Battery Lifetime Energy Throughput

[CaptainKlapton]

Hi all,
I have been working on a simulation program for electric motorcycles for the last year. Recently I have been focusing on the battery functions and realized that comparing cells in terms of lifetime energy output is not so easy to do. So here is what I came up with:

Most manufacturers give an approximate cycle life of the battery cells. But do we really care? I mean if the battery was only ever cycled to 50% DOD, the cycle life would approximately double from the spec sheet value for a given set of charge/discharge conditions. Or, consider the strangely realistic case where the cell is not cycled exactly the same way every time causing the cycle life count to get complicated or become completely useless. Counting cycles is not the best way, in my opinion, to get an idea of how long the battery will last because it is too application specific. Energy on the other hand is a constant measurement for all battery driven applications. Know how much you need? Then you can size a battery for it. So that gave me the idea for something I call a “throughput factor.” This number is a simply multiple of the beginning of life (BOL) nominal capacity of the battery. However, the number is calculated from the cycle life such that it reflects the number complete, nominal cycles to 80% of BOL capacity. That means all you have to do is multiply your cell count by the throughput factor and it will tell you how much total energy you can get out of the pack before end of life (EOL). This allows you can keep all your calculations working with values and units you already have with no reason to introduce a new term involving cycle count. It also allows you to more easily compare cells of different sizes and chemistries. For instance, say you are comparing LEAF cells and 20Ah A123's. The LEAF cell is about 1.67 times the Amp-hour capacity and it operates at a higher voltage. But the A123 maintains its voltage better and is rated for more recharge cycles. So which one will give you the highest energy output, aka throughput, for its useful life? Counting cycles won't help you. But if you use the throughput factor you can directly compare the two in terms of energy, which is what we really care about anyway. The one with the highest overall energy output, throughput factor times the number of cells, is the best option in terms of energy. Of course it is still dependent on temperature, mechanical pressure, current draw and all the other things that effect battery cycle life, but at a minimum the comparison between cells is now easier and more meaningful.

So here are the calculations:
Throughput factor = integral(capacity retention by cycle count)d_cycle (also known as the area under the cycle life curve)

Total throughput (Lifetime Energy Throughput) = throughput factor * BOL nominal capacity

Then I discovered this after I did all that math: See “Lifetime Energy Throughput” at http://www.mpoweruk.com/performance.htm

Make sense? The throughput factor is basically a fraction of the Lifetime Energy Throughput. Then the total throughput is expressed as a multiple of the BOL nominal capacity. So I reinvented the wheel a little bit but got to work through some things I never had before, plus I got some conformation that it is actually useful.

Here are the ones I have done so far:
A123 20Ah: 2918.7
EIG C020: 963.6
GBS 60Ah: 1859.2

And here are the graphs from the manufacturers I used to calculate those:

View attachment 1


Questions? Comments? Criticism? Have at it.

 

[parabellum]

Cycle life is not linear to DOD, and proportion is different for every chemistry. Ex. Cell reaching 80% capacyty after 50 100%DOD cycles, may give 500 cycles at 80% DOD. Same for discharge current, you can kill a cell going allways at max specyfied continuouse current in 1/10th of rated cycle life because rating is done in some special conditions. Do not forget calendar life and so on, to many unlinearly afecting variables. I believe, most of us are taking cycle life figures with a grain of salt and as superficial aproximate mention of coulombic efficiency.

 

[CaptainKlapton]

Agreed on the cycle life being highly nonlinear, bad choice of example on my part. I realize that battery life will be dependent on the end application and conditions(temperature, humidity, current draw etc.). What I was trying to do was provide something that is at least a somewhat more meaningful metric than cycle life, because it is even more application specific in my eyes. All of the conditions I simulated were based on the 1C charge 1C discharge to 100% DOD plots between 23-25degC from the manufacturers, so at least those parameters are relatively consistent. Not a cure all, but energy output under similar conditions is a bit better than counting cycles is it not?

