National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &
Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and
Technology, Pg. 14-21
Journal homepage: www.mjret.in
ISSN:2348 - 6953
Steady State Characteristics of Three-Phase Self
Excited Induction Generator Using
Numerical Technique
Shankargouda Koti, S. Vivek Bhat
Department of Electrical & Electronics Engineering
B.V.Bhoomaraddi College of Engineering & Technology
Hubballi, Karnataka, India
E-mail: shankaragoudakoti@gmail.com, svivek1993@gmail.com
Abstract: The work presented here describes a study on steady state characteristics of SelfExcited Induction Generator (SEIG) using Multiple Equation Newton-Raphson Method. From
per-phase equivalent circuit, non-linear system of equations has been formed using loopimpedance approach containing two unknowns. Computer program in CodeBlocks IDE
13.12 based on this method has been developed to find the unknowns and then the
characteristics have been analyzed using plotting software GNU plot. The simulation and
theoretical studies in graphical form are presented for No-Load Conditions. Very good
agreement between theoretical results and simulated results has been observed.
Keywords: Self Excited Induction Generator (SEIG), Steady State Analysis, Standalone Operation
1. INTRODUCTION
Traditionally, Induction machines are used as motors. However, when an induction machine
is driven by an external prime mover, it is called as Self Excited Induction Generator (SEIG),
which produces voltage and delivers electrical power, if an appropriate size of capacitor
bank is connected across its terminals [1].The use of capacitor bank in SEIG will provide
necessary reactive power for the excitation of the generator. The value of capacitance
depends on many factors viz. generator parameters, magnetic saturation characteristics,
rotor speed and load impedance. This project was selected because of the following needs:a) Depletion of conventional energy sources and environmental degradation have
emphasized on renewable sources of energy for power generation.
b) Induction machine as a generator is popular for renewable energy applications such as
mini hydro and wind power plant.
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National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &
Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and
Technology, Pg. 14-21
c) It has advantageous features over synchronous generator such as

No DC excitation required.

Low cost and brushless.

Robust in construction and

Simple to operate, self-protection against severe loads.
A.OBJECTIVES

To represent 3-φ SEIG using equivalent circuit in the form of various impedances.

To derive expressions for the impedances.

To solve the system of equations using various numerical methods to obtain the system
parameters.

To obtain the steady state characteristics of 3-φ SEIG using
numerical
methods.
B. CONCEPTUAL BACKGROUND
i. Grid connected Induction generator operation:
When the induction machine is driven by a prime mover above the rated speed, torque will
be supplied to the rotor and machine acts as generator, operating at negative slip and
supplying power to the connected grid. It takes magnetizing current from the grid for selfexcitation.
ii. Stand-alone Induction generator operation:
In case of stand-alone induction generator as shown in Fig.1, the magnetizing current for
self-excitation can be supplied by connecting capacitor bank, which provides necessary
reactive power for excitation of the generator. Required operating voltage at a particular rotor
speed can be obtained by selecting proper capacitance value.
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National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &
Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and
Technology, Pg. 14-21
Fig.1 Schematic diagram of a SEIG [2]
Fig.2 Per-Phase Equivalent Circuit of a 3-φ SEIG
The per-phase steady state equivalent circuit of a 3-φ induction generator with an excitation
capacitance and load is shown in Fig.2 where
R1– Stator Resistance
R2– Rotor Resistance
Rc – Core Loss Resistance
Rl- Load Resistance
I1- Stator Current
Ish- Excitation Current
Icr- Core Loss Component of Ish
X1– Stator Leakage Reactance
X2– Rotor Leakage Reactance
Xm – Magnetizing Reactance
Xl– Load Reactance
I2- Rotor Current
Im- Magnetizing Component of Ish
F- per-unit (pu) frequency
ω- per-unit (pu) speed
3-φ SEIG finds application in the following areas:

It is used in power generation using renewable energy sources such as in Wind and Mini
Hydro Power Plants [5].
SEIG has many advantages over permanent magnet synchronous motor (PMSM) viz.
lack of dc excitation, low cost, brushless, rugged construction, maintenance, operation
simplicity and self-protection against overloads and faults. Therefore it can be used in
Grid Connected Mode or Standalone Mode [5].
2. MATHEMATICAL MODEL
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National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &
Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and
Technology, Pg. 14-21
Fig.3 Simplified Representation of Fig.2
The steady-state equivalent circuit of Fig.2, when analyzed by loop impedance approach,
can be represented by three series impedances as shown in Fig.3, where
Z1  Stator Equivalent Impedance  R1 / F  jX 1 
 1

1
1

Z 2  Rotor Equivalent Impedance  


 RC / F jX m R2 / F     jX 2 

1
1
1 

Z 3  Load Equivalent Impedance  


2
jX
R
/
F

jX
/
F
L
L
C


1
1
V g – Air Gap Voltage
Vt - Terminal Voltage
The loop equation in Fig.3 can be written as
_
_
_
 _

