[RTF] dc offset in the voltage losses of an IGBT/diode with a given gate drive was eliminated by calculating the average voltage. The experimental configuration is shown in Fig. 2

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IGBT and PN junction diode loss modeling for system simulations

IGBT 开关器件损耗评估模型

IGBT and PN Junction Diode Loss ModelingSystem SimulationsCassimere, Scott D. Sudhoff, Senior Member, IEEE, Brandon Cassimere, Dionysios C. Aliprantis, Member, IEEE, Mike D. Swinney, Member, IEEE

—An accurate and numerically efficient method of calculating semiconductor losses in drive systems is set forth. In the proposed approach, switching events are modeled by ideal-ized voltage and current waveforms that yield the appropriate switching energy loss. The waveforms are specifically designed to allow for large time steps, thus retaining the computational efficiency of conventional ideal-switch time-domain simulations often used for system studies.Terms—modeling, simulation, semiconductor losseshave led to their widespread use. The Insu-lated Gate Bipolar Transistor (IGBT) is a common choice in switching device. Most existing IGBT models may be sepa-rated into two major categohttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlries: physics-based models and behavioral/instead of or empirical models.of physics-based IGBT models include [1]-[4]. Because of the computational intensity models, these are diffi-cult to use for system studies. As a result, there has been considerable interest in behavioral models [5]-[8]. A com-parative study of these models is set forth in [9]. However, although behavioral models are simpler than physics-based models, they still significantly slow system level simulations because the calculation of the

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switching waveforms requires a small time step, at least during the switching transients. For example, [8] reports use of a 10 ns time step, which leads to long run times when performing system level studies.the design of simple power converters (for example, a buck converter), the design may be optimized with respect to switching frequency using a behavioral model in which switching losshttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html is tabulated as a function of current so that losses can be computed as a function of switching frequencywork was supported in part by the National Science Foundation under Grant 9972752 – DGE, “IGERT: Variable Speed Electromechanical Device.” The work was also supported by the Office of Naval Research under Grant N00014-01-2-1099-0 entitled “Polytopic Model Based Stabil-ity Analysis and Genetic Design of Electric Warship Power Systems.”first three authors are with the School of Electrical Engineering, Purdue University, West Lafayette, Indiana 47907-2035 USA (e-mail: [email protected], [email protected], [email protected]). Dionysios Aliprantis is currently serving in the Greece armed forces (e-mail: [email protected]).Swinney is with Rockwell Automation/Reliance Electric (e-mail: mdswinney@http://www.wenkuxiazai.com). .

. INTRODUCTIONthttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlhe past forty years, advancements in semiconductor

[10]. However, as noted in [8], this cannot be done in many inverter applications because switching events are aperiodic for many modulators (for example, hysteresis or delta [11]). This paper proposes a new behavioral power semiconductor model which incorporates both conduction and switching losses. The proposed model is quite simple. Unlike existing behavioral models [5]-[8] the proposed model does not intro-duce fast dynamics (or complicated transient waveforms such as in [8]) into the simulation and can therefore take



large time steps. In fact, the use of a simulation time step size three or-ders of magnitude greater than that used in [8] is demonstrated herein., the computational efficiency of conventional ideal-switch time-domain models is retained, while the prediction accuracy is significantly enhanced. The proposed model is valuable for systehttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlm-level studies, where the main interest lies on the dynamic system performance and the overall power flow, rather than the specifics of the switching transients. This paper begins with a description of the procedure used to characterize semiconductor losses. Next, the modeling ap-proach, which is the principal contribution of this paper, is set forth. The model is tested in a case study that demonstrates the predictions of the proposed approach are in good agree-ment with experimentally observed behavior. Finally, thermal issues are considered.. LOSS CHARACTERIZATIONwork will begin by describing the procedure used to characterize the semiconductors. A FUJI 6MBI30L-060 6-pack three-phase inverter module [12] with a Fuji Electric EXB840 gate drive, configured with a gate resistance of 85 , an on voltage of 15V, and an off voltage of -5V (the manu-facturer’s recommended values) will be used as an exhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlample. A. Conduction Lossesdevice characterization process begins with the meas-urement of the transistor and diode forward voltage drops. These voltage drops can be expressed

ix=ax i

b

b ixi b



, (1)

