Evaluation Methodology and Control Strategies for ...bingsen/files_publications/J-14_TVT.pdf · power electronic converters, and the whole drivetrain of HEVs from the probabilistic

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 8, OCTOBER 2014 3661

Evaluation Methodology and Control Strategies forImproving Reliability of HEV Power

Electronic SystemYantao Song and Bingsen Wang, Senior Member, IEEE

Abstract—The reliability prediction of hybrid electric vehicles(HEVs) is of paramount importance for planning, design, control,and operation management of vehicles, since it can provide anobjective criterion for comparative evaluation of various config-urations and topologies and can be used as an effective tool toimprove the design and control of the overall system. This paperpresents a mission-profile-dependent simulation model based onMATLAB for quantitatively assessing the reliability of the elec-tric drivetrain of HEVs. This model takes into consideration thevariable driving scenarios, dormant mode, electrical stresses, andthermal stresses. Therefore, more reliable and accurate predictionof system reliability has been achieved. The methodology is ex-plained in detail, and the results of reliability assessment basedon a series HEV are presented. Based on reliability analysis, twocontrol strategies are proposed to increase the mean time to fail-ure of HEV powertrains: 1) variable dc-link voltage control and2) hybrid discontinuous pulsewidth modulation scheme. Thesenovel control schemes reduce the power losses and thermal stressesof power converters, and consequently, enhance system reliability.Numerical simulation results verify the benefits of two proposedcontrol strategies in terms of power losses and reliability.

Index Terms—Discontinuous modulation, failure rate, hybridelectric vehicle (HEV), powertrain, reliability.

I. INTRODUCTION

HYBRID electric vehicles (HEVs) with superior fuel econ-omy have been considered as a pivotal technology tomitigate concerns over the rapid rise in the cost of petroleum,increasingly worsening air pollution, and global warming asso-ciated with greenhouse gas emissions [1]. However, integrationof a great number of power electronic devices into drive sys-tems of vehicles could adversely impact the reliability of theoverall system [2]. The reduced reliability of HEVs not onlydiscounts fuel-saving premium but increases operation costsas well. Therefore, the reliability of HEV powertrains has in-creasingly attracted research attention from both academia andindustry. Research activities on the reliability of components,power electronic converters, and the whole drivetrain of HEVsfrom the probabilistic and deterministic perspectives have been

Manuscript received July 9, 2013; revised October 16, 2013 and February 2,2014; accepted February 8, 2014. Date of publication February 12, 2014; dateof current version October 14, 2014.The review of this paper was coordinatedby Prof. A. Davoudi.

The authors are with the Department of Electrical and Computer Engi-neering, Michigan State University, East Lansing, MI 48824 USA (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2014.2306093

reported in the literature [3]. From the component point ofview, the battery is the most important and the least reliablecomponent in HEVs, which has a crucial effect on the reliabilityand cost of HEVs. Qian et al. in [4] studied the influenceof the operating temperature on the cycle life of lead–acid,lithium–ion, and nickel–metal hydride (NiMH) batteries forHEVs based on simulation. The reliability of power electronicconverters in HEVs is also widely investigated. The reliabilityof a bidirectional dc/dc converter for the energy storage systemof HEVs is assessed in [5]. In this paper, the driving behaviorsare taken into account, and the failure rate models of thecomponents are obtained by Monte Carlo simulation. However,the reliability models introduced by the authors do not includeeffects of thermal cycling on component failures, which willlead to the results that may substantially deviate from reality.A test bench implemented with various driving cycles to verifythe reliability of new prototypes of inverters for electric motorsin hybrid vehicles is presented in [6]. Renken et al. in [7]presented a simulation concept that is used to assess the lifetimeof the inverter for HEVs in terms of the crack propagation speedof bond and solder joint connections. Hirschmann et al. pre-sented a simulation model to predict the reliability of invertersfor HEVs [8]. This reliability model is focused on the effectsof temperature and thermal cycle on the failure rates of keypower components of inverters. A reliability model based ona sequence tree is adopted to analyze various reliability indicesand related maintenance cost of the traction train within a fuel-cell car [9]. Negarestani et al. [10] evaluated and compared theavailability of pure electric vehicles, HEVs, and conventionalvehicles based on a part-count reliability model. This methoddoes not consider the practical driving scenarios and operatingconditions of vehicles.

To overcome the limitations of the existing methods, thispaper presents a reliability model for the power electronicsystem of HEVs. The proposed model can be employed toquantitatively evaluate the reliability of power electronic con-verters and energy storage unit in series HEVs (SHEVs). Thepractical scenarios, thermal stresses, and electrical stresses areconsidered in the model.

The accurate reliability analysis not only provides an impor-tant guideline for planning, design, and operation managementof HEVs, it also allows designers to pinpoint the dominantcauses of system failures and correspondingly make furtherdesign changes for improved reliability. Based on the reliabilityanalysis, two control strategies that reduce the power losses

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3662 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 8, OCTOBER 2014

Fig. 1. Schematic of the SHEV powertrain.

of converters are proposed to improve the reliability of anHEV’s powertain. The control methods are briefly introducedas follows.

The first control scheme to improve the reliability of anHEV’s powertrain is to allow the dc-link voltage of the inverterto vary according to the required output voltage. The reliabilityanalysis shows that the thermal stresses of the semiconductordevices in power converters have a significant influence on thefailure rates of the devices. The thermal stresses are determinedby the power losses of components. Therefore, reducing powerlosses of power components is an effective solution to improv-ing the reliability of an HEV powertrain. In fact, power losses ofpower components not only determine the reliability of powerconverters but also influence the size of power converters andfuel economy of HEVs. Therefore, a considerable amount ofresearch effort has been focused on reducing power losses ofHEVs’ drivetrain. Mapelli et al. in [11] investigated a motor-control method based on the direct self-control technique. Thismethod applies the six-step modulation scheme to the inverterto reduce its switching loss in the constant-power region ofmotors. The power loss of the auxiliary dc/dc converter forautomotive application is investigated in [12]. Some alternativetopologies of the dc/dc converter that interfaces the battery packand the high-voltage dc bus are investigated to achieve higherefficiency of the powertrain [13]–[15]. This paper presents avariable dc-link voltage control scheme for the power conver-sion unit of electric vehicles. Based on this control scheme,switching losses of the inverter and the dc/dc converter aregreatly reduced. In particular, the inverter always operates atits optimal point with the highest efficiency.

