J. Energy Power Sources
Vol. 2, No. 6, 2015, pp. 215-229
Received: April 15, 2015, Published: June 30, 2015
Journal of Energy
and Power Sources
www.ethanpublishing.com
Modeling and Performance of Wind Turbine Double
Output Induction Generator for Maximizing Output
Power
Haytham Gamal1 and Adel Shaltout2
1. Electrical Department, Faculty of Engineering, Modern Academy in Maadi, Egypt
2. Electrical Power and Machines Department, Faculty of Engineering, Cairo University, Egypt
Corresponding author: Haytham Gamal (hgamal@eng.modern-academy.edu.eg)
Abstract: A complete analysis of the operation of Double Output Induction Generator (DOIG) driven by variable speed wind turbine
and connected to utility grid is proposed, which is complicated by the fact that the region of interest is centered on the rotor and not in
the stator. This paper uses a hybrid model which retains the actual rotor phase variables but transforms the stator only to examine the
transient and steady state performance of a DOIG system. The use of the actual rotor state variables facilitates the detailed study of the
wind turbine DOIG system starting process. A computer program developed is used to examine the transient performance of DOIG to
maximizing the output power. Since the rotor excitation voltage affects the output power of a DOIG by controlling the firing angle of
the inverter in order to tract the maximum extracted mechanical power from the wind turbine at each wind speed. The results are
verified with the steady state model of DOIG that uses detailed expressions for stator power, rotor power, stator loss, rotor loss, and
electrical power as functions of the generator speed and the magnitude and phase angle of the rotor excitation voltage. Optimization
technique is also studied with the steady state model to determine the optimal rotor excitation voltage, which gives maximum output
power and minimum loss. Finally, the two control strategies results are compared.
Keywords: Double output induction generator (DOIG), wind turbine, maximum output power, renewable energy systems.
1. Introduction
The basic principles of operating an induction
machine as a grid connected generator are well
explained in literature [1-3]. In conventional use of an
induction generator, the machine has a short-circuited
rotor and is driven by a regulated source of mechanical
power. For such applications, the induction machine has
the advantages of allowing the use of a speed governor
mechanism simpler than that of a synchronous generator,
since the machine is able to produce electricity at a
constant frequency over a limited range of shaft speed.
Furthermore, when the generator is to be driven by an
unregulated source of mechanical power, such as a wind
turbine, it is advantageous to use an induction generator
as a Variable-Speed Constant-Frequency (VSCF) system
to maintain maximum power transfer conditions for
shaft speed variations over a wide range. This can be
achieved by the use of a converter cascade between the
slip-ring terminals and the utility grid to control the rotor
power. This scheme is called the DOIG, because power
can be tapped from both the stator and rotor circuits. The
use of a VSCF-DOIG as a wind turbine generator has
the following advantages [4]:
(1) It has no exciter, no automatic voltage regulator,
no synchronizer and no pitch angle control. Hence, it is
simple, cheap and easy to run;
(2) It is the only scheme known in which the
generator gives more than the rated power without
being overheated, because the power may be obtained
from both the stator and rotor terminals.
216
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
L =
Fig. 1 Schematic diagram of a slip energy recovery drive.
As the capital cost of wind energy is higher than the
conventional system, the objective is to maximize the
use of the available wind energy in order to maximize
the DOIG output power. This has been achieved by
employing a VSCF-DOIG with the proposed control
strategies.
2. System Description
The layout of the system under study is shown in Fig.
1, which comprises a VSCF-DOIG. The generator has
a slip-ring wound rotor which is connected to the utility
grid through an uncontrolled three-phase full-wave
phase-commutated rectifier bridge. This rectifies the
variable-frequency slip-ring energy and feeds it to a
controlled three-phase full-wave phase-commutated
six-pulse inverter in order to inject the slip power back
to the grid. The values of the parameters of the
induction generator are given in Appendix.
3. Induction Generator Model
A hybrid dq-abc model is considered for modeling
the induction generator. The stator of the induction
generator is modeled in the d-q reference frame
rotating with the rotor speed, while the rotor is modeled
in the direct phase reference frame (abc) [5-6]. The non
linear differential equations of the hybrid model can be
represented as follow:
[v] = [R] [i] + [L]p[i] +ωre [G] [i]
where
R`s
0
R = 0
0
0
0
R`s
0
0
0
0
0
Rr
0
0
0
0
0
Rr
0
0
0
0
0
Rr
(1)
Lrr
M
2
√3 M
2
Mr
M
2
√3 M
2
Mr
Mr
Lrr
Mr
Mr
Mr
Lrr
L`s
0
M
0
L`s
0
M
M
2
M
2
0
√3 M
2
√3 M
2
-L`s
0
`
G = Ls
0
M
0
0
0
0
0
0
0
0
0
0
-
-
-
√3 M √3 M
2
2
M
M
2
2
0
0
0
0
0
0
[v] = [vds`, vqs`, var, vbr, vcr]T
[i] = [ids`, iqs`, iar, ibr, icr]T
The abc stator terminal voltages are also transformed
to match the hybrid model and yields:
vds ` =
√3
vqs ` =
√3
√2
√2
n Vms cos( ωs t-θr )
(2)
n Vms sin( ωs t-θr )
(3)
ωs = 2Πf
(4)
dθr
(5)
dt
=ωr
The developed electromagnetic torque can be
obtained by the following equation [5]:
M
Tem =P (√3i`ds icr -ibr +3i`qs iar )
2
(6)
4. Three Phase Diode Bridge Rectifier
Modeling
Three phase bridge rectifiers are commonly used in
high power applications [7]. Fig. 2 shows a full wave
diode bridge rectifier. In this model, the effect of rotor
resistance and inductance are taken into consideration.