‘x’ is ‘t’ for transistor or ‘d’ for diode, vxcd is the static forward voltage drop across the transistor or diode, ix is the current through the transistor or diode, ax,bx, cx are model, and ibis the rated current for the device.fitting techniques yields the parameter values listed in Table I. The measured and fitted characteristics are de-picted in Fig. 1. The maximum percentage error is 5.6 % (IGBT) and 0.94 % (Diode), while the average percentage error is 2.0 % (IGBT) and 0.13 % (Diode). These values were taken with a heat sink temperature of approximately 25o C. The imhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlplications of performing the test at room tempera-ture will be discussed in Section V.

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Table I. Conduction Loss Parameters.ib -4. 2 – Switching loss measurement.signal conditioning steps are required to obtain2.01 x 10meaningful results. These will be illustrated by consideringoperating point wherein the average inductor current is bx 3.56

A and the dc voltage is 150 V. Unprocessed measured



- IGBT current and voltage waveforms are depicted in Fig. 3.waveforms were consequently filtered by a third-orderpass filter with a cutoff frequency of 25 MHz. This frequency is high enough to capture the switching transients and low enough to reduce measured noise.next step involves isolating the turn-on and turn-off events of the waveform. This is accomplishhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmled by first deter-mining the turn-on and turn-off points of each transient (switching on and off). The turn-on point is detected by find-ing the instant where the IGBT voltage falls below a threshold value (5 V herein). The turn-off point is found by locating the point when the IGBT voltage exceeds the dc voltage of inter-est. An additional length of time before and after the turn-on and turn-off points is included to ensure the full transient is captured. The resulting IGBT switch on waveforms arein Fig. 4.. 1 – IGBT and diode conduction loss measurements andpower calculation requires removal of measure-fitted characteristics.offsets. For current measurements, this is accomplished by computing the average measured current when the device B. Switching Lossesoff (and hence current equal to zero) and subtracting thatsection documents the procedurehttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html used to measurefrom the entire waveform. The dc offset in the voltagelosses of an IGBT/diode with a given gate drivewas eliminated by calculating the average voltage. The experimental configuration is shown in Fig. 2. Athe device was on, and then offsetting the entire wave-variable dc power supply (Sorensen DHP 400) in parallel withso that the average on-state voltage matches that ob-a 1000 µF capacitor is used to adjust the voltage across thefrom the static i–v measurements for the given current.under test (DUT). The IGBT is controlled with a hys- The instantaneous



switching loss may be expressedmodulator to regulate the current in an inductive load=it(vt vtcd(i)u(it)), (2) (1.5 mH). tgoal of this test is to characterize the turn-on energy where vtcd denotes thhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmle IGBT conduction losses, pt the IGBT loss and turn-off energy loss as a function of operating point;losses, and u(it) the unit step function (equal to onethe operating point is defined as the average inductor(which is approximately equal to the current com-when its argument is greater than zero, and zero otherwise).total energy lost over the switching event may be ex-mand) and the dc voltage. The turn-on and turn-off losses

with each event are found by measurement of volt-tfacross and current through each device, and then integrat-Wt=ptdt, (3)the product to determine the loss.

Wt is the IGBT switching energy loss, to is a time just prior to the beginning of the switching transient, and tf is a

∫after the switching transient. For the study herein, turn-on energy http://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlloss (i.e. the total loss associated with an IGBT t


f to= 5 µs. Fig. 5 depicts the power and energy losses as a turning off). Not unexpectedly, it can be seen the energy lost function of time. A similar procedure is followed to deter-during a switching event increases with both dc



voltage and mine the IGBT switching off loss, and the diode switching on average inductor current. It should be noted that this energycharacteristic is for an IGBT/diode with a specific gate


and switching off loss.circuit.. 3 – Unprocessed IGBT waveforms.



