International Journal of Computer and Electrical Engineering, Vol.4, No.2, April 2012
Dynamic Modeling and Control of Induction Generators in
Wind Turbines
T. Abedinzadeh, M. Ehsan, and D. Talebi

On the dynamic subject, several works have been done on
the analysis of power quality from wind turbines to the power
systems [6], [10]-[13]. An extensive analysis of the potential
impacts of wind turbines has been developed on the power
quality, where the work focused on the small scale
integration and is explained how to assess the voltage quality
from wind turbines using wind turbine characteristics.
The turbine of wind energy conversion systems can he
operated in one of two modes: constant-speed and
variable-speed. In constant-speed turbines, reactive power
cannot be controlled. But reactive power of variable-speed
turbines can be controlled in two ways. They can produce
power with constant power coefficient or they can be
controlled to adjust magnitude of voltage of PCC (Point of
Common Coupling). Presently, the trend of operating wind
turbines is in the variable-speed mode. One of the most
common type of wind turbines is the variable speed wind
turbines with Doubly-Fed Induction Generator (DFIG). In
the DFIG, the applied rotor voltage controls the real and
reactive powers and generator’s speed, when its stator
terminals are connected to a power system and the stator
voltage is held constant by the grid[2], [3], [5], [12]-[16].
Each one of these cases has different impact on the
distribution grids. For evaluation of these impacts, SCIG
(Squirrel Cage Induction Generator) that works in
constant-speed operation and DFIG generator that is used in a
variable-speed turbine have been simulated. A simulation
program of PSCAD/EMTDC is used to investigate the
impact of these turbines on a distribution grid. Both of
above-mentioned methods are applied under same
disturbances in wind speed in the simulation. This simulation
is based on a vector control of the DFIG machine. The
technique of vector control is used to control the output
parameters of the rotor in different loading conditions and
variable rotor speeds [9], [17], [18].
Abstract—As a result of increasing environmental concern,
more and more electricity is generated from renewable sources.
One way of generating electricity from renewable sources is to
use wind turbines. A tendency to erect more and more wind
turbines can be observed. Because of this, in the near future
wind turbines may start to influence the behaviour of electrical
power systems. Therefore, adequate models to study the impact
of wind turbines on electrical power system behaviour are
needed. The wind turbines can be operated in two modes:
constant-speed and variable-speed. Squirrel Cage Induction
Generator (SCIG) has been simulated that works in
constant-speed operation. Doubly Fed Induction Generator
(DFIG) that is used in a variable-speed turbine can be
controlled in two ways. They can produce power with constant
power factor or they control magnitude of voltage of PCC.
PSCAD/EMTDC simulation program is used to investigate the
impact of these turbines on a distribution grid. Each of these
has different impacts on the distribution grids. All of
above-mentioned methods are applied under same disturbances
in wind speed in the simulation. This simulation is based on a
vector control of the DFIG machine. The technique of vector
control is used to control the output parameters of the rotor of
DFIG in different loading conditions and variable rotor speeds.
The outcomes of the simulation demonstrate the effectiveness of
the proposed simulation and control schemes. Also, it is shown
that voltage control scheme has better results and improves the
voltage profile considerably.
Index Terms—DFIG, PSCAD/EMTDC, vector control, wind
turbine.
I. INTRODUCTION
Wind energy is said to be one of the most prominent
sources of electrical energy in years to come. Wind energy
conversion systems (WECS) are the devices which are used
to convert wind energy to electrical energy. The increasing
concerns to environmental issues demand the search for more
sustainable electrical sources [1]-[5]. With the wind farms
rating hundreds megawatts, the concerns start to focus on the
voltage problems of the power system [6]. For distribution
grids connected wind power generation, voltage quality is an
important issue for the system planning purpose. The
operation of wind turbines in the distribution networks may
affect the voltage quality offered to the consumers.
Most of the models used to represent a wind turbine are
based on a non linear relationship between rotor power
coefficient and linear tip speed of the rotor blade [5, 7-9].
II. WIND TURBINE MODELING
Wind energy conversion systems (WECS) are the devices,
which are used to convert the wind energy to electrical
energy. The total wind power entering the wind turbine is
given by:
1
(1)
PT  AV 3C p
2
where ρ is the density of air in kg/m3 and A is the area swept
by the blades of wind turbine, in m2 and V is the speed of
wind in m/s and CP is dimensionless power coefficient. Since
calculation of CP is too complicated, usually its value
calculates from simpler formulas. The formula that is used
for CP is [9]:
Manuscript received February 13, 2012; revised March 14, 2012.
