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Investigation and Implementation of MOS-FETs Losses Equations in a Three-phaseInverter

Master’s thesis in Electric Power Engineering

QUE WANG

Department of Energy and EnvironmentCHALMERS UNIVERSITY OF TECHNOLOGYGothenburg, Sweden 2015

Master’s thesis 2015

Investigation and Implementation of MOSFETsLosses Equations in a Three-phase Inverter

QUE WANG

Department of Energy and EnvironmentDivision of Electric Power Engineering

QUE WANGChalmers University of Technology

Gothenburg, Sweden 2015

Investigation and Implementation of MOSFETs Losses Equations in a Three-phaseInverterQUE WANG

© QUE WANG, 2015.

Supervisor: Joachim Lindström, Volvo Car GroupSupervisor: Magnus Ekvall, Volvo Car GroupExaminer: Torbjörn Thiringer, Department of Energy and Environment

Master’s Thesis 2015Department of Energy and EnvironmentDivision of Electric Power EngineeringQUE WANGChalmers University of TechnologySE-412 96 GothenburgTelephone +46 31 772 1000

Cover: MOSFET conduction losses plot during two periods.

Typeset in LATEXPrinted by Chalmers University of TechnologyGothenburg, Sweden 2015

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Investigation and Implementation of MOSFETs Losses Equations in a Three-phaseInverterQUE WANGDepartment of Energy and EnvironmentChalmers University of Technology

AbstractIn this master thesis, the operation model of a three-phase MOSFET inverter andthe corresponding current waveforms are analyzed. The mathematical expressionsof the conduction losses based on the three-phase MOSFET inverter using PWMcontrol method are presented. The algebraic equations are given with the param-eters of a MOSFET-diode module, such as the on-state resistance, the body dioderesistance and the voltage drop. Moreover, a numerical reference representation ofthe conduction losses is made to verify the analytical expressions.

Numerical analysis is firstly based on the pure sinusoidal reference three-phase volt-ages. The results of the numerical analysis and the results of the analytical equationsare coherent. A comparison of the MOSFET inverter with reverse conduction char-acteristics and the assumption without reverse conduction is made. Without reverseconduction, the losses of one power module are higher than the one with reverse con-duction at both the high and low current levels. The di!erence can be more than 20% compared to the case with reverse condition at the rated current of the selectedmodule, CAS300M12BM2, 150 A. When the phase current is low and there is nodiode conducting during the operation, the losses without reverse conduction canbe more than 100 % higher. Furthermore, the losses resulting from third harmonicinjection and using the common mode reduction are calculated, and compared withthe losses using a pure sinusoidal reference. The conduction losses of those twodi!erent PWM methods are found to be small and presented in tables.

Keywords: Power electronics, MOSFET, Power losses, Conduction losses, Reverseconduction, PWM, MATLAB.

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AcknowledgementsThis work has been carried out at Volvo Car Group and the Department of Energyand Environment at Chalmers University of Technology. The author would like tothank her supervisors at Volvo Car Group, Joachim Lindström and Magnus Ekvall,as well as her examiner at Chalmers, Torbjörn Thiringer, for their never-endingsupport and valuable advice. The author would also like to thank the Division ofElectric Power Engineering for the support of software and hardware when she waswriting the academic report.

QUE WANG, Gothenburg, August 2015

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Nomenclature and Abbreviations

Symbol Quantity UnitVA Potential of phase A VVB Potential of phase B VVC Potential of phase C V

VDC DC link voltage Vu1inst Instantaneous voltage of one phase V

d Duty cycle -M Modulation index -i Instantaneous current A

pdiode Instantaneous power losses of the diode Wv Instantaneous voltage Vi Instantaneous current A

irms Root mean square value of the current in the component Aiavg Average value of the current A

Pdiode Average power losses of the diode Wt Time msT Fundamental period ms

pIGBT Instantaneous power losses of the IGBT WPIGBT Average power losses of the IGBT W

RF Equivalent resistance of the IGBT !VT Equivalent voltage drop of the IGBT V

pMOSF ET Instantaneous power losses of the MOSFET WPMOSF ET Average power losses of the di MOSFET ode W

! Displacement power factor angle radians" Turn-on(conduction) angle radians

Ron Equivalent resistance of the MOSFET !Rd Equivalent resistance of the diode !Vd Equivalent voltage drop of the diode VI Peak value of the phase current A

Irms Root mean square value of the phase current Afsw Switching frequency Hzf1 Fundamental frequency HzU Peak value of the phase voltage V

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Abbreviation ExplanationHEV Hybrid electric vehiclesDC Direct currentAC Alternating currentSiC Silicon carbideMOSFET Metal-oxide-semiconductor Field-e!ect TransistorIGBT Insulated-gate Bipolar TransistorPWM Pulse Width ModulationSPWM Sine-triangle pulse width modulationRMS Root mean squareAVG AverageTHIPWM Third Harmonic Injection Pulse Width Modulation

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Contents

Abstract vi

Acknowledgements viii

Nomenclature and Abbreviations ix

1 Introduction 11.1 Background of power losses in inverters . . . . . . . . . . . . . . . . . 11.2 Purpose of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Theory of a Three-phase Inverter 52.1 Introduction of a three-phase inverter . . . . . . . . . . . . . . . . . . 5

2.1.1 PWM control method in a three-phase inverter . . . . . . . . 52.1.2 Operation model during di!erent time interval in one switch-

ing period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Introduction of semiconductor switches: MOSFET, IGBT and diode . 11

2.2.1 Functionalities of MOSFET, IGBT and diode . . . . . . . . . 112.2.2 Basic losses-equations of diode, IGBT and MOSFET . . . . . 16

3 Operation Model of a Three-phase MOSFET Inverter Using PWM 173.1 Three-phase MOSFET inverter system with reverse conduction MOS-

FET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1.1 The structure of a three-phase MOSFET inverter . . . . . . . 173.1.2 The structure of one leg of the three-phase MOSFET inverter 17

3.2 The current flow in one leg of a three-phase MOSFET inverter . . . . 193.2.1 Current waveforms of pure MOSFET conduction during low

current flow in the system . . . . . . . . . . . . . . . . . . . . 193.2.2 Current waveforms of both MOSFET and diode conduction

during high current flow in the system . . . . . . . . . . . . . 203.3 Current analysis in the reverse conductive MOSFET . . . . . . . . . 22

4 Conduction Losses Calculation and Analysis 254.1 MOSFET conduction losses . . . . . . . . . . . . . . . . . . . . . . . 254.2 Diode conduction losses . . . . . . . . . . . . . . . . . . . . . . . . . 264.3 Equations of conduction power losses during di!erent time interval . 26

4.3.1 The expressions of MOSFET conduction losses in one period . 27

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Contents

4.3.2 The expressions of diode conduction losses in one period . . . 284.3.3 Boundary condition when the diode starts conducting . . . . . 28

4.4 Total Conduction losses equations during one period . . . . . . . . . 29

5 Verification Using Numerical Analysis 315.1 Prerequisites of the numerical analysis . . . . . . . . . . . . . . . . . 315.2 Numerical losses calculation . . . . . . . . . . . . . . . . . . . . . . . 32

5.2.1 Calculation procedure . . . . . . . . . . . . . . . . . . . . . . 325.2.2 Results of the numerical reference system and verification with

theoretical calculation . . . . . . . . . . . . . . . . . . . . . . 34

6 Theoretical Analysis and Comparison between MOSFET with re-verse conduction and without reverse conduction 376.1 Theoretical analysis of the mathematical equations with MOSFET

reverse conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376.2 Comparison and analysis between MOSFET with reverse conduction

and without reverse conduction . . . . . . . . . . . . . . . . . . . . . 39

7 Conduction Losses Calculation using two di!erent PWM Methods 437.1 Numerical results with the third harmonic injection . . . . . . . . . . 43

