IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 1, FEBRUARY 2005

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Induction Motor Tests Using MATLAB/Simulink and Their Integration Into Undergraduate Electric Machinery Courses Saffet Ayasun, Member, IEEE, and Chika O. Nwankpa, Member, IEEE

Abstract—This paper describes MATLAB/Simulink implementation of three induction motor tests, namely dc, no-load, and blocked-rotor tests performed to identify equivalent circuit parameters. These simulation models are developed to support and enhance electric machinery education at the undergraduate level. The proposed tests have been successfully integrated into electric machinery courses at Drexel University, Philadelphia, PA, and Nigde University, Nigde, Turkey. Index Terms—Education, induction Simulink, software laboratory.

motors,

MATLAB/

I. INTRODUCTION

W

ITH THE advent of low-cost personal computers and various easily accessible software packages, computer-aided teaching tools have become an essential part of both classroom lectures and laboratory experiments in electrical machinery education [1]–[6]. The computer models and simulations of induction motors, as teaching tools, support the classroom teaching by enabling the instructor, through the computer-generated graphics, to illustrate easily steady-state operation of the motor under various loading conditions [2]–[5]. The computational tools as a part of laboratory experiments enhance laboratory experience by providing students with the opportunity to verify the results of laboratory experiments and compare them with those obtained by computer simulations. Such a comparison opportunity helps students realize the limitations of hardware experiments and, as a counterpoint, appreciate that computer models cannot substitute for actual hardware experiments that might not exactly represent the operation of induction motors because of some modeling assumptions [1], [2]. Moreover, an undergraduate electric machinery course that integrates up-to-date computer hardware and software tools in both lecture and laboratory sections also meets the expectations of today’s students who want to use computers and simulation tools in every aspects of a course, and thus, possibly attracts more students [2], [3].

Manuscript received March 6, 2003; revised November 22, 2003. This work was supported in part by the U.S. Department of Energy under Contract ER63384. S. Ayasun is with the Department of Electric and Electronics Engineering, Nigde University, College of Engineering, Nigde, 51200, Turkey (e-mail: [email protected]). C. O. Nwankpa is with the Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA 19104 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TE.2004.832885

Electrical machinery courses at the undergraduate level typically consist of classroom and laboratory sections. The classroom section covers the steady-state operation of the induction motor in which the per-phase equivalent circuit is used to compute various motor quantities, such as input current and power, power factor, developed torque, and efficiency. The computations associated with the steady-state operation require the knowledge of equivalent circuit parameters. These parameters are obtained by performing three tests, namely dc, no-load, and blocked-rotor tests on the motor in a typical laboratory experiment [7]. The laboratory section includes these tests and a load experiment that allows students to become familiar with the induction motor operation and to gain invaluable hardware and measurement experiences. The authors’ experience while teaching induction motors at Drexel University, Philadelphia, PA, indicates that students generally have difficulty when they come to the laboratory to carry out these experiments even though the corresponding theory is extensively covered in the classroom section with a detailed hand-out describing laboratory facilities and the procedure of the experiments, given to them at least a week before the laboratory. Students are not familiar with a laboratory environment that contains large machines and relatively complex measurement methods and devices as compared with other laboratories they have been to before. The time constraints during the laboratory exercise are also a difficult adjustment. In a usual two-hour laboratory section, students are required to set up and perform four induction motor experiments, to take the necessary measurements, and to investigate steady-state performance of the motor under various loading conditions. Because of the time limitations, students often rush through the experiments in order to finish them on time, which unfortunately prevents them from getting a true feeling of motor operation and from appreciating what has been accomplished during the laboratory practice. Therefore, simulation tools must be developed for induction motor experiments to serve as useful preparatory exercises before students come to the laboratory. The objective of this paper is to present simulation models of these induction motor experiments in an effort to design a computational laboratory. The dc, no-load, and blocked-rotor simulation models are developed as stand-alone applications using MATLAB/Simulink [8] and Power System Blockset (PSB) [9]. For the load experiment, students are required to write a computer program using MATLAB’s M-file programming for the per-phase equivalent circuit of the induction motor to compute operating quantities.

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Fig. 1. Per-phase equivalent circuit of an induction motor.

Fig. 2. Experimental setup of the dc test.

