎜
⎝ λi
⎠
+0.0068λ
here,
1
λi
=
(2)
1
0.035
− 3
λ + 0.08β β + 1
Fig. 2 Power coefficient as a function of tipspeed ratio and pitch angle.
The
C p = f ( λ , β ) curves for some β values
are shown in Fig. 2. It can be seen that as
β increases, Cp decreases, thus reducing the
power produced by the WT.
The mechanical output power of the wind
turbine can be expressed as
Pm = 0.5 ρ AC p ( λ , β ) V 3 = K1 (ωm )
3
(3)
where, ρ is the air density (kg.m-3) and A is the
rotor rotational area, i.e., πR2.
The corresponding torque produced by the wind
turbine is given by (4) which simplifies to (5)
Tm =
Pm
(4)
ωm
Tm = K1 (ωm )
where,
2
(5)
K1 = 0.5 ρ AC p ( λ , β )
R
yield (6) and the referenced wind turbine with a
variation in wind speed is presented in Fig 2.
3
λ 3OPT
This maximum power value at various wind
speed may be derived by using (1) and (4) to
Md. ARIFUJJAMAN M.T. IQBAL
(6)
In order to obtain the maximum power, the pitch
angle (β) is usually held to an optimum value
(typically less then 100 [4]) for BRWS and a
rate limiter is often used to limit the rate of
change of the pitch angle. Present concern of
this paper assumes the pitch
Fig. 3 Wind turbine output power as a function
of rotational speed of the turbine
4. DYNAMIC MODEL OF DFIG
In order to investigate the actual behavior of the
DFIG, dynamic equation needs to be considered
for more realistic observation. From the point of
view of the control of the machine, the dq
representation of an induction machine leads to
control flexibility. The dynamic behavior of the
DFIG in synchronous reference frame can be
represented by the Park equations provided all
the rotor quantities are referred to the stator
side. The stator and rotor voltages are expressed
as follows:
⎧
⎪Vds
⎪
⎪
V
⎪⎪ qs
⎨
⎪V
⎪ dr
⎪
⎪V
qr
⎩⎪
dϕ ds
⎫
− ωsϕ qs
⎪
dt
⎪
dϕ qs
⎪
= Rs iqs +
+ ωsϕ ds
⎪⎪
dt
⎬
dϕ
= Rr idr + dr − (ωs − ωr )ϕqr ⎪
⎪
dt
⎪
dϕ qr
= Rr iqr +
+ (ωs − ωr )ϕ dr ⎪
dt
⎭⎪
= Rs ids +
(7)
The flux linkage equations of the stator and
rotor can be related to their currents and are
expressed as follows:
J.E. QUAICOE
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Vector Control Of A Dfig Based Wind Turbine
⎧ϕds
⎪
⎪ϕqs
⎨
⎪ϕdr
⎪ϕqr
⎩
= Lss ids + Lm idr ⎫
⎪
= Lss iqs + Lm iqr ⎪
⎬
= Lrr idr + Lm ids ⎪
= Lrr iqr + Lm iqs ⎪⎭
•
(8)
where, Lss = Ls + Lm and Lrr = Lr + Lm
The electromagnetic torque developed by the
DFIG is related to the torque supplied by the
turbine and can be expressed as
d ωm
Te = 1.5 p (ϕ ds iqs − ϕ qs ids ) = 2 H
+ Bωm + Tm
dt
(9)
where, Tm is positive for motoring operation
and negative for generator operation. Equations
(7) to (9) are the set of differential equations
which represent a fourth order model for
describing the dynamic behavior of DFIG.
5. VECTOR CONTROL
STRATEGY
In order to achieve a decouple control of active
and reactive power, stator flux oriented vector
control scheme is adopted. Based on the
previous research the following assumptions are
considered:
•
•
Stator voltage drop across resistance
has been neglected as the effect of
stator resistance is quite low
compared to the grid voltage [5].
