Download A Power System Stabilizer for Variable Speed Wind Generators

Preprints of the 18th IFAC World Congress
Milano (Italy) August 28 - September 2, 2011
A Power System Stabilizer for
Variable-Speed Wind Generators
Georgios Tsourakis ∗ Sotirios Nanou ∗ Costas Vournas ∗
∗
National Technical University of Athens, School of Electrical and
Computer Engineering, Zografou Campus, 15780 Athens, Greece
(e-mail: [email protected], [email protected]).
Abstract: This paper focuses on the application of a special controller that can introduce
damping to interarea oscillations of electric power systems by modulating the active power
output of wind generators and can thus replace power system stabilizers of conventional
synchronous generator units. The controller is tested for Doubly Fed Asynchronous Generators,
as well as for Full Converter Wind Generators, on a simplified interconnected system and on an
autonomous four-generator, two-area system traditionally used for interarea oscillation analysis
and is shown to perform efficiently without significant adverse side effects.
Keywords: Power-system stabilizers, renewable energy systems.
1. INTRODUCTION
gear
box
Wind power penetration is continuously increasing in
many power systems around the world in an effort to
increase renewable energy penetration in the energy mix
with cost-effective solutions. In new wind power installations mostly variable-speed wind turbines with frequency
converters are used, instead of the older constant-speed,
squirrel-cage induction generators. The doubly fed asynchronous generator (DFAG, also known as DFIG: doubly
fed induction generator) is today the most popular scheme
for variable-speed wind turbines, followed by the full converter concept (see Fig. 1).
stator
rotor
AC
stator
DC
rotor side
converter
The advanced control capabilities of modern wind generators have been already used in the literature to enhance
network damping via auxiliary power system stabilizer
Copyright by the
International Federation of Automatic Control (IFAC)
AC
grid side
converter
(a) Doubly Fed Asynchronous Generator
Increased wind power penetration causes reasonable concerns as to possible stability threats that might be encountered, when a large percentage of system load is supplied by new technology wind generators. One particular
aspect of system stability is the electromechanical oscillations damping. Electromechanical oscillations stem from
the synchronous operation of interconnected synchronous
machines, i.e. basically the large synchronous generators of
thermal power plants. A mechanical analog of synchronous
generators operating in synchronism is masses interconnected with springs. In steady-state all generators rotate
at exactly the same speed (masses are at equilibrium),
producing the necessary power to cover the system load.
As interconnections expand and are more and more
stressed due to increased transactions, power system interarea oscillations can become a critical issue. Interarea
oscillation modes are associated with the swinging of many
machines in one part of the system against machines in
other parts (Kundur (1994)). In this paper the oscillation damping contribution of a simple controller added to
variable-speed wind generators is examined.
DC
stator
rotor
AC
DC
stator
DC
generator side
converter
AC
grid side
converter
(b) Full Converter Wind Generator
Fig. 1. Popular wind generation schemes
(PSS) loops, e.g. Hughes et al. (2006); Miao et al. (2009).
In Ledesma and Gallardo (2007) the fast active power
control of variable-speed wind turbines is utilized to provide network damping. A similar simple controller, which
was introduced in Tsourakis et al. (2009b), is used in
this paper to provide damping to interarea oscillations.
This type of controller has been also proposed to provide
equivalent inertia to the system, for example in Ekanayake
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Preprints of the 18th IFAC World Congress
Milano (Italy) August 28 - September 2, 2011
and Jenkins (2004); Lalor et al. (2005); Rodriguez-Bobada
et al. (2008).
+
Tm = Pωm
t
+
+
-
2. DFAG MODEL
The DFAG model is a variant of the generic type 3 wind
generator model used by the WECC, see WECC (2006);
Piwko et al. (2009), also included in the PSS/E software
(PSS/E (2009)).
′′
′′
1
1+sTcon
Pord
Ipmax
÷
Eq
IP cmd
1
Xeq
xy
↓
dq
dq
↓
xy
IP =iq
Iˆ
+
Te = ωPg
-
1
2Hg s
-
∆θm
Ktg
ωg
Fig. 3. Two-mass drive-train model
3. FCWG MODEL
A generic model of a full-converter wind generator
(FCWG) that represents the dynamics of relevance for
power system stability analysis is used. The modelling
approach follows Pourbeik et al. (2007), where simplified
control loops are assumed. The electrical behavior of the
FCWG as seen from the network is modeled as a controlled
current source dependent on voltage. Fig. 4 shows the
model block diagram.
