HACIL LC DFIG

Use of an LC filter to improve the quality of energy in a DFIG joined to the grid
M. Hacil, A. L. Nemmour, A. Khezzar and M. Boucherma
Département d’Electrotechnique, Université Mentouri, Constantine, Algérie. [e-mail]
Phone/Fax: [phone]
Abstract- In this paper, the application of an LC filter to
medium voltage rotor DFIG fed by inverters with switching
frequencies below fc is described. It is shown that the use of
LC filter gives several advantages for the drive system design,
how ever; a good system understanding is needed to utilize
these advantages. A vector control strategy for a doubly-fed
induction generator (DFIG) driven by a wind turbine and
connected to grid utility is presented. Although the rotor
inverter is controlled with an optimized space vector
modulation algorithm (SVM), the rotor currents are not
perfectly sinusoidal which causes undesirable fluctuations of
generating active and reactive stator powers. In order to more
improve the rotor current waveform, a second-order output
LC filter is inserted between the inverter and the rotor circuit.
Simulation studies of the proposed power generation system
were carried out. The obtained results show that the control
performances of the DFIG are clearly improved with the
proposed solution.
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.
Based on the rotor construction, induction generators can be
divided into wound-rotor induction generators and squirrel-
cage induction generators. The stator of wound-rotor
induction generators is directly connected to the grid utility,
and the rotor is also connected to the utility grid through a
power converter set. Since both the stator and rotor of
wound-rotor induction generators can transfer power, they
are also termed as double-fed induction generators. The
doubly fed induction generator (DFIG) can supply power at
constant voltage and constant frequency while the rotor speed
varies. This makes it suitable for variable speed wind energy
applications. Additionally, when a bidirectional AC-AC converter
is used in the rotor circuit, the speed range can be extended above
synchronous speed and power can be generated both from the
stator and the rotor. An advantage of this type of DFIG drive is
that the rotor converter need only be rated for a fraction of the
total output power, the fraction depending on the allowable sub-
and super-synchronous speed range.
[1][2].
High-frequency voltage-source inverters (VSI) have
been widely used to synthesize sinusoidal voltages for
many applications, such as uninterruptible power suppliers
(UPS), AC power sources and reactive static compensators.
As these inverters present a high total harmonic distortion
(THD) in the output voltages owing to the high-frequency
harmonics components introduced by the modulation, it is
often necessary to equip these converters with low-pass LC
filters.
These kind of filters have been designed to obtain the
highest natural frequency of the filter that meets a specified
maximum acceptable THD in the output voltages, taking
into consideration the modulation strategy used, it is
possible to make LC filter and command the inverter with
PWM or SVM for eliminate the high frequency in the
output signal.
This paper proposes a novel circuit configuration for
eliminate a high commutation frequency of the doubly fed
induction generator. This scheme employs a parallel LC
power filter connected to the rotor converter output. A
detailed mathematical model of the resulted system is
given.
II. GLOBAL SYSTEM MODELING
a- Vector control of the DFIG:
The DFIG must supply constant voltage and frequency at the
stator terminals irrespective of the shaft speed. Unlike the grid-
connected case; the stator flux is no longer determined by the grid
voltage and is thus set by regulating the rotor excitation current. A
decoupled orthogonal control using field-oriented techniques can
be used leading to direct control of the stator flux by one of the
rotor current components. The machine equations written in a
synchronously rotating d-q reference frame are:
[3][4][5]:
sqs
sd
sdssd
dt
d
iRv φω
φ
−+= (1)
sds
sq
sqssq dt
d
iRv φω
φ
++= (2)
rqr
rd
rdrrd
dt
d
iRv φω
φ
−+= (3)
rdr
rq
rqrrq dt
d
iRv φω
φ
++= (4)
srdsdssd MiiL
φ
φ
=
+
=
(5)
0
=
+
=
rqsqssq MiiL
φ
(6)
sdrdrrd MiiL
+
=
φ
(7)
sqrqrrq MiiL
+
=
φ
(8)

