Enhanced Plug-in Hybrid Electric Vehicles

Alan Millner, Nicholas Judson, Bobby Ren, Ellen Johnson, William Ross Massachusetts Institute of Technology Lincoln Laboratory. 244 Wood St. Lexington, MA 02420 {amillner, judson, bobby.ren, ejohnson, bross}@ll.mit.edu

Abstract—Plug-in hybrid electric vehicles (PHEVs) have By shifting our least efficient energy conversion step from the potential to reduce fossil fuel use, decrease pollution, inefficient small engines to central power plants, the total and allow renewable energy sources for transportation, but well to wheel efficiency of our transportation sector can be their lithium ion battery subsystems are presently too greatly improved. Also, use of electric power transmission expensive. Three enhancements to PHEVs are proposed and distribution allows the source of transport energy to be here that can improve the economics. First, the renewable sources, nuclear, or natural gas, with far greater incorporation of location information into the car’s energy long term supplies and lower carbon footprint. If half the management algorithm allows predictive control to reduce passenger vehicle fleet of the US were replaced by 100 mile fuel consumption through prior knowledge of the upcoming per gallon (mpg) plug-in hybrids, the petroleum use of the route and energy required. Second, the use of the vehicle US would be reduced by approximately the amount now battery while parked, offsetting the short peaks in imported from the Mideast. Our CO2 emissions would be commercial-scale facility electrical demand to reduce reduced by 0.5 billion tons per year, or 8%. Use of plug-in demand charges, can provide additional revenue to pay for hybrid electric vehicles (PHEVs) allows the limited use of the battery. Third, the battery cycle life must be maximized liquid fuels to extend range when that is needed for to avoid high replacement costs; a model of battery wear convenience, taking advantage of their very high energy out for lithium ion batteries is presented and is used to density, while addressing the need for fuel conservation confirm that the above strategies are compatible with long during the typical shorter commuting trips that dominate battery life. usage.

PHEVs are becoming available. Conversions such as the 1. BACKGROUND: A VISION FOR PHEVS A123 Systems, Inc. Hymotion L5 converted Toyota Prius hybrid have been sold in quantities of hundreds for several years now. The is due late The US energy economy suffers from the use of too much this year, and the Toyota Prius PHEV is scheduled for petroleum. This is a problem because the world’s oil release in 2011. Other sources are under development, reserves are in places far from our national borders and including some suitable for trucks and military vehicles. often governed by countries with different political agendas;

60% of the reserves are in the Mideast [1]. It is also a The problem holding back this technology now is the high problem because the long term supply of petroleum is cost of the battery subsystem. Lithium ion batteries, the limited, with discoveries declining since 1964 [2]. And, it is technology of choice today, are expensive and will probably a problem because our burning of this non-renewable remain so for some years to come. For example, the resource produces too much greenhouse gas, with 25% of aforementioned Toyota Prius conversion by A123 Systems CO production coming from the US, and 33% of US CO 2 2 in 2008 cost about $32,000: $22,000 for the hybrid car, and coming from oil. Transportation represents 28% of US $10,000 for the retrofit module with a 5 kWh battery pack. energy use and 70% of petroleum use [1]. Vehicles at this cost level can be leased for approximately

$400 per month. The larger the battery capacity, the more Power obtained from gasoline burned in automobile engines expensive the PHEV becomes. is extremely inefficient, with an average final efficiency of only 15%, with the rest wasted in heat and drive train losses The solution envisioned here is to first make use of an [3]. By comparison, central electric power plants operate at efficient vehicle with the battery sized to address common an efficiency of 35% [1]. commuting distances electrically. Then, make best use of

intelligent controls to minimize fuel consumption by ___ making predictive use of knowledge of the route to be This work was sponsored by the United States Government traveled. Third, use the battery to provide grid regulation under Air Force contract FA8721-05-C-0002. Opinions, services through peak power shaving while parked at work, interpretations, conclusions, and recommendations are those a version of vehicle to grid (V2G) power transfer that makes of the authors and not necessarily endorsed by the United use of the economic relationship between a commuter and States Government. employer and that we call vehicle to building (V2B), generating revenue to offset the battery cost. And finally, make use of good battery life models to minimize degradation of the battery while it is used for both Gas Gas Trans- transportation and regulation. By enhancing the PHEV in Shaft Road these ways, the high initial cost of battery subsystems can Tank Engine mission be addressed and moderated. By allowing economies of Friction Electric scale to be reached through the manufacture of the large Generator Acceleration production quantities of PHEVs, this may bootstrap the Motor Elevation technology into a viable production range. Wind