7.1.1 Reference voltage design principle . . . . . . . . . . . . . . . . 437.1.2 Results and comparison . . . . . . . . . . . . . . . . . . . . . 43

7.2 Results with the common mode reduction . . . . . . . . . . . . . . . 457.2.1 Voltage design principle . . . . . . . . . . . . . . . . . . . . . 457.2.2 Results and comparison . . . . . . . . . . . . . . . . . . . . . 46

8 Conclusion 49

9 Future Work 51

Bibliography 54

10 Appendix 1 55

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1Introduction

Currently, with the development of the worldwide automotive industry and the in-crease of the world population, the demand of vehicles for personal transportationhas increased dramatically, especially in China, India and some developing coun-tries [1]. Moreover, the environmental awareness, continuous oil price increase andnational or European environmental ambitious such as the 20-20-20 target [2], haveincreased the importance of the research on electrification of vehicles more andmore. Thus, the analysis of power losses in the advanced vehicular power systemneeds more e!ort to contribute to the development of the automotive world. In thischapter, some background of power losses in inverters, the purpose of the thesis andinvestigation methods will be introduced.

1.1 Background of power losses in invertersWith more regulations and constraints on the energy resources, hybrid and electriccars are attracting attention by automakers, governments, and customers [3]. Thedemands for improved fuel economy and more electric power are driving advanced ve-hicular power system voltages to higher levels. Since hybrid electric vehicles (HEV)are likely to dominate the advanced propulsion in coming years, the hybrid tech-nology becomes significant. Furthermore, power electronic devices such as DC toAC inverters are inherent parts of electrified vehicles. Moreover, in the design ofthe powertrain components, power electronics converters are shown to be one ofthe most challenging parts presented in advanced propulsion systems. Besides, inbattery chargers and a class of DC and AC motor drives, the application of powerelectronic converters with controllable switches is quite necessary. Therefore, signif-icant amount of research has been conducted on three-phase inverters.

In today’s propulsion systems of hybrid cars, it is common to use IGBT invert-ers operating according to the PWM principle. The losses equations of the IGBTinverters have been solved and can be used for the calculation [4]. Based on thecomparisons of the MOSFET and IGBT inverters in the motor drive systems in theliterature, the SiC MOSFET inverters have the advantages of lower losses, bettere"ciency and smaller size in the same motor drive application [5]. Due to the pos-sible reverse conduction opportunities of MOSFETs, the equations of the IGBTs in[4] are insu"cient to be used for calculating the conduction losses of the MOSFETinverters. Thus, it is significant to derive the conduction losses equations of the

1

1. Introduction

MOSFET inverters, so they can be used for future calculations. According to theauthor’s search, the conduction losses equations of the MOSFET inverters have notbeen found in available publications. For future use, the equations of power lossesin MOSFET inverters need to be derived.

1.2 Purpose of the thesisThe main objective of the work reported in this thesis is to derive the mathemat-ical expression of the conduction losses in a three phase MOSFET inverter. Withthe equations, the inverter power losses under various DC voltages, various phasecurrents, various modulation indices, and various basic parameters based on thephysical structures of the inverters, can be calculated instantaneously by the soft-wares, for instance, MATLAB. The results presented in this thesis are from ananalytical model as well as from a numerical reference model.

1.3 MethodsIn order to be able to calculate the power losses in MOSFET inverters, it is vitalto have a good understanding of the components functionalities, and the on-statecharacteristics. Equivalent circuits will be investigated when each component isconducting.

Once the relation is known, the current waveforms of di!erent components canbe produced in detail. The conduction losses equations are given from [6]. Thus,the equations in one leg of the three-phase MOSFET inverter can be derived, bothfor the MOSFET and the diode.

The following task is to derive the conduction power losses equations mathemat-ically. Thus, the algebraic formulas are necessary to be used. The final conductionlosses expressions will be implemented in MATLAB for further use.

After the investigation of the losses equations, the numerical calculations will bepresented. This part is done using MATLAB. The conduction losses will be shownin tables and will be verified with the analytical results utilizing the selected com-ponent.

Moreover, the comparison of the MOSFET inverter with reverse conduction char-acteristics and the assumption without reverse conduction is made. The loss-calculation are performed at both the high and low current levels. The di!erencesare shown in tables.

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1. Introduction

The last task is to investigate the conduction power losses in realistic inverter de-signs, using third harmonic injection and the common mode reduction, using theresults from the previous tasks. The deviations will be presented and compared topure sinusoidal reference voltages.

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1. Introduction

4

2Theory of a Three-phase Inverter

In this chapter, the theory of a three-phase inverter will be presented. First, thetopology of a three-phase inverter will be shown and the explanation of the opera-tion principle and performance will be given. Secondly, the functionalities and basicpower losses equations of the semiconductor switches will be introduced.

2.1 Introduction of a three-phase inverterThe topology of a three-phase inverter is shown in Figure 2.1. The inverter consistsof three phase legs, each leg includes two non-reverse conduction switches in eitherthe up or down position. There is a diode in anti-parallel with each correspondingswitch, which is used to provide a path for a current flowing in the opposite direction.It always occurs due to the loads are inductive. For example, if the load current isnegative at the instant when the upper transistor is gated on, the diode in parallelwith the upper transistor will conduct until the load current becomes positive, andat that time the upper transistor will begin to conduct. There is a capacitor on theDC side, which is assumed to supply a sti! DC voltage in this analytical model. Andthe loads of the system are modeled with large inductors, which give the continuouscurrents following the reference current waveforms. The inductive loads with a backemf represent the electric machine in an electric drive system. There is a 120 ° shiftbetween each phase.

2.1.1 PWM control method in a three-phase inverterOne of the widely used inverter control methods covered in power electronics is thesine-triangle pulse width modulation (SPWM) control. With the SPWM controlmethod, the switches of the inverter are controlled based on a comparison of si-nusoidal control reference signals and a triangular carrier wave [7]. The sinusoidalcontrol waveform establishes the fundamental frequency of the inverter output, whilethe triangular waveform presents the switching frequency of the inverter. The ratiobetween the frequencies of the sinusoidal reference wave and the triangular wave isreferred to as the modulation frequency ratio [8].

The switches in each leg of a three-phase inverter are never both on or o! simultane-ously; therefore, the potentials VA, VB, and VC alternate between the input voltage

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2. Theory of a Three-phase Inverter

Figure 2.1: The structure of a three-phase inverter with non-reverse conductionswitches, an associated DC link capacitor and inductive loads.

(VDC) and zero. Using this method, the phase potentials are AC, with a funda-mental frequency corresponding to the frequency of the sinusoidal reference signals.The magnitude of the triangle wave is fixed. Thus, the amplitude of the output po-tential is controlled by adjusting the amplitude of the sinusoidal reference signals. [8]

Based on the research in [9], using the PWM modulation method, the instanta-neous duty cycle can be written as

d(t) = 12(1 + M sin t) (2.1)

for a pure sinusoidal wave. In (2.1), d is the duty cycle of one leg. M is the mod-ulation index of the PWM control method, which is between 0 and 1. The timeintervals when the upper semiconductors are conducting can be calculated from(2.1). Consequently, (1-d) gives the time intervals when the lower semiconductorsare conducting. [9]

The output potential of one phase is shown in Figure 2.2 using SPWM in the one-leg model. The DC link voltage is 400 V in this case, which can be utilized in theelectric drive system of a hybrid car. The switching frequency of the theoreticalmodel in this case is 2 kHz, which is suitable for the analysis of the waveforms. Theblack curve in Figure 2.2 represents the triangle wave, the magenta curve, u1, isthe reference signal of one phase, the blue curve, u1inst, shows the instantaneousvoltage of the phase, and the red line, u1(time), is the fundamental output potentialof the phase. Therefore, the corresponding phase current waveform can be drawn asin the following section. Since all of the three phases in the inverter have a 120° shiftbetween the other two phases, it is enough to analyze the operation principle usingone leg of the three-phase inverter. There is an impact due to the natural pointwill not be zero all the time in the three-phase inverter, but it will not influence thecoming visualizations. Thus, the total losses in a three-phase inverter will be threetimes of the losses in one leg. For the analysis part, the one-leg topology will be

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introduced.

