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Abstract-- This paper presents a user friendly software based

solution for complete evaluation of steady-state behavior of SEIG

under different operating conditions. The mathematical modeling

of the machine is carried out and then simulated in MATLAB’s

Graphical User Interface (GUI) environment and active windows

are created with these models. In this software package the

complex nonlinear equations are solved by a numerical based

routine ‘Fsolve’ in the tool box of MATLAB to find the values of

saturated magnetizing reactance Xm and the output p.u.

frequency F for the given values of machine parameters. Some of

MATLAB’s GUI operations are implemented in creating an

active link with these models. The simulation results obtained by

the presented methodology are also compared with the

corresponding experimental values and are found to be in very

good agreement.

Index Terms-- Graphical user interface (GUI), MATLAB

simulation, Self excited induction generator (SEIG)

I. NOMENCLATURE

List of symbols

Rs, Rr per phase stator and rotor (referred to stator) resistance

Xls, Xlr per phase stator and rotor (referred to stator) leakage reactance

Xm magnetizing reactance

Xc per phase capacitive reactance of the terminal capacitance C

RL per phase load resistance

F, ν p. u. frequency and speed, respectively

Is, Ir, IL per phase stator, rotor (referred to stator) and load current

Vt, Vg terminal voltage and airgap voltage, respectively

Pi input power

Po output power

(All the above reactances are referred to base frequency f)

II. INTRODUCTION

UE to the current increasing concerns on green house gas

emission and climate change, renewable energy has come

to center stage for power conversion. Among the possible

S S Murthy is with the Department of Electrical Engineering, Indian

Institute of Technology, Delhi, New Delhi -110016 , India (e-mail:

ssmurthy@iitd.ac.in).

Rajesh Kr. Ahuja, Research Scholar is with the Department of Electrical

Engineering, Indian Institute of Technology, Delhi, New Delhi -110016 ,

India (e-mail: rajeshkrahuja@gmail.com).

generators Self Excited Induction Generator (SEIG) is the

most cost effective option with the advantage of rugged,

brushless and maintenance free feature. Self excited induction

generator has been a subject of considerable research over last

few decades [1-8] because of its perception as the simplest

energy conversion device to produce electricity in off-grid,

stand alone mode using different types of prime movers and

employing different conventional and renewable energy

resources such as oil, bio-fuel, wind and small hydro. The

steady state analysis of self excited induction generator (SEIG)

is vital for proper implementation of induction machine

operation as a generator in a stand alone mode through

appropriate modeling.

However its operation and analysis as a stand-alone power

source, i.e., as a Self Excited Induction Generator (SEIG), is

complicated since both the voltage and frequency are now

variables and the analysis of an SEIG involves solving non

linear equations of higher orders [1]. At the initial stage of

research on SEIG a break through was made [1] where in

analytical methods were presented using Newton-Raphson

method to estimate the unknown parameters. Based on this

paper several variants of the same were published extending

similar concepts. In this paper the “fsolve” optimization tool of

MATLAB is used to solve the aforesaid complex non linear

equations.

Our objective is to provide quality power at constant

voltage and frequency to the consumer, appropriate system

design has to be effected for different types of prime movers

and loads at suitable power ratings. Therefore, a system

designer would require a very user friendly tool to be able to

predict the performance under varying load conditions, easily

design the system and fix the parameters of the components

used e.g. the capacitors and VAR controllers. All the methods

used in the references are involved needing complicated

procedure and coding. In this paper it is demonstrated that the

versatile facility available through MATLAB tool boxes can

be effectively used to provide such a software and design

package to interested users. Only a limited effort is made in

literature [8,9] to this effect. This paper attempts to provide

such a user friendly software package using MATLAB tool

boxes with GUI facility for comprehensive analysis, design

and capacitor estimation under different operating conditions.

GUI facility is shown to be an effective tool for the design to

visualize the results.

Design and Analysis of Three Phase Self Excited

Induction Generator Using MATLAB Graphical User Interface Based Methodology

S S Murthy, Senior Member, IEEE, and Rajesh Kr. Ahuja, Student Member, IEEE

D

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III. MODELING AND ANALYSIS OF SEIG

The steady-state equivalent circuit of a SEIG with a resistive

load connected at its terminal is shown in Fig. 1 from which

loop equation for the current Is can be written as [1],

Fig. 1.

0=ss IZ (1)

where

( )( ) ( )lrm

r

lrr

m

lss

cL

Lcs

XXjF

R

jXF

RjX

jXF

R

FjXFR

FRjXZ

++−

+

−+

++

−

−=

ν

ν2

3

//

/ (2)

Under self-excited condition, 0≠sI and therefore, from

(1), 0=sZ , which implies that both the real and imaginary

parts of the right-hand side of ( 2) would be separately zero.

Substituting llrls XXX == , this simplifies to the following

two nonlinear simultaneous equations with Xm and F as

unknown variables [1].

