XVIII Congresso Brasileiro de Automática / 12 a 16 Setembro 2010, Bonito-MS.
INFLUENCE OF CONTROL STRATEGIES ON DFIG-BASED WIND FARMS
INTEGRATION IN THE POWER SYSTEMS
Romeu Reginatto∗, Carlos da Rocha∗
∗
Center for Engineering and Applied SciencesWestern Paraná State University - UNIOESTE - Brazil
Emails: romeu@unioeste.br, rrocha@hotmail.com
Abstract— In this paper the integration of wind farms equipped with DFIG-based wind turbines in the power
system is considered. The effect of wind farm control policies on the maximum power that can be connected to a
given grid point is analyzed. Reactive power regulation, power factor regulation and terminal voltage regulation
are considered as control policies. The maximum integration level is determined on the basis of 3 interconnection
criteria: acceptable terminal voltage variation, power transfer margin, and acceptable range for the internal
voltage angle. Analytical and numerical results are provided to illustrate the advantages and drawbacks of each
control strategy with regard to the integration level.
Keywords—
1
Wind power; DFIG; Integration level; DFIG control.
tions, a minimum active power margin relative to
the maximum power transferable to the grid, and
an acceptable range for the internal voltage angle.
The satisfaction of such interconnection criteria
was referred to as a safe interconnection, and conditions for it were numerically determined for a
particular wind farm. Further results were given
in (Reginatto et al., 2009) in which the individual
effect of each interconnection criterion on the integration level was considered. It was seen that the
tolerance on voltage variation has a major impact
on such limits.
The present paper concentrates on the effect
of the DFIG-VSWT control strategy on the wind
power integration level. Three different control
strategies are considered for the DFIG-VSWT: (i)
reactive power regulation; (ii) power factor regulation; (iii) terminal voltage regulation. The
analysis is performed by means of both analytical
developments and numerical results. The characterization of such effects is provided in terms of
the safe integration region concept introduced in
(Reginatto et al., 2009; Reginatto et al., 2008).
The results provide a first general view of how
control strategies impact on the DFIG-VSWT integration in the power system.
The paper is organizes as follows. Section 2
introduces modeling, systems and control considerations for DFIG-VSWT. The same section also
discusses interconnection issues. The main results
on the analysis of the influence of the control strategy on wind power integration level are given in
section 3. Section 4 provides concluding remarks
Introduction
Wind energy integration into the power systems is
continuously growing. Penetration levels of 20%
to 30% have been reached in certain regions in
Europe (Soder et al., 2007) and this continuous
growth has demanded for advancements in several
directions in order to guarantee a safe interconnection of wind energy in the network.
Integration of wind farms into the power system is subject to technical regulation which usually specify operating characteristics that wind
farms have to comply with (Matevosyan et al.,
2005; Ackermann, 2005). Several factors influence those operating characteristics and thus the
amount of wind power that can be integrated
at a given grid point, for instance, wind energy
conversion system technology, the control policy
adopted, and characteristics of the point of common connection (PCC). Among the different technologies, the doubly-fed induction generator variable speed wind turbine (DFIG-VSWT) has interesting advantages regarding the control flexibility
and low converter losses(Ackermann, 2005), allowing active power regulation (Tarnowski and Reginatto, 2007), reactive power and/or voltage control (Pálsson et al., 2003; Cartwright et al., 2004)
(see also (Le and Santoso, 2007)).
The integration level has been analyzed in
(Lundberg, 2000) for fixed-speed wind turbines
with squirrel-cage induction generators with respect to point of common connection (PCC) parameters, namely the short-circuit power (Ssc )
and the X/R ratio. In that case, terminal voltage variations and voltage flicker were taken to
assess interconnection properties. In (Reginatto
et al., 2008) the analysis was extended to the
DFIG-VSWT case with reactive power regulation,
besides considering the influence of reactive power
compensation in the SQIG-FSWT case. Moreover, a set of 3 criteria was employed to characterize the interconnection of a wind farm to the
grid, namely: acceptable terminal voltage varia-
2
Modeling and System Considerations
Figure 1 shows a simplified representation of the
connection of a wind farm to the grid, here represented as a single DFIG-based wind turbine
(DFIG-VSWT). The local wind turbine transformer is represented by T r1 while the wind farm
connecting transformer is represented by T r2.
