Education on Vehicle Electrification:Battery Systems, Fuel Cells, and Hydrogen

(Special Session: New Vehicle Education Programs)

Scott J. Moura, Jason B. Siegel, Donald J. Siegel, Hosam K. Fathy, Anna G. StefanopoulouDepartment of Mechanical Engineering

University of Michigan, Ann ArborAnn Arbor, Michigan USA 48109-2125

Email: {sjmoura,siegeljb,djsiege,hfathy,annastef}@umich.edu

Abstract—A new education program is under developmentat the University of Michigan to educate engineers in thefundamentals of electrochemical propulsion systems for vehicleelectrification. This paper describes two courses that are part ofthis larger program: “Battery Systems & Control” and “FuelCell Vehicles & Hydrogen Infrastructure.” These courses seek toeducate undergraduate, graduate, and professional (i.e. distancelearning) students in the fundamentals of modeling, control, anddesign of batteries, fuel cells, and hydrogen storage systems.These courses apply a systems-level approach to electrochemicalpropulsion systems with particular emphasis placed on modeling,design, and control issues encountered in practice. In the batterycourse students are introduced to electrochemical-based models,model reduction techniques, simulation procedures, and real-life control problems such as state-of-charge estimation. Topicscovered in the fuel cell course include: PEM fuel cell operatingfundamentals, hydrogen production pathways, hydrogen storage,and well-to-wheels CO2 and efficiency analyses. This paperbroadly outlines the curriculum for both courses using specificassignments as illustrative examples of the program’s content.Together these two courses provide fundamental skills directed atdeveloping engineering leadership and knowledge in sustainabletransportation systems.

I. INTRODUCTION

This paper describes two courses under development atthe University of Michigan, Ann Arbor, focusing on bat-tery systems and fuel cells-hydrogen storage for automotiveapplications. The objective is to provide to undergraduate,graduate, and professional students the technical skills nec-essary for developing a new generation of green vehicletechnology. Emphasis is placed upon systems-level modeling,design, and control, oriented towards solving issues relevantfor new vehicle development. The battery course specificallyfocuses on system-level modeling, model order reduction fromelectrochemical models to surrogate models for load control,estimation, on-board identification and diagnostics for lithium-ion batteries. The hydrogen and fuel cell course focuses onsystem-level modeling and control issues of polymer elec-trolyte membrane (PEM) fuel cells, materials and systems foron-board hydrogen storage, hydrogen production, and well-to-wheels (WTW) analyses of CO2 emissions and efficiency.Together these courses constitute a comprehensive curriculumon vehicle electrification systems aimed toward invigoratingand transforming the automotive industry’s workforce.

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The performance characteristics of batteries and fuel cellscan be placed in context with those of other energy storage &conversion devices by their specific power and energy density,as demonstrated by the Ragone plot in Fig. 1. The slopedlines indicate the relative time required to extract and/or storeenergy from the device. This figure demonstrates that bothbatteries and fuel cells have high theoretical specific energy,but lower power density when compared to conventionalinternal combustion (IC) engines. For this reason, batteriesand fuel cells are sometimes combined with high specificpower devices to form “hybrid” vehicle propulsion systemsthat achieve the desirable power characteristics. Whether usedin solitary or hybrid applications, there exists a plethora ofsystems-level integration issues for both battery and fuel cellsystems, upon which modeling, design, and control play keyroles. Given their novelty and potential for reducing the carbonintensity of the transportation sector [2], there is a great needfor courses that introduce the fundamental features of thesesystems as well as strategies for their integration.

An outline of topics for both courses is provided in Table

TABLE I: Outline of Course Topics & Winter 2010 Enrollment

Battery Systems & ControlWinter 2010 Enrollment: 59 (including 5 distance learning students)• Overview of chemistries, technologies, and challenges• Equivalent circuit and electrochemical models• Model reduction techniques and applications• SOC estimation & HEV power management• Battery health degradation modeling and control• Battery pack management systems• Projects on topics not covered in class

Fuel Cell Vehicles & Hydrogen InfrastructureWinter 2010 Enrollment: 47 (including 4 distance learning students)• Fuel cell vehicle and hydrogen state of art and challenges• PEM fuel cell modeling• The air, thermal, and water management problems• Hydrogen production technologies• Hydrogen distribution infrastructure• Hydrogen storage: materials and systems• Life-cycle and Wheel-to-Wells Analysis

I, along with student enrollment numbers for the first offeringin the Winter 2010 term. The pedagogical approach in bothcourses is to (1) examine high-level technical challenges andapplications, (2) focus in on fundamental tools and theorynecessary to solve specific problems, and (3) allow studentsto exercise these tools on practical issues through applicationdriven homework assignments and projects.

