of Back-to-Back PWM Converters for DFIG
Wind Turbine Systems under Unbalanced Grid
Control
Voltage
Ahmed G. Abo- Khalil, Dong-Choon Lee
Jeong-Ik Jang,
R&D Department
KR Group
Tower 98-4, Garak-Dong, Songpa-Gu, Seoul, Korea
Email: knightO318gyumail.ac.kr
Department of Electrical Engineering
Yeungnam University
214-1, Daedong, Gyeongsan, Gyeongbuk, Korea
Email: dcleegyu.ac.kr
Abstract
This paper presents a new control scheme for
minimizing the torque ripple of the generator under unbalanced
grid voltage for wind turbine systems using doubly-fed induction
generators, where the negative sequence component of the rotor
current is utilized. It is found that the generator torque ripples
are related with the reactive power component. Increase of stator
active power ripples caused by reducing the torque ripple is
compensated by controlling the active power ripples of grid-side
converter. Simulation results using PSCAD and experimental
results show that the conventional vector control of DFIG without
considering grid voltage unbalance results in excessive oscillations
on the stator active and reactive power, and electromagnetic
torque. On the other hand, with the proposed control strategy,
improved system control and operation such as reducing
oscillations of active power and generator torque can be achieved.
I.
INTRODUCTION
Nowadays, variable speed wind turbines with a DFIG
directly connected to the grid are widely used in the field. For
the dynamic feature, the DFIG becomes the most popular
generator for wind power generation system. Firstly, DFIG
can supply power to the grid at constant voltage and constant
frequency while the rotor can operate at sub-synchronous
mode or super-synchronous mode. Secondly, the rating of the
power converter is only about 30% of the rated power of the
wind turbine. At third, the generated active and reactive
power can be controlled independently.
The performance of the DFIG-based wind turbines under
the normal condition are now well understood [1]-[4]. For
conventional wind farms connected to an electric network, the
turbines are disconnected from the grid if voltage unbalance
of 6% or more is detected [5]. Then, the continuity of the
power generation in the wind energy system may be affected
by tripping the wind turbine from utility grid. Hence it is
desirable to implement the generator control system to
withstand to a certain level of voltage unbalances. If the
voltage unbalance is not taken into account in the control
system, a highly unbalanced stator current could be produced
even with a small unbalanced stator voltage. The unbalanced
currents cause unequal heating on the stator winding as well
as torque and power pulsation in the generator [6]. The torque
ripples can be a source of mechanical stress on the drive train
1-4244-0755-9/07/$20.00 (C2007 IEEE
and gearbox as well as a source of acoustic noise [7].
Control of DFIG systems for network unbalance has been
studied in [5], [7], and [8]. In [5], the current reference for
compensation was calculated in order to minimize the torque
pulsation without using machine parameters. However, the
rotor current controller is not easy to design and implement for
controlling both dc component in the synchronous reference
frame and the compensating rotor current which oscillates at
twice the line frequency. Also the paper shows only simulation
results without experimental results. In [7] the torque pulsation
was used as an input of a lead-lag controller to derive the
compensating rotor voltage. Also, these controllers need to be
carefully designed for both dc component and the doublefrequency current component.
In [9], an efficient dual current control algorithm using
positive and negative sequence current components in ac/dc
PWM converter systems was proposed. In DFIG control, due
to the existence of the double frequency rotor current
components, a dual current controller for positive and negative
sequence current components has been introduced in [10].
With this method, the generator torque ripple decreases,
however, the stator active power ripple appears. So, the power
flow into the grid is fluctuated. Applying the same concept in
[9] to the control of grid-side converter, the power ripples flow
into the grid can be decreased significantly.
In this paper, a novel control algorithm is proposed to reduce
the active power ripples flowing into the grid as well as the
torque ripple of the DFIG by controlling the grid-side
converter when the grid voltage is unbalanced. The double
frequency components of the stator reactive power are
controlled to zero to minimize the torque pulsations. Hence
two separate current controllers for the positive and negative
sequence components of rotor currents are designed and
implemented which allow significant reduction for the torque
pulsations. Similarly, the double-frequency components of the
grid active power are controlled to zero to minimize the grid
power ripples. Another two separate current controllers for the
positive and negative sequence components of the grid currents
are designed and implemented. Simulation results for a 2[MW]
DFIG wind turbine system are provided and experimental
result for a 3[kW] wind turbine simulator verifies the validity
of the proposed control strategy.
2637
'ds
Turbine
L
L
R
IbX
s
Wind
r
vde
( )r
R(e
(Sj, jr
VdsL
Lm
dr
+
Vdr
Fig. 1. Configuration of DFIG wind power systems.