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Figure 1: Wind farm connection to the network simplified view.
Figure 2: DFIG equivalent circuit representation.
The network viewed from the PCC is taken as
its static equivalent (infinite bus with a series
impedance) and represented by its short-circuit
power (Ssc ) and X/R ratio. Let the nominal
power of the wind farm be represented by Pn and
define the ratio
Pn
(1)
ρ=
Ssc
rated generator power so as to allow approximately 30% speed variation around rated speed.
Active power flow from the rotor to the grid for
supersynchronous speeds and from the grid to
the rotor for subsynchronous speeds(Ackermann,
2005; Müller et al., 2002). This structure allows
different control policies to be employed with a
DFIG-VSWT(Anaya-Lara et al., 2007; Cartwright
et al., 2004; Müller et al., 2002).
Typically, the GSC is operated with unity
power factor. Reactive power is then exchanged
only through the stator. With balanced active
power flow through both converters and assuming
a unitary power factor for the GSC, the current
flowing from the converter to the network is given
by
Pr
6 θs
(9)
I˜g =
Vs
where Pr is the rotor active power and Vs 6 θs is
the stator voltage. The effect of the GSC in steady
state can then be captured by a controlled current
source, as shown in Figure 2, which is an equivalent circuit representation for the system of Figure 1. The RSC is represented by an ideal voltage
source.
The sharing of active power by the stator and
rotor of the DFIG is determined by the generator slip frequency (Müller et al., 2002; Tarnowski,
2006), according to Pr = −sPs , where s is the
slip, and Ps is the stator active power. Then, the
total generated active power is
as the wind power integration level.
The DFIG can be represented by its 3rd order simplified model given in the synchronous reference frame by (Feijóo et al., 2000; Holdsworth
et al., 2003)
ωs Xm
−1
Ed − (X − X ′ )Iqs + sωs Eq −
Vqr
To
Xr
−1
ωs Xm
Ėq =
Eq + (X − X ′ )Ids − sωs ed +
Vdr
To
Xr
1
ω̇r =
(Tmg − (Eq Iq + Ed Id ) − F ωr )
2H
Ėd =
(2)
(3)
(4)
and
Vds
Vqs
=
=
Ed − Rs Ids + X ′ Iqs
Eq − Rs Iqs − X ′ Ids
(5)
(6)
where To = Xr /ωs Rr , s = 1 − ωr , X = Xs ,
X2
X ′ = σXs , σ = 1 − Xs m
Xr ; Xs , Xr and Xm are the
stator, rotor, and magnetizing reactance, respectively; Rs , Rr are the stator and rotor resistance;
H is the inertia constant; F is the damping; Tmg is
the mechanical torque; Vdr , Vqr are rotor voltage
components; Vds , Vqs , Ids , Iqs are stator voltage
and current components, respectively.
Letting Ẽ = Ed +jEq to represent the internal
voltage and similar notation for the stator and
rotor voltages and currents, the following equation
can be derived from (2)-(6)
Ṽs
=
(7)
sXr
Ẽ
Xm
Ẽ − (Rs + jX ′ )I˜s
=
Ṽr + Rr I˜r
(8)
1−s
Pr
(10)
s
The generated active power depends on the available wind speed. In order to maximize the generated active power, in general the maximum power
tracking (MPT) (Amenedo et al., 2002) strategy is
employed, in which the generated active power is
maximized for the available wind speed by allowing the wind turbine speed to vary in accordance
with the wind speed. Active power can also be regulated within the available wind power (Tarnowski
and Reginatto, 2007).
P = Ps + Pr = (1 − s)Ps = −
Control of DFIG main variables is performed
by acting on the rotor-side converter (RSC) while
the grid-side converter (GSC) keeps a constant DC
link voltage (Müller et al., 2002; Pena et al., 1996).
