publicité

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 1, JANUARY 1999 23 Predicting the Transient Effects of PWM Voltage Waveform on the Stator Windings of Random Wound Induction Motors G. Suresh, Student Member, IEEE, Hamid A. Toliyat, Senior Member, IEEE, Dudi A. Rendusara, Student Member, IEEE, and Prasad N. Enjeti, Senior Member, IEEE Abstract— In this paper, the effect of pulsewidth modulation (PWM) voltage waveform on the voltage distribution among the stator windings of random wound cage induction motors is studied. First, a method of estimating the high-frequency distributed-circuit parameters of the motor using finite-element analysis is described. From these parameters, an equivalent circuit is formed with the windings represented by partially distributed and partially lumped parameters. Using this equivalent circuit, the voltage distribution among the turns and coils of the motor are simulated using the SABER simulation package. Through simulation, the effect of rise time of the PWM wavefront on the voltage distribution is studied, and it is shown that the rise time of the wavefront has influence on the additional voltage stress on the line-end coil. In order to validate the simulation procedure adapted, the simulation results are compared with experimental results. Index Terms— dv=dt, induction motor, PWM drives, transient effects, voltage stress. I. INTRODUCTION W HEN INDUCTION motors are fed from pulsewidth modulation (PWM) inverter power supplies, the stator winding is subjected to high-voltage stresses caused by the train of wavefronts in the PWM voltage waveform. The voltage distribution among the turns and coils is highly nonlinear of the wavefront, and this often because of the high results in higher voltage stresses in the first few turns of the line-end coil. These voltage stresses are several times higher compared to stresses caused by sinusoidal waveforms. The voltage withstanding capability of the commonly used magnet ’s and wire is worsened when waveforms with high fast switchings are imposed on the windings. This causes premature failure of insulation and, hence, results in forced outage of the drive system. Most of the low- and medium-size induction motors are fed from PWM voltage source inverters employing insulated gate bipolar transistor (IGBT) switches because of several advantages. With the advancement in power semiconductor technology, it has been possible to keep the switching times as low as 0.1 s. Although the inverter switching losses are Manuscript received March 18, 1997; revised May 14, 1998. Recommended by Associate Editor, A. Goodarzi. The authors are with the Department of Electrical Engineering, Texas A&M University, College Station, TX 77843-3128 USA. Publisher Item Identifier S 0885-8993(99)00284-7. reduced by keeping the switching time low, the insulation integrity is affected because of the detrimental effects of the sharp wavefronts on the motor windings. This problem is worsened when the motor is connected to the inverter through feeder cables. Depending on the surge impedances of the cable and motor, the motor terminal voltage can be much higher than the dc bus value and sometimes can even double because of voltage reflections. Many papers discuss the impact of PWM waveforms on the motor windings [1]–[8]. In [1] and [2], the impact of PWM waveforms on the random wound induction motors is analyzed. References [3] and [4] give methods of simulating the voltage distribution among the turns of random wound machines using equivalent circuits. The parameters used in the equivalent circuits are based on terminal measurements. Reference [6] considers the effect of feeder cable and presents a simulation procedure to compute machine terminal voltage transients. References [3]–[5] and [7]–[12] explain the voltage reflections caused at the motor terminals due to long feeder cables and a few practical ways of suppressing the terminal voltage transients. However, the distributed-circuit parameters of the individual turns would be needed if the voltage distribution among the turns and coils needs to be estimated. In the past, field analysis results have been reported for studying high-frequency field effects in form wound induction motor parameters for surge studies [13]–[16]. In this paper, a method of deriving these parameters for a random wound induction motor using finite-element analysis is presented. Random wound motors differ significantly from form wound motors because of their constructional differences. In form wound motors, each turn in a coil occupies the same