This document presents a MATLAB GUI tool for modeling and analyzing the performance of a 3-phase self-excited induction generator (SEIG). The tool has four sections: 1) comparative modeling of SEIG using Newton Raphson and Fsolve techniques to determine magnetizing reactance and frequency, 2) performance analysis of how circuit parameters affect terminal voltage, 3) conversion between per-unit and actual values for different SEIG connections, and 4) experimental validation of simulated results. The GUI tool provides a user-friendly interface for comprehensively studying SEIG under various operating conditions and comparing simulated outcomes to experimental data.

1. 978-1-4673-6540-6/15/$31.00 ©2015 IEEE
A comprehensive MATLAB GUI tool for modeling
and performance analysis of 3-phase SEIG
Appurva Appan1
, Anurag Yadav2
Alternate Hydro Energy Centre,
Indian Institute of Technology Roorkee, India - 247667
appurvaappan.ee2013@gmail.com
anuragyadav.iitr@gmail.com
Kavita Yadav3
Department of Electrical and Instrumentation Engineering,
Thapar University, Patiala, India - 147004
kavitayadavee2013@gmail.com
Abstract—This paper presents an easy to use MATLAB GUI
based tool for comprehensive analysis of 3-phase SEIG. The
software comprises of four sections that includes comparative
modeling, performance analysis, per unit to actual value
conversion and experimental validation of the simulated result.
Steady state performance analysis of a 3-phase SEIG is generally
done through the proposed mathematical modeling. The
impedance model can be reduced in terms of two nonlinear
simultaneous equations consisting of unspecified variables as
magnetizing reactance Xm and generated frequency F. A
comparative GUI methodology has been employed to evaluate the
parameters using conventional Newton Raphson technique and
novel Fsolve technique. The steady state performance analysis of
SEIG becomes uncomplicated once the values of Xm and F are
explicitly evaluated. Active windows have been created for
assessing the impact of distinct circuit parameters on the
terminal voltage. A per unit to actual value conversion GUI tool
for distinct SEIG connections have also been integrated for
proper understanding in industrial applications. The yielded
outcomes of the designed software tool are compared with the
experimental results are found to be in close agreement. The GUI
approach is found to be user friendly, application specific, facile
and simpler.
Keywords—Fsolve technique, Generated frequency, Graphical
User Interface (GUI), Magnetizing reactance, Performance
analysis, Newton Raphson technique, Self Excited Induction
Genrator (SEIG)
NOMENCLATURE
C : capacitance
F : frequency
Fb : base frequency
Ib : base current
IL : load current
ILp : load current in per unit
Ir : rotor current
Irp : rotor current in per unit
Is : stator current
Isp : stator current in per unit
Pb : base power
Pin : input power
Pinp : input power in per unit
Pout : output power
Poutp : output power in per unit
q : number of phases
RL : load resistance
Rr : rotor resistance
Rs : stator resistance
v : speed
Vb : base voltage
Vg : air gap voltage
Vt : terminal volatge
Xc : excitation capacitor reactance
Xm : magnetizing reactance
Xl : stator or rotor reactance
Xlr : rotor reactance
Xls : stator reactance
Zb : base impedance
Zs : stator impedance
I. INTRODUCTION
The extension of electrification and electricity amenities are
crucial to the financial, social and balanced growth of a country
and providing “Electricity to everybody” has proven to be a
substantial challenge for engineers in the present day scenario.
After US and China, India ranks 3rd
in the largest production of
electricity [1] but still there is shortage in the electricity
generation capacity. Power plant operation in far flung areas
demands less operation and maintenance costs, robust
construction, exemption from the requirement of state of the art
expertise of the operator etc.Rural areas have facile availability
of non-conventional energy resources like wind, hydro, solar,
biomass etc. There is a vast potential which still remains
impalpable. There is a need for a proper technology in order to
fathom the problem of rural electrification. Aforesaid
arguments in collusion demand for a sustainable autonomous
solution for which SEIG appears to be a captivating alternative
due to its inherent advantages like robust construction, less
maintenance, inherent short-circuit and overvoltage protection
etc. In order to develop this new-fangled concept of rural
electrification using SEIG there is a need for a user-friendly
interface in order to analyze the performance of SEIG under
various operating conditions [2].
II. SEIG MODELING AND ANALYSIS
The induction generator has the ability to yield electricity at
variable speeds and this feature is used for its application in
various means such as Self-excited mode. The steady state
evaluation of SEIG is performed using its per-unit equivalent
circuit diagram with a resistive load as shown in Fig. 1 [3].

