Plug-in Hybrid Electric Vehicle Applications Research Articles

Parametrization of a Doyle-Fuller-Newman (DFN) Model for a Commercial 37Ah Li-Ion Battery and Validation with Incremental Capacity Analysis

Physico-chemical modeling is considered as a very interesting way of simulating the behavior of a Li-ion battery cell by linking its internal state to its performance and aging. However, an accurate parametrization of such models is necessary for a truly representative outcome. In the case of commercial batteries, the parametrization procedure is hardly ever entirely undergone, leaving room for parameters tweaking and inaccurate simulation results. In the framework of this work, over 70% of the parameters were measured for a Samsung SDI 37Ah Li-ion prismatic battery (NMC111/Graphite) for PHEV (Plug-in Hybrid Electric Vehicle) applications. A Doyle-Fuller-Newman (DFN) Pseudo 2D model is chosen based on the work of Dufour et al.1. The major electrochemical characterization technics and measurement results for every component in the cell will be presented. The cells were opened in the ante-mortem procedure2, materials were identified, geometrical parameters were measured and samples were taken for coin-cell experiments. A small portion of the electrolyte was recovered and studied to conclude that it was made of EC-DMC-EMC at 1:1:2 portions. A similar solution was synthetized in order to conduct ionic conductivity measurements at temperatures ranging from -30 to 60°C. Samples from the separator were taken for both effective ionic conductivity and porosity measurements. The tortuosity of the electrodes was calculated via an EIS (Electrochemical Impedance Spectroscopy) with a blocking-electrodes configuration, and finally the diffusion factor in the active particles was estimated via GITT (Galvanostatic Intermittent Titration Technique) experiments. A very slow current regime was used to lithiate and de-lithiate the active materials in a half-cell experiment for electrode balancing purposes. The model was compiled using COMSOL Multiphysics 5.5, and results were compared to validation experiments conducted on the full-setup prismatic cell. The charge curve was validated under different current and power regimes at 25°C, and the Incremental Capacity (IC) curve showed a reasonable accuracy. With this in hand, the following step would be to couple this performance model to an aging model and to compare the evolution of the IC peaks with the experimental aging.

Battery total capacity estimation based on the sunflower algorithm

Battery total capacity estimation is crucial for battery management systems (BMSs). Accurate knowledge allows BMSs to anticipate potential failures in advance, through indicators such as the state of health. In this paper, we suggest a new capacity estimation framework based on the sunflower optimization algorithm (SFO). The technique reported accounts for capacity error sources, including measurement and estimation noises, in addition of being recursive. SFO is applied to find the best candidate that has the minimum objective function value in a population of sunflowers. A reduction strategy of the search space is used to enhance the solution accuracy. The best candidate is then used through a forgetting factor to update battery capacity. The algorithm's accuracy was verified using NASA Prognostic Data Repository, in addition to three scenarios of a battery in electric and plug-in hybrid electric vehicle applications. As far as we can tell, this is one of the first attempts to use SFO to estimate battery capacity. SFO showed great performance: SFO recorded a maximum error of 1.26% in the worst-case scenario. Moreover, all predictive performance indicators (root mean square error RMSE, mean absolute error MAE, and mean absolute percentage error MAPE) did not exceed 0.4% in all tests.

An Evaluation Framework for Second-Life EV/PHEV Battery Application in Power Systems

Energy storage is essential for balancing the generation and load in power systems. Building a battery energy storage system (BESS) with retired battery packs from electric vehicles (EVs) or plug-in hybrid electric vehicles (PHEVs) is one possible way to subsidize the price of EV/PHEV batteries, and at the same time mitigating forecast error introduced by load and renewable energy sources in power systems. This paper proposes a detailed framework to evaluate end-of-life (EOL) EV/PHEV batteries in BESS application. The framework consists of three parts. A generalized model for battery degradation is first introduced. It is followed by modeling the battery retirement process in its first life. Two vehicle types—EV and PHEV—as well as two retirement modes—nominal and realistic modes—are considered. Finally, the application of the second-life BESS in power systems is modeled in a detailed economic dispatch (ED) problem. This is how second-life BESS’s performance translates into cost savings on power generation. An optimization problem is formulated to maximize total cost savings in power generation over the battery’s second life. This is done by striking a balance between short-term benefit (daily cost savings) and long-term benefit (cost savings through service years). Numerical results validate the effectiveness of the proposed framework/models. They show that battery usage and retirement criterion in its first life directly affect the performance in its second life application. In our case study, EV battery packs possess larger EOL energy capacities and consequently generate more cost savings in the second life. However, the BESS built from retired PHEV batteries has higher cost savings per MWh. It is because, with the proposed degradation model, battery health is better preserved in PHEV applications. Compared to nominal retirement mode, realistic retirement mode results in extra cost savings due to the reduced first-life service years.

