International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
Fixed-Pitch Wind Turbine Interfaced Self-Excited Multi-Phase Induction
Generator for Stand-Alone Renewable Power Generation-An Operational
Review
Alok Kumar Mohanty
Department of Electrical and Electronics Engineering
National Institute of technology, Jamshedpur, Jharkhand, India, 831014
Correspondence Author
K B Yadav
Department of Electrical and Electronics Engineering
National Institute of technology, Jamshedpur, Jharkhand, India, 831014
of this, the investigation of the self-excited induction
generator has gained importance as it is particularly for
renewable power generation applications [1]. The application
of self-excited induction generator due to its decreased unit
cost, simple to operate and ease in maintaining is most suited
in renewable energy systems. The advantages of self excited
induction generator are no separate source for excitation is
required, protection from overload, good transient
performance, simple and robust construction and ease in
maintenance.
In comparison with three phase machines, multi-phase
machines are considered as an alternative for variable speed
applications. As the rating of power is increased and high
reliability requirements, research in the area of multi-phase
machines [2, 3, 4] have been increasing. Machines having
more than three phases as in a conventional machine are
referred to as a high phase order machine on multiphase
machines. Multiphase machines have certain advantages over
the conventional three phase machines such as capability to
start and run even one or two of its stator phase open or short
circuited, lower current per phase without increasing voltage
per phase, increased power in the same frame, for a given
machine output power utilization of more than three phase
enables splitting of power across larger number of inverter
legs. Additional number of phase added to the machine also
brings additional freedom for improvements in the system.
Basically a multiphase induction machine can have two
different types of configurations.
Split phase electrical machines-Split phase electrical
machines consist of two similar stator windings sharing the
same magnetic circuit. Such a construction has made it
possible to extend the power range by sharing the total power
into two parts. Usually a split phase machine is built by
splitting the phase belt of a conventional three phase machine
into two equal parts with phase separation of 30 electrical.
By using this arrangement for the same air gap flux, the
inverter voltage can be reduced by half as compared to the
three phase machines since the number of turns is reduced.
Dual stator electrical machines-This type of electrical
machines consists of two separate independent stator windings
sharing the same magnetic circuit. Six different voltage
magnitudes could be used for each winding group. One set of
the stator winding is used for electromechanical power
Abstract
In this paper the performance of a standalone self excited
induction generator operating in six-phase mode undergoing
transient have been analyzed. The multi-phase machine used
in the analysis is operating in six-phase mode which is driven
by a fixed-pitch wind turbine. The analysis made in this paper
constitutes the turbine model, six-phase self excited induction
generator model and the behavior of the machine when is
subjected to different types of loads when they are connected
to the two three phase winding sets in the machine. The
models for the analysis have been made in an arbitrary
reference frame. The results obtained in the simulation
analysis shows good functioning of the system under various
loading conditions which are quite acceptable for a wide range
of loads in remote areas.
Keywords: Multi-phase, Isolated, Self-excited Induction
Generator, Wind
INTRODUCTION
The generation of pollution less electrical power has now-adays become the main aim of the experts in the field of
electrical power generation. Due to rapid depletion of fossil
fuels aid the priority switching over to the renewable and
pollution free energies such as solar, wind etc amid which
wind energy is considered as the most efficient and wide
spread source of energy as wind is a free, clean and
inexhaustible in nature. Huge capital costs and the uncertainty
in the availability of wind had placed wind power generation
have placed wind power at an economic unfavorable position.
In the last five decades methods for electrical power
generation by employing hydro and wind energy and
technology for such alternate systems for power generations
have been proposed. In recent time wind energy is drawing
great attention in the per generation sector. If the available
wind energy could be adequately captured then the problems
of pollution and unavailability of fossil fuel resources could
be sorted out. These facts give the motivation of setting up of
wind power generation system which would have better
performance and efficiency. As there is an increase in demand
of energy demand during the last few decades, the use of
renewable energy sources has become essential and as a result
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
conversion while the second set of stator winding can be used
for excitation purpose. In dual stator electrical machines, the
power can be extended without the need to use multilevel
converters.