In addition to the optimized dc-link voltage, the switchinglosses of the inverter can be further reduced through a hybridpulsewidth modulation (PWM) scheme. For a two-level three-phase inverter, switching loss of semiconductors is dominant.Much effort is devoted to various techniques to reduce theswitching loss, such as soft-switching technology and variousmodulation schemes. Different PWM schemes significantlyinfluence performances of the three-phase inverter, particularlythe harmonic distortion and switching loss. Continuous carrier-based PWM or space vector PWM (SVPWM) schemes areextensively investigated and widely applied [16], [17]. By

changing the positions of active voltage vectors or zero-sequence component in modulation signals, various discontinu-ous PWM (DPWM) schemes are formed to optimize switchinglosses or total harmonic distortion [18]–[21]. In comparisonwith continuous PWM schemes, the main benefit of DPWMschemes is that the number of the switching transitions duringone carrier cycle is reduced from 6 to 4, and correspondingly,the switching loss of the converter is reduced [17]. However,the harmonic distortion for DPWM schemes under a low mod-ulation index increases as compared with continuous PWMschemes, which impedes the wide application of the DPWMschemes. In the paper, combined with the variable dc-linkvoltage control, the DPWM schemes will operate at a highmodulation index. Hence, they can be applied to the inverter toreduce switching loss without compromising waveform qual-ity. A hybrid DPWM scheme with minimal switching loss isproposed to further reduce the inverter losses and improve thereliability of the overall system.

The rest of this paper is organized as follows: Since thereliability evaluation model is based on the power electronicsystem of SHEVs, the SHEV drive system is first reviewedin Section II. The reliability model is illustrated in detail inSection III. In Section IV, the results of reliability assessmentand a brief analysis are presented. Two strategies to improve thereliability of HEV powertrains are presented in Sections V andVI. Finally, a summary in Section VII concludes this paper.

II. SERIES HYBRID ELECTIC VEHICLE POWERTRAIN

Prior to evaluating the reliability of the SHEV’s power elec-tronic system, the SHEV’s powertrain is first introduced. Asshown in Fig. 1, an SHEV power system consists of three powerelectronic converters, namely, a three-phase PWM rectifier, athree-phase inverter, and a bidirectional dc/dc converter, and anenergy storage unit that is composed of battery cells connectedin parallel and series manners. Since there exist two energysources, the traction power will be divided between the engineand the battery bank in accordance with the specific energymanagement strategy, driving conditions, and state of charge(SoC) of the battery pack. Correspondingly, there are fiveoperating modes for SHEVs, and the operating conditions of

SONG AND WANG: IMPROVING RELIABILITY OF HEV POWER ELECTRONIC SYSTEM 3663

Fig. 2. Block diagram of the reliability simulation model.

the power converters and the battery bank are different for eachmode from the others. As a result, the electrical and thermalstresses of components in SHEVs greatly vary during a drivingcycle, which will be considered in the reliability analysis modelpresented in the following section.

III. RELIABILITY SIMULATION MODEL OFSERIES HYBRID ELECTIC VEHICLES

Here, a reliability simulation model that takes various op-erating conditions of SHEVs into consideration is built toevaluate various reliability metrics of SHEVs. The structureof the reliability simulation model is shown in Fig. 2. In thismodel, the input data are derived from the operating conditionsof vehicles. Herein, various standard driving cycles are used tosimulate the driving scenarios. The failure rates and mean timeto failure (MTTF), lifetime, and other reliability indices of thecomponents, converters, and the whole system can be obtainedfrom the model. Each functional block will be introduced asfollows.

A. Driving Cycle

The first function block is used to simulate various drivingcycles that are represented by standard temporal sequences ofvehicle speeds and to finally determine load profiles of HEVs.

The torque–speed characteristics of vehicles versus timedetermine the operating conditions of the power electronicconverters in the drive system, which finally affect the electricaland thermal stresses of the key power components. However,the torque–speed profiles of vehicles depend on the behaviorsof drivers and the road conditions. Uncertainty in driving pat-terns challenges the reliability prediction of HEVs. Fortunately,various driving cycles that are temporal sequences of speeds,such as NEDC, FTP-72, FTP-75, US06, and so on, have beendeveloped in different countries to provide test benchmarks forevaluating the efficiency and emission of vehicles. Since thesedriving cycles have been accepted by the industry and widelyused to assess performance of vehicles, herein they are em-ployed to emulate the operating patterns of HEVs. The drivingcycle provides the instantaneous speed V and acceleration a tothe motor model and the vehicle model, as shown in Fig. 2.

B. Vehicle Model

In the vehicle model, the vehicle speed and accelerationthat are obtained from the driving cycle model are utilized

TABLE IPARAMETERS ASSUMED OF VEHICLE

TABLE IIPOWER RATINGS OF THE SHEV POWERTRAIN

to calculate the instantaneous traction torque and mechanicalspeed of the traction motor.

The instantaneous speed and acceleration will not exclu-sively determine the instantaneous electrical stresses of vehi-cles’ powertrain. The electrical stresses also depend on theparameters of vehicles and the road conditions, such as windspeed, gradient, and roughness of the road surface. The pa-rameters of HEV and assumed road conditions determine notonly the power ratings of energy sources and power electronicconverters but their instantaneous power as well [1]. The pa-rameters of the vehicle, such as vehicle weight, front area,and diameter of wheels, are obtained from the commercialvehicle Toyota Prius. The rolling resistance coefficient, theaerodynamic drag coefficient, and transmission efficiency thatare indispensable parameters for traction force analysis areobtained from the literature [1]. These parameters have beentabulated in Table I. The traction torque and the motor speedthat are obtained from this vehicle model serve as inputs to themotor model.

C. Motor Model

The motor model simulates the steady-state operation of thetraction motor and is used to compute the stator voltages andcurrents by the use of the traction torque and the rotor speedthat are obtained from the vehicle model.

The sizing of the traction motor in SHEVs is based onperformance requirements of the vehicle, which mainly includemaximal speed, acceleration, and gradiability; the vehicle’s pa-rameters; and the road conditions. The specific design processand methodology are detailed in [1]. The motor’s power ratingis listed in Table II. Herein, an interior permanent magnet(IPM) motor is utilized as the traction motor, and its modelis developed to calculate the instantaneous stator current andvoltage by using known torque and speed. The simulationmodel is based on the steady-state model of IPMs [22]. TheIPM’s operating modes, such as maximal torque per ampereand fluxing weakening, are also considered in this model tosimulate practical operating conditions. The stator voltages andcurrents from the motor model directly determine the operatingconditions of power converters in an HEV’s driving system.


TABLE IIICOMPONENTS FOR POWER CONVERTERS OF SHEV’S POWERTRAIN

D. Loss Model

The stator voltages and currents obtained from the motormodel determine the power losses of converters. The loss modelis utilized to compute the power losses of components in theconverters of an SHEV’s powertrain. The loss model dependson the operating principles and component parameters that aredetermined by the ratings of power converters. Therefore, thefirst step in building the loss model is to determine the powerratings of converters in an SHEV’s powertrain.

The basic rules in sizing three power converters are explainedas follows. The inverter is utilized to control the traction mo-tor. Therefore, voltage and current ratings of the inverter aredesigned to meet the requirements of the motor. The outputvoltage of the inverter should match the stator voltage of themotor, whereas the maximal output current is determined bythe maximal electromagnetic torque of the motor. Therefore,voltage and current ratings rather than power rating are listed inTable II. In the drive system of the HEVs, the engine/generatorprovides the total energy, whereas the battery pack only worksas a power buffer that provides or absorbs peak power for theacceleration or deceleration of the vehicle. Therefore, the powerrating of the engine/generator system should be equal to theaverage power of the traction motor in a standard driving cycle.Herein, FTP-75 is used as the benchmark to determine thecapacity ratings of the engine/generator system and the rectifier.It is obvious that the available peak power of the rectifier ismuch lower than that of the motor. During acceleration, theengine/rectifier system only provides partial power that themotor requires, whereas the remaining part has to be providedby the battery pack. Correspondingly, the power ratings of thebattery pack and the dc/dc converter should be equal to themotor’s power rating minus that of the rectifier if the powerlosses are neglected. The power ratings of the three powerconverters are listed in Table II. Based on the power ratings,the components used in these converters can be selected, andthey are listed in Table III.

