Dynamic Modeling and Analysis of Six-Phase Self-Excited Induction Generator

53 International Journal for Modern Trends in Science and Technology
Dynamic Modeling and Analysis of Six-Phase
Self-Excited Induction Generator
D.Milantha Minnet1
| M.Venkatesh2
| G.Prem Kumar3
1,2,3Assistant Professor, Department of EEE, ACT College of Engineering and Technology, Kancheepuram, Tamilnadu,
India.
To Cite this Article
D.Milantha Minnet, M.Venkatesh and G.Prem Kumar, “Dynamic Modeling and Analysis of Six-Phase Self-Excited Induction
Generator”, International Journal for Modern Trends in Science and Technology, Vol. 03, Issue 04, 2017, pp. 53-58.
This paper presents a simple d–q model of a saturated multi-phase (six-phase) self-excited induction
generator (SP-SEIG). Multi-phase AC machines are nowadays widely considered as potentially viable
solutions for numerous variable-speed drive applications. With an increased emphasis on renewable electric
energy generation, while interfacing with the grid typically take place by means of power electronic converter,
if the generator is used for stand-alone application. The main advantages of multi-phase machines that make
them viable for drive can also be effectively exploited in generating application. In particular, it is shown that
the SP-SEIG can operate with a single three-phase capacitor bank. The generator can also supply two
separate three-phase loads, which represents an additional advantage. In this paper proposes the modeling
and analysis of six phase self excited induction generator under R and RL load condition and also torque and
rotor dynamic equation are discussed. The simulation results obtained and compared with three phases self
excited induction generator. Results obtained compared with three phase self excited induction generator
performance. In power generation application of practical usage this system has sufficient capability.
KEYWORDS: Six-phase machine, self-excited induction generator, capacitor Excitation, Renewable energy,
d-q model.
Copyright © 2017 International Journal for Modern Trends in Science and Technology
All rights reserved.
I. INTRODUCTION
Apart from their general use as motors,
induction machines (IMs) are also used as
generators in electric power systems [8]. The
induction generator offers advantages for hydro
and wind applications [12] in terms of cost and
simplicity and it play an important part in the
renewable energy industry today .However, the
induction generator has limitation and generally
need an external power source to provide its
excitation. These mean that it is difficult to employ
in remote areas where there is no electrical power
supply network.
The possibility of using a Self-excited Induction
Generator (SEIG) [1]-[4] where a three-phase
capacitor bank is connected across the stator
terminals to supply the reactive power requirement
of a load and generator was discovered by Basset
and Potter When such an induction machine is
driven by an external mechanical power source,
the residual magnetism in the rotor produces an
Electromotive Force (EMF) in the stator winding. In
this mode of operation, the capacitor bank supplies
the reactive power requirement of the load and
generator and the real power demand of the
terminal load is supplied by the prime mover. Now
a day’s six phase self excited induction generator
are used for various application.
Permanent magnet generators can also be used
for energy applications but it can be suffer from the
uncontrollable magnetic field, which decay over a
ABSTRACT
International Journal for Modern Trends in Science and Technology
Volume: 03, Issue No: 04, April 2017
ISSN: 2455-3778
http://www.ijmtst.com