relative position within the slot unlike random wound motors. Using the method described, it is possible to compute the parameters corresponding to different rise times of the PWM wavefront. With the partially distributed surge equivalent circuit, SABER [23] simulation is performed in order to estimate the voltage distribution among the turns and coils of the motor. In order to validate the method proposed, the simulation results are compared with experimental results. The organization of the paper is as follows. Section II describes the problem under consideration in detail. Section III details the method of estimating the high-frequency parameters of the motor winding. In Section IV, the details of the partially distributed equivalent circuit model used for 0885–8993/99$10.00 1999 IEEE 24 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 1, JANUARY 1999 simulation are presented. Simulation and experimental results are presented and discussed in Section V. A brief review of recently published literature on the practical remedies is given in Section VI. Section VII presents the summary and conclusions. II. DESCRIPTION OF THE PROBLEM In order to estimate the voltage distribution among the coils of the stator during a typical PWM wavefront, it is necessary to use a high-frequency distributed-circuit model for the stator winding [15]. This is mainly because of the high-frequency content of the wavefront with sharp rise time. The machine behavior at such high frequencies (which are in the order of megahertz) corresponding to fast switching transients is totally different than at power frequency, and, hence, calculating the distributed parameters is very difficult. For example, at megahertz-range frequencies corresponding to switching times in the order of fractions of microseconds, the steel laminations act like flux barriers, and, hence, most of the flux produced by the windings will be leakage fluxes. The high-frequency eddy currents induced in the rotor confine the flux to the air gap itself, and, hence, there will be no flux penetration across the air gap. Since the magnetic steel laminations act as flux barriers, the flux lines are confined to the stator slot portion itself, as will be shown later. It is also essential to represent the winding by its distributed equivalent circuit since the wavelength of the high-frequency traveling wave is very small compared to that of the power frequency. The distributed-circuit parameters to be calculated for the individual turns are the self-inductance and resistance of each turn, mutual inductances between turns within the same slot, turn-to-ground capacitances, and turn-to-turn capacitances [3], [4], [7], [8], [15], [16]. The distributed parameters of the individual turns depend on the slot geometry and also on their relative position within the slot. For example, a turn located near the slot wall will have a higher turn-to-ground capacitance compared to a turn located in the middle of the slot. A turn which is located in the middle of the slot will have a lesser turn-to-ground capacitance because of the larger separation between the turn conductor and ground. Furthermore, the conductors around the turn located in the middle of the slot act as a shield between the turn and ground. These factors complicate the computation of the parameters. Another difficulty with random wound machines is that the relative positioning of the individual turns in different slots may not be the same. In order to overcome these difficulties, finite-element analysis techniques are used to compute the circuit parameters of the coils even at high frequencies. A single-slot model of the machine will be enough to calculate all the parameters required for simulation if it is assumed that the relative positioning of the individual turns within the slots remains the same in a given phase which is a reasonably good assumption. The following are the advantages of using finite-element analysis. • Actual material properties can be defined for computing the parameters. • High-frequency field effects on the parameters can be considered. • The exact geometry of the slot can be modeled for computing the parameters. The details of the finite-element model along with the procedure of computing the various parameters are presented in the following section. III. FINITE-ELEMENT ANALYSIS OF THE SINGLE-SLOT MODEL For computing the equivalent circuit parameters of the coils, a single-slot model of the cage induction motor was used. The motor used for analysis in the present work has the following specifications: 3 