Inverter Charger 2. PREDICTIVE CONTROL OF VEHICLE ENERGY

Battery The concept of improving fuel economy by foreknowledge of the route to be traveled, using global positioning satellite V2B (GPS) and other available sources of information, has been V2G considered for some years now [4, 5]. The creation of Utility Charger simple control algorithms making use of specific information for a parallel or series-parallel hybrid vehicle Figure 1. Vehicle energy model; each boxed element has an has not been clear. Presented here is an approach that makes efficiency dependent on energy flow through that element. use of at least the distance to be traveled, and potentially the Energy flow directions are indicated by arrows and external elevation changes to be encountered, speed changes sources of energy and driving conditions that affect energy including expected traffic congestion, road surfaces, and expenditure are indicated. other factors affecting dynamic vehicle power demand, to predict the requirements on the vehicle power plant over its A simple power flow model of a PHEV vehicle was created trip, and schedule the use of electrical or liquid fuel energy using MATLAB [7] with vehicle weight, rolling resistance, to optimize engine efficiency and minimize fuel use. and aerodynamic parameters modeled on the 2010 Toyota Prius. This included a model of each major component The present state of the art is to operate a PHEV with as (Figure 1), with energy efficiency as a function of power much energy as possible coming from the battery until it level through that component. A state diagram control reaches a low state of charge [6]. Then energy is obtained strategy was implemented for this vehicle diagram (Figure from the liquid fuel engine to sustain this minimum battery 2), in which the state variables are the power required of the charge for the rest of the trip. The problem with this strategy system at that time and the state of charge (SOC) of the is that over that last part of the trip, the engine is often battery. required to operate at a power level that is not its optimum operating point. If more battery energy is saved until later in the trip, however, this optimization can be extended and fuel Full saved. Mech- anical Braking To test this concept, a model was needed of the vehicle, the Max Variable Electric Maximum Electric Max vehicle energy control system, and the driving cycle or route Only + Variable Gas Electric including speed vs. time. This allows evaluation of + predictive control strategies and comparison with Max Gas conventional strategies, to determine quantitative benefits in Target Optimum terms of improved fuel consumption. Regen Variable Electric Gas Charging + Optimum Gas Battery SOC Charging Min

Variable Gas Only Maximum Gas Charging Only Empty

Max Braking Zero Power Max Electric Max Electric Max Electric Gas Optimum + Max GasMax Demand + Gas Optimum Power Demand by Car

Figure 2. Vehicle controller state machine; states are dependent on power demand and battery SOC.

As part of this control strategy, there is a parameter representing the target SOC of the battery. If this is taken to 3. VEHICLE TO BUILDING be the minimum SOC, then this strategy reduces to the conventional one of charge depletion followed by charge sustaining mode [6]. However, if this parameter is allowed Electric power customers with high power demand service, to vary over the trip, gradually reducing and reaching the such as large commercial and institutional ones, in addition minimum only at the end of the trip, then a more flexible to charges per kWh as residential customers are accustomed strategy emerges. to, also pay demand charges for the maximum number of kilowatts drawn during the billing period. These demand A comparison of control strategies was done for the charges generally start for customers exceeding 100-500 kW modeled vehicle with a 5 kWh battery capacity (the same as of peak power demand, depending on the utility provider. the A123 Systems, Inc. Hymotion L5 PHEV conversion) Often these charges are then the largest portion of the bill. over a route made up of three US06 driving cycles [8], to For MIT Lincoln Laboratory in the Boston area, the demand make a 24 mile trip typical of the length of daily commute charge is most of the electric bill. of US drivers. The US06 driving cycle is one of the published test cycles by the US Environmental Protection If electric vehicles are used in V2G mode, they can level the Agency and is the most aggressive available standard test peaks in demand and reduce these charges. As commuters cycle, although it does not capture the full range of driving will be at work during peak demand hours, and since styles of all US drivers [9]. The conventional control employees have a ready means of exchanging money with strategy resulted in a trip averaging 66 mpg, whereas the their employer, this is a compelling model for realizing the same vehicle parameters simulated using a gradual specific mode of V2G that we refer to as V2B. This is also a depletion resulted in a trip of 71 mpg (Figure 3). For trips of way of aggregating the potentially many small utility this length and similar parameters, the fuel savings using interfaces of PHEV’s. Looking at the electrical usage of this simple control improvement, knowing the length of the MIT Lincoln Laboratory in 15 minute power demand trip, was between 7 and 10%. increments during the month of July 2008 (the time scale over which demand charges are calculated in this case) there were three narrow peaks well above the power drawn for the 1 rest of the days (Figure 4). Baseline night load in July was about 8 MW.