The presence of the rotor inductance cause that the
current cannot fall to zero immediately and the transfer
of the current (commutation) between diodes cannot
happen abruptly. The rotor reactance that is responsible
for the process is known as the commutating reactance.
As a result of the commutation phenomena, the output
voltage is reduced. Furthermore, the rotor resistance
leads to a further reduction in the output voltage. The
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
commutation period depends on the rotor inductance,
resistance, and the output current of the rectifier. In this
regards, the diode bridge rectifier should be analyzed
into the following three conducting modes of
operation:
• Mode 1: In this mode only two diodes conduct,
one from the upper half and the other from the lower
half;
• Mode 2: In this mode three diodes conduct, these
take place during the commutation period;
• Mode 3: In this mode four diodes conduct. This
mode occurs if the commutation period exceeds 60º in
a certain half and so a commutation takes place in the
other half before the commutation settle down in the
first one. This occurs rarely especially in slip energy
system [8], and so it is neglected.
4.1 Diode States
Referring to the diodes numbered in Fig. 2, the diode
bridge rectifier can have twelve possible conducting
states under the assumption that no more than three
diodes conduct simultaneously. The conduction states
are summarized in Table 1.
It is evident that there are two types of conduction
states. The first type is represented by the odd states
where only two diodes conduct simultaneously. On the
other hand, the second type is represented by the even
conduction states where three diodes conducts in these
states simultaneously under commutation overlap
conditions.
4.2 Conduction Logic
In the proposed system, the bridge rectifier is
connected to a star circuit as shown in Fig. 2. In each
state, the conduction logic can be defined by using the
phase voltages and the phase currents as shown in Fig. 3.
Since the sequence of the phase voltages and the phase
currents are reversed as the mode of operation changed
from sub-synchronous mode to super-synchronous
mode. This is due to the direction of the slip rotating
field of the rotor in the sub-synchronous mode is
opposite to its direction in the super-synchronous mode
as shown in Fig. 4. Therefore, two different conduction
logic tables must be used to decide the starting instant of
each conduction of the two modes of operation of the
induction machines; namely the motor mode
(sub-synchronous mode for case under study) and the
Fig. 2 Diode bridge rectifier fed by a rotor star circuit.
Table 1 Conduction states of the diodes in rectifier.
Conduction states
1
2
3
4
5
6
7
8
9
10
11
12
13
D1
ON
ON
OFF
OFF
OFF
OFF
OFF
OFF
OFF
ON
ON
ON
OFF
D2
OFF
ON
ON
ON
ON
ON
OFF
OFF
OFF
OFF
OFF
OFF
OFF
DIODES
D3
D4
OFF OFF
OFF OFF
OFF OFF
OFF ON
OFF ON
ON ON
ON ON
ON ON
ON OFF
ON OFF
OFF OFF
OFF OFF
OFF OFF
D5
OFF
OFF
OFF
OFF
OFF
OFF
OFF
ON
ON
ON
ON
ON
OFF
D6
ON
ON
ON
ON
OFF
OFF
OFF
OFF
OFF
OFF
OFF
ON
OFF
217
Fig. 3 Schematic diagram of conduction sequence.
218
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
generator mode (super-synchronous range for case
under study). In this regards, the decision on the starting
instant of each conduction state can be obtained by
checking the voltages and the currents of each mode of
operation. Tables 2-3 summarize the starting conditions
of each conduction state, in terms of the phase variables,
for motor and generator modes respectively.
Fig. 4 Schematic diagram of rotor voltage sequence
generation.
Table 2 Rectifier conduction logic with sub-synchronous
mode.
