Stabilization of a Fixed Speed Wind Turbine
with a Variable Speed Wind Turbine
Kenneth E. Okedu
University of Port Harcourt
Nigeria
E-mail : kenokedu@yahoo.com
amount of wind power after a fault in the network.
Nowadays, the most widely used Variable
Speed Wind Turbine (VSWT) in wind farms is based
on a Doubly Fed Induction Generator (DFIG) due to
noticeable advantages; the variable speed generation, the decoupled control of active and reactive
powers, the reduction of mechanical stresses and
acoustic noise, and the improvement of the power
quality [6].
During grid faults the DFIG experiences over
currents which lead to increasing DC voltage on the
converter side. To avoid damage some special measures are necessary which however should not contravene grid requirement. Therefore, understanding
between power engineers and developers of wind
turbine converters is one of the pre-requisites for
mutually acceptable technical solutions [5]. The
crowbar can be used for fast separation of the DFIG
from the grid [5],[7],[8], and [9], but is not a favorable option since utilities expect voltage support
during the fault and in its aftermath, besides the
active power in-feed should not be interrupted for a
long period of time[5].
FSWT technology has limited ability to provide voltage and frequency control. Therefore, it is
paramount to use a VSWT like the DFIG to stabilize a FSWT (IG) in a wind farm, because the reactive power control can be implemented at a lower
cost, since the DFIG system basically operates in a
similar manner to that of a synchronous generator,
as the excitation is provided by the converter. This
paper deals with the stabilization of an Induction
Generator (IG) which is a Fixed Speed Wind Turbine
(FSWT) that is unstable during grid fault with a Doubly Fed Induction Generation (DFIG) which is a Variable Speed Wind Turbine (VSWT) that is more stable
during wind change and grid fault.
A simulation model of a wind turbine with a
DFIG and an IG developed in PSCAD/EMTDC (Power
ABSTRACT
This paper tackles the instability of a wind farm
made of a Fixed Speed Wind Turbine (FSWT)/an Induction Generator (IG) and a Variable Speed Wind
Turbine (VSWT)/Doubly Fed Induction Generator
(DFIG) during wind change and grid fault. Simulation results show that the VSWT can effectively stabilize itself and the FSWT because it can provide
enough reactive power through the frequency converter control to the wind farm without external reactive power compensation unit during wind speed
change and grid fault.
INDEX TERMS
Grid Fault, Stability, Wind Farm, Wind Turbine.
I.INTRODUCTION
Wind energy is the fastest growing and most widely
utilized of the emerging renewable technologies in
electrical systems [1]. Based on the recent growth
of wind power capacity, the power system must be
able to recover after the loss of a great number of
wind farms during a fault due to disconnection.
This recovery may be particularly difficult in periods of low load and high wind power penetration.
This led to system operators publishing several requirements (grid codes) for the connection of new
wind farms, in order to ensure the proper behavior
of wind farms after network fault. Wind farms may
be required to remain connected and to maintain stability at short-circuits in the network cleared by the
primary network protection, as stated by the Danish
Operator Eltra or the German Operator E.ON [2].
Recently, the grid codes require to take into
account the reactive power of the wind farm in order to contribute to the network stability [3],[4], thus
operating the wind farm as active compensator devices [5]. By means of these grid codes, the operator
ensures that the power system will not lose a great
25
Systems Computer Aided Design/Electromagnetic
Transient Including DC) [10] is presented. The simulation results show the effectiveness of using a
VSWT in stabilizing the voltage, rotor speed, active
and reactive powers of the FSWT and hence the terminal voltage of the wind farm.
power coefficient which can be expressed as a function of the tip speed ratio and pitch angle given by
λi
II. WIND AND WIND TURBINE MODEL
The wind effect is very important in modeling wind
turbines. Wind models describe wind fluctuations
in wind speed which causes power fluctuation in a
generator. Four components are considered in describing a wind model [11] as shown below:
Vwind = Vbw + Vgw + Vrm + Vnm
ρπ R 3C p (λ , θ )Vwind 2
Pw
=
ωrotor
2λ
=
Tw
Pw =
λ=
ρπ R 2 C p (λ , θ )Vwind 3
2
λi
(5)
1
(6)
1
0.035
− 3 )
(
λ + 0.08θ θ + 1
Figures 1 and 2 show the wind turbine characteristics [12] used for this study for both FSWT and
VSWT respectively.