12

0.7 Gradual Depletion $15 - $20 / kW / month SOC 11 0.4 Power Demand (MW) Conventional Control 0.1 0 600 1200 1800 10 Time (seconds) 12AM 6AM12PM 6PM 12AM Time of Day Figure 3. Vehicle control strategies with and without knowledge of trip length: battery SOC vs. time. Figure 4. Electric power demand at MIT Lincoln Laboratory for days in July 2008. Each day is shown as a Use of more information about the trip in advance, available different series of 15 minute power consumption points (the at the vehicle via GPS, the web, real-time traffic updates, or graph is truncated below demands of 10 MW). The vehicle to vehicle communication, might include elevation difference in power demand for three peaks that could be changes, speed variation over the trip, traffic patterns, road shaved with a V2B approach is shown. surfaces and conditions, weather, air temperature, and individual driver driving habits. It remains to be seen which These peaks are due to heating, ventilation, and air of these are worthwhile to include in the energy conditioning system transients, and are typical for many management algorithms. months of the year. Their duration of fewer than 30 minutes is a good match to the capabilities of PHEV batteries. As demand charges in the summer and winter are on the order control safe charging. This charger can serve as a building of $20 and $14 per kW respectively, reduction in these control interface to the vehicle and request V2B services peaks offers significant savings. Initial calculations showed when it senses the building demand is rising. that if a V2B system could identify and reduce these peaks in real-time, the resulting savings were over $100 per month The algorithm for controlling such a charger would make per car. This could go far to offset the high cost of the use of rapidly sampled (1 or 5 minute) building demand. battery subsystem in the vehicle. Given the building load, the number of cars, the available energy storage and V2B power level per car, there are two Subsequent analyses varying the number of vehicles parameters to adjust. ΔP represents the rate of change of available for V2B, the power capability of their bi- building power demand representing a peak worth leveling. directional chargers, and the size of their batteries led to the PTHRESHOLD represents the difference in power level below the emergence of several patterns (Figure 5). current monthly maximum below which peaks will be ignored. The algorithm would turn on the V2B when the building demand is rapidly ramping up (successive samples 600 13.3kWh battery, 3C discharge rate (40kW charger) of demand differ by more than ΔP), and is near the 5kWh battery, 4C rate (20kW charger) 13.3kWh battery, 1.13C (15kW charger) maximum power demand level to date in the billing period

5kWh battery, 3C (15kW charger) (demand greater than maximum - PTHRESHOLD). The algorithm must also turn off the peak shaving pulses if they continue 400 to the maximum time (Pulse # •0) or if the vehicles are below the desired depth of discharge (Energy •0)(Figure 6).

Peak power level: Start peak shave V2B 200 P > max-PTHRESHOLD AND ramp rate: pulse,