Conduction
states
1
2
3
4
5
6
7
8
9
10
11
12
Conduction logic for each state
|ibr| < im & vcr < 0 & vbar < 0 & idc ≥ 0
vbar ≥ 0 & iar < 0 & icr > 0 & vcr < 0 & idc ≥ 0
|iar| < im & vbr > 0 & vacr > 0 & idc ≥ 0
vacr ≤ 0 & ibr < 0 & icr > 0 & vbr > 0 & idc ≥ 0
|icr| < im & var < 0 & vcbr < 0 & idc ≥ 0
vcbr ≥ 0 & iar > 0 & ibr < 0 & var < 0 & idc ≥ 0
|ibr| < im & vcr > 0 & vbar > 0 & idc ≥ 0
vbar ≤ 0 & iar > 0 & icr < 0 & vcr > 0 & idc ≥ 0
|iar| < im & vbr < 0 & vacr < 0 & idc ≥ 0
vacr ≥ 0 & ibr > 0 & icr < 0 & vbr < 0 & idc ≥ 0
|icr| < im & var > 0 & vcbr > 0 & idc ≥ 0
vcbr ≤ 0 & iar < 0 & ibr > 0 & var > 0 & idc ≥ 0
where im is the holding current of the diode, and idc is
the DC link current of the rectifier.
5. Naturally Three Single Phase Bridge
Commutated Inverter Modeling
Three single phase bridge inverters [6] can be used
instead of a three phase bridge. The ripple factor of
three single phase bridge inverters during normal
operation is greater than that of a three phase bridge
inverter. The three single phase bridge inverters inject
third harmonic components of current into the supply.
However, triplen harmonics are absent with the
application of a three phase bridge inverter. Therefore
the primary of the recovery transformer is connected in
delta when using three single phase bridge inverters to
eliminate the third harmonic on supply side. The main
advantages that three single phase bridge inverters
have over a three phase bridge inverter are:
(1) The rate of change of voltage during
commutation is lower;
(2) The power factor is higher during freewheeling
operation;
(3) The effective voltage x current rating is lower.
The freewheeling technique can be applied by
adjusting the firing angles (α, and β) of thyristors
properly [9], and therefore requires a more complex
Table 3 Rectifier conduction logic with super-synchronous
mode.
Conduction
states
1
2
3
4
5
6
7
8
9
10
11
12
Conduction logic for each state
|ibr| < im & var > 0 & vcbr < 0 & idc ≥ 0
vbar ≤ 0 & ibr< 0 & icr > 0 & vcr < 0 & idc ≥ 0
|iar| < im & vcr < 0 & vbar > 0 & idc ≥ 0
vacr ≥ 0 & iar> 0 & ibr < 0 & vbr > 0 & idc ≥ 0
|icr| < im & vbr > 0 & vacr < 0 & idc ≥ 0
vcbr ≤ 0 & iar > 0 & icr < 0 & var < 0 & idc ≥ 0
|ibr| < im & var < 0 & vcbr > 0 & idc ≥ 0
vbar ≥ 0 & ibr> 0 & icr < 0 & vcr > 0 & idc ≥ 0
|iar| < im & vcr > 0 & vbar < 0 & idc ≥ 0
vacr ≤ 0 & iar < 0 & ibr >0 & vbr < 0 & idc ≥ 0
|icr| < im & vbr < 0 & vacr > 0 & idc ≥ 0
vcbr ≥ 0 & iar < 0 & icr > 0 & var > 0 & idc ≥ 0
Fig. 5 Schematic diagram of three single phase bridge
inverter.
219
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
control. A schematic diagram of three single phase
bridge inverters is shown in Fig. 5.
The voltage waveform at the dc link side of the
three phase recovery bridge inverter can be expressed
in the following form:
5Π
2Π
+α≤ ωs t≤
+α
π
3
3
-aT √3Vms cos ωs t-Π
-4Π
6
+α≤ωs t≤ +α
3
3
V i1 =
2Π
Π
+β
- +β<ωs t ≤
π
3
3
aT √3Vms cos ωs t8Π
5Π
6
+β< ωs t≤
+β
3
3
π
α ≤ ωs t ≤ π+α
-aT √3Vms cos ωs t+
2
Vi2 =
π
-π+β< ωs t ≤β
aT √3Vms cos ωs t+
2 π+β< ωs t ≤ 2π+β
7Π
4Π
+α≤ωs t≤
+α
7π
3
3
-aT √3Vms cos ωs t+
Π
-2Π
6
+α≤ωs t≤ +α
3
3
V i3 =
4Π
Π
+β<ωs t≤
+β
7π
3
3
aT √3Vms cos ωs t+
-2Π
-5Π
6
+β<ωs t≤
+β
3
3
The resultant voltage waveform can be calculated by
using Vi1, Vi2, and Vi3 as follows:
(7)
Vi = - (Vi1+ Vi2 + Vi3)
6. System Transition Models
Fig. 2 is an effective equivalent circuit of the rotor
rectifier fed with the rotor voltages var, vbr, and vcr
including the link inductance and the instantaneous
value of the inverter voltage Vi. In Table 1, conduction
state one corresponds to D1 and D6 conducting. On the
other hand, conducting state two corresponds to diodes
D1, D2, and D6 conducting which occurs when currents
commutates from rotor phase a to b. The duration of
the overlap depends on the machine parameters as well
as the operating speed [6]. After commutation is
completed, diodes D2 and D6 conduct. From Table 1, it
is clear that at any given state; most of the diodes do not
conduct which means that some part of the rotor is
non-conducting. Hence (1) can be simplified in any
given state by removing those circuits that are
non-conducting.