Vref
V
V̂
V θ
id
1
1+sTcon
2 ωb
p s
Dtg
A DFAG model with detailed control loops originally
developed in Miller et al. (2003) and described in Appendix
B of Pourbeik et al. (2007) is used in this paper. This
model has been redeveloped for the Matlab/Simulinkbased educational tool described in Vournas et al. (2004)
and used for teaching and research in NTUA and the
University of Liege.
Eqcmd
ωt
1
2Ht s
vd
vq
θpll
θ̇max
Kpll
θ̇min
KpQ
Vmeas
1
s
+
1
1+sTr
jXeq
1
1+s0.01
Qmax
+
Qord
Qmax
-
KiQ
s
+
Qmin
Qmin
tanφref
X
ωg
∆ωwpss
Pord
MP P T
Fig. 2. Generator/converter model
θ
Figure 2 shows a block-diagram illustrating the modeling
of the generator and converter as a controlled current
source. Xeq is the equivalent Norton reactance introduced.
The phase locked loop (PLL), used for machine vector
control, is explicitly modeled. The PLL aligns the current
control dq reference frame to the terminal voltage and,
thus, allows for independent control of active and reactive
′′
power. Eq is an equivalent voltage that controls the
DFAG reactive current injection and comes from the
reactive power controller (not shown here). The active
power reference Pord comes from the rotor speed controller
(shown in Fig. 5).
Fig. 4. Generic full converter WG model
As the rotor-side converter drives the rotor current very
fast, the rotor flux dynamics are neglected. Nevertheless,
the model includes two small time constants (Tcon in
Fig. 2 is of the order of 20 ms) to represent lags in the
corresponding control loops. Figure 2 also depicts the
signal that will be used as input to the proposed Wind PSS
(with dashed line) which will be described in Section 4.
As in the DFAG case, first order transfer functions with
a typical 20 ms time constant (Tcon ) to represent lags in
measurements and converter action are used. Note that
these lags also simplify the simulation as the current
injections become state variables and are, thus, decoupled
from the terminal voltage.
The two-mass drive-train model of Fig. 3 is used in order
to represent shaft torsional oscillations. The DFAG rotor
speed is noted as ωg and the wind turbine rotor speed
as ωt . The DFAG model includes also submodels not
repeated here: wind turbine model, pitch controller and
reactive power controller. The latter has been discussed in
detail in Tsourakis et al. (2009a). In particular the pitch
controller is not considered in this paper, as the operating
point considered is below rated power.
The active power command Pord is determined by the
maximum power point tracking strategy, based on rotor
speed measurement, while the reactive power command
Qord is dictated either for power factor or for voltage control. The full converter wind generator model is completed
with submodels not repeated here: wind turbine model and
pitch controller. It is assumed that a multi-pole generator
is used and the gear box is omitted. Therefore, all rotating
masses are mounted on the same short shaft and, thus, a
Qord
÷
IQ
current
limiter
Iˆc
V
Pord
&
IP
÷
V θ
1
1+sTcon
Iˆtot
dq
↓
xy
V
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Preprints of the 18th IFAC World Congress
Milano (Italy) August 28 - September 2, 2011
one-mass model is used for the mechanical part, instead of
the two-mass model of Fig. 3.
3
SG
4. WIND PSS
5
The proposed controller is shown with dashed line in Fig. 5
with the block-diagram of the doubly fed wind generator
speed control loop. The rate of change of the PLL angle is
used to obtain the input signal (equivalent to the DFAG
bus frequency), taking into account a small measurement
delay (Fig. 2). The controller uses a simple wash-out filter
with time constant Tw , so that the power setpoint is not
affected in steady state.
1
2
4
8
∞
6
7
WG
PL6
PL4
Fig. 6. Small interconnected system.
(2004); Lalor et al. (2005). Note that the controller has to
be fit in each individual wind generator of a wind power
plant.