High efficiency two stroke opposed piston engine for plug-in hybrid electric vehicle applications: Evaluation under homologation and real driving conditions

The potential of plug-in hybrid electric vehicles (PHEV) to reduce greenhouse gas emissions highly depends on the vehicle usage and electricity source. In addition, the high costs of the battery pack and electric components suppose a challenge to the vehicle manufacturers. However, the internal combustion engine complexity can be reduced due to its lower use as compared to the no-hybrid vehicles. This work evaluates the use of a new opposed piston 2-stroke engine, based on rod-less innovative kinematics, in a series PHEV architecture based on rod-less innovative kinematics along different driving routes in Europe. A 0D-vehicle model fed with experimental tests is used. The battery size is optimized under homologation conditions for two different vehicle types. The optimum case is tested in several real driving conditions under different vehicle modes and battery states of charge. The main contribution of this work is the demonstration of the potential to reduce the vehicle CO2 emissions and cost with an innovative 2-stroke engine. The results show that 24 kWh is the optimum battery size for both vehicle platforms. Charge depleting mode shows 70% of CO2 tailpipe reduction in urban cycles and 22% in long travels compared to the no-hybrid version. Charge sustaining mode results show a CO2 tailpipe reduction of 20% in urban cycles and 2% in long distance travels with respect to the no-hybrid version. In spite of the CO2 contribution of the battery manufacturing, the results show a reduction of LCA CO2 emissions in 52% in charge depleting and 7% charge sustaining against the no-hybrid case.

Differential Power Processing Converter Enhancing Energy Yield of Curved Solar Roofs of Plug-In Hybrid Electric Vehicles

In photovoltaic (PV) panels consisting of multiple substrings connected in series, mismatch in substring characteristics due to partial shading causes the significant reduction in energy yield and the occurrence of multiple maximum power points. In solar roofs of plug-in hybrid electric vehicles (PHEVs), substring characteristics are always unavoidably mismatched due to the curvature of solar roofs, resulting in the mismatch issues similar to partial shading. Various kinds of differential power processing (DPP) converters have been proposed to preclude mismatch issues in traditional flat PV panels. The key contributions and novelties of this paper are summarized as follows. Firstly, uneven irradiance on the solar roof of Prius PHEVs is investigated. Secondly, existing DPP converter architectures are reviewed to select a proper DPP converter topology for PHEV applications. Thirdly, the selected topology is improved to be better suitable for PHEV applications, followed by the detailed operation analysis. Lastly, the experimental results of the laboratory and field testing using a prototype are presented. Field testing using an actual solar roof of Prius PHEV was performed, and the results demonstrated the daily energy yield enhancement of 4%–5% by the proposed DPP converter.

Comparison of economic viability of series and parallel PHEVs for medium-duty truck and transit bus applications

This article performs a novel comparison of the life-cycle costs of the series and parallel architectures for plug-in hybrid electric vehicles. Economic viability is defined as having a payback period less than 2 years and number of battery replacements less than or equal to three over a vehicle life of 12 years along-with drivability and gradability constraints. Economic viability is compared for two plug-in hybrid electric vehicle applications (Medium-duty Truck and Transit Bus) using series and parallel architectures over multiple drivecycles, for three economic scenarios (viz. 2020, 2025 and 2030 where the fuel price, battery price and motor price are varied such that latter scenarios are more favorable for hybridization). One battery overnight recharge is assumed. The results demonstrate that by 2020 the plug-in hybrid electric vehicle transit buses are viable for the duty cycles Manhattan, Orange County, and China (Normal and Aggressive). By 2025, plug-in hybrid electric vehicle Class 6 trucks are viable for all duty cycles considered (Pick-up and delivery, Refuse and New York Composite). The parallel architectures generally require less than 50% of the initial cost of the series architecture, due to smaller motor sizes, driving earlier viability for parallel architectures. The transit bus scenarios generally achieve payback sooner than the medium-duty truck due to higher fuel cost savings, driving earlier viability for transit bus applications.

