Electric shock




All those amazing cars (such as Tesla) are based on Lithium Ion battery. Much like any other battery, this one uses electrodes, one made of lithium compound and the other out of a form of carbon such as graphite. The electrolyte in between these electrodes typically contains cobalt (typically in the form of an oxide). The exact chemistry varies between different types of cells but overall positively charged lithium ions get carried from the anode to cathode during discharge and the reverse is happening during charging. Cobalt oxide mediates the ions. So in some sense the electric car actually has zillions of moving parts if we count all these ions traveling from anode to cathode every charge cycle! Jokes aside, this is a fairly complex chemical process and these batteries degrade eventually. Degradation is a function of cycles on the battery but also simply a function of time - electrodes may slowly dissolve (varying temperature alone is enough to facilitate this process).  My personal experience with consumer electronics has been rather bad: I think I never had a Li-ion battery that would last for more than 1000 cycles, even the supposedly fancy batteries that apple puts in their MacBooks/iphones have failed me numerous times. Arguably the cells they put in a car should be better quality, but I'm not sure how far that goes.

The typical behavior at the end of battery life is that the battery indicator (a software algorithm meant to predict remaining charge based on operation time and voltage) becomes "inaccurate". Typically it will indicate certain amount of battery charge left (say 30%) and then it will very rapidly decay to zero or in the worst case just randomly shut down the device.

There is a fair bit of anecdotal evidence that this is actually happening with electric cars. In the first article the owners claim to have owned a Nissan leaf since 2011. In their own words:

At 91,000 miles, our battery pack is at less than 60 percent of original capacity and our range is around 35 miles

And in addition:

When we bought the car, Nissan's official statement was that the battery should be at 70 to 80 percent of capacity at 100,000 miles, and it was backed by an 8-year/100,000-mile warranty.Today, Nissan Leaf Customer Support tells us that our battery condition is normal and to be expected, and that the car is not worth enough to spend more than $8,000 on a new battery.

Another data point is the experience of Tesloop, a company that has been offering a ride service from LA/San Diego to Las Vegas. Their cars have been used extensively, so any problems could show up much faster than in regular use. Nevertheless from the article describing their findings after 200,000 miles we find that:

The Tesloop Model S has only degraded about 6%, even though it’s being charged to 100% every day, rather than the default—and recommended—90% charge.

This seems really great, but as we continue to read:

Then, just as the car hit 200,000 miles, the range estimator became inaccurate. Though the car didn’t actually lose any range, the estimator would say it could go another ten miles—and then power down. Tesla looked into the issue, and told Tesloop that there’s a battery chemistry state that high-mileage cars go into, and the software isn’t properly compensating for that change. There will be a firmware update in three months that will take care of the discrepancy, but Tesla just replaced the battery to solve the problem. “We got our 6% range back with the new battery,” Sonnad said with a laugh. “But had the firmware been updated, we’d be fine and plugging along.”

"Inaccurate" charge indicator sounds quite familiar to me. Now it needs to be noted that this car had driven 200,000 miles in only one year (assuming 200 miles per charge this roughly corresponds to 1000 charging cycles). If it wasn't for the other factor in battery degradation, namely time, less than 10% loss after a year would be an amazing news - likely hardly any Tesla used by a typical consumer will ever clock 200,000 miles. But the time is a another factor - batteries degrade whether their being used or not, particularly when the temperature varies a lot, which is certainly true in automotive case. Will an 8 year old Tesla with say 90,000 miles driven have much juice left? Remains to be seen.

Some insight into these questions could be found on forums, Maarten Steinbach maintains some pretty cool data on his blog (however this is not a scientific study). The data presented there looks extremely good: no data point shows less than 85% battery capacity even after 250,000km (156000 miles). However one has to be careful interpreting this data, as this is what the battery/range indicator claims. A deeper dive into the comments sections reveals a few interesting statements by the apparent owners:

(Peter Lucas): In my car, the truth is much worse than the numbers. My 2016 90D battery capacity repeatedly calculates to 71 to 73 kwh. And it has a 200 mile maximum range. Despite attempts at very docile driving. Service rep says my battery is functioning normally.
The real deception is that the cars instruments continue to display the untrue range of 275 miles per 100% SOC.

And below:

(Henning Kilset): Does this take into consideration that the km remaining at 100% charge has been modified several times in software?

I know they’ve changed the calculation method at least once during the past 12 months, which resulted in an approx 5% drop in “perceived capacity”, but not “real capacity”.

This appears to be consistent with Tesloop experience.

There are several techniques that can be used to extend the battery life, particularly in the "perception" of battery life. Battery balancing combined with additional (often undocumented) capacity may greatly extend the time during which the battery appears to be completely healthy. Tesla is famous for doing this particularly after hurricane Irma when the company temporarily increased the range of their vehicles by software unlocking the extra capacity, we read:

The vehicles are equipped with a 75 KWH battery, but they are software locked to use only 80 percent of that available power.

This extra capacity is almost certainly used in load balancing as the battery deteriorates enhancing the lifetime of the the component. This technique is used in solid state drives and many other applications where things have limited lifetime. Although very powerful, what that solutions does it prolongs the life of a component, but the eventual decay follows a much steeper slope. We can see this in the following simulation:

Assume that a single cell has expected lifetime of 1000 cycles with standard deviation of 17. Assuming there are 1000 cells in a battery, 200 extra cells that get enabled as the older ones reach their maximum cycle count. Here is what we get:

Without extra cells (red plot) we'd begin to see a gradual battery decay well before 500 cycles. With extra cells (blue plot) we can't see any decay all the way until past 700 cycles. However once the decay shows up, it is much less gradual: at half the capacity the lifetime difference is only ~140 cycles, rather than > 350 cycles at close to 100% capacity. My hunch is that what we see in electric cars these days,  is the blue line, well before it starts it's rapid decay. If that is so, many EV owners may get an unpleasant surprise, much like the owners of the 2011 Leaf in the first of the linked articles.

