2010 International Conference on Electrical and Control Engineering
Study on the Connection of DFIG to Grid Based on
Double-vector PWM
Xueqin Zheng 1,2
Donghui Guo1
1.Department of Electronic Engineering
Xiamen University
Xiamem, Fujian Province, China
2.Department of Electronic and Electrical Engineering
Xiamen University of Technology
Xiamem, Fujian Province, China
AbstractWith the increasing of wind penetration in power
systems, many national grid codes demand complete models and
simulation studies under different system conditions in order to
ensure that the connection of a wind farm would not have a
detrimental impact on the grid . It is now recognized that doubly
fed induction generators (DFIG) are used in many large farms. A
systematic control methodology for connection of wind-turbinedriven DFIGs to the grid is presented in this paper. The purpose
is to optimize control and enhance performance doubly fed
induction generator wind power system by using double-vectorpwm control. The control strategies of DFIG under vector
control in stator flux orientation of rotor side converter and
vector control of grid side PWM converter are investigated. A
dynamic model of the DFIG wind turbine is derived to develop a
vector controller to decouple dynamically active and reactive
power control ,and keep the DC link voltage stable, and supply
low distortion currents both in the machine rotor and the supply
grid. The simulations confirm the response of the DFIG
independent of speed and dynamic performance of the complete
system. The model is suitable to be used in a wind farm and the
network under various system disturbances .
However, vector-control method is known to give better
dynamic performance and is independent control of the active
and reactive power output of the DFIG drive[9][10].There are
two kinds of vector control. One is stator flux orientation
(SFO),the other is stator voltage orientation (SVO) [11]. The
controller[12] is used by SVO , but this approach increases the
complexity and computational burden. Petersson et al.[13]
assert that such stability problems do not exist when an SVO
is employed.
This paper proposes a systematic approach for connection
of DFIGs to the grid. The control strategies of DFIG under
vector control in stator flux orientation of rotor side converter
and PWM control of grid side convert are investigated. The
load voltage is maintained at constant frequency and its
magnitude is regulated through control of the stator flux of the
generator. The DC link voltage keeps stable. At the same time,
this control method is characteristic by supplying low
distortion currents both in the machine rotor and the supply
grid.
Keywords-doubly fed induction generator; power system
modelling; double-vector-pwm control
I.
II.
The configuration of a DFIG driven by a wind turbine is
shown in Fig.2. The wind turbine is connected to the DFIG
through a mechanical shaft system, which is composed of a
low speed shaft and a high-speed shaft and a gearbox in
between. The wound-rotor induction machine in this
configuration is fed from both stator and rotor sides. The rotor
is fed through a variable frequency converter ,while the stator
is directly connected to the grid.
INTRODUCTION
Due to the increasing concern about environmental
pollution and a possible energy shortage, the renewable energy
systems and generation have attracted great interests in recent
years[1][2]. Wind energy is one of the fastest growing energy
sources, and is regarded as an important alternative to
traditional power generating sources. The large wind farms
have been planned or installed around the world, at the same
time the power ratings of the wind turbines are increasing. For
many wind farms, wind turbines based on the doubly fed
induction generator (DFIG) technology whose converters
rating are about 25%30% of the generator. Compared with
wind turbines using other generators[3], DFIG-based wind
turbines have several advantages including cost effective,
providing simple pitch control, reducing mechanical stress,
compensating torque and power pulsations, improving power
quality and so on[4].
Figure 1. Wind power generation general system scheme
A number of scalar control algorithms have been
developed for DFIG, such as closed-loop frequency control[5]
,open-loop control[4][6], phase-angle control[7][8]. It was
shown to stabilize the machine over a wide speed range.
978-0-7695-4031-3/10 $26.00 2010 IEEE
DOI 10.1109/iCECE.2010.526
WIND TURBINE GENERATOR MODEL
A. Wind Turbine aerodynamic model
The aerodynamic model of a wind turbine can be
characterized by the well-known C p curves. C p is the
2139
power coefficient, which is a function of both the blade pitch
angle and tip speed ratio .The tip speed ratio is defined
by:
wwind R
v
C. Modeling of the DFIG
The DFIG must supply constant voltage and frequency at
the stator terminals irrespective of the shaft speed. A
decoupled control using field-oriented techniques can be used,
which leads to direct control of the stator flux by one of the
rotor current components.