In power electronic systems, power components suchas insulated-gate bipolar transistors (IGBTs), metal–oxide–semiconductor field-effect transistors, diodes, capacitors, in-ductors, and transformers are key components that producemost of power losses. The power loss calculation is the basisof thermal design and instantaneous thermal analysis. Thelosses of semiconductor devices include conduction loss andswitching loss. For the capacitor and the battery, the resistivelosses dissipated in the equivalent series resistance (ESR) andinternal resistance (for the battery) are dominant. To reduce thecomputational burden of simulation, analytical loss models arebuilt upon the behavioral device models [23]. Thus, the powerlosses of semiconductor devices and dc-link capacitors in the

Fig. 3. Thermal equivalent circuit of a semiconductor device and heatsink.

inverter and the dc/dc converter can be obtained. The losses ofcomponents are further used as inputs to the thermal model toestimate the junction temperature.

E. Thermal Model

The thermal model performs two functions: calculating junc-tion temperatures of power semiconductors and core tempera-tures of batteries and capacitors and detecting thermal cycling.The junction temperature and temperature variation of powerdevices are key factors that affect reliable operation and lifespan of components, which can be observed in the failure ratemodels of the devices.

The essence of the thermal model is to mathematically de-scribe the thermal transfer process of devices based on the var-ious basic heat transfer mechanisms. The simplified dynamicthermal equivalent circuit of a semiconductor and a coolingsystem is shown in Fig. 3. The junction temperature and itsvariation of the component depend on power losses, the thermalresistances and capacitances of components and the coolingsystem, and ambient temperature. The thermal resistances andcapacitances of components are obtained from data sheets,whereas the thermal parameters of the heatsink are determinedby the geometry and materials of the heatsink.

F. Failure Rate Model

The functional block of the reliability model is employedto calculate various reliability metrics of power devices bythe use of the electrical and thermal stresses obtained fromthe loss model and the thermal model. The reliability modelscan determine the failure numbers, MTTF, lifetime, and otherreliability indices. The empirical-based failure rate models usedin this paper are explained as follows.

There are many empirical-based reliability models of elec-tronic devices. The military handbook for the reliability predic-tion of electronic equipment (MIL-217F) [24] is well knownand widely accepted in military and industrial applications.However, the handbook does not contain the necessary data toassess the influence of dormant modes on components nor thedata that reflect the effects of thermal cycling. The reliabilityhandbook RDF 2000 [25] is another important data source ofempirical-based failure rate models. It covers dormant modesand effects of the temperature cycles. In addition, RDF 2000contains IGBT data that are not available from MIL-217F.Herein, the component failure rate models provided by RDF


2000 are utilized to analyze the reliability of HEV powertrains.The failure rate models of power components are introducedas follows. The IGBT failure rate model in [25] can beexpressed as⎧⎪⎪⎨⎪⎪⎩

λIGBT = λdie + λpackage + λoverstress

λdie = πs ∗ λ0 ∗∑y

i=1(πt)i∗τi

τon+τoff

λpackage = 2.75 ∗ 10−3 ∗ λb ∗∑z

i=1(πn)i ∗ (ΔT )0.68λoverstress = πI ∗ λEOS

(1)

where λdie represents the failure rate component related to thedie of IGBTs and is further related to the junction temperature,λpackage denotes IGBT package failures that are caused by thenumber and magnitudes of thermal cycles that devices undergo,and λoverstress reflects the contribution of the overcurrent andovervoltage stresses to the total component failure rate and canbe neglected since the overstress operating conditions shouldnot occur in normal operating conditions. The unit of thefailure rate in the given equation is the number of failures per109 hours.

The parameters in (1) are further explained as follows. πsrepresents the influence of the voltage stresses on the failureof the IGBT’s die and is determined by the ratios of the app-lied collector-to-emitter and gate-to-emitter voltages to thecorresponding ratings. λ0 and λb are base failure rates of thedie and the package, respectively. (πt)i represents the effect ofthe actual junction temperature on the failure of the die in theith phase of the IGBT’s mission profile, and it is determinedby the junction temperature. Parameter τi is the working timeratio of the IGBT in the ith phase of the mission profile. τonand τoff correspond to the total working time ratio and the totaldormant time ratio, respectively. These three parameters, i.e.,τi, τon, and τoff , account for the effect of the dormant modeon the failure of IGBTs. (ΔT )i denotes the amplitude of thethermal variation that the device undergoes in the ith phase ofthe mission profile. (πn)i is the influence factor that is relatedto the annual number of the thermal cycles experienced by thepackage with the amplitude of (ΔT )i. The failure rate modelfurther demonstrates that the junction temperature and thetemperature cycle have a significant influence on IGBT failure.

Failure rate models of diodes and capacitors have the formsimilar to IGBTs. The reliability prediction procedure in RDF2000 and Bellcore TR-332 [26] published by Bell Communica-tion Research, Inc. provides a simple failure model of batterycell. Thus

λbattery = λ0 ∗ 10−9/h. (2)

From this model, the failure of the battery is independent of allstresses and is only dependent on base failure rate λ0 that isrelated with the type of the battery cell.

IV. RELIABILITY ASSESSMENT AND DISCUSSION

The reliability of SHEVs’ powertrain is evaluated based onthe presented simulation model. This simulation model utilizestwo different driving cycles, i.e., FTP-75 and US06, which rep-resent driving conditions on the urban route and on the highway,respectively. Furthermore, the simulation model assumes the

Fig. 4. Junction temperatures of inverter semiconductor devices in the firsthalf of four consecutive FTP-75 driving cycles. (a) IGBT. (b) Diode.

Fig. 5. Junction temperatures of dc/dc converter lower IGBT and upper diode(for boost mode) in the first half of four consecutive FTP-75 driving cycles.(a) IGBT. (b) Diode.

closed-loop liquid-cooling method that is commonly used inpractical vehicles to dissipate the heat generated by the powerconverters. The proper regulation of inlet coolant temperaturemakes it a valid assumption that the heatsink temperature isconstant and set to 60 ◦C. With the constant heatsink temper-ature, the thermal model and thermal analysis are simplifiedsince the thermal resistance and capacitance of the heatsinkare not necessarily known. The average total running time ofa vehicle is about 500 hours per year [8]. The thermal cycles ofthe magnitude lower than 3 ◦C have little influence on failureof components and, consequently, can be neglected [25]. In thepaper, reliability of the components in the inverter and dc/dcconverter is assessed.