In general, the converters are rated 30% of the
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XVIII Congresso Brasileiro de Automática / 12 a 16 Setembro 2010, Bonito-MS.
By acting on the rotor side converter, the reactive power delivered by the stator can be controlled (Tarnowski, 2006; Tarnowski and Reginatto, 2007). Under the assumption that the grid
side converter power factor is unitary, the total
reactive power delivered by the generator to the
grid is (Müller et al., 2002; Tarnowski, 2006)
Q = Qs
3
For a given X/R ratio, a given tolerance on each
interconnection criterion limits the wind power integration level ρ. The maximum integration level
satisfying all three criteria defines the boundary of
the safe integration region (Reginatto et al., 2009;
Reginatto et al., 2008). The safe integration region concept is brought to this paper as a means
to characterize the influence of different control
strategies applied to DFIG-VSWT’s on the wind
power integration level.
Analytical derivations are presented for each
control strategy considered: (i) reactive power
regulation; (ii) power factor regulation; (iii)
terminal voltage regulation. Then, numerical results are given to illustrate the potential and drawbacks of each control strategy regarding the maximum attainable wind power integration level. Due
to space limitation, the numerical results are given
for specific operating conditions, which are representative of actual cases. A wind farm with 10
generators of 2MW is considered, whose equivalent model has the following parameters: 690V ,
50Hz, 4 poles, H = 3.5s, Xm = 3.95pu, Xs =
Xr = 4.04pu, Rs = 0.00488pu, Rr = 0.0047pu.
Base values are: Vb = 690V and Pb = 20M W . An
individual 0.69/11kV transformer is connected to
each turbine, with 5.9% leakage reactance (Tr1).
The whole wind farm is connected to the grid by a
11/33kV transformer with leakage reactance 10%
(Tr2).
The following considerations are made regarding the wind farm electric and control structure:
(11)
where Qs is the stator reactive power. By acting on the stator reactive power, power factor
and terminal voltage control can also be regulated
(Anaya-Lara et al., 2009; Cartwright et al., 2004;
Pálsson et al., 2003).
2.1
Analysis of Control Strategies for
DFIG-VSWT
Wind farm interconnection
The goal in this paper is to analyze how control
strategies influence the amount of wind power that
can be connected to a given grid point (integration level). Three control strategies are considered
for a DFIG-VSWT: (i) reactive power regulation;
(ii) power factor regulation; (iii) terminal voltage regulation.
To assess the integration level, 3 criteria are
considered as measures of the interconnection
quality, all of them related to static characteristics of the system(Reginatto and da Rocha, 2009;
Reginatto et al., 2009; Reginatto et al., 2008):
1. Voltage variation. A range of allowable terminal voltage variation, given in terms of the
inequality Vmin ≤ Vt ≤ Vmax , where Vmin
and Vmax are given constants.
• The grid static equivalent representation is
taken from the high-voltage side of the
wind farm grid connection transformer (33kV
level).
2. Power transfer margin. The maximum power
transferable to the network (Pk ) at the PCC
is sufficiently larger than the nominal power
of the wind farm Pn , as given by the relation Pk ≥ (1 + MP ) Pn , where MP is a given
margin.
• All regulated variables are considered at the
high voltage side of the wind farm transformer (33kV level).
3. Internal voltage angle. The value of the internal voltage angle, δ, should lie within the
range 0 ≤ δ ≤ δmax , where δmax is a given
constant.
In the sequel, the following notation is used: Ṽt
is the voltage at the high-voltage side of the wind
farm transformer (bus bar 2); I˜t = I˜s + I˜g .
The maximum integration level is determined
considering the following tolerances for the interconnection criteria: Vmax = 1.1pu, Vmin = 0.9pu,
MP = 1, δmax = 40o . The apparent power of
each generator is considered limited 1.12 times the
nominal active power.
Besides the 3 criteria defined above, maximum
line losses are also evaluated as a comparative
measure of the control strategies influence on the
integration level.
Since the active power generated by the wind
farm depends upon the available wind speed and
since the wind speed may vary substantially, it
is necessary to consider a wide operating range
for the generated active power. So, a criteria is
considered satisfied if it holds for all possible operating conditions in which the generated active
power lies in the range of 0.1 to 1.05 per unit of
the nominal active power.
