Quantitative Evaluation for Reliability of Hybrid Electric Vehicle Powertrain

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1 Quantitative Evaluation for Reliability of Hybrid Electric Vehicle Powertrain Yantao Song and Bingsen Wang Department of Electrical and Computer Engineering Michigan State University 2120 Engineering Building East Lansing, MI 48824, USA Abstract The reliability prediction of hybrid vehicles is of paramount importance for planning, design, control and operation management of vehicles, since it can provide an objective criterion for comparative evaluation of various structures and topologies and can be used as an effective tool to improve the design and control of vehicles. This paper presents a loaddependent simulation model based on MATALAB for quantitatively assessing the reliability of hybrid electric vehicles. The model takes into consideration the variation of driving scenarios, dormant mode, electrical stresses, thermal stress and thermal cycling. Therefore the more reliable and accurate reliability prediction can be obtained. The model is demonstrated in detail and the result of reliability assessment based on a series hybrid electric vehicle is presented and analyzed. I. INTRODUCTION Hybrid electric vehicles (HEVs) with their superior fuel economy have been considered as a pivotal technology to mitigate concerns over the rapid rising of petroleum cost, increasingly worsening air pollution and global warming associated with greenhouse gas emission [1]. However, inclusion of a great number of power electronic devices into drive systems of vehicles deteriorates reliability of the overall system [2]. The reduced reliability of HEVs not only discounts fuelsaving premium, but also increases operation cost. Therefore the reliability of HEVs powertrain has increasingly attracted research attention from both the academia and the industry. Research activities on the reliability of components, power electronic converters and the whole drivetrain for HEVs from the probabilistic and deterministic perspectives have been reported in literature [3]. From system point of view, battery is the most important and also the least reliable component in HEVs, which has a crucial effect on the reliability and cost of HEVs. The authors of [4] study the influence of the operating temperature on the cycle life of lead-acid, lithiumion and NiMH batteries for HEVs based on simulation and numeric analysis. The reliability of power electronic converters in HEVs is also widely investigated. In [5] the reliability of a bidirectional dc/dc converter for the energy storage system of HEVs is assessed. In this paper the driving behaviors are taken into account and the failure rate models of the components are obtained by using Monte Carlo Simulation. But the reliability models introduced by the authors do not include effects of thermal cycling on component failures, which will lead to the results that may substantially deviate from reality. A test bench implemented with various driving cycles to verify the reliability of new prototypes of inverters for electric motors in hybrid vehicles is presented in [6]. Authors of [7] presents a simulation concept that is used to assess the lifetime of the inverter for HEVs in terms of the crack propagation speed of bond and solder joint connections. Hirschmann, et al. present a simulation model to predict the reliability of inverters for HEVs [8]. This reliability model focuses on the effects of temperature and thermal cycle on the failure rates of key power components of inverters. A reliability model based on a sequence tree is adopted to analyze various reliability indices and related maintenance cost of the traction train within a fuel cell car []. The authors of [10] evaluate and compare the availability of pure electric vehicle, hybrid electric vehicle, and conventional vehicles based on part-count reliability model. This method does not consider the practical driving scenarios and operating conditions of vehicles. In order to overcome the limitations of the existing methods, this paper presents a reliability model for hybrid electric vehicles. The model includes power electronic converters and energy storage unit in SHEVs. The practical scenarios, thermal stress and electrical stresses are considered in the model. The accurate reliability analysis provides an important guideline for planning, design and operation management of HEVs. The SHEV drive system is reviewed in Section II. The reliability model is illustrated in detail in Section III. In Section IV the results of reliability assessment and a brief analysis are presented. Finally a summary in Section V concludes the paper. II. SERIES HYBRID EELECTRIC VEHICLE POWERTRAIN As shown in Fig. 1, an SHEV power system consists of three power electronic converters, a three-phase PWM rectifier, a three-phase inverter and a bidirectional buck/boost dc/dc converter, and energy storage unit that is composed of battery cells connected in parallel and series manners. Since there are two energy sources, the traction power will be divided between the engine and the battery bank in accordance with the specific energy management strategy, driving conditions, and state of charge of the battery pack. Correspondingly there are