(1)
The DFIG wind turbines utilize a wound rotor induction
generator, where the rotor windings are fed through back-toback variable frequency, voltage source, converters. The
DFIG can be regarded as a traditional induction generator with
a non zero rotor voltage. Under the condition of the stator
transients neglected, the electrical equations of the DFIG can
be written as following. These equations are transformed from
three-phase to two-phase components and subsequently rotate
all variables into a synchronous reference frame(m-t axis).
Where wwind is the wind turbine rotor speed in rad/s, R is
the blade length in m, v is the wind speed in m/s. The
C p curves depend on the blade design.
C p (, ) = 0.5175(116
0.4 5)e
21
+ 0.0068
(2)
i must satisfy the following equation:
Where the
+ 0 .08
0 .035
3 +1
The DFIG model is developed based on the following
assumptions. The equations are derived in the synchronous
reference frame using direct (m) and quadrature (t) axis
representation. The stator current is assumed positive when
flowing toward the machine. The m-axis was assumed to be
90 lag of t-axis in the direction of rotation.
(3)
The curve of C p is shown in Fig 3.
Given the power coefficient C p ,the mechanical power that
Stator voltage
the wind turbine extracts from the wind is calculated by:
1
P = C p Sv 3
2
u sm = Rs i sm + 1 st sm
.
u st = Rs i st + 1 sm st
(4)
Where is the air density in kg/m3, S is the area swept
by the rotor blades in m2.
(6)
Rotor voltage
.
u rm = Rr i sm s rt rm
.
u rt = Rr irt + s rm rt
(7)
Stator flux linkage
sm = L s i sm L m i rm
st = L s i st L m i rt
Figure 2. Wind power Cp curves for different blade angles .
B. Modeling of the Wind Speed
Wind resource at a geographic location is highly variable.
Power generated from wind generator depends on the wind
speed, which fluctuates randomly with time. Wind power
studies, therefore, require the models to represent the wind
speed variation for wind farm locations of interest. Wind
speed distributions are often characterized by Weibull
distributions.
Rotor flux linkage
rm = L r i rm L m i sm
rt = L r i rt L m i st
(9)
Electromagnetic torque
Me =
The wind speed at any given time for a particular
geographic location can be simulated using:
VW = VB + VWG + VWR + VG
(8)
Lm
L
ir s = m (irt sm irm st )
Ls
Ls
(10)
u sm the m-axis stator
u
the t-axis stator voltage, rm the m-axis rotor
where the following notations apply :
(5)
voltage,
where VB is base wind, VWG is gust wind, VWR is random
wind VG is gradient wind.
voltage,
linkage,
u st
u rt the t-axis rotor voltage, sm the m-axis stator flux
st
rotor flux
the t-axis stator flux linkage,
linkage, rt
2140
the m-axis
the t-axis rotor flux linkage,
Electromagnetic torque (p.u.),
Figure 3. Curve of wind speed
rm
Me
i sm the m-axis stator current, i st
Where C the filter capacitor, r the input resistance of
converter, L the input inductance of converter, u dc the filter
the t-axis stator current, rm the m-axis rotor current, rt the taxis rotor current, Rs the stator resistance (p.u.) , Rr the rotor
voltage, idc the filter current, e the grid voltage.
resistance(p.u.), s the stator self induction(p.u.), r the rotor
self induction(p.u.),Lm the mutual inductance between rotor
and stator(p.u.), 1 the synchronous speed and s the slip
electrical frequency,
In a synchronous reference frame, the grid side current
equations can be written as
s = 1 2 , 2 the rotor speed.
L i sd = risd + Lisq + Em urd
Equations (6)(10) are used to obtain the dynamic model
of the DFIG.
III.
(13)
L i sq = risq Lisq urd
CONTROL SCHEME DESCRIPTION
(14)
The equation of AC and DC power can be written as
A schematic diagram of a DFIG-based wind energy
generation system is shown in Fig.4. The main circuit
topology of a DFIG system with a back-to-back PWM
converter, which consists of a grid-side converter(connected to
the grid,),a rotor-side converter(connected to the generator)
and a dc-link capacitor. In order to gain electrical active power
at constant voltage and frequency to the grid over a wide
operation range from super-synchronous to sub-synchronous
speed, the active power flow between the grid and the rotor
circuit must be controlled both in direction and in magnitude
.Therefore, Both of the converters have six four-quadrant
power electronic devices.
P=
3
3
(eqisq + ed isd ) = Emisd = u dc idc
2
2
(15)
So
.