Monthly Savings ($) Test: power, Change in power > ΔP Pulse # = power ramp maximum Read in rate next meter 0 data Continue... Not pulsing Otherwise 0 51510 20 not pulsing Car Number Time t Figure 5. V2B cost savings for analysis of all peaks at MIT Power p Lincoln Laboratory during 2009, a cooler than normal year. The maximum possible savings ($25,068) can be divided Peak shaving Cont. peak pulse shave pulse, among different numbers of cars, depending on battery size Pulse # > 0 AND P > max-PTHRESHOLD Decrement and discharge rate. Pulse # Test: power, Pulse #, Each billing period was analyzed and all peaks in power Energy demand that lasted <45 minutes were reduced to the non- peak maximum power draw in that billing period. The Pulse # == 0 OR number of cars, the size of their batteries, and the rate of Stop P < max-PTHRESHOLD OR pulsing discharge of those batteries were varied to calculate cost Energy <=0 savings per additional car added to the system. It is clear that as more vehicles are added, the incremental value of Figure 6. Algorithm for peak selection for V2B peak each subsequent vehicle goes down as the peaks requiring shaving. the fewest cars have already been addressed. From this analysis, approximately 150 kW of chargers and 50 kWh of The algorithm was implemented in MATLAB [7] and then car batteries are good numbers. This would be 10 cars at applied to data on power consumption from the main power 5 kWh and 15 kW each, or could be divided among more meter at MIT Lincoln Laboratory for the first five months of cars with smaller depth of discharge and smaller chargers. 2010. The performance of the algorithm was tested by Δ changing the values of the parameters of P, PTHRESHOLD, and One challenge is that bidirection chargers appropriate for a 3 Pulse #. The results for a day in May 2010 are shown in phase power interface in the 10 to 30 kW range do not at Figure 7. The algorithm was optimized with a total of 20 present exist as commercial products, but it is well within cars having 9 kWh batteries discharged to up to 80% depth technical possibility. It could be beneficial to have the of discharge (DOD) per peak shaved. The algorithm chargers in the building rather to avoid the weight penalty in required an average of 7 peak shaving pulses per month per the vehicle. The charger might have a DC interface to the car of 15 kW for 20 minutes. This provided 300 kW of peak vehicle and allow the vehicle battery management system to power capacity; for these months in 2010 this produced a mean value of peak shaving per month of $3160 total or convenience would probably dictate more like an 80% DOD $158 per car. to keep this from reducing battery life significantly more than the pure driving cycle effect. It was noted that 2009, an unusually cool summer, worked well with lower values of 13 Actual maximum Δ Shaved maximum P. These parameters will need to be adjusted to the particular building and climate for best results.

Power Demand 4. BATTERY MODELING

12 In order to assess the total value of using a PHEV battery to reduce peak power loads, it is important to correctly evaluate the added cost of cycling the battery in this way. Power Demand (MW) For this, as well as to calculate cost to the battery for general vehicle driving and storage conditions, a battery 11 Shaved power demand cycle life model is needed. Such a model is described in V2B Pulse [10] and is not repeated here. The development of a new Ramp(t) model is motivated by the observation that physical models Peak power(t) in the literature predict battery life to be linearly 6AM 12PM 6PM 12AM proportional to the amount of charge removed from it Time of Day (“constant throughput”) [11] and therefore to the depth of discharge. However, empirical data shows an exponential Figure 7. Peak shaving simulation for power demand at relationship of life to depth of discharge, not a linear MIT Lincoln Laboratory on a day in May 2010. Note when relationship. This has been approximated over limited power demand approaches the maximum, when ramps ranges of DOD by power law models, without a theoretical occur, and when the vehicle provides shaving pulses. justification [12]. However, a truly exponential model is a

better fit to data on modern lithium ion battery cells [13, 14] (Figures 9 and 10).

Rosenkranz original data 600 1000000 Rosenkranz linear model Peterson data 400 Peterson linear model Peterson data adjusted 100000 to 50% SOC 200