The outline of this paper is as follows: In Section II wediscuss the methodology behind a systems-level modeling ap-proach. Specifically, this section discusses the construction offirst-principle models, model reduction, and finally simulationtools and techniques. In Section III we introduce estima-tion and control problems relevant for vehicular applications.Examples discussed from the battery course include state-of-charge estimation and charge balancing control. FinallySection IV summarizes the course objectives and plannedimprovements.

II. SYSTEM-LEVEL MODELING,REDUCTION, AND SIMULATION

Mathematical models of electrochemical propulsion devicesspan a spectrum - from high-fidelity physics-based modelsto simplified phenomenological models. The appropriate bal-ance between model accuracy and simplicity depends on thespecific modeling objective. For example, if one desires todesign improved material structural properties for a batteryor fuel cell electrode, it may be important to account forparticle-level mechanical stresses and electrochemical kinetics.However, if the aim is to analyze life cycle carbon footprints,then a relatively simple phenomenological model may suffice.The main focus of these courses falls near the middle of thespectrum - a systems-level model appropriate for powertrainintegration, design, and control. As such, both courses applythe following pedagogical modeling approach: First, constructa high fidelity physics-based model suitable for validation or

high accuracy simulation purposes. Then, depending on themodeling objective, utilize model reduction and simulationtechniques to achieve the desired tradeoff between modelaccuracy and computational complexity. The subsequent threesubsections describe how this process is applied within thecontext of both propulsion systems, utilizing specific examplesfrom the courses.

A. Model Development

1) Electrochemical-based Lithium-ion Battery Models: Thebattery systems and control course presents students withphysical models of lithium-ion batteries based on electrochem-istry principles [3]. These models are useful for vehicularapplications because they explicitly predict critical systemstates (e.g. cell state-of-charge) and physical operating con-straints (e.g. charge/discharge limits). These characteristicsare important when considering the highly transient loadingconditions typically experienced in automotive applications. Inparticular, the students are introduced to the electrochemicalmodel of lithium-ion cells originally developed by Doyle,Fuller, and Newman [4], [5]. Due to the importance of batterylifetime, we also review degradation mechanisms. Throughoutthis discussion we emphasize fundamental principles, sincethe students generally do not have extensive background inelectrochemistry or materials science.

The model by Doyle, Fuller, and Newman, describedschematically in Fig. 2, captures the spatiotemporal evolutionof phenomena such as diffusion dynamics, reaction kinetics,and electric potential. The model is divided into three sections:anode, separator, and cathode. Each electrode contains anelectrolyte solution, represented by the x-axis in Fig. 2. Theanode also contains a solid material (typically carbon, graphite,or coke). The cathode material structure varies across man-ufacturers but the most common chemistries include cobalt-oxide (LiCoO2), manganese (LiMn2O4), polymer (Co/Mn),and iron-phosphate (LiFePO4). The solid materials in eachelectrode are modeled by porous spherical particles whichlithium-ions can penetrate during the charge and dischargeprocesses.

2) Polymer Electrolyte Membrane Fuel Cells (PEMFCs)and Hydrogen Storage: During operation of PEM fuel cells,hydrogen supplied to the anode channels diffuses though theGas Diffusion Layer (GDL) to the catalyst layer (CL), whereit disassociates into protons and electrons. The protons aretransported though the membrane to the cathode side, whilethe electrons travel back though the carbon structure of theGDL and through an external circuit, providing useful work.The protons crossing the membrane combine with oxygen andelectrons to form heat and liquid water. The liquid water,produced in the cathode catalyst layer, must be effectivelyremoved or else it can cover the catalyst sites preventing thereaction. On the other hand, over drying of the membrane isundesirable as it increases protonic resistance which yieldslower cell efficiency. Consequently, the water managementissue is a critical problem discussed in the course.