Cu dc u dc = udc iL +
3
Emisd
2
(16)
The double close loops of the grid side converter which
include voltage and current control can be seen in Fig5.
Figure 4. Main circuit topology of a back-to-back PWM converter for DFIG
In this section, a balanced grid voltage supply is assumed.
The rotor-side converter controls torque and reactive power,
while the grid-side converter controls the dc voltage and gridside active power.
Figure 5.
B. Rotor side Converter
In the rotor side converter, reactive power and the
referenced torque determine the current references, which
determine the voltages to be applied to the rotor side.
A. Grid side Converter
The rotor grid converter P-Q capability depends mainly on
grid side converter dc bus voltage. So it is important to control
the dc link voltage and keep it stable. In this section, the
vector PWM converter will be introduced in detail.
A wind-turbine generator must be fully controllable so
that it can operate at a shaft speed that is independent of wind
conditions to gain the stator voltage which is the same to grid
voltage, including the same amplitude, frequency and phase.
The dc bus voltage and reactive power references
determine the current references, which determine the voltages
to be applied in the grid side converter.
In this section, the control model of rotor side converter
is analyzed. The synchronous reference frame is linked to the
stator flux of the machine.
Suppose that three phases of the grid voltage are
symmetrical :
e = ris + Lis + ur
Aligning the m-axis of the reference frame on the stator
flux vector gives:
(11)
sm = s
st = 0
C u dc = idc iL
Control scheme of grid side converter
(12)
(17)
The m axis voltage component is zero.
u sm = 0 , u st = U m
2141
(18)
So,
.
s = 0
Um
s =
s
(19)
The active and reactive power delivered to the rotor by the
four-quadrant converter and the mechanical power delivered
to the shaft of the generator are calculated as followings. The
instantaneous active and reactive power under m-t reference
frame can be expressed as
3
p = 2 (u sm i sm + u st i st )
3
q = (u st i sm u sm i st )
From equations , The closed loop control strategy is
shown in Fig6. The current error (the difference between the
achieved and desired) together with a PI controller was used to
u'
obtain rm . The rotor voltage in m-t axis is determined
mainly by the output of a PI controller with an input of the
control error. Feed-forward compensation terms are often used
for enhancing the response of the controller. They usually
include the compensation of the coupling components and the
stator flux associated induced electromotive force components.
( Lr
(20)
'
urm
*
irm
L2m
) s irt
Ls
*
urm
irm
The mean power
3
P = 2 U m i st
3
Q = U m i sm
2
Figure 6. Current close loop control of rotor M-axis
(21)
The vector control schematic of the rotor side converter is
shown in Fig.7.
From above power equations, it is clear to describe the
power flow in the DFIG for sub-synchronous and supersynchronous operation. Above synchronous speed, the fourquadrant converter operates as a generator of active power
delivering power to the grid .Under the condition of subsynchronous, the four-quadrant converter circulates active
power from the grid into the rotor circuit.
Using equations (17) to (21),the rotor currents can be
derived in the following form.
irm = ( s + Ls ism ) / Lm
Li
irt = s st
Lm
(22)
The rotor flux are calculated using
Figure 7.
L
Lm
)irm
rm = s + Lr (1
Ls Lr
Ls
L2
rt = Lr (1 m )
L s Lr
2
m
(23)
Finally, the rotor reference voltages are calculated using
L2 di
L2
u rm = R r i rm + ( L r m ) rm ( L r m ) s i rt
(24)
L s dt
Ls
2
2
u = R i + ( L L m ) di rt ( L L m ) i + L m s
r rt
r
r
s rm
s
rt
L s dt
Ls
Ls
IV.
Vector control diagram of rotor side converter
SIMULATION RESULTS AND ANALYSIS
The theoretical analysis is evaluated through simulations in
MATLAB. The machine parameters are given as following.
According to the theoretical analysis, the stability of the DFIG
vector control depends only on the speed of the machine. It is
independent of the reactive power output, wind speed.
The machine parameters are rated power=6.8kW,
Frequency=50 Hz, stator rated voltage=690V, Rs=0.00788 pu,
Rr=0.00559 pu, Ls=0.173 pu, Lr=0.157 pu and Lm=2.95pu.