Thanks for the reply parabellum

 

[mvly]

This is an interesting topic you brought up. I am sure you are not the first to think about it.

In practice, I think it would matter little if a battery cell can provide some capacity after some time period with some number of cycle count.

Let's take some example to illustrate in detail:

1) DIY ebikes: most people here are looking for something they can use for 2-3 years and toss. If they are using it daily, we are looking at around 1000 cycles. Even after those 1000 cycles, the battery is typically 80% which means the battery is still very usable, albeit with much higher IR. By the time they upgrade, much better and cheap solutions will be available.
LESSON: batteries with > 1000 cycles is plenty for the DIY ebikers.

2) Production ebikes: current ebike manufactures are focusing in making a few bucks. They will use the lowest "best" capacity type of cells if they are smart. Though I have seen plenty offer cheap chinese cells with horrible reliability. However, this does not matter much because most people who buy production ebikes do not use them very often. How do I know? I have seen them on the roads. I have seen ebikers here and there on my daily commute to work. A very few would be consistent enough for me to see them daily. However, after a month or two, I would never see them again. I don't know what happened to them, but this has happened to ALL the ebikers I have seen here so far. I would even argue those with high end production ebike like stealth bomber would not care too much about battery because they would look into replacing them or selling the bike after a period of time for something better.
LESSON: batteries with low cycle count are required for production ebikes.

3) DIY motorcycles/car: Maybe these DIYers are looking to build something they can use daily and for a while. But currently, I've only seen enthusiasts. They would build to prove something, use it sparingly, and then move on to better projects. Moreover, it is much costlier to DIY electric cars or electric motorcycles than going out and buying one yourself.
LESSON: battery not use very often and most of the time doesn't really matter just as long as it can source the current. Usage would look like DIY ebikers at best.

4) Production electric car: Replacement batteries will be cheaper as the technology gets better. Again manufacturers will use the solution that will solve the problem with minimal cost. Even with electric cars, which are meant to run for thousands of miles, will only need about 1000 cycles. By then the IR of the cells will dictate when the cells should be replaced, not the cycle. If the cells sag too much, the battery will be no good any longer.
LESSON: > 1000 cycles and you are good to go.

Though it might be good to have this battery lifetime energy throughput factor and all, in practice most people would not care as much as the cycle count. I think there was a thread talking about something similar. The current solution? Count the Ah passed through the battery and always keep at least 20% of capacity in your battery. Mine is around 5000Ah so far with the Nissan Leaf Packs.

But here is the real kicker which, in my opinion, will throw a wrench in your system: Lack of data on battery longevity under normal usage condition.

We all know battery cells eventually die out. Because we live in the real world, every cells are manufactured differently. Moreover, every cells are subjected to different environmental conditions during usage. These are the two main factors that WILL effect the longevity of the cells.
The battery manufacturer's lab can do all these simulations and testing like heat aging, cell cycling, etc. to simulate usage, but in truth, the cells may not be used that way the lab intended or anticipated, hence longevity can vary quite a bit. Think of the Nissan LEAF in hot Arizona summers.

I have been toying with the idea of building a smart BMS which will take all these factors into account and log such data. Then have this data made available to everyone so they can learn how to build and use battery better.

 

[dogman dan]

In my too warm climate, often the real problem is that batteries just time out. Sure, store not fully charged, etc. But then you constantly have a bike not ready to go when you need it. If I know I won't ride tomorrow I don't charge, but usually I do ride, and often early in the AM.

3 years, and it don't matter very much how many cycles with my Hobby king lico stuff. It's done. However, if I pile up enough of my old stuff, I can still squeeze out 50% capacity fom them. Those old packs usually run my lawnmower if still only slightly puffy.

More and more, I just don't think in terms of cycles, or total wh, I just think in terms of cost per month, to 3 years. Then based on my average yearly mileage, come up with a cost per mile number.