1

3 2

2 3 4 5 6

7 8

( , ) ( ) ( ) ( )

( ) 0

m m m m

m

f X F CX C F CX C F C X C F

C X C

= + + + + +

+ + = (3)

0)()(),( 543

2

21 =++++= DFDXDFDXDFXg mmm (4)

Here C1 – C8 and D1 – D5 are constants as defined in [1].

As (3) and (4) are not easily solvable, numerical methods are

employed. Although Newton-Raphson method [1] which

requires the partial derivatives of the equations has been

employed, the earlier reported methodology required detailed

programming based on a flow chart [1]. The availability of

MATLAB tool boxes facilitates obtaining similar results in a

much simplified manner. Thus a designer can visualize all the

needed characteristics of SEIG in a comprehensive manner

and zero on the needed system parameters for the required

application under a windows environment. GUI will help one

to arrive at needed design/ analytical output in a short time. In

this software package the aforementioned nonlinear equations

are solved by a numerical based routine ‘Fsolve’ in the tool

box of MATLAB to find the values of saturated magnetizing

reactance Xm and the output p. u. frequency F for the given

values of machine parameters such as RL, Xc, and ν. The constants of (3), (4) are in terms of machine constants, speed

and load.

The created Matlab code for ‘Fsolve’ is:

fsolve(@(x)myfun1(x,C1,C2,C3,C4,C5,C6,C7,C8,D1,D2,D3,D

4,D5),[2.2;1.0]

The output of this step would be unknown saturated

magnetizing reactance Xm and p.u frequency F.

As explained in [1] a curve of Vg/F against Xm can be

plotted using the experimental results. From this curve, Vg/F

for the above steady state saturated Xm can be obtained.

Knowing F, the air gap voltage Vg can be computed.

With Vg, Xm, F, Xc, ν, RL and machine parameters known,

calculation of the terminal voltage Vt and the load current can

be obtained using the equivalent circuit of Fig. 1 and the

relevant expressions summarized in [1].

Based on the above analytical technique, a MATLAB’s

GUI program is developed which determine the load

characteristics and complete steady state analysis by

computing Vt, F, Po, etc under different operating conditions .

IV. DEMONSTRATION OF DEVELOPED TOOL

This section presents the new GUI based methodology and

explains how different needed characteristics of SEIG can be

obtained elegantly.

(a) Effect of Stator Resistance on terminal voltage

(b) Effect of Rotor Resistance on terminal voltage

(c) Effect of Magnetizing Reactance on terminal voltage

(d) Effect of Leakage Reactance on terminal voltage

(e) Effect of Capacitance on terminal voltage

(f) Effect of Load power factor on terminal voltage

(g) Effect of speed on terminal voltage

The ease of using the presented tool for analysis of SEIG is

demonstrated by obtaining different (relevant) characteristics

of SEIG, the variations of terminal voltage Vt with output

power Po for different values of capacitance C. The SEIG

chosen for verification of the developed program and

experimentation is a 3-phase, 4-pole, 50 Hz, 7.5 kW,

415/240V, 14.6 / 26.2 A star/delta connected squirrel cage

induction machine whose per phase equivalent circuit

parameters in p.u. are:

Rs=0.0544, Rr=0.041, Xls = Xlr=0.0869

A MATLAB based computer program is written for

complete evaluation of the performance of the SEIG under

different operating conditions. MATLAB’s GUI capabilities,

menu and plotting commands are implemented in a script file

to provide interactive windows for the users. Running the

created GUI M-file, called main-menu, from MATLAB

workspace will display the main window. The main window

has all the icons like Rs, Rr, Xl (or Xm), Xls, Xlr, frequency,

number of phases ‘q’, p. u. speed ‘ν’ and susceptance ‘gc ’. Various results obtained for different operating conditions are

presented.

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This GUI design software tool can facilitate the user for

accurate and speedy analysis of SEIG. The mathematical

models representing all the operating conditions of a SEIG

have been programmed in script files (M-files) using

conventional MATLAB language in GUI environment which

makes it a very user friendly design tool. This will provide the

interactive windows for all simulated operating conditions as

shown below.

A. Simulation Results

The main menu which is displayed after running the file is

shown in Fig. 2. After clicking on ‘Effect of Parameters’

button an interactive window as shown in Fig. 3 will appear

with blank grid and all default parameters in edit box for

predicting the performance.

In the window shown in Fig. 3, by changing the p.u.stator

resistance in stator resistance edit box i,e ‘Rs’, the user can

simulate the effect of stator resistance on terminal voltage as

depicted in Fig 4. Similarly, clicking on respective buttons in

main menu the user can interact with this tool and will be able

to compute the desired results by changing the parameters in

edit boxes. Some simulation results are shown in Figs. 4, 5 and

6

Fig. 2. The main window of the developed software tool

Fig. 3. The interactive window with clear grid and editable

parameters

In Fig. 4 the window is showing the simulation results of effect

of changing the stator resistance equal to KRs

in edit box. Results are simulated for K= 1, 1.1 and

1.2 keeping capacitive susceptance (gc)= 0.695 constant for all

values of stator resistances. The clicking on evaluate button

processes the values of parameters mentioned in respective

edit boxes as described in (11) of [1].