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The PDE modeling framework, and the equations whichdescribe the operation of a PEM fuel cell are very similarto the battery system. The system performance is limited byreactant (gas) transport, specifically the diffusion of oxygenfrom the channel though the GDL to the catalyst sites. Theterminal voltage is calculated from the theoretical open circuitvoltage minus the anode and cathode over-potentials, whichare also calculated using a Butler-Volmer equation, and ohmiclosses. However, unlike the battery system where all of thereactants are contained within the device, the problem ofreactant delivery and the removal of product water (a two-phase system with both liquid and vapor) compound thedifficulty of controlling these devices. Specific examples fromresearch on “control of fuel cell breathing” for cathode airflow are used to elucidate the challenges of supplying reactantsduring step changes of load current in power-autonomous fuelcells when the air compressor is driven directly by the fuelcell [6].

Widespread adoption of hydrogen as a vehicular fuel de-pends critically upon the ability to store hydrogen on-boardat high volumetric and gravimetric densities, as well as onthe ability to extract it/refuel at sufficiently rapid rates [7].As current storage methods based on physical means - high-pressure gas or (cryogenic) liquefaction - are unlikely tosatisfy targets for performance and cost, in this course wedescribe the potential for using chemical means to storehydrogen in condensed phases. At present, no known materialexhibits a combination of properties that would enable high-volume automotive applications. Thus new materials withimproved performance, or new approaches to the synthesisand/or processing of existing materials, are highly desirable[8]–[10]. Starting from the general requirements of a fuel cellvehicle, the course illustrates how these requirements translateinto desired characteristics for the hydrogen storage material.Key amongst these are: (a) high gravimetric and volumetrichydrogen density, (b) thermodynamics that allow for reversiblehydrogen uptake/release under near-ambient conditions, and(c) fast reaction kinetics. Regarding thermodynamics, Fig. 3

Fig. 3: Equilibrium H2 desorption pressure (P) for a generichydrogen storage material as a function of desorption enthalpy(∆H) for various choices of desorption entropy (∆S) at T =80◦C. Adapted from Ref. [7]. The minimum pressure for thefuel cell inlet is taken to be 3 bar; the refueling pressure isassumed to be 350 bar.

illustrates how the operating conditions of a fuel cell (mini-mum 3 bar inlet H2 pressure, 80 C waste heat) in conjunctionwith the properties of the forecourt (350 bar H2 refuelingpressure) determine an optimal range of desorption enthalpy(approximately 20-50 kJ/mol H2) for a hypothetical hydrogenstorage reaction.

To further illustrate desired attributes of the storage system,the four major classes of candidate storage materials - conven-tional metal hydrides, chemical hydrides, complex hydrides,and sorbent systems - are introduced and their respective per-formance and prospects for improvement in each of these areasis discussed. Finally, and although not specifically related tovehicle systems and controls, we discuss two additional areasof relevance to FC vehicles; (i) aspects of a possible hydrogenfuel infrastructure, including advantages and disadvantagesassociated with various approaches to hydrogen productionand distribution [11], and (ii) well-to-wheels analyses of theCO2 emissions, fossil fuel consumption, and energy efficiencyof FC and other vehicle technologies [2]. An example of thecourse content focused on the latter topic is illustrated usinga WTW study performed by Argonne National Laboratories,Fig. 4. This study [2] found that electric vehicles can leadto a reduction in emissions and petroleum use compared toconventional gasoline vehicles. However, the magnitude of thatreduction depends sensitively upon the production pathway forelectricity or hydrogen.

