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### Battery Aging Model

Posted: Sun Oct 14, 2012 4:59 pm
I am starting this thread to discuss various battery aging models. Surfingslovak developed a battery aging model referenced in the Wiki:

Since some of the numbers didn't fit with Nissan's claims (even after they mentioned the "glideslope" in Arizona to 76% battery capacity remaining, and the fact that only 7500 miles were assumed for Arizona), I decided to see if I could tweak the model to fit TickTock's graph:

Here are my results (you may have to make text smaller in browser to fit on screen):

Summary:

Model fits the data from Nissan quite well using following assumptions:

Calendar loss first year without aging factor - 6.5%
Calendar loss slows with square root of time

Cycling loss per 12500 miles without aging factor - 1.5%
Cycling loss is linear

Boston aging factor adjusted to 0.75
"Normal" aging factor adjusted to 0.90
Phoenix aging factor adjusted to 1.35

Aging factors relative to "Normal" are:

Boston - 0.83
Normal - 1.00
Phoenix - 1.50

Note: while it might seem that my selections were random, or that many combinations could give the same results, I found that changing any of the values from this set of numbers caused increasing errors in predicting the numbers found on the graph. I make no claim that these numbers are good predictions of reality, only that they fit Nissan's figures closely. Comments, discussion, suggestions for improvement, etc. are welcome. If anyone wants to play with the actual spreadsheet, let me know.

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 5:54 pm
I checked the model that Surfingslovak created, and to my surprise he came up with the exact same calendar loss and cycling loss figures. The reasons that his results differ from mine:

1) Different aging factor was used - mine were derived empirically rather than calculated. Mine could be correct depending on the activation energy, as tbleakne pointed out.

2) His model uses 7500 miles as the baseline for all cities; I used 7500 miles for Phoenix, 12500 miles for "Normal" and Boston. I believe this is an error on his part, and leads to results showing more degradation than Nissan predicts. However, I could be wrong.

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 6:39 pm
I'm not sure it is worthwhile trying to fit a model to the curves which Nissan gave to TickTock. Frankly, I don't expect to see any LEAFs in Phoenix with 76% capacity left after five years, regardless of miles driven. Why? Because I think Nissan's faith that the degradation will taper off after a year or so is only valid in a usage regime where cycling dominates degradation. In the cases we have in Phoenix where calendar life is the dominant (or at least A dominant) force, I expect the degradation will be closer to linear. Additionally, as these batteries age, the daily DOD increases. This is another effect which I don't think is being properly accounted for.

As usual, I hope I am wrong about this. OTOH, Nissan's track record for making predicitions in Phoenix is quite poor to date.

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 6:50 pm
Of course, I think all the data needs to be corrected for 12,000 or 12,500 miles. Just because Nissan pulled some number out of their posterior, it doesn't reflect the average driver.

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 6:56 pm
RegGuheert wrote:I'm not sure it is worthwhile trying to fit a model to the curves which Nissan gave to TickTock. Frankly, I don't expect to see any LEAFs in Phoenix with 76% capacity left after five years, regardless of miles driven. Why? Because I think Nissan's faith that the degradation will taper off after a year or so is only valid in a usage regime where cycling dominates degradation.
From what I have read, calendar life loss does follow the square root of time, so presumably the calendar life loss will slow. If it doesn't the Phoenix batteries are definitely cooked. I added an additional factor to my model, miles per kwh. Nissan stated that their assumptions were based on the LA4 drive cycle, which is why they focused in on highway driving as a factor in the Phoenix Leaf accelerated losses. Based on 100 mile range and usable capacity of 21.381 kwh, I calculated that the miles per kwh for that drive would be 4.68. If one is driving less efficiently, more cycling of the battery will be involved. Using a figure of 3.5 miles per kwh for TickTock (I have no idea what his longterm average is, just a made up number), my model predicts for his car (84.7% capacity measured at Casa Grande after 1.3 years):

Calendar loss - 10.01%
Cycling loss - 3.16%
Cycling loss corrected for less efficient driving - 4.22%
Total capacity loss - 14.23

Predicted capacity - 85.8%

Difference from actual capacity - 1.07%

This doesn't take into account solar loading, which I imagine Nissan may not have included in their model. I don't know if TickTock's Leaf spends a large portion of its time in direct sun (if he reads this post, he can certainly chime in with more info).