2 TABLE I PARAMETERS ASSUMED OF VEHICLE Parameter Value Vehicle weight 1243 kg Front area m 2 Rolling resistance coefficient 0.01 Aerodynamic drag coefficient 0.26 Diameter of tire 0.62 m Transmission efficiency Fig. 1. Schematic of the SHEV powertrain ! Fig The diagram of the reliability simulation model. 1 five operating modes for SHEVs, and the operating conditions of the power converters and the battery bank are different from each mode to others. As a result, the electrical and thermal stresses of components in SHEVs greatly vary during a driving cycle, which will be considered in the reliability analysis model presented in the paper. III. RELIABILITY SIMULATION MODEL OF SHEVS The structure of the reliability simulation model is shown in Fig. 2. In this model, the input data are the operating conditions of vehicles. Herein, various standard driving cycles are used to simulate the driving scenarios. The failure rates and mean time to failure (MTTF), lifetime and other reliability indices of the components, converter and the whole system can be obtained from the model. Each functional block will be introduced as follows. A. Driving Cycle The torque-speed characteristics of vehicles versus time determine the operating conditions of the power electronic converters in the drive system, which finally affect the electrical and thermal stresses of the key power components. However, the torque-speed profiles of vehicles depend on the behaviors of drivers and the road conditions. Uncertainty of driving patterns 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 been developed in different countries to provide a test benchmark for evaluating efficiency and emission of vehicles. Since these driving cycles have been accepted by the industry and widely used to assess performance of vehicles, herein they are employed to emulate the operating patterns of HEVs. The driving cycle provides the instantaneous speed and acceleration information to HEVs model, as shown in Fig. 2. B. Vehicle Model The driving cycle emulates vehicles instantaneous speed and acceleration that cannot exclusively determine the instantaneous electrical stresses of vehicles powertrain. The specific electrical stresses also depend on the parameters of vehicles and the road conditions, such as wind speed, gradient and roughness of the road surface. The parameters of HEV and assumed road conditions not only determine the power ratings of energy sources and power electronic converters, but also determine their instantaneous powers [1]. The parameters of the vehicle used in this paper are obtained from the commercial vehicles and literature [11], and have been tabulated in TABLE I. In HEV model, the vehicle speed and acceleration are used as inputs to obtain the instantaneous torque of the electric motor. C. Motor Model The design of the traction motor in SHEVs is based on performance requirements of vehicle that mainly include maximum speed, acceleration and gradiability, vehicle parameters and the road conditions. The specific design process and methodology is detailed in [1]. The motor s power rating is illustrated in TABLE II. Herein the interior permanent magnet motor (IPM) is utilized as the traction motor and its model is developed to calculate the instantaneous stator current and voltage by using known torque and speed. The simulation model is based on the steady-state model of IPMs [12]. The IPMs operating modes, such as maximum torque per ampere, fluxing weakening, are also considered in this model to simulate practical operating conditions. The stator voltage and current from the motor model directly determine the operating conditions of power converters in HEVs driving system. D. Loss Model The basic design rules of three power electronic converters are explained as the following. The inverter is utilized to control the traction motor, therefore its voltage and current

3 Parameter TABLE II POWER RATINGS OF THE SHEV POWERTRAIN Traction motor Engine/ generator power rating Inverter power rating Rectifier power rating DC/DC convertere Battery pack Value 67 kw, base speed 1200 RPM, maximum speed 6000 RPM 30 kw V ll = 400 V, I = 121 A 28.5 kw 46. kw 4.3 kw, 2.5 kwh ratings are designed to meet requirements of the motor. The output voltage of the inverter should match the stator voltage of the motor, while the maximum output current is determined by the maximum achievable torque of the motor. Therefore, the voltage and current ratings rather than power rating are demonstrated in TABLE II. In the drive system of the HEVs, the engine/generator provides the total energy, while the battery pack only works as a power buffer that provides or absorbs peak power for the acceleration or deceleration of the vehicle. Therefore, the power rating of the engine/generator system should be equal to the average power of the traction motor in a standard driving cycle. Herein, FTP-75 is used as the benchmark to design the ratings of the engine/generator system and the rectifier. It is obvious that the available peak power of the rectifier is much lower than that of the motor. During the interval of acceleration, the engine/rectifier system only provides part of the power that the motor requires, while the remaining part has to be provided by the battery pack. Correspondingly, the power ratings of the battery pack and the buck/boost converter should be equal to the motor s power rating minus that of the rectifier if the power losses are neglected. The power ratings of the three power converters are listed