Prediction of Switching Loss Variations by Averaged Switch Modeling

Osama Al-Naseem and Robert W. EricksonDepartment of Electrical and Computer Engineering

University of Colorado at Boulder, 80309-0425(303) 492-7003, FAX (303) 492-2758

al@ucsub.colorado.edu

Palmer CarlinNational Wind Technology Center

National Renewable Energy LaboratoryGolden, CO

Abstract- An analytical averaged equivalent circuit model isderived revealing how dominant loss mechanisms vary withconverter operating point in a PWM converter. The model isbased on the operational characteristics of power diodes andIGBTs. Laboratory experiments support the derived model andconfirm that IGBT current tailing and diode reverse-recoveryare indeed the most critical losses in a PWM converter. Theselosses are more significant at light load, hence reducing theenergy capture of converters used in wind generation.

I. INTRODUCTION

Power electronic converters in wind generators operateunder the requirement of high efficiency at light load. Thisrequirement is not necessary in most conventionalapplications, provided that the total power loss is no worsethan at maximum load. This unique requirement in windgeneration applications evolves from the very nature ofoperation of typical wind turbines. Because wind turbinesmay operate for long periods of time under low wind speedconditions, variable-speed wind generators may showsignificant degradation in energy capture capabili ty whenusing PWM converters of low efficiency at light load.Hence, the phenomenon and origins of lower eff iciency atlight load need to be studied in depth to achieve better energyconversion rates.

If losses vary linearly with output power, then theconverter efficiency is independent of load. Conductionlosses of typical PWM inverters vary linearly with or as thesquare of output power, and hence cannot explain theobserved eff iciency degradation at light load. As described inthis paper, switching losses typically exhibit a less-than-lineardependence on output power. Hence, reducing the outputpower does not proportionately reduce the switching loss. Inparticular, the switching loss induced by diode reverse-recovery has been found to dominate at light load.

The averaged switch modeling approach [1,2] isemployed here, to explain how the major loss mechanismsvary with converter operating point. Averaged switch modelsof two-level and three-level PWM converters have beenderived and analyzed. These models incorporate simpleapproximate relationships that describe how switching lossparameters vary with the converter operating point. Theserelationships are based on physical understanding ofsemiconductor devices, and have been verified in thelaboratory.

In Section II , the important switching loss mechanisms aredescribed, and the first-order dependencies of the switching

loss parameters are derived. The results of extensivelaboratory tests to measure these dependencies aresummarized in Section III . Averaged switch models of two-level and three-level converters are developed in Section IV.The predictions of these models for a variable-speed windgeneration application are discussed in Section V.

II . SWITCHING LOSS MECHANISMS

Switching loss can be resolved into components inducedby the diode reverse-recovery mechanism, the IGBT current-taili ng phenomenon, the IGBT turn-on time, and the outputcapacitances of the IGBTs and diodes. Each mechanism leadsto energy loss that is a function of the semiconductor on-statecurrent and off -state voltage:

WD = Energy loss induced in IGBT by diode reverse-recovery

Wtail = Energy loss during IGBT turn-off transition,owing to current tail

Wr = Energy loss during IGBT turn-on transition,during rise of collector current

WC = Energy loss induced in IGBT by semiconductoroutput capacitances (1)

The sum of these switching energy losses, multiplied bythe switching frequency, is equal to the average switchingpower loss. Thus, the total switching loss is directlyproportional to switching frequency.

A. DIODE REVERSE-RECOVERY

Well -known waveforms for the turn-off transition of asili con diode are ill ustrated in Fig. 1. While the diodeconducts, it contains stored minority charge of magnitude Qdependent on the forward current IF. This minority chargemust be removed before the diode can become reverse-biased. There are two mechanisms for removal of this charge:passive removal through recombination inside the diode, andactive removal through negative diode current. The amountof charge that recombines is dependent on the rate di/dt atwhich the diode current changes during the turn-offtransition, which in turn depends on the IGBT turn-onswitching speed and stray inductances. The remaining storedcharge is actively removed. The actively removed charge iscalled the “recovered charge” Qr. During the reverse-

recovery time, of length tr, negative current flows through thediode, the diode remains forward-biased, and theinstantaneous power loss in the transistor is very high. Thevoltage Vg , in Fig.1, is the dc link voltage (i.e., Vg = v1).