D.Milantha Minnet, M.Venkatesh and G.Prem Kumar : Dynamic Modeling and Analysis of Six-Phase Self-Excited Induction
Generator
period due to weakening of the magnet and the
generated voltage tend to fall steeply with load.
Multiphase induction machines are nowadays
widely considered as potentially viable solutions for
numerous variable-speeds drive applications
[2]-[7].
The advantage of multiphase machine can be
making them viable for drive application and also
be effectively exploited in generating application. A
further advantage of using the SP-SEIG (six phase
self excited induction generator) with respect to a
three-phase SEIG is the possibility of combining
the output of the two three-phase winding for the
supply of a single three-phase load, by means of a
three-winding transformer with dual star-delta
connected primary. This paper, therefore,
discusses modeling of a six-phase self excited
induction generator (SP-SEIG). Regarding the
mathematical modeling of six-phase self-excited
induction generators (SPSEIG) [10], [11]-[12], the
concept of three-phase and single-phase
self-excited induction generator modeling can be
utilized
II. THREE PHASE SELF EXCITED INDUCTION
GENERATOR
A d–q-axis IM flux model in the stationary
reference frame is used for the simulation of the
SEIG system in MATLAB/ Simulink [16]. The
electrical system of the SEIG is represented
through fourth-order flux state-space model
equations and mechanical systemby a first-order
torque balance equation. The mathematical model
is simulated in the form of matrices to solve the
d–q-axis fluxes and finally, their respective
d–q-axis currents and corresponding three-phase
stator currents. The saturation in the SEIG is
incorporated through a relation-ship between
magnetizing inductance (Lm) versus magnetizing
current (Im), obtained from the synchronous speed
test on the SEIG [3]. The developed model is also
used to simulate a three-phase, P-pole, IM in the
stationary reference frame with a delta-connected
stator winding and a squirrel-cage rotor.
The d–q-axis flux state-space model equations of
an IM are described as,
Where subscripts s, r, l, and m denote stator, rotor,
leakage, and magnetizing quantities, respectively,
in d- and q-axis.
The magnetizing inductance Lm is calculated from
the synchronous speed test on IM [3] and is
represented in the form of a polynomial as follows:
𝐿 𝑚 = 𝑎 + 𝑏𝑙 𝑚 + 𝑐𝑙 𝑚
2
+ 𝑑𝑙 𝑚
2
(13)
Where a, b, c, and d are constants given in the
Appendix. The magnetizing current of a SEIG is
computed as,
a
ii
I
qsds
m
)( 

(14)
The electromechanical equation of the SEIG can be
written as,
𝑇𝑠ℎ − 𝑇𝑒 =
2𝑗
𝑝
𝑃𝑤𝑟 (15)







j
p
TTp shewr
2
(16)
Where Te is the electromagnetic torque, Tsh is the
shaft torque, J is the combined rotor and load
inertia, ωr is the electrical rotor speed (rad/s), and
P is the number of poles in machine. The prime
mover torque speed characteristic is given as,
𝑇𝑠ℎ = 𝐾1 − 𝐾2. 𝜔𝑟 (17)
Where Te is the electromagnetic torque, Tsh is the
shaft torque, J is the combined rotor and load
inertia, ωr is the electrical rotor speed (rad/s), and
P is the number of poles in machine. The prime
mover torque speed characteristic is given as,
𝑇𝑠ℎ = 𝐾1 − 𝐾2. 𝜔𝑟
III. SIX PHASE SELF EXCITED INDUCTION
GENERATOR
Induction machine (IM) is quite popular with
isolated micro hydro power plants. It is a