I 1  Z1  Z 2  Z 3   0


Under normal operating condition, the stator current (I1) is not zero and thus the loop
impedance must be zero. Thus,
_
_
 _

g 1  real  Z 1  Z 2  Z 3   0
(1)


_
_
 _

g 2  imag  Z 1  Z 2  Z 3   0
(2)


Note that (1) and (2) are the basic equations and must be satisfied for all operating
conditions of the generator. In general, the above equations are solved to find the values of
F and Xm and it requires assigning some feasible values to rest three unknowns ω, Xc and
RL.
A.SOLUTION FOR EQUIVALENT CIRCUIT USING NUMERICAL TECHNIQUE

The partial derivatives of the system of equations are computed.

They are evaluated at the initial guesses of two unknowns.
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National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &
Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and
Technology, Pg. 14-21

The values of the functions are evaluated at initial guesses.

The two unknowns for next iteration are evaluated using Multiple Equation Newton
Raphson formulae [4].

All the above mentioned steps are repeated with new values of unknowns till
convergence takes place.
Advantage: Convergence takes place faster if initial guesses are close to the true solution.
B. ALGORITHM OF THE C-PROGRAM

Two equations Zr (real part of net impedance) and Zi (imaginary part of net impedance)
are taken as two functions.

Each function is differentiated partially with respect to x
(F) and with respect y (Xm).

Partial derivatives are substituted in C-program for multiple-equation NR Method
formula.

N no. of iterations is carried out until the difference between the two subsequent values
of an unknown is less than 0.0001.

The values of F & Xm thus obtained are used to find different parameters of the machine
like terminal voltage, stator current.
3. RESULTS & DISCUSSIONS
A. Variation of No-Load Terminal Voltage against Capacitance
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National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &
Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and
Technology, Pg. 14-21
Fig.4 Using GNU Plot
Fig.5 From Reference Paper
No-load characteristic of self-excited induction generator are obtained with RL = XL = ∞ and
ω = 1.0 pu (1500rpm). In this case, the terminal voltage (Vt) is a function of excitation
capacitance. The variation of Vt against C is shown in Fig.4. Minimum capacitance of 23 µF
is needed to initiate self-excitation as in Fig.5[1]. However, to obtain the rated voltage at no
load, the capacitance needs to be increased further (Xc).
B. Variation of Frequency against Capacitance
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National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &
Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and
Technology, Pg. 14-21
Fig.6 Using GNU Plot
Generally, the induction generator is connected to a live system (power grid) of constant
voltage and constant frequency for proper synchronization. So it is very important to
maintain the frequency of induction generator, same with that of bus-bar frequency. Fig.6
shows the variation of frequency in output versus capacitance of self-excited induction
generator, it is seen that frequency is almost constant (≃ 1pu).
C. Magnetization Characteristics of the Generator
Fig.7 Using GNU Plot
Fig.8 From Reference Paper
Fig.7 shows the magnetization characteristics of induction generator, which is drawn from
the synchronous speed test data i.e. coefficients k0, k1, k2 and k3 are obtained from the per
unit values of air-gap voltage and magnetizing reactance. Vg/F ratio is decreasing with
increase in Xm as shown in Fig.8 [1], as the coefficients have alternate positive and negative
values.
4. CONCLUSIONS
Thus, the following steady-state characteristics of a 3-φ self-excited induction generator
have been verified and the simulation plots are in good agreement with the theoretical
studies.

Variation of No-load terminal voltage against capacitance
20 | P a g e
National Conference-NCPE-2k15, organized by KLE Society's Dr. M. S. Sheshgiri College of Engineering &
Technology, Belagavi, Special issue published by Multidisciplinary Journal of Research in Engineering and
Technology, Pg. 14-21

Magnetization Characteristics of the Generator

Constant Frequency operation
ACKNOWLEDGEMENT
We express our gratitude to Mr. Sachin Angadi, our project guide, Department of E&E,
BVBCET, Hubballi for his immense help and support in guiding our project work.
REFERENCES
[1]
M.H.Haque, “Capacitance Requirement in a three phase SEIG under No-Load and Load Conditions”, 2012
IEEE International Conference, Auckland
[2]
Manoj K.Arya, “Steady State Analysis for Self Excited Induction Generator for Balanced and Unbalanced
Conditions”, M.E.Thesis in Power Systems & Electric Drives, July 2009, Thapar University, Patiala
[3]
[4]
[5]
P.C.Sen, “Principles of Electrical Machines & Power Electronics”, 2E, John Wiley & Sons, Inc., 1997
Steven C. Chapra, Raymond P. Canale, “Numerical Methods for Engineers”, 6E, Mc Graw Hill Publications,
2010
M.H.Haque, “A Novel Method of Evaluating Performance Characteristics of Self-Excited Induction
Generators”, IEEE Transactions on Energy Conversions, Vol 24.
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