Grid
Wind
FEC
Rotor converter
Grid converter
Shaft
Turbine
DFIG
Fig.1. Block diagram of the global system conversion
LC Filter
( )
sdrqsqrd
s
eii
L
pM
T φφ −= (9)
( )
r
m
sdrqsqrd
s
mT
J
p
J
f
ii
JL
Mp
dt
d−−−=
ωφφ
ω
2
(10)
Equations (5) and (6) give:
rd
ss
s
sd i
L
M
L
i−=
φ
(11)
rq
s
sq i
L
M
i−= (12)
The electromagnetic torque Te becomes:
srq
s
ei
L
pM
T φ −= (13)
Assuming that the stator resistance is negligible
compared with the magnetizing reactance and also that the
stator flux vector has a constant magnitude and rotates at a
constant angular speed equal to the supply frequency.
Equations (1), (2) are simplified to (14) and (15):
0
=
sdv (14)
ssssq Vv
=
=
φ
ω
(15)
The stator active and reactive powers of a DFIG can be
derived using equations (11), (12), (14) and (15) as:
()
−==−=
−==+=
*
*
rd
s
sssdsqsqsdsdsqs
rq
s
ssdsdsqsqsdsds
i
L
M
VivivivQ
i
L
M
VivivivP
φ
(16)
As can be seen, Ps and Qs are proportional to * rdiand
*
rqi respectively. Provided the magnitude of stator flux is
kept constant, both power components can be controlled
linearly by adjusting the relative rotor current components.
Erreur !
Rr Rs
Lr
Ls
abc
dq
Currents
Controllers+
Decoupling
i
rd
*
DFIG
Filtering capacitors
Grid
Filtering inductors
Cf
C
Lf
irq
*
dq
αβ
v
rβ
*
vrα
*
Fig. 2. Control structure used
ird
irq
ir
if
uc

b- The second order LC filter model:
the application
The conversion system including the LC filter is shown in
Fig. 2, where if and ir are the input and output filter currents
respectively, cuis the capacitor filter voltage. The general
state space model of the second order LC filter is given by
[6]:
DvBuAxx
+
+
=
& (17)
Where:
[
]
t
c
f
ruiix=,
[
]
t
c
uv 00=;
And:
−
−−
−−
=
0
11
1
0
1
0
ff
ff
f
r
r
CC
LL
RLrL
R
A, =0
1
0fL B,
[
]
00
1
rL
D=
Fig.3.a. illustrates the equivalent per phase circuit of the
cascaded structure rotor inverter-LC filter-rotor DFIG
circuit. The current if across the filtering inductor can be
expressed in terms of the rotor inverter voltage U and the
rotor voltage V as:
VpGUpFif)()(
+
=
(18)
Where:
43
2
2
3
1
1
)( apapapa pF +++ = (19)
)())(1)((
)(1
)(
fffffrr
fff
RpLRpLpCRpL
RpLpC
pG +++++
+
+
=(20
)
The denominator coefficients in (19) are given by:
ffr CLLa = 1, frfffr CRLCRLa += 2,
ffrfr CRRLLa ++= 3, fr RRa += 4.
If the all resistances effects are neglected, relation (19)
becomes:
( )
pLLpCLL
pF
frffr ++
≈3
1
)( (21)
Finally, the resonance frequency of the LC filter is
computed as:
f
fr
fr
a
C
LL
LL
+
=1 ω (22)
III. FRONT END CONVERTER CONTROL
The grid converter allows the DC-bus voltage regulation
and the operating at unity power factor. In this case, the
currents drawn from the grid are perfectly sinusoidal.
When the output current reverses its direction, the boost
rectifier reverses the power flow through it and operates as
a voltage source inverter. By averaging the switching action
of the semiconductor switches and applying the dq
transformation to the resulting average model, a large signal
average model in dq coordinates is obtained. The equivalent
circuit is shown in Fig.4.b. The grid converter mathematical
model is given by [7][8]:
(
)
( )
( )
( )
−++=
−+=
−−=
−+=
oqqddcco
oqqdd
c
oqdggq
g
q
odqggd
g
d
iididRVV
iidid
Cdt
dV
VdiLV
Ldt
di
VdiLV
Ldt
di
2
3
2
31
3
3
1
3
3
1
ω
ω
(23)
Fig.3.b. Equivalent circuit of three phase LC
filter system in
dq
coordinates
Ud
Uq
Vcd
id
idf
iq
Vcq
iqf
3Lf
3Lf
3
ω
Lfiq
3
ω
Lfid
ω
CfVcq
ω
CfVcd
f
R
f
C
r
R
Fig.3.a. Equivalent circuit of one phase LC filter system
r
L
f
L
U V
u
c
if