Fig. 6 – IGBT turn-on plus diode turn-off energy losses.

. 4 – IGBT turn-on switching transients.


. 7 – IGBT turn-off plus diode turn-on energy losses.. PROPOSED MODEL://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlrthis section, a model for an inverter phase leg which in-corporates the loss data is set forth. Fig. 8 depicts an inverter phase leg, where xcan represent thea,b, or c-phase. The inputs to the phase leg model will be sxu (a switching com-mand specifying whether the upper (sxu=1) or lower (sxl=1) device is turned on, the dc voltage vdc, and the load current ixs (assumed to be constant during the



switching tran-sition because of the inductive nature of the load); outputs will be the x-phase line-to-bottom rail voltage vxr and the current from the upper rail ixdc.proposed approach will lead to an inverter model that incorporates the conduction and switching losses in a compu-tationally efficient manner. To this end, inverter operation at any given instant is categorized into one out of three intervals: (i) a conduction interval (not associated with switching), (ii) switching interval 1 (associated with logihttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlc propagation

. 5 – IGBT turn-on power and energy loss.final compiled measurements for an IGBT–diode com-bination transient loss are depicted in Fig. 6 and Fig. 7. Fig. 6the sum of the IGBT turn-on plus diode turn-off en-ergy loss (i.e. the total loss associated with an IGBT turning on) and Fig. 7 depicts the sum of the IGBT turn-off plus diode), and (iii) switching interval 2 (associated with the ac-tual switching event). The model may be divided in two sub-models—a conduction sub-model and a switching loss sub-model.. Conduction Loss Sub-ModelSection II, the technique for measuring the static i–v characteristics of the transistor and diode was presented. The incorporation of this into the inverter phase leg model is straightforward and is summarized in Table I.. Switching Loss Sub-Modellosses are represented by intrhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmloducing an artificial square-wave switching transient that results in the same en-ergy loss as the actual switching transient but using a simpli-fied transient waveform. These idealized waveforms are not representative of the actual device voltage and current but they yield the same loss.circumventing the details of the switching transient, considerable



computational burden is avoided. In addition, the use of square-wave transients allows the simulation to effectively use scheduling [13], a technique used to insure that discrete events always occur at the boundaries between simu-lation time steps, so that large time steps can be used in sys-tems with discontinuous waveforms – as is the case of many power electronics based systems.. 9 summarizes the assumed waveforms. As can be seen, depending upon the polarity of the current and the switch command, four cases need to be considered. In Case 1, the phahttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlse current is positive and there is a transition between the upper transistor conducting and the lower diode conduct-ing. The time instant (denoted by the dotted line) between the Initial Conduction Interval and Switching Interval 1 corre-sponds to the moment of change in switching command (sxubeing turned off). After a logic propagation delay of tldoff (Switching Interval 1), the assumed switching transient

vxr-

. 8 – Inverter phase leg.

Case 2 and Case 3, current is transferred from the diode to the IGBT. In both cases, the specified waveforms will dis-sipate an energy of



=ixsvdctedt, (5)tedt is the effective diode-to-IGBT transition time.any case, the appropriate amount of loss may be readily injected provided that tetd and tedt are set accord-ingly. Using the energy loss dathttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmla discussed in Section II (See Fig. 6 and 7), tetd and tedt may be readily calculated as a function of operating point. In particular,

= (6)