HP, 3 phase, 4 pole, 60 Hz, and 230/460 V. The stator has 36 slots and has a single-layer random winding with 6 coils per phase, each coil having 54 turns. The Ansoft [24] package is used for performing finiteelement analysis of the single-slot model which basically consists of one stator slot pitch with all the turns placed randomly to simulate random winding. The slot wall insulation and individual turn insulation are also modeled in order to compute the capacitance values accurately. Although the flux lines do not penetrate the air gap, the rotor slot portion is also modeled. The package computes the field quantities per unit length of the single-slot model assuming symmetry in the axial direction. There are different solvers available in the package for performing electric and magnetic field analysis. From the finite-element analysis results, the impedance and capacitance matrices are obtained which are then used for forming the equivalent circuit. The details of the finite-element analysis are explained in the following sections. A. Computation of the Inductance and Resistance Matrices For computing the inductance and resistance matrices, an eddy-current analysis option available in the Ansoft package is used. Once the geometry of the single-slot model is created, an eddy-current analysis solver is used. The setting up of the eddy-current analysis includes setting up the excitation, defining boundary conditions, etc. When eddy-current analysis is used, the package automatically defines each conductor as a current source. The only boundary condition used is balloon boundary condition in which a surface far away from the slot model is set to zero magnetic vector potential. The frequency for which the eddy-current analysis has to be computed is also defined in the analysis. The main advantage of using an eddy-current solver is that the effects of time-varying currents in parallel conductors are considered in the analysis. Furthermore, the eddy-current effects caused in the conductors at high frequencies are taken care of. Time-varying currents flowing in a conductor produce a time-varying magnetic field in planes perpendicular to the conductor. In turn, this magnetic field induces eddy currents in the source conductor and in any other conductor parallel to it. The eddy-current field solver calculates the eddy currents and in the field equation by solving for (1) SURESH et al.: PREDICTING THE TRANSIENT EFFECTS OF PWM VOLTAGE WAVEFORM 25 where is the magnetic vector potential Wb/m, is the elecis the relative magnetic permeability, tric scalar potential, is the angular velocity at which all quantities are oscillating, is the conductivity, and is the relative permittivity. The simulator computes the impedance matrix in two steps. First, it solves for the inductance matrix associated with the model. Then it solves for the resistance matrix and then computes them to form the impedance matrix using the relationship (2) The individual elements in the impedance matrix are computed as follows. The simulator generates an eddy-current field solution for each conductor in the model. The first turn is set to 1-A current in the first solution with all the other turns set to zero current. In the second solution, only the second turn is set to 1-A current with all the other turns set to zero current. After each field solution, the inductance and resistance are computed using the following relations: (3) Fig. 1. Flux distribution in the slot during eddy-current analysis. (4) is the energy stored in the magnetic field (J), is where is the peak value of the current the ohmic loss (W), and (amp) (in this case, the peak value of the current is 1 A). After each field solution, the solver calculates the selfinductance of the conductor which was assigned 1-A current during the analysis. Also, the mutual inductances of the conductor with all the other conductors are computed. Similarly, the resistance terms are also computed after each field solution. The final output of the eddy-current analysis is a 54 impedance matrix. Thus, the complete impedance 54 matrix required for the circuit simulation is obtained in one eddy-current analysis. The flux plot obtained from the eddy-current analysis shows some interesting results of the high-frequency behavior of the machine. The flux plot obtained from the eddy-current analysis is shown in Fig. 1. The flux plot shows that the flux lines are confined to the slot portion itself, and the flux lines do not penetrate the steel laminations because of high-frequency effects. Also, there is no flux passing