The reliability of the powertrain depends on the type ofdriving cycles, the energy management strategy, and initialconditions of the battery pack. To evaluate the effects of thevarious driving cycles on the reliability of SHEVs’ powertrain,


Fig. 6. Junction temperatures of dc/dc converter upper IGBT and lower diode(for buck mode) in the first half of four consecutive FTP-75 driving cycles.(a) IGBT. (b) Diode.

Fig. 7. Numbers and amplitudes of inverter semiconductor device thermalcycles in the four consecutive FTP-75 driving cycles. (a) IGBT. (b) Diode.

the simulations based on FTP-75 and US06 are implementedand analyzed. The energy management strategy determinesthe power distributions between two energy sources, i.e., thebattery pack and the engine, and further determines electricaland thermal stresses of the rectifier and the dc/dc converter.

Herein, the engine on/off control is utilized. In this strategy,the battery pack is used as the main energy source, and itprovides total drive power to the inverter/motor while theengine is turned off if the SoC of the battery pack is withina preset range. Once the SoC of the battery pack drops toits lower threshold, the engine is turned on and charges thebattery pack at full power capacity. The benefit of the engineon/off control lies in the fact that the engine always worksin the high-efficiency range. However, the battery pack has toundergo deep charge/discharge cycles, and the dc/dc converterconsequently has to experience higher electrical and thermal

Fig. 8. Numbers and amplitudes of dc/dc converter lower IGBT and upperdiode (for boost mode) thermal cycles in the four consecutive FTP-75 drivingcycles. (a) IGBT. (b) Diode.

Fig. 9. Numbers and amplitudes of dc/dc converter upper IGBT and lowerdiode (for buck mode) thermal cycles in the four consecutive FTP-75 drivingcycles. (a) IGBT. (b) Diode.

stresses. To avoid uncertainty in the simulation results causedby the initial condition of the battery pack, simulations overfour consecutive US06 cycles and four consecutive FTP-75cycles are implemented, in which the battery pack experiencesa full charge/discharge cycle.

Figs. 4–6 show the junction temperature profiles of IGBTsand diodes in the inverter and dc/dc converter in the first halfof four consecutive FTP-75 driving cycles. It can be observedthat the junction temperatures of devices dramatically fluctuatein a driving cycle, although the absolute temperatures are notvery high. Figs. 7–9 show the numbers and correspondingamplitudes of thermal cycles that the semiconductor devices inthe inverter and dc/dc converter undergo in four consecutiveFTP-75 cycles. It is observed that the amplitudes of most


TABLE IVFAILURE RATES AND MTTFS OF SHEV FOR FTP-75 DRIVING CYCLE

TABLE VFAILURE RATES AND MTTFS OF SHEV FOR US06 DRIVING CYCLE

thermal cycles stay under 15 ◦C. Moreover, IGBTs of theinverter and the dc/dc converter experience more thermal cyclesof higher amplitudes since the IGBTs generate higher lossesand correspondingly experience higher junction temperatures.The failure rates of components are related to the temperaturecycles.

The failure rates and MTTFs of the power semiconductors,dc-link capacitors, and battery cells are listed in Tables IVand V for FTP-75 and US06 driving cycles, respectively. It isworth noting that each of the failure rates in these two tablesis for a single device. Table IV shows that the IGBTs of theconverters have higher failure rates and, therefore, are less reli-able. The higher failure rate of IGBTs is due to the fact that thepower losses dissipated in the IGBTs are much higher than thelosses of the diodes, and correspondingly, the thermal stressesare much higher, as shown in Figs. 4–6. Another importantobservation is that the failure rate of the dc-link capacitors islower than that of semiconductor devices by approximately fourorders of magnitude.

The failure rate model of the battery, as shown in (2), isutilized for reliability analysis. This model is independent of itsoperating conditions and only depends on the type and numberof the battery cells. In the simulation model, 640 lithium–ionbattery cells are used to form the battery bank in series andparallel manners. The failure rate of a single cell is listedin Table IV. Although the failure rate of each cell appearsinsignificantly high, the failure rate of the whole battery packis as high as 96 failures per 106 hours, which is four times thetotal failure rate of the semiconductor devices and capacitors.Correspondingly, the MTTF of the overall system would bereduced from 38 030 to 8180 hours by taking the battery bankinto consideration, as shown in Table IV. The failure rate of thebattery pack dominates the overall system. However, the failurerate model that is provided in the Bellcore reliability handbook[26] is independent of the operating conditions of batter cells,such as battery core temperature, charge/discharge current, anddepth of charge/discharge. As a result, any improvement ofdesign and control strategies has little effect on the failure rateand MTTF of the SHEV powertrain, which does not matchpractical observations and suggests that a more accurate batteryreliability model be developed. In fact, some lifetime models of

battery based on electrochemical theories that include effectsof some operating conditions have been developed [27], [28].Nonetheless, these models depend on detailed battery designparameters that are unavailable in the public domain, which ren-ders it difficult for these models to be applied to the reliabilityanalysis of battery systems. Therefore, in view of lack of theaccurate applicable battery reliability model, the battery bankis excluded from the reliability analysis of the SHEV’s powerelectronic system in the following two sections that present twocontrol strategies to improve the reliability of the system.

Since US06 emulates the highway driving behaviors andconsequently features higher speeds and accelerations thandriving cycle FTP-75, the higher electrical and thermal stressesof the converters in US06 cycles result in much higher failurerates and lower reliability, as shown in Table V.

V. VARIABLE DC-LINK VOLTAGE CONTROL

Improving the reliability of an HEV’s drivetrain is as impor-tant as obtaining the reliability indices. Reliability evaluationis an effective approach to pinpointing the weakest link of thesystem and main causes of failure of an HEV’s power electronicsystem. From the aforementioned reliability analysis, the semi-conductor devices are much less reliable than capacitors. There-fore, reducing the failure rates of these semiconductor devicescan effectively enhance the reliability of an HEV’s powertrain.The failure models of the IGBT and the diode indicate that thejunction temperature and thermal cycling of devices dominatetheir failure rates. Except for the cooling system and the envi-ronment in which the system operates, the thermal stresses ofthe components in the system are exclusively dependent uponpower losses of the components. Therefore, reducing losses ofcomponents is an effective approach to reducing the failurerates of a power electronic system. The following subsectionspresent the proposed variable dc-link voltage control to improvethe reliability of HEV’s power converters.

A. Stator Voltage Profile of the Traction Motor

In the SHEV’s drive system, the engine/generator and thebattery unit can separately or jointly supply traction power


Fig. 10. Peak values of the traction motor’s line-to-neutral stator voltage andstator current in an FTP-75 driving cycle. (a) Peak value of stator voltage.(b) Peak value of stator current.

to the inverter that directly controls the traction motor. Byemploying the PWM scheme, the inverter converts the dc-link voltage into the variable-frequency and variable-magnitudestator voltage suitable for the traction motor. The relationshipbetween the root mean square (RMS) value of the line-to-linestator voltage and the dc-link voltage for the SVPWM schemecan be mathematically expressed as

Vs = 0.612 ∗MI ∗ Vdc (3)

where MI denotes the modulation index that ranges be-tween 0 and 1.15 [29]. It can be observed that two free-doms are available to control stator voltage: modulation indexand dc-link voltage. In practical scenarios, the required statorvoltage of the motor depends on its operating modes, suchas maximum-torque-per-ampere mode and flux-weakeningmode for permanent-magnet machines, and loading conditions.Fig. 10 shows the dramatic fluctuation of the peak stator voltageof the traction motor in an FTP-75 driving cycle. Correspond-ingly, the dc-link voltage or the modulation index has to beregulated so that the output voltage of the inverter allows themotor to produce a demanded torque at a given rotor speed. Theconventional control scheme is to regulate the output voltage ofthe inverter by varying the modulation index while the dc-linkvoltage is maintained constant.