Speed Regulation Enhancement for SRM Drive in PHEV Applications by using Hybrid Fuzzy Logic controller

Speed regulation enhancement of a Switched Reluctance Motor (SRM) Driveby using modularfront-endintegrated multilevel converter for plug-in hybrid electric vehicle (PHEV) applications are studied and evaluated in this paper. Theoperating modes of the system are basing on Turn-On &Turn OFF of the switches in the converter circuit. In order to achievefast demagnetization and excitation, during generator driving mode, the battery bank is used to elevate the phase voltage. To get the multiple voltage responses and torque increment, an additional charging capacitor and a reframed four-level structure from the converter during battery driving mode is required. A hybrid Fuzzy Logic Controlleris proposedin orderto control the speed of the SRM motor. This paper mainly focuses on the comparison of the hybrid fuzzy logic controller with conventional P & PI and to prove the proposed controller provides the best performance and high robustness compared to a conventional P & PI controller. Matlab / Simulink is used to simulate.

Interleaved Current-Driven Phase-Shift Full-Bridge Converter With Magnetic Integration and Voltage Doubler Rectifiers

This paper presents an interleaved current-driven phase-shift full-bridge converter for plug-in hybrid electric vehicle (PHEV) applications. In the proposed converter, soft switching of the active switches can be realized for a wide range of operating conditions by using a simple auxiliary circuit. Due to the current-driven nature of secondary rectifiers, the proposed converter is able to eliminate the voltage spikes across the output diodes and provides smooth commutations for the secondary rectifiers. Thus, diodes with lower breakdown voltage rate and lower forward voltage drop can be used to further improve the efficiency. All the passive magnetic components are integrated into the main transformer. The numbers of the output diodes are minimized because of the voltage doubler rectifier configuration. The input filtering requirements, as well as the current stresses of the switch devices, are also significantly reduced owing to the interleaving approach. Therefore, the proposed converter would be a good candidate for PHEV applications. The steady-state operation and relevant analysis results of the proposed converter are presented. Experimental results obtained from a 2-kW prototype with a peak efficiency of 97.4% validate feasibility of the proposed converter.

An Integrated Energy Management Strategy With Parameter Match Method for Plug-In Hybrid Electric Vehicles

A battery-ultracapacitor hybrid energy storage system (HESS) is a reliable candidate to overcome the drawbacks of a single power source system for its complementary features of power and energy in plug-in hybrid electric vehicle application. In this paper, an integrated energy management strategy procedure, which consists of three layers, is presented to distribute the power of the battery packs and the ultracapacitor packs. First, an HESS parameter match method is developed under different driving cycles with optimization objectives of cost and weight. Second, three-level wavelet transform (WT) algorithm is employed to isolate the different frequency components of power demand. The low-frequency components with less transients and sharps in power demand are provided by extending the battery lifetime, while an ultracapacitor satisfies the high-frequency components for its nice features of high specific power. Finally, fuzzy logic control is used to manage power flows between various components for guaranteeing the HESS performance. The simulation results show that compared with WT-based-only energy management strategy, the proposed procedure can always control the battery currents within 2C rate and reduce the energy consumption of about 6.54%.

Modelling and simulation of current fed dc to dc converter for PHEV applications using renewable source

With the current rate of depletion of the fossil fuel the need to switch on to the renewable energy sources is the need of the hour. Thus the need for new and efficient converters arises so as to replace the existing less efficient diesel and petroleum IC engines with renewable energy sources. The PHEVs, which have been launched in the market, and Upcoming PHEVs have converters around 380V to 400V generated with a power range between 2KW to 2.8KW. The fundamental target of this paper is to plan a productive converter keeping in mind cost and size restriction. In this paper, a two-stage dc-dc converter is proposed. The proposed converter is utilized to venture up a voltage from 24V (photovoltaic source) to a yield voltage of 400V to take care of a power demand of 2.4kW for a plug-in hybrid electric vehicle (PHEV) application considering the real time scenario of PHEV. This paper talks about in detail why the current fed converter is utilized alongside a voltage doubler thus minimizing the transformer turns thereby reducing the overall size of the final product. Simulation results along with calculation for the duty cycle of the firing sequence for different value of transformer turns are presented for a prototype unit.