ωg
P
ωref
1
1+sTw
torque
control
ωerr
Kptrq +
-
+
5. APPLICATION TO A SIMPLIFIED
INTERCONNECTED SYSTEM
ωerr
MP P T
Tmax
ωg
5.1 Test system description
Pmax &Ṗmax
Pmax
+
Kitrq
s
X
1
1+sTpc
Tmin
Pord
Pmin
Pmin &Ṗmin
∆ωwpss
Kwpss
sTw
1+sTw
∆Pwpss
Fig. 5. DFAG speed control with Wind PSS
In the FCWG model (see Fig. 4) a simpler controller is
used, but the Wind PSS is added in a similar way as in
the DFAG. In this case a PLL model, like the one used
in the DFAG model, is added to obtain a measurement of
the bus frequency.
The Wind PSS was introduced in Tsourakis et al. (2009b)
and its basic concept is to superimpose on the wind
generator active power production an oscillation in antiphase with the wind generator bus frequency. This active
power oscillation has a net damping effect introduced
to the nearby synchronous generators. Indeed, assuming
that the wind power plant and the nearby synchronous
generators belong in the same area and thus oscillate in
phase against the external system, when the active power
injected by the wind generators decreases for a frequency
increase, the synchronous generator power will increase
to cover the load and thus its rotor acceleration will be
decreased introducing essentially a damping torque.
Note that the proposed controller is based on simple physical considerations and does not require the design of special lead/lag compensators as in Hughes et al. (2006); Mendonça and Lopes (2007); Martinez et al. (2009); Fernández
et al. (2010). So the concept of the Wind PSS is simple and
based on:
In this section the Wind PSS is applied in a small interconnected system. The one-line diagram of the test system
is drawn in Fig. 6. A conventional power plant is interconnected through a step-up transformer and two parallel
High Voltage (HV) lines to an infinite bus representing a
large interconnection. The synchronous generator of the
conventional power plant is represented by a fourth order
model. Constant mechanical power input is assumed. An
IEEE type DC1A excitation system model is used, without
considering saturation effects.The loads of buses 4 and 6
are modeled as constant admittances. A wind farm (WF)
equipped with variable speed wind generators is connected
to HV bus 4. The WF is represented by a single wind
generator and step-up transformer and is connected to
the HV system via a Medium Voltage (MV) line and
an MV/HV substation transformer. The equivalent wind
generator is assumed to operate with unity power factor.
At the considered operating point, the conventional power
plant produces its nominal power, which is 380 MW and
the wind farm produces 45 MW (88% on its rated MW).
This system is scalable and can represent the equivalent
of one area of a large system by properly selecting base
power values.
5.2 Wind farm with DFAGs
Without stabilizing action the electromechanical oscillation (interarea mode) of the test system is marginally
stable as seen in Table 1.
The Wind PSS washout filter is designed to be active for
frequencies as low as 0.1 Hz, so the time constant Tw
is taken equal to 20 s. With Tw = 20 s, the Wind PSS
adds zero phase at the frequency of the electromechanical
oscillation and, thus, contributes a damping torque as
explained in Section 4.
• The capability of modern wind generators for fast
control of their power injection by use of power
electronics converters;
• The inertia of the wind turbine rotor that can provide
a zero mean oscillating power without significantly
affecting rotor speed and mechanical power.
Adding the Wind PSS to the equivalent DFAG and increasing gradually its gain (from 0 to 1), we plot the root
locus of Fig. 7, where we can observe the movement of the
system dominant eigenvalues (only the upper half of the
complex plane is shown).
This type of controller also provides equivalent inertia
to the system, as pointed out in Ekanayake and Jenkins
As can be seen, the interarea mode damping increases
considerably by applying the Wind PSS. At the same
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Preprints of the 18th IFAC World Congress
Milano (Italy) August 28 - September 2, 2011
50.15
14
SG rotor
speed (Hz)
50.1
12
50
49.95
49.9
10
imag
50.05
DFAG shaft mode
49.85
0
SG electromechanical
mode
8
2
4
6
8
10
12
14
16
18
20
70
No Wind PSS
With Wind PSS
60
WF active
power (MW)
6
DFAG VAR
control mode
4
50
40
30
−1
−0.8
−0.6
real
−0.4
−0.2
0
20
0
2
4
6
8
Fig. 7. Small system root locus for DFAG PSS gain 0-1.
Torsional mode
Kwpss
0
0.8
Kwpss
0
0.8
Eigenvalue
-0.004 ±j4.765
-0.151 ±j4.971
Eigenvalue
-1.087 ±j12.51
-0.730 ±j12.27
freq.