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Figure 2.2: The potential waveforms over one switch during one period usingPWM. The upper one shows the triangular wave and the sinusoidal reference signalof one phase, u1. The lower one shows the instantaneous phase potential, u1inst,and the fundamental output potential, u1(time).

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2.1.2 Operation model during di!erent time interval in oneswitching period

Figure 2.3 shows a one-leg topology of a three-phase inverter with general control-lable switches. The one-leg topology contains T1 and D1 in the upper part and T4and D4 in the lower part. A DC voltage(VDC) and an inductive load are utilized inthe description. Each of the switches and diodes in Figure 2.3 are drawn in di!erentcolours to facilitate in the upcoming analysis regarding the current waveforms.

Figure 2.3: One leg of the three-phase inverter with back emf.

The corresponding phase current waveforms in one diode-switch combination duringone period using PWM are reached under u1(time) of Figure 2.2. Since the systemincludes inductive loads, thus, the output current is often lagging, which can beexpressed as

i(t) = Isin(#t ! $), (2.2)

where $ is the angle di!erence between the fundamental phase potential and thecurrent waveform. In Figure 2.4, the current through the upper switch and diodeis shown. The dashed line, i1, is the phase current with Irms being 375 A, which ishigh enough and can be used in the hybrid system with the IGBT inverter. In thisfigure, a phase shift is shown. The red curve, iT 1U , represents the current throughthe switch, and the magenta, iD1U , curve provides the current through the corre-sponding diode.

Correspondingly, the current through the lower switch and diode is presented inFigure 2.5. The blue curve, iT 1L, represents the current through the lower switch,and the black curve, iD1L, is the current through the corresponding diode. Fromthose two figures, it can be seen that the upper switch and lower diode take up thewhole positive load current shape, and the lower switch and the upper diode takeFup the negative half period.

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Figure 2.4: The current waveform in upper diode and switch during one periodusing PWM. The dashed line is the phase current, i1, the red curve representsthe current through the upper switch, iT 1U , and the magenta curve is the currentthrough the corresponding diode, iD1U .

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Figure 2.5: The current waveform in lower diode and switch during one periodusing PWM. The dashed line, i1, is the phase current, the blue curve, iT 1L, representsthe current through the lower switch, and the black curve, iD1L, is the currentthrough the corresponding diode.

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2.2 Introduction of semiconductor switches: MOS-FET, IGBT and diode

2.2.1 Functionalities of MOSFET, IGBT and diodeEach component in a three-phase inverter has a unique functionality, which is whydi!erent forms of equations are used in the losses calculation. Thus, the character-istics of each component need to be introduced in this section.

Firstly, the symbol and the steady-state i-v characteristic of a diode are shownin Figure 2.6 [6]. When the diode is forward biased, it begins to conduct with asmall forward voltage across it. Thus, the characteristics can be simplified as shownin Figure 2.7. In the analysis of the inverter topology, the on-state condition of thediode can be represented by a resistor in series with a voltage source.

Figure 2.6: Diode: (a) symbol, (b) i-v characteristic.

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Figure 2.7: Simplified characteristics of the diode. The red curve shows the relationbetween the voltage and the current, and the linearized line gives the equivalentresistance of the diode and the small voltage drop, Vd.

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Secondly, Figure 2.8 shows the symbol for an IGBT to the left and its i-v characteris-tics to the right [6]. Similar to a diode, the simplification of the IGBT characteristicscan be draw as it is shown in Figure 2.9. The equivalent model of an IGBT can bedrawn as a resistance, Rf , and a voltage drop, VT , in series.

Figure 2.8: An IGBT: (a) symbol, (b) i-v characteristic.

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Figure 2.9: Simplified characteristics of the IGBT. The red curve shows the relationbetween the voltage and the current, and the linearized line gives the equivalentresistance of the IGBT, Rf , and the small voltage drop, VT .

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The circuit symbol of an n-channel MOSFET is shown in Figure 2.10 (a). The i-vcharecteristics are shown in Figure 2.10 (b). The di!erences are shown in Figure2.10 (b),when VGS is high enough, the current increases while the voltage increases,and there is no constant voltage-drop term. Then the simplified characteristics canbe draw in Figure 2.11. Therefore, the equivalent circuit of an on-state MOSFETcan be drawn as a resistor, Ron [6].

Figure 2.10: N-channel MOSFET: (a) symbol, (b) i-v characteristic.

Figure 2.11: Simplified characteristics of the MOSFET. The linearized curve showsthe equivalent resistance of the MOSFET, Ron.

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2.2.2 Basic losses-equations of diode, IGBT and MOSFETThe on-state losses-equations of the diode can be written as

pdiode(t) = v(i(t))i(t) = (Rdi(t) + Vd)i(t) = Rdi2(t) + Vdi(t), (2.3)

Pdiode = 1T

! T

0v(i(t))i(t) dt

= 1T

! T

0(Rdi(t) + Vd)i(t) dt

= 1T

! T

0(Rdi2(t) + Vdi(t)) dt

= Rdi2rms + Vdiavg,

(2.4)

where pdiode is the instantaneous power losses of the diode, and Pdiode is the averagepower losses of the diode during one fundamental period. irms is the root meansquare(RMS) value of the current and iavg is the average value of the current. T isthe fundamental period.

pIGBT (t) = v(i(t))i(t) = (Rf i(t) + VT )i(t) = Rf i2(t) + VT i(t), (2.5)Similarly, the on-state power losses equations of the IGBT can be written as

PIGBT = 1T

! T

0v(i(t))i(t) dt

= 1T

! T

0(Rf i(t) + VT )i(t) dt

= 1T

! T

0(Rf i2(t) + VT i(t)) dt

= Rf i2rms + VT iavg,

(2.6)

where pdiode is the instantaneous power losses of the diode, and Pdiode is the averagepower losses of the diode during one fundamental period.

pMOSF ET (t) = v(i(t))i(t) = Roni2(t) (2.7)

PMOSF ET = 1T

! T

0v(i(t))i(t) dt

= 1T

! T

0Roni2(t) dt

= Roni2rms

(2.8)

The power losses equations of the MOSFET are given in (2.7) and (2.8), wherepMOSF ET is the instantaneous power losses of the MOSFET, and PMOSF ET is theaverage power losses of the MOSFET during one fundamental period. It can beseen in those equations that there is no constant voltage-drop term in the lossescalculation.

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3Operation Model of a Three-phase

MOSFET Inverter Using PWM

In this chapter, the investigation is focused on using MOSFETs as the switches in-stead of IGBTs. The MOSFET inverter is analyzed in detail. This part is conductedbased on one leg of the three-phase inverter. Current waveforms are shown both atthe high amplitude level and at the low amplitude level.