Such an assignment improves students’ programming skills that would be helpful in other classes as well. The remainder of the paper is organized as follows. Section II describes the dc, no-load, and blocked-rotor tests. For the sake of completeness, first the experimental setup for each test is provided with a brief explanation of how these tests are conducted and how the corresponding measurements are used to compute the equivalent circuit parameters. Then, for each test, the corresponding Simulink/PSB model is presented and compared with the actual experimental setup emphasizing the similarities and discrepancies. Section III compares the equivalent circuit parameters determined using simulation data and data obtained from experiments. Section IV explains how to integrate these simulation models into undergraduate electric machine courses at two different universities, while the last section concludes the paper. II. INDUCTION MOTOR TESTS: EXPERIMENTAL SETUPS AND SIMULINK/PSB MODELS The steady-state operating characteristics of a three-phase induction motor are often investigated using a per-phase equivaand replent circuit as shown in Fig. 1. In this circuit, resent stator resistance and leakage reactance, respectively; and denote the rotor resistance and leakage reactance referred to the stator, respectively; resistance stands for core represents magnetizing reactance; and denotes the losses; slip. The equivalent circuit is used to facilitate the computation of various operating quantities, such as stator current, input power, losses, induced torque, and efficiency. When power aspects of the operation need to be emphasized, the shunt resisis usually neglected; the core losses can be included tance in efficiency calculations along with the friction, windage, and

stray losses. The parameters of the equivalent circuit can be obtained from the dc, no-load, and blocked-rotor tests [7], [10]. In the following, both experimental setup and Simulink/PSB models of each test are described. The PSB is a useful software package to develop simulation models for power system applications in the MATLAB/Simulink environment. With its graphical user interface and extensive library, it provides power engineers and researchers with a modern and interactive design tool to build simulation models rapidly and easily. MATLAB and Simulink/PSB have been widely used by educators to enhance teaching of transient and steady-state characteristics of induction machines [2], [3], [11]. Of course, other commercial software packages, such as Maple and MathCad, are commonly used in electrical engineering education with their advantages and disadvantages [12]. The reason that MATLAB with its toolboxes was selected is that it is the main software package used in almost all undergraduate courses in the authors’ institutions as a computation tool to reinforce electrical engineering education. Therefore, students can easily access to MATLAB, and they already have the basic programming skills to use the given Simulink models and to write computer programs when required before coming to the machinery class. A. dc Test The dc test is performed to compute the stator winding resistance . A dc voltage is applied to the stator windings of an induction motor. The resulting current flowing through the stator windings is a dc current; thus, no voltage is induced in the rotor circuit, and the motor reactance is zero. The stator resistance is the only circuit parameter limiting current flow. Fig. 2 shows

AYASUN AND NWANKPA: INDUCTION MOTOR TESTS USING MATLAB/SIMULINK

Fig. 3.

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Simulink/PSB implementation of the dc test.

Fig. 4. Experimental setup of the no-load test.

the experimental setup of the dc test conducted at the Interconnected Power Systems Laboratory (IPSL) [13] of Drexel University. A 120-V dc power source is applied to the two phases of a Y-connected induction motor. A group of light bulbs are installed in the circuit as a resistive load in order to adjust dc current to the rated value. The current in the stator windings and voltage across the two phases of the motor are measured. Fig. 3 depicts the Simulink/PSB implementation of the dc test. From the PSB machine library, an induction motor block is used whose electrical parameters (such as nominal voltage and equivalent circuit parameters) and mechanical parameters (such as inertia and number of poles) can be specified in either International System of Units (S.I.) or in per unit [9]. Similar to the experimental setup, a 120-V dc source is applied to the two phases (phases A and B) of the induction motor through a series resistance, while the phase C is grounded through a re-

sistance branch in order to have a complete electrical connection. The purpose of the series resistance between the dc source and the induction motor is to limit the current flowing through the two windings of the motor to its rated value, which is similar to the lighting bulbs used in the hardware setup of Fig. 2. Voltage and current measurement blocks measure the instantaneous voltage across two phases and the current flowing through the windings, respectively. Two scopes display the waveforms of the voltage and current, while two display boxes are used and curto obtain the steady-state values of the dc voltage, rent . With these two measurements, the stator resistance can easily be computed as (1) The stator resistance obtained from the dc test is an approximate value of the actual one since the skin effect observed when

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Fig. 5.