=

(7)

interpolation purposes, it is convenient to represent the turn-on and turn-off times as a function of operating point. The effective times may be represented by

vdc=ay by v

dcb

dyxs

vdc fy v

dcb



(8). During Switching Interval 2, the line-to-bottom rail voltage vxr is zero but the current ixdc is still positive, so the

x denotes the phase, y can be ‘etd’ or ‘edt’, ay, by, cy, dy, ey,fy, gy, and hy are constant coefficients,leg dissipates a power equal toixsvdc. The energy dis-and vdcbis the rated semhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmliconductor voltage. Fig. 10 and 11tetdand tedt as calculated using (6) and (7), as well sipated during Switching Interval 2 isthe fitted characteristics based on (8). The average per- Etd=ixsvdctetd, (4)error for all data points is 4.1 % for the turn-on timetetd denotes the effective transition time from the and 6.1 % for the turn-off time. Numerical values of the coef-IGBT to the diode. The losses incurred during tetd are the ficients, as well as logic propagation delay times, are listed in sum of the IGBT turn-off loss and the diode turn-on loss. The Table II.expression holds for Case 4 in which current is again At this point, it is appropriate to summarize the model., during the conduction interval, the line-to-rail voltage being transferred from the IGBT to the diode.dc current component of phasex, denoted vxr andixdc,://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlaras specified in Table III. Therein, vtcd and vdcd areby (1). After a change in switching status, Switch-ing Interval 1 occurs for the specified duration which is de-termined by the speed of the logic and control circuitry. Again, values of vxrand ixdcare listed in Table III. Next, Switching Interval 2 begins where the duration is as specified



. 9 – Effective switching waveforms.a power supply whose output voltage was maintained200V, PA denotes a power analyzer used to measure the(8). After Switching Interval 2 is complete the next con-inverter input and output power, DO denotes a digital oscil-loscope used to record the output current and used to deter-


duction interval begins.the power loss in the inverter’s electrolytic capacitor. IV. CASE STUDY In this section, the use of the model is explorhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmled in the con-text of a motor drive as depicted in Fig. 12. Therein, PS



Table III. Model Summaryvxr Time Period


Conduction Interval≥0 vdc vtcd -=1<0 vdc vdcd -



vdc vdcd

0=0≥0 ixs<0 ixs≥0 ixs<0 ixs≥0 ixs<0

-

vdcd

Interval 1

. 10 – Effective turn-on time measurements and fit.

=1

tldon tldon tldoff

vtcd vdc vdcd vdcdvdc vdcd

0=0



Interval 21 Case 2 Case 3 Case 4tedt tedt tetd

vtcd vdc vdcd

vdcd

://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlr. 11 – Effective turn-off time measurements and fit.II. Switching Parameters.vdcb ay by cy dy ey fy gy hy

.303 x 10-7 3.951 x 10-7s - s -. 12 – Brushless DC motor drive.

.289 x 10-6 -3.500 x 10-6 1.454 x 10-1-1.467x 10



.660 x 10

.623 x 10-13.645 x 10-6 5.762 x 10-2 5.646 x 10-2 3.2 x 10

control of the inverter was as follows. First, for a

.643 x 10-6 storque command Te* a q-axis current command wasin accordance with

.6 x 103.2 x 10-6-6

.142x 10-2

*iqs

Te*

(9) =

Pλm1.6 x 10-6



P is the number of poles and λm is the peak flux link-age induced into each phase due to the permanent magnet.*d-axis current command idshttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html is set to zero. Based on the current command and the measured stator currents, an abc

*found in accordance with variable current command iabcblock diagram depicted in Fig. 13.model with the higher bandwidth machine model was


25.32 s.

. 13 – Inverter control.transformation matrix Ksris to transform phase variables to the rotor reference frame as set forth in [11] and


Fig. 14 – A-phase current waveforms.

the upper two rows.delta modulator is used to obtain the desired currents. In particular, the current in each phase is compared to the com-manded current at a frequency of fs/3 Hz, where fsis the aggregate sampling frequency. The sampling is



staggered between phases so that only one switching event can occur at a time. Note that with thishttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html modulator, the maximum possible switching frequency isfs/6, though the actual switching fre-quency can be well below this bound.machine used for the tests was a 4 pole device rated at 1 hp at 2000 rpm (Reliance Electric Model #B14H1050R-FD). In terms of the non-salient machine model set forth in [11], its parameters are P=


