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GM researchers posit simple model to assist in balancing high energy density vs fast charging in EV design

With an eye toward balancing higher energy density batteries and fast charging capability, General Motors researchers Mark Verbrugge and Charles Wampler have derived and implemented a simple model to assist in evaluating factors such as cell performance, cost, life, and fast-charge capability in the design of electric vehicles.

In a paper published in the Journal of Power Sources, they suggest that their approach is useful in terms of comparing and contrasting battery systems and shedding light on technological tradeoffs.

We are at a crossroads in terms of balancing two promising technologies: (1) higher energy density (Wh/L) and specific energy (Wh/kg) batteries, relative to today’s conventional graphite/metal-oxide lithium ion systems, and (2) fast-charge capability, defined here as greater than Level 2 charging, or greater than about 20 kW. Currently in the United States, conventional Level 2 charging of 6.6 kW is available in homes and various community locations. In the ideal case, high energy batteries would be able to accommodate fast charge, but two of the most promising high-energy cell technologies, i.e., cells employing Si-enhanced or Li-metal negative electrodes, are problematic insofar as they cannot at present accept fast charging without significant degradation in cell life.

… The tradeoff between high-energy, as provided by cells with Li-Si and Li metal negative electrodes, and fast-charge capability, which can be obtained from conventional lithium ion cells employing lithiated graphite or titanate negative electrodes, for examples, poses a dilemma in the design of electric vehicles (EVs).

—Verbrugge and Wampler

For their analysis, Verbrugge and Wampler considered costs associated with the cells, added mass due to the use of larger batteries, and charging, as well as a new cost input—the cost of adaption, corresponding to the days a customer would need an alternative form of transportation, as the EV would not have sufficient range on those days.

The end result is a qualitative model that can be used to calculate the optimal EV range (which maps back to the battery size and performance), including the influence of fast charge. Verbrugge and Wampler cautioned that the results are qualitative, given the complexity of the problem; their approach does, however, identify key factors to be considered in battery sizing.

Optimal value of EV range x. The ordinate is common to both plots. For the curves labeled sA, scell, and sM, f = 0 (no fast charge). Base values for the cell cost ($/kWh) and specific energy (Wh/kg) are provided in each plot. The dashed lines result from subtracting off the range contribution from one fast charge, xf, from the upper curves that reflect the total vehicle range, (1 + f)x, including one fast charge. Verbrugge and Wampler. Click to enlarge.

Of particular note is the cost of adaptation. When we exercise the model with inputs one can associate with a battery like that of the Chevrolet Bolt EV, we find that the net cell volume and the vehicle range are consistent with an adaptation cost of $165/day, three times the average cost per day to rent a car in the United States. This adaptation cost would be appropriate for customers having a strong desire to avoid relying on some alternative method of transportation for the days in which the EV could not supply the needed miles. … the Bolt EV’s 238 miles range would mean that the 75th percentile drivers would need an alternative form of transportation—that is, they would need to adapt—about 5 days per year.)

The results … allow one to assess whether fast-charge of a conventional lithium ion battery is superior to the implementation of a high-energy density cell that cannot be fast charged. For the parameters chosen, fast-charge of a conventional lithium ion battery offers superior value to the customer relative to the high-energy density cell.

—Verbrugge and Wampler


  • Mark W. Verbrugge, Charles W. Wampler (2018) “On the optimal sizing of batteries for electric vehicles and the influence of fast charge,” Journal of Power Sources, Volume 384, Pages 312-317 doi: 10.1016/j.jpowsour.2018.02.064



The Daimler FCEV PHEV is superior to long distance big battery BEVs on all parameters.

No need for fast charge, so energy density can be optimised.

No need for a very large battery, so material constraints such as cobalt can be avoided.

Much faster refuelling than any BEV, even the projected ones from Porsche.

Far superior cold weather performance.

For everyday running around, the whole notion of the superior energy efficiency of BEVs, dubious anyway once the full supply chain is taken into account, is avoided.

The very high energy and emissions of building a very large battery which make the lifetime emissions of big battery BEVs problematic are also avoided.


It appears to me that a large segment of consumers are going to purchase as big and as versatile a vehicle as they can afford without much regard for the carbon footprint so unless that attitude changes, the FCEV powered by solar generated hydrogen may be the best option for personal vehicles in a low carbon world. EV's may be a better solution for bus's, delivery and freight moving vehicles if the claims about the Tesla semi are anywhere's near accurate.


Current batteries relative low performance (slow charge and low power per Kg) and high cost are major challenges to current and near future all weather extended range affordable BEVs. The problems with batteries may not be solved much before 2030.

Good interim solutions are PHEVs with just enough batteries for daily use and a smaller, lighter, higher efficiency ICE generator or FC for extended range and to handle harsh weather conditions and longer trips.


Why introduce all the expensive complexity of a hybrid when you can keep it simple with less maintenance with one power unit that contains one moving part, an electric motor, and the promise of an ever advancing battery technology system? BEVs go 300 miles right now on less money and quick charge in less than 30 minutes...that just the beginning.



Have another read of the article.

'Ever-advancing' battery technology is not so much, but is a series of trade offs.

What they hope to be able to do somehow using battery technology can be done right now using fuel cells, and they are advancing too.



All weather, extended range BEVs will require up to 200 kWh of high performance costly batteries. Weight, high cost, volume and longer charging time will be a major challenge for another 15 years or so.

Affordable, quick charge, all weather extended range BEVs may not be available much before 2030-2035?

PHEVs with a small liquid fuel on board generator, to extend range, is a good short to mid-term solution.

PHEVs with an on board small FC to extend range is a long term clean operation solution.

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