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Simulink/PSB implementation of the no-load test.

an ac voltage is applied to the stator windings and temperature effects are not taken into consideration. However, this approximation is reasonable enough for teaching purposes. B. No-Load Test The no-load test on an induction motor is conducted to measure the rotational losses of the motor and to determine some of its equivalent circuit parameters. In this test, a rated, balanced ac voltage at a rated frequency is applied to the stator while it is running at no load, and input power, voltage, and phase currents are measured at the no-load condition. Fig. 4 illustrates the experimental setup of the no-load test conducted at Drexel University’s IPSL. Fig. 5 shows the Simulink/PSB realization of the no-load test, where a three-phase balanced Y-connected ac source whose per-phase voltage is 120 V/60 Hz is applied to the stator terminal of the induction motor. The electrical inputs of the induction motor block are the three electrical connections of the stator (terminals A-B-C), while the electrical outputs (terminals a-b-c) are the three electrical connections of the rotor, which is short-circuited. The input block (terminal Tm) is the mechanical torque at the machine’s shaft. This torque is set to be zero to simulate the no-load condition. The equivalent circuit parameters obtained from experimental data and the number of poles are specified using the induction motor-block dialogue box. Three current measurement blocks are used to measure the instantaneous current of each phase. The output of each current measurement block is connected to a root-mean-square (rms) block, called signal rms, to determine the rms value of each

phase current. This block computes the rms value of the input signal over a running window of the one cycle of the specified fundamental frequency (60 Hz). Three display boxes read these rms values. Similarly, a voltage measurement block, an rms block, and a display box are used to measure the phase A voltage. The outputs of the voltage measurement block and the current measurement block of phase A are connected to a power measurement block, called the active and reactive power measurement, that computes the active power and reactive power. The output of this block is connected to a scope and to a display and . The block to obtain the waveforms and the values of output terminal of the induction motor block (terminal m-SI) allows for the measurement of several variables, such as speed and electrical torque. A machine measurement block is used to get the mechanical speed. Through the scope and display block, the waveform and the steady-state value of the rotor speed can easily be measured in rad per second, or the corresponding data can be written to MATLAB’s workspace to make use of other graphical tools available in MATLAB. Fig. 6 shows the evolution of the mechanical speed during the no-load simulation. The rotor speed reaches its steady-state value (188.5 rad/s for the tested motor) quickly, indicating that MATLAB/Simulink is an appropriate tool to investigate steady-state behavior of induction motors as well. One can see that there are some differences between the hardware setup and Simulink/PSB model. For example, the per-phase-based real and reactive input power is measured in the simulation model, while in the experiment the total three-phase real input power is measured. However, this difference is

AYASUN AND NWANKPA: INDUCTION MOTOR TESTS USING MATLAB/SIMULINK

Fig. 6.

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Evolution of the mechanical speed during the no-load test simulation.

not significant since under the three-phase balanced operation, computations are usually completed using the per-phase quantities. Similarly, the per-phase voltage is measured in the simulation, as opposed to the line-to-line voltages measured in the hardware experiment. These measurements enable the approximate computation and the stator of the sum of the magnetizing reactance as follows [7]: leakage reactance or

(2)

where is the per-phase voltage , is the phase A measured reactive power, and is the average phase current . Using measured input power measured and the stator resistance obtained from the dc test, rotational losses of the motor given by the sum of the friction, windage, and core losses can be found, as follows: (3)

installed in the circuit in order to perform the blocked-rotor test at various frequencies and to control input voltage to the stator. Fig. 7 shows the Simulink/PSB model of the blocked-rotor test. This model is almost the same as that of the no-load test shown in Fig. 5. However, there is a slight difference between the two models. In the blocked-rotor model, the inertia of the induction motor is set to infinity in order to simulate the blocked-rotor condition. Several measurements blocks are used to measure the current, voltage, and active/reactive powers. The mechanical torque to the rotor is set to an arbitrary nonzero 5 Newton-meter (N.m)], which value [in this case, will not affect the blocked-rotor condition since the inertia is infinite. Because of the infinite inertia, rotor speed remains at zero during the blocked-rotor simulation. Various test frequencies for blocked-rotor simulation can be easily achieved by changing the frequencies of the -connected voltage sources rather than using a synchronous generator coupled with a dc motor. The measurement data from the blocked rotor test enables one to determine approximately the blocked-rotor resistance and reactance at the test frequency

C. Blocked-Rotor Test The blocked-rotor test on an induction motor is performed to determine some of its equivalent circuit parameters. In this test, the rotor of the induction motor is blocked, and a reduced voltage is applied to the stator terminals so that the rated current flows through the stator windings. The input power, voltage, and current are measured. For some design-class induction motors, this test is conducted under a test frequency, usually less than the normal operating frequency so as to evaluate the rotor resistance appropriately [7]. The experimental setup of the blocked-rotor test is not shown here since it is similar to that of the no-load test shown in Fig. 4. The only difference is that a synchronous generator coupled with a dc motor and auto transformer were