3.1 Three-phase MOSFET inverter system withreverse conduction MOSFET

3.1.1 The structure of a three-phase MOSFET inverterFigure 3.1 shows the topology of a three-phase MOSFET inverter. All of the switchesare n-channel MOSFETs in this case. For the analytical model, the capacitor onthe DC side is assumed to be large enough to provide a sti! voltage. The inverterhas a large inductive load which gives a continuous current. As it is mentioned inChapter 2, due to the 120 ° shift principle, all of the three phases carry the sameshape of the currents during one period, therefore, it is enough to analyse only oneleg of the three-phase inverter to derive the losses equations. Then the total lossesin the inverter will be three times of the losses of one leg. Thus, in the followingsections, the one-leg topology will be analyzed in detail.

3.1.2 The structure of one leg of the three-phase MOSFETinverter

In Figure 3.2, the one-leg topology of a three-phase inverter is shown, which willin principle give the same results as one leg of the three-phase MOSFET inverter.The upper MOSFET, M1, is marked in red, and the lower MOSFET, M4, is drawnin blue. Meanwhile, the upper diode, D1, is presented in magenta, and the lowerdiode, D4, is in black. In the following analysis of current flow, the current curveswill be shown using the corresponding colours.

Since during one period, each time point can correspond to a certain phase angle,

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3. Operation Model of a Three-phase MOSFET Inverter Using PWM

Figure 3.1: The structure of a three-phase MOSFETs inverter with large capacitorand large inductive loads.

which can be expressed as! = 2%

Tt, (3.1)

thus, the output current is marked as i(!) in Figure 3.2. From the same method,all calculations are based on the angle in the following analysis of the current flowand power losses.

Figure 3.2: The topology of one leg of a three-phase MOSFETs inverter with aninductive load.

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3.2 The current flow in one leg of a three-phaseMOSFET inverter

In the following analysis, the circuit in Figure 3.2 is chosen to be the model whenthe currents are simulated. Unless stated in this chapter, 2 kHz will be used as theswitching frequency. All the currents in the MOSFETs and diodes are shown as theabsolute values in the figures in this section.

3.2.1 Current waveforms of pure MOSFET conduction dur-ing low current flow in the system

Using the one-leg topology analysis, the current flows of the leg can be shown inFigure 3.3, Figure 3.4 and Figure 3.5 for one fundamental period. In this case, inorder to have no current in the diode, the RMS value of the load phase current isselected to be 20 A. It can be seen from Figure 3.3 and Figure 3.4, if the amplitudeof the phase current is not high enough, only the MOSFETs are conducting. Fig-ure 3.5 shows that during one period, the phase current is the sum of the currentsthrough the upper MOSFET and the lower MOSFET.

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Figure 3.3: The currents through M1 and D1 and the phase current i(!) duringone period.

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Figure 3.4: The currents through M4 and D4 and the phase current i(!) duringone period.

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Figure 3.5: The currents through M1, D1, M4 and D4 and the phase current i(!)during one period when the RMS value of the phase current is 20 A.

3.2.2 Current waveforms of both MOSFET and diode con-duction during high current flow in the system

Based on the same method of current simulation, when the RMS value of the phasecurrent is increased to 150 A, which is based on the rated current of the MOSFETselected in the following chapter, the current will flow in both the MOSFETs and

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the diodes. The current curves are shown in Figure 3.6 for one fundamental period.The current waveforms are in accordance with the explanation of the theory part,which shows that the diodes start conducting if the amplitude of the phase currentis high enough.

From Figure 3.6, it is shown that up until a certain time instant, the diode willstill not conduct even though the polarity of the current has changed. In this the-sis, this start-conduction angle is called ", and will be stated and utilized in thecalculation part.

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Time (s)

Curre

nt (A

)

iM1iM4iD1iD4i(α)

Figure 3.6: The currents through M1, D1, M4 and D4 and the phase current i(!)in one period when the RMS value of the phase current is 150 A.

21


3.3 Current analysis in the reverse conductive MOS-FET

For the one-leg topology, since the current waveform is sinusoidal, thus, the uppercombination of MOSFET-diode and lower combination of MOSFET-diode can beseen as symmetrical in the calculation part.

Figure 3.7 shows the details of the current waveforms through di!erent componentsin one leg of the three-phase inverter when the phase current is positive. Corre-spondingly, Figure 3.8 is the topology which also presents the current flow duringdi!erent time intervals. For instance, during time d, only M1 is conducting with thesame value as the phase current. During time (1-d), M4 and D4 are both conduct-ing, and the sum of those two currents equals the phase current, i(!).

0.008 0.0085 0.009 0.0095 0.01 0.0105 0.011 0.0115 0.012 0.0125

0

50

100

150

Time (s)

Curre

nt (A

)

iM1iM4iD1iD4i(α)

Figure 3.7: Zoomed in current waveforms: When the current is positive, the figureshows the currents through the upper MOSFET and lower MOSFET and diodeduring time d and (1-d).

When the current is still positive, but the magnitude of the current is not highenough for D4 to conduct, then the current flow in the one-leg topology is shown inFigure 3.9.

If it comes to the negative half period of the phase current, the same procedure asfor the positive phase current is used. The current flows are draw in Figure 3.10 andFigure 3.11 for high magnitudes of the phase current and for the low magnitude ofthe phase current.

22


Figure 3.8: One leg topology: When the current is positive and high enough, thedi!erent directions of the currents through the upper MOSFET and lower MOSFETand diode during time d and (1-d).

Figure 3.9: One leg topology: When the current is positive and low, the di!erentdirections of the currents through the upper MOSFET and lower MOSFET duringtime d and (1-d).

In the following section, the current in those di!erent time intervals will be describedusing mathematical expressions.

23


Figure 3.10: One leg topology: When the current is negative and high enough, thedi!erent directions of the currents through the upper MOSFET and lower MOSFETand diode during time d and (1-d).

Figure 3.11: One leg topology: When the current is negative and low, the di!erentdirections of the currents through the upper MOSFET and lower MOSFET duringtime d and (1-d).

24

4Conduction Losses Calculation

and Analysis

This chapter includes the mathematical explanation of the conduction losses-equations.The steps of the derivation will be presented. The calculation is based on the one-leg topology of a three-phase MOSFET inverter. The characteristics of the reverseconduction are analyzed and implemented in the final equations.

4.1 MOSFET conduction lossesThe average value of the MOSFET conduction losses can be written as

PMOSF ET cond = 1T

! T

0d(t)v(i(t))i(t) dt, (4.1)

where v(i(t)) is the instantaneous value of the voltage over the MOSFET switchand i(t) is the instantaneous value of the current through the MOSFET. The in-tegration of the instantaneous power losses over one switching cycle thus gives anaverage value of the MOSFET conduction losses.

Since! = 2%

Tt, (4.2)

Thusdt = T

2%d!, (4.3)

The average value of the MOSFET conduction losses can now be determined as

PMOSF ET cond = 12%

! 2!

0d(!)v(i(!))i(!) d!. (4.4)

An approximation of the drain-source on-state resistance, Ron, is made when thecalculation is derived as mentioned in Chapter 2. Thus,

v(i(!)) = Ron(i(!))i(!), (4.5)Therefore, (4.4) can be rewritten as

PMOSF ET cond = 12%

! 2!

0d(!)Roni2(!) d!. (4.6)

25

4. Conduction Losses Calculation and Analysis

whered(!) = 1

2(1 + M sin !). (4.7)

where M is the modulation index [9]. Equation (4.6) is written in the form for lateruse when deriving the expression of diode losses.