4, rs=2.6 , Lss=12.4mH, andλm=0.286Vs.investigating power loss, it is interesting to exam-ine the prediction of the time domain performance. Fig. 14 depicts measured and simulated performance with a torque command of 1.5 Nm at a speed of 1800 rpm. Fig. 15 again depicts the current waveform, though with the fundamental component removed. As can be seen, the classical qd model (CQDM) underestimates the current ripple because of the re-duction of effective inductance with frequency. To capture this effect, a higher bandwidth machine model (HQDM) ihttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmls needed; Appendix A describes such a model which is based on concepts set forth in [14-15]. The extended bandwidth model is seen to improve the prediction of ripple.claim of this paper is that the proposed model is compu-tationally efficient. To demonstrate this, the simulation times using the proposed model were compared to those using an ideal switch based model. All simulations were implemented using ACSL [13] with a 10 µs time step with a 4th order Runge-Kutta integration algorithm on a 1.67 GHz AMD Ath-lon processor running the Windows XP operating system. The time required to run an idealized switch model with a standard qd machine model [11] was 23.02 s. The time re-quired to run the proposed inverter model with the standard qd machine model was 23.11 s, only slightly slower than the ide-alized switch model. The time required to run the proposed



. 15 – A-phase current ripple.://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlarsecond claim of this work is that it can provide a reason-able estimate of losses. To demonstrate this, a second study was performed in which the sampling frequency of the delta modulator is varied for fixed values of commanded torque, speed, and dc voltage. The measured inverter losses are com-pared to the predicted values obtained from the proposed model in Fig. 16. As can be seen, the proposed model pro-


vides a reasonable prediction of the measured inverter losses.

. 16 – Inverter power loss.

. THERMAL EFFECTSand switching losses are a function of tempera-ture. The model presented herein can readily incorporate this temperature dependence. In the case of conduction loss this is accomplished by modifying (1) so that it is a function of tem-perature. Such an expression is suggested in [10], along with parameters for a number of devices.http://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html Inclusion of thermal ef-fects in switching losses is accomplished by modification of (8) to incorporate temperature. As an example, [10] cites IGBT switching energies as a function of temperature, from which (6) and (7) could be used to calculate effective transi-tion times as a function of temperature.it is clearly advantageous to include thermal effects, thermal effects were not included in the case study set forth here, and yet the results were reasonably accurate. This leads to the question of how critical the inclusion of thermal effects is. This is a function of the specific device considered, the temperature of characterization, and the temperature variation from the characterized condition. However, as an example, consider an IRGBC30S IGBT. Based on



the data set forth in [10], the percent error in the calculation of the switching losses at 75o C and 125o C are shown in Fig. 17, assuming the devihttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlce is characterized at 100o C. The error in the loss calcu-lation is significant, but of a magnitude such that neglecting thermal effects can still yield useful estimates, an observation


consistent with the case study.addresses similar phenomenon in induction machines. Model development begins by expressing the stator voltage equation as vabc,s=vabc,z vabc,pm, (10) where vabc,s is the vector of stator phase voltages, vabc,z is the voltage drop across the stator impedance and vabc,pm isstator voltage due to the permanent magnet. The impedance drop may be expressed vabc,z=Zabc,s(p)iabc,s, (11) where p is Heaviside notation for the time derivative opera-tor, iabc,s is the vector of machine currents and where,s(p) is a impedance matrix of the form

Zss(p)Zm(p)Zm(p)

Zabc,s(p)= Zm(p)Zss(p)Zm(p) . (12)

Zm(p)Zm(p)Zss(p) duhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmle to the permanent magnet may be expressed vabc,pm=pλabc,pm, (13)λabc,pm is the vector of flux linking each of the three phase windings and is of the form

λabc,pm=λm[sin(θr)sin(θr 2π/3)sin(θr 2π/3)]T

(14) Using co-energy techniques the electromagnetic torque may be expressed



=λm[cos(θr)cos(θr 2π/3)cos(θr 2π/3)]iabcs.