Comparative Analysis of Unipolar and Bipolar Control of Modular Battery for Thermal and State-of-Charge Balancing

Thermal and state-of-charge (SOC) imbalance is a well-known issue that causes nonuniform aging in batteries. The modular battery based on cascaded converters is a potential solution to this problem. This paper presents bipolar control (BPC) of a modular battery and compares it with previously proposed unipolar control (UPC) mode in terms of thermal/SOC balancing performance and energy efficiency. The BPC needs four-quadrant operation of a full-bridge (FB) converter using bipolar pulsewidth modulation (PWM) inside each module, whereas UPC only needs a half-bridge (HB) converter with unipolar PWM. The BPC, unlike UPC, enables charging of some cells while discharging others. An averaged state-space electrothermal battery model is derived for a convex formulation of the balancing control problem. The control problem is formulated on a constrained linear quadratic (LQ) form and solved in a model predictive control (MPC) framework using one-step-ahead prediction. The simulation results show that BPC, without even requiring load current variations, gives better balancing performance than UPC but at the cost of reduced efficiency. The UPC requires at least current direction reversal for acceptable balancing performance. In short, the UPC is a more cost- and energy-efficient solution for electric vehicle (EV) and plug-in hybrid EV applications, whereas the BPC can be beneficial in applications involving load cycles with high current pulses of long duration.

A study on specific heat capacities of Li-ion cell components and their influence on thermal management

Abstract Thermal models of Li-ion cells on various geometrical scales and with various complexity have been developed in the past to account for the temperature dependent behaviour of Li-ion cells. These models require accurate data on thermal material properties to offer reliable validation and interpretation of the results. In this context a thorough study on the specific heat capacities of Li-ion cells starting from raw materials and electrode coatings to representative unit cells of jelly rolls/electrode stacks with lumped values was conducted. The specific heat capacity is reported as a function of temperature and state of charge (SOC). Seven Li-ion cells from different manufactures with different cell chemistry, application and design were considered and generally applicable correlations were developed. A 2D thermal model of an automotive Li-ion cell for plug-in hybrid electric vehicle (PHEV) application illustrates the influence of specific heat capacity on the effectivity of cooling concepts and the temperature development of Li-ion cells.

Lifetime Prediction of Massively Parallelized Lithium-Ion Batteries

Batteries need to pass several stress tests before deployment. These tests can range in complexity from seconds (short-time electrochemical impedance spectroscopy) to several years during life time estimation tests. Several publications have shown that at the end of life, the behavior of specimens can drastically differ, even though initial measurements indicate identical behavior [1,2]. The effect of highly volatile ageing in specimens can be attributed to mainly two factors, discrepancies during production batches [3] and thermal inhomogeneities [4]. Cooling and pack design can be optimized to minimize the thermal effects on ageing. However, it is still unclear to what extent the risk of a single faulty battery cell, which might impact the whole pack performance, can be minimized. Therefore, it is useful to design tests that have a statistical significance to estimate and reduce the risk of faulty battery packs. One way to design a test setup is to create a serial connection of batteries and measure voltage over every specimen and the current in the string. This method has decisive drawbacks. Depending on the number of test subjects, the total voltage of the string might exceed extra-low voltage regulation and therefore only specialized personnel are allowed to handle the test equipment. Another drawback is that the weakest battery limits the total amount of energy that can be used. The discharge voltage limit of the weakest battery will be reached faster and therefore the measurement has to be stopped. Thus, it leads to inhomogeneities in the depth of discharge. To overcome these disadvantages the specimens can be connected in parallel, forcing an equal voltage and a homogeneous depth of discharge. This setup is especially challenging as the current of every parallel path has to be measured separately. To research the influence on the specimen and the accuracy of the measurement, the project openBat has been established. The project openBat examines the effect of a mass parallelization on the failure rate of lithium-ion-battery-packs and creates a statistical lifetime model. Overall, more than 600 specimens of the type NCR 18650B of Panasonic with a rated capacity of 3.20 Ah will be measured over the lifetime of the cells. The operating temperature and the cycle depth will be varied. The specimens are connected in smaller packages (30 specimens), each with its own synchronous current and voltage measurement. Each channel can be sampled at a maximum sampling rate of 1 kHz with 24 bit resolution. This enables the calculation of the impedance during the different stages of the life cycle without changing the test setup. Likewise, it is possible to measure the capacity of every single cell and the total pack. The impedance and capacity allow modeling the terminal voltage behavior and the heat generated by the batteries. To minimize temperature differences, all cells are closely fitted into an aluminum block and therefore allow temperature to be distributed evenly. The aluminum block is placed inside a temperature chamber and is actively cooled by a special cooling system. The submission will cover the hardware setup and preliminary measurement results. References x [1] Thorsten Baumhöfer, Manuel Brühl, Susanne Rothgang, and Dirk Uwe Sauer, "Production caused variation in capacity aging trend and correlation to initial cell performance," Journal of Power Sources, vol. Volume 247, pp. 332-338, February 2014. [2] Matthieu Dubarry, Cyril Truchot et all., "Evaluation of commercial lithium-ion cells based on composite positive electrode for plug-in hybrid electric vehicle applications," Journal of Power Sources, vol. 196, no. 23, pp. 10336 – 10343, 2011. [3] Shriram Santhanagopalan and Ralph E. White, "Quantifying cell-to-cell variations in lithium ion batteries," International Journal of Electrochemistry, 2012. [4] Sebastian Paul, Christian Diegelmann, Herbert Kabz, and Werner Tillmetz, "Analysis of ageing inhomogeneities in lithium-ion battery systems," Journal of Power Sources, 2013. x Figure 1