The functional dependence of Qr and tr on the diodeforward current iL is determined by the physical mechanismswithin the diode, [3,4]. At very low current, Shockley-Read-Hall recombination dominates the diode behavior, and thedependence of the stored charge Q on the forward current canbe approximated as linear. For intermediate currents (i.e., theusual operating range of the diode), injection efficiencytypically dominates the device behavior, and Q varies as thesquare root of forward current. For very large currents, Augerrecombination may become dominant, leading to a cube rootdependence of Q on forward current. The recovered chargeQr and reverse-recovery time tr will be proportional to Q.

The result is that the forward current can be represented asa third-order polynomial function of Q. Since injectionefficiency usually dominates over the normal operating rangeof the power diode, a simpler approximation is to simply letQ be proportional to the square root of the forward current:

FQr IkQ = (2)

This less-than-linear dependence means that stored chargeis only a weak function of on-state current. Hence, theswitching loss arising from the diode reverse-recoverymechanism will have a greater impact on eff iciency as theload power is reduced. The coeff icient kQr is also a functionof the junction temperature and the turn-off di/dt.

The relationship between the on-state stored charge Q andthe recovered charge Qr depends on rate of change di/dt ofthe diode current during the IGBT turn-on transition. If di/dtis very high (tending towards a step change of diode current),then Qr ≈ Q. It may then be possible to expect the recoveredcharge Qr to depend on IF in the same way as Q:

FQrr IkQ = (3)

Lower rates of di/dt cause a significant amount of thestored charge to recombine during the diode turn-off process,so that Qr < Q. The quantities Qr and tr then additionallydepend on di/dt. For very slow di/dt, Qr and tr becomeindependent of IF and are functions solely of di/dt.

The reverse-recovery time tr is related to the recoveredcharge Qr according to

)/(

)1(2

dtdi

SQt rr

+= (4)

where S is the “snappiness factor” of the diode and isdetermined by the physical diode construction [5]. The aboveequation is derived in numerous texts and is sometimesquoted on manufacturer’s data sheets. Derivation of thisequation is based solely on the geometry of the waveforms ofFig. 2, and is not dependent on the internal construction ofthe diode. Equations (3) and (4) predict that, for fixed di/dt,the diode reverse-recovery time tr should vary with on-statecurrent IF according to

4Ftrr Ikt = (5)

where ktr is a proportionali ty coefficient that is a function ofdi/dt.

This is a very weak dependence. Thus tr can be accuratelymodeled as independent of on-state current IF. Equation (4)further suggests that tr varies as the inverse square-root ofdi/dt; this is also a weak dependence, but variations in tr maybe measurable if di/dt varies significantly.

B. IGBT CURRENT TAILING

The IGBT can be viewed as a MOSFET cascaded by aPNP bipolar junction transistor. When the IGBT conducts,part of its current flows through the effective MOSFET,while the remainder flows through the PNP; the ratio of thesetwo currents is determined by the device construction.

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didt

, - . /

Fig. 1 Reverse-recovery occurring during diode turn-off . Diode inducedenergy loss is VgiFtr +VgQr, where Qr = recovered charge and tr = reverse-recovery time. Qr and tr are both proportional to on-state stored charge, Q.

01 2 3 4 5 4 67 8 9 9 6 1 4 : ;

<= > ? @ A @ BC D E F G HI J K L M NO

Augerrecombination

Q ∝ IF3

InjectionefficiencyQ ∝ IF

Q ∝ IF

P Q R S

T U V W X

Fig. 2 Theoretical variation of diode stored charge with on-state current,and the dominant physical mechanisms.

During the turn-off transition, the MOSFET turns off veryquickly, and its share of the on-state current is thereforeinterrupted quickly. However, the current of the PNPcontinues to flow until the stored minority charge within then- region has recombined.

The IR data sheets for recent devices [6] ill ustrate thatQtail exhibits a linear dependence on the on-state current, IF.Current tail ing can be the largest single loss mechanism of anIGBT inverter and any dependence of Qtail is critical. It isassumed here that simple recombination leads to a lineardependence:

FQttail IkQ = (6)

This linear dependence implies that the effect of currenttaili ng on inverter percent efficiency is independent of loadpower.

C. IGBT TURN-ON LOSS

Significant losses can also be observed during the risetime of the collector current during the IGBT turn-ontransition. During this interval, the gate driver charges thegate capacitance of the IGBT. At high currents, some timemay be required to supply minority charge to the effectivePNP transistor within the IGBT, further slowing the turn-ontransition. Time ton is required for the IGBT collector currentto rise from zero to the inductor current IF; during this time,the diode remains on and the IGBT collector-to-emittervoltage remains fixed at the dc link voltage Vg.

