International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
Fuzzy Based Controllers for Dynamic Response
Analysis of DFIG based Wind Farm
R.Vijay Veera Karthick#1, M.Bhavani#2
#1
#2
PG student, Dept. of Electrical and Electronics Engg., Anna University, Regional Centre Madurai, Tamilnadu, India
Assistant Professor, Dept. of Electrical and Electronics Engg., Anna University, Regional Centre Madurai, Tamilnadu, India
Abstract— The global electrical energy consumption is rising and
there is steady increase of the demand on power generation. In
addition to conventional power generation units a large number
of renewable energy units are being integrated into the power
system. The Wind Energy Conversion system (WECS) is the
most cost competitive of all the environmentally clean and safe
renewable energy sources in world. Doubly fed induction
generator (DFIG) based wind farm is today the most widely used
concept. This paper presents the dynamic response analysis of
DFIG based wind farm under remote fault condition using the
fuzzy logic controllers. The goal of the work is to analyze the
dynamic response of DFIG based wind farm during and after the
clearance of fault using the proposed fuzzy logic controller. The
stability of wind farm during and after the clearance of fault is
investigated. The effectiveness of the fuzzy logic controller is then
compared with that of a PI controller. The validity of the
controllers in restoring the wind farms normal operation after
the clearance of fault is illustrated by the simulation results
which are carried out using MATLAB/SIMULINK.
Index Terms— Doubly fed induction generator, wind farm,
remote fault, fuzzy logic controller, simulink
I. INTRODUCTION
Due to the conventional energy sources consumption and
increasing environmental concern, great efforts have been
done to produce electricity from renewable sources, such as
wind energy sources. Proposals for wind developments in the
hundreds of MWs are currently being considered.
Interconnection of these developments into the existing utility
grid poses a great number of challenges [13]. The doubly fed
induction generator (DFIG) based wind turbines are nowadays
more widely used in large wind farms. The main reasons for
the increasing number of DFIGs connected to the electric grid
are low converter power rating and ability to supply power at
constant voltage and frequency while the rotor speed varies
[8].
Improved Direct Power Control (DPC) strategy for gridconnected wind-turbine-driven doubly fed induction
generators (DFIGs) when the grid voltage is unbalanced is
considered. The DPC scheme is based on the sliding mode
control (SMC) approach, which directly regulates the
instantaneous active and reactive powers. The SMC-based
DPC during network unbalance is proposed to achieve three
selective control targets, i.e., obtaining sinusoidal and
symmetrical stator current, removing stator interchanging
reactive power ripples and canceling stator output active
ISSN: 2231-5381
power oscillations [3]. Improved Direct power control (DPC)
strategy for a doubly fed induction generator (DFIG) based
wind power generation system under unbalanced grid voltage
dips is proposed. Two resonant controllers, which are tuned to
have large gain at the power pulsation frequencies, are applied
together with the proportional-integral controller to achieve
full control of the DFIG output power. The fundamental and
double grid frequency power pulsations, which are produced
by the transient unbalanced grid faults, are mathematically
analyzed and accurately regulated [4]. Stability study of a
variable-speed directly-driven permanently- excited 2-MW
wind generator connected to ac grids of widely varying
strength and very weak grids are carried out. Two alternative
controller designs are studied for their potential to enhance
system robustness to changes in ac grid strength [5].
Optimum design procedure for the controller used in the
frequency converter of a variable speed wind turbine driven
permanent magnet synchronous generator using Genetic
algorithm (GA) and response surface methodology (RSM) is
presented. The effectiveness of the designed parameters using
GAs-RSM is compared with that obtained using a generalized
reduced gradient (GRG) algorithm considering both
symmetrical and unsymmetrical faults [1].
Different combinations of reactive power control of rotorand grid-side converters are investigated for voltage-control
purposes. The performance of alternative voltage control
strategies applied to doubly fed induction generator (DFIG) is
compared [6].
In this paper, a detailed model for representation of DFIG
based wind farm in power system dynamics simulations is
presented. MATLAB/SIMULINK dynamic software program
is used for this study. This paper presents dynamic response
analysis of DFIG based wind farm under remote fault
conditions using the fuzzy logic controller. The goal of the
work is to enhance the dynamic response of DFIG based wind
farm during and after the clearance of fault using the proposed
fuzzy logic controller.
