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IEEE TRANSACTIONS ON EDUCATION, VOL. 44, NO. 2, MAY 2001 165

Using MathCad in Understanding the InductionMotor Characteristics

Khalid A. Nigim , Member, IEEE, and Ronald R. DeLyser , Senior Member, IEEE 

 Abstract—Computer-aided multimedia education is in-creasingly popular within the classroom and laboratory. Theapplications of market-ready mathematical and database pro-gramming software for teaching engineering course outline iswell appreciated. This article shows how MathCad can be used tointroduce electrical machine characteristics simulated at differentpossible control modes. The undergraduate students requireminimum knowledge of a programming language. The examplespresented in the article show how MathCad software can be usedto simplify some of the characteristics of the three-phase andone-phase induction machine. The result of introducing mathsoftware as a teaching tool at the third- and fourth-year level havebeen accepted and are now used as part of the practical sessionsfor the electrical machine and other credited courses at Birzeit

University, West Bank and Gaza in the Palestine.

 Index Terms—Computer application in education, electric ma-chines, MathCad application.

I. INTRODUCTION

CURRENT mathematics software packages are equipped

with highly interactive displays, signal processing, proto-

typing, three–dimensional (3-D) plots, – graphs, word pro-

cessing and data layering to enable rapid interpretation and pre-

sentation of results and trends. The direct use of this type of 

software is a major advancement in simplifying simulation pro-

cedures for many practicing engineers as well as for undergrad-

uate engineering students [1]–[3]. The integration of the motor

and electronics to adjust the inherent motor characteristics make

it difficult for the tutor to simplify and present the subject to un-

dergraduates without the assistance of some kind of simulation

tools. A successful simulation tool requires time, energy, and

skills in computing languages and general knowledge of the op-

erational characteristics of the electrical machine and its perfor-

mance.

To keep sustainable interest in the education process and

with many students enrolling in colleges with some computer

literacy, it is essential to reinforce the engineering education

curriculum with computer-aided teaching tools that are interac-

tive as well as educational. For these reasons a mathematicalpackage was introduced to initiate the changes in teaching

methodology at the author’s engineering college.

Manuscript received October 20, 1999; revised October 31, 2000.K. A. Nigim is with Birzeit University, Electrical Engineering Department,

Birzeit, Palestine (e-mail: kldngm@excite.com).R. R. DeLyser is with the Department of Natural Science, Mathematics

and Engineering, University of Denver, Denver, CO 80210 USA(e-mail:rdelyzer@du.com).

Publisher Item Identifier S 0018-9359(01)01769-1.

Fig. 1. The electronic handbook main menu designed with MS-Access tool.

II. MATH SOFTWARE AS AN EDUCATIONAL TOOL FOR

ELECTRIC MACHINE CASES

The early versions of software to simulate motor performance

are presented in references [4]–[6]. The work introduces the ba-

sics of teaching electric machines using programmable routines

and was dedicated to a few aspects of the phenomena of electric

machines using the DOS environment and interactive graphics

software. In early 1994, the electrical engineering department

at Birzeit University used MathCad in the teaching classrooms

and PC laboratory on a trial basis in order to enhance interactive

teaching and learning. Equation solution of the electrical motor

and drives performance is straightforward once the basic fea-tures of MathCad software are learned [7].

Of course, MathCad software is widely used for many sci-

entific and engineering principles and is not the only package

available [8], [9]. Itis easyto use and has manybuilt-in functions

that facilitate its use in many textbook applications. The next

sections will demonstrate the versatility of adopting MathCad

in evaluating the characteristics of three-phase and one-phase

induction motors under variable input conditions. Study cases

1 and 2 present the steady state characteristics of the three-

phase induction motor under varying input conditions, while

case 3 presents the one-phase motor characteristics. The exam-

ples were presented to and accessed by the student through the

creation of an interactive electronic handbook page created byMS Access software as seen in Figs. 1 and 2. The multiple-

choice menu given to the student is used to navigate through

solved examples as the syllabus developed.

 A. The Presentation of the Electric Motor Characteristics by

 MathCad 

In electrical motors, the electrical energy input and the me-

chanical energy output can be presented in mathematical form,

after presenting the physical operation of the motor with the

equivalent electric circuit shown in Fig. 3. The electric circuit

0018–9359/01$10.00 © 2001 IEEE

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166 IEEE TRANSACTIONS ON EDUCATION, VOL. 44, NO. 2, MAY 2001

Fig. 2. MathCad induction motor solved examples menu.

Fig. 3. The three-phase induction motor equivalent circuit.

is used to facilitate the calculation of the current once the values

of the resistive and inductive motor windings components aregiven at thebase frequency andsupply voltage. The values could

be evaluated experimentally by conducting the running light

(no-load) and locked rotor tests on the motor if that is possible;

otherwise, the manufacturer should be contacted for the infor-

mation.