10000 0 Cycles (log #) 25 Total Power Shaved (kW) Total 50 300 1000 75 200 100 150 110 100 125 100 Depth of Discharge (log %) PTHRESHOLD (kW) 200 75 50 ΔP (kW) 25 Figure 9. Mismatch of linear models to battery aging data. Data shown in the figure comes from Rosenkranz [12], Figure 8. Performance of the peak detection algorithm with which refers to a battery produced by Varta, Inc., and from power demand data from MIT Lincoln Laboratory for Peterson [13], which refers to a battery produced by A123 January - May 2010. The total demand power shaved from Systems, Inc. the peak of the electric bill is shown as it varies with a changing P and ΔP. THRESHOLD In searching for a theoretical basis for an exponential model, the physical nature of cell degradation, as previously The parameters in the algorithm showed a sharp optimum at described in the literature [11], is based on crack ΔP = 150 kW (Figure 8), and a weak optimum at P = THRESHOLD propagation phenomena. Battery cells degrade as lithium 50 kW. This compares with a battery aging cost of ions form a precipitate in cracks in the carbon anode approximately $7 per car per month for a battery electrode. This low conductivity insoluble precipitate replacement cost of $5000, or $1 per Wh. Therefore, over a removes lithium ions from active electrolyte chemistry, wide range of assumed parameters, the peak shaving of the reducing the cell capacity and increasing cell resistance. building looks worthwhile. Depth of discharge for the V2B Another crack propagation mechanism, less important in function is financially optimized at full discharge, but owner low resistance cells, interrupts the electrical connection between the electrode materials and the metal current Los Angeles, and $0.11/ kWh for Dallas). Total costs were collectors. calculated for a baseline condition of 80% discharge of a 5 kWh vehicle battery, full recharge each evening at 8 PM Crack propagation is a thermal mechanism activated by at a 5 hour rate, and keeping the battery at 100% charge stress [15], which suggests an exponential dependence for before driving the same 24 mile commute as described battery degradation. The model therefore uses exponential above. Average daytime battery SOC was set at 80%. dependence of aging rate for all stress mechanisms. The resulting life prediction, when applied to lithium ion battery As shown in Figures 11, 12, and 13, the effect of climate life, fits well to test data [12-14]. and local electric rates causes only slight differences from one US city to another. Los Angeles and Dallas have higher summer temperatures than Boston, increasing the general Rosenkranz original data Rosenkranz exponential degradation of the battery in a PHEV, but both cities have Peterson original data lower electricity rates, decreasing costs to recharge the Peterson exp. model battery. There effects tend to cancel each other. Each effect 1000000 Peterson data adjusted individually tends to tip the curves so that only the most to 50% SOC Peterson adjusted to extreme battery prices give a curve with an optimum DOD 50% SOC exp. model between the extremes. High temperatures encourage 100000 gasoline use over accelerated battery aging; high electricity prices encourage gasoline use over utility charging. 10000

Cycles (log #) 900 Battery cost $5000 1000 110 100 $4000 Depth of Discharge (log %) $3000 800 $2000 Figure 10. Exponential model match to battery aging data. Data shown in the figure comes from Rosenkranz [12], which refers to a battery produced by Varta, Inc., and from

Peterson [13], which refers to a battery produced by A123 Annual Cost ($) Total 700 Systems, Inc. 020 40 60 80 100 DOD Centered on a 60% mean SOC (%) This aging model is combined with the equivalent circuit model of a lithium ion battery [16] to give terminal Figure 11. Annual cost due to degradation of vehicle characteristics at any rate and temperature; the resulting loss batteries using Boston climate and electric rates ($0.163/ of capacity at a standard rate (1C) is then calculated for the kWh) and $3 per gallon gasoline, as it varies with battery vehicle battery. replacement cost.

For each cost level of a 5 kWh battery, the effect on battery lifetime was tested and monetized with a mean battery state 5. OVERALL EFFECTS ON BATTERY LIFETIME of charge centered on 60%. For example, with a 60% depth

of discharge, the SOC varied from 30% to 90%. Gasoline The battery life model was then used to compute the cost of was fixed at $3 per gallon, electricity at $0.163/ kWh, and use over the lifetime of the battery including the effect of historical temperatures for Boston were used to calculate temperatures in different locations in the country, the effect aging to the battery. of variation of the DOD of the battery, the effect of varying mean value at which the battery SOC is maintained and 900 used, the sensitivity to cost of gasoline, and the sensitivity to Battery cost replacement cost of the battery, ranging from a typical cost $5000 today of $5000 for a 5 kWh battery [17] to $2000. (A $2500 $4000 $3000 battery ($500/ kWh) would be an aggressive US Advanced $2000 Battery Consortium (USABC) target for future cost 800 reductions [18].)

The model was applied to three locations, Boston, MA, Annual Cost ($) Total Dallas, TX, and Los Angeles, CA to evaluate the effects of 700 020 40 60 80 100 temperature [19] on battery use and storage conditions. This DOD Centered on a 60% mean SOC (%) analysis also used local EIA residential electricity pricing for each area ($0.163/ kWh for Boston, $0.125/ kWh for Figure 12. Annual cost due to degradation of vehicle If the battery is not fully charged immediately, but is batteries using Los Angeles climate and electric rates maintained at a constant SOC until just before it is needed, ($0.125/ kWh) and $3 per gallon gasoline, as it varies with the mean SOC has an effect on battery lifetime, with battery replacement cost. maintenance of the battery at full charge having a negative effect on battery lifetime (Figure 15). This effect is 900 Battery cost exacerbated by temperature, with the rate of degradation at $5000 night being half as much as during the day. The effects are $4000 additive. $3000 800 $2000 800 day night

both Total Annual Cost ($) Total 700 020 40 60 80 100 DOD Centered on a 60% mean SOC (%)