In this regards, the corresponding system transition
models for each of the twelve states with their
associated circuits and constrain are derived in [5].
7. Wind Turbine Modeling
The mechanical power from the wind turbine,
whose parameter are given in Appendix, is defined by
[10].
Pm = 0.5 ρ A Cp (λ, β) Vw3
(8)
where Pm is mechanical power output of the turbine in
Watt, ρ is the air density in kg m-3, A is the area swept
by the blades in m2, Vw is the wind velocity in m s-1,
and Cp is the power coefficient of the turbine, which is
related to the blade pitch angle β and the tip speed
ratio λ according to Eq. (9) [11].
Cp = c1
c2
1
=
λi
- c3 β - c4 e
c
λi
(- 5 )
+ c6 λ
(9)
where
λi
1
λ + 0.08 β
-
0.035
β3 + 1
(10)
and
λ=
R.ωt
Vw
(11)
where R is the blade length, ωt is the turbine angular
speed, and C1 to C6 are coefficients: C1 = 0.5176, C2 =
116, C3 = 0.4, C4 = 5, C5 = 21, C6 = 0.0068.
For a particular value of pitch angle, e.g., β = 0, the
mechanical power generated by the wind turbine at
different wind speed versus the turbine speed referred
to the generator side is shown in Fig. 6.
Fig. 6 Wind turbine mechanical power versus generator
speed.
8. Double Output Induction Generator
Operation
Electromagnetic Torque
Slip Power Extracted
Two modes of operation are possible; namely the
sub-synchronous mode and the super-synchronous
mode as shown in Fig. 7. Sub-synchronous speed range
is achieved by extraction of power from the rotor
terminals and returning it back to the supply for motor
mode, while for generator mode the sub-synchronous
speed range is achieved by injection of the power into
the rotor terminals. On the other hand, supersynchronous range is accomplished by injection of the
power into the rotor terminals for motor mode, while for
generator mode, super-synchronous range is
accomplished by extraction of power from the rotor
terminals and returning it back to the supply. This can be
explained by assuming that the electromagnetic torque is
constant, and then the air-gap power will be also
constant. So, for generator mode, to inject extra power to
the rotor, the electrical power converted from
mechanical power should be decreased, so, the
rotational speed should be also decreased to maintain the
electromagnetic torque constant that is why the
induction generator operates in the sub-synchronous
when absorbing power from the grid. For motor mode,
to inject extra power to the rotor, the electrical power
converted from mechanical power should be increased,
so, the rotational speed should be also increased to
maintain the electromagnetic torque constant that is why
the induction motor operates in the super-synchronous
when absorbing power from the grid.
On the other hand, for generator mode, to provide
extra power from the rotor, the electrical power
converted from mechanical power should be increased,
so, the rotational speed should be also increased to
maintain the electromagnetic torque constant that is why
the induction generator operates in the supersynchronous when delivering power from the rotor. For
motor mode, to provide extra power from the rotor, the
electrical power converted from mechanical power
should be decreased, so, the rotational speed should be
also decreased to maintain the electromagnetic torque
Slip Power Fed
ns
Slip Power Fed
Sub-synchronous Range
Motor Mode
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
Speed
Slip Power Extracted
Generator Mode
220
Super-synchronous Range
Fig. 7 Modes of operation of the induction machine.
constant that is why the induction motor operates in the
sub-synchronous when delivering power from the rotor.
The two modes of operation can be implemented by
using the dc-link converter, which can be treated as two
stage controlled ac to dc converters that are connected
back to back with an intermediate stage of a smoothing
inductor. One of the two converters operates in the
inversion mode, while the other operates in the
rectification mode. Obviously, the use of the two
controlled ac-dc converters can give a reversible
direction of power flow. Thus, the two modes of
operation are possible by this dc-link converter when it
is connected to the rotor terminals.
In this regards, when the power extracted from the
rotor terminals and returned back to the supply, the
converter that is connected to the rotor terminals should
operate in the rectification mode, while the other
converter that is connected to the matching transformer
at the supply side should operate in the inversion mode.
This process is reversed when the power is injected to
the rotor terminals, the converter which is connected to
the rotor terminals works in the inversion mode, while
the other converter operates in the rectification mode.