0.76 Hz
0.79 Hz
freq.
1.99 Hz
1.95 Hz
14
16
18
20
20.1
No Wind PSS
With Wind PSS
20.05
20
19.95
19.9
0
damp.
0.09 %
3.03 %
damp.
8.65 %
5.94 %
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
time (s)
12
14
16
18
20
45.15
45.1
WT mechanical
power (MW)
e/m mode
12
Fig. 8. Synchronous generator rotor speed (upper graph)
and WF active power production (lower graph) with
and without Wind PSS.
WT rotor
speed (RPM)
time, a decrease of the shaft torsional oscillation mode
damping is observed, which may limit the value of the
Wind PSS gain. The VAR control mode stems from the
DFAG reactive power controller (not discussed in this
paper), and as seen is not at all affected by the Wind
PSS. From the root locus of Fig. 7, we choose Kwpss =0.8.
The corresponding eigenvalues of the electromechanical
and torsional modes are shown in Table 1.
Table 1. Electromechanical and torsional
modes with and without Wind PSS
10
time (s)
The decrease of the torsional mode damping is obviously
limiting the stabilizer gain. In practice, the application
of the Wind PSS needs to be examined also with more
detailed models (including the control loop often used in
DFAGs to increase the damping of the torsional oscillation
mode as in Pourbeik et al. (2007)), whereas the model used
in this paper aims to examine the effect of WPSS on bulk
power system studies, thus the shaft damping is modeled
with a simple damping coefficient.
45
44.95
44.9
44.85
0
Fig. 9. Wind turbine rotor speed (upper graph) and
mechanical power (lower graph) with and without
Wind PSS.
0.15
No Wind PSS
With Wind PSS
Figures 8, 9, 10 show simulation results with and without
Wind PSS. The simulated disturbance is a three-phase
50 ms self-cleared fault at bus 3 of Fig. 6. We observe
that the oscillation introduced by the Wind PSS to the
wind farm active power results to an important increase of
the electromechanical oscillation damping. Without Wind
PSS, the rotor oscillation damping is negligible, while after
the Wind PSS introduction, the oscillations practically die
out after about 10 s. The amplitude of the wind farm active
power oscillation is limited to less than 15 MW, i.e. about
30 % of its power rating.
As seen in Fig. 9, the oscillation introduced in the wind
turbine rotor speed and mechanical power is of very
small amplitude. Finally, Fig. 10 shows the rotational
speed difference between the two rotating masses of the
DFAG model (with and without Wind PSS). The torsional
oscillatory mode, with a frequency of about 2 Hz, can be
seen clearly in this response. Even though the damping is
45.05
0.05
g
t
ω − ω (RPM)
0.1
0
−0.05
−0.1
0
1
2
3
4
5
time (s)
6
7
8
9
10
Fig. 10. Speed difference of the two DFAG model rotating
masses
decreased because of the stabilizer action, the tortional
oscillation still dies out significantly after 5 s, and the
Wind PSS effect on the torsional mode is considered
acceptable.
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Preprints of the 18th IFAC World Congress
Milano (Italy) August 28 - September 2, 2011
5
17.5
WT rotor
speed (RPM)
4.95
4.9
4.85
imag
4.8
K
SG
electromechanical
mode
=0.5
wpss
17.4
17.3
No Wind PSS
17.2
With Wind PSS
17.1
0
4.75
5
10
15
20
5
10
time (s)
15
20
4.7
45.04
WT mechanical
power (MW)
4.65
4.6
4.55
4.5
−0.5
−0.4
−0.3
−0.2
−0.1
0
real
45.02
45
44.98
44.96
0
SG rotor
speed (Hz)
Fig. 11. Small system root locus for FC PSS gain 0-1.
Fig. 13. Wind turbine rotor speed (upper graph) and
mechanical power (lower graph) with and without
Wind PSS.
electromechanical oscillation damping, while the resulting
oscillation in the wind turbine rotor speed and mechanical
power is of very small amplitude (Fig. 13).
50.1
50
49.9
0
5
10
15
20
6. APPLICATION IN A TWO-AREA AUTONOMOUS
SYSTEM
WF active
power (MW)
60
50
6.1 System description
40
No Wind PSS
With Wind PSS
30
20
0
5
10
time (s)
15
20
Fig. 12. Synchronous generator rotor speed (upper graph)
and WF active power production (lower graph) with
and without Wind PSS.