4.2 Diode conduction lossesThe average value of the diode conduction losses can be derived using the samemethod as that of the MOSFET, which is

Pdiodecond = 1T

! T

0d(t)vd(i(t))i(t) dt, (4.8)

where v(i(t)) is the instantaneous value of the voltage over the diode and i(t) isthe instantaneous value of the current through the diode. The integration of theinstantaneous power losses over one fundamental cycle thus gives an average valueof the losses in the diode.

Using the same procedure as (4.2) and (4.3), the average value of the diode conduc-tion losses can now be determined as

Pdiodecond = 12%

! 2!

0d(!)vd(i(!))i(!) d!. (4.9)

An approximation with the resistance, Rd, and voltage drop, Vd, is made when thecalculation is derived.

Thus,

vd(i(!)) = (Rd(i(!) + Vd)i(!). (4.10)Therefore, (4.9) can be rewritten as

Pdiode = 12%

! 2!

0d(!)(Rdi2(!) + Vdi(!)) d!, (4.11)

Equation (4.11) is written in the form for later use when deriving the expression ofdiode losses.

4.3 Equations of conduction power losses duringdi!erent time interval

As it is stated in Chapter 3, since the output current waveform is sinusoidal, thus,the upper package and lower package can be seen having the same power losses in

26


the calculation part. In this chapter, all the calculations are based on the currentanalysis presented in Figure 3.3 to Figure 3.7.

4.3.1 The expressions of MOSFET conduction losses in oneperiod

Since all the figures above are taking the voltage as a reference, so in Figure 4.1there is an angle di!erence between the voltage and the current, $, where cos $ isthe displacement power factor of the electric drive system. As it is shown in Figure4.1, the angle from the current zero-crossing angle to the angle when the diode startsconducting, is called ". According to the symmetrical theory, the angle between theinstance when the diode ends conducting and the next zero-crossing angle is also ".

Figure 4.1: The currents waveforms of one period where the RMS value of the phasecurrent is 150 A. $ is the angle of the displacement power factor. " is the anglebetween the zero-crossing angle and the angle when the diode starts conducting.

Thus, for one MOSFET, for example M1, the conduction losses can be divided tothree terms, which can be written as

PMOSF ET cond = 12%

! !+"+#

"d(!)v(i(!))i(!) d!

+ 12%

! 2!+"!#

!+"+#d(!)v(i(!))i(!) d!

+ 12%

! 2!+"

2!+"!#d(!)v(i(!))i(!) d!.

(4.12)

The duty cycle di!ers from each angle, however, the expression of the duty cycle

27


d1 = 12(1 + M sin !1) (4.13)

is the same if only one point is considered. Besides, the voltage expressions can berewritten using the equations of the current. Therefore, the only di!erence of thosethree parts is the currents during di!erent time intervals.

Since only the MOSFET is conducting in the first term and the third term of(4.12), the expressions of the current through the MOSFET have the same formas the phase current. For the second term of (4.12), the sum of the currents throughthe MOSFET and the diode equals the phase current. Moreover, the voltage overthe MOSFET and the voltage over the diode have the same value. Therefore, theexpressions of the currents through the MOSFET and the diode can be calculatedas

iMOSF ET = RdI sin(! ! $) ! Vd

Ron + Rd(4.14)

and

idiode = RonI sin(! ! $) + Vd

Ron + Rd(4.15)

where I is the peak value of the phase current.

4.3.2 The expressions of diode conduction losses in one pe-riod

Based on Figure 4.1, each diode conducts for less than half a period. For instance,D4 conducts from % + $ + " to 2% + $ ! ", and the current expression has alreadybeen derived in the last section. Thus the conduction losses of the diode during oneperiod can be written as

Pdiodecond = 0

+ 12%

! 2!+"!#

!+"+#d(!)vd(i(!))i(!) d!

+ 0

(4.16)

where the current expression of the diode is the same as (4.15).

4.3.3 Boundary condition when the diode starts conductingSince the final equation will be implemented in MATLAB, it is better to utilizeone expression which can merge two conditions of di!erent current levels into onemathematical expression. Therefore, the boundary condition is significant.

In this work, the boundary condition is shown as below,

28


I sin " = Vd

Ron. (4.17)

The boundary condition of " can be defined using (4.17). With the settings of", the losses-equations will be valid for all the calculation, no matter if the currentis high enough or not for the diodes conducting.

4.4 Total Conduction losses equations during oneperiod

From Section 4.3.1 and Section 4.3.2, the total conduction losses of the MOSFETcan be expressed using the equations of the power losses, (4.12) and (4.16), and theexpressions of the currents, (4.14) and (4.15). Thus the expression of the MOSFETlosses can be rewritten as

PMOSF ET cond = 12%

! !+"+#

"

12(1 + M sin !)RonI2 sin2(! ! $)) d!

+ 12%

! 2!+"!#

!+"+#

12(1 + M sin !)Ron

"RdI sin(! ! $) ! Vd

(Ron + Rd)2

#2d!

+ 12%

! 2!+"

2!+"!#

12(1 + M sin !)RonI2 sin2(! ! $) d!.

(4.18)

Using the same method, the diode losses during one period can be expressed as

Pdiodecond = 12%

! 2!+"!#

!+"+#

12(1 + M sin !)

$Vd

"! RonI sin(! ! $) + Vd

Ron + Rd

#+ Rd

"RonI sin(! ! $) + Vd

Ron + Rd

#2%d!.

(4.19)The expressions shown above are straightforward to understand according to (4.12)and (4.16). Regarding the implementation in MATLAB, the speed of running thecalculation needs to be taken into consideration. One way to improve the compu-tation speed is to derive a simpler algorithmic calculation instead of the integrationfor MATLAB. To derive those algebraic expressions, the expressions need to be inte-grated. However, due to the asymmetry of the conduction behavior of the MOSFETand the diode in the positive half period and the negative half period, the simpli-fied algebraic equations are more complicated than the ones of an IGBT inverter in[4]. The reason of the complexity is the angle ", which means that the MOSFETsconduct more than half of a period during the whole period. Moreover, during thereverse conduction of the MOSFET, the phase current is divided into two expres-sions for the MOSFET and the diode. The expressions of the currents shown in

29


(4.14) and (4.15) give more complicated results than using the expression of thephase current in the IGBT losses-calculation.

The derived losses-equations of the MOSFET can be written as

PMOSF ET cond = 18%

I2Ron

$% + " + M cos($ + ") + M cos $ ! 1

2 sin 2"

+ M

2 cos($ ! ") + M

2 cos $ ! M

6 cos($ + 3") ! M

6 cos $%

+ 18%

I2Ron

$" ! M cos $ + M cos($ ! ") ! 1

2 sin 2"M

2 cos $

+ M

2 cos($ + ") + M

6 cos $ ! M

6 cos($ ! 3")%

+ 14%

Ron

(Ron + Rd)2

&R2

dI2(2% ! 4" + 2 sin 2") + V 2d (% ! 2")

+ 4RdI cos "

+ 112MR2

dI2$

! 9 cos(" ! $) ! 9 cos(" + $)

+ cos(3" ! $) + cos(3" + $)%

! MV 2d

$cos($ ! ") + cos($ + ")

%

! 12MRdI

'(2% ! 4") cos $ + sin(2" ! $) + sin(2" + $)

().

(4.20)

The derived losses-equations of the diode can be written as

Pdiodecond = 14%

1(Rd + Ron)2

$12M(Ron ! Rd)(!Vd)RonI((% ! 2") cos $

+ sin(2" ! $) + sin(2" + $)%

+ MV 2d Ron

$cos($ ! ")

+ cos($ + ")%

+ 112MRdR2

onI2$

! 9 cos($ + ") ! 9 cos($ ! ")

+ cos($ ! 3") + cos($ + 3")%

+ 2(Ron ! Rd)VdRonI cos "

! V 2d Ron(% ! 2") + 1

4RdR2onI2(2% ! " + 2 sin 2").