New Integrated Multilevel Converter for Switched Reluctance Motor Drives in Plug-in Hybrid Electric Vehicles With Flexible Energy Conversion

This paper presents an integrated multilevel converter of switched reluctance motors (SRMs) fed by a modular front-end circuit for plug-in hybrid electric vehicle (PHEV) applications. Several operating modes can be achieved by changing the on-off states of the switches in the front-end circuit. In generator driving mode, the battery bank is employed to elevate the phase voltage for fast excitation and demagnetization. In battery driving mode, the converter is reconfigured as a four-level converter, and the capacitor is used as an additional charge capacitor to produce multilevel voltage outputs, which enhances the torque capability. The operating modes of the proposed drive are explained and the phase current and voltage are analyzed in details. The battery charging is naturally achieved by the demagnetization current in motoring mode and by the regenerative current in braking mode. Moreover, the battery can be charged by the external AC source or generator through the proposed converter when the vehicle is in standstill condition. The SRM-based PHEV can operate at different speeds by coordinating the power flow between the generator and battery. Simulation in MATLAB/Simulink and experiments on a three-phase 12/8 SRM confirm the effectiveness of the proposed converter topology.

A Brushless Double Mechanical Port Permanent Magnet Motor for Plug-In HEVs

This paper proposes a new brushless double mechanical port flux-switching permanent magnet (BDMP-FSPM) motor for plug-in hybrid electric vehicles applications. The key is to highly integrate two rotors and single stator into one motor frame, which is based on the concept of incorporating the double-rotor motor into a stator-permanent-magnet motor. In addition, by combining the non-contact magnetic planetary gear with the proposed motor, the new resulting electric continuous variable transmission system can not only realize the required speed and torque transmission, but also manage the power split and combination in various driving cycles. The electromagnetic performances of the proposed motor are analyzed by using the finite-element method, such as magnetic field distribution, coupled back-EMF, torque performances, torque-speed curves, and power-speed curves. Experimental results of the BDMP-FSPM prototype are also given to verify the validity.

An Experimental Investigation - How Much Influence Has the Electrolyte Composition on the Ageing Behaviour of Separators in Lithium-Ion Cells?

The most widely used liquid non-aqueous electrolytes for lithium-ion cells used in HEV (hybrid electric vehicle), PHEV (plug-in-hybrid electric vehicle) and EV (electric vehicle) applications consist of LiPF6 dissolved in carbonates (e.g. EC, DMC and DEC). These electrolytes undergo a variety of hydrolysis and thermal aging mechanisms [1]. Ongoing decomposition reactions lead to further impurities inside the lithium-ion cell which are not well-known. The separator is a second critical component in lithium-ion cells, which can be classified into three groups according to structure and composition: microporous polymer membranes, non-woven fabric mats and inorganic composite membranes [2]. In this contribution, the decomposition reaction mechanisms are evaluated under a number of different thermal conditions for various commercial electrolytes from automotive lithium-ion cells. Furthermore, their influences on the ageing behaviour of different separator types are investigated. Details of the experimental procedure, analytical methods (NMR, GC-MS, SEM/EDX) and first results will be presented. Finally, we will give an overview of our mechanistic interpretation.