In a conventional three phase machine, the conductors are
distributed in slots symmetrically for each phase group and
the conductors belonging to each phase group are series
whereas in a multiphase induction machine we subdivide each
phase group of a usual three phase machine into equal
subgroups by disconnecting the series connection of the
conductors. More number of three phase groups can be
obtained from the same machine. In this way multi-phase
machine such as six-phase, nine-phase, twelve-phase, fifteenphase, and eighteen-phase can be produced from a three phase
machine by subdividing the phase groups into two, three, four
subgroups respectively.
In this paper the performance of a standalone self-excited
induction generator operating in six-phase mode driven by
wind power when subjected to different types of loads under
different conditions have been analyzed. The analysis includes
the modeling of wind turbine, a multi-phase induction
generator, modeling of the excitation capacitor and the
modeling of load impedance respectively. The performance of
the machine is analyzed when fed to resistive, resistiveinductive and resistive-inductive-capacitive loads respectively
when they are connected to both the three phase windings sets
of the six-phase machine. Different constraints taken in to
consideration during the analysis are variation in wind speed,
variation in excitation and load and accordingly the effect on
generated voltage and current have been analyzed.
Substituting equation, we get
1
2
(4)
Then the ratio of wind power extracted by the wind turbine to
the total wind power is the dimensionless power coefficient
Cp, which will also effects the power extracted from wind. So
the equation can be written as
1
2
(5)
1
П
2
(6)
Where
D is the sweep diameter of the wind turbine.
This is the total wind power entering the wind turbine. This
calculation of power developed from a wind turbine is an
idealized one-dimensional analysis where the flow velocity is
assumed to be uniform across the rotor blades, the air is
incompressible and there is no turbulence where flow is in
viscid (having zero viscosity). The volume of air entering the
wind turbine should be equal to the volume of air leaving the
wind turbine because there is no storage of air in the wind
turbine. As a result volume flow rate per second, Q, remains
constant, which means the product of A and V remains
constant. Hence when the wind leaves the wind turbine, its
speed decreases and expands to cover more area [5, 6, 7]. The
coefficient of power of a wind turbine is a measurement of
how efficiently the wind turbine converts the energy in the
wind into electricity. The coefficient of power at a given wind
speed can be obtained by dividing the electricity produced by
the total energy available in the wind at that speed. The
maximum value of power coefficient Cp gives the maximum
power absorbed by the wind turbine. In practical designs, the
maximum achievable Cp is below 0.5 for high speed, two
blade wind turbines, and between 0.2 and 0.4 for slow speed
turbines with more blades.
MODELING OF WIND TURBINE
The developed model of wind turbine in this paper has been
designed taking the actual parameters of the turbine in to
consideration. A fixed-pitch wind turbine has been used for
the analysis hence the pith angle of the turbine was set to zero.
As wind is the movement of air, it possesses kinetic energy.
To convert this kinetic energy of the wind to electrical energy
in wind energy conversion system the turbine captures the
kinetic energy of the wind and then drives the rotor of a self
excited induction generator. The kinetic energy possessed by
the wind is given by
1
2
(1)
m is the mass of the air in Kg and V is the speed of air in
m/sec.
The power in wind is calculated as flux of the kinetic energy
per unit area in a given time which is expressed as
1
1
2
2
(2)
Where m is the mass flow rate of air per second, in kg/s, and it
can be expresses in terms of the density of air (ρ in kg/m ) and
air volume flow rate per second (Q in m /s) as given below
m = ρ Q = ρ AV
(3)
Where A-is the area swept by the blades of the wind turbine,
in m2
TIP SPEED RATIO
A tip speed ratio TSR is simply the rate at which the ends of
the blades of the wind turbine turn (tangential speed) in
comparison to how fast the wind is blowing. The tip speed
ratio TSR is expressed as:
TSR (λ) =
(7)
Where
Vm-tangential speed of the blades at the tips
ɷT-angular velocity of the wind turbine
r-Radius of the wind turbine
Vw-Undisturbed wind speed in the site.
