Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3 (4): 729-733
© Scholarlink Research Institute Journals, 2012 (ISSN: 2141-7016)
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Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3(4) 729-733 (ISSN: 2141-7016)
Modeling of a Stand-Alone Induction Generator on Load
Using MATLAB Simulink
Tilak Thakur and Shailendra Kumar Gupta
Punjab Engineering College, Chandigarh.
Corresponding Author: Shailendra Kumar Gupta
___________________________________________________________________________
Abstract
The work in this paper had been motivated by the increased role of renewable source based energy generating
systems in today’s world of power deficit and increased complexity in power generation. Also, it gives a
simulated platform to study the physical system before making it operational. This paper proposes a MATLAB
simulink model of a stand-alone induction generator used in renewable source based power generation on load.
Rotor and stator d-q axis current has been chosen as state variable in the mathematical model with an aim of
developing a simple stand-alone induction generator simulink model. The proposed simulink model was then
used to study the electrical and mechanical dynamics of the generator on varying the load across the machine
also, the operating phenomenon is analyzed and the discussion is verified by referred papers. This paper also put
forward the increased role played by induction generator in the field of stand-alone generation.
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Keywords: renewable source, matlab simulink, microgeneration, self excitation, single phase induction
generator (SEIG)
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INTRODUCTION
circuit in which the transient voltage and current have
In present scenario due to increased power demand,
terms of the form k*exp(st). The root s is often a
limited fuel supply, emission of green house gases and
complex quantity and its real part, which is adjusted by
increase in the complexity of system need for a standthe saturation of the magnetic circuit. In this paper the
alone non-conventional renewable source based
simulink model, to simulate the SEIG, is developed
generating system has increased. These generating units
[Dawit, Colin, and Muhammed 2003].
are helpful in lighting remote areas where transmission
is not only difficult but also not cost effective. Among
MATHEMATICAL MODEL
distinct stand alone generation alternative, small hydro
For the modeling of the self-excited induction
power station using synchronous generator (SG) can be
generators, the main flux path saturation is accounted
considered the most efficient one.SG has many
for while the saturation in the leakage flux path, the
technical advantage such as good voltage control,
iron and rotational losses are neglected [Dawit, Colin,
stability, frequency control and thus, its complexity and
and Muhammed 2003]. Therefore in the following
it’s demand of skilled labour force for maintenance and
analysis the parameters of the induction generator are
operation
make
it
sometime,
economical
assumed constant except the magnetizing inductance
unviable[Guiliani and Figueiredo 2011]. Thus, self
which varies with saturation [Dawit, Colin, and
excited induction generator (SEIG) comes into picture.
Muhammed 2003]. In the proposed simulink model d-q
SEIG use induction machine that are low cost, robust,
current of rotor,Idr and Iqr, and stator,Ids and Iqs, are
easily available in market and also needs low skilled
taken as state variable.
labour force for its maintenance and operation [Bhim
Murthy, and Gupta,” (2005) [Grantham, D. Sutanto and
Current Equations
B. Mismail, 1989].
The current equation in the stationary reference frame
for squirrel cage or wound rotor induction machine in
As far as operation of SEIG is considered it is an
the generating mode are [4]
induction generator that is governed by self excitation
pIqs = a1Iqs +a2Ids +a3Iqr +a4Idr +a5Kq+ b6Vcq (1)
phenomenon to generate a steady voltage across its
pIds = b1Iqs +b2Ids +b3Iqr +b4Idr +b5Kd + b6Vcd (2)
terminal. The initiation of the self-excitation process is
pIqr = c1Iqs +c2Ids +c3Iqr +c4Idr +c5Kq + c6Vc (3)
a transient phenomenon and is better understood if the
pIdr = d1Iqs +d2Ids +d3Iqr +d4Idr +d5Kd + d6Vcd (4)
process is analyzed using the transient model for both
the voltages and currents. Granthum et al. have
Where a1, a2, a3, a4…. are variables and there values
demonstrated the initiation of the voltage build-up
are given in appendix. Here, Kq and Vcq0 are initial
process by discussing the transient phenomenon in the
voltage across q-axis rotor winding and stator winding
RLC circuits. In this case the stator of the self-excited
respectively and Kd and Vcd0 are initial voltage across
induction generator may be represented by an RLC
d-axis rotor winding and stator winding respectively.