in TABLE II. In power electronic systems, power components such as IGBTs, MOSFETS, diodes, capacitors, inductors and transformers are key components that produce most of power losses. The power loss calculation is the basis of thermal design and instantaneous thermal analysis. The losses of power semiconductors include conduction loss and switching loss. For capacitor and battery the resistive losses dissipated in the equivalent series resistance (internal resistance for battery) are dominant. In order for efficiency of simulation, analytical loss models are built, which are based on the basic investigation of converter topologies [13]. Fig. 3 shows the loss profile of the inverter s IGBT in a US06 driving cycle. E. Thermal Model The junction temperature and temperature variation of power devices are key factors that affect their reliable operation and lifespan, which can be observed in the failure rate models of the devices. The thermal model performs two functions: calculating junction temperatures of power semiconductors and core temperatures of batteries and capacitors, and detecting thermal cycling. The simplified dynamic thermal Fig. 4. Fig. 3. Inverter IGBT loss profile in a US06 driving cycle The thermal equivalent circuit of semiconductor and heatsink. equivalent circuit of a semiconductor and a cooling system is shown in Fig. 4. The junction temperature and variation of the component depends on the power losses, the thermal resistances and capacities of components and the cooling system, and the ambient temperature. The thermal resistances and capacities of components from datasheets, while the thermal parameters of the heatsink are determined by the geometry and materials of the heatsink. F. Failure Rate Model There are many empirical-based reliability models of electronic devices. The military handbook for the reliability prediction of electronic equipments (Military-Handbook-217) [14] is well known and widely accepted in military and industrial applications. However, the handbook does not contain necessary data to assess the influence of dormant modes on components, and the data that reflect effects of thermal cycles. The reliability handbook RDF 2000 [15] is another important data source of empirical-based failure rate models. It considers dormant modes, effects of the temperature cycles and data of IGBTs. Herein the component failure rate models provided by RDF 2000 are utilized to analyze reliability of HEV powertrain. The failure rate models of power components are introduced as follows. The IGBT failure rate can be

4 determined by λ IGBT = λ die + λ package + λ overstress y i=1 λ die = π s λ 0 (πt) i τi τ on+τ off λ package = λ b z i=1 (π n) i ( T ) 0.68 λ overstress = π I λ EOS (1) where, the first term λ die, which is mainly determined by the junction temperature in the mission profile, represents the failure-rate component related to the die of IGBTs; and the second term λ package denotes IGBT package failures that are caused by the number and magnitudes of thermal cycles that devices undergo. The last term λ overstress, which reflects contribution of the over-current and over-voltage stresses to the total component failure rate, can be neglected since in practical applications the over-stress operating conditions should not occur in normal operating conditions. The unit of the failure rate in the above equation is the number of failures per 10 hours. The parameters in (1) will be further explained as the following. The parameter π s represents the influence of the voltage stresses on the failure of the IGBT s die, and is determined by the ratios of the applied collector-to-emitter and gate-to-emitter voltages to the corresponding ratings. λ 0 and λ b are base failure rates of the die and the package, respectively. (π t ) i represents the effect of the real junction temperature on the failure of the die in the i th phase of the IGBT s mission profile and is determined by the junction temperature. The parameters τ i is the working time ratio of the IGBT in the i th phase of the mission profile. τ on and τ off respectively correspond to the total working time ratio and the total dormant time ratio. These three parameters account for the effect of the dormant mode on the failure of IGBTs. ( T ) i represents the amplitude of the thermal variation that the device undergoes in the i th phase of its mission profile. (π n ) i is the influence factor that is related to the annual number of the thermal cycle experienced by the package with the amplitude of ( T ) i. The failure rate model further demonstrates that the junction temperature and the temperature cycle have a significant influence on failure of IGBTs. Failure rate models of diodes and capacitors have the same form as that of IGBTs. However, the reliability handbooks RDF2000 and MIL-217F do not contain the failure rate model of battery. The reliability prediction procedure Bellcore TR- 332 [16] published by Bell Communication Research, Inc provides a simple failure model of battery cell, which is λ battery = λ 0 10 /hour (2) From this model the failure of the battery is independent of all stresses, but only depends on the base failure rate λ 0 that is related with the type of the battery cell. Therefore it is a very rough model. IV. RELIABILITY ASSESSMENT AND ANALYSIS The reliability of SHEVs powertrain is evaluated based on the presented simulation