Fig. 2. Equivalent circuit of DFIG.
II. DFIG MODEL AND CONTROL
Configuration of the overall wind generation system is
shown in Fig. 1. The stator of DFIG is directly connected to the
grid and the rotor is connected through back-to-back PWM
converters. The DFIG is controlled in a rotating d-q reference
frame, with the d-axis aligned with the stator flux vector. The
stator active and reactive power is controlled by regulating the
current and voltage of the rotor. Therefore the current and
voltage of the rotor needs to be decomposed into the
component related to stator active and reactive power.
A. DFIG model
Figure 2 shows the d-q equivalent circuits of DFIG. Under
stator flux-oriented control, the fluxes, currents and voltages
can be expressed as [11 ]
'dqs =Lsidqs + LmIdqr
(1)
kdqr = Lridqr + Lmidqs
(2)
Vds=Ri
vdqs
Rsdqs+
vdqr
d
dt
dqs + jO)e2dqs
r1dqr++d
ddqr + j(0)e O)r)Adqr
-Ri
-
(3)
(4)
B. Power control
Stator-flux oriented control is adopted in this control scheme
where the d-axis is aligned with the stator flux space vector.
The q-axis component of the rotor current can control either
the generator torque or the stator active power. On the other
hand, the rotor d-axis current component can control directly
the stator reactive power. Using (1)-(6), the stator active and
reactive power can be expressed as
2 2LL5
3
QS
Ls
2L
III. DFIG CONTROL UNDER UNBALANCED GRID VOLTAGE
A.
Generator torque
For unbalanced grid voltage, (1)-(4) are not sufficient to
derive the generator torque equation. Expressing the negative
sequence components for the fluxes and voltages,
'dqs =sidqs +Lmidqr
Ls
'dqr =r
Ad,qs
vn
Vdqs
Stator self-inductance;
Lr Rotor self-inductance;
Stator d-q axis flux linkage;
dqs otor d-q axis flux linkage;
lds, ldq: Stator and rotor d-q axis currents.
Oe X jr: Source and rotor angular frequencies
d
=RJidqs ++dt
s
(10)
+Lm dqs
eL)A+
dqs i(We)dqs
(1 1)
J
+
rd
)rdqr
(12)
where, the superscripts 'p' and 'n' indicate the positive and
negative sequence components, respectively.
The total apparent power of the generator can be expressed
(5)
as
(6)
where the superscript '"' means the complex conjugate and
S*)
ST=1.5(vsi-s*
Vdqs ldqs +s
Vdqr6dqr
s
qs
dr
(9)
- RPidqr + d idqA
vaqr
dqr -rdqr
dt dqr + j( O)
The phase angle of the stator flux vector is calculated as
follows;
6 =tan-1
(8)
-dr)
'rm
Lm Magnetizing inductance;
J(VdqRsidqs)dt
Vj(lms
7
where
is the magnetizing current.
It is noticeable that the stator active and reactive power
components are proportional to iqr and idr, respectively.
where
dqs
Vqslqr
ds
where the superscript 's' indicates quantities in the stationary
reference frame.
2638
VcqVdqr
id
dqr
ei9'-C9w)tvpdqr + ej.(
-=e
te)tiPdqr + ej
(13)
C9C)t ndqr
W),- trin
dqr
=s 1 .5(vqpsidps
-v
iqps + vqnsids-vdnsiqns)
svi +dsf
*5(VqsidsVdpsiqn
Vqnsidp svi$)
_VniqpS
QSc2 =1.5(vqpdJ
+
Qsc21
Qss 2
converter
Q.a
SVPWM
Fig. 3. Power control of DFIG system under unbalance grid voltage.
Taking the real part of (13) and dividing it by the mechanical
speed, the instantaneous torque is obtained as [12]
(14)
+
sin(2 oet)
Te(t) = TeO +
where
TO =1 .5Lm (iqs idr + iqns idn
.5Vids
+Vqsiq
-dsid-qiP
The d-axis of both positive and negative sequence
components are aligned with the positive and negative
components of the stator flux. Hence the positive and negative
sequence components of the stator d-axis voltage are zeros.
The generator torque and stator active and reactive power are
expressed in terms of the stator and rotor currents, which was
derived in [10]. It is found that the stator reactive power ripple
is related with the generator torque ripple. So, to reduce the
generator torque ripple, an additional controller for reactive
power ripples is added, which is shown in Fig. 3.