So, the current io is given by:
qfqfdfdfo ididi
+
=
(24)
Where:
Vgd and Vgq are the grid voltage components in dq
coordinates. dd and dq are the duty cycle components in dq
coordinates of the grid converter. ddf and dqf are the duty
cycle components in dq coordinates of the rotor inverter.
Generaly, the grid converter is governed by the vector
control strategy. In this case, the Dc-bus voltage Vc is
controlled by the grid current component iq and the grid
side power factor is fixed by the id comoponent.
IV. SIMULATION RESULTS
a- Rotor converter control
To evaluate the effect of the proposed filter, a step
reference changing of the rotor current is applied. The filter
inductor value is mHL f270=, when the capacitor is
determined from the equation (22), resulting in
FC f µ 66,24=. Figures 5.a, 5.b show the rotor current,
stator current and the torque performances with and without
the LC filter addition respectively. The rotor currents i THD
is reduced from 0.41% to 0.13%. The rotor inverter
performances are shown in Fig 5.c.
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
-50
0
50
ira(A)
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
-20
0
20
isa(A)
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
-100
-50
0
Temps(sec)
Cem(N.m)
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
-50
0
50
ira(A)
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
-20
0
20
isa(A)
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
-50
0
Temps(sec)
Cem(N.m)
1 1.2 1.4 1.6 1.8 2
0
500
1000
Va(V)
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
-1000
0
1000
Temps(sec)
vra(V)
Fig.4.b. Equivalent circuit DC converter
in dq coordinates
3
ω
Lgiq
id
iq
Vo
Vgq
3Lg
3Lg
3
ω
Lgid
ddVo
dqVo
2
3dqiq
2
3ddid
io
Rc
C
ga
V
Fig.4.a. Block diagram of the vector control
method of applied to the grid converter
PWM Rectifier
PI
*
a
i
*
b
i
abc
dq
*
q
i
*
q
i
*
d
i
Grid
*
c
V
a
i
Rg Lg
(a) DFIG’s rotor side performances without the LC filter
(b) DFIG’s rotor side performances with the LC filter.
(c) Rotor side converter performances

Figures 6.a and 6.b illustrate the LC filter effect on the
power utility supply current. The DFIG’s stator currents
i
THD is significantly reduced from 4.49% to 0.186%.
1 1.01 1.02 1.03 1.04 1.05 1.06
-4
-2
0
2
4
Temps(sec)
isa(A)
THD=4,99
Without LC
1 1.01 1.02 1.03 1.04 1.05 1.06
-4
-2
0
2
4
Temps(sec)
isa(A)
THD=0,10
With LC
The slip value effect on the DFIG’s stator and rotor
currents is shown in Fig. 7. It is clear that the rotor current
waveform is improved for the for a small values of slip.
1 1.01 1.02 1.03 1.04 1.05 1.06
-5
0
5
isa(A)
1 1.01 1.02 1.03 1.04 1.05 1.06
-20
-10
0
Temps(sec)
ira(A)
THD=3,3
THD=0.2
1 1.01 1.02 1.03 1.04 1.05 1.06
-5
0
5
isa(A)
1 1.01 1.02 1.03 1.04 1.05 1.06
-20
0
20
Temps(sec)
ira(A)
THD=15.32
THD=0.46
The effect of the LC filter on the stator active and reactive
powers are presented in Fig. 8.
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
-8000
-6000
-4000
-2000
0
2000
temps(sec)
P(watt), QVAR)
Q(VAR)
P(watt)
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
-8000
-6000
-4000
-2000
0
2000
Temps(sec)
P(watt), Q(VAR)
Q(VAR)
P(watt)
b- grid converter control
Fig. 9 shows the response to a step change in active power via
the DFIG rotor currents chanching introduced at t=0.08s. An
augmentation in the grid currents ref
grabc
iin the front-end
converter is produced. Excellent Dc-link voltage regulation
when a step variation of 30% is applied at t=0,05s. The
Fig. 5. Effects of the LC filter on the DFIG’s
rotor side converter performances
(a) DFIG’s stator current performances without the
LC
filter
(b) DFIG’s stator current performances with the
LC
filter
Fig. 6. Effects of the LC filter on the DFIG’s
stator current waveform.
(a) DFIG’s stator and rotor currents (Slip=5%)
(b) DFIG’s stator and rotor
currents (Slip=30%)
Fig. 7. Effect of the slip values on the DFIG’s
stator and rotor currents waveform.
(a) Stator active and reactive powers (without the LC filter)
(b) Stator active and reactive powers (with the LC filter)
Fig. 8. Effects of the LC filter on the DFIG’s stator
active and reactive powers