T. Abedinzadeh is with the Islamic Azad University, Shabestar Branch,
Shabestar, Iran (e-mail: taherabedinzade@yahoo.com).
M. Ehsan is with Sharif University, Tehran, Iran. (e-mail: Ehsan@sharif.
ac.ir).
D. Talebi is with the Islamic Azad University, Bonab Branch, Bonab, Iran
(e-mail: dtalebi@gmail.com).
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International Journal of Computer and Electrical Engineering, Vol.4, No.2, April 2012
  (  c1 ) 
  0.00184 (  c1 ) 
C p  (0.44  0.0167  ) Sin
 c 2  0.3 
(2)
Fig. 3. DFIG overall system in a wind turbine-generator
ds   Ls ids  Lm idr
Fig. 1. Pitch angle control block diagram of a wind turbine
(4)
 qs   Ls i qs  Lm i qr
where λ is Tip-Speed Ratio and β is the blade pitch angle.
A. Pitch Angle
The block diagram that is used to control pitch angle is
shown in below. This controller increases pitch angle if
turbine shaft speed exceeds its maximum speed. However, it
should be mentioned that pitch angle can only rise some
degrees (here 20 degrees).
v ds   Rs i ds   s  qs 
(5)
d ds
dt
v qs   Rs i qs   s  ds 
(6)
d qs
dt
(7)
For the rotor side:
B. Turbine Simulation
Below equation is used for turbine simulation:
DT2V 3C p
P
(3)
TT  T 
T
2T
where ρ and r are air density and turbine blade radius and they
have been replaced by 1.225 and 23 respectively. V is wind
speed and ωT is angular velocity of wind turbine.
dr  Lr idr  Lmids
(8)
qr  Lr iqr  Lm iqs
vdr  Rr idr  s s qr 
ddr
dt
vqr  Rr iqr  ss dr 
(10)
dqr
III. SCIG GENERATOR
A squirrel cage induction generator that is simulated in the
paper is shown in fig. 2. In the SCIG generator, the control of
speed and power is done by regulating of pitch angle.
(9)
dt
(11)
The electrical output power from the induction generator is
given by:
Ps 
IV. DFIG GENERATOR
3
(vdsids  vqsiqs )
2
3
Pr  (vdr idr  vqr iqr )
2
A double-Fed induction generator is a standard wound
rotor induction generator with its stator windings directly
connected to the power grid and rotor connected to the power
grid through a frequency converter [7]. (Fig.3)
In modern DFIG designs, the frequency converters are
usually built by two, three phase self commutated
back-to-back PWM converters with an intermediate capacitor
link for DC bus voltage regularity. The converter that is
connected to the rotor called ‘rotor side converter’ and the
other named 'grid side converter'. By controlling the grid and
rotor converters, the DFIG can be adjusted to achieve many
capabilities versus conventional squirrel cage induction
generators. dq representation of DFIG machine for the stator
side are given by:
Pg  Ps  Pr
(12)
(13)
(14)
where Ps is the power delivered by the stator, P r is the power
to the rotor, Pg is the total power generated and delivered to
the grid.
In addition, reactive power:
3
Qs  (vqs ids  vds iqs )
2
(15)
The electrical torque generated by induction machine is
given by:
Te  
3
P (ds iqs  qs ids )
2
(16)
V. VECTOR CONTROL
The technique of vector control will be used in the control
of induction generator to control the generated voltage for
different loading conditions and variable rotor speeds.
The total stator flux is aligned along the d-axis of the
Fig. 2. The simulated SCIG connected to the grid
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International Journal of Computer and Electrical Engineering, Vol.4, No.2, April 2012
rotating reference frame [7] so that:  qs  0
The secondary stage of the controller is constructed using
the primary stage reference current compared to the direct
component of measured rotor current. The required rotor
voltage is obtained from a PI controller and the summation of
the quadrature rotor current compensation term, derived from
(15). This control scheme is shown in Fig. 5(b).