This simulation is only to get some intuitions, particular numbers are made up, but you can play with it using the following python code:

import matplotlib.pyplot as plt
import numpy as np

Expected_cycles = 1000
Expected_variability = 300
N_cycles = 10000
N_cells = 1000
N_extra = 200
N_active = N_cells
Cycles = np.zeros((N_cells+N_extra), dtype=np.int)
Enabled = np.ones((N_cells+N_extra), dtype=np.int)
Lifetimes = Expected_cycles+(Expected_variability*np.random.randn(N_cells+N_extra)).astype(np.int)
Capacity = np.zeros(N_cycles, dtype=np.int)

for i in range(N_cycles):
    for n in range(N_active):
        Cycles[n] += 1
        if Cycles[n] >= Lifetimes[n]:
            Enabled[n] = 0

plt.plot(range(plot_range), Capacity[:plot_range], "r-")

Capacity = np.zeros(N_cycles, dtype=np.int)

for i in range(N_cycles):
    for n in range(N_active):
        Cycles[n] += 1
        if Cycles[n] >= Lifetimes[n]:
            Enabled[n] = 0
    if Capacity[i]<N_cells:
        if N_active<N_cells+N_extra:

plt.plot(range(plot_range), Capacity[:plot_range], "b-")

by tweaking the above code in various ways we can obtain other interesting results. E.g. we can only enable leveling to prolong the 90% capacity by modifying the line 36 from "if Capacity[i]<N_cells:" to say "if Capacity[i]<N_cells-100:". In such case we can get:

Here the battery lasts at 90% capacity to almost 900 cycles. By varying the strategy we can get to say 1000 cycles at 80% capacity and so on. In all cases though, once the system runs out of extra cells, a rapid decline begins.

Magical battery

An argument often rolled out when battery issues are being raised is that technology goes on, and in a few years battery packs will be cheap and will squeeze 10x the energy density. Well, I sure hope they will be cheap, but there is almost no hope for the 10x (or even several x) energy capacity. The reason is simple: even todays Li-ion batteries with energy density of roughly 0.8MJ/kg (Mega Joules/kilogram) are already quite hazardous, to the point of being banned from check-in baggage on a plane and requiring special handling during shipping. To put this into perspective, gunpowder has the energy density of roughly 3MJ/kg while TNT is approximately 4.6MJ/kg. So a 10x energy density battery would have to have ~8MJ/kg, substantially more than TNT! I don't think there would be many places who would want to keep such "bombs" in their parking lots. It is important to note that given the heat capacity of those batteries, increasing energy density by a factor of few, changes the behavior in case of catastrophic failure from a violent fire (as it is now) to an explosion. Current Li-ion batteries combust in a rapid fire that is very hard to extinguish (since it is a chemical reaction that does not need external oxygen). At ~4x the energy density (gun powder) we already have a quite powerful explosion.

So why would anyone bother, since gasoline has absolutely extreme energy density of 46MJ/kg and yet we drive gasoline powered cars every day!? To understand this apparent paradox, we need to realize that energy density of gasoline is posted under availability of external oxygen for combustion. Gasoline needs approximately 2x (by mass) of oxygen to release all the energy, so if we were to count it fairly (adding oxygen into the mix), the energy density of both (gasoline plus oxygen) would be more like 15MJ/kg. That is still 3x more than TNT and is the primary reason why rockets essentially run on gasoline and liquid oxygen. It is a fabulously energy rich fuel! However in the case of cars, gasoline is in liquid form and needs external oxygen. So even in the case of a catastrophic failure it burns rather than explodes (since liquid form limits the area of contact between gasoline and oxygen, plus air contains only 21% of oxygen) and moreover can be relatively easily extinguished by severing access to oxygen (e.g. with CO2 based extinguisher). So even with its extreme energy content, gasoline is in fact quite safe.

The economy

The average age of car in the USA is 11.6 years (as of 2017), and likely much more in poorer parts of the world. The median is roughly similar, so vast majority of cars in operation are much older than 8 years, which is the battery warranty on a Tesla. For EV's to become a real mass market product, their longevity has to match that of combustion engine cars. This would suggest that an EV should last for about 20 years without substantial battery/range decay. I don't think we are any close to that. Looking at available anecdotal data and some other studies (as well as the actual cell specs themselves).

A lot can be said about combustion engine, but in one aspect it actually blows EV's out of the water: it last for many years (even with all the moving parts), and even when it finally brakes down and rusts, in many cases it can be restored to working condition with relatively unsophisticated work using relatively unsophisticated tools and processes. An average guy with some time and a garage can restore even quite complex modern engine to a good working condition within a few days and maybe at most a few thousands of dollars. Parts can be sourced from junkyard for cheap, or even custom made with a simple lathe/mill. This cannot be said about Li-ion batteries, which need a complex industrial process to be reconditioned. Without the ability to be cheaply reconditioned, EV's have no chance of penetrating the lower half of the market, which may indicate that their resale value will begin dropping rapidly, once these issues catch attention (which they will as more EV's age).


I'd love electric vehicles to be practical and cheap for everybody. There is no doubt they are superior to ICO (Internal Combustion) cars in many ways. But in order to become anything more than a fad, they have to prove cheap and practical enough to penetrate the "poorer part" of the market. And in many ways the "poorer part" of the market is much tougher to satisfy than the "rich part" of the market. This seems quite difficult given the contemporary battery technology which faces substantial challenges due to fundamental issues of energy density. Every buyer of EV should be aware of the issues discussed in this post as it is potentially important for the resale value of the car and the economy of the entire investment.



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