The power flow, shown in Fig. 4, within the motor is tracked

by balancing the input and the output taking into account the

heat and magnetic power losses. The losses are quantified by

performing several standard tests on the motor. The current

flowing in the motor can be calculated using the equivalent cir-

cuit representing the motor physical elements. The steady-state

developed torque and power that are a function of the motor

current and speed are then evaluated and plotted to reveal themotor characteristics. The expected efficiency of those par-

ticular parameters can also be plotted. Almost every textbook 

presents the induction motor by its per phase equivalent circuit

and shows how steady-state current and power are estimated.

In many cases, the iron and mechanical losses are ignored to

simplify the procedures.

In many textbook examples, the induction motor current can

be estimated with fairly acceptable accuracy using the above

methodology. Example 1 (shown in the Appendix) presents the

standard steps to determine the current, the developed torque

and power using the equivalent circuit for squirrel-cage induc-

tion motor.

Fig. 4. The three-phase induction motor power flow diagram.

 B. The Student Interaction with the Software

At the beginning of the electric machine course, the studentreceives a hand out showing the key features of the software and

how the MathCad main built-in features work with the coursematerial. The practicality of using MathCad software instead of using the handheld calculator for the student is that it will bepossible to input various configurations of variables without anyprogramming knowledge. The use of the built-in functions of MathCad in an interactive and easy way to generate the com-plete motor characteristics over the entire speed range ratherthan one operating point will be more informative for the stu-dent. This is one of the advantages over the numerical examplesnormally presented in the textbook. Therefore, the student canverify all the possible operating points along the motor char-acteristics. The examples stored for the student in the electronichandbook database of the course generate complete characteris-

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NIGIM AND DELYSER: USING MATHCAD IN UNDERSTANDING 167

Fig. 5. Case 1. Studies of the effect of drop in the supply voltage by 20%.

Fig. 6. Case 2. A look at the effect of maintaining constant magnetic field bymaintaining constant voltage to frequency ratio v = f  0  k  .

tics over the whole speed range allowing the student to examinethe shape and verify different operating points. To produce afamily of curves on one plot only requires the keying in of vari-able definitions, data and the formulas acceptable to MathCad,

Fig. 7. Case 3. A look at the effect of maintaining constant magnetic field bymaintaining constant voltage to frequency ratio v = f  0  k  for permanent splitcapacitor-start capacitor-run, one-phase induciton motor.

as shown in Example 1. The second step is to verify numericallythe solution by comparison with the textbook result. The numer-ical values of the calculated variables can be checked using theMathCad built-in calculator. It is possible to generate a numberof plots representing different operating conditions such as thevariations of voltage and frequency by using “cut and paste” of the main keyed-in variables and data.

The copied section is pasted on to an empty area in the docu-ment as many times as required and each time a new subscriptfor the variables have to be labeled.

For the tutor, the example should be laid out in a way to beas close as possible to the text presented in the textbook so asto assist the student in following the solution procedures. Later

on, the students will be capable of creating their own routinesneeded to represent the operating characteristics of the motornumerically and graphically in a short time without the need of any programming tool. Furthermore, the software can be usedfor verifying laboratory experiments after entering the labora-tory motor data and the operating conditions using data importfacilities incorporated in MathCad. The recorded test results forthe laboratory machines could be compared for further verifica-tion between theory and practice.

III. SIMULATION CASES

To investigate the motor characteristics under varying con-

ditions the following cases were presented and included in the

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168 IEEE TRANSACTIONS ON EDUCATION, VOL. 44, NO. 2, MAY 2001

electronic handbook as examples for the student to search in

and alter the input conditions to examine the resulting effect

(some parts of the examples cannot be modified “using the

lock area facility”). Only the graphical format is presented

here as the variables and equations are based on Example 1

data.

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NIGIM AND DELYSER: USING MATHCAD IN UNDERSTANDING 169

The three cases of this section (Cases 1 and 2 regarding the

three-phase motor, and Case 3 for the single-phase induction

motor). The three phase motor input current, developed torque,

developed mechanical power and the efficiency for variable

input conditions for the motor used in Example 1 are listed. The

data and input conditions presented by the equivalent circuit

(for the three-phase motor) were varied to investigate the motor

characteristics under different possible control modes:Case 1, where the supply voltage is reduced by 20%. The

Supply frequency is kept unchanged. The mode is known as

the variable voltage constant frequency operation. The voltage

is reduced either by resistance or autotransformer connected

in series with the supply voltage. Recently phase controlled

thyristors configurations have been used to vary the supply

voltage instead of the autotransformer in many applications.

In this method of speed control, the developed torque per

ampere of input motor current is reduced as the stator voltage is

reduced. Therefore, for constant load torque characteristics, the

motor input current increases as the speed decrease, resulting

in more copper losses (heat) and causes the motor insulation to

deteriorate. This method is well suited for cubic torque-speedcharacteristics (such as air blowers and fans).