 

[CaptainKlapton]

Good points mvly and dogman dan.
I get that battery life is nearly impossible to determine without actually using it until its time is up, but isn't that why there are testing standards in the first place? Spec sheets would literally be infinitely long if the manufacturer tried to account for every case, so they all test their cells under similar conditions to allow some sort of comparison before the cell has been purchased and later deemed at the EOL by the user. Both of you have come up with ways of dealing with cell aging which work best for your applications, which is great! But if you hadn't bought the cells yet and wanted to get an idea of how long they will last, what would you do? I like the idea of cost per unit time like dogman uses because it is probably the most practical consideration for most of us and doable before the cell is purchased. But it is an estimate in itself relying on the user to have prior knowledge of longevity in the application and its conditions, so that only really works if you have already have run a similar pack (please correct me if I am wrong).

My goal is not to give an exact indication of life (though that would be amazing), but rather give something that is at worst additional information about the cells. One could work out about how many cycles they would use in a year or something. If you use an estimate of energy rather than an estimate of cycle count, you can use a typical wh/mi number to get an idea of how many miles you can go. Both have the same crux of being inaccurate estimates as soon as they deviate from that cycle or wh/mi estimate, so the "best" one is determined by which one is easier to think about. For a vehicle, distance makes more sense to me.

Not trying to be difficult, just trying to learn as much as I can and maybe help someone in the process

 

[major]

Then I discovered this after I did all that math: See “Lifetime Energy Throughput” at http://www.mpoweruk.com/performance.htm

Interesting. Intend reading over linked article later. Thanks.

 

[dogman dan]

With 4-6 ebikes laying around the house, multiple batteries, some used on the yard tools, it's just gotten too big a pita to try to track cycles, or even miles for a given battery. At one point I did count cycles, by dropping a penny in a jar each ride.

But nothing wrong with doing some theoretical calculations, based on 1000 cycles, or whatever they promise for that type battery. When I bought my first ping, I tried to pre calculate every thing, down to the tires and brake pads I'd use. I got pretty close, and in those first 3 years I came in at about 25 cents per mile. But then I started building fun bikes, that used up stuff faster. Go fast cost a lot more. And never again was a battery as cheap as that first pingbattery in 2008. Better cells, but mo money after that one. Costs are just guessed at now, but 35 cents per mile is plausible. Close to the same cost per mile as a 150cc gas scooter.

On thing for sure, it was a lot easier to predict how many cycles, and how deep those cycles would be when I rode a bike to work. Back then, I could tell you almost to the watt hour how much energy I'd use per year. Same 30 mile ride over and over.

Now, working at home, the use is a lot more variable. Some cycles are 1 ah, others use 25 ah, and fully discharge several batteries. I can't really predict how many cycles or how deep they will be at all anymore. The use pattern is so random. Even with 4 CA's, all I really know is how much each bike did. Or not, as CA's get moved around when I build another ebike. Still tend to have more bikes than CA's. I don't really track anything anymore, other than use during one ride so I don't over discharge. I still ride about 2000 miles a year that is tracked on a CA, but other bikes get ridden without CA when I have more than 4 around.

But since 2008, one thing has remained the same, whether it's a pingbattery lifepo4 or cheap hobby lico. About 3 years is the max for my climate. Even though I store the batteries at room temp, you have to go out in summer to use them. 90-110 F out there.

If usable after 3 years, it's with greatly diminished capacity. So I just buy a battery, divide it's cost by 3 years, and call anything after 3 years gravy. I still ride enough to need a lot of battery, so I try to budget $300-600 for new stuff every year. This way only a third of my total battery supply is 3 years old any given year. Three year old stuff is used less, as it weighs more for its real world capacity, and by year 4 it's only going to be used to mow the lawn.

So in the end, riding as much as I do, costs $500 a year on average for the battery. Cost to build a new ebike constantly for the fun of it, can be infinite. Always something I want to buy, a tool, a frame, whatever and building bikes from junk bikes always means new tires and tubes.