through the air gap to the rotor. The impedance matrix also shows that the different turns have different impedances depending on their relative positioning within the slot. B. Computation of the Capacitance Matrix The capacitance matrix is also computed in a similar way. For computing the capacitance matrix, the Ansoft electrostatic analysis package is used. During the electrostatic analysis, each conductor is defined as a voltage source and assigned 1 V with all the other conductors set to 0 V. A boundary value condition is used for electrostatic analysis in which the stator laminations are defined to be at zero electric potential. The electrostatic field simulator computes the static electric fields arising from potential differences and charge distri- butions. The field simulator solves for the electric potential in the field equation derived from Gauss’ law and is given by (5) is the charge density. where After each field simulation, the capacitance values associated with the conductor which was assigned 1 V are computed, which includes the turn-to-ground and turn-to-turn capacitances between the turn being excited and all the other turns. Thus, 54 different solutions are required to obtain the capacitance matrix. However, one electrostatic analysis performs all the simulations required automatically. After the electrostatic analysis is complete, a capacitance matrix of order 54 54 is obtained. The capacitance between conductors “ ” and “ ” is calculated as follows: (6) is the energy in the electric field associated with where flux lines that connect charges on conductor “ ” to those on conductor “ ” From the analysis results, it was found that the turn-to-ground capacitance values in the capacitance matrix are all not equal because of their relative positioning. For computing the capacitance matrix, electrostatic analysis is performed because of the fact that the variation of the capacitance terms with frequency is negligible unlike the inductance and resistance values [4], [15]. This completes the computation of the equivalent circuit parameters of the stator winding which are used for simulating the voltage distribution. In the present work, it is aimed at explaining a method of using finite-element analysis techniques to estimate the high-frequency circuit parameters of the turns in the stator winding. Using this method, the circuit parameters are computed at two different frequencies and later used 26 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 1, JANUARY 1999 Fig. 2. Partially distributed equivalent circuit of the line-end coil. for circuit simulation. The parameters of the winding which correspond to the rise time of the wavefront for which analysis has to be done were used for simulating the circuit. For example, when it is desired to simulate the voltage distribution with a 0.2- s wavefront, the surge equivalent circuit is formed with parameters corresponding to 5-MHz frequency and so on. The details of circuit simulation performed to determine the nonlinear voltage distribution are explained in the next section. IV. SIMULATION OF SURGE EQUIVALENT CIRCUIT In the previous section, the methods of estimating the highfrequency parameters of the turns and coils were explained. The procedure adopted to form a partially distributed equivalent circuit from these parameters in order to estimate the voltage distribution among the turns and coils is presented in this section. The motor used for analysis has 36 stator slots with 6 coils per phase, each coil having 54 turns, two groups of 3 coils each connected in parallel. Although it is desired to represent all the turns in the stator phases with distributed parameters, it is not practical to implement it, and, hence, a simplified equivalent circuit as suggested in [4] is used for simulation. It is well known that during the PWM wavefront, the first few turns in the line-end coil will have higher voltage stress compared to the other turns. Hence, for circuit simulation, the first five turns of the line-end coil are modeled with their distributed parameters. The other turns in the first coil as well as the other coils in the phase are represented by their lumped parameters. For obtaining the lumped parameters, the diagonal terms in the impedance matrix and capacitance matrix are considered, and the nondiagonal terms are ignored. Fig. 2 shows the distributed-circuit model of the line-end coil. The other coils in the phase are modeled with their lumped parameters. The parameters used in the circuit are turn resistances, turn self-inductances (mainly