The DFIG is connected to a stiff
grid, i.e., the frequency and
Md. ARIFUJJAMAN M.T. IQBAL
•
•
amplitude of the stator or grid
voltage is assumed constant [7].
Magnetizing current of the stator is
assumed to be determined by the
grid [7].
The q-axis is 900 ahead of the d-axis
and rotating at synchronous speed in
the direction of rotation [8].
The stator flux vector is aligned with
the d-axis of the stator [8].
The above assumptions lead to the following
⎪⎧Vds = 0 ⎪⎫
⎪⎧ϕ ds = ϕ s ⎪⎫
(10)
⎨
⎬ and ⎨
⎬
=
V
V
⎪⎩ qs
⎪
s⎭
⎩⎪ϕ qs = 0 ⎭⎪
Neglecting the stator resistance, i.e., Rs = 0 (7)
becomes
dϕds
⎧
⎫
⎪Vds = 0 = dt − ωsϕqs
⎪
⎪
⎪
dϕqs
⎪
⎪
⎪⎪Vqs = ωsϕ ds = Vs = dt + ωsϕ ds ⎪⎪
(11)
⎨
⎬
⎪V = R i + dϕ dr − (ω − ω )ϕ ⎪
r dr
s
r
qr
⎪ dr
⎪
dt
⎪
⎪
d
ϕ
⎪V = R i + qr + (ω − ω )ϕ ⎪
qr
r qr
s
r
dr
dt
⎩⎪
⎭⎪
And (8) becomes
⎧ϕ s = Lss ids + Lm idr ⎫
⎪
⎪
⎪0 = Lss iqs + Lm iqr ⎪
⎨
⎬
⎪ϕdr = Lrr idr + Lm ids ⎪
⎪
⎪
⎩ϕqr = Lrr iqr + Lm iqs ⎭
J.E. QUAICOE
(12)
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Vector Control Of A Dfig Based Wind Turbine
Fig. 4 Block diagram of the control system
Fig. 5 Simulink model of the DFIG based wind turbine
The rotor voltages are then obtained as
Md. ARIFUJJAMAN M.T. IQBAL
J.E. QUAICOE
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Vector Control Of A Dfig Based Wind Turbine
⎧
⎪Vdr
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪Vqr
⎪
⎪
⎪
⎩⎪
⎫
⎪
⎪
⎪
⎪
⎪
⎪
⎬ (13)
⎪
⎪
⎪
⎡⎛
Lm 2 ⎞
LmVs ⎤ ⎪
+ (ωs − ωr ) ⎢⎜ Lrr −
⎥⎪
⎟ idr +
Lss ⎠
ωs Lss ⎦⎥ ⎭⎪
⎢⎣⎝
⎛
L 2 ⎞ di
= Rr idr + ⎜ Lrr − m ⎟ dr
Lss ⎠ dt
⎝
⎡
⎛
L 2 ⎞⎤
− ⎢(ωs − ωr ) ⎜ Lrr − m ⎟ ⎥ iqr
Lss ⎠ ⎦⎥
⎝
⎣⎢
2
⎛
L ⎞ diqr
= Rr iqr + ⎜ Lrr − m ⎟
Lss ⎠ dt
⎝
The active and reactive power produced in the
stator, the rotor fluxes and voltages can be
written in terms of the rotor current as [9]
− Lm
⎧
⎫
⎪ Ps = L Vs * iqr
⎪
⎪
⎪
ss
⎨
⎬
2
V
V
L
⎪Q = s − s m * i ⎪
dr
⎪⎩ s ωs Lss
⎪⎭
Lss
(14)
Thus from (14), the q-axis current vector
component, iqr can be used to regulate the active
power generated by the stator of DFIG while, idr
can be used to control the reactive power
produced by the stator. Essentially, control of
the active and reactive power is decoupled and a
decoupler is not necessary. A block diagram of
the control system is presented in Fig. 4.