3.1
DFIG-VSWT with Reactive Power Regulation
When the DFIG-VSWT is operated with reactive power regulation, active power is determined
by the available wind speed and control settings
whereas reactive power is determined by control
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settings. In this situation, the generator bus bar
can be viewed as a PQ bus.
Let S = P + jQ be the complex power transfered from the generator to the network, measured
at bus bar 2, then S = Ṽt I˜t∗ = (Ṽt Ṽt∗ −Ṽt V∞ )/(R−
jX). Solving this equation, the terminal voltage
Ṽt = Vtr + jVti is found to satisfy the relation
0.6
0.5
0.4
ρ
4
3
0.3
2
Vtr2
Vti V∞ − P X + QR =
− V∞ Vtr + Vti2 − (P R + QX) =
0 (12)
0 (13)
"
β
+ β2
X/R
2
#
4Q
1 2Q
1+
+
β Pcc
X/R Pcc
(14)
6
8
X/R
10
12
14
p
1 + (X/R)2
X/R
and the following fact has been used
2
V∞
4
Figure 3: Integration level for DFIG-VSWT with
reactive power regulation: (1) Q = −0.5pu; (2)
Q = −0.25pu; (3) Q = 0pu; (4) Q = 0.25pu; (5)
Q = 0.5pu.
s
where
β=
1
0.1
The maximum power transfer to the network
Pk can be found from (13) as the limiting value
for which a real solution for Vsr exists. This value
is computed as
Ssc
Pk =
2
5
0.2
0.6
p
= Ssc R 1 + (X/R)2
3
0.5
Known the solution of (12)-(13), the generator
internal voltage Ẽ can be found by
2
0.4
ρ
1
0.3
Ẽ = Ṽt −(Rtr +jXtr )I˜t −(Rs +jX ′ )(I˜t − I˜g ) (15)
4
5
0.2
where Rtr + jXtr is the total transformer
impedance (Tr1 and Tr2). Finally, active power
loss on the network can be calculated as
0.1
2
Ploss =
RIt2
(16)
Figure 3 shows the limit of the integration
level that can be obtained with a DFIG-VSWT
operated with reactive power regulation, as the reactive power is varied. A negative reactive power
means that the wind farm is absorbing reactive
power from the grid. The curve 3 shows the zero
reactive power case, which is commonly applied in
wind farms (Ackermann, 2005). As the wind farm
absorbs more reactive power from the grid, the
integration level diminishes for large X/R ratios
while it increases for low X/R ratios. It is seen
that the pick of the integration level curve moves
to the left (toward lower values of X/R ratio). The
opposite effect tends to occur as the wind farm delivers more reactive power to the grid, as it can be
seen from curves 4 and 5. The integration level reduction that occurs for small X/R ratio, however,
can be quite significant and extend over a wide
X/R range, as curve 5 shows, ending up reducing the integration level over all practical values
of X/R.
4
6
8
X/R
10
12
14
Figure 4: Integration level for 10% network losses
with reactive power regulation: (1) Q = −0.5pu;
(2) Q = −0.25pu; (3) Q = 0pu; (4) Q = 0.25pu;
(5) Q = 0.5pu.
Figure 4 shows the integration level that is
compatible with an active power loss on the network corresponding to 10% of the nominal wind
farm active power. The figure considers the maximum power loss for all operating conditions considered. In general, the integration level increases
as the wind farm absorbs less from or delivers
more reactive power to the grid. This means that
losses are smaller when the wind farm delivers reactive power to the grid. Also, the power losses
are larger when the X/R ratio is smaller, due to
higher line resistance, which is compatible with a
smaller integration level shown in the figure for
such range of X/R.
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XVIII Congresso Brasileiro de Automática / 12 a 16 Setembro 2010, Bonito-MS.
3.2
factor is less significant than in the reactive power
regulation case.