Although, Slip Energy Recovery System (SERS) can
be referred to the two modes, it is most commonly used
to refer to the super-synchronous speed range where
the energy is recovered back to the supply. Hence the
DOIG term is more suitable for the super-synchronous
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
speed range, where the power is output from both
terminals of the rotor and the stator.
SERS is most commonly used in the supersynchronous speed range with a much simpler and
cheaper dc-link converter; the controlled rectifier at the
rotor terminals is replaced by uncontrolled three phase
diode bridge rectifier as shown in Fig. 1. Thus, only the
super-synchronous range becomes possible. The rotor
circuit in the system under study is delivering only
electric power to the grid [12].
In the SERS shown in Fig. 1, the slip power is only
delivered to the grid from the rotor circuit, which leads
to sub-synchronous operation for motor mode and
super-synchronous operation for generator mode. Hence,
the rectifier conduction logic should also be changed as
shown in Tables 2-3 providing the fact that the induction
machine started as motor driving the wind turbine to
speed very close to ωs, then wind turbine mechanical
torque drive the induction machine above ωs, changing
the mode of operation to the generator mode.
9. Maximum Power
Strategy of DOIG
Tracking
Control
A simple control strategy is applied to a grid
connected wind driven system to facilitate harnessing
maximum power. The principles of this strategy are
demonstrated in a system which comprises a DOIG
driven by a variable-speed wind turbine as shown in
Fig. 1. This strategy is based on controlling the slip
power, which is extracted from the rotor circuits and
fed to the grid though a rectifier/inverter branch.
The firing angle of the inverter is used to control the
slip power and, hence, the operating point.
The objective of this control strategy is to regulate
the output power of the generator to force the turbine to
operate as follows:
(1) At low wind speeds, the wind turbine speed
must change with varying wind velocity in order to
achieve maximum extracted mechanical output power.
This can be done by adjusting the triggering angle of
the inverter to force the wind turbine to operate along
221
the maximum mechanical power line. In this case,
mechanical output power of the wind turbine which is
the generator input power does not exceed the rated
mechanical power of the turbine;
(2) At high wind speeds, the generator input power
exceeds the rated mechanical power of the turbine, so,
the induction generator must be operated at the rated
mechanical power in order to avoid generator overload.
This is done by adjusting the triggering angle of the
inverter to force the wind turbine to operate along the
rated mechanical power line.
10. Simulation Results
The simulation of the SERS shown in Fig. 1 with the
control strategy discussed above has been carried out.
The DOIG under study has been simulated at different
wind speeds, and the firing angle of the inverter has been
controlled at different wind speeds, in order to achieve
the desired objective. This is done by using a computer
program which has been developed to simulate the
performance of the DOIG. The state-space equations are
solved by numerical integration using the fourth order
Runge-kutta technique with appropriate initial
conditions and step length. The step length is chosen
very small to increase the accuracy of computation.
The system and control matrices in (1) must be
reformed at each step of integration depending on the
conducting state satisfied. The integration is done at
each step to calculate the currents, the speed, the rotor
voltage, and the torque of the induction machine, and
the results are stored.
Different cases are studied to verify the control
strategy stated above and simulation results are as
follows:
10.1 For Low Wind Speed
To track the maximum mechanical power of the
wind turbine at wind speed equals nine meter per
second, the firing angle of the inverter should be
adjusted at 106.3º. Results obtained for this operating
condition is shown in the following Figs. 8-14.
222
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
Fig. 8 Stator phase current versus time for 9 m sec-1.
Fig. 12 Electromagnetic torque versus time for 9 m sec-1.
Fig. 9 Rotor phase current versus time for 9 m sec-1.
Fig. 13 Generator rotational speed versus time for 9 m
sec-1.
Fig. 10 Rotor phase voltage versus time for 9 m sec-1.
Fig. 14 Prime torque of the wind turbine versus time for 9
m sec-1.
10.2 For High Wind Speed
Fig. 11 DC-link current versus time for 9 m sec-1.
When the wind velocity is high and the generator
input power exceeds the rated mechanical power of the
turbine, the DOIG must be operated at the rated
mechanical power mode in order to avoid generator
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
Fig. 15 Stator phase current versus time for 10.05 m sec-1.
223
Fig. 19 Electromagnetic torque versus time for 10.05 m
sec-1.
Fig. 16 Rotor phase current versus time for 10.05 m sec-1.
Fig. 20 Generator rotational speed versus time for 10.05 m
sec-1.
Fig. 17 Rotor phase voltage versus time for 10.05 m sec-1.
Fig. 21 Prime torque of the wind turbine versus time for
10.05 m sec-1.
Fig. 18 DC-link current versus time for 10.05 m sec-1.
overload. So, for Vw = 10.05 m sec-1, the firing angle of
the inverter should be adjusted at 144.3º to operate at
the rated mechanical power of the wind turbine.
Results obtained for this operating condition are shown
in the Figs. 15-21.