Fig. 10(a) shows that the stator voltage is much lower thanits maximal value during a large fraction of one driving cycle.Correspondingly, the modulation index deviates from its max-imal value if the dc-link voltage is maintained at the constantvalue that accommodates the maximum stator voltage. It isfurther known that the switching loss of the semiconductors inthe inverter is approximately proportional to the dc-link voltage[23]. Thus

Psw =6π∗ fs ∗ (Eon + Eoff + Err) ∗

Vdc ∗ IpkVref ∗ Iref

(4)

where fs is the switching frequency; Eon, Eoff , and Err denotethe turn-on and turn-off energy losses of the IGBT and reverse

recovery energy loss of the antiparallel freewheeling diode,respectively, for the given reference commutation voltage Vrefand current Iref ; Vdc is the dc-link voltage; and Ipk is thepeak value of the inverter output current. For a specific statorvoltage, if the dc-link voltage can be regulated to follow thedesired stator voltage while the modulation index of the inverteris kept constant and equal to its maximal value, the dc-linkvoltage is minimized during a large fraction of a driving cycle,and consequently, the switching loss of the inverter would beminimized.

B. Variable DC-Link Voltage Control

In view of the aforementioned analysis, the variable dc-linkvoltage control strategy is proposed in this paper. The principleis that the modulation index is kept constant and set to itsmaximal value, whereas the dc-link voltage is regulated bythe dc/dc converter to track the desired stator voltage of thetraction motor. If the desired dc-link voltage is lower than theterminal voltage of the battery pack, the upper switch Sp ofthe dc/dc converter, as shown in Fig. 1, would be constantlyforced on, and correspondingly, the battery pack is directly tiedto the dc bus. In such a case, the dc-link voltage is clampedby the terminal voltage of the battery pack and is unable totrack the required stator voltage. The engine/generator andrectifier system is controlled by the SoC and the upper levelenergy management strategy of vehicles. The implementationof the proposed variable dc-link voltage control scheme will beintroduced in the following paragraphs.

Fig. 11 shows the control block diagram of an SHEV’s motordrive system with the variable dc-link voltage control. Theblock diagram includes the conventional motor control diagramand the inverter and dc/dc converter’s control diagram. Herein,the control algorithms are implemented in the d− q rotationalframe.

As shown in Fig. 11, dual loops are utilized to control thetraction motor. In the outer loop, motor speed ω is regulated.The error signal between the reference motor speed ωref andthe actual motor speed ω is amplified by a proportional–integral(PI) controller that generates reference torque Tref . By the useof the motor model in conjunction with rotor speed, referencetorque Tref can be translated to reference currents iqref andidref . In the inner current loop, the actual stator currents idand iq are regulated by two PI controllers, which generate theoutputs that are further decoupled to form reference voltagesVdref and Vqref .

Since the stator voltages are the output voltages of theinverter, stator reference voltages Vdref and Vqref are also thereference voltages of the inverter. Magnitude Vdc_ref is usedas the reference value of the dc-link voltage and of the dc/dcconverter’s output voltage. Normalized signals V pud and V

puq

can provide the phase angle that is used to calculate three-phasemodulation signals ma, mb, and mc for the inverter.

The principle of the variable dc-link voltage control schemehas been introduced. Since the classic control algorithms canbe applied to the control of the motor and the dc/dc converter,the detailed design of the motor and converters’ control systemis not included in this paper. The feasibility of this control


Fig. 11. Control block diagram of the motor drive system with the variable dc-link voltage control.

Fig. 12. DC-link voltages for variable dc-link voltage control and variablemodulation index control in an FTP-75 driving cycle.

strategy has been verified by the dynamic simulation based ona MATLAB/Simulink model. It is worth mentioning that thevariable dc-link voltage control can be implemented to retrofitthe existing software-based control method without changein hardware. Therefore, the control strategy does not incuradditional components, nor does it incur associated cost andreliability concerns.

Fig. 12 shows the dc-link voltage profiles for the variabledc-link voltage control as compared with the conventionalvariable modulation index control. Since the output voltage ofthe bidirectional dc/dc converter is practically lower boundedby its input voltage, the reference dc-link voltage is clampedto the battery voltage when the dc-link voltage required by themotor is below the lower limit. The upper bound of the dc-linkvoltage is determined by the maximal stator voltage. Herein, thenominal terminal voltage of the battery pack and the nominalline-to-line stator voltage of the traction motor are 264 and400 V, respectively, and the resultant maximal dc-link voltageis 568 V. It can be observed that during an FTP-75 drivingcycle, the variable dc-link voltage is much lower than the dc-link voltage under variable modulation index control.

C. Verification of Benefits by Simulation

The lower dc-link voltage will result in lower switching lossfor the inverter. In comparison with the variable modulationindex control, the modulation index for the variable dc-linkcontrol is higher. Although the modulation index affects theconduction loss of the inverter [23], the total power loss isstill greatly reduced since the switching loss is dominant. Thepower loss of the dc/dc converter also decreases. The benefit ofreduction in the overall loss can be verified by the simulation,

Fig. 13. Loss profiles for variable dc-link voltage control and variable modu-lation index control in the first half of four consecutive FTP-75 driving cycles.(a) Inverter loss. (b) DC/DC converter loss. (c) Total loss.

as shown in Fig. 13. For demonstration of the reduced losses ofthe proposed control over the conventional control scheme, thelosses of the inverter, the dc/dc converter, and the overall systemin a half FTP-75 driving cycle are shown in Fig. 13(a)–(c),respectively. The total losses include conduction and switchinglosses of semiconductor devices in the dc/dc converter and theinverter, core and winding losses of the inductor in the dc/dcconverter, and the ESR loss of dc-link capacitors and inputfilter capacitors of the dc/dc converter. It can be observed thatnot only the loss of the inverter but also the loss of the dc/dcconverter is greatly reduced.

Since the HEV powertrain experiences manifold operatingconditions in terms of voltage stress, current stress, and powerstress in a driving cycle, it is inadequate to evaluate the over-all efficiency of converters in a driving cycle by the use ofefficiency data at several selected operating points. Therefore,the total dissipated energy in one or several driving cyclesis utilized to evaluate the efficiency of an HEV powertrain.