5.3 Wind farms with full-converter units
In this section the Wind PSS is applied in a variant of
the well-known two-area system, traditionally used for
interarea oscillation studies and power system stabilizer
tuning, e.g. Kundur (1994); Rogers (2000). An overview
of this section’s results has been presented in Tsourakis
and Vournas (2010). In this paper the Wind PSS design is
presented in detail.
The system one-line diagram is shown in Fig. 14. The
1
11
5
Area 1
The same system is examined, but now it is assumed
that the wind farm is equipped with full-converter units.
Without Wind PSS the interarea mode is again marginally
stable as seen in Table 2. Adding the Wind PSS (with
Tw =20 s) to the equivalent FCWG and increasing gradually its gain (from 0 to 1), we plot the root locus of Fig. 11
(only upper half plane). In this case there is no shaft
torsional mode. From the root locus, we choose Kwpss =0.5.
The corresponding eigenvalues of the electromechanical
mode are shown in Table 2.
Table 2. Electromechanical and mode with and
without Wind PSS
e/m mode
Kwpss
0
0.5
Eigenvalue
-0.006 ±j4.667
-0.263 ±j4.837
freq.
0.74 Hz
0.77 Hz
3
Area 2
G1
G3
6
2
7
8
9
10
4
G4
G2
WG
12
13
14
Fig. 14. Two area system
damp.
1.38 %
5.43 %
Figures 12, 13 show simulation results from this system
with and without Wind PSS. The simulated disturbance
is the same (three-phase, 50 ms, self-cleared fault at bus
3).
Again, the wind farm active power oscillation, introduced
by the Wind PSS, results to an important increase of the
original system consists of 11 buses and 4 generators
separated by the long transmission corridor 7-9 into two
areas. In this paper a wind power plant with DFAGs is
added to bus 7, represented by a one-machine equivalent,
its step-up transformer and a medium voltage line (13-14)
to the HV/MV substation. Loads and shunt capacitors
are connected to buses 7 and 9, represented as constant
admittances.
Each synchronous generator is 900 MVA rated and represented by a sixth order model. The AVR is modeled with a
measurement filter with time constant Tf in series with a
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Preprints of the 18th IFAC World Congress
Milano (Italy) August 28 - September 2, 2011
first-order transfer function with gain G and time constant
(Te ). A three-stage steam turbine model and governor
model are used, following Kundur (1994).
At the considered operating point, each conventional plant
produces around 700 MW and the wind power plant
produces 450 MW. About 400 MW are exported from Area
1 to Area 2. Since there are four synchronous generators,
there exist three electromechanical oscillation modes: one
interarea (area 1 - area 2) and two local modes (G1 against
G2 and G3 against G4). For the operating condition
considered, the interarea oscillation mode is marginally
unstable.
generators in order to add damping to the interarea mode,
counteracts the system frequency control.
To keep this adverse interaction low, we choose a relatively
low value for Tw , so that the corner frequency 1/Tw is
located between the frequency of the interarea mode and
the frequency of the system frequency control mode, i.e.
between 3.5 and 0.5 rad/s. Based on the root locus of
Fig. 15, we choose Tw =0.3 s. With a higher value, the
benefit in increasing the interarea mode damping is rather
minor. At the same time, keeping a low value for Tw gives
more room to increase the gain, since the effect on the
system frequency control mode is smaller.
The system root locus for Tw =0.3 s and Wind PSS gain
Kwpss varying from 0 to 0.5 is shown in Fig. 16. We can
6.2 Wind PSS design
We assume that a Wind PSS is added to the equivalent
generator of the wind farm. In order to choose a value for
the Tw time constant, we draw the system root locus for
a small value of the Wind PSS gain (Kwpss = 0.1) and
Tw values from 0 to 5 in Fig. 15. The eigenvalues of the
state matrix without WPSS (Tw =0) are marked with a
circle. It can be seen that for all Tw values the interarea
14
12
DFAG shaft
ζ=3%
ζ=5%
10
G3−G4
imag
8
6
14
G1−G2
interarea
4
12
DFAG shaft
ζ=50%
2
10
system frequency
control
ζ=70.7%
0
G1−G2 & G3−G4
−1
−0.8
−0.6
real
−0.4
−0.2
0
imag
8
6
Fig. 16. Root locus for Tw =0.3 s and Kwpss from 0 to 0.5.