2. Fig. 1. Equivalent per-phase diagram of SEIG with resistive load.
Zs Is = 0 (1)
where,
(2)
ConsideringIsis not equal to zero under self-excitation and
thus, from (1), it can be deduced that the real and imaginary
parts of (2), which is the per-unit stator impedance can be
equated to zero. The derived nonlinear simultaneous equations
in terms of magnetizing reactance Xm and frequency F can be
represented as in (3) and (4) [4].
f1 (Xm,F) = (A1 Xm+ A2) F3
+ (A3Xm+A4) F2
+(A5 Xm +A6) F +
(A7Xm + A8) = 0 (3)
f2 (Xm,F) = (B1 Xm+ B2) F2
+ (B3Xm+B4) F + B5 = 0 (4)
Here A1-A8 and B1-B5 are constant values and defined in (5).
A1 = -2 RLXl,
A2 = -RLXl
2
,
A3 = 2 RLXl,
A4 = RLXl
2
A5 = (Rr+ Rs+ RL)Xc,
A6 = (Rr+ Rs+ RL) XlXc + RrRs RL
A7 = -(RL + Rs) Xc,
A8 = -(RL + Rs) XlXc
B1 = (Rs + Rr) RL + 2 Xc Xl,
B2 = (Rr + Rs) XlRL+ Xc Xl
2
B3 = 2 Xc Xl + RLRs,
B4 = -(Xc Xl+ RLRs) Xl
B5 = -(RL + Rs)RrXc (5)
Having known all the machine parameters, the evaluation
of load voltage Vt and load current IL is simple. The
corresponding variables can be represented in (6) and (7).
Vg
F
= (3.015 − 1.052 ∗ Xm) ∗ F
Is =
(Vg/F)
Rs
F
+ jXl −
jXcRL
F2RL−jFXc
Ir =
−(Vg/F)
Rr
F−v
+ jXl
IL =
−jXcIs
RLF − jXc
Vt = ILRL (6)
Pin =
−q|Ir
2
|RrF
F − v
Pout = q|IL
2
|RL (7)
III. METHODOLOGY
A. Xm and F evaluation
The solution of simultaneous nonlinear equations of (3) and
(4) is a complicated and rigorous process. The analytical
iterative technique of Newton Raphson method involves partial
derivatives of the equations for building up Jacobian matrix [5]
and the designed algorithm is shown in Fig. 2. A new elegant
and simpler technique would be MATLAB Fsolve optimization
tool as it reduces the length of algorithm and also provides the
accurate result without inputting the degree of error.
Fig. 2. NR Flowchart for determination of Xm and F.
The NR formula is stated as in (8) where Xm0 and F0 are the
initial guess of the unknown values of Xm and F. The Jacobian
matrix denoted by [J] is defined in (9) [3].
[Xm1
F1
] = [Xm0
F0
] − [J]−1
[
f1(Xm0, F0)
f2(Xm0, F0)
] (8)
[J] = [
J11 J12
J21 J22
]

3. J11 =
∂f1
∂Xm
; J12 =
∂f2
∂F
; J21 =
∂f1
∂𝑋 𝑚
; J22 =
∂f2
∂F
(9)
The Fsolve technique is an inbuilt MATLAB optimization
tool which gives the solution of multiple simultaneous
nonlinear equations with accuracy without any need to input
the desired rate of error. The designed algorithm for
determination of Xm and F consists of following three steps:
Step 1: Read Rs, Rr, RL, Xl and Xc.
Step 2: Read initial assumptions (Xm0, F0).
Step 3: Output Xm1 and F1 as the solution.
B. Performance Analysis
Substantial efforts have been made in literature in this
regard [6-9] of performance analysis. The planned algorithm
for performance study and calculation of Is, Ir, IL, Vt, Pin and
Poutconsists of following steps:
Step 1: Read Rs, Rr, Xm, Xl, Xc, f, v and q.
Step 2: Define the load variation RL for which performance is
studied.
Step 3: Choose whether effect of which parameter on terminal
voltage is studied? Rs, Rr, Xl, Xc, Xm, v and pf.
Step 4: Define three different values of that parameter.
Step 5: Compute Vg/F, Is, Ir, IL, Vt, Pin and Pout from their
respective formulas.
Step 6: Output three different Vt vs. Pout curves on the same
plot that represents the effect of that parameter on terminal
voltage.