Figure 1. Cp -λ curves for different pitch angles for
FSWT
(2)
Figure 2. Turbine characteristic with maximum power point tracking for VSWT
(3)
Figures 3 and 4 respectively show the pitch angle
controllers for both the FSWT and VSWT used.
Rω rotor
(4)
Vwind
Where ρ is the air density in (kg / m3), R is the wind
turbine rotor radius in (m), Vwind is the equivalent
wind speed in (m / s), θ is the pitch angle of the rotor
in (deg.), λ is the tip speed ratio ωrotor,is the mechanical speed of the generator in (rad/s) and Cp is the
26
λi =
−12.5
(1)
Where, Vbw, Vgw, Vrm, Vnm are the Base wind, Gust
wind, Ramp wind and Noise wind components respectively in (m/s). The base component is a constant speed; the wind gust component could be
described as a sine or cosine wave function or combination; a simple ramp function and a triangular
wave may describe the ramp and the noise components respectively. The wind speed in this study is
shown in the simulation results for the dynamic
analysis of the system during wind speed change,
while a fixed speed was used for the transient analysis, because it is assumed that wind speed does not
change dramatically during the short time interval
of the simulation.
For electrical analysis, a simplified aerodynamic model of a wind turbine is normally recommended as described by the set of equations below
where the aerodynamic torque (Nm) extracted from
the wind is given by [9],[11]:
116
C p (λ ,=
θ ) 0.22(
− 0.4θ − 5)e
Figure 3. Pitch angle controller for FSWT
j o u r n a l o f a p p l i e d s c i e n c e & e n g i n e e r i n g t e c h n o l o g y 2011
Figure 4. Pitch angle controller for VSWT
In Figure 1, beta (β) represents the pitch angles of the
fixed speed wind turbine at various tip speed ratio.
In Figure 2, Pmax represents the maximum power that
can be tracked by the variable speed wind turbine,
while Pref shows the maximum power point tracking
(MPPT) control for the reference active power of the
turbine. The red line indicates the range of operation
of the rotor speed for the variable speed wind turbine whose limit is chosen between 0.7-1.3pu for the
lowest and highest wind speed to be encountered.
The rated wind speed of the turbine is 12.43m/s.
In Figure 3, the proportionate integral (PI)
controls the difference between reference and the
active power of the FSWT with a gain Kp and time
constant Ti of 100 and 0.001sec respectively, while
G and T are the gain and time constant for the control system. The rate of servo-mechanism which
affects the mechanical operation of the control is
10(deg. /sec). The output (β2) is the pitch controller
that controls the active power when the wind speed
is above or below the rated value.
The pitch controller for the VSWT works in
a quite different way. The controller does not activates until the rotor speed ωr of the turbine exceeds
1.3pu, which is the maximum allowable rotor speed
as shown in Figures 2 and 4 respectively. The PI then
controls the difference between the reference and
the rotor speed of the turbine. The gain and time
constant of the PI controller are Kp and Ti. The output
which is (β1) is the pitch controller that controls the
range of operation of the rotor speed of the VSWT between 0.7pu and 1.3pu at low and high wind speed.
Table I gives the parameters of the FSWT
and the VSWT [13].