(4) where is the blocked-rotor resistance, and blocked-rotor reactance at the test frequency [7].

is the

or (5) If the test frequency is different from the rated frequency, one can compute the total equivalent reactance at the normal

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Fig. 7. Simulink/PSB implementation of the blocked-rotor test.

operating frequency as follows since the reactance is directly proportional to the frequency:

TABLE I EQUIVALENT CIRCUIT PARAMETERS OF THE INDUCTION MOTOR TESTED

(6) When the three tests are completed, equivalent circuit parameters can easily be computed. 1) The stator resistance is directly computed from the dc test. 2) The no-load test gives the sum of the magnetizing reacand the stator leakage reactance . tance 3) The blocked-rotor test gives that of the stator and rotor leakage reactances. One needs to refer to test codes to find out the empirical proportions for stator and leakage reactances given for three-phase induction motors by class [7], [14]. When the classification of . the motor is not known, one assumes that The magnetization reactance can now be evaluated using (2), as follows: (7) , a better approximation is reAs for the rotor resistance quired since it has a more significant effect on the motor performance when compared with the other circuit parameters. Using

the equivalent circuit under blocked-rotor condition, the following expression achieves the desired approximation [10]: (8)

III. COMPARISON OF EQUIVALENT CIRCUIT PARAMETERS To illustrate the effectiveness of the proposed simulation models, one compares the equivalent circuit parameters determined by simulations with those obtained from hardware experiments. The motors used for this purpose are the three-phase 60-Hz Y-connected, and the 5-Horse Power (HP) induction motors of 200-V rating 1735 r/min located at Drexel University’s IPSL. A set of hardware experiments are first performed (i.e., dc, no-load, and blocked-rotor tests) on four induction motors to obtain appropriate equivalent circuit parameters for software simulations. The resulting parameters are presented in Table I.

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TABLE II SIMULATION RESULTS OF THE INDUCTION MOTOR TESTS FOR MOTOR 1

TABLE III EQUIVALENT CIRCUIT PARAMETERS DETERMINED BY SIMULATION AND THE CORRESPONDING ERRORS

For each induction motor tested the Simulink/PSB models of the dc, no-load, and blocked-rotor tests were run. The simulation data of no-load and blocked-rotor tests for motor 1 is shown in Table II, where various quantities, such as voltage, current, and power required to compute equivalent circuit parameters, are presented. The dc test simulation data for motor 1 is as follows: 12.66 V and 15.74 A. The simulation data for the other three motors is similar to that of Motor 1 and, thus, is not given here. Table III gives the equivalent circuit parameters computed, using the simulation data and the corresponding errors relative to those obtained experimentally. The error computations assume that equivalent circuit parameters determined experimentally are accurate. The results indicate that relative errors are negligible, and the proposed simulation models accurately predict equivalent circuit parameters. The largest error occurs in the stator and rotor leakage reactances, since one assumes that two reactances have equal contributions to the blocked-rotor reactance, which might not be the real case. IV. INTEGRATION OF SIMULATION MODELS INTO ELECTRIC MACHINERY COURSES In this section, the authors describe the integration of these simulation models into electric machinery courses at two different universities, Drexel University and Nigde University, Nigde, Turkey. The Electrical and Computer Engineering (ECE) Department of Drexel University offers a pre-junior-level machine course (ECE-P 352 Electric Motor Control Principles) that concentrates on the fundamentals of electromechanical energy conversion and related control theory. This five-hour course required for those who are in the power and control track has both lecture and laboratory sections that must be taken in the same quarter. The lecture section (three hours a week) introduces students to operation principles of transformers, induction motors, dc motors, and various motor control techniques, including the power-electronics-based ones. In the laboratory section (two hours a week), students are required to perform various experiments for which the necessary theoretical background is developed in the lecture