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Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3(4) 729-733 (ISSN: 2141-7016)
Voltage Equation
Voltage across the terminal of the SEIG are given by
[Dawit, Colin, and Muhammed 2003]
Vcq= (1/C)*ʃIqs dt +Vcq0
(5)
Vcd= (1/C)*ʃIds dt +Vcd0
(6)
C. Mechanical dynamic equation
Governing mechanical equation of SEIG are [4]
Tsh =Te + J*(2/P)*pωr
Thus,
Pωr = (P/2J)*(Tsh-Te)
(7)
here, Te is taken as
Te = (3/2)*(P/2)*Lm*(Ids*Iqr –Iqs*Idr)
(8)
The model consist of 3 subsystem accommodating
varying inductance (subsystem 1), machine internal
behavior (subsystem 2) and mechanical dynamics of
machine (subsystem 3) respectively. The machine
subsystem models the equation of induction machine
on load in d-q axis in stationary reference frame that
has been shown in figure 2.
Here, Te is the electromagnetic torque generated by
machine, Tsh is the turbine input torque, J is inertia of
the machine plus turbine, P is the no. of pole, pis the
derivative, wr is the rotor speed of machine in radian
per second and Lm is the magnetizing inductance.
Magnetizing Characteristic
Since the operation of the SEIG takes place in the
nonlinear region of the magnetization characteristics,
therefore the magnetization current should be
calculated in each step of integration in terms of both
stator and rotor currents using the following formula.
Im =sqrt(Imq^2+Imd^2)
Where,
Imq= Iqr + Iqs
Imd= Idr +Ids
Fig 2. Machine subsystem simulink model
In ‘varying magnetizing system’ the inductance is
varied in accordance to magnetizing current by
equation 12. This varied inductance is then feed to
machine governing equation that is governed by
equation 1-6 and mechanical dynamics governing
equation 7 and 8 that produces new set of stator and
rotor current which is then feed back to the subsystem 1
and accordingly inductance of the magnetic circuit is
changed. This cycle continues until steady state
condition is reached where current generated by
capacitor is equal to the magnetizing current.
(9)
(10)
(11)
Accounting the saturation of magnetic circuit, on
experimental basis, the saturated magnetizing
inductance is varied in terms of magnetizing current
which is given by [Dawit, Colin, and Muhammed,
2003]
Lm=a+bIm+cIm2+dIm
(12)
MODELING OF LOADED MACHINE
Modeling of a Loaded induction generator takes into
the effect of load into equation 5 and 6. The equation
can be rewritten as
Icq= Iqs + ILq
(13)
Icd= Ids + ILd
And as per capacitor equation
Vcq= (1/C)*ʃIcq dt +Vcq0
Vcd= (1/C)*ʃIcd dt +Vcd0
a, b, c, d are constants whose values are given in
appendix II The above set of equation is then modeled
by using MATLAB simulink model as shown in
figure1
Putting Icq and Icd values in above equation we get,
Vcq= (1/C)*ʃ(Iqs+IqL) dt +Vcq0
(14)
Vcd= (1/C)*ʃ(Ids+IdL) dt +Vcd0
(15)
Where,
IqL=Vqs/RL and
IdL=Vds/RL;
Here IqL and IdL are quadrature axis and direct axis
current component of load current, Vqs and Vds are
quadrature axis and direct axis stator voltage
component and RL is the load applied to the generator
in ohms. Equation 13 and 14 implementation has been
shown in machine model (fig.2) [Dawit, Colin, and
Muhammed, 2003] [Ekanayake, 2002] [Fathy, 2006]
[Smith, 1996]
Fig 1. System simulink model
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Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3(4) 729-733 (ISSN: 2141-7016)
RESULTS
The parameters of the machine used in the simulation
are 230 V, 26.2 A, 7.5 kW three phase squirrel cage
induction machine whose stator resistance is 1 Ω , a
rotor resistance referred to the rotor side of 0.77 Ω, a
stator leakage reactance of 1 Ω, rotor leakage reactance
referred to the rotor side of 1 Ω, The moment of inertia
of the drive system is 0.1384 kg.m^2 [8]. Load taken is
in the form of resistance applied to the machine and the
load variation is given in fig 8.The result are
analytically justified and compared to the paper referred
[Smith, 1996]
In this paper at time t=2.5 sec the machine is loaded by
a load of RL=120 ohm, the load is then varied and at
time t=5 sec it is decreased to RL=240 ohm then at time
t=7.5 sec the machine is loaded by RL=360 ohm and at
t=10 sec it is loaded by RL=480 ohm. The results are
given below
Fig 5. c phase voltage curve
Fig 3, 4 and 5 shows the voltage variation generated by
generator when varying load is connected across it.