(4.21)

Equation (4.20) and (4.21) give the same results as the expressions in (4.18) and(4.19). Furthermore, the results are needed to be verified through another methodof power losses calculation, which will be explained in the next chapter.

30

5Verification Using Numerical

Analysis

5.1 Prerequisites of the numerical analysis

In this chapter, numerical calculations are performed in MATLAB to verify the the-oretical losses-equations. The MOSFET module, CAS300M12BM2 from CREE, isselected in the numerical calculation for the following reasons. CAS300M12BM2 hasa rated current of 300 A, which is high enough for a three-phase MOSFET inverterof an electric drive system. The drain-source voltage of CAS300M12BM2 can reach1.2 kV. Due to the better switching performance of the MOSFET, the switchingfrequency, fsw, is selected to be 20 kHz in the calculation. The DC voltage is set tobe 400 V in this case, which can be selected as the DC voltage of the inverter in anelectric drive system. However, with the development of the Silicon carbide (SiC)devices, the components chosen in this project can be used also for higher voltagelevels, such as hybrid buses or trucks.

Based on the schematic circuit of CAS300M12BM2, the corresponding data of theanti-parallel diode can be obtained from the data sheet of the MOSFET module[11]. Table 5.1 presents the equivalent values of the voltage drop and the resistanceswhich are used in the following calculations [12].

Table 5.1: Set up of the simulation.

Name ValueIrms 150AVDC 400Vfsw 20kHzf1 50HzRon 0.0098!Vd 0.75VRd 0.005!

31

5. Verification Using Numerical Analysis

5.2 Numerical losses calculation5.2.1 Calculation procedureTo calculate the conduction losses numerically, a reasonable time step should be set.The fundamental period is 0.02 s. In this verification, the time step is selected to be0.1 µs, from which each discrete sample of voltage and current are used to calculatethe losses.

Figure 5.1 shows the phase current and the MOSFET conduction losses using thenumerical calculation. Each point represents the instantaneous losses at the sam-pled time. When the phase current is at a high value, the losses is at a higher level.Correspondingly, when the amplitude of the phase current is low, the losses is at alower level. The conduction losses of the MOSFET exist during the whole period.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04−400

−200

0

200

400

600

800

1000

Time(s)

Pow

erlosses(W

)an

dcurrenti1(A

)

Figure 5.1: The phase current and MOSFET losses during two periods, when thecurrent is high enough for the diode to conduct.

The corresponding diode conduction losses are shown n Figure 5.2. From Figure 5.1and Figure 5.2, it can be seen that when the diode generates losses, the losses in theMOSFET increase moderately.

32


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04−300

−200

−100

0

100

200

300

Time(s)

Pow

erlosses(W

)an

dcurrenti1(A

)

Figure 5.2: The phase current and diode losses during two periods.

33


5.2.2 Results of the numerical reference system and verifi-cation with theoretical calculation

The results from the analytical and numerical calculation are presented and com-pared in Table 5.2 to Table 5.5. The RMS value of the phase current is 150 A in thiscase. The examples of the verification are selected to show the results from the twodi!erent methods. In addition, the di!erences of each MOSFET and diode lossesbetween the analytical calculation and numerical calculation are given in the tables.

Table 5.2: Calculation results when M = 0.7 and $ = 0.82.

Component Analytical Losses(W) Numerical Losses(W) Di!erence (%)MOSFET 89.82 89.83 0.01

Diode 7.80 7.80 0

Table 5.3: Calculation results when M = 0.6 and $ = 0.8.


Diode 7.16 7.16 0

Table 5.4: Calculation results when M = 1 and $ = 0.


Diode 1.49 1.49 0

Table 5.5: Calculation results when M = 1 and $ = %.


Diode 23.17 23.16 -0.04

To make the verification having an overall consideration, another value of the phasecurrent is necessary to be selected below the diode conduction threshold. In thiscase, the power losses are calculated when the RMS value of the phase current is 20A. The results are shown in Table 5.6.

Table 5.6: Calculation results when M = 1 and $ = 0 with Irms = 20A.

Component Analytical Losses(W) Numerical Losses(W) Di!erence (%)MOSFET 1.96 1.96 0

Diode 0 0 0

34


All the di!erences shown in Table 5.2 to Table 5.6 are not more than 0.04%. Itindicates that the theoretical expressions and the numerical reference system agreewith each other. The two methods can be used to calculate the conduction lossesin the MOSFET three-phase inverter.

35


36

6Theoretical Analysis and

Comparison between MOSFETwith reverse conduction andwithout reverse conduction

6.1 Theoretical analysis of the mathematical equa-tions with MOSFET reverse conduction

The relations between $, M , and the conduction losses are shown in Figure 6.1 andFigure 6.2. In this simulation, Irms is 150 A, which makes both of the diode and theMOSFET conducting. It can be seen that the conduction losses of the MOSFETvary following a cosine function of $, while the conduction losses of the diode followsa (-cosine) function of $. Even though those two equations have opposite tendency,the total losses in one MOSFET-diode module shown in Figure 6.1 give the similartendency as the conduction losses of the MOSFET. In addition, the conductionlosses of the MOSFET increase linearly as M increases. However, the conductionlosses of the diode decrease when M increases. Since the conduction losses in thediodes are lower than the ones in the MOSFET within one module, the total lossesin one module shown in Figure 6.1 and Figure 6.2 have the similar tendency as thatof the MOSFET.

37

6. Theoretical Analysis and Comparison between MOSFET with reverseconduction and without reverse conduction

0 1 2 3 4 5 60

20

40

60

80

100

120

!

Con

ductionLosses(W

)

PdiodePMOSFETPtotal

Figure 6.1: The relation between MOSFET conduction losses and $ when M = 1with reverse conduction characteristics.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

20

40

60

80

100

120

M

Con

ductionLosses(W

)

PdiodePMOSFETPtotal

Figure 6.2: The relation between MOSFET conduction losses and $ when M = 1with reverse conduction characteristics.

38


6.2 Comparison and analysis between MOSFETwith reverse conduction and without reverseconduction

According to the analysis in previous chapters, the complexity of the equations ofthe MOSFET inverter is due to that the reverse conduction can be utilized. Thus,it is necessary to find out the di!erence between the losses resulting with reverseconduction and without reverse conduction. Table 6.1 and Table 6.2 present bothMOSFET and diode losses for di!erent values of M , when Irms is 150 A and $ is0.8. The total di!erences are calculated and shown in Table 6.3.

Table 6.1: MOSFET losses with and without reverse conducting when Irms is 150A.

M Losses with reverse conducting(W) Losses without reverse conducting(W)0 77.81 55.12

0.2 81.81 61.650.4 85.81 68.160.6 89.81 74.680.8 93.82 81.201 97.82 87.73

Table 6.2: Diode losses with or without MOSFET reverse conducting when Irms

is 150 A.


0.2 10.82 47.340.4 9.31 41.250.6 7.80 35.150.8 6.29 29.061 4.78 22.96

Since the value of the total losses in one MOSFET-diode module is relevant for theloss evaluation in the inverter, the di!erences are calculated and compared in Table6.3. As it can be seen above, the MOSFET with reverse conduction characteristicsmakes the total conduction losses in one module less than the assumption withoutreverse conduction. It is due to that the conduction losses depend mainly on thecurrents through the components instead of other factors, such as the voltages overthe components or the equivalent resistance of the components. If a lower current isapplied to this kind of inverter, for instance Irms is 20 A, the di!erences are shownin Table 6.4 to Table 6.6. In that case, there are much less conduction losses in onemodule than the case without reverse conduction. The current dependency can also

39


Table 6.3: Total losses with or without MOSFET reverse conducting when Irms is150 A.