Rated Power
Rated Voltage
Stator Resistance
Stator Leakage
Reactance
Magnetizing
Reactance
Rotor Resistance
Rotor leakage
Reactance
Inertia Constant
30MVA(IG)
690V
0.01pu
20MVA(DFIG)
690V
0.01pu
0.07pu
0.15pu
4.1pu
3.5pu
0.007pu
0.01pu
0.07pu
0.15pu
1.5secs
1.5secs
Table I: Parameters of FSWT and VSWT
From Table 1, the rated power of the FSWT and
VSWT used for this study are 30MVA and 20MVA
respectively, with a rated voltage each of 690V. The
values of the stator resistance, leakage reactance,
magnetizing reactance, rotor resistance and the rotor leakage reactance affects the operation of the
turbines. These values are based on the designer
available data. The inertia constants value affects
primarily the rotor speed of the wind turbines.
III. MODEL SYSTEM
Figure 5. Model system for VSWT and FSWT
Figure 5 displays the model system for this study,
where the FSWT is connected to the VSWT, then via
the transmission lines to an infinite bus. A capacitor bank (QC) is connected to the FSWT for reactive
power compensation during the steady state of operation. The frequency converters connections for
the VSWT are also shown. The FSWT has no control system for active and reactive power, unlike the
VSWT which has two control systems; the Rotor Side
Converter (RSC) and the Grid Side Converter (GSC)
for active and reactive power control as discussed in
the next section.
IV. CONTROL SYSTEM FOR THE VSWT
The Rotor side converter (RSC) and the Grid side converter (GSC) control blocks for the DFIG are shown
in Figures 6 and 7 respectively. In Figure 6, the rotor
side converter controls the terminal (grid) voltage
Vg to 1.01pu at normal working condition. The daxis current (Idr) controls the active power, while the
q-axis current (Iqr) controls the reactive power. Both
currents are gotten from an abc-to-dqo transformation of the sources voltages Va, Vb, and Vc through a
transformation angle θr gotten from the difference
between the angular frequency of the rotor position 2π f and the angle θPLL of the phase locked loop.
There are two–stage proportionate integral (PI) con-
Stabilization of a Fixed Speed Wind Turbine with a Variable Speed Wind Turbine27
trols with a phase compensator with gain value of G
= 0.01, having a leading and lagging time constants
of 0.05sec and 0.0009sec respectively, connected in
between the two PI controllers. The gain and time
constants of the PI controllers are Kp and Ti with
their values given in the control block diagram
of Figure 6. PDFIG and QDFIG are the active and reactive powers of the DFIG which are been controlled,
while Pref is the optimum reference value (MPPT) of
the DFIG system. After dq0-to-abc transformation,
Vdr * and Vqr * which are the output of the control
system are sent to the PWM (Pulse Width Modulation) signal generator and Vabc * are the three-phase
voltages desired at the rotor side converter output
for switching of the insulated gate bipolar transistors (IGBTs).
Also, Figure 7 shows the control block for
the GSC control, where PLL provides the angle θPLL
and θs is the effective angle for the abc-to-dq0 (and
dq0-to-abc) transformation. The direct axis component is used to regulate the DC-link voltage (Edc ) to
1.0pu. The d-axis current (Id) controls the DC-link
voltage, while the q-axis current (Iq) controls the reactive power of the grid side converter. The Id and Iq
currents are derived from the Va, Vb and Vc transformation through the angle θ s as shown in the block
diagram. Edc, Edc*, Qgsc, and Q*ref represents the DClink voltages and the reactive powers of the actual
and reference values of the DFIG variables that are
been controlled by the GSC. A phase compensator
with gain value of G = 0.06, and having a leading
and lagging time constants of 0.03sec and 0.002sec
respectively, are connected between the two PI controllers. The gain and time constants of the PI controllers are Kp and Ti respectively as shown in the
block diagram. After a dq0-to-abc transformation,
Vq* and Vd* which are the output variables of the
GSC controller are sent to the PWM signal generator.
Finally Vabc* are three voltages at the GSC output for
the IGBT`s switching.
V. SIMULATION RESULTS
Simulations were run in PSCAD/EMTDC for 100s
with different wind speed for the FSWT and the
VSWT for dynamic analysis and simulations for
transient analysis was run for 20s, where the wind
speed was assumed to be fixed and at rated condition, with a three phase fault
28
Figure 6. Control block for the rotor side converter
Figure 7. Control block for the grid side converter
applied at 10.1s and the circuit breakers on the
faulted lines opened and reclosed at 10.2s and 11.0s
respectively. The results are shown in the Figures 8
to 21.