Therefore, iqs is derived:
iqs  
Lm
iqr
Lls  Lm
(17)
Substituting iqs in (10), (11) will result in:

L2   
L2  d
vdr  Rr idr  ss   Lr  m iqr    Lr  m  idr
Ls   
Ls  dt

(18)

 L V  
L2 
L2  d
vqr  Rr iqr  ss   Lr  m idr   m s     Lr  m  iqr
Ls 
Ls  dt
 Lss   

(19)
Lm
3
Te   P
dsiqr
2 Lls  Lm
(20)
a) Primary stage
Neglecting stator resistance will lead to [7]:
Vds  0
Vqs   s ds
(21)
(22)
Substituting for Vds=0, Eqs. (14) and (15) will be
simplified as follows:
3
(23)
P  (vqs iqs )
2
3
(24)
Q  (vqs ids )
2
b) Secondary stage
Fig. 5. Voltage control scheme based on vector control
A. Electromagnetic Torque/Speed Control
Optimum Power Extractor calculates desired torque for
turbine. Therefore, iqrref will be derived as shown in Fig.4 (a).
Comparing the reference variable to the actual machine
current, an error signal required for controlling the speed of
the machine is obtained. To determine the required rotor
voltage, a standard PI controller and the summation of the
direct rotor current compensation term, derived from (19), is
implemented. This control scheme is shown in Fig. 4(b).
Fig. 6. Reactive power control scheme: primary stage
C. Reactive Power Control
For controlling reactive power, idrref is obtained from (26).
Its control scheme is shown in Fig. 6. The secondary stage for
controlling reactive power is similar to Fig. 5(b).
a) Primary stage
VI. CASE STUDY
To illustrate the impact of a wind turbine on the voltage
profile along a line, a distribution grid is considered [10] (Fig.
7).
b) Secondary stage
Fig. 4. Speed control scheme based on vector control
Fig. 7. Simplified one-line diagram of the simulated case study network
B. Voltage Control
In order to control terminal voltage, the amplitude of idr is
controlled. In order that control voltage, reference voltage is
compared with the terminal voltage. Then error control signal
is produced to an integral controller, as shown in Fig. 5(a).
The node 1 is connected to the high voltage grid. The rated
voltage is 15 kV. On average, the X/R ratio of the distribution
lines in the studied grid is approximately 7.5. The total load is
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International Journal of Computer and Electrical Engineering, Vol.4, No.2, April 2012
10 MVA. A wind turbine is assumed to be connected to node
9. Fig. 8 shows the wind speed at hub height, used as input for
the simulation.
variations of voltage and reactive power are more than the
other two cases.
The reactive power for case 2 is permanently controlled to
zero. In case 3 that the DFIG is controlled in constant voltage
state, the voltage in node 9 has been constant in 1 p.u. in all
wind speeds. In the fourth second of simulation that wind
varies so much, the voltage variation is 0.8% for case 1 and
0.7% for case 2 and 0.2% for case 3.
Fig. 8. Assumed wind speed, as input for the simulation
Three cases for the turbine type are considered in the
following scenarios (Table I).
TABLE I: CASES CONSIDERED FOR SIMULATIONS
Generator
Reactive
Speed controller
type
power control
Case 1
fixed speed
SCIG
no
Case 2
variable speed
DFIG
cos ϕ = 1
Case 3
variable speed
DFIG
voltage control
a) Case 1
b) Case 2
a) Case 1
c) Case 3
Fig.10. Reactive power waveforms of the DFIG in two cases of simulation
b) Case 2
a) Case 1
c) Case 3
Fig. 9. Active power waveforms of the DFIG in two cases of simulation
b) Case 2
Fig. 9 shows the active power of turbines in all cases. As it
can be seen, variation of active power in case 1 is more than
other cases. The control of active power in DFIG generators
with controlling of rotor voltage causes that. But in SCIG
generators, it is only pitch angle control that is used to vary
the output active power.
The reactive power of generator and voltage of PCC have
been shown in Fig. 10 and Fig. 11.
The reactive power output of a SCIG (cases 1) is always
negative (inductive behavior) and cannot be controlled, so the
c) Case 3
Fig. 11. Voltage waveforms of PCC in two cases of simulation
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International Journal of Computer and Electrical Engineering, Vol.4, No.2, April 2012
VII. CONCLUSION
In this paper, dynamic performance of induction
generators that are controlled in different ways have been
simulated and compared under same disturbances in wind
speed. We have used a simulation program of
PSCAD/EMTDC to investigate the impact of these turbines
on a distribution grid. When output voltage of generator is
controlled, it is shown that voltage control scheme has better
results and improves the voltage profile considerably.
[5]
[6]
[7]
[8]
[9]
APPENDIX
TECHNICAL SPECIFICATIONS OF DFIG
Winding connection (Stator/Rotor)
Frequency
Number of Poles
Rated Speed
Rated Slip
Rated Power Output
Number of Rotor Systems
Rotor Inertia
Stator Resistance
Stator Reactance
Rotor Resistance
Rotor Reactance
Iron Loss
Magnetizing Reactance
[10]
Star/Star
50 Hz
2
3000 RPM
5%
2 MW
1
29 Kg.m2
0. 0201 p.u
0. 0349 p.u.