B. Model Reduction

The high-fidelity physical models of lithium-ion batterycells and PEM fuel cells discussed above are well-suitedtoward high accuracy simulation and validation. However, theygenerally are not implementable on a real-time on-board elec-tronic control unit for automotive applications. As such, weintroduce the students to approximation methods that preserve

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FIGURE 24 Summary of WTW Petroleum Energy Use and GHG Emissions for Combined

CD and CS Operations Relative to Baseline Gasoline ICEV

The isolated markers in Figure 24 represent the regular HEVs (AER 0). The positions of these isolated markers relative to the baseline conventional gasoline ICEV marker indicate the reduction in petroleum energy and GHG emissions due to the (grid-independent) hybridization technology (CS operation) of these vehicles. In addition, the position of these markers relative to the PHEV markers represents the change in relative petroleum energy use and GHG emissions because of the partial displacement of VMT from the CS operation of the regular HEV to the CD operation of the PHEV. The displaced CS VMT in this case is represented by the UF (23% for PHEV 10, and 63% for PHEV 40). For a carbon-intensive generation mix, such as that of Illinois, Figure 24 shows that PHEVs produce more WTW GHG emissions compared with regular HEVs for most fuels. Such implication becomes more pronounced as the AER increases from 10 mi to 40 mi, especially for E85 and hydrogen fuels, which highlights the significance of the electricity generation mix for charging PHEVs.

Fig. 4: Comparison of well-to-wheels petroleum energy use and greenhouse gas emissions for gasoline (GV), hybrid electric(HEV), and plug-in hybrid electric [PHEV, with all electric range (AER) of 10 or 40 mi] vehicles as a function of fuel type orelectricity source. Data are normalized relative to the performance of a GV at coordinates (1.0, 1.0). Adapted from Ref. [2].

important system dynamics while eliminating unnecessarycomplexity within the context of the control objective. Thisprocess, known as model reduction, is fundamental to almostall practical system-level modeling and control problems -particularly in automotive applications.

Several battery model reduction techniques are discussed inthe class, including the electrode average model [12], Padeapproximations, and constraint linearization [13]. For severalassignments we consider the following example: Suppose ourbattery system does not experience extreme charge/dischargeloads such that the concentration distributions along the lengthof the electrodes and separator remain fairly constant. Inthis case, it may be reasonable to approximate the spatialdistributions by their average values. This produces the so-called electrode average model shown schematically in Fig.5. The reduced model equations that result after applying thisconcept produce a state-space system with linear dynamics and

a nonlinear output equation. The linear dynamics correspondto spherical diffusion in the solid material of the electrodes.The output equation computes cell voltage, which is nonlineardue to the thermodynamic and kinetic properties of the battery.The structure of this reduced model is extremely appealingfor control applications, rendering it amenable to a vast rangeof control and estimator design techniques. In Section III wedescribe how students utilize this model to design a Kalmanfilter for SOC estimation.

C. Simulation Tools & TechniquesGiven the mathematical physics-based models for each

system, the next step for students is to develop simulationtechniques. Nonlinear partial differential-algebraic equationsystems, which characterize both battery and fuel cells, aretypically difficult to simulate numerically.

To give students some appreciation for these issues, weinstruct them to simulate a simple linear diffusion PDE us-

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ing several finite differencing methods: forward-differencesand Crank-Nicholson [14]. These two methods produce nu-merical simulations that are, respectively, conditionally-stableand unconditionally-stable. That is, the forward-differencesmethod requires a condition on the discrete simulation time-step to be satisfied in order to obtain physically meaningfulresults. The students discover that for discretizations of thespatial dimension typical for battery or fuel cell models, thetime step must be prohibitively small (on the order of 1µs).This motivates the use of more elegant finite differencingmethods, such as Crank-Nicholson, which are uncondition-ally stable. That is, they produce stable simulations for anygiven time step, although the simulations themselves are notnecessarily accurate for large time steps.

Through this focused exercise, students learn about thetechniques associated with simulating partial differential equa-tion systems. Once mastering this basic skill, students havethe foundational knowledge for simulating systems of PDE’srepresenting more complex electrochemical devices.

III. ESTIMATION AND CONTROL PROBLEMS

Following the model development, reduction, and simu-lation of the battery and fuel cell system models, we turnthe students’ attention toward practical estimation and controlproblems. The scope of these problems involve systems-levelintegration issues often encountered in vehicle applications.Examples from the battery course include SOC estimation[12], HEV power management [15], charge balancing in bat-tery packs [16], [17], and PHEV charging pattern optimization[18]. Examples from the fuel cell course include air flow [19]and water management [20], [21]. Due to space constraints weonly discuss the battery SOC estimation and charge balancingproblems in detail here.