The tip speed ratio dictates the operating condition of a
turbine as it takes into account the wind created by the
rotation of the rotor blades. As the wind speed changes, the tip
speed ratio and the power coefficient will vary. The power
coefficient characteristic has single maximum at a specific
value of tip speed ratio. Therefore if the wind turbine is
operating at constant speed then the power coefficient will be
maximum only at one wind speed. The curve between power
coefficient and tip speed ratio is shown in the Figure1.
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
Figure 1: Power coefficient characteristics of wind energy
conversion system
Figure 2: Turbine speed versus turbine power characteristics
The polynomial relation between Cp and λ at particular pitch
angle for considered wind turbine [14] is represented by
equation.
,
In a wind power system typically the wind turbine starts (cut
in speed) when the speed of the wind exceeds 4-5m/s, and is
shut down at speeds beyond 25 to 30m/s. Between this
interval the turbine can operate in the optimum constant Cp
region, the speed-limited region or the power limited region.
This design choice was made in order to limit the strength and
therefore the weight and cost of the components of the wind
turbine [8, 9]. The developed wind turbine model is shown in
Figure 3.The Cp curve required for this analysis was
developed in Matlab and the model is shown in Figure 4.
During the analysis the speed of the wind is considered to be
equal to or less then rated speed of the wind and the pitch
angle (β) of the turbine is assumed to be zero as it is a fixedpitch wind turbine.
+
(8)
Where
C1=0.5176, C2=116, C3=0.4, C4=5, C5=21 and C6=0.0068.
The power characteristics is given by
116
0.5
0.5176
116 0.035 5
.
0.0068
(9)
TORQUE DEVELOPED
The torque developed is given as
116
0.5
0.5176
116
.
0.035
5
0.0068
(10)
Figure 2 shows the output power versus speed characteristics
curve of a typical wind turbine for various wind speeds.
Figure 3: Simulation of wind turbine model
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
Figure 4: Simulation of CP evaluation in a wind turbine model
MODELING OF A MULTI-PHASE (SIX-PHASE) SEIG
The schematic diagram of the basic two-pole six-phase
induction generator is discussed in [10, 11, 12]. A Six phase
induction generator consists of two stator winding sets namely
abc and 123, whose magnetic axes are displaced by an
arbitrary angle α. The windings of each three-phase set are
uniformly distributed and have axes that are displaced
1200apart. The three-phase rotor windings ar, br, cr a s
Figure 6: Circuit representation self excited induction
generator in six phase operation
For the development of model of the six-phase machine
operating in generating mode the following differential
equations are derived from the equivalent circuit of the
machine. In the above equivalent circuit applying KVL
equations we get the following voltage equations.
=
+ɷ
(11)
=
+ɷ
(12)
=
+ɷ
(13)
=
+ɷ
(14)
-ɷ
ɷ
0
(15)
+ɷ
ɷ
0
(16)
Where is the reference frame speed, is the rotor speed. In
this analysis the rotor quantities are referred to stator.
The flux linkage expressions in terms of currents obtained
from the equivalent circuit.
s h o wn i n F i g u r e 5 are also sinusoidally distributed and
has axes that are displaced by 1200.
Figure 5: Phasor diagram representation of stator and rotor
windings of six-phase induction generator
(17)
=
The equations for the self excited induction generator
operating in six phase mode, describes the behavior of a
multi-phase machine, it is assumed that the neutral of both
the stator winding sets are separate so that if a fault occurs in
one set of the stator windings it does not propagate to the
other set. The following voltage equations are written for a
multi-phase induction machine as shown in equivalent circuit
of the machine in Figure 6.