Fig. 4. The window of the computed result for effect of stator resistance on

Terminal Voltage with fixed capacitance

Rs =K Rs (nominal)

Fig. 5. The window of the computed result for effect of rotor resistance on

Terminal Voltage with fixed capacitance

Rr =K Rr (nominal)

Fig. 5 shows the effect of rotor resistance on terminal voltage

at fixed value of capacitance. It is evident that simulation

catches the essence of plots. The above simulation plots are in

close agreement with those in [1]. In a similar manner the plots

from this tool for effect of magnetizing reactance and leakage

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reactance on Terminal voltage is shown in Fig. 6 and Fig. 7

respectively.

Fig. 6. The window of the simulated result for effect of magnetizing

reactance on Terminal Voltage

Xm =K Xm (nominal)

Fig. 7. The window of the simulated result for effect of leakage reactance on

Terminal Voltage

Xl =K Xl (nominal)

Figs. 8,9 and 10 are showing the simulation results of effect

of capacitance, load power factor and speed on terminal

voltage respectively by changing the corresponding parameters

in the respective edit boxes.

Fig. 8. The window of the simulated result for effect of capacitance on

Terminal Voltage

Fig. 9. The window of the simulated result for effect of load power factor on

Terminal Voltage

Fig. 10. The window of the simulated result for effect of speed on Terminal

Voltage

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B. Experimental Verification

Fig 11 shows some of the experimental wave forms of load

voltage, load current and power in one of the phases. Fluke

43B power analyzer is used to measure these quantities.

Fig. 11. Load voltage and current waveforms of delta connected generator for

R-L load at constant speed with capacitance of 83 micro farad in each phase

Fig. 12. The window of the simulated and experimental result for effect of

Speed on Terminal Voltage

The Terminal Voltage and Power output at p.u speed v =

0.9 as obtained from these experimental results are

incorporated in the GUI interactive window and compared

with the simulated results as shown in Fig.12.

The simulated results are found very close to experimental

values which demonstrate satisfactory performance of the

proposed software package under different operating

conditions.

V. CONCLUSION

The user-friendly tool for steady state analysis and design of a

three phase SEIG has been presented in this paper. All the

operating conditions are mathematically modeled and then

simulated using MATLAB instruction in GUI environment.

Close agreement between simulated and experimental results

demonstrates the usefulness for designing SEIG based stand

alone systems using this software.

The developed analytical design tool and software using

MATLAB tool boxes such as “Fsolve” routine and GUI can be

effectively used to predict the performance of SEIG with

different types of prime movers in stand alone mode.

VI. REFERENCES

[1] S. S. Murthy, O.P. Malik, and A.K. Tandon, “Analysis of self excited

induction generators,” Proc.1982 IEE, vol. 129, Pt. C, no. 6, pp. 260–

265,Nov.1982

[2] S. S. Murthy, O. P. Malik and P.Walsh, "Capacitive VAR requirements

of Self-excited Induction Generators to Achieve Desired Voltage

Regulation", IEEE Conference Record of Industrial and Commercial

Power Systems Technical Conference. Milwaukee (USA), pp124-128,

Jun. 1983

[3] A. K. Tandon, S. S. Murthy, and G. J. Berg, “Steady state analysis of

capacitor self excited induction generator,” IEEE Trans Power

Apparatus and Systems, vol. PAS-103, no. 3, pp. 612-617, March 1984

[4] S. S. Murthy, B. P. Singh, C. Nagmani, and K. V. V. Satyanarayana,

“Studies on the use of conventional induction motors as self-excited

induction generators,” IEEE Trans. Energy Conversion, vol. 3, pp. 842–

848, Dec. 1988

[5] S. S. Murthy, B. Singh, S. Gupta, and B. M. Gulati, “General steady-

state analysis of three-phase self excited induction generator feeding

three-phase unbalanced load/single-phase load for stand-alone

applications”, Proc. 2003 IEE, vol. 150, no. 1, pp. 49-55, Jan.2003

[6] G. K. Singh, “Modeling and experimental analysis of a self-excited six-

phase induction generator for stand-alone renewable energy generation,”

Renewable Energy, vol. 33, pp. 1605-1621, Jul. 2008

[7] S. N. Mahato, S. P. Singh, and M. P. Sharma, “Excitation capacitance

required for self excited single phase induction generator using three

phase machine,” Energy Conversion and Management, vol. 49, pp.

1126-1133, Nov. 2008

[8] S. S. Murthy and A. J. P. Pinto, “A generalized dynamic and steady

state analysis of self excited induction generator (SEIG) based on

matlab,” in Proc. 2005 ICEMS Conf Nanjing (China)., vol. 3, pp.

1933-1938,2005

[9] Y. N. Anagreh and I. M. Al-Refae’e, “Teaching the self excited

induction generator using Matlab”, Intl. Journal of Electrical

Engineering Education, vol. 40, no.1, pp. 55-65, Jan. 2003