1) Dynamic Analysis
Figure 8. Wind speed for VSWT and FSWT
j o u r n a l o f a p p l i e d s c i e n c e & e n g i n e e r i n g t e c h n o l o g y 2011
Figure 9. Active and reactive power of VSWT
Figure 13. DC-link capacitor voltage of VSWT
Figure 10. Active power of FSWT
Figure 14. Terminal voltage of FSWT
2) Transient Analysis
Figure 11. Pitch angle of FSWT
Figure 15. Active power of VSWT
Figure 12. Rotor speed of VSWT
Figure 16. Active power of FSWT
Stabilization of a Fixed Speed Wind Turbine with a Variable Speed Wind Turbine29
Figure 17. DC-link capacitor voltage of VSWT
Figure 18. Rotor speed of FSWT
Figure 19. Rotor speed of VSWT
Figure 20. Reactive power of grid side inverter of VSWT
30
Figure 21. Terminal voltage of FSWT (IG)
VI. SIMULATIONS DISCUSSION
From the simulation results where a variable speed
is used for both the FSWT and the VSWT in Figure 8,
it can be seen that both the active and reactive powers of the VSWT changes as the wind speed changes as shown in Figure 9. Despite the high value of
the wind speed above the rated wind speed value
of 12.43m/s as shown in the turbine characteristics
(Figure 2), the active power of the VSWT does not
exceed the rated per-unit value of 1.0pu, while reactive power is been absorbed (negative value) or
supplied (positive value) to the system, depending
on the nature of the wind speed, due to the independent controllability of the active and reactive powers of the DFIG VSWT system by the RSC control
system. The active power of the FSWT is also controlled to a limit of 1.0pu in Figure 10 by the pitch
angle controller whose response is shown in Figure
11. It could be observed that the pitch angle controller for the FSWT does not work until the active
power of the FSWT exceeds its rated value of 1.0pu
due to high wind speed above the rated wind speed
of 12.43m/s, for the FSWT after 80sec.
The rotor speed response for the VSWT is
shown in Figure 12, where at 20sec and at 70sec,
when the wind speed of the VSWT exceeds the rated
wind speed of 12.43m/s, the pitch angle control system tries to limit the rotor speed of the wind turbine
to a limit of 1.3pu. The rotor speed varies as the
wind speed varies, while the GSC control maintains
the DC-link voltage constant at 1.0pu as shown in
Figure 13. In Figure 14, the terminal voltage of the
FSWT is maintained constant when the VSWT is connected to it despite the changes in the wind speed.
When the VSWT was not connected, it is seen that
the terminal voltage of the FSWT varies with the
wind speed.
j o u r n a l o f a p p l i e d s c i e n c e & e n g i n e e r i n g t e c h n o l o g y 2011
Figure 15 and 17 shows the active power of
the VSWT and the DC-link voltage for transient analysis. It is seen that the VSWT was able to assume
the initial steady state after the three phase fault,
thus stabilizing itself. In Figure 16 and 18, the active
power and the rotor speed of the FSWT was not able
to maintain its steady state after the three phase
fault, but when it was connected to the VSWT, the
initial steady states were achieved after the three
phase fault. The rotor speed of the VSWT and the reactive power of the GSC are shown in Figures 19 and
20 respectively. It could be observed that reactive
power was supplied to the system during grid fault
through the grid-side inverter control of the VSWT
as shown in Figure 20. Figure 21 shows the terminal voltage of the FSWT (IG) with and without the
VSWT connected. A better performance of assuming
the initial steady state of the FSWT terminal voltage
after the three phase fault was achieved when the
VSWT is connected to the FSWT.
VII.CONCLUSION
A simple wind farm composed of a Variable Speed
Wind Turbine (VSWT) and a Fixed Speed Wind Turbine
(FSWT) connected to an infinite bus has been studied
and simulated in PSCAD/EMTDC environment.
