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. [email protected]
Phone/Fax: +0021331819013
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.
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
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 squirrelcage 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 suband 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
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 gridconnected 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]:
dφsd
−ωsφsq
dt
(1)
dφsq
+ωsφsd
dt
(2)
dφrd
−ωrφrq
dt
(3)
dφrq
+ωrφrd
dt
(4)
vsd = Rsisd +
vsq = Rsisq +
vrd = Rrird +
vrq = Rrirq +
φsd = Lsisd + Mird =φs
(5)
φsq = Lsisq + Mirq =0
(6)
φrd = Lrird + Misd
(7)
φrq = Lrirq + Misq
(8)
Te =
pM
(irdφsq −irqφsd )
Ls
constant angular speed equal to the supply frequency.
Equations (1), (2) are simplified to (14) and (15):
(9)
2
dωm = p M (irdφsq −irqφsd )− f ωm − p Tr
dt
J
J
JLs
vsd =0
vsq =ωsφs =Vs
(10)
(14)
(15)
Equations (5) and (6) give:
φs
isd = − M ird
The stator active and reactive powers of a DFIG can be
derived using equations (11), (12), (14) and (15) as:
(11)
Ls Ls
isq =− M irq
Ls
(12)
 Ps =vsd isd +vsqisq =vsd isd =−Vs M irq*

Ls
(16)

M *
Qs =vsqisd −vsd isq =vsqisd =Vs φs − Ls ird
*
As can be seen, Ps and Qs are proportional to ird and
Te =−
)
(
The electromagnetic torque Te becomes:
*
pM
irqφs
Ls
irq respectively. Provided the magnitude of stator flux is
(13)
kept constant, both power components can be controlled
linearly by adjusting the relative rotor current components.
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
Grid converter
Turbine
FEC
Rotor converter
Erreur !
Wind
LC Filter
Grid
Shaft
DFIG
Fig.1. Block diagram of the global system conversion
Filtering inductors
Rr
ir
Lf
if
Ls
Rs
Grid
Lr
C
Cf
uc
abc
Filtering capacitors
dq
ird
vrα*
vrβ*
dq
αβ
DFIG
irq
Currents
Controllers+
Decoupling
ird*
irq*
Fig. 2. Control structure used
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, uc is the capacitor filter voltage. The general
state space model of the second order LC filter is given by
[6]:
x& = Ax + Bu + Dv
Finally, the resonance frequency of the LC filter is
computed as:
(22)
Lr L f
Lr + L f
Cf
(17)
Where:
x=[ir i f uc ] , v=[uc 0 0] ;
Lf
Rf
if
t
1
ωa =
Rr
Lr
t
U
Cf
V
uc
And:
 − Rr 0 − 1 
 Lr
Lr 
R
f

A= 0 − − 1  , B= 0 1 0 , D= 1 0 0
 L f 
Lf Lf 
Lr

− 1 1 0 
 C f C f

[
Fig.3.a. Equivalent circuit of one phase LC filter system
]
idf
i f = F(p)U +G(p)V
(18)
Where:
iqf
Uq
Vcd
3ωLfid
3Lf
iq
ωCfVcd
Vcq
Fig.3.b. Equivalent circuit of three phase LC
filter system in dq coordinates
III. FRONT END CONVERTER CONTROL
F(p)=
G ( p) =
id
ωCfVcq
Ud
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:
3ωLfiq
3Lf
1
a1 p +a2 p 2 +a3 p+a4
(19)
3
1 + C f p( L f p + R f )
( Lr p + Rr )(1 + C f p( L f p + R f )) + ( L f p + R f )
(20
)
The denominator coefficients in (19) are given by:
a1 = Lr L f C f , a2 = Lr R f C f + L f Rr C f ,
a3 = Lr + L f + Rr R f C f , a4 = Rr + R f .
If the all resistances effects are neglected, relation (19)
becomes:
F ( p) ≈
1
(
)
Lr L f C f p 3 + Lr + L f p
(21)
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]:
(
)
(
)
did
1
=
V gd + 3ωL g iq − d d Vo
dt
3L g
diq
1
=
V gq − 3ωL g id − d qVo
dt
3L g
dVc
1 3