0.0377 p.u.
0. 0349 p.u.
0.054 Ω
1.2028 p.u.
[11]
[12]
[13]
[14]
REFERENCES
[1]
[2]
[3]
[4]
[15]
S. Z. Chen, et al, "Integral Sliding-Mode Direct Torque Control of
Doubly-Fed Induction Generators Under Unbalanced Grid Voltage,"
IEEE TRANSACTIONS ON ENERGY CONVERSION vol. 25, JUNE
2010.
S. Foster, et al, "Coordinated reactive power control for facilitating
fault ride through of doubly fed induction generator- and fixed speed
induction generator-based wind farms," IET Renewable Power
Generation, vol. 4, pp. 128-138, 2010.
D. Zhi, et al. "Model-Based Predictive Direct Power Control of
Doubly Fed Induction Generators," IEEE TRANSACTIONS ON
POWER ELECTRONICS, vol. 25, FEBRUARY 2010.
L. Yang, et al, "Optimal controller design of a doubly-fed induction
generator wind turbine system for small signal stability enhancement,"
[16]
[17]
[18]
169
IET Generation, Transmission & Distribution, vol. 4, pp. 579-597,
2010.
J. G. Slootweg, et al, "General model for representing variable speed
wind turbines in power system dynamics simulations," IEEE
Transactions on Power Systems, vol. 18, pp. 144-151 2003.
N. G. Boulaxis, et al, "Wind Turbine Effect on The Voltage Profile of
Distribution Networks," Renewable Energy, 2002.
E. Muljadi and C. P. Butterfield, "Pitch-controlled variable-speed
wind turbine generation," IEEE Transactions on Industry Applications,
vol. 37, pp. 240-246, Jan/Feb 2001.
J. Kabouris and F. D. Kanellos, "Impacts of Large-Scale Wind
Penetration on Designing and Operation of Electric Power Systems,"
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, vol. 1, JULY
2010.
S.-K. Kim and E.-S. Kim, "PSCAD/EMTDC-Based Modeling and
Analysis of a Gearless Variable Speed Wind Turbine" IEEE
Transactions on Energy Conversion, vol. 22, pp. 421-430, June 2007.
G.
Abad,
et
al,
"Direct
Power
Control
of
Doubly-Fed-Induction-Generator-Based Wind Turbines Under
Unbalanced Grid Voltage," IEEE TRANSACTIONS ON POWER
ELECTRONICS, vol. 25, FEBRUARY 2010.
A. Abedini and H. Nikkhajoei, "Dynamic model and control of a
wind-turbine generator with energy storage," IET Renewable Power
Generation, vol. 5, 2011.
L. Chien-Hung and H. Yuan-Yih "Effect of Rotor Excitation Voltage
on Steady-State Stability and Maximum Output Power of a
Doubly-Fed Induction Generator," IEEE Transactions on Industrial
Electronics, vol. 58, pp. 1096 - 1109 April 2011.
P. Li, et al, "Development and simulation of dynamic control
strategies for wind farms," Published in IET Renewable Power
Generation, vol. 3, pp. 180–189, 2009.
L. Fan, et al. "Modeling of DFIG-Based Wind Farms for SSR
Analysis," IEEE TRANSACTIONS ON POWER DELIVERY, vol. 25,
OCTOBER 2010.
M. Rahimi and M. Parniani, "Transient Performance Improvement of
Wind Turbines With Doubly Fed Induction Generators Using
Nonlinear Control Strategy," IEEE TRANSACTIONS ON ENERGY
CONVERSION, vol. 25, JUNE 2010.
A. Luna, et al. "Simplified Modeling of a DFIG for Transient Studies
in Wind Power Applications," IEEE TRANSACTIONS ON
INDUSTRIAL ELECTRONICS, vol. 58, JANUARY 2011.
S. Li and S. Sinha, "A Simulation Analysis of Double-Fed Induction
Generators for Wind Energy Conversion Using PSpice," IEEE
Transaction on Energy Conversion Systems, vol. 32, 2006.
V. K. M. Tazil, R.C. Bansal, S. Kong, Z.Y. Dong, W. Freitas, H.D.
Mathur, "Three-phase doubly fed induction generators: an overview,"
IET Electric Power Applications, vol. 4, pp. 75–89, 2010.