Case 2, where both voltage and frequency wasvaried to main-

tain constant magnetic flux. The technique is well adopted in

all ac drives to control the speed and torque of the induction

motors. Since the motor is operated at a constant air gap flux

(the motoring speed range below the synchronous speed), the

torque per ampere is high permitting fast transient response of 

the drive system. An another advantage of this type of control

is the capability of starting the motor at the maximum torque. It

is also possible to drive the motor above the synchronous speed

by reducing the voltage and increasing the frequency of what is

known as flux weakening mode (constant power mode).

Case 3, for the one-phase permanent split capacitor induction

motor in which the supply voltage and frequency were main-

tained constant. The motor base supply voltage and frequency

are 110 V at 60 Hz. The control technique is well adopted in

all ac drives to control the speed and torque of the three-phase

induction motor, but has constraints when applied to one-phase

since the motor developed torque decreases below 50% of the

speed due to the inherited one-phase motor characteristics [7].

IV. CONCLUSION

MathCad is a good tool to introduce an easy way to evaluate

the steady-state characteristics of the induction motor. The soft-

ware has a high potential for the analysis of system performanceand can be used in simulation techniques effectively. The use

of the built in functions of the software in an interactive and

easy way to generate the complete motor characteristics over

the entire speed range rather than one operating point is more

informative for the student. This is one of the advantages over

the numerical examples normally presented in the textbook. As

computing languages are not essential, the undergraduate engi-

neer can investigate the motor characteristics quickly and easily.

APPENDIX

The following shows the result of simulating the motor

characteristics under normal operating conditions for full speed

range. The text was copied from MathCad and inserted in

this document using “cut and paste” through the Windows

clipboard. The example solution procedures were sectionalized

for clarity. The equations were presented in the format that

normally appears in the textbooks.

REFERENCES

[1] G. Bengu and W. Swart, “A computer aided, total quality approach tomanufacturing education in engineering,” IEEE Trans. Educ., vol. 39,Aug. 1996.

[2] K. Foster, “Abstract math made practical,” IEEE Spectrum, Nov. 1993.[3] G. Kaplan, “Math, visualization and data acquisition,” IEEE Spectrum,

Nov. 1993.[4] R. Krishnan, A. Bharadwaj, and P. Materu, “Computer aided design of 

electrical machine for variable speed applications,” IEEE Trans. Ind.

 Electron., vol. 35, no. 4, Nov. 1988.[5] S. Linke, J. Torgeson, and J. Au, “An interactive computer-graphics pro-

gram to aid instruction in electric machinery,” IEEE Comput. Applicat.Power , July 1989.

[6] S. E. Zocholl, “Motor Analysis for Protection Engineers,” IEEE Comput. Applicat. Power , Oct. 1993.

[7] K. A. Nigim, “PC Based Single and Three Phase Induction Motor DrivePerformance Simulation,” in 7th Mediterranean Electrotech. Conf., An-talya, Turkey, Apr. 1994.

[8] R. Delyzer, “Using MathCad in electromagnetic education,” IEEE Trans. Educ., vol. 39, pp. 198–209, May 1996.

[9] MathCad version 6 user manual.

Khalid A. Nigim (M’85) was born in Gaza in 1955. He received the B.Sc. de-gree in electrical engineering from Zagazig University, Egypt, in 1979. He re-ceived the Ph.D. degree from the University of Leicester, U.K., in 1983.

He has been an Assistant Professor of Electrical Engineering at Birzeit Uni-versity, West Bank,since 1983. He was granted several honarary research grantsin the United Kingdom, Germany, and the United States. His research interestsinclude induction motor speed controllers, solar and wind energy controllers,FACTS, and microcontrollers for the control of industrial equipment.

Ronald R. DeLyser (S’74–M’75–SM’87) received the B.S. degree from theUniversity of Florida, Gainesville, in 1974, the M.S. degree from the Universityof NewMexico,Albuquerque, in 1978, and the Ph.D. degree fromthe Universityof Colorado, Boulder, in 1991, all in electrical engineering.

As a member of the United States Air Force between 1965 and 1986, held ateaching position at the United States Air Force Academy, served as a Develop-

ment Engineer at the Air Force Weapons Laboratory at Kirtland AFB in NewMexico andwas theRequirements Officer forthe NellisAFB Rangesin Nevada.He is currently an Associate Professor of Engineering in the Engineering De-partment of the University of Denver, where he has been on the faculty since1986. His research areas include pedagogy, outcomes bases assessment, thestudy of periodic gratings used as antennas and in antenna systems, high powermicrowave interactions with large complex cavities, anechoic chambers, andanechoic chamber absorbing materials.