(18)
=
(19)
=
(20)
=
(21)
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
=
+
-
]
= [
+
-
]
(41)
is not a constant but a
The magnetizing inductance
function which depends on the instantaneous value of
given by
=function ( ). During
magnetizing current
is
simulation, in each step, the magnetizing inductance
. The
updated as a function of the magnetizing current
magnetizing current is represented by equation
=
(42)
is calculated from the
The magnetizing inductance
magnetizing characteristics fourth order polynomial for the
test machine . The 4th order polynomial is arrived at, by
applying curve fit technique to the relationship between
and ,obtained by performing synchronous speed test on
the test induction machine.
+
(43)
Where , . , are constants values
The torque balance equation is expressed as the derivative of
the speed
(24)
(25)
= [
+
]
-
(26)
=
]
(27)
=
]
(28)
Substituting the values of the currents obtained in the
equation(23) to (28) in the voltage equations (11) to (16) the
following expressions are obtained.
=∫{
+
+
}
(29)
=∫{
+
+
+
2
}
(44)
(30)
=∫{
+
1
+
MODELING OF EXCITATION CAPACITANCE
The excitation system of the six-phase machine introduces
the following state equations which uses d-q components of
the stator voltages as state variables in the equivalent circuit.
}
(31)
=∫{
+
+
+
=
(45)
-
+
=
}
=∫{-
-
+
=
}
+
=
]
+
]
MODELING OF LOAD IMPEDANCES
An induction generator is made self-excited by providing the
magnetizing reactive power provided by the capacitor bank.
The current expressions for balanced resistive load can be
expressed as
(36)
]
(37)
1
(48)
(35)
= [
(47)
(34)
= [
(46)
(33)
1
-
}
(32)
=∫{
2
(40)
Where is the moment of inertia, P is is the number of poles,
is the shaft torque.
(23)
= [
1
=
(22)
Solving this equations (17-22) for obtaining current equations
= [
+
]
1
(49)
(38)
The torque can be computed as a function of q and d axes
stator and rotor currents and represented in equation
= 2 32
(39)
The rotor equation is expressed as
(50)
Where R is the resistive load.
The load impedance model for RLC load expressed in
arbitrary reference frame is as follows
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
=
(51)
=
(52)
=
(53)
=
(54)
DEVELOPMENT OF FIXED-PITCH BASED WIND
TURBINE SPSEIG MODEL
The wind turbine acts as a prime mover for the multi-phase
induction machine and both are being coupled through a gear
box. The model of wind turbine based induction generator
operating in multi-phase mode is implemented in simulink
platform by considering the above stated equations and the
flow chart as shown in Figure 7. Initiation of the machine is
based on the residual magnetism residing in rotor circuit and
voltage starts building up with the assistance of reactive
power provided by the bank of capacitors. Loads are to be
connected to the machine only after the machine has attained
its steady state voltage values. The Simulation model of wind
energy conversion system employing six-phase self-excited
induction generator is shown in Figure 8.The simulation block
for magnetic induction and torque estimation block is shown
in Figure 9 and 10 respectively
Figure 8: Simulation model of wind energy conversion
system employing six-phase self-excited induction generator
Figure 9: Simulation model of magnetic induction block
Figure 10: Simulation model of torque estimation block
RESULTS AND DISCUSSIONS
The simulation model for the wind energy conversion system
employing a six-phase self excited induction generator is
shown in the Figure8.The blocks made for the machine
include fixed-pitch wind turbine block, six-phase machine
block, magnetic induction block, torque block and the load
block. The dynamic response of the system is analyzed of the
SPSEIG driven by wind turbine in MATLAB platform when
the machine is subjected to balanced and unbalanced loads.
The data of the machine used for the simulation model are
given in the Appendix.
Figure 7: Flow chart for dynamics of wind turbine driven
SPSEIG model
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
Build-up of voltage and current when excited by different
capacitances under no load condition
Figure 11 and 12 shows the voltage and current build up of
the induction machine under no load condition when the
machine is excited under different excitation capacitances
values. In the first case the machine is excited by 40µF
capacitance as a result the voltage build up is much faster. In
the second case machine is excited by 30µF capacitance. It is
observed that the magnitude of steady state voltage attained
by the system is more when the machine is excited by larger
values of excitation capacitance values. The excitation current
is depicted in the figure and it is observed that the magnitude
of current increases with the increase in capacitance values.