Generator
singly-excited ac machine. Stator winding of a
3-phase IM is connected to a 3-phase ac source
and rotor winding receive its energy from stator by
means of electro-magnetic induction.
a) In motoring mode (0 < slip < 1), rotor rotates
in the direction of rotating field produced by the
stator current. The slip varies from range 1 at
stand still to 0 at synchronous speed.
b) In generating mode (-1 < slip < 0), stator
terminals are connected to a constant frequency
voltage source and rotor driven at above
synchronous speed by a prime mover.
Fig. 1. Schematic diagram of six-phase SEIG
SEIG employ cage rotor construction with shunt
capacitor connected at its terminal for excitation.
The shunt capacitor may be variable. As the speed
during induction generator operation is not
synchronous, it is also called an asynchronous
generator. The diagram hardware description given
this paper [15].
IV. MATHEMATICAL MODELING OF SEIG
The parameter is used in the SEIG can be obtained
by conducting test on the induction generator when
act as motor. The traditional test is used to
determine the parameter consists of open circuit (no
load) test and the short circuit (locked rotor) test. In
this paper [14] the d-q model is developed for easy
to get the complete solution, transient and steady
state response of the self-excitation.
Fig.2. Two-pole phasor diagram of six-phase
induction machine
A schematic representation of the stator and rotor
winding for a two pole, six phase induction
machine is depicted in fig. 1. Six-phase stator are
divided into two Y connected three phase set abc
and xyz, whose magnetic displaced by an arbitrary
angle α. The winding of each 3 - phase set are
uniformly distributed and displaced 120 degree.
The following voltage equation of a multi-phase
induction machine in arbitrary reference frame is:
V𝑞1 = −𝑟1 𝑖q1 + 𝜔 𝑘 𝜆 𝑑1 + Pλq1
V𝑑1 = −𝑟1 𝑖d1 + 𝜔 𝑘 𝜆 𝑞1 + Pλd1
V𝑞2 = −𝑟2 𝑖q2 − 𝜔 𝑘 𝜆 𝑑2 + Pλq2
V𝑑2 = −𝑟2 𝑖d2 − 𝜔 𝑘 𝜆 𝑞2 + Pλd2
0 = 𝑟𝑟𝑖 𝑞𝑟 + 𝜔 𝑘 − 𝜔𝑟 𝜆 𝑑𝑟 + 𝑝𝜆 𝑞𝑟
0 = 𝑟𝑟𝑖 𝑑𝑟 − 𝜔 𝑘 − 𝜔𝑟 𝜆 𝑞𝑟 + 𝑝𝜆 𝑑𝑟
(19)
The torque and rotor dynamics equations can be
expressed as:
𝑇𝑒𝑚
=
3
2
𝑃
2
𝐿 𝑚
𝐿 𝑟
𝑖 𝑞1 + 𝑖 𝑞2 𝜆 𝑑𝑟
− 𝑖 𝑑1 + 𝑖 𝑑2 𝜆 𝑞𝑟
(19)
𝜔 𝑟
𝜔 𝑏
=
1
𝑃
1
𝜔 𝑏
𝑃
2
1
𝐽
𝑇𝑒𝑚 − 𝑇𝑠ℎ (20)
Fig. 3 q and d axis equivalent circuit of a six-phase
induction machine
Where, Tsh is shaft torque, P represent the number
of poles, J denote as moment of inertia, 𝜔 𝑏 defined
as the base speed (rad/sec.). 𝐼 𝑚 is given by,
𝐼 𝑚 = −𝑖 𝑞1 − 𝑖 𝑞2 + 𝑖 𝑞𝑟
2
+ −𝑖 𝑑1 − 𝑖 𝑑2 − 𝑖 𝑑𝑟
2 (21)
Where, 𝜔 𝑘 -the speed of the reference frame, P =
differentiation w.r.t. time,𝜔𝑟 = the rotor speed, and
all other symbols have their usual meaning.
V. MODELING OF STATIC LOAD
5.1 No Load Condition and Purely Resistive Load
(R)
If a resistive load is connected to across the
terminal generator, the load current (without series
capacitor) can be expressed by,
𝑖 𝑑1𝐿 =
𝑉 𝑑1
𝑅1
𝑎𝑛𝑑 𝑖 𝑞1𝐿 =
𝑉𝑞1
𝑅1
(22)
𝑖 𝑑2𝐿 =
𝑉 𝑑2
𝑅2
𝑎𝑛𝑑 𝑖 𝑞2𝐿 =
𝑉𝑞2
𝑅2
(23)
Applying Kirchhoff’s current law at capacitor
terminal, the current flowing through the shunt
capacitor given by,