leakage), turnto-turn mutual inductances, turn-to-ground capacitances, and turn-to-turn capacitances. In order to simulate a typical PWM wavefront, a step voltage source is used as input to the equivalent circuit, and the circuit is simulated using SABER package on a SUN platform. The rise time of the step voltage source can be changed to any desired value depending on the rise time of the actual wavefront in the inverter output. A. Voltage Distribution Among the Machine Winding with 0.2- s Rise Time For simulating the voltage distribution among the turns of the winding corresponding to 0.2- s rise time, the circuit described earlier was used. A rise time of 0.2 s is chosen since the switches in the inverter used to perform experiments have a turn-on time of 0.2 s. The first few turns of the phase A windings are represented by their distributed parameters with the remaining turns in phase A modeled by lumped parameters. The phase B winding is modeled wholly by its lumped parameters. It is assumed that only phases A and B are conducting, and, hence, phase C is not modeled. All the parameters are obtained from the finite-element analysis results which were performed at 5-MHz frequency. In SABER, the rise time of the step voltage source is set at 0.2 s and its amplitude at 295 V which is the dc bus voltage, and the transient analysis option is used to obtain the voltage distribution. The transient analysis results include the voltage distribution among all the turns and coils modeled. B. Voltage Distribution Among the Machine Winding with 0.1- and 1- s Rise Time Simulations of the transient voltage distribution which correspond to a rise time of 0.1 and 1 s were also carried SURESH et al.: PREDICTING THE TRANSIENT EFFECTS OF PWM VOLTAGE WAVEFORM Fig. 3. PWM wavefront model used for simulation (rise time of the wavefront = 0:2 s). 27 Fig. 4. Simulated voltage drop across the line-end coil (rise time of the wavefront = 0:2 s). out in the same way as that of the previous case mainly to study the effect of rise time of the wavefront on the voltage distribution. The same equivalent circuit is used for this case also. The parameters used in the simulation are derived from the finite-element analysis results performed at 1-MHz frequency corresponding to 1- s rise time. While performing analysis for 0.1 s, the parameters obtained at 5 MHz are used assuming these parameters to be almost equal to 10 MHz. Detailed discussion on the simulation results and the comparison with the experimental results are presented in the next section. V. DISCUSSION AND COMPARISON OF SIMULATION AND EXPERIMENTAL RESULTS In this section, the results obtained through simulation are discussed and compared with the experimental results. The details of the induction motor used to obtain the experimental results are given in the Appendix. The IGBT switches used in the inverter have a typical rise time of 0.2 s. As described in the previous section, the first set of simulations is carried out with rise time equal to 0.2 s in order to make comparison with experimental results. A. Comparison of Simulation and Experimental Results with 0.2- s Rise Time Fig. 3 shows the PWM wavefront used for simulation. The dc bus voltage for this operating condition is 295 V. Fig. 4 shows the simulated voltage drop across the line-end coil. It should be noted that the voltage reaches a peak value of 105 V and oscillates before settling down at around 50 V. Fig. 5 shows the corresponding experimental results. The upper trace in Fig. 5 shows the inverter output voltage which is applied to the motor through a short cable. Trace 2 shows the motor terminal voltage, and trace 3 shows the line-end coil voltage which corresponds to the result shown in Fig. 4. Comparing these two results, it should be noted that the oscillations seen in the simulation results are not so much pronounced in the experimental results. A close agreement between simulation Fig. 5. Experimental results of a PWM induction motor drive with a short cable between the inverter and motor. Trace 1: inverter output voltage. Trace 2: motor terminal voltage. Trace 3: line-end coil voltage. Trace 4: Turn 1 voltage in the line-end coil. and experimental results cannot be expected anyway because of the complex nature of the problem and also the assumptions made in simulation and in the formation of the equivalent circuit. Interestingly, the peak values of the two voltages, viz., simulated and experimental line-end coil voltages, match reasonably well which is important from the motor design point of view. Also, the two waveforms