Stability analyses were carried out when the
VSWT is connected and not connected to the FSWT.
The VSWT can be used to stabilize the FSWT and
hence the wind farm during wind speed change and
grid fault as shown in the simulation results, because
it can provide enough reactive power to the wind
farm system through its frequency converter control
without using external reactive power compensation.
The results help to understand the transient
stability phenomena in fixed speed wind farms, and
could help to design fixed speed wind farms attending to transient stability requirements, by including
some variable speed wind turbines.
REFERENCES
[1]
[2]
[3]
[4]
T. Ackermann, Wind Power in Power Systems,
John Wiley and Sons, Ltd., 2005.
P. Ledesma, J. Usaola, and J. L. Rodriguez,
“Transient stability of a fixed speed wind
farm,” Renewable Energy, vol.28, pp. 13411355, 2003.
E.ON NETZ GmbH, Grid Connection Regulation for High and Extra High Voltage, 2006.
R. D. Fernanadez, R. J. Mantz, and P. E. Battaiotto, “Potential contribution of wind farms
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
to damp oscillations in weak grids with high
wind penetration,” Renewable and Sustainable Energy Reviews, vol. 12, pp. 1692-1711,
2008.
I. Erlich, H. Wrede, and C. Feltes, “Dynamic
behavior of DFIG-Based wind turbines during
grid faults,” IEEJ Trans on Power and Energy,
vol. 128, no. 4, pp. 396-401, 2008.
L. M. Fernandez, C. A Garcia, and F. Jurado,
“Comparative study on the performance of
control systems for doubly fed induction
generator (DFIG) wind turbines operating
with power regulation,” Energy Journal, vol.
33, pp. 1438-1452, 2008.
A. D. Hasan, and G. Michalke, “Fault ridethrough capability of DFIG wind turbines,”
Renewable Energy, vol. 32, pp. 1594-1610,
2007.
B. H. Chowdhury, and S. Chellapilia, “Doublyfed induction generator control for variable
speed wind power generation,” Electric Power
System Research, vol. 76, pp. 786-800, 2006.
T. Sun, Z. Chen, and F. Blaabjerg, “Transient
stability of DFIG wind turbines at an external
short circuit fault,” Wind Energy Journal, vol.
8, pp. 345-360, 2005.
PSCAD/EMTDC Manual, Manitoba HVDC Research Center, 1994.
H. Karim-Davijani, A. Sheikjoleslami, H.
Livani, and M. Karimi-Davijani, “Fuzzy logic
control of doubly fed induction generator
wind turbine,” World Applied Science Journal,
vol. 6, no. 4, pp. 499-508, 2009.
O. Wasynczuk, D. T. Man, and J. P. Sullivan,
“Dynamic behavior of a class of wind turbine
generator during random wind fluctuations,”
IEEE Transactions on Power Apparatus and
Systems, vol. PAS-100, no.6, pp. 2837-2845,
1981.
R. Takahashi, J. Tamura, M. Futami, M. Kimura and K. Ide, “A new control method for
wind energy conversion system using double
fed synchronous generator,” lEEJ Transactions o Power and Energy, vol. 126, no.2, pp.
225-235, 2006.
Kenneth E. Okedu obtained his Ph.D. in the department of Electrical and Electronic Engineering,
Kitami University of Technology, Hokkaido, Japan
in 2011. He received his B.Sc. and M. Eng. degrees in
Electrical and Electronic Engineering from the University of Port Harcourt, Nigeria in 2003 and 2006
respectively. His research interests include renew-
Stabilization of a Fixed Speed Wind Turbine with a Variable Speed Wind Turbine31
able energy, stabilization of wind farm with doubly
fed induction generator variable speed wind turbine, augmentation of renewable energy to power
system and power system stability analysis.
32
j o u r n a l o f a p p l i e d s c i e n c e & e n g i n e e r i n g t e c h n o l o g y 2011