M Total losses with Total losses without Di!erence(%)reverse conducting(W) reverse conducting(W)

0 90.14 108.57 +20.450.2 92.63 108.99 +17.660.4 95.12 109.41 +15.020.6 97.62 109.84 +12.520.8 100.11 110.26 +10.141 102.60 110.68 +7.88

be verified in the next chapter when using di!erent forms of reference voltages inthe inverter.

Table 6.4: MOSFET losses with and without reverse conducting when Irms is 20A.


0.2 1.96 1.090.4 1.96 1.210.6 1.96 1.320.8 1.96 1.441 1.96 1.56

Table 6.5: Diode losses with or without MOSFET reverse conducting when Irms

is 20 A.

M Losses with reverse conducting(W) Losses without reverse conducting(W)0 0 3.87

0.2 0 3.440.4 0 3.020.6 0 2.590.8 0 2.161 0 1.73

40


Table 6.6: Total losses with or without MOSFET reverse conducting when Irms is20 A.

M Total losses with Total losses without Di!erence(%)reverse conducting(W) reverse conducting(W)

0 1.96 4.86 +147.960.2 1.96 4.54 +131.630.4 1.96 4.23 +115.820.6 1.96 3.91 +99.490.8 1.96 3.60 +83.671 1.96 3.29 +67.86

41


42

7Conduction Losses Calculation

using two di!erent PWM Methods

In this chapter, the results from two di!erent PWM methods will be calculatedusing the numerical system and compared to the results obtained in Chapter 6.

7.1 Numerical results with the third harmonic in-jection

7.1.1 Reference voltage design principleThe third harmonic injection PWM(THIPWM)is a common way to utilize the DCvoltage source in the system [13] [14]. Since the THIPWM can make more use ofthe DC voltage source than the PWM method using the pure sinusoidal referencevoltages, this section presents the losses using THIPWM [16].

Figure 7.1 shows the reference voltages under THIPWM. For instance, one phase ofthe reference voltages is composed by

uT HIP W MA = U sin(#t) + 0.17U sin(3#t). (7.1)

Equation (7.1) is used in the losses calculation in this section.

7.1.2 Results and comparisonThe di!erent losses using THIPWM are calculated using various $, when M is fixed,as well as various M when $ is a fixed value. The results are shown in Table 7.1,Table 7.2, Table 7.3 and Table 7.4.

The di!erences can be seen by comparing the total losses in one MOSFET-diodemodule with or without THIPWM, for example when $ = 0.8 and M = 0.6, thetotal losses using a pure sinusoidal reference voltages are 97.62 W in Table 6.3, andthe losses with THIPWM are 98.07 (90.50 +7.57) W. The new total losses will in-crease by 0.46%. Based on (4.12) and (4.16), the losses mostly depend on the currentflowing through the components. However, when the reference voltages change the

43

7. Conduction Losses Calculation using two di!erent PWM Methods

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04−200

−150

−100

−50

0

50

100

150

200

Time(s)

Vol

tage

(V)

Reference voltage AReference voltage BReference voltage C

Figure 7.1: Three phase reference voltages with the third harmonic injection .

Table 7.1: Results without third harmonic injection when M = 0.6.

$ MOSFET losses(W) Diode losses(W)0 95.03 5.83

0.8 89.81 7.801 87.11 8.82

1.8 73.89 13.81% 60.58 18.84

Table 7.2: Results with third hamonics injection when M = 0.6.

$ MOSFET losses(W) Di!erence(%) Diode losses(W) Di!erence(%)0 94.11 -0.97 6.15 5.48

0.8 90.50 0.76 7.57 -2.941 88.04 1.07 8.51 -3.51

1.8 73.31 -0.70 14.01 1.45% 61.51 1.54 18.51 -1.75

expressions, there are di!erent forms of the duty cycle in the formula. The expres-sions under di!erent reference voltages are suggested to be valuable for the futurework of research.

44


Table 7.3: Results without third hamonics injection when $ = 0.

M MOSFET losses(W) Diode losses(W)0 77.50 12.28

0.2 83.53 10.170.4 89.28 8.000.6 95.03 5.830.8 100.78 3.661 106.52 1.49

Table 7.4: Results with third hamonics injection when $ = 0.

M MOSFET losses(W) Di!erence(%) Diode losses(W) Di!erence(%)0 77.50 0 12.28 0

0.2 83.23 -0.36 10.27 0.980.4 88.68 -0.67 8.21 2.630.6 94.10 0.97 6.14 5.310.8 99.57 -1.20 4.07 11.201 104.99 -1.44 2.01 34.89

7.2 Results with the common mode reduction7.2.1 Voltage design principleThere is another method to utilize the DC voltage source in the system in the bestway, which is the common mode reduction. In this study, the common mode ischosen to be the symmetrical triangular wave. The PWM method is based on sinu-soidal waveforms with reduced common mode. The following algorithm is used inthe losses-calculation in this section.

The common mode, Cm, is defined as

Cm = (umin + umax)/2. (7.2)

In (7.2), the value of umin is the minimum value of the three-phase sinusoidalreference voltages, and the value of umax is the maximum value of those threevoltages. Thus, the three-phase reference voltages can be written as

uasym = U sin(#t) ! Cm (7.3)ubsym = U sin(#t ! 120°) ! Cm (7.4)ucsym = U sin(#t ! 240°) ! Cm. (7.5)

The reference voltages under symmetrical triangular wave injection are shown inFigure 7.2. The losses are calculated and compared in the following section.

45


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04−150

−100

−50

0

50

100

150

Time(s)

Vol

tage

(V)

Reference voltage AReference voltage BReference voltage C

Figure 7.2: Three phase reference voltages with the symmetrical triangular waveinjection.

7.2.2 Results and comparisonThe results of losses using the symmetrical triangular wave injection are calculatedusing the same method as used when determing the losses in the THIPWM case.The results are shown in Table 7.5, Table 7.6, Table 7.7 and Table 7.8.

Table 7.5: Results without the symmetrical triangular wave injection when M =0.6.

$ MOSFET losses(W) Diode losses(W)0 95.03 5.83

0.8 89.81 7.801 87.11 8.82

1.8 73.89 13.81% 60.58 18.84

The di!erences can be seen by comparing the total losses in one MOSFET-diodemodule with or without the common mode reduction, for example when $ = 0.8and M = 0.6, the total losses using a pure sinusoidal reference voltages are 97.62 Win Table 6.3, and the losses with the common mode reduction are 98.16 W (90.50+7.57 W) . The new total losses will increase by 0.55%. Based on (4.12) and (4.16),the losses mostly depend on the current flowing through the components. However,when the reference voltages change, there are di!erent forms of the duty cycle inthe formula. Those questions is suggested to be a valuable future research.

46


Table 7.6: Results with the symmetrical triangular wave injection when M = 0.6.

$ MOSFET losses(W) Di!erence(%) Diode losses(W) Di!erence(%)0 93.90 -1.19 6.21 6.52

0.8 90.64 0.92 7.52 -3.591 88.23 1.28 8.43 -4.42

1.8 73.18 -0.96 14.05 1.74% 61.72 1.88 18.44 -2.12

Table 7.7: Results without symmetrical triangular wave injection when $ = 0.