take around the same time to settle down to the final steady-state value. Fig. 6 shows the simulated voltage wave form across Turn 1 of the line-end coil with 0.2- s rise time. In Fig. 5, Trace 4 shows experimentally recorded voltage drop across Turn 1 of the line-end coil which corresponds to Fig. 6. B. Simulation Results with 0.1- and 1.0- s Rise Time As described in the previous section, the circuit simulations were carried out with 0.1- and 1- s rise time for the step 28 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 1, JANUARY 1999 Fig. 6. Voltage drop across the first turn of the line-end coil (rise time of the wavefront = 0:2 s). Fig. 8. Simulated voltage drop across the line-end coil (rise time of the wavefront = 1:0 s). when the motor is fed from the inverter through feeder cables. This results in much higher voltage stresses due to voltage reflections. As a result, the motor terminal voltages may become double or even triple [1]–[5]. VI. REVIEW OF RECENTLY PUBLISHED LITERATURE ON PRACTICAL REMEDIES TO OVERCOME THE PROBLEM Fig. 7. Simulated voltage drop across the line-end coil (rise time of the wavefront = 0:1 s). voltage. Fig. 7 shows the simulated line-end coil voltage with 0.1- s rise time for the wavefront. Fig. 8 shows the line-end coil voltage when the rise time is 1 s. It can be seen that the peak value of the voltage drop across the line-end coil is highly influenced by the rise time of the wavefront. The peak of the line-end coil voltage shoots up to 190 V when the rise time is 0.1 s, and it is less than 60 V when the rise time is 1 s. This clearly shows that with larger rise times, the peak voltage stress on the motor windings can be kept within reasonable limits. The only problem in having larger rise time for the switches in the PWM inverter is that the switching losses increase and the advantages of using fast switching devices are lost. Another interesting point is that the simulated and measured peak values of the voltage drops across the line-end coil are around 105 V with 0.2- s rise time. If the first turn and last turn of the line-end coil are placed near each other within the slot, which may happen in a random wound machine, then the voltage stress caused during the transients on the thin coating separating the two turns may result in dielectric breakdown over a period of time and consequently reduce the life of the insulation system. This problem gets aggravated Insulation failure due to steep-fronted wavefronts in a PWM inverter drive has been addressed by many researchers in literature [3], [5], [7], [9]–[12], [18], [21], [22]. As it was mentioned earlier, the transient effects of the sharp wavefronts become worse when the motor is connected to the inverter through feeder cable, typically 50–600 ft long. This causes terminal voltage doubling due to voltage reflections caused by the mismatch of the cable and motor characteristic impedances. Several practical remedies have been reported in literature to overcome these problems, and a few of them are mentioned below. A. Installing Terminal Filters By installing filters, the doubling at the motor terminals can be avoided. Different filter configurations have been reported in [3], [5], [7], [9]–[12], [21], and [22], and the parameters of the filters basically depend on the characteristic impedance of the cable connecting the inverter and motor. It has been mentioned in [22] that introduction of a terminal filter of the wavefront at the motor effectively decreases the terminals. This consequently will reduce the additional voltage stress on the motor windings, especially the line-end coil. In [9] and [10], methods of eliminating the voltage doubling/tripling at the motor terminals using the pulseelimination technique in PWM inverters are explained. B. Application of Soft-Switching Inverters [18] One of the methods of avoiding the overvoltages is to employ soft switching inverters [18]. With a normal hardswitching inverter, a resonant capacitor and inductor are added that would allow soft switching. By doing this, the sharp wave- SURESH et al.: PREDICTING THE TRANSIENT EFFECTS OF PWM VOLTAGE WAVEFORM fronts occurring in a hard-switching inverter are eliminated. Since soft-switching is employed, the switching losses are also reduced drastically. VII. CONCLUSIONS In this paper, a method of estimating voltage distribution among the turns and coils of PWM inverter-fed random wound induction motors was presented. In this paper, a method for deriving random wound induction motor parameters based on finite-element analysis was explained. The