(15) Note that (15) does not include cogging torque.is convenient to transform the machine description into the stationary reference frame [11]. Although the rotor refer-ence frame is normally used for synchronous machines, the stationary reference frame is advantageous in this case to fa-cilitate manipulation of the transfer functions in the stator im-pedance matrix.(10) and (11) yields where and

Zs(p)

. (18) ZpZqd0,s(p)= 0()0s

Z0(p) 0 0

. 17 – IRGBC30S conduction &amphttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html; switching losses.. CONCLUSIONthis paper, an approach to include semiconductor lossessystem simulations has been set forth. The proposed ap-proach has been shown to be simple, accurate, and computa-tionally efficient. Future work in this area is to further vali-date the proposed model, especially in regard to the inclusion of thermal effects.A – MACHINE MODELclassical qd model as presented, for example, in [11], will underestimate current ripple. To correctly predict current ripple, a higher bandwidth machine model is needed. The model set forth herein is somewhat analogous to that in [14]



=vqdo,z vqd0,pm, (16),z=Zqd0,s(p)iqd0,s (17)(18),(p)=Zss(p) Zm(p), (19) Z0(p)=Zss(p) 2Zm(p). (20) Transformation of (13) and (14) yields and,pm=pλqd0,pm (21)

λqd0,pm=λm[shttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlin(θr)cos(θr)0] (22) ings from IEEE International Conference on Electronics, Circuits, and

[7] Monti, “Fuzzy-based black-box approach to IGBT modeling,” Proceed-, vol. 2, 1996, pp.1147-1150

[8] C. Wong, “EMTP modeling of IGBT dynamic performance for power

,pm=ωrλmcos(θr) sin(θr)0. (23) dissipation estimation,” Proceedings from Conference Records – Indus-try Applications Society Annual Meeting, vol. 3, 1995, pp. 2656-2662 Combining the q- and d-axis components of (16) and (17), [9] Kuang Sheng, Barry W. Williams, and Stephen J. Finney, “A Review ofModels,” IEEE Trans. Power Electronics, vol. 15, No. 6, Nov. sss,s=Zs(p)iqd,s vqd,pm. (24)

.the stationary reference frame (15) becomes [10] S. M. Clemente and D. A. Dapkus II, “IGBT Models Account forAnd Conduction Losses,” Power Electronics Technology, 3Pss=λmihttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlqscosθr idssinθr. (25) Aug. 1993, pp. 51-54



[11] P.C. Krause, O. Wasynczuk, S. D. Sudhoff, Analysis of Electric Machin-From a simulation standpoint, it is assumed the line-to-ery and Drive Systems, New York, NY: IEEE Press, 2002.rail voltages of an inverter are known. The first step is [12] Fuji Electric, “6MBI 30L-060 Data Sheet,” Fuji Semiconductor, P.O.702708 Dallas, TX. to calculate the q- and d-axis voltages. In particular,

[13] Aegis Technologies Group, Inc. Advanced Continuous Simulation Lan-s(ACSL) Reference Manual, Huntsville, AL, 1999. vqd=Ksvabc,x (26) s[14] S.D. Sudhoff, P.L. Chapman, B. T. Kuhn, D. Aliprantis , “An AdvancedMachine Model for Predicting Inverter-Machine Interaction,”the upper two rows of Kswhere Kss and where sIEEE Transactions on Energy Conversion, Vol. 17, No. 2, June 2002, utr. 203http://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html-210.,x denotes the vector of line-to-node x voltage, where x [15] S. D. Sudhoff, P. .L. Chapman, D. C. Aliprantis, and B. T. Kuhn, “Ex-perimental Characterization of an Advanced Induction Machine Model,”typically the bottom rail of an inverter. IEEE Transactions on Energy Conversion, Vol. 18, Mar 2003, pp. 48-From (23), (24), and (18) the currents are expressed 56.