Evaluation of Commercial Lithium-Ion Cells Based on Composite Positive Electrode for Plug-In Hybrid Electric Vehicle (PHEV) Applications: IV. Over-Discharge Phenomena

Lithium-ion cells with composite positive electrodes are attractive and promising for EV and PHEV applications. For powertrain applications, the battery packs are required to have multiple-cell configurations, where some battery management is needed to protect cells from experiencing overcharging and overdischarging. Here, we show how to analyze the effect of slight overdischarge in a graphite || {LixMn1/3Ni1/3Co1/3O2 + LixMn2O4} cell, when it was overdischarged to 2.0 V. We found a peculiar behavior at low voltages that is imputable to the composite nature of the positive electrode. Under certain circumstances, due to differences in kinetic limitations in each of the constituents in the composite electrode, although LixMn1/3Ni1/3Co1/3O2 were discharged normally, LixMn2O4 could be overdischarged to Li2Mn2O4 and cause capacity fade.

Optimal economy-based battery degradation management dynamics for fuel-cell plug-in hybrid electric vehicles

This work analyses the economical dynamics of an optimized battery degradation management strategy intended for plug-in hybrid electric vehicles (PHEVs) with consideration given to low-cost technologies, such as lead-acid batteries. The optimal management algorithm described herein is based on discrete dynamic programming theory (DDP) and was designed for the purpose of PHEV battery degradation management; its operation relies on simulation models using data obtained experimentally on a physical PHEV platform. These tools are first used to define an optimal management strategy according to the economical weights of PHEV battery degradation and the secondary energy carriers spent to manage its deleterious effects. We then conduct a sensitivity study of the proposed optimization process to the fluctuating economic parameters associated with the fuel and energy costs involved in the degradation management process. Results demonstrate the influence of each parameter on the process's response, including daily total operating costs and expected battery lifetime, as well as establish boundaries for useful application of the method; in addition, they provide a case for the relevance of inexpensive battery technologies, such as lead-acid batteries, for economy-centric PHEV applications where battery degradation is a major concern.

Rule-Based Control Strategy With Novel Parameters Optimization Using NSGA-II for Power-Split PHEV Operation Cost Minimization

One of the major considerations in the automotive industry is the reduction of hybrid electric vehicle fuel consumption and operation cost. This paper is the first to use the nondominated sorting genetic algorithm-II (NSGA-II) for power-split plug-in hybrid electric vehicle (PHEV) applications. The NSGA-II, one of the most efficient multiobjective genetic algorithms (MOGAs), simultaneously optimized operation cost, including gasoline and electricity consumption. The Pareto optimal solutions are discussed for the parameter calibrations of the rule-based control strategy as a useful guide in PHEV development, particularly in the earlier phases. The optimized operation cost at the different power-split device (PSD) gear ratios is used to determine the ideal PSD gear ratio to further minimize the operation cost. To validate the proposed strategy, dynamic PSD and powertrain models of PHEV are developed in the numerical analysis. The two typically different driving cycles, namely, the Urban Dynamometer Driving Schedule (UDDS) and the Highway Fuel Economic Drive Schedule (HWFET), with different numbers of driving cycles, are used for control strategy optimization.

Comparison of Three Electrochemical Energy Buffers Applied to a Hybrid Bus Powertrain With Simultaneous Optimal Sizing and Energy Management

This paper comparatively examines three different electrochemical energy storage systems (ESSs), i.e., a Li-ion battery pack, a supercapacitor pack, and a dual buffer, for a hybrid bus powertrain operated in Gothenburg, Sweden. Existing studies focus on comparing these ESSs, in terms of either general attributes (e.g., energy density and power density) or their implications to the fuel economy of hybrid vehicles with a heuristic/nonoptimal ESS size and power management strategy. This paper adds four original contributions to the related literature. First, the three ESSs are compared in a framework of simultaneous optimal ESS sizing and energy management, where the ESSs can serve the powertrain in the most cost-effective manner. Second, convex optimization is used to implement the framework, which allows the hybrid powertrain designers/integrators to rapidly and optimally perform integrated ESS selection, sizing, and power management. Third, both hybrid electric vehicle (HEV) and plug-in HEV (PHEV) scenarios for the powertrain are considered, in order to systematically examine how different the ESS requirements are for HEV and PHEV applications. Finally, a sensitivity analysis is carried out to evaluate how price variations of the onboard energy carriers affect the results and conclusions.