model. The driving cycles FTP-75 and US06 are utilized, which represent driving conditions on the urban route and on the high way, respectively. The ambient temperature is set to be 45 C. The average total running time of a vehicle is about 500 hours per year [8]. The thermal cycles of the magnitude of lower than 3 C have little influence on the failure of components and therefore can be neglected. The reliability of the powertrain depends on the type of driving cycles, the energy management strategy and initial conditions of the battery pack. In order to evaluate the effects of the various driving cycles on the reliability of SHEVs powertrain, the simulations based on FTP-75 and US06 are implemented and analyzed. The energy management strategy determines the power distributions between two energy sources, the battery pack and the engine, and therefore determines electrical and further 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 it provides total drive power to the inverter/motor while the engine is turned off if the state of charge (SOC) of the battery pack is within the set range. Once the SOC of the battery pack drops to its lower threshold, the engine is turned on and charges the battery pack with the full power. The benefit of the engine on/off control lies in the fact that the engine always works in the high-efficiency range. However, the battery pack has to undergo deep charge/discharge cycles and the buck/boost converter consequently has to experience higher electrical and thermal stresses. In order to avoid unfairness of the simulation results caused by the initial condition of the battery pack, simulations respectively based on five consecutive US06 cycles and two consecutive FTP-75 cycles are implemented. Fig. 5 and Fig. 6 illustrate the junction temperatures of the inverter IGBT and diode in the last cycle of five consecutive US06 driving cycles. Compared with Fig. 3, it can be observed that the junction temperatures of devices follow the profiles of their power losses and that the junction temperatures fluctuate dramatically in one driving cycle although their absolute values are not much high. Fig. 7, 8, and 10 demonstrate the numbers and corresponding amplitudes of thermal cycles that the semiconductors in the inverter and DC/DC converter undergo in five consecutive US06 cycles. It is shown that the amplitudes of the thermal cycles are mainly under 35 C, and that the IGBTs of the inverter and DC/DC converter experience more thermal cycles of higher amplitudes since the IGBTs have higher losses and correspondingly have higher junction temperatures. The failure rates of components are related to the temperature cycles. The failure rates and MTTFs of the components are demonstrated in TABLE III. It should be noted that failure rates of components in TABLE III is that of a single device and that the failure rate of the whole system does not include the battery pack and the rectifier. Since the battery pack consists of hundreds of cells connected in parallel and series manners, the failure rate of the whole battery pack is relatively high and dominant in the overall system. And the failure rate of the battery back is independent of its operating conditions but only depends on the number of the battery cells. As a result,

5 TABLE III FAILURE RATES AND MTTFS OF SHEVS Driving cycle Reliability index Inverter IGBT Inverter diode Boost IGBT Boost diode Dc-link capacitor System FTP-75 Failure rate (/10 6 hours) MTTF (10 5 hours) US06 Failure rate (/10 6 hours) MTTF (10 5 hours) !"#$% Fig. 5. The junction temperature of inverter IGBT in a US06 driving cycle. Fig. 7. The numbers and amplitudes of inverter IGBT thermal cycles in five! "#$ Fig. 6. The junction temperature of inverter diode in a US06 driving cycle. Fig. 8. The numbers and amplitudes of inverter diode thermal cycles in five any improvement of design and control strategies has a little effect on the failure rate and MTTF of the SHEV powertrain, which does not match practical observations. Therefore the failure rates and MTTF of the system in TABLE III exclude the contribution from the battery pack. Our ongoing effort is devoted to accurate lifetime model of battery cells. TABLE III also shows that the IGBT of the boost converter features the highest failure rate and therefore is the least reliable. It is because the power loss dissipated in the switch of boost converter is much higher than the losses of the other components and correspondingly its thermal stress is the worst, as shown in Fig Since US06 emulates the highway driving behaviors and have higher speeds and accelerations than the driving cycle FTP-75, in the US06 driving cycles, the electrical and thermal stresses of the power converters are much worse and correspondingly much higher failure rates and lower reliability can be predicted, as shown in TABLE III. V. CONCLUSION A reliability prediction model for electric vehicles has been presented. Compared with the part-count method that determines the reliability of a system only based on the types and numbers of components used in the system, the model presented in this paper not only considers the thermal and electrical stresses, but also includes the effects of load variations related to driving behaviors and road conditions on the reliability of components since the model is based on the stan-

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