TABLE VIENERGY CONSUMPTION AND LOSS FOR VARIABLE MODULATION INDEX

CONTROL AND VARIABLE DC-LINK VOLTAGE CONTROL INFOUR CONSECUTIVE FTP-75 DRIVING CYCLES

TABLE VIIENERGY CONSUMPTION AND LOSS FOR VARIABLE MODULATION INDEX

CONTROL AND VARIABLE DC-LINK VOLTAGE CONTROL INFOUR CONSECUTIVE US06 DRIVING CYCLES

Fig. 14. Junction temperatures of the inverter IGBT and diode for variabledc-link voltage control and variable modulation index control in the first half offour consecutive FTP-75 driving cycles. (a) IGBT. (b) Diode.

Herein, the energy consumption and energy loss in several driv-ing cycles are defined to quantitatively evaluate the efficiencyof power converters for variable modulation index control andvariable dc-link voltage control. The energy loss is defined by

Eloss =

∫driving cycles

(Ploss)dt (5)

where Ploss is the total loss of the inverter and the dc/dc con-verter. The energy consumption is defined as the total energy in-put in driving cycles, and it can be mathematically expressed as

Econsum =

∫driving cycles

(Prectifier + Pbattery)dt (6)

where Prectifier and Pbattery are the output power of therectifier and the battery pack, respectively. Numericalsimulations based on four consecutive FTP-75 driving cyclesand four consecutive US06 driving cycles have been conducted.

Fig. 15. Junction temperatures of dc/dc converter lower IGBT and upperdiode (for boost mode) for variable dc-link voltage control and variablemodulation index control in the first half of four consecutive FTP-75 drivingcycles. (a) IGBT. (b) Diode.

Fig. 16. Junction temperatures of dc/dc converter upper IGBT and lowerdiode (for buck mode) for variable dc-link voltage control and variable mod-ulation index control in the first half of four consecutive FTP-75 driving cycles.(a) IGBT. (b) Diode.

The energy consumption and loss for both types of drivingcycles are tabulated in Tables VI and VII. In comparisonwith variable modulation index control, for variable dc-linkvoltage control, the power converters’ energy loss in fourFTP-75 driving cycles is reduced by 33%, whereas in fourUS06 driving cycles, the energy loss decreases by 11%. Theenergy consumption for two types of driving cycle is reducedby 7.2% and 1.4%, respectively. US06 driving cycle representshighway-driving behaviors, and the required stator voltageand corresponding dc-link voltage are closer to their upper


TABLE VIIIFAILURE RATES AND MTTFs OF SHEV FOR VARIABLE DC-LINK VOLTAGE CONTROL

limits. In contrast, FTP-75 models the frequent stop-goingurban-driving behavior that features low speeds and low torque,and the corresponding stator voltage and dc-link voltage aremuch lower than their upper limits. As a result, the variabledc-link voltage control strategy brings forth greater reductionin energy loss for urban driving, which makes variable dc-linkvoltage control particularly suitable for urban driving.

The decreased switching losses also reduce the temperatureof semiconductor junctions and capacitors, as illustrated bythe junction temperature profiles of semiconductor devices inthe first half of the four consecutive FTP-75 driving cyclesin Figs. 14–16. It can be observed that under variable dc-linkvoltage control, the junction temperatures of the IGBT andthe diode in the inverter and the IGBT and the lower diodein the dc/dc converter are much lower since the losses of thesemiconductors are reduced. One exception is the upper diodein the dc/dc converter. Under certain operating conditions,the thermal stress of the diode is elevated in the case of thevariable dc-link voltage control. It is because in the case ofthe variable dc-link voltage control, the conduction loss of thedc/dc converter’s upper diode increases while its switching lossdecreases, and the resultant total loss may increase.

The reliability data are further calculated from the simulationresults. The failure rates and MTTFs are tabulated in Table VIII.When the proposed variable dc-link voltage control is utilized,the failure rates of the inverter IGBT and the diode are reducedby approximately 32% and 20%, respectively, for the FTP-75 driving cycles. The failure rates of the lower and upperIGBTs in the dc/dc converter decrease by approximately 47%and 22%, respectively. The failure rate of the overall system isreduced by 27%, and its MTTF is improved by 37%. However,the failure rate and MTTF of dc-link capacitors almost remainunchanged. The upper diode of the dc/dc converter becomesless reliable. For US06 driving cycles, the reliability of the maincomponents and the system is improved with various degrees.Therefore, in comparison to conventional variable modulationindex control, the proposed variable dc-link voltage controlgreatly improves the reliability of key power components andthe power electronic system of an HEV powertrain.

D. Experimental Verification

A prototype of the three-phase inverter, as shown in Fig. 1,has been built to verify the performance of the proposed vari-able dc-link voltage control. Since the classic control schemescan be applied to the motor and the bidirectional dc/dc con-verter, the implementation of the variable dc-link voltage con-

TABLE IXDEVICES AND OPERATION PARAMETERS OF THE INVERTER PROTOTYPE

trol is not presented. The losses of the inverter with variable dc-link voltage control and the variable modulation index controlare experimentally evaluated.

Three single-phase electronic loads in Y-connection are usedas the inverter load, and a second-order low-pass filter isinserted between the inverter and the load to attenuate high-frequency harmonics generated by the inverter. The continuousSVPWM is utilized to control the inverter. The selected devicesand operation parameters of the inverter prototype are shown inTable IX.

To compare the losses of the inverter with the variable dc-link voltage control and variable modulation index control,four operating points are selected. At each operating point, theinverter outputs the same line-to-line voltage and line currentfor the variable dc-link voltage control and variable modulationindex control. For variable modulation index control, the dc-link voltage remains constant while the modulation index ofthe inverter is regulated to generate the desired ac voltage.On the contrary, in the case of the variable dc-link voltagecontrol, the inverter maintains a constant and maximal modu-lation index while the dc-link voltage is regulated so that theinverter outputs the desired ac voltage. At these four operatingpoints, the currents are selected such that the inverter outputsapproximately 4 kVA apparent power. The four operating pointsand corresponding parameters of the inverter are shown inTable X. The loss of the inverter for each operating point isalso listed in Table X. Herein, the inverter losses mainly includesemiconductor losses and filter inductor losses. The profile ofthe inverter loss versus the output ac voltage is shown in Fig. 17.At the first operation point, for variable dc-link voltage controland variable modulation index control, the inverter has the samemodulation index and dc-link voltage, and consequently, theinverter has the same loss for both control schemes. At otherthree operation points, in comparison to the variable modulationindex control, the inverter losses are reduced by 18%, 38%, and37%, respectively, when the proposed variable dc-link voltagecontrol is utilized. The experimental results validate that thevariable dc-link voltage control greatly reduces the loss of theinverter.


TABLE XFOUR OPERATING POINTS AND CORRESPONDING OPERATION PARAMETERS AND LOSSES

Fig. 17. Profile of the inverter loss versus the ac line-to-line voltage forvairable dc-link voltage and variable modulation index control.

VI. HYBRID DISCONTINUOUS PULSE WIDTHMODULATION SCHEME WITH MINIMAL

SWITCHING LOSS

The proposed variable dc-link voltage control improves theefficiency of power converters and reliability of an SHEV pow-ertrain. The variable dc-link voltage control features a constantmodulation index that is set to its maximal value. Discontinuousmodulation schemes are particularly suitable for the inverterunder variable dc-link voltage control, since at the maximalmodulation index, DPWM schemes have the harmonic perfor-mance comparable to continuous PWM. In comparison withcontinuous modulation schemes, DPWM schemes can furtherreduce the switching loss of the inverter. Here, the applicationof discontinuous modulation to HEVs is investigated in termsof switching loss and harmonic distortion.