Figure 13. Annual cost due to degradation of vehicle Annual Cost ($) Total 750 batteries using Dallas climate and electric rates 40 60 80 100 ($0.11/ kWh) and $3 per gallon gasoline, as it varies with Mean State of Charge (%) battery replacement cost. Figure 15. The effect of mean SOC on total annual cost, As the top curves ($5000 battery replacement cost) in each using temperature and electricity prices in Boston. of the three city graphs do not reach a minimum, we can see that with $3 per gallon gasoline and today’s battery prices, This result leads to the observation that if the battery is to be the replacement cost of the battery is so high that it is recharged at work, perhaps under a V2B scenario, it appears cheaper to burn gasoline and not use the battery to even a that an optimum strategy might be to charge the battery

40% DOD (assuming the cost of CO2 production is not fully, including equalization, and then bring it down to 80% included). At target future battery costs, the battery would charge for most of the day – to leave room for peak shaving be most cost effective used at a deep discharge. At in to the building’s electricity grid, but also to optimize intermediate battery costs, a broad shallow optimum occurs battery lifetime. An evening charging strategy for at home at 60% DOD, reducing battery aging cost while displacing use might be to charge the car to 80%, then wait until early some gasoline. morning a few hours before normal commuting time to charge it the rest of the way and equalize it.

It may also be useful, but has not been analyzed, to thermally condition the vehicle (heating or air conditioning Battery cost the space) just before the commute in either direction, using $5000 1200 the inexpensive electric utility energy without giving up $4000 battery capacity. Depending on climate and driver $3000 preferences, this would be easy to implement with the same $2000 smart controller used for battery charging. 1100

Total Annual Cost ($) Total 6. CONCLUSIONS 1000 020 40 60 80 100 DOD Centered on a 60% mean SOC (%) Models were developed for plug-in Figure 14. Annual cost due to degradation of vehicle operation, both on the road, and used while parked as a batteries using Boston climate and electric rates ($0.163/ vehicle to building peak leveling system. A battery life kWh) and $5 per gallon gasoline, as it varies with battery model was used to evaluate the cost of battery aging during replacement cost. these activities. Total subsystem costs including battery, electricity, and gasoline were compared for a baseline However, the effect of the price of gasoline is dramatic. If vehicle in Boston, Los Angeles, and Dallas using the gasoline increases from $3 per gallon to $5 per gallon, the weather and electric rate data for each location. Boston graph changes to the one shown in Figure 14. In this case it is most cost effective to discharge the battery fully If the battery replacement cost is close to the USABC goal while driving. levels, the economics of driving the PHEV show an optimum for all locations with a depth of discharge of 60%. Economics are enhanced if the battery SOC during long [9] J. Gondor, et al., "Using global positioning system travel parked periods, such as during the work day and overnight, data to assess real-world energy use of plug-in hybrid are maintained at 80% rather than full charge. Battery electric vehicles," Transportation Research Record: Journal thermal management to keep batteries close to ambient air of the Transportation Research Board, vol. 2017, pp. 26-32, temperature is important. 2007. [10] A. Millner, "Modeling lithium ion battery degradation Vehicle to building peak leveling has attractive economics in electric vehicles," presented at the 2010 IEEE Conference and can be realized with a simple practical algorithm for on Innovative Technologies for an Efficient and Reliable peak selection. The aging model predicts that the cost of up Energy Supply, Waltham, MA, 2010. to 7 V2B cycles a month on the vehicle battery will be less [11] G. Ning, et al., "A generalized cycle life model of than $7 per month of added battery replacement cost; rechargeable Li-ion batteries," Electrochimica Acta, vol. 51, comfortably less than the projected $158 per month of pp. 2012-2022, 2006. potential revenue from V2B operations. Therefore, V2B has [12] C. Rosenkranz, "Plug in hybrid batteries," presented at the potential to provide far more value than the battery the EVS20: The 20th International Electric Vehicle aging will cost. Symposium and Exhibition, Long Beach, CA, 2003.

[13] S. B. Peterson, et al., "Lithium-ion battery cell

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