A
4
interarea
B
2
0
see that with a WPSS gain of 0.5 the damping ratio of
the interarea mode is more than 5 % (ζ >0.05), while the
damping ratio of the system frequency control mode is still
above 50 % (ζ >0.50). , but not yet below this limit. At the
same time the damping of the DFAG torsional mode has
decreased and the damping of the intra-area mode of area 1
(G1-G2) has increased. We thus choose Kwpss =0.5, as this
value corresponds to adequate damping of the interarea
mode, while further increase of the gain would result to
a damping ratio of the system frequency control mode of
less than 50 % (ζ < 0.50).
system frequency
control
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
real
3.6
0.6
3.58
ζ=70.7%
system frequency
control
Tw=0.3
3.54
imag
imag
0.5
3.56
interarea
0.4
0.3
0.2
3.52
3.5
−0.05
Tw=0.3
DFAG speed
control
0.1
0
real
0.05
0
−0.6 −0.5 −0.4 −0.3 −0.2 −0.1
0
real
Fig. 15. Root locus for Kwpss =0.1 and Tw from 0 to 5.
oscillation eigenvalue moves to the left. There is also a
small favorable effect on the intra-area mode of area 1
(G1-G2). Also, similarly to the case of section 5, the DFAG
torsional oscillation damping is reduced.
It should be noted that the system examined in this
Section is autonomous and thus its electrical frequency
is varying. Since the governors of the conventional power
plants are explicitly modeled, there exists a low-frequency
oscillation mode due to the effort to maintain system
frequency close to its nominal values (system frequency
control mode). As seen, the damping of this mode decreases when the Wind PSS is introduced. This indicates
that the active power oscillation introduced by the wind
To verify the performance of the Wind PSS, we simulate
a 10 % step increase of load admittance at bus 7 for case
with (blue continuous line) and without (red dashed line)
Wind PSS. Figure 17 shows the simulated responses of
one tie-line active power flow and DFAG generation. The
disturbance is applied at t=1 s. We can clearly see in the
DFAG active power response of Fig. 17b the oscillation
introduced by the stabilizer, which results in introducing
damping to the interarea oscillation, as shown in the
interconnection line power flow response of Fig 17a.
The abrupt change of the DFAG active power, right after
the load step increase, is due to the instantaneous voltage
change caused by the disturbance (since the electromagnetic dynamics are neglected). When the load of bus 7
is increased, the voltage angle of this bus decreases. The
DFAG terminal voltage angle also follows this behavior,
the PLL angle however still holds its pre-disturbance value,
as it is a state variable. This results to the DFAG active
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Preprints of the 18th IFAC World Congress
Milano (Italy) August 28 - September 2, 2011
(a)
P 7−> 9 (MW)
300
200
100
0
0
5
10
15
20
25
30
(b)
P DFAG (MW)
500
No WInd PSS
With Wind PSS
480
460
440
420
0
5
10
15
time (s)
20
25
30
Fig. 17. Responses to a 10 % step increase of bus 7 load
power increase. The slower frequency control oscillation
with a period around 10 s is also evident in Fig. 17.
7. CONCLUSION
This paper presented a Wind PSS that can efficiently
damp out unstable or marginally stable interarea oscillations as was confirmed by testing on two test systems
using two types of wind generators, namely DFAG and
FCWG. The resulting oscillations introduced in the rotor
speed and the mechanical power of the wind turbine were
shown to be very minor.
The stabilizing capability of wind generators is very important, because it allows wind farms to contribute the
same system stabilization services usually provided by
conventional synchronous generators. This is achieved with
only a slight modification of the wind generator active
power controls that introduce a rather negligible cost.
It should be noted that similar controllers are already
available by some WG manufacturers with the scope of
adding inertia to weak autonomous systems.
The only adverse interactions seen in this study were related to the damping decrease of the DFAG shaft torsional
oscillation and the interaction with the frequency control
mode in autonomous systems. Both these problems were
successfully overcome with reasonable effort taken at the
controller design stage.
The torsional oscillation problem of the DFAG can be
further controlled by special devices introduced in the
power electronics controls that are not considered in this
introductory paper. The FCWGs do not usually need a
drive train and are thus not prone to shaft oscillations.
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