When the wind turbine operates with positive power factor (delivering reactive power to the
grid) the integration level diminishes unless for
large values of X/R ratio. Such influence is due
to the terminal voltage that tends to increase in
such condition. In order to comply with the 10%
variation tolerance, the integration level has to decrease. As the power factor gets lower, such effect
extends over the whole range of practical values
of X/R (curve 5).
DFIG-VSWT with Power Factor Regulation
Another operating control polity for DFIG-VSWT
is the power factor regulation. This case can be
treated as a special case of reactive power regulation in which the reactive power is varied according to the generated active power. Let F P be the
a given power factor, then the generator reactive
power has to satisfy
√
1 − FP2
P =fP
(17)
Q=
FP
The generator can still be considered as a
PQ bus, similarly as the reactive power regulation case. The terminal voltage can be determined from (12)-(13) considering the reactive
power given by (17). The maximum power transfer, in this case, can be computed as
"
#
p
Ssc (1 + f X/R + βF ) 1 + (X/R)2
(18)
Pk =
2
(f − X/R)2
0.6
3
0.5
0.4
2
ρ
1
0.3
4
5
where
0.2
βF =
p
(1 + f X/R)2 + (f − X/R)2
0.1
2
The internal voltage angle and power losses
can be computed by (15) and (16), respectively.
4
6
8
X/R
10
12
14
Figure 6: Integration level for 10% network losses
with power factor regulation: (1) P F = −0.9; (2)
P F = −0.95; (3) P F = 1; (4) P F = 0.95; (5)
P F = 0.9.
0.6
0.5
0.4
4
ρ
The power losses on the network are illustrated in Figure 6 for the power factor regulation case. Again, the figure shows the integration
level that is compatible with a 0.1Pn power loss
on the network. Since the curves take into account the maximum power loss for all generated
active power of the wind farm, the overall figure
is similar to the reactive power regulation case.
0.3
3
5
0.2
2
1
0.1
2
4
6
8
X/R
10
12
14
3.3
DFIG-VSWT with Voltage Regulation
Terminal voltage of a DFIG-VSWT can be regulated by acting on the reactive power delivered/absorbed from the grid. In this operating
policy, active power is determined by the available wind speed and control settings whereas the
terminal voltage is determined by control settings.
Thus, as long as voltage regulation is possible, the
generator bus bar can be seen as PV bus. The
generated active power, in this case, satisfies the
relation
Figure 5: Integration level for DFIG-VSWT with
power factor regulation: (1) P F = −0.9; (2)
P F = −0.95; (3) P F = 1; (4) P F = 0.95; (5)
P F = 0.9.
The limits of the integration level attainable
with DFIG-VSWT operated with power factor
regulation are shown in Figure 5. In this case,
a negative power factor means that the wind farm
is absorbing reactive power from the grid. Curve
3 coincides with curve 3 of Figure 3 since it is for
unity power factor. The overall influence is similar to the case of power factor regulation. Here,
however, the increase in the integration level for
lower values of the X/R ratio for negative power
P = Ssc
1
Vt
V∞ βX/R
Vt
X
− cos(θt ) +
sin(θt )
V∞
R
(19)
where Ṽt = Vt 6 θt . The terminal voltage angle
θt varies according to the generated active power,
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XVIII Congresso Brasileiro de Automática / 12 a 16 Setembro 2010, Bonito-MS.
while Vt is regulated and V∞ is considered constant. The corresponding angle for a given active
power is given by
0.8
0.7
0.6
θt = −θz + cos
P V∞
Vt
cos(θz ) −
V∞
Ssc Vt
1
(20)
−1
where θz = tan (X/R). Taking the derivative
of P with respect to θt , in (19), and equating to
zero, the maximum power transfer to the network
can be deduced as
Pk = Ssc
Vt
V∞
Vt
1
p
+1
V∞ 1 + (X/R)2
#
3
4
5
0.4
0.3
0.2
1
0.1 5
4 3
5
2
4
2
"
2
0.5
ρ
−1
4
6
8
X/R
10
12
14
(21)
Figure 7: Integration level for DFIG-VSWT with
voltage regulation: (1) Vt = 0.95; (2) Vt = 0.975;
(3) Vt = 1; (4) Vt = 1.025; (5) Vt = 1.05.
which occurs for θt = π − θz .