distributed parameters of the machine are derived from field analysis rather than terminal measurements which makes estimation of voltage transients possible at the design stage itself. The simulation results show the nonlinear nature of voltage distribution among the turns and coils of the machine windings during transients caused by PWM wavefront. The simulation results give an idea about the level of voltage stress which the turns and coils undergo when the motor is fed from the inverter power supply, and, hence, the insulation integrity can be ensured during the manufacturing process. Using the procedure explained, it is possible to simulate the effect of variation of rise time of the PWM wavefront on the transient voltage distribution, and, hence, optimum value of rise time can be chosen for the inverter. By introducing appropriate equivalent circuits, the effect of feeder cable can also be simulated prior to manufacturing and commissioning. 29 [11] A. Hussain and G. Joos, “Modeling and simulation of traveling waves in induction motor drives,” in IEEE APEC Conf. Rec., 1997, pp. 128–134. [12] S. Kim and S. Sul, “A novel filter design for suppression of high voltage gradient in voltage-fed PWM inverter” in IEEE APEC Conf. Rec., 1997, pp. 122–127. [13] P. G. McLaren and H. Oraee, “Multiconductor transmission line theory model for the line-end coil of large ac machines,” Proc. Inst. Elect. Eng., vol. 132, pt. B, pp. 149–156, May 1985. [14] R. G. Rhudy, E. L. Owen, and D. K. Sharma, “Voltage distribution among the coils and turns of a form wound ac rotating machine exposed to impulse voltage,” IEEE Trans. Energy Conversion, vol. EC-1, pp. 50–60, June 1986. [15] J. L. Guardado and K. J. Cornick, “Calculation of machine winding electrical parameters at high frequencies for switching transient studies,” IEEE Trans. Energy Conversion, vol. 11, pp. 33–40, Mar. 1996. [16] Y. Tang, “Analysis of steep-fronted voltage distribution and turn insulation failure in inverter fed ac motor,” in IEEE IAS Conf. Rec., 1997, pp. 509–516. [17] M. Melfi, J. Sung, S. Bell, and G. Skibinski, “Effect of surge voltage rise-time on the insulation of low voltage machines fed by PWM converters,” in IEEE IAS Conf. Rec., 1997, pp. 239–246. [18] D. Divan, “Low stress switching for efficiency,” IEEE Spectrum Mag., Dec. 1996, pp. 33–39. [19] H. A. Toliyat, G. Suresh, and A. Abur, “Simulation of voltage stress on the inverter fed induction motor windings supplied through feeder cable,” in IEEE IAS Conf. Rec., 1997, pp. 143–150. [20] G. Suresh, H. A. Toliyat, and A. Abur, “Analysis of the effect of feeder cable on the stator winding voltage distribution in a PWM induction motor drive,” in Electrical Insulation Conf. Rec., 1997, pp. 407–412. [21] B. Mokrytzki, “Filters for adjustable frequency drives,” in IEEE APEC Conf. Rec., 1994, pp. 542–548. [22] A. Von Jouanne, P. N. Enjeti, and W. Gray, “Application issues for PWM adjustable speed ac motor drives,” IEEE Industrial Applications Society Mag., pp. 10–18, Sept./Oct. 1996. [23] SABER-Power Express User’s Guide, Release 4.0, Analogy Inc., Beaverton, OR, 1993. [24] Maxwell 2D Field Simulator, User’s Reference, Release Notes Version 6.3, 1995, Ansoft Corp., Pittsburgh, PA. APPENDIX The marathon electric induction motor specifications include: 3 hp, 182-T frame, 230/460 V, 60/50 Hz, 4 poles, 36 stator slots, 44 rotor slots, 54 turns per coil, 6 coils per phase, and two groups of three coils connected in parallel in each phase. REFERENCES [1] A. H. Bonnett, “Analysis of the impact of pulse-width modulated inverter voltage waveforms on ac induction motors,” IEEE Trans. Ind. Applicat., vol. 32, pp. 386–392. Mar./Apr. 1996. [2] E. Persson, “Transient effects in application of PWM inverters to induction motors,” IEEE Trans. Ind. Applicat., vol. 28, pp. 1095–1101, Sept./Oct. 1992. [3] R. Kerkman, D. Leggate, and G. Skibinski, “Interaction of drive modulation and cable parameters on AC motor transients,” in IEEE IAS Conf. Proc., 1996, pp. 143–152. [4] L. Gubbala, A. von Jouanne, P. N. Enjeti, C. Singh, and H. A. Toliyat, “Voltage distribution in the windings of an ac motor subjected to high dv=dt PWM voltages,” in IEEE PESC Conf. Proc., 1995, pp. 579–585. [5] G. Skibinski, “Design methodology of a cable terminator to reduce reflected voltage on ac motors,” in IEEE IAS Conf. Proc., 1996, pp. 153–161. [6] D. B. Hyypio, “Simulation of cable and winding response to steepfronted voltage waves,” in IEEE IAS Conf. Rec., 1995, pp. 800–806. [7] A. von Jouanne, D. A. Rendusara, P. N. Enjeti, and W. Gray, “Filtering