M MOSFET losses(W) Diode losses(W)0 77.50 12.28

0.2 83.53 10.170.4 89.28 8.000.6 95.03 5.830.8 100.78 3.661 106.52 1.49

Table 7.8: Results with the symmetrical triangular wave injection when $ = 0.

M MOSFET losses(W) Di!erence(%) Diode losses(W) Di!erence(%)0 77.50 0 12.28 0

0.2 83.17 -0.43 10.29 1.180.4 88.55 -0.82 8.24 1.030.6 93.90 1.19 6.21 6.510.8 99.28 -1.49 4.17 13.931 104.66 -1.75 2.13 42.95

47


48

8Conclusion

It can be concluded that the theoretical equations of the conduction losses showgood agreement with the results from the numerical reference system. The derivedlosses-equations can be implemented in MATLAB for the future losses calculation.Moreover, the conduction losses in one MOSFET-diode combination have a similartendency of the MOSFET, regardless of M or $. The reverse conduction of theMOSFET gives lower conduction losses in one module compared to not using reverseconduction. Without the reverse conduction, the losses of one power module arehigher than the case with reverse conduction at both the high and low current levels.CAS300M12BM2 is selected to be the power module in the numerical calculation.The di!erences are shown in tables and the losses can be more than 20 % higherthan the case with reverse condition at the rated current of the selected module,150 A. When the phase current is low and there is no diode conducting duringthe operation, the losses regardless of reverse conduction can be more than 100% higher. Furthermore, the conduction losses mainly depend on the values of thecurrents through the components.

49

8. Conclusion

50

9Future Work

In this work, the equations of conduction losses in a three-phase MOSFET inverterare derived. The equations are based on the reverse conduction of the MOSFET.However, the goal of the future is to derive the equations which can reflect the realsystem. The blanking time is significant, and it should not be neglected. Thus, theequations, with blanking time accounted for, are needed. Moreover, for the numeri-cal reference system, further developed equations under di!erent PWM methods willbe valuable to solve. With those considerations, the conduction losses equations ofthe three-phase inverter model can be improved.

51

9. Future Work

52

Bibliography

[1] Evan Hirsh, Arjun Kakkar, Akshay Singh, Reid Wilk 2015 Auto Industry Trends.http://www.strategyand.pwc.com/perspectives/2015-auto-trends, Strat-egyand, Jan 2015.

[2] Tracking progress towards Kyoto and 2020 targets in Europe.http://www.eea.europa.eu/publications/progress-towards-kyoto, EEA(European Environment Agency), 12 Oct 2010.

[3] C. C. Chan. The State of the Art of Electric, Hybrid, and Fuel Cell Vehicles.Proceedings of the IEEE, Vol. 95, No. 4, April 2007.

[4] SEMIKRON. Basics Inverter Loss Calculation. SEMIKRON innovation service,2009.

[5] Tiefu Zhao, Jun Wang, Alex Q. Huang. Comparisons of SiC MOSFET and SiIGBT Based Motor Drive Systems. Cree Inc., Durham, NC 27703, USA.

[6] Ned Mohan, Tore M. Undeland, William P. Robbins. Power Electronics Con-verters, Applications, and Design. John Wiley and Sons, INC, 2003.

[7] K. Vinoth Kumar, Prawin Angel Michael, Joseph P. John and Dr. S. SureshKumar. SIMULATION AND COMPARISON OF SPWM AND SVPWM CON-TROL FOR THREE PHASE INVERTER. #2006-2010 Asian Research Publish-ing Network (ARPN), VOL. 5, NO. 7, JULY 2010.

[8] Steven Pekarek, Timothy Skvarenina. Graphic Modeller Component Models forElectric Power Education. Proceedings of the IEEE, 1998.

[9] Johann W. Kolar, Hans Ertl, and Franz C. Zach. Influence of the ModulationMethod on the Conduction and Switching Losses of a PWM Converter System.IEEE Transaction on Industry Applications, VOL. 21, NO. 6, November, De-cember,1991

[10] B. Wrzecionko, D. Bortis, J. W. Kolar. A 120 !C Ambient Temperature ForcedAir-Cooled Normally-o" SiC JFET Automotive Inverter System. IEEE Transac-tions on Power Electronics, Vol. 29, No. 5, pp. 2345-2358, May 2014.

[11] S. Matsumoto. Advancement of hybrid vehicle technology. Eur. Conf. PowerElectron. Appl., Dresden, Germany, Sep. 1114, 2005.

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Bibliography

[12] Jih-Sheng Lai, Wensong Yu, Hao Qian, Pengwei Sun, Parish Ralston, and Kath-leen Meehan. High Temperature Device Characterization for Hybrid Electric Ve-hicle Traction Inverters. 978-1-422-2812-0/09 #2009 IEEE

[13] M.A.A. Younis, N. A. Rahim, and S. Mekhilef. Harmonic Reduction In Three-Phase Parallel Connected Inverter. World Academy of Science, Engineering andTechnology 50 2009.

[14] I. J. Pitel, S. N. Talukdar, and P. Wood. Characterization of Programmed-Waveform Pulse-Width Modulation. IEEE Transactions on Industry Applica-tions, Vol. IA-16, Sept./Oct. 1980, pp. 707715.

[15] Ken Berringer, Je! Marvin, Philippe Perruchoud Semiconductor Power Lossesin AC Inverters. Industry Applications Conference, 1995. Thirtieth IAS AnnualMeeting, IAS ’95, Conference Record of the 1995 IEEE, Oct 1995.

[16] N. A. Rahim and S. Mekhilef Simulation of Grid Connected THIPWM-Three-Phase Inverter Using SIMULINK. IEEE Symposium on Industrial Electronicsand Applications (ISIEA2011), September 25-28, 2011.

[17] Ion Boldea, S. A. Nasar Electric Drives. CRC Press, LLC, 1999.

54

10Appendix 1

Data sheet of CAS300M12BM2.

55

1Subject to change without notice.www.cree.com

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99 CAS300M12BM2 Rev. -

Copyright © 2014 Cree, Inc. All rights reserved. The information in this document is subject to change without notice. Cree, the Cree logo, and Zero Recovery are registered trademarks of Cree, Inc.

Cree, Inc.4600 Silicon Drive

Durham, NC 27703USA Tel: +1.919.313.5300

Fax: +1.919.313.5451www.cree.com/power

5R+6&RPSOLDQFH The levels of RoHS restricted materials in this product are below the maximum concentration values (also referred to as the threshold limits) permitted for such substances, or are used in an exempted application, in accordance with EU Directive 2011/65/EC (RoHS2), as implemented January 2, 2013. RoHS Declarations for this product can be obtained from your Cree representative or from the Product Documentation sections of www.cree.com.

5($&K&RPSOLDQFH REACh substances of high concern (SVHCs) information is available for this product. Since the European Chemi-cal Agency (ECHA) has published notice of their intent to frequently revise the SVHC listing for the foreseeable future,please contact a Cree representative to insure you get the most up-to-date REACh SVHC Declaration. REACh banned substance information (REACh Article 67) is also available upon request.

This product has not been designed or tested for use in, and is not intended for use in, applications implanted into the human body nor in applications in which failure of the product could lead to death, personal injury or property damage, including but not limited to equipment used in the operation of nuclear facilities, life-support machines, FDUGLDFGH¿EULOODWRUVRUVLPLODUHPHUJHQF\PHGLFDOHTXLSPHQWDLUFUDIWQDYLJDWLRQRUFRPPXQLFDWLRQRUFRQWUROV\VWHPVDLUWUDI¿FFRQWUROV\VWHPV

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