In the case of voltage regulation, the generator rating limits to deliver/absorb reactive power
play a major role. Both generator apparent power
rating and converter maximum current limits impact on the generator capacity to regulate terminal voltage. To take this effect into account, the
region where terminal voltage regulation can be
achieved is found and used as an integration criterion, replacing the terminal voltage variation criterion. Such region is determined on the bases of
the generator capacity to regulate terminal voltage as restricted by the generator apparent power
rated value Sn = 1.12pu. Moreover, instead of the
internal voltage angle, the terminal voltage angle
is considered, since the terminal voltage is kept
constant.
0.8
0.7
5
0.6
4
3
ρ
0.5
2
0.4
1
0.3
0.2
0.1
2
Figure 7 shows the integration level obtained
for a DFIG-VSWT with terminal voltage regulation. Recall that, in this paper, the terminal voltage is measured at the high-voltage side of the
wind farm transformer (bus bar 2). Integration
levels that comply with the interconnection criteria considered belong to the region inside the
curves of the figure. The left and lower limits
of the integration level are mainly due to apparent power rating limits of the generators. Beyond
those integration levels, the generator is not able
to maintain voltage regulation.
4
6
8
X/R
10
12
14
Figure 8: Integration level for 10% network losses
with voltage regulation: (1) Vt = 0.95; (2) Vt =
0.975; (3) Vt = 1; (4) Vt = 1.025; (5) Vt = 1.05.
The integration level compatible with 0.1Pn
network power loss is shown in Figure 8 for the
same values of terminal voltage regulation as in
Fig. 7. As the terminal voltage is increased so
is the integration level, representing a power loss
reduction. Compared to the reactive power and
power factor regulation cases, power loss is worse
for low X/R ratio (below 2) but is better for
medium to high values (greater than 3).
It is seen that as the terminal voltage value
is increased (from 0.95 to 1.05) while the infinite
bus voltage is kept constant at 1pu, the region of
safe integration levels tends to enlarge at the top
(large integration levels) and to shrink at the bottom (low integration levels). For larger terminal
voltage values, small integration level are not possible since in such cases the network impedance
would be too small for the wind farm to be able
to deviate its voltage at PPC with respect to the
infinite bus. That’s the reason why the curves 4
and 5 in Figure 7 impose a lower boundary for the
integration level.
4
Concluding Remarks
The effect of the DFIG control strategy on the integration level of wind farms equipped with DFIGVSWT was analyzed for 3 cases: reactive power
regulation; power factor regulation; and terminal
voltage regulation. The wind power integration
level was determined so as to comply with 3 inter-
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XVIII Congresso Brasileiro de Automática / 12 a 16 Setembro 2010, Bonito-MS.
connection criteria: a tolerance on terminal voltage variation; a power margin relative to the maximum power transferable to the grid; and a maximum value for the internal voltage angle.
The reactive power regulation and power factor regulation cases have shown similar influences
on the integration level. Absorbing reactive power
from the grid (or negative power factor) tend to
reduce the integration level for medium to large
X/R ratios and to increase for low X/R ratios.
In general it is not possible to take advantage of
such increase since network power losses would be
too high for such integration levels and X/R ratios. Delivering reactive power to the grid (positive power factor) is advantageous only for large
X/R ratios. After a certain amount of reactive
power (power factor) the integration level falls bellow the zero reactive power (unitary power factor)
case over all practical values of X/R.
Terminal voltage regulation differs significantly from the other two cases. Here the voltage
regulation capability of the wind farm becomes an
issue. Apparent power rating imposes limitation
on the integration level for low X/R ratios. Generally, the integration level increases as the terminal voltage regulated value increases relative to
the infinity bus voltage. However, high values of
terminal voltage are not achievable if the network
impedance is too small, so very low integration
level are also not possible in such case.
With the analysis carried out so far, it can
be said that no control strategy is the best for all
situations. For X/R > 3, terminal voltage regulation lead to larger integration levels, while either
reative power or power factor regulation show better results for small X/R.
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