techniques to minimize the effect of long motor leads on PWM inverter fed ac motor drive systems,” in IEEE IAS Conf. Proc., 1995, pp. 37–44. [8] C. J. Melhorn and L. Tang, “Transient effects of PWM drives on induction motors,” in IEEE/I&CPS Conf. Rec., May 1995, pp. 1–7. [9] R. J. Kerkman, D. Leggate, D. Schlegel, and G. Skibinski, “PWM inverters and their influence on motor over-voltages,” in IEEE APEC Conf. Rec., 1997, pp. 103–113. [10] G. Skibinski, D. Leggate, and R. J. Kerkman, “Cable characteristics and their influence on motor over-voltages,” in IEEE APEC Conf. Rec., 1997, pp. 114–121. G. Suresh (S’95) received the B.E. degree in 1989 from Annamalai University, Annamalai Nagar, India, and the M.S. degree in 1992 from the Indian Institute of Technology, Madras, India, both in electrical engineering. He is currently working toward the Ph.D. degree in electrical engineering at Texas A&M University, College Station. From June 1992 to August 1995, he was a Senior Engineer in the Research and Development Department, Kirloskar Electric Company, Bangalore, India. Hamid A. Toliyat (S’87–M’91–SM’96) received the B.S. degree in 1982 from Sharif University of Technology, Tehran, Iran, the M.S. degree in 1986 from West Virginia University, Morgantown, and the Ph.D. degree from the University of Wisconsin, Madison, in 1991, all in electrical engineering. He was an Assistant Professor of Electrical Engineering at Ferdowsi University of Mashhad, Mashhad, Iran. In March 1994, he joined the Department of Electrical Engineering, Texas A&M University, College Station, as an Assistant Professor. His main research interests and experience include fault diagnosis of electric machines, analysis and design of electrical machines, and variable-speed drives. He is actively involved in presenting short courses and consulting in his area of expertise to various industries. Dr. Toliyat is active in the IEEE Industrial Applications, Industrial Electronics, Power Electronics, and Power Engineering Societies. He was the recipient of the 1996 IEEE Power Engineering Society Prize Paper Award for his paper “Analysis of concentrated winding induction machines for adjustable speed drive applications.” He is serving on several IEEE committees and subcommittees and is a Member of Sigma Xi. 30 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 1, JANUARY 1999 Dudi A. Rendusara (S’95) received the B.S. degree in electrical engineering from the University of Nebraska, Lincoln, in 1992 and the M.S. degree in power electronics from Texas A&M University, College Station, in 1995. He is currently working toward the Ph.D. degree in power electronics at Texas A&M University. He was selected by the Indonesia Government to join overseas fellowship programs in 1988. Since then, he has been pursuing higher education in the United States. Since 1995, he has been involved in advanced research topics in the area of power electronics at the Power Quality Laboratory of Texas A&M University. He has published several papers. His interests are power electronic applications to power quality and clean power converters. Mr. Rendusara is active in the IEEE Industrial Applications Society. Prasad N. Enjeti (SM’88) received the B.E. degree from Osmania University, Hyderabad, India, in 1980, the M.Tech. degree from the Indian Institute of Technology, Kanpur, India, in 1982, and the Ph.D. degree from Concordia University, Montreal, P.Q., Canada, in 1988, all in electrical engineering. He joined the Department of Electrical Engineering, Texas A&M University, College Station, where he is currently a Professor. His primary research interests are: advance converters for power supplies and motor drives; power quality issues and active power filter development; utility interface issues and “clean” power converter designs; and electronic ballasts for fluorescent HID lamps. He holds one U.S. patent and has licensed two new technologies. He is the Lead Developer of the Power Quality Laboratory at Texas A&M University and is actively involved in many projects with industries while engaged in teaching, research, and consulting in the area of power electronics, power quality, and clean power utility interface issues. Dr. Enjeti was the recipient of the IEEE-IAS Second and Third Best Paper Awards in 1993 and 1996, respectively, the Second Best IEEE-IA Transaction Paper, and the IEEE-IAS Magazine Prize Article Award in 1996. He is currently a Transactions Editor for the Industrial Power Converter Committee (IPCC) of the IEEE IAS. He is a registered Professional Engineer in the State of Texas.