Figure 12: Phase voltages of abc and 123 sets and current
response under 30µF capacitor excitations at no-load
Voltage and current when the machine is subjected to
resistive load
In this mode of operation, at time t = 0.3s the machine is
loaded by a load of R = 200 ohm with a c-bank connected
across both the three-phase winding sets abc and 123
respectively. The results are shown in Figure.The terminal
voltage has decreased from 240 volts to 200 when the
machine is subjected to load at 0.3 seconds. The effect of the
decrease in terminal voltage will cause a decrease in the
capacitor current; this further affects the voltage regulation of
the generator.
Figure 11: Phase voltages of abc and 123 sets and current
response under 40µF capacitor excitations at no-load
Figure 13: Phase voltage when the machine is subjected to
resistive load
Figure 14: Phase current when the machine is subjected to
resistive load
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
Voltage and current when the machine is subjected to
resistive-inductive load
At t = 0 s, a capacitor with capacitance 40μF is connected
across both the winding terminals of the induction generator
without any load, and voltage is generated. The load is
switched on at t = 0.5 seconds at R=200Ω and L=0.07H.It is
observed that the terminal voltage is reduced by bigger value
as shown in Figure 15. RL loading operation causes a poor
voltage characteristic of the SPSEIG. This is due to the main
disadvantage of this generator and can be explained as
resulting from under excitation of the machine. In detail, the
connection of the load causes the reactive power absorbed by
the load and by the leakage reactance of the generator to
increase. On the other hand, it engenders some voltage drop in
the stator windings, which consequently causes the voltage
across the excitation capacitors also to decrease. This
reduction in the reactive power produced by the SEIG, in
addition to the increase of the demand of reactive power,
constrains the SEIG to operate with weak excitation and thus,
with lower output voltage.
Figure 16: Phase voltages in abc and 123 sets when the
machine is subjected to RLC load
Figure 17: Phase currents in abc and 123 sets when the
machine is subjected to RLC load
Figure 15: Phase voltage and current when the machine is
subjected to RL load
CONCLUSION
In this paper model of a wind turbine and six-phase induction
generator has been developed. The machine functionality
when subjected to different types of load at different
excitation capacitance conditions were investigated. The
proposed model is found suitable for studying the machine
performance under different conditions. The main aim of this
paper is to find the possibility of supplying two separate
winding sets of the multi-phase machine which has the added
advantage that if faults occurs in one set of stator winding it
does not propagate to the second set of stator winding as a
results it does not lead to complete shutdown of the system
due to the presence of other healthy set of phase.
Voltage and current when the machine is subjected to
resistive-inductive-capacitive load
The transient response of the SPSEIG is feeding an RLC load
(200 ohm. 0.8H, 10μF) as shown. The load is turned on at t =
1s. It is found from the results shown as in Figure 16 and 17
respectively that the terminal voltage and current attain their
new steady-state operation, but with a slight reduction of
output voltage. The effect of load on the induction machine
output voltage can be compensated using a series capacitor. It
is observed that for this load used in the test, the output
voltage is affected by the connection of the load.
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 8 (2016) pp 5834-5842
© Research India Publications. http://www.ripublication.com
Appendix
Six-phase machine stator resistance, =4.2Ω
Six-phase machine stator resistance, =4.2Ω
Six-phase machine rotor resistance, =8.8Ω
=0.025H
Leakage inductance in stator winding,
=0.025H
Leakage inductance in stator winding,
=0.04H
Leakage inductance in rotor winding,
=0.074H
Mutual inductance,
Moment of inertia, =0.03Kg/m2
Six-phase self-excited induction generator constants of
magnetization characteristics are as follows:
=550.85, =0.065, =-25.05, =-0.09
[11]
[12]
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