section. The experiments conducted during the term at the IPSL of Drexel University include open-circuit, short-circuit, and load tests for transformers, speed control experiments for dc motors, and induction motor tests. The IPSL is a computerized, small-scale, energy management system that was designed to provide students with a hands-on learning experience about the attributes and implications involved in the management and control of a small electric power system. With its customized graphic-intensive environment, it provides a set of experiments on the interaction of various system components in a real-life power system operating environment [13]. In order to incorporate simulation models of induction motor tests into the course, the laboratory section is divided into two main components, each of which is a two-hour section: software laboratory and hardware laboratory. After being introduced to the theory and operating characteristics of the induction motors, including per-phase equivalent circuit and torque-speed curve and speed control methods, students simulate three induction motor tests presented in the previous section and record the data required to compute per-phase equivalent circuit parameters. A week before the software laboratory, the Simulink/PSB models of the tests and a detailed hand-out describing how each model is to be simulated are made available to students. An example of the procedure showing the steps involved in simulating a no-load condition is given in the Appendix. An essential part of the software laboratory is an assignment given to students to develop a computer model for the per-phase equivalent circuit of the induction motor using the MATLAB programming language. Using the computer program, students investigate motor characteristics under varying conditions. Examples of simulations obtained by students’ computer programs for the motor 1 are presented in Figs. 8–10. Fig. 8 shows motor quantities, such as input current and power, power factor, developed torque and power, and efficiency as a function of rotor speed, and how these quantities are affected by a 20% drop in the supply voltage when the frequency is kept constant at the nominal value. Fig. 9 illustrates the same quantities when the frequency is reduced by 25% while the supply voltage is kept unchanged. Fig. 10 shows the torque-speed characteristic of the motor for different values of rotor resistance. Such studies

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Fig. 8. Effect of a 20% drop in the supply voltage on various motor quantities.

on the motor characteristics over a wide speed range help students better understand various operation modes, such as variable voltage fixed frequency mode (Fig. 8) or fixed voltage variable frequency mode (Fig. 9)—material also covered in the lecture section. Furthermore, students gain experience and confidence in induction motor operation, which will be very helpful for them when they perform hardware experiments in the following week at the IPSL. In the hardware laboratory, students are asked to set up and conduct four induction motor experiments: the dc test, the no-load test, the blocked-rotor test, and the load experiment. Similar to what is performed in the software laboratory, they take measurements required to compute motor parameters and to examine the motor characteristics under varying load. During the laboratory section, students appear to be more familiar with induction motors theory and operation because of the experience gained during the software laboratory. A week after they complete hardware experiments, students are required to submit a report that must combine results from both simulations and experiments. The emphasis is that the report should compare simulation results with experimentally recorded data, mainly focusing on the differences/similarities. One can assume that parameters obtained from simulation data would be the same as those obtained from experimental data since motor parameters determined from experimental data are used in simulations. However, as can be seen in Table III, this equivalency is not the case, and negligible errors are observed. In their reports, stu-

dents are encouraged to provide explanations for these errors. These errors might be the result of modeling of the induction motor in Simulink or measurements errors often observed in the hardware experiments. Nevertheless, proposed simulations give students insight as to the experimental procedure and the expected results before they go into the electric machinery laboratory to perform the physical experiments. The Department of Electrical and Electronics Engineering at Nigde University offers two machinery courses. These are EEM 308 Electric Machinery I (five hours a week) and EEM 435 Electric Machinery II (three hours week). The former, which must be taken by all undergraduate students, mainly focuses on transformers and induction motors. The latter, designed for power system majors only, introduces operation principles of dc motors (25%) and synchronous generators (75%). Similar to Drexel University, a software laboratory (two hours a week) as a part of Electric Machinery I has been established, and students simulate induction motor experiments. A laboratory facility, which will enable students to validate simulation results experimentally, is under construction and will be available for use in the next academic year. V. CONCLUSION AND FUTURE WORK In this paper, the authors presented simulation models of induction motor tests performed to obtain parameters of the per-phase equivalent circuit of three-phase induction motors.

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Fig. 9. Effect of a 25% drop in supply voltage frequency on various motor quantities.

MATLAB paired with Simulink/PSB is a good simulation tool to model induction motor tests and to evaluate steady-state characteristics of the induction motor. Furthermore, a successful integration of simulation models is described in a software laboratory in an electric machines course, which complements classroom lecture and laboratory practice. A logical extension to the software laboratory would be to include Simulink/PSB models of experiments of transformers, dc machines, and synchronous machines so that a complete computational laboratory is available to support electric machinery education.

APPENDIX PROCEDURE FOR THE NO-LOAD TEST SIMULATION

Fig. 10.

Torque-speed characteristics for different rotor resistance values.