A. The Battery SOC Estimation Problem

In the battery course the students are instructed to solve themost prominent battery estimation problem - SOC estimation.In many battery powered systems (e.g. laptops, electronicportable devices, and electric vehicles) one typically desiresto know the battery SOC level, which represents the remain-ing available energy. Unfortunately, it is often impractical

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to implement sensors that directly measure the lithium-ionconcentration in the solid material of the electrodes. Wedo, however, typically have access to voltage and currentmeasurements. These measurements in combination with acontrol-oriented battery cell model allow us to dynamicallyestimate SOC [12]. A block diagram of the estimation schemeis provided in Fig. 6.

In this assignment the students apply a linearized versionof the electrode average model described in section II-B witha Kalman filter to estimate battery SOC. The students thenlearn how Kalman filters can be tuned to tradeoff sensor noisewith modeling errors by injecting Gaussian noise into themeasured signals and applying incorrect initial conditions tothe estimator. Consequently, the students learn about Kalmanfiltering theory while simultaneously solving a very practicalbattery systems problem using physical models developed inclass.

B. The Battery Charge Balancing Problem

A second battery systems and control problem relevantfor vehicle applications is charge balancing. This problem ismotivated by the fact that cells connected in series withinbattery packs may have unequal charge levels. This situation isproblematic because individual cells can be inadvertently over-charged or over-discharged because the battery managementsystem considers total battery pack voltage without knowledgeof individual cell voltage. The end result is accelerated batterypack degradation and possibly catastrophic thermal runaway.This situation can be mitigated via a charge balancing scheme.A survey of such schemes can be found in [22].

In this assignment the students design and simulate abattery management system that utilizes shunt resistors tobalance the voltage levels of two unbalanced cells connectedin series. A schematic of the balancing scheme is shown inFig. 7. The students are instructed to use their creativity todesign logic that compares the individual voltage levels toactuate the switches in a manner that equalizes cell voltage.Moreover, they are free to design the resistance value of theshunt resistors. They use simulation results and mathematical

Batt 1 Batt 2

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Fig. 7: Circuit diagram of shunt resistor equalization circuit.

arguments to analyze how the shunt resistor method suffersfrom an inherent tradeoff between equalization time and powerefficiency. Finally, they discover how voltage balancing doesnot necessarily balance SOC, motivating the application ofSOC balancing schemes [16].

IV. CONCLUSION

This paper describes newly developed courses in elec-trochemical vehicle propulsion systems at the University ofMichigan, Ann Arbor, focused on system-level modeling, de-sign, and control. The objective of these courses is to educatea new generation of engineers capable of developing advancedsustainable transportation systems. Specifically, the coursesfocus on system-level modeling, simulation, estimation, andcontrol issues in battery and hydrogen fuel cell poweredvehicles.

For the first offering of each course, topics were cov-ered in a conceptual manner. However, we recognize thatstudent engagement thrives on application case studies andhardware experiments. In future terms we will add laboratorycomponents to each course. This equipment will be sharedfor instruction across multiple courses and research acrossmultiple teams/departments, thus financially benefiting fromhigh-throughput. For education in the battery systems andcontrol course, the students will solve homework problemsvia analysis and simulation first, then apply their designs toa laboratory battery test system. We also plan to expand thetopics to include thermal modeling and control, capacity fademanagement, and vehicle/infrastructure integration issues. Forthe Hydrogen and Fuel Cells course, we envision includinga laboratory demonstration of hydrogen storage in solid statematerials and examples of prototype storage systems. Peda-gogically, these enhancements will marry conceptual analysiswith hardware implementation - effectively increasing theimpact and accessibility of each course. Through these effortswe anticipate a profound impact on job creation in sustainabletransportation systems through education.

ACKNOWLEDGMENT

This material is based upon work supported by the Depart-ment of Energy National Energy Technology Laboratory underAward Number DE-EE0002119. The project is a joint collab-oration between the University of Michigan-Ann Arbor, theUniversity of Michigan-Dearborn, and Kettering University.

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