Assuming a constant slope rise, di/dt, of the collectorcurrent, then it is possible to form the following equations:

)/(22

2

dtdi

IVtIVW

dt

di

t

I

FgonFgr

on

F

==

=

(7)

As was mentioned previously, it was observed that di/dtdecreases at large load currents and low dc link voltage. Thiscauses the energy loss induced by this mechanism to increasesignificantly at high current. The loss during the turn-ontransition is not significant at light load current and highvoltage, because of the strong dependence on IF and becausedi/dt is dominated by the fast switching of the effective IGBTMOSFET at low current.

D. DEVICE OUTPUT CAPACITANCES

The output capacitances of the IGBT and diode arenonlinear elements, whose incremental values varyapproximately as the inverse square root of applied voltage.The energy stored in these capacitances is lost in the IGBTduring the IGBT turn-on transition.

As il lustrated in Fig. 5, each inverter phase contains twoIGBTs and two diodes, each of which exhibits outputcapacitance. During the turn-on transition of the upper IGBT,the lower diode turns off and undergoes the reverse-recovery

process. The switching loss caused by the output capacitanceof the lower diode is included in the reverse-recoverycomputations discussed in subsection (A) of this section.However, it remains to include the energy stored in thecapacitances of the upper diode and both IGBTs.

The incremental output capacitance of an IGBT or diodecan be modeled by a function of the form

v

C

dv

dqC o≈= (8)

This model is sufficiently accurate for computation of theswitching losses induced by output capacitance. The constantCo is extracted from the incremental capacitance specified onthe manufacturer’s data sheet. V is the applied collector-to-emitter or cathode-to-anode voltage. The energy stored in theoutput capacitance is found by integration of (8), as follows:

∫ ∫ ∫ ====max

0

5.1max02)(

Vo

c VCvdvv

CvdvvCvdqW (9)

where Vmax is the off-state voltage of the device. In a dc-linkinverter, this loss is a function of the dc link voltage but isindependent of current. Hence, this loss is independent ofpower throughput.

MOSFETs tend to exhibit higher output capacitances thanIGBTs or diodes, because of the relatively large chip area ofsimilarly rated MOSFETs. In consequence, this source ofswitching loss is more significant in MOSFET inverters thanin systems containing IGBTs. Nonetheless, it can be asignificant loss at light load operating conditions.

III . LABORATORY EXPERIMENT

In the laboratory, efficiency and loss tests were performedon the power stage il lustrated in Fig. 3. The circuit wasoperated at various constant values of duty cycle D, dc linkvoltage Vg, and dc current I. Losses in each semiconductordevice were separately measured. This data was then used topredict losses when ac modulations are present. 1200Vdevices were employed. The IGBTs were InternationalRectifier IRGPH50F with ratings of 42A at 25ºC, 25A at100ºC. The power diodes were International RectifierHFA30PB120 ultrafast with ratings of 30A average.

YZ

[\

] ^_

Fig. 3 One phase of a two-level PWM inverter circuit

IGBT switching times and diode stored charge exhibit asignificant temperature dependence. To obtain an accuratemodel, it is necessary to operate the semiconductor devices ata fixed junction temperature [3,4]. Each semiconductordevice was mounted on a separate heatsink. Several powerresistors are mounted on the same heatsink, and were drivenby an adjustable voltage source with known power. Thisthermal system was calibrated by applying a known dc powerto the IGBT. Given the manufacturer’s published junction-to-case thermal resistance, the case temperature required toproduce a given junction temperature can be calculated. Theexternal resistor power was increased until this casetemperature is attained. The relationship between resistorpower, case temperature, and the semiconductor devicepower dissipation is then known. The thermal systems foreach IGBT and diode were calibrated in this manner.

Switching losses were measured in two ways: (a) thethermal approach described above, and (b) using oscilloscopewaveforms. Good agreement between the two methods wasobtained. Based on the measured date, the model parameterslisted in Table 1 were obtained. It was found that IGBT turn-on switching time and IGBT output capacitance did not leadto significant switching loss, while the other modeled losseswere significant.