Generator
𝑖 𝑞1𝑐 = 𝑖 𝑞1 − 𝑖 𝑞1𝐿 𝑎𝑛𝑑 𝑖 𝑑1𝑐 = 𝑖 𝑑1 − 𝑖 𝑑1𝐿 (24)
𝑖 𝑞2𝑐 = 𝑖 𝑞2 − 𝑖 𝑞2𝐿 𝑎𝑛𝑑 𝑖 𝑑2𝑐 = 𝑖 𝑑2 − 𝑖 𝑑2𝐿 (25)
Hence, with pure resistive load the voltage
equations can be modified as
𝑃𝑉𝑞1 =
𝑖 𝑞1
𝐶 𝑠ℎ1
−
𝑣 𝑞1
𝑅1 𝐶 𝑠ℎ1
− 𝜔 𝑏 𝑣 𝑑1 (26.1)
𝑃𝑉𝑑1 =
𝑖 𝑑1
𝐶 𝑠ℎ1
−
𝑣 𝑑1
𝑅1 𝐶 𝑠ℎ1
+ 𝜔 𝑏 𝑣 𝑞1 (26.2)
𝑃𝑉𝑞2 =
𝑖 𝑞2
𝐶 𝑠ℎ2
−
𝑣 𝑞2
𝑅2 𝐶 𝑠ℎ2
− 𝜔 𝑏 𝑣 𝑑2 (26.3)
𝑃𝑉𝑑2 =
𝑖 𝑑2
𝐶 𝑠ℎ2
−
𝑣 𝑑2
𝑅2 𝐶 𝑠ℎ2
− 𝜔 𝑏 𝑣 𝑞2 (26.4)
Where, R1 and R2 is the load resistances
connected across the winding set I and II
respectively
5.2 Lagging Power Factor Load (RL)
Assume that the load is R1L1 and R2L2 (per phase
value) series circuit connected across winding set 1
and 2 respectively. The voltage equation in this
case expressed by,
𝑃𝑉𝑞1 =
𝑖 𝑞1
𝐶 𝑠ℎ1
−
𝑖 𝑞1𝐿
𝐶 𝑠ℎ1
(27.1)
𝑃𝑉𝑑1 =
𝑖 𝑑1
𝐶 𝑠ℎ1
−
𝑖 𝑑1𝐿
𝐶 𝑠ℎ1
(27.2)
𝑃𝑉𝑞2 =
𝑖 𝑞2
𝐶𝑠ℎ2
−
𝑖 𝑞2𝐿
𝐶𝑠ℎ2
(27.3)
𝑃𝑉𝑑2 =
𝑖 𝑑2
𝐶 𝑠ℎ2
−
𝑖 𝑑2𝐿
𝐶 𝑠ℎ2
(27.4)
Where, q- and d- axis load currents are
expressed as,
𝑃𝑖 𝑞1𝐿 =
𝑣 𝑞1
𝐿1
−
𝑅1
𝐿1
𝑖 𝑞1𝐿 (28.1)
𝑃𝑖 𝑑1𝐿 =
𝑣 𝑑1
𝐿1
−
𝑅1
𝐿1
𝑖 𝑑1𝐿 (28.2)
𝑃𝑖 𝑞2𝐿 =
𝑣 𝑞2
𝐿2
−
𝑅2
𝐿2
𝑖 𝑞2𝐿 (28.3)
𝑃𝑖 𝑑2𝐿 =
𝑣 𝑑2
𝐿2
−
𝑅2
𝐿2
𝑖 𝑑2𝐿 (28.4)
VI. SIMULATION RESULT
The theoretical studies using Matlab /Simulink
have been carried out on a three phase self excited
induction generator and six-phase self-excited
induction generator. In the study, the effect of
cross saturation has been neglected [13]. The
performance six phases SEIG with R load and RL
load result compared with three phase self excited
induction generator given below.
Fig.4 Circuit diagram for three phase self excited
induction generator with R-load
Fig.4 (a) Three phase SEIG voltage waveform with R-load
Fig.4 (b). Motor & Generator performance with R-load
Fig.5. Circuit diagram for three phase self excited
induction generator with RL-load

Generator
Fig.5 (a) Three phase SEIG voltage waveform with RL-load
Fig.5 (b). Motor & generator performance with RL-load
Fig.6. Circuit diagram for six phase self excited induction
generator with R-load.
Fig.6 (a) Six phase SEIG waveform with R-load
Fig.6 (b) Motor & generator performance with R-load
Fig.7. Circuit diagram for six phase self excited
induction generator with RL-load.
Fig.7(a) Six phase SEIG waveform with RL-load
Fig. 7(b) Motor & generator performance with RL-load
VII. CONCLUSION
This papers the analyzing and modeling of three
phases and six phases self excited induction
generator was discussed. With a proper choice of
series and shunt capacitors, the quality of output
voltage and current waveforms can also be

Generator
controlled. Mainly analyzed the six phase SEIG
with R and RL load and implemented by using
Matlab. The simulation result discussed this
paper. R and RL load generator performance of
speed and torque is achieved.
APPENDIX
THE PARAMETERS OF INDUCTION MACHINE
5hp , 60Hz ,
1750rpm,
4p=
1.115Rs = W,
1.083Rr = W
5.974mHLs = ,
5.974mHLr = ,
203.7mHLm =
20.02 .J kg m= ,
0.005752 . .N m sb =
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