II. MATHEMATICAL MODEL OF DFIG
For analysis of control strategies, the mathematical model
of doubly fed induction machine, in per unit notation with
motor convention in d–q reference frame is
=
−
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+
(1)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
=
−
=
−
=
−
+
(
)
(
)
(2)
+
(3)
+
(4)
In these equations, ω is the rotational speed of the d–q
reference frame (rad/sec), and it represents the grid
frequency.
is the base speed which will be the systems
nominal speed
(rad/s) and is the electrical speed of the
rotor (rad/s). and are the stator and rotor voltages (pu).
and are the stator and rotor currents (pu). and are the
stator and rotor resistances (pu). and are the stator and
rotor magnetic fluxes linkage (pu).
shown in Fig. 2. This implies that
= 0 and
= . This
approach is useful for doubly fed machines where the control
is performed by a means of the rotor voltage. The stator
voltage is the grid voltage, which is approximately constant in
a stable grid. The rotor voltage is referred to the same frame. It
consists in general of two non- zero d–q components. This d–q
frame orientation decouples the active power from reactive
power and they can be con- trolled independently. The stator
active power
and reactive power
are expressed as
follows
=
=
(10)
(11)
III. WIND TURBINE MODEL
A. The Aerodynamic Model
The aerodynamic model of a wind turbine is determined by
its power speed characteristics. For a horizontal axis wind
turbine, the mechanical power output that a turbine can
produce is given by
( , )
=
(12)
Where is the air density (kg/m ), u is the wind speed
(m/s), A is the area covered by the rotor (m ), and is the
power coefficient which is a function of tip speed ratio, λ, and
blade pitch angle β (deg). In this work, the equation is
approximated using a non-linear function accordingly
Fig. 1. DFIG Wind Turbine system.
.
( , ) = 0.22
Where
=
− 0.4 − 5
(13)
is given by
.
−
.
(14)
The turbine power characteristics are illustrated as shown
in Fig. 3. These characteristics are plotted at pitch angle β= 0
Fig. 2. Choice of d-q frame orientation.
The correlation between fluxes and currents is
=
=
=
=
+
+
+
+
(5)
(6)
(7)
(8)
Where and are the stator and rotor leakage reactances
(pu),
is the mutual magnetizing reactance (pu). The
electromechanical torque
(pu) is given by
=
−
(9)
Here the d–q frame is rotating at the synchronous speed i.e.
=
. The q axis is aligned with the stator voltage, as
ISSN: 2231-5381
(deg).
Fig. 3. The Turbine Power Characteristics.
B. Pitch angle controller
In this study, the conventional pitch angle controller shown
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
in Fig. 4 is used. The minimum pitch angle
is 0◦ and the
maximum pitch angle
is 45◦. Accordingly, for a more
realistic simulation, a rate limiter is implemented in the pitch
controller model. In this paper the maximum pitch angle rate is
set at 2 degrees/second. The purpose of using the pitch
controller is to maintain the output power of wind generator at
rated level by controlling the blade pitch angle of turbine blade
when wind speed is over the rated speed.
Fig. 4. The Rotor speed control diagram.
IV. WIND FARM MODEL SYSTEM
Fig. 5. The Model System.
The power system model used for dynamic response of
DFIG based wind farm is as shown in Fig. 5. Here, a 9 MW
wind farm consisting of six 1.5 MW wind turbines connected
to a 25 kV distribution system exports power to a 120 kV grid
through a 30 km, 25 kV feeder. A 500 kW resistive load and a
0.9 Mvar (quality factor=50) are connected at the 575 V
generation bus. This filter is used for reactive power
compensation. The turbine power characteristics are illustrated
as shown in Fig. 3. Wind turbines using a doubly-fed induction
generator consist of a wound rotor induction generator and an
AC/DC/AC IGBT- based PWM converter. The switching
frequency is chosen to be 1620 Hz. The stator winding is
connected directly to the 60 Hz grid while the rotor is fed at
variable frequency through the AC/DC/AC converter. The
DFIG technology allows extracting maximum energy from the
wind for low wind speeds by optimizing the turbine speed,
while minimizing mechanical stresses on the turbine during
gusts of wind. The optimum turbine speed producing
maximum mechanical energy for a given wind speed is
proportional to the wind speed.
frequency converter. The simulation program is carried out in
a numerical simulation, using one of Matlab toolboxes,
Simulink. All the system components are simulated using this
program blocks.
The stator currents
- , the rotor currents
- and the
grid converter currents are
transformed
into the
d–q quantities - , - and respectively.