5. SIMULATION RESULTS
The system described above is simulated using
Matlab-SimulinkTM blocks and the simulink
model is presented in Fig 5. The stator of the
DFIG is connected to a 690 V rms, 60 Hz
network. The DFIG is rated at 2MW and the
1.2
Rotational speed (pu)
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
Time (sec)
2.5
Fig. 6 Variation of rotational speed with time
Md. ARIFUJJAMAN M.T. IQBAL
J.E. QUAICOE
3
3.5
4
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Vector Control Of A Dfig Based Wind Turbine
4
q-axis rotor current component
d-axis rotor current component
3.5
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
Time (sec)
2.5
3
3.5
4
Fig. 7 q- and d- axis rotor current component
6
Stator active power
Stator reactive power
4
2
Power (pu)
Current (pu)
3
0
-2
-4
-6
-8
0
0.5
1
1.5
2
Time (sec)
2.5
3
3.5
Fig. 8 Stator generated active and reactive power
Md. ARIFUJJAMAN M.T. IQBAL
J.E. QUAICOE
4
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Vector Control Of A Dfig Based Wind Turbine
rotor is fed to the grid via an ac-dc (RSC) and
dc-ac (GSC) converters. Built-in converters of
Simulink for the RSC and GSC are considered
for the simulation. The nominal DC link voltage
is set to 1200V and the DC capacitance is 16mF.
through d-axis rotor current. Further
development of the system including grid side
converter control will be presented in a future
paper.
A step increase in wind speed from 8.4 m/s to
12.0 m/s is applied after a stable condition (2
seconds). Although such a step change is not
very realistic, the change can be considered as
the most drastic change from the point of the
control of the system. The simulation is started
from 2 seconds and within 3 seconds all the
quantities reach to their steady state values. The
speed of the wind turbine increases (from .82 pu
to 1.2 pu) due to the change in wind speed (Fig.
6) which ensures the maximum power
production as found in the reference wind
turbine modeling curve corresponding to this
two wind speeds(Fig. 3). The corresponding
power increase from 0.21 pu to 0.7 pu (Fig. 8)
while reactive power remains the same. The
power curve for both active and reactive power
contains ripple and is mainly due to the
controller parameters. An average value is
considered to describe the power quantity.
ACKNOWLEDGEMENTS
As a result of the change in active power
production by the DFIG, the q-axis component
of the rotor current increases to 0.5 pu and
remains at that value afterwards while d-axis
component of the rotor current remain
unchanged (Fig. 7) thus show the effectiveness
of the proposed control strategy.
Lumped
constant
Various challenges to system simulation were
experienced during the simulation. Limiters and
memory elements have been placed in several
nodes to eliminate convergence problems.
However, this limits the range of effective
parameter variations. In particular, the controller
parameters tuning need more attention. In
further work, methods of removing such
limitations will be reported.
7. CONCLUSIONS
Discussion of the dynamic modeling and
associated control strategy of a DFIG based
wind turbine has been presented. The stator
flux oriented vector control scheme is
incorporated with the DFIG control to realize
the fast and accurate control. Active power
production by the DFIG is controlled through
the q-axis rotor current while reactive power
Md. ARIFUJJAMAN M.T. IQBAL
The authors would like to thank the National
Science and Engineering Research Council
(NSERC) Canada for providing financial
support of this research
Appendix
TABLE A.1 PARAMETERS
OF THE SIMULATED
DFIG
Rated power
Stator voltage
2MW
690V
0.0108pu
Rs
Rr
0.0121pu
Lm
3.362pu
Lls
0.102pu
Llr
0.11pu
Inertia
3
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Chen, J. “Maximal Power Point Tracking
under Speed-Mode Control for Wind
Energy Generation System with Doubly
Fed Introduction Generator,” Proceedings
of the IEEE International Power
Electronics and Motion Control Conference
2006, Shanghai; China, Vol: 1, pp.1 – 5,
2006
[2] Cardenas,
Roberto.,
Pena,
Ruben.,
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[3] Li, H., Chen, Z., Pedersen J.K., “Optimal
Power Control Strategy of Maximizing
Wind Energy Tracking and Conversion for
VSCF Doubly Fed Induction Generator
System,” Proceedings of the IEEE
International
Power Electronics and
J.E. QUAICOE
1065
Vector Control Of A Dfig Based Wind Turbine
Motion
Control
Conference
2006,
Shanghai; China, Vol: 3, pp.1 – 6.2006
[4] Senjyu, T., Sakamoto, R., Urasaki, N.,
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Jenkins, N., “Comparison of fixed speed
and doubly-fed induction wind turbines
during power system disturbances,”
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Transmission and Distribution, Vol:
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[9] Toufik, B., Machmoum, M., Poitiers, F.,
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[6] Siegfried, Heier. “Grid Integration of Wind
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[7] He, Yikang., Hu, Jiabing, Zhao, Rende.
