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].

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 = -RLXl2,

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 Xl2

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|IL2|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].

[Xm1F1

] = [Xm0F0

] − [J]−1 [f1(Xm0 , F0)f2(Xm0 , F0)

] (8)

[J] = [J11 J12

J21 J22]

J11 = ∂f1

∂Xm; J12 =

∂f2

∂F; J21 =

∂f1

∂𝑋𝑚; 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

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.

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]:

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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