Based on the simulated result in Figs. 8-21 presented
above, the following observations are in order:
224
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
(1) The objective to maximize the use of the
available wind power is achieved by extracting the
maximum mechanical power output of the wind
turbine at different wind speed up to its rated
mechanical power;
(2) A simple control strategy is used to achieve this
objective by controlling the trigger angle of the
thyristor in the inverter in order to control the slip
power extracted from the rotor circuit by:
Fig. 22 Steady-state equivalent circuit of a DFIG.
• Forcing the wind turbine to operate in the
maximum mechanical power line until reaching the
rated power for low wind speed;
both stator and rotor windings. The stator output power
Ps and the rotor output power Pr is derived from the
steady-state equivalent circuit [13-14] of a DFIG in Fig.
• Forcing the wind turbine to operate in the rated
mechanical power line for high wind speed.
(3) The DOIG operates in the super-synchronous
mode, so the rotational speed is increased when the
wind speed is increased;
(4) From the electromagnetic torque curves, it is
observed that the induction machine starts as motor in
the sub-synchronous mode driving the wind turbine
from zero speed till the speed becomes very close to the
synchronous speed, and then the wind turbine
mechanical torque helps the induction machine in
exceeding the synchronous speed and acts a generator
in the super-synchronous mode;
(5) There is a period of zero torque. This occurs
when the mode of operation changes from motor to
generator. In the system under study the power cannot
fed to the rotor and then the torque becomes zero as the
speed reached the no load motor speed. The zero torque
is sustained up to the no load generator speed;
(6) The dc-link current behavior is similar to that of
the electromagnetic torque, but its direction is not
reversed as the torque since the slip power is extracted
from the rotor circuit only.
22, where Vs is the stator voltage, Vr is the rotor
excitation voltage, Is is the stator current, Ir is the rotor
current, E is the air-gap voltage, Rs is the stator
resistance, Rr is the rotor resistance, Xls is the stator
leakage reactance, Xlr is the rotor leakage reactance, Xm
is the magnetizing reactance, Xs (= Xls + Xm) is the stator
reactance, Xr (= Xlr + Xm) is the rotor reactance, s (= (ωs ωr)/ωs) is the slip, ωs is the stator synchronous speed, ωr
is the rotor speed, Pm is the mechanical power, and Pe is
the electrical power converted from mechanical power.
11. Double Fed Induction Generator Steady
State Model
The mechanical power from the wind turbine is
converted by the double fed induction generator (DFIG)
into electrical power which is delivered to the grid from
12. Steady-State Model Verification
The dynamic model results of DOIG which
presented in section x is used to verify steady-state
model described above. The results of the steady state
model are compared, and summarized in Table 4. From
which, it is concluded that the results of the two model
are very close although the steady state model ignored
the rectifier commutation overlap and inverter
harmonics. This justifies the use of the steady-state
model for the maximum output power optimization.
In this section, it is assumed that the power can be fed
or extracted from the rotor terminals. This will allow the
DFIG to generate power at the sub-synchronous or the
super-synchronous speed. This is assumed to provide
more general results. The control strategy described in
section x is based the maximum power extraction.
However, this does not necessarily mean maximum
output. The maximum output which is the main objective
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
225
Table 4 Comparison between dynamic model and steady state results.
Parameter
Slip
Speed
Stator current
Rotor current
Pcus
Pcur
Pem
Pout
Dynamic model
-0.1575
181.8256
12.5071
16.8385
221.8410
162.4655
6925.5
6541.2
Vw = 9 m s-1
Steady state model
-0.1577
181.8511
13.2743
16.2217
249.8940
150.7813
6925.5
6524.8
of this paper is achieved by controlling the injected rotor
voltage to minimize the generator copper losses which
ensures, in collaboration with the maximum extracted
power, a maximum output power.
12. Maximum Power Output of DFIG
The DFIG powers and currents are affected to a large
extent with rotor excitation voltage magnitude and angle
[15-16]. So, the objective now is to find proper values
for Vr and Ф which gives the maximum output power,
without exceeding the rated condition of the DFIG [17].
Vw = 10.05 m s-1
Dynamic model
Steady state model
-0.3825
-0.3824
217.1616
217.1469
12.6955
14.3473
17.4917
18.6552
228.5748
291.9275
175.3155
199.4144
9499.7
9500
9095.8
9008.7
• Vr ≤ Vr,max
• Is ≤ Is,max
• Ir ≤ Ir,max
After the optimal rotor excitation voltage had been
determined, the powers Ps, Pr and Pout, the losses (Ps,loss
+ Pr,loss), and the currents Is and Ir were computed. The
results are shown in the Figs. 23-28.
12.1 Maximum Extracted Power Tracking Mode
The objective of maximum power output during this
mode of operation is achieved in two steps:
(1) Ensure that the wind turbine is tracking the
maximum power line to extract the maximum available
power. In this regard, it should be noted that:
• Active power is fed to the rotor terminals in the
sub-synchronous range;
• Active power is extracted out of the rotor
terminals at the super-synchronous range.