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2005
Md. ARIFUJJAMAN received his M.Eng. degree in Electrical and Computer
Engineering from Memorial University of Newfoundland (MUN), Canada on
September 2006. Prior to that, he fulfilled his B.Sc. degree in Electrical and Electronic
Engineering from the Khulna University of Engineering and Technology (KUET),
Bangladesh. Afterwards he joined as a lecturer at the same university and
consequently held the position of a Consultant and Research Testing Officer for about
2 years before starting his M. Eng. at MUN. He is currently working on his Ph.D. in
the wind energy at the High Voltage Engineering Laboratory of MUN. His research
involves simulation, control and innovative design level approach of renewable energy
systems with an intense to small wind energy conversion systems.
M. T. IQBAL received the B.Sc.(EE) degree from the University of Engineering and
Technology, Lahore in 1986, the M. Sc. Nuclear Engineering degree from the Quaid-eAzam University, Islamabad in 1988 and the Ph.D. degree in Electrical Engineering
from the Imperial College London in 1994. From 1988 to 1991 and from 1995 to 1999
he worked at the Pakistan Institute of Engineering and Applied Science
(www.pieas.edu.pk), Islamabad, Pakistan as an Assistant Engineer and later as a
Senior Engineer. From 1999 to 2000 he worked as an Associate Professor at, Riphah
International University (www.riphah.edu.pk). Since 2001 he is working at Faculty of
Engineering and Applied Science, Memorial University of Newfoundland. His
teaching activities cover a range of electrical engineering topics including control
systems, power electronics and renewable energy systems. His research focuses on
modeling and control of renewable energy systems.
Md. ARIFUJJAMAN M.T. IQBAL
J.E. QUAICOE
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Vector Control Of A Dfig Based Wind Turbine
John E. QUAICOE received the B.Sc. degree from the University of Science and
Technology, Kumasi, Ghana in 1973, and the M.A.Sc. and Ph.D. degrees from the
University of Toronto, Canada in 1977 and 1982 respectively. In 1982 he joined the
Faculty of Engineering and Applied Science at Memorial University of
Newfoundland, where he is presently a Professor and Associate Dean (Undergraduate
Studies) with teaching and research activities in power electronics and related areas.
His undergraduate and graduate teaching activities are in the areas of electric circuit
analysis, electronic circuit analysis and design, energy systems, power electronics and
power electronics systems, including modeling, analysis, control and design of power
converters for various applications. Dr. Quaicoe was the recipient of the President’s
Award for Distinguished Teaching at Memorial University of Newfoundland for 2001
and the IEEE Canada Outstanding Educator Medal for 2002. His research activities
include inverter modulation and control techniques, utility interface systems and
power quality, and uninterruptible power supplies. His recent research activities focus
on the development of power electronic systems and control strategies for fuel cells and wind generation systems.
He is a member of the Association of Professional Engineers and Geoscientists of Newfoundland and Labrador.
Md. ARIFUJJAMAN M.T. IQBAL
J.E. QUAICOE