The
voltage of the bus
is
. Three‐phase phase locked loop
(PLL) can be used to get the frequency of the voltage
waveform and the angle theta (theta = ). A torque controller
is used to control the torque and maintains the speed
at
certain constant value. The inputs of the torque controller
are , - , - and , frequency and - . The
output of the torque controller is the d-axis desired rotor
current ∗ . The torque controller consists of two cascaded
blocks. The first block is called torque reference, which can be
used to produce the command torque signal
. The second
block is the torque regulator, which can be used to
produce ∗
Inside the torque reference block, the power
losses of DFIG is subtracted from the input mechanical power
of DFIG to obtain the reference electrical output power
of DFIG.
is divided by the generator speed to get
the torque command
. In the torque regulator, stator flux
estimator is used to estimate the magnetic flux. The magnetic
flux and
are used to get ∗
. The reactive power
controller (Q regulator) is used to produce the q -axis desired
rotor current ∗ where the
is compared with the actual Q
of bus
and the reactive power error is used to produce ∗
via a PI controller. A current regulator is used to produce the
reference voltages ∗ . These d–q voltages can be
transformed into abc quantities to produce the control signals
of the rotor converter. These control signals feed three phase
pulse width modulation (PWM) generator to produce the firing
pulses to the rotor converter.
VI. GRID SIDE CONVERTER CONTROLLER
In the grid side converter controller, the voltage of bus
and the grid converter currents are
transformed into the d–q quantities
and respectively. A
dc bus voltage regulator is used to produce
. The inputs of
the dc bus voltage regulator are the reference dc bus voltage
and the actual value of dc bus voltage
. is
compared with to yield the voltage error which feeds a
PI controller to get
. A current regulator is used to
produce the reference voltages ∗ . These d–q voltages can
be transformed into abc quantities to produce the control
signals of the grid converter. These control signals feed three
phase PWM generator to produce the firing pulses to the grid
converter.
VII. THE FUZZY LOGIC CONTROLLER
V. ROTOR SIDE CONVERTER CONTROLLER
The stator of DFIG is connected directly to the grid. The
rotor of DFIG is connected to the grid through AC/DC/AC
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For a good performance of DFIG based wind farm, four
fuzzy logic controllers FLC1, FLC2, FLC3, and FLC4 are
used. The PI controller in the dc bus voltage regulator is re-
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
placed by the FLC1. The PI controller in the reactive power
regulator is replaced by the FLC2. The PI controllers in
current regulators of rotor side converter controller and grid
side converter controller are replaced by the FLC3 and FLC4
respectively.
In FLC1, the reference dc bus voltage is compared
with the actual voltage to obtain the voltage error
( )as shown in Fig. 6. Also this error is compared with
the previous error
( − 1) to get the change in error
( )and∆
∆
( ). The inputs of FLC1 are
( ). The
output of the proposed controller is ∆
( ) which is added
to the previous state of current
( − 1)to obtain the
reference current
( ). The others FLCs are based on the
same approach as in FLC1.The membership functions are
defined off- line, and the values of the variables are selected
according to the behavior of the variables observed during
simulations. The selected fuzzy sets for FLC1 are shown in
Fig. 6. The control rules of the FLC1 are represented by a set
of chosen fuzzy rules. The designed fuzzy rules used in this
work are given in Table 2. The fuzzy sets have been defined
as: NB, Negative Big, NS, Negative Small, ZR, Zero, PS,
Positive Small and PB, Positive Big respectively.
Fig. 9. Membership function of fuzzy output.
error
error rate
NB
NS
ZE
PS
PB
NB
NS
ZE
PS
PB
NB
NB
NB
NS
ZE
NB
NS
NS
ZE
PS
NB
NS
ZE
PS
PB
NS
ZE
PS
PS
PB
ZE
PS
PB
PB
PB
Table 1: Fuzzy Rules
VIII. SIMULATION DIAGRAM
In this study, the steady state operation of the DFIG and its
dynamic response to voltage sag resulting from a remote fault
on the 120 kV grid are observed. The wind speed is
maintained constant at 10 m/s. The power system model used
for dynamic response of DFIG based wind farm is as shown in
Fig.5. Here, a 9 MW wind farm consisting of six 1.5 MW
wind turbines connected to a 25 kV distribution system
exports power to a 120 kV grid through a 30 km, 25 kV
feeder.
Fig. 6. FLC1
Fig. 7. Membership function of input Error.
Fig. 9 System Response with PI controllers (V ,w , P, Q parameters.)