A. Hybrid DPWM

PWM schemes exert a significant influence on the perfor-mance of the inverters, particularly switching loss and harmonicdistortion. Although continuous PWM schemes are commonlyapplied to the inverter, various DPWM schemes have beeninvestigated to reduce switching loss of the inverter [17], [30].Several DPWM strategies, such as 60◦ DPWM, 30◦-lagging 60◦

DPWM, 30◦-leading 60◦ DPWM, and 30◦ DPWM, have beenanalyzed in [17]. The common feature of these discontinuousmodulation schemes is that one of three phase legs of theinverter is clamped to the negative or positive rail of the dcbus and does not switch over one sixth of a fundamentalcycle. Therefore, the advantage of the DPWM schemes over

Fig. 18. Normalized switching losses for various DPWM schemes with thesame carrier frequency [30].

continuous modulation is that the number of the switchingtransitions during each carrier cycle is reduced from 6 to 4.Correspondingly, the switching loss of the inverter is reduced.

Fig. 18 shows the normalized switching losses of the inverterfor various discontinuous modulation schemes [30]. Herein,the normalized switching losses are obtained by dividing theswitching losses for various PWM schemes with that for thecontinuous SVPWM. It can be observed that for discontinuousmodulation, the averaged switching loss of the inverter over onefundamental cycle depends on the power factor angle of theload. The 60◦ DPWM results in half switching loss of contin-uous PWM at a unity power factor. The reduction in switchinglosses peaks at a unity power factor, since the peak of the loadcurrent flows through the nonswitching leg. In comparison with60◦ DPWM, the switching-loss curve of the 30◦-lagging 60◦

DPWM is only shifted by 30◦ in phase angle, whereas the losscurve of 30◦-leading 60◦ DPWM is shifted by −30◦ in phaseangle. In fact, the switching loss for various DPWM schemesis a periodic function of the power factor angle, and the periodsfor 60◦ DPWM and 30◦ DPWM are 180◦ and 90◦, respectively.The switching loss for discontinuous modulation is lower thanthat for continuous PWM schemes in the full range of the powerfactor angle.

If the switching loss curves in Fig. 18 are further scrutinized,an optimal discontinuous modulation scheme with minimalswitching loss can be obtained by following the lower envelopeof multiple modulation schemes. For the power factor anglebetween −30◦ and 30◦, the minimal loss can be obtained by theuse of 60◦ DPWM with a phase shift in the power factor angle.


TABLE XIHYBRID DPWM SCHEME

Fig. 19. Harmonic distortion factors HDF for various modulation schemesas a function of modulation index [17].

For the power factor angle between 30◦ and 75◦, 30◦-lagging60◦ DPWM results in the lowest switching loss. For the powerfactor angle from −30◦ to −75◦, 30◦-leading 60◦ DPWMresults in the lowest switching loss. In the remaining rangeof the power factor angle, the optimized switching loss canbe obtained when 30◦ DPWM is utilized. Therefore, a hybridPWM scheme with minimized switching loss is formed if theappropriate DPWM schemes are employed for various powerfactor angles. The hybrid DPWM is tabulated in Table XI asa function of the power factor angle. The minimized switch-ing loss for the hybrid PWM is also a periodic function ofthe power factor angle with the period of 180◦, as shownin Fig. 18.

In comparison with continuous PWM, discontinuous modu-lation schemes reduce the number of switching transitions perphase leg over each fundamental cycle but lead to suboptimalharmonic performance. The increased voltage harmonics couldpotentially result in higher harmonic current and correspondingharmonic loss of loads. To properly evaluate harmonic losses,the harmonic distortion factor (HDF) is defined, which is afunction of the modulation index and independent of dc-linkvoltage and load inductance [17]. According to [17], the RMSvalue of the harmonic current for the three-phase inverter withdelta-connection load is related to HDF(M) by

Ih =

(Vdc

24fsLσ

)2∗HDF (M) (7)

where Vdc is dc-link voltage, fs is carrier frequency, and Lσ isload inductance. The HDFs for continuous and discontinuousmodulation schemes are shown in Fig. 19. It is apparent thatthe harmonic distortion of the inverter with discontinuous mod-

Fig. 20. Loss profiles for hybrid DPWM and continuous PWM in the first halfof four consecutive FTP-75 driving cycles. (a) Inverter loss. (b) Total loss.

TABLE XIIENERGY CONSUMPTION AND LOSS FOR CONTINUOUS PWM AND HYBRID

DPWM IN FOUR CONSECUTIVE FTP-75 DRIVING CYCLES

ulation schemes is higher when compared with the continuousSVPWM scheme for a lower modulation index. However, theHDFs for DPWM schemes are comparable to that for continu-ous modulation in the vicinity of a maximal modulation index.Herein, the variable dc-link voltage control is utilized, and thecorresponding modulation index is set to its maximal valueat which discontinuous modulation schemes have comparableharmonic performance of the continuous modulation scheme.Therefore, the combination of variable dc-link voltage controland DPWM schemes achieves the minimized switching loss ofthe inverter without compromising the harmonic performance.

B. Verification of Benefits by Simulation

The improved performance of the hybrid DPWM schemein terms of loss has been verified by simulation. From thesystem point of view, the hybrid DPWM only reduces the lossof the inverter, with little influence on the dc/dc converter. Thelosses of the inverter and the system for variable dc-link voltagecontrol in conjunction with the continuous SVPWM schemeand the hybrid DPWM scheme are shown in Fig. 20. It canbe observed that the losses of both the inverter and the overallsystem are reduced by the adoption of the hybrid DPWMstrategy. The quantitative evaluations of the loss reduction areillustrated in Tables XII and XIII. Over four FTP-75 drivingcycles, the energy consumption and energy loss are reduced by3.4% and 22%, respectively. In the case of four US06 drivingcycles, the energy consumption and energy loss decrease by2.9% and 19%, respectively.


TABLE XIIIENERGY CONSUMPTION AND LOSS FOR CONTINUOUS PWM AND HYBRID

DPWM IN FOUR CONSECUTIVE US06 DRIVING CYCLES

Fig. 21. Junction temperatures of the inverter IGBT and diode for hybridDPWM and continuous PWM in the first half of four consecutive FTP-75driving cycles. (a) IGBT. (b) Diode.

Likewise, the junction temperatures of the inverter IGBT andthe diode are reduced, as shown in Fig. 21, since the hybridDPWM strategy reduces the switching loss. Table XIV listsfailure rates and MTTFs of semiconductors and capacitors inthe power converters. In comparison with Table VIII, the failurerates of the inverter IGBT and the diode are further reduced,while other components’ failure rates remain unchanged. Thefailure rate of the overall system is also greatly reduced by theuse of the hybrid DPWM scheme. Therefore, the proposed hy-brid discontinuous modulation in conjunction with the variabledc-link voltage control greatly reduces the loss of the inverterand improves the reliability of an HEV powertrain withoutcompromising the harmonic performance of the inverter. Con-sequently, the hybrid modulation scheme in conjunction withthe variable dc-link voltage control does not compromise theharmonic losses of loads and filters.