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 7:05 pm
TonyWilliams wrote:Of course, I think all the data needs to be corrected for 12,000 or 12,500 miles. Just because Nissan pulled some number out of their posterior, it doesn't reflect the average driver.
I totally agree. I used the 7500 mile number to develop the model, not because I think that is a valid assumption. Using 12500 miles per year, my model predicts a 29.75% loss of capacity at 5 years in Phoenix--and that doesn't include the effects of driving faster, which would lead to more cycling.

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 8:01 pm
After seeing what's expected best case scenerio, worst case scenerio . . . . I must admit I am one of the VERY lucky ones - still getting 100 miles per . . . and 280 gids (knock on wood)

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 8:09 pm
RegGuheert wrote: Using a figure of 3.5 miles per kwh for TickTock (I have no idea what his longterm average is, just a made up number), my model predicts for his car (84.7% capacity measured at Casa Grande after 1.3 years)
4.44 is my overall efficiency (from the dash) since I started logging last October. Nissan claims my accelerated degradation is just due to higher then 7500/year milage (i.e. more battery cycles).

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 8:22 pm
TickTock wrote:
RegGuheert wrote: Using a figure of 3.5 miles per kwh for TickTock (I have no idea what his longterm average is, just a made up number), my model predicts for his car (84.7% capacity measured at Casa Grande after 1.3 years)
4.44 is my overall efficiency (from the dash) since I started logging last October. Nissan claims my accelerated degradation is just due to higher then 7500/year milage (i.e. more battery cycles).
My model changes only slightly with that figure: difference is 1.97 between predicted and actual. My model slighly under-predicts at one year, is very close at two years, and very slightly over-predicts at 5 years. That's the closest I could get it. Of course, it might help to have the actual numbers from TickTock's graph (hint, hint). I estimated them by looking at the graph. Also, wondering how much you parked in the sun, TickTock. Based on the Prius study of solar loading, parking in the sun full-time can cause a 10% (low solar load) to 24% (high solar load like Phoenix) increase in battery aging compared to avoiding parking in the sun completely. The solar loading depends on geographic location. Of course, the Leaf may be designed in such a way that the solar loading factor would be less.

### Re: Battery Aging Model

Posted: Sun Oct 14, 2012 8:56 pm
Stoaty wrote:
TickTock wrote:
RegGuheert wrote: Using a figure of 3.5 miles per kwh for TickTock (I have no idea what his longterm average is, just a made up number), my model predicts for his car (84.7% capacity measured at Casa Grande after 1.3 years)
4.44 is my overall efficiency (from the dash) since I started logging last October. Nissan claims my accelerated degradation is just due to higher then 7500/year milage (i.e. more battery cycles).
My model changes only slightly with that figure: difference is 1.97 between predicted and actual. My model slighly under-predicts at one year, is very close at two years, and very slightly over-predicts at 5 years. That's the closest I could get it. Of course, it might help to have the actual numbers from TickTock's graph (hint, hint). I estimated them by looking at the graph. Also, wondering how much you parked in the sun, TickTock. Based on the Prius study of solar loading, parking in the sun full-time can cause a 10% (low solar load) to 24% (high solar load like Phoenix) increase in battery aging compared to avoiding parking in the sun completely. The solar loading depends on geographic location. Of course, the Leaf may be designed in such a way that the solar loading factor would be less.
I almost never park in the sun (usually get one of the covered parking spots). For a couple of months I was plugging in at work and taking advantage of the pre-cool feature before I left the office (but very rarely actually charged there - only if I had a far errand over lunch). Since the AC condenser seems to dump the heat into the cavity above the battery, I wouldn't be surprised if that contributed.
Here are the numbers I managed to jot down. Keep in mind *I* didn't see the actual numbers either and read these values off the graph. I would guess I am within 0.5%.
• Age Nom Boston Phoenix
0.5 ??? 94% 92%
1.0 92% 93% 89%
2.0 88% 90% 85%
5.0 80% 84% 75%