IV. AVERAGED SWITCH MODELING

A. TWO-LEVEL CONVERTER MODEL

Figure 4 ill ustrates one phase of a conventional two-levelPWM inverter circuit switch network, and Fig. 5 shows itstypical switching waveforms. The salient features shown onthe waveforms are defined as follows:

tr Diode reverse-recovery timeton Current rise time, IGBT turn-on transitiont1 IGBT on-state conduction timeVsat IGBT forward voltage dropVD Diode forward voltage dropQtot The sum of the diode recovered charge Qr and the

total charge Qc stored in the output capacitances ofthe IGBTs and reverse-biased diodes

Qtail Integral of the collector current waveform duringthe current fall time (area of the current tail )

For positive current, IF, the upper IGBT and lower diodeconduct. The average values of the upper IGBT voltage andcurrent waveforms of Fig. 5, for positive IF, are equal to

s

tailtotF

s

onr

Tc

sats

Dgs

sTce

T

QQI

T

ttti

VT

tVV

T

tTv

s

s

++

++=

++−

=

21

1

11 )(

(10)

The idealized waveforms of Fig. 5 ignore voltage rise andfall t imes, and assume hard-recovery diodes. The notation⟨ x⟩Ts denotes the average value of x, averaged over theswitching period Ts.

The average value is computed by finding the area underthe waveform, and dividing by Ts. The average values of theterminal waveforms of the switch network are computedusing Kirchoff’ s laws, as follows:

( ) sats

Dgs

sgTcegT

VT

tVV

T

tTVvVv

ss

112 −+−−=−= (11)

s

tailtotF

s

onr

TcT T

QQI

T

tttii

ss

++

++== 2

11

1 (12)

Simplification leads to

DsatgTVDDVDVv

S'2 −−= (13)

s

tailtotF

s

onrFT T

QQI

T

ttDIi

s

++

++= 2

1

1 (14)

`ab c

d e

f g h i j kl m i g n o p

q

r s t u v

w

xy z | ~

Fig. 4 Two-level converter switch network

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§ ¨ ©«ª ¬

­ ® ¯ °

± ²³ ´ µ ¶ ·¸ ¹ º » ¼ ½ º ¾ ¿ À Á Â º Ã ÄÅ Æ

Ç

didt

Fig. 5 IGBT voltage and current waveforms (IF >0)

TABLE 1MODEL PARAMETERS, BASED ON EXPERIMENTAL DATA

Vsat = 1.34 V RT = 43 mΩVD = 1.50 V RD = 28 mΩ

ss TTr tvtiQ )()()103.2( 128 ⋅⋅= −

4 28 )()100.8(

sTr tit ⋅⋅= −

sTtail tiQ )(100.3 27 ⋅⋅= −

where the effective transistor duty cycle is D = t1/Ts and D’ =1 – D.

An averaged equivalent circuit model corresponding to(13) and (14) is ill ustrated in Fig. 6(a). A similar procedureleads to the model of Fig. 6(b), for negative current. Thesemodels represent the low-frequency components of theterminal waveforms of the switch network. The average inputand output powers are correctly represented. The effective1:D transformer models the conversion of power from theinput to the output ports of the switch network. Switchinglosses are modeled with the two current sources. Qr is thediode recovered charge, Qtail is the area of the IGBT currenttail , and tr is the diode reverse-recovery time. Diode andIGBT voltage drops are modeled as two voltage sources andtwo resistors in the secondary side of the circuit model. Notethat each source consumes power, hence reducing the switchnetwork efficiency. The charge Qc was found to be smallerthan Qr in our laboratory experiment; hence Qtot ≈ Qr. Noticealso that the term ton has been discarded from the averagedmodel due to its negligible effect.

B. THREE-LEVEL CONVERTER MODEL

The averaged switch approach can also be applied tomodel the dependence of efficiency on load in other PWMconverters. A three-level inverter circuit, also known as aneutral-point clamped PWM inverter [7], ill ustrated in Fig. 7,is modeled using a procedure similar to that used in theprevious subsection.

Figure 8 ill ustrates the resulting averaged switch model ofthe upper half of the three-level converter circuit. As in Fig.6, the effective 1:D transformers model the conversion ofpower from the input to the output ports of the switchnetwork. Figure 8 (a) models the network for positive i2,when Q1 and D5 switch with pulse-width modulation. Figure8 (b) models the network for negative i2, when Q3 and D1 arepulse-width modulated. Models for the lower half of thethree-level switch network are symmetrical.