These transients can be clearly seen in the fig where, at
t=2.5 sec the voltage rms value dips to 92 volts from its
no load rms voltage of 108V it can also be seen that
voltage increases as the load is decreased from RL=120
ohm to RL=240 ohm at time t=5 sec which again varies
at t=7.5 second at t=10 sec. The transient at t=2.5
second in the generated voltage is due to the decreased
rotor speed to produce required slip and
electromagnetic torque to supply the instantaneous
load[9].The transients at t=5 sec, t=7.5 sec and t=10 sec
is due to the increase in rotor speed to supply reduced
torque on reduced load.
Fig 3 a phase Voltage curve
Fig 6. Magnetizing current curve
Figure 6 shows the magnetizing current Vs time graph
which shows the behavior of SEIG whose magnetizing
current decreases on loading. The decrease in
magnetizing current can be justified by the decreases in
generating frequency on load which in turn decreases
the reactance of machine that demands reduced
magnetizing current.
Fig 4 b phase Voltage curve
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Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3(4) 729-733 (ISSN: 2141-7016)
Fig 7. Magnetising inductance Vs time curve
Figure 7 shows the magnetizing inductance curve
which varies as per magnetizing characteristic of SEIG
as per equation 12. Figure 6 and 7 shows the
obvious relation between operating flux (magnetizing
current) and generated voltage.
Fig 10. Rotor speed Vs time curve
Fig 11. Input torque,Electromagnetic torque Vs time
curve
Figure 10 and 11 shows the mechanical dynamics of
the machine. Rotor speed decreases as the machine is
loaded to supply required electromagnetic torque which
is then fed by increasing the input torque from turbine
coupled to the rotor of the machine. Figure 11 clearly
shows the transients in electromagnetic torque (Te) and
the way input turbine torque tracks Te.
Fig 8. Stator phase current
Fig 9. Phase load current
Figure 8 and 9 shows the stator and load current curve
respectively. Stor current curve clearly shows the
obvious effect on variation of load on stator and load
current as per equation 13 and 14. Load current is zero
till machine is loaded at time t=2.5 sec and thereafter
starts building up and decreases as the load is decreased
at time t=5, 7.5 and 10 sec.
Fig 12. Output power generated Vs time curve
Fig 12 shows the output power generated as per loading
of the machine.
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Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3(4) 729-733 (ISSN: 2141-7016)
CONCLUSION
A sophisticated mathematical model has been chosen
for simulating self excited induction generator on load
which uses d-q axis current as state variable. A detailed
analysis of the variation in SEIG upon loading has been
done which is then compared with reference papers
[Smith, 1996]
Fathy M. M. bassiouny,”(2006): Dynamic Performance
of Isolated Asynchronous Generators Under Different
Loading Conditions Using Matlab Simulink”, the
eleventhinternational middle eastpom (er systems
conference (mepcon'2oo6)
Ofualagba, G and Ubeku, E.U ,” The Analysis and
Modelling of a Self-excited Induction Generator Driven
by a Variable Speed Wind Turbine”, Federal University
of Petroleum Resources, Effurun Nigeria
The study done in this thesis is based on resistive load
and further study is to be done on inductive load on
which the performance of SEIG is poorer.
Smith, N.P.A ,”(1996): Induction generators for stand alone micro - hydrosystems”, Power Electronics,
Drives and Energy Systems for Industrial Growth,
1996., Proceedings of the 1996 International
Conference on Volume: 2 ,Pp: 669 - 673 vol.2.
APPENDIX I
a1= -Lr*Rs/L; a2= -Lm^2*ωr/L; a3=Lm*Rr/L; a4= Lm*ωr*Lr/L; a5=Lm/L; a6=-Lr/L
b1=Lm^2*ωr/L;
b2=-Ls*Rs/L;
b3=Lm*ωr*Lr/L;
b4=Lm*Rr/L
b5=Lm/L; b6=-Lr/L
c1=Lm*Rs/L;
c2=Ls*ωr*Lm/L;
c3=-Ls*Rr/L;
c4=Ls*ωr*Lr/L
c5=-Ls/L; c6=Lm/L
d1=-Ls*ωr*Lm/L; d2=Lm*Rs/L; d3=-Ls*ωr*Lr/L;
d4=-Ls*Rr/L
d5=-Ls/L; d6=Lm/L
where, L=Ls*Lr-Lm^2
Ls= Lls+Lm
Lr=Llr+Lm
Yaser N. Anagreh and Imadden M. AlRefae’e,”Teaching the self-excited inductiongenerator
using Matlab,” Department of Electrical Power
Engineering, Yarmouk University, Irbid, Jordan
APPENDIX II
a=0.1407, b=0.0014, c=-0.0012, d=0.0005
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