IV. CONTROL OF GRID-SIDE CONVERTER
T12 cos(2?),t) T'2
It is known from the stator active and reactive power
equations that stator active power ripples are increased by
applying the power control for torque ripple reduction. This
means that active power ripple flows into the grid since the
Te2 =1. 5Lm (iqP idr +iq- idr )
stator terminal is connected to the grid directly. Since this
situation
is not desirable, the active power ripple component
=
Te 2 1 .5Lm (iqpsiqnr-iqnsiqpr )
should be reduced. This can be achieved by controlling the
It is shown from (14) that the generator torque due to the grid-side converter to compensate for the active power ripples.
Just as it was derived in case of the generator control in the
source voltage unbalance includes the dc component( TO) and
previous section, the active and reactive power equations can
ac components( Tec2 X Ts2 ) which have the double frequency of be expressed as
the source. The torque pulsation can be decreased by
(18)
p(t) = Po + 'c2 cos(2wet) + 's2 sin(2 Wet)
controlling the negative-sequence component of the rotor
current.
B. Control ofgenerator-side converter
Next, the relationship of the stator power and the torque is
investigated. The stator-side apparent power under unbalanced
grid voltage can be expressed in terms of the positive and
negative sequence components as [10]
q(t) = Qo + Qc2 CoS(2Cw)et) + Qs2 sin(2ct)
where
Po=1.5(vp idp + vqps iqp + vds id + vqs iqn)
=12 1.5(vdsid + vqsiq + vdsid + vqsiq )
=
ei c,vdqs + e
e dqs +
dqs.
From (15), instantaneous active power ps(t) and reactive
power qs (t) are obtained as
PsO + Psc2 CoS(2o(et) + Pss2 sin(2o(et)
qs (t) = Qso + Qsc2 CoS(2cWet) + Qss2 sin(2cWet)
Ps (t)=
~1.s(dds
.5(vPidPss +v46qsP~qs+vP dsn(lds
+
PSs2= 1 . (qs is
n
=qs
Vs iqs
+v
iqn -V nidp _Vqnsiqp )
The current reference of the grid-side converter
compensating for the stator active power ripple can be derived
Q2=
vaq
dlqs dewqsJ~ +'
]1~c2=1 .5(vdpidns +pv'qcs
Vdnsiqp _Vqpidn + Vdp in )
Qc 2= 1.*5(vqps idn-vdps iqn + vqns idp -vdns iqp )
idqs
where
1 . 5(Vn idp
Qo =1.5(vqpsidp-vdpiqp +vqsidn -vdsiq)
Ss=1*5dqs dqs(15
where
vaq
(19)
qs qs)
ip +nvVqs iqspj~
+ Vds
cds
-Vqs ids + VdPs iqs)
nd
+
Vp
as
dP* (t)
(16)
qP* (t)
id(t
(17)
_q* (t)
+
1.*5(vdp
Vdcs
_
Vqns
VdS
vP
qs
-Vds
Vdn
qs
-Vds
n
-VPqs
vn
Vds
qs
Vqs
PV
ns
.PO
0
(20)
-P*
_i
sc~2
_j
where, PO0 means the power reference for the constant dc
voltage which is the product of the dc voltage controller output
and the dc voltage reference. Fig. 4 shows the control block
2639
Fig. 4. Control diagram of grid side converter under unbalance grid voltage.
diagram of the grid-side converter under unbalanced grid
voltage. The dual current controller is employed as in the
generator-side converter.
V. SIMULATION RESULTS
Simulations of the proposed control scheme for a DFIGbased generation system were performed using PSCAD
software. The DFIG used for simulation is rated at 2[MW] and
the wind speed is constant at 10[m/s]. The grid voltage is
Fig. 5. Power control without controlling the unbalanced grid voltage.
690[V] and 60[Hz]. For 2 [MW] DFIG system, 20% unbalance
voltages are applied at the grid side.
Initially, the system runs under balanced condition and then
the grid voltage is disturbed at 1.5[sec] and then the voltage
balance is recovered at 3.5[sec]. Fig. 5 shows the DFIG
performance with the conventional stator-flux oriented control
without considering the unbalanced condition. It is shown that
the positive and negative sequence components of the rotor
current include 120[Hz] components, which means the stator
current highly unbalanced. Similarly, the stator active and
reactive powers, and the electromagnetic torque all contain
significant pulsations at 120[Hz]. The magnitude of the torque
and speed ripples is 0.12[pu] and 13[rpm], respectively.
Fig. 6 shows the DFIG performance only with control of the
generator-side converter considering unbalanced condition.