C. Per Unit to Actual value conversion
The base values will be selected and the real values will be
calculated for different connections that are Star/Star, Delta
Delta, Star/Delta and Delta/Star. The base values are
represented with subscript b. The algorithm for Delta/Star
connection is as listed in (10).
Vb = Vs , Ib =
Is
√3
, Zb =
Vb
Ib
, Pb = P , Fb = F
Is = Ib ∗ Isp ∗ √3;Ir = Ib ∗ Irp , Il = Ib ∗ Ilp ∗ √3
Vt = Vb ∗ Vtp, Pin = Pb ∗ Pinp , Pout = Pb ∗ Poutp (10)
IV. DEMONSTRATION OF DEVELOPED TOOL
This segment demonstrates the comprehensive MATLAB
GUI approach for evaluation of saturated Xm and F of 3-phase
SEIG. The primary window of the designed software consists
of respective tabs:
 Determination of generated frequency and saturated
magnetizing reactance.
 Performance analysis: Effect of parameters on
terminal voltage.
 Per unit to real value conversion
 Experimental validation
A. Determination of Xm and F
The window for Xm and F determination comprises of
Equivalent circuit diagram of SEIG, Equations, NR
Algorithm, NR program, Fsolve Algorithm, Fsolve Program
and Interactive window for NR and Fsolve with editable
parameters. The machine opted for validation of GUI is 3-
phase, 50Hz, 4-pole, 415/240V, 13.2/22.9A, 6.8 kW star/delta
connected SCIM where the per-unit equivalent parameters are:
RS = 0.0602, Rr = 0.0453, Xls = Xlr = Xl = 0.0961
The calculated outcomes in Xm and F evaluation window for a
particular value of load, speed and capacitance is given in Fig.
3.
Fig. 3. Window of evaluated output for a specific value of load, speed and
capacitance.
In case of NR method, in addition of defining the initial
assumption of Xm and F, the degree of error up to which the
result is desired also needs to be mentioned. An additional
block of Max. It. has been included to define the Maximum
Iterations beforehand in case the program gets into an
indefinite loop.
The outcomes obtained from the Fsolve method is found to
be substantially faster than the outcomes obtained from the NR
method in the designed GUI application. The worthiness of
suggested method is revealed with the calculated values of Xm
and F under distinct working speed, capacitance and load as
shown in Table I and Table II. The calculation of base value for
machine parameters is given in Appendix A. It is seen that the
values of Xm and F increases with increase in load and decrease
in excitation capacitance values.
TABLE I. VALUES OF MAGNETIZING REACTANCE AND FREQUENCY AT
NO LOAD WITH C = 25 µF
Xm(p.u.) Xm(Ω) F(p.u.)
0.0290 0.527 0.5706

4. TABLE II. VALUES OF MAGNETIZING REACTANCE AND FREQUENCY
WITH LOAD
C(µF) RL (Ω) RL(p.u.) Xm(p.u.) Xm(Ω) F(p.u.)
25
100 5.5 0.4899 8.907 0.9911
200 11 0.7723 14.042 0.9954
400 22 1.0934 19.880 0.9976
800 44 1.3839 25.162 0.9987
50
100 5.5 0.3659 6.653 0.9890
200 11 0.5436 9.884 0.9944
400 22 0.6855 12.464 0.9968
800 44 0.7896 14.357 0.9980
75
100 5.5 0.3182 5.786 0.9883
200 11 0.4173 7.587 0.9932
400 22 0.4961 9.020 0.9957
800 44 0.5485 9.973 0.9969
100
100 5.5 0.2697 4.904 0.9866
200 11 0.3374 6.135 0.9916
400 22 0.3871 7.038 0.9942
800 44 0.4182 7.604 0.9955
B. Performance Analysis
The window for assessment of SEIG performance under
distinct operating circumstances comprises of Axes, Interactive
window with editable parameters, Control Parameter, Output,
Controls and Description.
The machine parameters provides editable window for
entering machine parameters such as Rs, Rr, Xl, Xc, Xm, F,
vand q. Control parameter consists of a drop down menu from
where the parameter can be selected whose effect on terminal
voltage is to be studied. Output icon will display the evaluated
values of circuit variables such as Is, Ir, IL, Vt, Pin and Pout. The
effect of various circuit parameters, speedand power factor
onterminal voltage could be comprehensively studied through
the designed interfaces as shown in Figs. 4-10. The machine
selected for validation is same as that used for Xm and F
determination.
Fig. 4. Impact of stator resistance on terminal voltage.
Fig. 5. Impact of rotor resistance on terminal voltage.