=Ys(p)vqs ωrλmcos(θr), (27)from Southern University A&M College in 2001. Brant also ss=Ys(p)vds ωrλmsin(θr), (28) received his M.S. in electrical engineering from Purdue University in 2003he is currently working towards the Ph.D. degree. His interests include wheremachines, power electronics, and genetic algorithms.

(p)=. (29)(p)Scott Sudhoff received the B.S. (highest distinction), M.S.,Ph.D. degrees in electricalhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html



engineering from Purduetime domain realization of Yp(p) may be used to im-University in 1988, 1989, and 1991, respectively. From 1991-1993, he served as visiting faculty with Purdue University. plement the transfer functions; the output of the realizations1993 to 1997, he served as an Assistant Professor at thebe the q- and d-axis currents. The currents are then used University of Missouri - Rolla, and in 1997 he joined theof Purdue University, where he currently holds the in (25) to predict the electromagnetic torque.of Full Professor. His interests include electric machines, power electron-Based on the open circuit voltage and stand-still frequency, finite-inertia power systems, applied control, and genetic algorithms. Hetesting, it was determined that the amplitude of the has published over fifty journal papers, including six prhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlize papers, in these


flux linkage established by the permanent magnet was 0.286 areas.and that the admittance transfer function was

.14e 34.11e 13.94e 4engineering from Southern University A&M College in 2001. Brandon also= . (30) received his M.S. in electrical engineering from Purdue University in 2003 4 3 6

.34ep 15.54ep 15.08ep 1where he is currently working towards the Ph.D. degree. His interests includemachines, power electronics, and genetic algorithms. REFERENCES

[1] A.R. Hefner, “Analytical modeling of device-circuit interactions for the cal and computer engineering from the National Technical



insulated gate bipolar transistor (IGBT),” Conference Records - University of Athens, Greece, in 1999. He was awarded the Industry Applications Society Annual Meeting, vol. 35, no. 6, 1988, pp. PhD in electrical ahttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.htmlnd computer engineering from Purdue, West Lafayette, IN, in December 2003. He is 606-614.serving in the armed forces of Greece. His interests [2] A.R. Hefner, “Dynamic electro-thermal model for the IGBT,” IEEEthe modeling and simulation of electric machines and


Transactions on Industry Applications, vol. 30, Mar./Apr. 1994, pp. 364-power systems and evolutionary optimization methods. 405

[3] R. Kraus and K. Hoffmann, “Analytical model of IGBTs with low emit-ter efficiency," Process International Symposium on Power Semiconduc-Technology from Purdue University in 1971, a BSEE degree from Cleveland tor Devices ICs, 1993, pp. 30-34

[4] B. Allard, H. Morel, C.C. Lin, H. Helali, and J.P. Chante, “Rules for State University in 1976, and a MBA from Indiana Wesleyan University in

. He has been employed by Rockwell Automationhttp://www.wenkuxiazai.com/doc/25bdaff6b8f67c1cfad6b870.html for the past 37 years. deriving basic semiconductor region models”, IEEE Annual Power Elec-Starting out as a draftsman and electrical engineering technician while con-tronics Special Conference-PESC, 1994, pp. 44-51.

[5] J.T. Hsu and K.D.T. Ngo, “Behavioral modeling of the IGBT using the tinuing his education, he has held positions as a Electrical Development En-gineer, Industrial Engineering Manager and is currently the Engineering Man-Hammerstein configuration,” IEEE Transactions on Power Electronics,



for the small ac motor line at the Rockwell Madison, IN plant. vol. 11, Nov. 1996, pp. 746-754.

[6] J. L. Tichenor, S. D. Sudhoff, J. L. Drewniak, “Behavioral Modeling forHigh Frequency Effects in Motor Drives,” IEEE Transactions on Power Electronics, Vol. 15 No. 2, March 2000(21) and (22)

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[RTF] dc offset in the voltage losses of an IGBT/diode with a given gate drive was eliminated by calculating the average voltage. The experimental configuration is shown in Fig. 2