V. DISCUSSION

The model of Fig. 6 and the parameter values of Table 1were used to predict the efficiency of a two-level PWM dc-link rectifier/inverter system, Fig. 9, in a variable-speed windgeneration application. Generator power is assumed to varyas the cube of turbine speed. The dc link voltage is a fixed825 V, and the 60 Hz ac system voltage is 480 V three phase.The generator voltage varies between zero and 480 V. Themodel was solved analytically for sinusoidal pulse-widthmodulation, and the average input and output powers of theswitch network were computed. Unity power factor wasassumed. Predicted eff iciencies of the PWM rectifier andinverter stages are plotted in Fig. 10, for a switchingfrequency of 10 kHz. Notice how efficiency drops rapidly atlight load; a typical obstacle in variable speed windgenerators. The rectifier efficiency is lower than the inverterefficiency because the rectifier must operate with a lower ac-side voltage and hence with higher currents. The compositeefficiency is the products of the rectifier and inverterefficiencies. This plot includes the losses of thesemiconductor devices only; losses of the reactive elementsand control circuitry are not included.

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âã ä å æç

è é

ê ë

ì í

î ï

ð ñ

ò ó

ô õ

ö ÷

ø ù

ú û

ü ýÿþ

Fig. 7 One phase of a three-level inverter circuit

(a) Averaged switch model during positive inductor current

"! #"$% & '( ) * +

,

- . / 0 1 2 3 4 5

6

7

8 9 : ; < = > ? @

A

B C D E F G H I J K L M N O P Q R S

Qr + Qtail

Ts

tr

Tsi2(t) Ts

T U V W

X Y[Z \ ] ^

_ ` a b c

d e f g h

(b) Averaged switch model during negative inductor current

i j kl m n o p q

r

s t u v w x y z

|

~

Qr + Qtail

Ts

¡ ¢ £ ¤¦¥ § ¨ © ª « ¬­® ¯°

tr

Ts

i2(t) Ts

Fig. 8 Averaged circuit models for the upper half of the three-level PWMswitch network of Fig.7

(a) Averaged switch model during positive inductor current

±³² ´³µ¶ · ¸¹ º » ¼ ½

¾

¿ À Á Â Ã Ä Å Æ Ç

È

É

Ê Ë Ì Í Î Ï Ð Ñ Ò

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Ô Õ Ö × Ø Ù Ú Û Ü Ý Þ ß à á â ã ä å

Qr + Qtail

Ts

tr

Tsi2(t) Ts

æ ç è é

ê ë ìîí ï ð ñ

(b) Averaged switch model during negative inductor current

ò ó ôõ ö ÷ ø ù ú

û

ü ý þ ÿ

! "

Qr + Qtail

Ts

tr

Tsi2(t) Ts

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& ' ( )+* , -./ 01

Fig. 6 Averaged circuit models of the PWM switch network of Fig. 4

Losses in one phase of the rectifier are detailed in Fig. 11.It can be seen that, at 10 kHz and lower output powers, thelosses caused by the diode reverse-recovery and IGBTcurrent tail are most significant, followed by conductionlosses. Hence switching losses dominate at light load,especially the diode reverse-recovery loss. The reducedefficiency at light load can therefore be ascribed to the less-than-linear dependence of diode reverse-recovery loss onload current.

Figure 12 ill ustrates the more severe switching losses thatare observed when the switching frequency is doubled.Therefore, converter eff iciency is also lower at 20 kHz asill ustrated in Fig. 13.

Figures 11 and 12 describe how dominant lossmechanisms vary with converter operating point. Variation

of switching loss mechanisms with operating point is centralto the issue of wind inverter efficiency at low wind speed.

Figure 14 shows variations in efficiency of a three-levelrectifier/inverter system operating at 10 kHz. Figure 15shows the corresponding distribution of losses in theconverter at 10 kHz. As in Fig. 10-13, the previouslydeveloped averaged switch model of the three-level converteras well as the laboratory acquired model parameters havebeen used to generate these plots. With a three-levelconverter, we are able to double the DC link voltage and thusdouble the maximum possible load power. The increase inconduction loss is associated with the increase in the numberof switching devices in the three-level converter. Theswitching loss is reduced because of the decreaseed