Fig. 6. Impact of leakage reactance on terminal voltage.
Fig. 7. Impact of capacitive reactance on terminal voltage.

5. Fig. 8. Impact of magnetizing reactance on terminal voltage.
Fig. 9. Impact of prime mover speed on terminal voltage.
Fig. 10. Impact of power factor on terminal voltage.
Enhancing Rs leads to drooping characteristics and reduced
Pout. Thus, it is advantageous to use minimum possible value
of Rs in spite of the fact that its impact is minor. Enhancing Rr
reduces Vt and Pout. However, reduced Rr leads to significant
drop in frequency with load [3]. Thus, it is beneficial to design
optimum possible value of Rr and its impact is minor as
well.For higher loads, the Vt and Pout are low for small Xl. For
lighter loads, the Vt and Pout are high for small Xl. Thus, Xl
must be optimally selected. The Vt and Pout reduces with
increase in the value of Xc which ultimately means higher
value capacitor needs to be employed since Xc = (1/jωC).
However, the designer must select an optimum valued
capacitor bank keeping the economy into consideration for the
wanted outcome.
Increase in value of Xm yields higher value of Vt and Pout.
The impact of this parameter is quite pronounced. Higher
values of Xm must be selected for design considerations. The
prime mover speed in wind power plants is continuously
varying. Thus, it becomes essential to determine the impact of
v on Vt for design of suitable regulators. Increase in vresults in
higher value of Vt for the same Pout. Thus, SEIG must be
operated at higher speeds. Higher values of pf yields higher
Pout. This can be ensured by providing more lagging VARs in
the lines.
C. Per Unit to Actual value conversion
The window for per unit value to real value conversion
comprises of Connection, Machine parameters, Per unit values,
Base values and Actual values.
Fig. 11. Window of evaluated output.
The per unit unit to real value conversion of the similar
machine used for performance analysis is shown in Fig. 11.
D. Experimental Validation
The experimental validation of the simulated results is done
for the impact of capacitive reactance and prime mover speed
on the terminal voltage. The machine chosen for
experimentation is a 3-phase, 4-pole, 50 Hz, 7.5 kW, 415/240
V, 14.6/26.2 A star/delta connected squirrel cage induction
machine whose per phase equivalent circuit parameters in p.u.
are [8]:

6. Rs = 0.0544, Rr = 0.041, Xls = Xlr = 0.0869
The window of the simulated and experimental result for
impact of speed on terminal voltage is shown in first outcome
in Fig. 12. The simulated and experimental results are obtained
for prime mover speed, v = 0.9.
Fig. 12. Window of simulated and experimental result for the impact of speed
and capacitive reactance on terminal volatge.
The window of the simulated and experimental result for
impact of capacitive reactance on terminal voltage is shown in
second outcome in Fig. 12. The simulated results are obtained
for capacitive reactance, Xc = 1.750 and experimental results
are obtained for capacitive reactance, Xc = 1.639.
The profile of the software outcomes are detected to be in
close proximity to the experimental results which showcases
acceptable performance of the designed software under
distinct operating circumstances. A slight variation in the
magnitude is due to the difference in machine parameters
chosen for simulated and experimental outcomes.
V. CONCLUSION
An effort is made in this paper to solve the SEIG problem of
not penetrating the consumer market by development of an
easy to use application of MATLAB GUI. The feature of
Newton Raphson and Fsolve technique has been integrated in
the GUI where the Fsolve method has been found to be
comparatively suitable for evaluation of Xm and F. Fsolve
promises substantially simpler algorithm, faster response and
comparatively accurate result since degree of error need not be
defined in its case. Assessment of the impact of different
circuit parameters on the terminal voltage is a major stride in
the evaluation of SEIG performance. The detailed assessment
of each parameter has been conducted for the degree and
nature of its impact. This tool also makes per unit to real value
conversion of circuit variables for proper understanding of the
designer. The simulation results are found to be in close
agreement with the experimental results which proves the
worthiness of the developed software. This technique can be
contemplated for assessing performance analysis of 1-phase
SEIG.
VI. APPENDIX
A. Machine Parameters
Vbase = Phase voltage (rated) = 240 V
Ibase = Phase current (rated) = 13.2 A
Zbase = Base impedance = 18.182 Ω
Pbase = Base power = 3.17 kW
Fbase = Base frequency = 50 Hz
The machine parameters in per-unit are:
Rs = 0.602, Rr = 0.0453, Xls = Xlr =Xl = 0.0961
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