'
Let u rm = u rm
+ u rm
2
where u ' = R i + ( L Lm ) dirm
rm
r rm
r
Ls dt
u rm = ( Lr
L2m
) s i rt
Ls
Figure 8. Waveform of DC bus voltage
2142
converter and vector control of grid side PWM converter. The
stability of the control strategy is verified with the operation of
the DFIG despite wind speed variations. The system decouples
dynamically active and reactive power control, and the values
keep as the given references .
REFERENCES
Figure 9. Input current of grid side converter
[1]
[2]
[3]
Figure 10. Waveform of the stator voltage and current of DFIG
[4]
[5]
[6]
Figure 11. Waveform of active and reactive of DFIG
Simulations with random wind speed has been carried out
to test the proposed control schemes.Fig.8-11 illustrate that the
DC bus voltage keeps stable(1000v). The voltage and current
waveform of the grid side converter have good sinusoidal
wave ,furthermore the power factor is approximately unity.
The stator voltage in this simulation is constant(690V), as
there is no change in the reactive power. The responses of
both active and reactive power during step change of their
references are 0.18s and then keep stable as their references.
There is no over shoot of either the stator currents or the active
and reactive power. The DFIG has stable operation even with
wind speed variation.
V.
CONCLUSION
[7]
[8]
[9]
[10]
[11]
[12]
[13]
The double-vector-pwm control strategy for a DFIG
system has been presented in this paper. The strategy makes
use of the vector control in stator flux orientation of rotor side
2143
Fadaeinedjad R,Moallem M and Moschopoulos G, Simulation of a
Wind Turbine With Doubly Fed Induction Generator by FAST and
Simulink[J].IEEE Transactions on Energy Conversion, vol.23, no.2,
pp.690-700,2008.
Gomis Bellmunt 0,Junyent Ferre A,Sumper A,et al, Ride-Through
Control of a Doubly Fed Induction Generator Under Unbalanced
Voltage
Sags[J].
IEEE
Transactions
on
Energy
Conversion,vol.23,no.4,pp. 1036-1045,2008.
Lie Xu, Phillip Cartwright, Direct Active and Reactive Power Control
of DFIG for Wind Energy Generation, IEEE Transactions on Energy
Conversion,vol.21,no.3,pp. 750-758,2006.
Bys.Mll E R,M.Deicke,Rik W, De Doncker, Doubly Fed Induction
Generator Systems for Turbines,IEEE Industry Application,pp. 2633,MAY/JUNE 2002.
R.Li,R.Spee,A.K.Wallace,and G.C.Alexander, Synchronous Drive
Performance of Brushless Doubly-fed Motors[J], IEEE Industry
Application,vol.30,no.4,pp. 963-970 ,1994.
D.Feng,P.C.Roberts,and R.A.McMahon, Control Study on Starting of
BDFM,in Proc.41st Int.UPEC,2006(2):660664.
S.Shao,E.Abdi,and R.A.McMahon, Operation of Brushless Doubly-fed
Machine for Drive Applications, in Proc.Power Electron.Mach.Drives
Conf.,Apr.2008,pp.340344.
S.Shao,E.Abdi,and R.A.McMahon, Stable Operation of the Brushless
Doubly-fed Machine(BDFM),in Proc.Power Electron. Drive Syst. Conf.
,Nov.2007,pp.897902.
Y.Tang and L.Xu, A Flexible Active and Reactive Power Control
Strategy for a Variable Speed Constant Frequency Generating System,
IEEE Trans. Power Electron.,vol.10,no.4,pp.472478,Jul.1995.
Shiyi Shao,Ehsan Abdi, Stator-Flux-Oriented Vector Control for
Brushless Doubly Fed Induction Generator, IEEE Transactions on
Industrial Electronics,vol.56,no.10,pp.4220-4228,2009.
Agiou Pavlou, Stability of Doubly-fed Induction Generator under
Stator Voltage Orientated Vector Control, IET Renew.Power Gener.,
Vol.2, No.3, pp.170180, 2008 .
D.Zhou,R.Spee,G.C.Alexander,and A.K.Wallace, A Simplified Method
for Dynamic Control of Brushless Doubly-fed Machines,in Proc.22nd
Annual.IEEE IECON, vol.2 ,pp.946951,Aug.1996.
Petersson A.,Harnefors L.,Thiringer T, Comparison between Statorflux and Grid-flux-oriented Rotor Current Control of Doubly-fed
Induction Generators,IEEE 35th Annual Power Electronics Specialists
Conf., vol.1,pp.482486,2004.