Fig. 8. Membership function of input Error Rate.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
compared both graphically as well as numerically with PI and
FLC. The dynamic response is found to be superior to that
corresponding to the conventional PI controller. The proposed
methodology is even suitable to other power systems related
applications such as FACTS devices, voltage source converter
based HVDC system and so on, especially in the cases where it
is difficult to determine the suitable transfer function of a
complex and larger system.
REFERENCES
[1]. Hasanien H. M, Muyeen S. M, “Design Optimization
of Controller Parameters used in Variable Speed Wind Energy
Conversion System by Genetic Algorithms,” IEEE
Transactions on Sustainable Energy, vol.3, no. 2 ,pp.200208,April 2012.
Fig. 10 System Response with FLCs (V ,w , P, Q parameters.)
The Fig. 10 & 11 shows the dynamic response of DFIG
based wind farm for a remote fault condition. From this, it is
obvious that the proposed fuzzy based controller provides an
enhancement in the dynamic response of DFIG wind farm. At
t = 0.03 s, the positive-sequence voltage suddenly drops
causing an oscillation on both the dc bus voltage and the
DFIG output power. During the voltage sag, the control
system regulates dc bus voltage and reactive power at their set
points.
PI Controller
Fuzzy Logic
Controller
ISE for
0.077
0.0146
Table 2: Numerical comparison between PI and FLC.
Performance Index is a quantitative measure of the
performance of a system and is chosen so that emphasis is
given to important system specifications. A suitable
performance index is the integral of the square of errors (ISE)
[2]. Hasanien H. M, Muyeen S. M, “Speed Control of GridConnected Switched Reluctance Generator Driven by Variable
Speed Wind Turbine using Adaptive Neural Network
Controller,” Electric Power Systems Research 84 no.1,
pp.206–213, March 2012, Elsevier.
[3]. Lei Shang , Jiabing Hu, “Sliding Mode Based Direct
Power Control of Grid Connected Wind Turbine Driven
Doubly Fed Induction Generators Under Unbalanced Grid
Voltage Conditions,” IEEE Transactions on Energy
Conversion, vol. 27,no.2,pp.362-373, June 2012.
[4]. Heng Nian, Yipeng Song, Peng Zhou, Yikang He,
“Improved Direct Power Control of a Wind Turbine Driven
Doubly Fed Induction Generator During Transient Grid
Voltage Unbalance,” IEEE Transactions on Energy
Conversion, vol. 26,no.3,pp.976-986,Sep. 2011.
[5]. Nicholas P. W. Strachan, Dragan Jovcic, “Stability of a
Variable-Speed Permanent Magnet Wind Generator With
Weak AC Grids,” IEEE Transactions on Power Delivery, vol.
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[6]. Mustafa Kayıkci, Jovica V. Milanovic, “Reactive Power
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on Energy Conversion, vol. 22,no.2,pp.389-396,June 2007.
Which is defined as
ISE = ∫ e(t)
(15)
To have a better performance, the ISE value needs to be
reduced. Hence from table 2 showing the comparative values
of ISE for PI and FLC, it is observed that the ISE value for
is reduced with Fuzzy based controller, showing improved
performance.
IX. CONCLUSION
This paper has presented a fuzzy based controller to ensure
the dynamic response improvement of doubly fed induction
generator based wind farm under remote fault condition. The
response of the system under fault condition has been
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[7]. Daniel J. Trudnowski, Andrew Gentile, Jawad M. Khan,
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
[9]. Datta, R., Ranganathan, V. T, “Variable-Speed Wind
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APPENDIX
System Data
Doubly-fed induction generator data, PWM and DC link data and wind farm data.
[a]
[b]
[C]
Doubly-fed induction generator data:
The number of units
The nominal apparent power for each unit
The total apparent power (
)
The nominal line-line voltage (
)
The nominal frequency ( )
The stator resistance ( )
The stator inductance ( )
The rotor resistance ( )
The rotor inductance ( )
The mutual inductance ( )
Number of pole pairs
Inertia constant (H)
Friction factor (F )
6
1.666 MVA
10 MVA
575 V
60 Hz
0.00706 pu
0.171 pu
0.005 pu
0.156 pu
2.9 pu
3
5.04 s
0.01 pu
Wind Farm:
Number of units
The nominal mechanical power of each unit(
)
The total mechanical power
The base wind speed
Base rotational speed (pu of base generator speed)
6
1.5MW
9MW
10m/s
1.2 pu
PWM AND DC LINK DATA:
The PWM frequency
The nominal DC link Voltage
The DC bus capacitor (C)
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27 *
1200 V
60000 (µF)
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