2-Level Converter Loss Summary @ 10 kHz

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Output power, per phase

Loss

Diode Reverse-Recovery Loss

Conduction Loss

IGBT CurrentTail Loss

Fig. 11 Sources of loss in two-level converter (per phase) at 10 kHz

2-Level Converter @ 10 kHz

80%

85%

90%

95%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%P/Pmax

Effi

cien

cy

CompositeRectifier

Inverter

Fig. 10 Two-level converter eff iciency vs. load power at 10 kHz

2-Level Converter @ 20 kHz

75%

80%

85%

90%

95%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

P/Pmax

Effi

cien

cy Composite

Rectifier

Inverter

Fig. 13 Two-level converter eff iciency vs. load power at 20 kHz

2 3 4 5 6 78 9 : ; < : ; = > ? @

A B C D EGF H H I J K L M N O P O L QR S T U T S VW X Y Z\[ ] ^ Y _ `

a b c d egf h i j k l j k

Fig. 9 DC link rectifier / inverter system used in the analysis

2-Level Converter Loss Summary @ 20 kHz

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

200.00

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Output power, per phase

Loss

Diode Reverse-Recovery Loss

Conduction Loss

IGBT CurrentTail Loss

Fig. 12 Sources of loss in two-level converter (per phase) at 20 kHz

semiconductor voltage stresses. Figure 16 and 17 ill ustratethe same three level converter characteristics at 20 kHz.

VI. CONCLUSION

Wind generators operate most often at a fraction of theirrated power. For example, a typical wind distribution may becentered at 25% to 35% of rated power. It is critical to theeconomic success of wind generation that output kWh bemaximized, and hence system efficiency at power levels wellbelow rated power is extremely important [8]. Therequirement of high efficiency at light load is unique to windgeneration. In other applications, efficiency of the electrical

machines and power converters at light load is not important,provided that the total power loss is no worse than atmaximum load. Indeed, the efficiency of a typical PWMconverter is maximum at a point near rated load power, andfalls off rapidly at light load. This behavior can significantlydegrade the energy captured by a variable-speed windgenerator. Hence, there is a need to develop a betterunderstanding of the mechanisms that degrade efficiency atlight load, and to create new approaches to optimizingconverter efficiency over a wide range of load powers.

In this paper, we presented experimentall y verifiedaveraged switch models for two-level and three-level PWMconverters. By incorporating the extensively tested modelparameters of Table 1 into the developed averaged switchmodels, we were able to relate variations in converterefficiency to variations in converter operating point. Thesechanges in efficiency were further explained in terms ofchanges in converter’s most significant loss mechanisms. Atlight load, losses due to the diode reverse-recoverymechanism were observed to dominate. Comparing the plotspresented in Section V of this paper provides the necessaryinsight needed prior to selecting the specific components andconverter type for a given PWM converter design.

REFERENCES

[1] R. Erickson, Fundamentals of Power Electronics, New York: Chapman& Hall , 1997, pp. 241-245.

[2] V. Vorperian, “Simplified Analysis of PWM Converters Using theModel of the PWM Switch: Parts I and II,” IEEE Transactions onAerospace and Electronic Systems, Vol. AES-26, pp. 490-505, May1990.

[3] S. Ghandi, Semiconductor Power Devices: Physics of Operation andFabrication Technology, New York: John Wiley & Sons, 1977.

[4] J. Baliga, Modern Power Devices, New York: John Wiley & Sons,1987.

[5] N. Mohan, T. Undeland, and W. Robbins, Power Electronics:Converters, Applications, and Design, second edition, New York:John Wiley & Sons, 1995.

[6] International Rectifier Corp., IRGPH50F IGBT data sheet.[7] A. Nabae, I. Takahashi, H. Akagi, “Anew neutral-point clamped

PWM inverter,” IEEE Transactions on Industry Applications, Vol.IA-17, No. 5, Sep/Oct 1981, pp 518-523.

[8] P. Carlin, “Analytic Expressions for Maximum Wind TurbineAverage Power in a Rayleigh Wind Regime,” ASME Wind EnergySymposium, Jan. 1997.

3-Level Converter @ 10 kHz

85%

90%

95%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

P/Pmax

Effi

cien

cy

CompositeRectifier

Inverter

Fig. 14 Three-level converter eff iciency vs. load power at 10 kHz

3-Level Converter Loss Summary @ 10 kHz

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

200.00

0 2500 5000 7500 10000 12500 15000 17500 20000

Output power, per phase

Loss

Conduction Loss

Diode Reverse-Recovery Loss

IGBT Current Tail Loss

Fig. 15 Sources of loss in three-level converter (per phase) at 10 kHz

3-Level Converter @ 20 kHz

85%

90%

95%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

P/Pmax

Effi

cien

cy Composite

Rectifier

Inverter

Fig. 16 Three-level converter efficiency vs. load power at 20 kHz

3-Level Converter Loss Summary @ 20 kHz

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

200.00

0 2500 5000 7500 10000 12500 15000 17500 20000Output power, per phase

Loss

Conduction Loss

Diode Reverse-Recovery Loss

IGBT Current Tail Loss

Fig. 17 Sources of loss in three-level converter (per phase) at 20 kHz