(2) While maintaining the wind turbine operating at
the maximum extracting power point, the rotor voltage
is controlled to minimize the induction generator losses.
The optimization technique of the Matlab [11] is
used to determine the magnitude and the phase angle of
the optimum rotor excitation voltage according to the
following constraints.
Maximize Ps + Pr
(12)
subject to the following constraints:
• Pe = Pm,max
Fig. 23 Optimal rotor excitation voltage magnitude versus
generator slip.
Fig. 24 Optimal rotor excitation voltage phase angle versus
generator slip.
226
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
Fig. 25 Stator real power and rotor real power versus
generator slip.
Fig. 28 Stator current and rotor current versus generator
slip.
(2) The rotor absorbs real power from the grid (Pr <
0) when the wind speed and the rotor speed are low and
delivers real power to the grid (Pr > 0) when the wind
speed and the rotor speed are high.
12.2 Rated Mechanical Power Mode
Fig. 26 Total output power versus generator slip.
Fig. 27 Total power loss versus generator slip.
Based on the results in the figures, the following
observations are in order.
(1) The magnitude Vropt and phase angle Фopt for the
optimal rotor excitation voltage vary with rotor speed
to a great extent.
When the DFIG is operated at this mode, the
electrical power is fixed at the corresponding rated
mechanical power. In this case, the optimal rotor
excitation voltage can be determined by solving the
following optimization problem [11]:
Minimize Ps,loss + Pr,loss
(13)
subject to the following constraints:
• Pe = Pm,rated
• Vr ≤ Vr,max
• Is ≤ Is,max
• Ir ≤ Ir,max
After the optimal rotor excitation voltage had been
determined, the powers Ps, Pr and Pout, the losses (Ps,loss
+ Pr,loss), and the currents Is and Ir were computed. The
results are shown in the Figs. 29-34.
In this mode, the input mechanical power is kept
constant at its rated value. The optimum rotor
excitation voltage is calculated to minimize the total
power losses. This allows an increase in the total output
power. In this regard, this output power may exceed the
rated power of the stator winding, since it is delivered
from both stator and rotor windings.
Finally, the output power when controlling both Vr and
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
227
Fig. 29 Optimal rotor excitation voltage magnitude versus
generator slip.
Fig. 32 Total output power versus generator slip.
Fig. 30 Optimal rotor excitation voltage phase angle versus
generator slip.
Fig. 33 Total power loss versus generator slip.
Fig. 31 Stator real power and rotor real power versus
generator slip.
Fig. 34 Stator current and rotor current versus generator
slip.
Ф is maximized and becomes greater than the output
power when controlling Vr only at all wind speeds. A
comparison between the two control strategies is shown
in Table 5 for low wind speed (sub-synchronous) and
high wind speed (super-synchronous).
13. Conclusions
Modeling and performance of the DOIG has been
studied to predict the detailed operation of the DOIG
both in transient and steady state. The hybrid model
228
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
Table 5 Comparison between two control strategies.
Parameter
Slip
Speed
Stator current
Rotor current
Pcus
Pcur
Pem
Pout
Vw = 6 m s-1
Maximum tracking
0.2282
121.2341
10.0982
13.1127
144.6174
29.8034
2052
1877.6
Optimum operation
0.2282
121.2341
6.6763
10.0685
63.2117
58.0872
2052
1930.8
combines the well known d-q and the phase variable
models, which retains the actual rotor state variables.
The actual rotor variables are used to decide the
starting instant of each conduction of the rectifier for
the two modes of operation of the induction machines;
namely the motor mode and the generator mode in
order to include the rectifier commutation and
harmonics. The two modes of operation are required as
the induction machine starts as motor driving the wind
turbine from zero speed till the speed becomes very
close to the synchronous speed, and then the wind
turbine mechanical torque helps the induction machine
in exceeding this synchronous speed and acts a
generator.
The results obtained from the dynamic model are
verified by using steady state model, and it is
concluded that the results are very close.
Two control strategies are used to maximize the
output power for a DOIG driven with wind turbine. The
first one adjust the triggering angle of the inverter to
control the magnitude of the rotor excitation voltage
only, in order to extract the maximum mechanical
power of the wind turbine at each wind speed. But it is
concluded that this is not sufficient to obtain maximum
power output of the DOIG. The other control strategy is
based on the fact that the rotor excitation voltage has
two degrees of freedom; namely magnitude and phase
angle. Therefore, it is modulated at each wind speed to
maximize the extracted mechanical power and to
minimize the generator copper losses. Comparing the
results obtained from the two control strategies, it is
concluded that the output power is increased with the
Vw = 10.1 m s-1
Maximum tracking
-0.4266
224.0955
14.0841
18.0713
281.3134
187.125
9500
9031.6
Optimum operation
-0.4266
224.0955
10.7035
19.2022
162.473
211.2781
9500
9126.2
second control strategy, taken into consideration the
complicity and the expense of this control system
compared with the first one.