=  d d i d + d q i q − io 
dt
C2

3

Vo = Vc + Rc  d d id + d q iq − io 
2

(
)
(
)
(23)
So, the current io is given by:
io =ddf idf +dqf iqf
(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.
Lg
Rg
ia
determined from the equation (22), resulting in
C f = 24,66 µF . 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 THDi
is reduced from 0.41% to 0.13%. The rotor inverter
performances are shown in Fig 5.c.
Vga
50
0
-50
1.4
20
Cem(N.m)
isa(A)
Grid
Vc*
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 L f = 270mH , when the capacitor is
ira(A)
PWM Rectifier
IV.
PI
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.45
1.5
1.55
1.6
1.65
Temps(sec)
1.7
1.75
1.8
1.85
1.9
0
-20
1.4
0
-50
-100
1.4
i q*
(a) DFIG’s rotor side performances without the LC filter
ib*
abc
Cem(N.m)
dq
i q*
0
-50
1.4
20
isa(A)
ia*
ira(A)
50
i d*
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.45
1.5
1.55
1.6
1.65
1.7
Temps(sec)
1.75
1.8
1.85
1.9
(b) DFIG’s rotor side performances with the LC filter.
io
500
0
C
Rc
dqVo
Vo
1
1.4
1.6
1.8
2
0
-1000
1
Fig.4.b. Equivalent circuit DC converter
in dq coordinates
1.2
1000
vra(V)
3 dqiq
2
Va(V)
1000
ddVo
Vgq
1.55
-50
1.4
id 3Lg 3ωLgiq
iq
1.5
0
-20
1.4
0
Fig.4.a. Block diagram of the vector control
method of applied to the grid converter
3 ddid
2
3
ω
L
i
g
d
3Lg
1.45
1.1
1.2
1.3
1.4
Temps(sec)
1.5
(c) Rotor side converter performances
1.6
1.7
5
isa(A)
Fig. 5. Effects of the LC filter on the DFIG’s
rotor side converter performances
1
1.02
1.03
1.04
1.05
1.06
THD=0.46
0
-20
1
0
1.01
1.02
1.03
1.04
1.05
Temps(sec)
(b) DFIG’s stator and rotor currents (Slip=30%)
1.06
Fig. 7. Effect of the slip values on the DFIG’s
stator and rotor currents waveform.
-2
-4
1.01
20
ira(A)
THD=4,99
Without LC
2
isa(A)
0
-5
Figures 6.a and 6.b illustrate the LC filter effect on the
power utility supply current. The DFIG’s stator currents
THDi is significantly reduced from 4.49% to 0.186%.
4
THD=15.32
1
1.01
1.02
1.03
Temps(sec)
1.04
1.05
1.06
(a) DFIG’s stator current performances without the LC filter
4
The effect of the LC filter on the stator active and reactive
powers are presented in Fig. 8.
2000
THD=0,10
With LC
0
P(watt), QVAR)
isa(A)
2
0
-4000
P(watt)
-6000
-2
-8000
1.4
-4
Q(VAR)
-2000
1
1.01
1.02
1.03
Temps(sec)
1.04
1.05
1.06
1.45
1.5
1.55
1.6
1.65
1.7
temps(sec)
1.75
1.8
1.85
1.9
(a) Stator active and reactive powers (without the LC filter)
(b) DFIG’s stator current performances with the LC filter
2000
Fig. 6. Effects of the LC filter on the DFIG’s
stator current waveform.
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.
P(watt), Q(VAR)
0
Q(VAR)
-2000
-4000
-6000
-8000
1.4
isa(A)
5
1.45
1.5
1.55
1.6
1.65
1.7
Temps(sec)
0
1.8
1.85
1.9
Fig. 8. Effects of the LC filter on the DFIG’s stator
active and reactive powers
1
1.01
1.02
1.03
1.04
1.05
1.06
0
b- grid converter control
THD=0.2
Fig. 9 shows the response to a step change in active power via
the DFIG rotor currents chanching introduced at t=0.08s. An
-10
augmentation in the grid currents
-20
1.75
(b) Stator active and reactive powers (with the LC filter)
THD=3,3
-5
ira(A)
P(watt)
1
1.01
1.02
1.03
1.04
1.05
Temps(sec)
(a) DFIG’s stator and rotor currents (Slip=5%)
1.06
i grabcref
in the front-end
converter is produced. Excellent Dc-link voltage regulation
when a step variation of 30% is applied at t=0,05s. The
rotor power variaton which acts as disterbance is
immediately rejected.
[9]
Gonzalo Abad, Miguel Ángel Rodríguez “Three-Level NPC
converter-Based Predictive Direct Power Control of the Doubly Fed
Induction Machine at Low Constant Switching Frequency“IEEE
transactions on industrial electronics, vol. 55, no. 12, december 2008
[10]
isr(A)
20
0
-20
0
0.05
0.1
0.15
0.2
0
0.05
0.1
0.15
0.2
40
0.05
0.1
0.15
0.2
0.05
0.1
Temps(sec)
0.15
0.2
Vc(V)
4000
2000
0
io(A)
800
Ps(watt)
1000
600
2
0
0
Fig. 9. Grid converter performances under the rotor
power variation
V.
CONCLUSION
A complete variable speed wind power generator using a
doubly-fed induction generator with an AC-DC-AC
converter is proposed. In order to more improve the stator
current waveform and consequently the quality of generating
stator active and reactive powers, a second-order output LC filter
is inserted between the inverter and the rotor circuit. This
simplest solution provides a several advantages that are
very necessary for any electrical power system generation.
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