Due to dual current control, the rotor current ripple is
suppressed. Accordingly, the generator torque and speed
ripples almost disappear. However, it is shown that the stator
active power ripples increase, of which magnitude are 0.02[pu]
and 1 [rpm], respectively. Next, consider the case that the gridside converter is controlled together with the generator-side
converter by the dual current control mode. Fig. 7 shows the
DFIG power control performance is not changed with the
additional dual current control of the grid-side converter.
Figure 8 shows the active and reactive power of the stator, the
grid-side converter, and the grid. The ripple component of the
stator active power appears due to suppression control of the shown in Fig. 8. Instead, the stator active power ripple is
DFIG torque ripple. To get rid of the power ripple, the grid- increased a little higher, however, it is insignificant since it has
side converter injects the compensating power into the grid. So, no effect on the power factor.
the grid active power ripple has been reduced to the level as
2640
Fig.
r
(a),-,
1
hVc
1
T
-Vt
-V-a
DD ;,t AnAjj
iov
, 1i
Fig. 7.
ia
abC'C
75[M/d iv
.
(b),
O[A]
~ 5[A]/div
I
Fig. 10 The grid phase voltages and stator currents under unbalanced
conditions
Fig. 8. Active and reactive power at the grid power smoothing control.
VI. EXPERIMENTAL RESULTS
To verify the feasibility of the proposed control scheme, a
small scale 3[kW] laboratory prototype is used to verify the
control scheme, which is shown in Fig. 9. The stator of the
DFIG is connected to the utility grid. The rotor is connected to
the grid through the back-to-back PWM converters to provide
bidirectional power flow. The converter switching frequency is
5 [kHz], and the current and the speed control sampling periods
are 100 [,Ls] and 1 [ms], respectively.
For the experiments, the amplitude of the a-phase voltage
Va is reduced to produce the unbalance as shown in Fig. 1 0(a).
Fig. 10(b) shows the stator currents which are also unbalanced.
Without regulating the stator and grid ripples, the stator active
power is fluctuated around the reference value, which is
2000[W], with a frequency of 120[Hz]. The stator reactive
power also oscillates around the 0[VAR] reference value with
the same frequency. As a result of the unbalanced stator
voltages and currents, the generator torque pulsates around the
average value as shown in Fig. 11. The oscillations of the
stator active power and electromagnetic torque are 20% and
22% of their rated values, respectively. The grid active and
reactive power is fluctuated at the same frequency as shown in
Fig. 12.
With regulating the ripple components of the stator reactive
power and grid active power, the stator reactive power and
generator torque ripples have been decreased significantly as
shown in Fig. 13. On the other hand, the reduction of the stator
active power ripples is lower than the reactive power. The grid
active and reactive power ripples have been decreased
significantly as shown in Fig. 14. The controller performance
is shown to be effective in reducing the stator reactive power
ripples and the grid active power ripples.
2641
r)
St
(a)
<
(a ) D:
200 O[VA
'./o
I..N
IN /.\
.;.J'
\,)
%/
X,
250 V\/div
i.,,
.,,/
5 O[\/d iv
i
(b)
(b)
0 [VAR]
i
'0\L/
2000[W
I
0-'O [VAR]
250[VAR]Idiv
2 50 [VARI/]d iv
T
(c)
5
\
I
Nm]v
(c )
A4/
5[Nm]
1 [Nm]/div
1 [N m]ld iv
Fig. 11 Stator active, reactive power and generator torque under
unbalanced voltages
p
-A
'i
Fig. 12 Stator active, reactive power and generator torque with ripple
elimination control
gt- id
j
1,
.1,
ir
(a)
1 500 [E
-t-
(a)
1500 [V
250[\AJ/di
(b)
250 [VW /d iv
0
[VAR]
(b) c
10
250 VAR] d iv
[VAFI
250[VAR]/iv
Fig. 12 Grid active and reactive power under unbalanced voltages
Fig. 13 Grid active and reactive power with ripple elimination control
VII. CONCLUSIONS
In this paper, a novel control scheme has been proposed for
reducing the DFIG torque ripple as well as the active power
ripple in to the grid, under grid voltage unbalance. The
principle of the control algorithm is to compensate for the
stator active power ripple increased due to suppressing the
generator torque ripple by the grid-side active power control.
Conventional DFIG control system shows excessive
fluctuations of the stator active and reactive powers, and
electromagnetic torque in both simulation and experimental
results. The proposed control algorithm shows the possibility
of reducing the generator torque ripples by controlling the
stator reactive power ripples and reducing the stator active
power ripples by controlling the active power ripples of the
grid side.
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