Finally, it is concluded that if full converters are used
at both sides power flows in and out of the rotor circuits
and, thus, the generator can be operated at all speeds
above and below the synchronous speed. Furthermore,
the system can be optimized to generate maximum
power. However, a less expensive system which allows
power flow in one direction may be used but it
generates power only at super-synchronous speeds and
the output power cannot be maximizes.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Y. Lei, A. Mullane, G. Lightbody, R. Yacamini, Modeling
of the wind turbine with a doubly fed induction generator
for grid integration studies, IEEE Trans. on Energy conv.
21 (1) (2006) 257-264.
S. Yuvarajan, L. Fan, A doubly-fed induction
generator-based wind generation system with quasi-sine
rotor injection, Journal of Power Sources 184 (2008)
325-330.
P. Ledesma, J. Usaola, Doubly fed induction generator
model for transient stability analysis, IEEE Trans. on
Energy conv. 20 (2) (2005) 388-397.
A.A. Shaltout, A.F. El-Ramahi, Maximum power
tracking for a wind driven induction generator connected
to a utility network, Applied Energy 52 (1995) 243-253.
E. Akpinar, P. Pillay, Modeling and performance of slip
energy recovery induction motor drives, IEEE Trans. on
Energy conv. 5 (1) (1990) 203-210.
E. Akpinar, P. Pillay, A computer program to predict the
performance of slip energy recovery induction motor
drives, IEEE Trans. on Energy conv. 5 (2) (1990) 357-365.
M.H. Rashid, Power Electronics Handbook, Academic
Press, Canada, 2001.
Modeling and Performance of Wind Turbine Double Output Induction
Generator for Maximizing Output Power
[8]
[9]
[10]
[11]
[12]
[13]
E. Akpinar, P. Pillay, A. Ersak, Calculation of the overlap
angle in slip energy recovery drives using a d,q/abc model,
IEEE Trans. on Energy Conv. 8 (2) (1993) 229-235.
W. Drury, W. Farrer, B.L. Jones, Performance of thyristor
bridge converters employing flywheeling, in: IEE Proc.
Electric Power Application, vol. 127, no. 4, pp. 268-276,
July 1980.
S.N. Bhadra, D. Kastha, S. Baberjee, Wind Electrical
Systems, Manzar Khan, Oxford University Press, 2005.
Matlab help, R2010.
I. Boldea, The Electric Generators Handbook—Variable
Speed Generators, Taylor and Francis Group, LLC, USA,
2006.
H. Gamal, A. Shaltout, Maximum output power of wind
turbine doubly fed induction generator connected to utility
grid, in: International Conference on Renewable Energy:
Generation and Applications, UAE, March 4-7, 2012.
[14] M.R. Islam, Y. Guo, J.G. Zhu, Steady state characteristic
simulation of DFIG for wind power system, in: 6th Int.
Conf. on Elect. Comp. Eng., Dhaka, Bangladesh, pp.
151-154, Dec. 2010.
[15] S. Li, T.A. Haskew, J. Jackson, Integrated power
characteristic study of DFIG and its frequency converter in
wind power generation, Renewable Energy 35 (2010)
42-51.
[16] H. Gamal, Maximum output power of wind turbine doubly
fed induction generator connected to utility grid, Ph.D.
Dissertation, Dept. Elect. Eng., Cairo Univ., Giza, Egypt,
2012.
[17] B.A. Chen, T.K. Lu, Y.Y. Hsu, W.L. Chen, Zh.C. Lee, An
analytical approach to maximum power tracking and loss
minimization of a doubly fed induction generator
considering core loss, IEEE Trans. on Energy conv. 27 (2)
(2012) 449-456.
Appendix
A. Induction Generator Parameters
Nameplate data;
Three phase, slip ring induction machine, 7.5 kW, 50 Hz, Y- connected, four poles;
Stator: 415 V, 14.2 A.
Rotor: 52.25 V, 25.8182 A.
The following are the machine parameters referred to the rotor side:
Rs` = 0.143 Ω;
Rr = 0.191 Ω;
ls` = 0.0018 H;
lr = 0.0018 H;
Mm = 0.0235 H;
Turn ratio (Nr/Ns) =0.55;
Rf = 0.2 Ω;
Lf = 0.039 H;
aT = 0.1.
B Wind Turbine Parameters
Power = 9.5 kW;
Radius = 3.2 m;
Rated rotational speed = 242 rpm;
Rated wind speed = 10 m s-1;
Cut-in speed = 5 m s-1;
Maximum speed = 11 m s-1;
Gear box = 8.
229