Each Simulink/PSB model is explained in detail and compared with the corresponding experimental setup. Circuit parameters obtained from simulation results are compared with those obtained from hardware experiments. The error studies show that

Step 1) Set the rms value of single-phase voltage sources to 120 V (or their peak amplitudes to 169.7056 V). Make sure that the phase angles of the voltage sources are 120 apart from each other and frequency is 60 Hz. Step 2) Choose one of the induction motors at IPSL and use its equivalent circuit parameters to specify the electrical and mechanical parameters of induction motor block. Note that the inertia is not available from the hardware tests; use the default value

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Step 3)

Step 4) Step 5) Step 6) Step 7)

0.089 kg.m . The true value of the inertia is not important since the steady-state values of motor quantities need to be read. Set the frequency attributes of all the signal rms blocks and the active and reactive power measurement block to 60 Hz. Make sure that the mechanical torque to the shaft is exactly zero . Specify the stop time of the simulation and integration method. Run the simulation. Read the following data from the display boxes: (rms), (rms), (rms), (rms), , , and , and record all the data in a table. REFERENCES

[1] H. A. Smolleck, “Modeling and analysis of induction machine: A computational/experimental approach,” IEEE Trans. Power Syst., vol. 5, pp. 482–485, May 1990. [2] M. H. Nehrir, F. Fatehi, and V. Gerez, “Computer modeling for enhancing instruction of electric machinery,” IEEE Trans. Educ., vol. 38, pp. 166–170, May 1995. [3] M. W. Daniels and R. A. Shaffer, “Re-inventing the electrical machines curriculum,” IEEE Trans. Educ., vol. 41, pp. 92–100, May 1998. [4] K. A. Nigim and R. R. DeLyser, “Using MathCad in understanding the induction motor characteristics,” IEEE Trans. Educ., vol. 44, pp. 165–169, May 2001. [5] S. Linke, J. Torgeson, and J. Au, “An interactive computer-graphics program to aid instruction in electric machinery,” IEEE Comput. Appl. Power, vol. 2, pp. 19–25, July 1989. [6] T.-F. Chan, “Analysis of electric machines using Symphony,” IEEE Trans. Educ., vol. 35, pp. 76–82, Feb. 1992. [7] S. J. Chapman, Electric Machinery Fundamentals, 3rd ed. New York: WCB/McGraw-Hill, 1998.

[8] SIMULINK, Model-Based and System-Based Design, Using Simulink, MathWorks Inc., Natick, MA, 2000. [9] Power System Blockset for Use With Simulink, User’s Guide, MathWorks Inc., Natick, MA, 2000. [10] M. S. Sarma, Electric Machines: Steady-State Theory and Dynamic Performance, 2nd ed. St. Paul, MN: West, 1994. [11] K. L. Shi, T. F. Chan, Y. K. Wong, and S. L. Ho, “Modeling and simulation of the three-phase induction motor using Simulink,” Int. J. Electr. Eng. Educ., vol. 36, pp. 163–172, 1999. [12] C. A. Canizares and Z. T. Faur, “Advantages and disadvantages of using computer tools in electrical engineering courses,” IEEE Trans. Educ., vol. 40, pp. 166–171, Aug. 1997. [13] S. P. Carullo and C. O. Nwankpa, “Interconnected power system laboratory: A computer automated instructional facility for power system experiments,” IEEE Trans. Power Syst., vol. 17, pp. 215–222, May 2002. [14] Standard Test Procedure for Polyphase Induction Motors and Generators, IEEE Standard 112, 1996.

Saffet Ayasun (S’97–M’02) was born in Tokat, Turkey, on October 27, 1968. He received the M.S. degree in electric engineering, the M.S. degree in mathematics, and the Ph.D. degree in electrical engineering from Drexel University, Philadelphia, PA, in 1997, 2001, and 2002, respectively. He is currently working as an Assistant Professor in the Electrical Engineering Department of Nigde University, Nigde, Turkey. His research interests include stability of the nonlinear dynamical system, applied mathematics, nonlinear control theory, power systems, and bifurcation theory.

Chika O. Nwankpa (S’88–M’90) was born in Owerri, Nigeria, in 1962. He received the Magistr Diploma in electric power systems from the Leningrad Polytechnical Institute, Russia, in 1986 and the Ph.D. degree in electrical and computer engineering from the Illinois Institute of Technology, Chicago, in 1990. He is currently a Professor of electrical and computer engineering at Drexel University, Philadelphia, PA. His research interests are in the areas of power systems and power electronics. Dr. Nwankpa received the Presidential Faculty Fellow Award in 1994 and the NSF Engineering Research Initiation Award in 1991.