In addition to the uncompromised harmonic losses, thehybrid modulation scheme in conjunction with the variabledc-link voltage control does not increase the stresses of theswitches either. The voltage stress of the switches in the in-verter is determined by the dc-link voltage. Since the hybriddiscontinuous modulation scheme does not change the achiev-able modulation index, the required dc-link voltage for thesame output voltage does not change. Therefore, the hybridmodulation scheme does not increase the voltage stress ofthe switches. The current stress of the switches depends onthe RMS value of the inverter output current. As analyzedin the previous paragraph, the hybrid modulation scheme in

conjunction with the variable dc-link voltage control does notincrease the harmonic current. Therefore, it will not increasethe RMS value of the inverter output current, and consequently,the current stress of the switches remains the same.

Since the hybrid discontinuous modulation in conjunctionwith the variable dc-link voltage control does not increase theharmonic current and switch stresses, hardware modification tothe inverter is not necessary. Consequently, the combination ofhybrid modulation and the variable dc-link voltage control re-duces the losses of the inverter without increasing the losses ofpassive components and changing hardware of the inverter. Theloss performance of the inverter with the proposed modulationscheme is experimentally verified in the following subsection.

C. Experimental Verification

The hybrid discontinuous modulation scheme in conjunctionwith variable dc-link voltage control is experimentally verifiedby the use of an inverter prototype. The main devices andoperation parameters of the inverter prototype have been shownin Table IX. The continuous SVPWM and four discontinuousmodulation schemes, i.e., 60◦ DPWM, 30◦-leading 60◦ DPWM,30◦-lagging 60◦ DPWM, and 30◦ DPWM, are tested. For eachmodulation scheme, the loss of the inverter is measured at thefour operation points. The modulation index for all modulationschemes is set to 1.15, and the dc-link voltage is varied togenerate the desired ac voltage. At these four operation points,the inverter outputs different ac voltages and currents, andthe load has different displacement angles, while the apparentpower is maintained at approximate 4 kVA.

The operating parameters and losses are listed in Table XV.Due to the effects of the dead time and the voltage drop acrossthe filter inductors, the inverter output line-to-line voltage isslightly lower than the theoretical value that is calculated by(3), as shown in Table XV. It can be observed that the lossesof the inverter for all discontinuous modulation schemes arelower than the continuous modulation scheme. Since the phase-shift angle at the first operation point is −38.6◦, 30◦-leading 60◦DPWM results in the minimal inverter loss that is 70% of theinverter loss for the continuous modulation scheme. At the sec-ond and third operation points, the inverter ac current also leadsthe ac voltage; hence, 30◦-leading 60◦ DPWM is the optimalscheme with the minimal loss. At the fourth operation point, theinverter ac voltage is almost in phase with the ac current; there-fore, 60◦ DPWM results in the minimal inverter loss that is only61% of the loss of the inverter with the continuous modulationscheme. Therefore, the experimental results verify the superiorloss performance of the discontinuous modulation scheme, asshown in Fig. 18. It is worth noting that the inverter losses inthe experiments include the switching and conduction losses ofthe semiconductor devices and the filter inductor losses.

VII. CONCLUSION

A reliability prediction model for electric vehicles has beenpresented. In comparison to the existing part-count method thatdetermines the reliability of a system solely based on the typesand numbers of components used in the system, the modelpresented in this paper not only takes into account the thermal


TABLE XIVFAILURE RATES AND MTTFs OF SHEV FOR VARIABLE DC-LINK VOLTAGE CONTROL IN CONJUNCTION WITH HYBRID DPWM

TABLE XVFOUR OPERATING POINTS AND CORRESPONDING OPERATION PARAMETERS AND LOSSES FOR VARIOUS MODULATION SCHEMES

and electrical stresses but includes the effects of load variationsrelated to driving behaviors and road conditions as well sincethe model is based on the standard driving cycles. Althoughthis model is developed in the context of SHEVs, it is equallysuited for other types of electric vehicles with minimal modifi-cation/extension. The results of a case study have shown that thefailure rates of semiconductor devices are strongly correlatedto the driving behaviors. Thermal stresses have a significantinfluence on the reliability of devices. For the batteries, a moreaccurate reliability model needs to be further investigated. Onthe basis of accurate reliability analysis results, the variabledc-link voltage control and a hybrid discontinuous modulationscheme are presented. Both simulation and experimental resultshave verified that the proposed methods are effective in reduc-ing losses of the HEV powertrain and improving reliability.The proposed methods can be applied to retrofitting existingsystems and/or integrated with other methods in various designaspects of powertrain systems.

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Yantao Song received the B.S. degree fromZhengzhou University, Zhengzhou, China, in 2004and the M.S. degree in electrical engineering fromZhejiang University, Hangzhou, China, in 2006. Heis currently working toward the Ph.D. degree withMichigan State University, East Lansing, MI, USA.

From 2006 to 2008, he was an Electrical Engi-neer with Emerson Network Power. Then, he joinedFSP-Powerland Technology Inc. as a Senior DesignEngineer. His research interests include switching-mode power supplies, power conversion for renew-

able energy generation, powertrains for hybrid electric vehicles, and reliabilityof power electronic systems.

Bingsen Wang (S’01–M’06–SM’08) was born inChina. He received the M.S. degree from ShanghaiJiao Tong University, Shanghai, China, in 1997;the M.S. degree from the University of Kentucky,Lexington, KY, USA, in 2002; and the Ph.D. de-gree from the University of Wisconsin—Madison,Madison, WI, USA, in 2006, all in electricalengineering.

From 1997 to 2000, he was an Electrical Engineerwith Carrier Air Conditioning Equipment Company,Shanghai. He was also a Power Electronics Engineer

with the General Electric Global Research Center, Schenectady, NY, USA,where he was engaged in various research activities on power electronics,mainly focusing on the high-power area. From 2008 to 2009, he was with thefaculty of the Department of Electrical Engineering, Arizona State University,Tempe, AZ, USA. Since 2010, he has been a faculty member with the De-partment of Electrical and Computer Engineering, Michigan State University,East Lansing, MI, USA. He has authored and coauthored 35 technical papers inrefereed journals and peer-reviewed conference proceedings. He is the holderof one Chinese patent and one U.S. patent, with two patents pending. Hiscurrent research interests include reliability and dynamic modeling/control ofpower electronic systems; power conversion topologies, particularly multilevelconverters and matrix converters; application of power electronics to renewableenergy systems; power conditioning; flexible ac transmission systems, andelectric drives.

Dr. Wang received the Prize Paper Award from the Industrial Power Con-verter Committee of the IEEE Industry Application Society in 2005. Since2009, he has been an Associate Editor of the IEEE POWER ELECTRONICSLETTERS.

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Evaluation Methodology and Control Strategies for ...bingsen/files_publications/J-14_TVT.pdf · power electronic converters, and the whole drivetrain of HEVs from the probabilistic