Tuning the Battery Aging Model

[Stoaty]

I took a quick look at the readings submitted so far, and found (as expected) a systematic bias of the model to under predict the amount of capacity loss. The error ranged from about 1% too optimistic (DaveinOlympia) to about 11% for jmh614 in Texas (predicted 20% capacity loss, actual loss about 31%). Early indications are that the model is quite good in the Pacific Northwest and does a progressively poorer job as the average temperature increases.

We need a lot more data from places like Texas and Arizona.

 

[Stoaty]

OK, here is the initial data. To my surprise, all predicted percent capacity loss values are within 3.75% with the exception of the readings from Dallas, TX and Ridgecrest, CA. So far, the Battery Aging Model is doing fairly well, except in places that get really hot.

 

[tivollix]

Thank you very much for this work, very interesting.
Would it be possible for you to share the calculation sheet?
It would be interesting to add the projected date for 70% remaining capacity.

 

[opencar]

Before we get to conclusions, I remember you wanted to collect substantially more responses to be statistically meaningful. Also, the prediction model has a rate of loss that tapers over time; if the loss is instead linear over time, then the small difference between predicted vs actual in year 1 and 2 becomes a much bigger amount in year 5-10.

OK, here is the initial data. To my surprise, all predicted percent capacity loss values are within 3.75% with the exception of the readings from Dallas, TX and Ridgecrest, CA. So far, the Battery Aging Model is doing fairly well, except in places that get really hot.

 

[Stoaty]

Before we get to conclusions, I remember you wanted to collect substantially more responses to be statistically meaningful. Also, the prediction model has a rate of loss that tapers over time; if the loss is instead linear over time, then the small difference between predicted vs actual in year 1 and 2 becomes a much bigger amount in year 5-10.

Agreed. That's why I said "so far". However, the research paper cited in the Wiki uses the same assumption (that calendar loss is proportional to the square root of time), so I think it is reasonable to infer that this has been seen in previous studies:

http://www.nec.com/en/global/techrep/journal/g12/n01/pdf/120112.pdf" onclick="window.open(this.href);return false;

Recall from the Wiki that the assumptions made for the model were:

Loss for the first calendar year - 6.5% (in "normal" climate)
Cycling loss per 10,000 miles - 1.5% (using the miles/kwh from LA4 cycle, again in "normal" climate)

My guess is that these parameters need to be tweaked to fit the actual data, but I need both more data from different Leafs in different climates, and some serial data (every 3 months) for the same Leaf.

 

[bradbissell]

Manufactured - 03/13
Delivered - 3/31/13
P3227 update - NA
Location - Boston, MA
Miles/kwh - 4.3
Odometer - 6415
Capacity - 65.37
Date - 9/06/13
Parked in sun - 2 day/wk (in partial shade)

 

[WetEV]

Before we get to conclusions, I remember you wanted to collect substantially more responses to be statistically meaningful. Also, the prediction model has a rate of loss that tapers over time; if the loss is instead linear over time, then the small difference between predicted vs actual in year 1 and 2 becomes a much bigger amount in year 5-10.

Loss is not linear. Don't make that assumption/conclusion. Assuming linear loss would be like trusting the GOM on a mountain drive.

I don't have the P3227 update. Sorry, I'd love to add a data point.

+1 on waiting for more data. We know more now than we did a year ago, and will know more in a year than we do now.

 

[vegastar]

In the table my location is Lisbon, Portugal but my actual location is Porto (Oporto), Portugal. There are significant temperature differences between the two (Porto is cooler), so the error is a little bigger than reported.

I think an importante parameter for the model is if the car is parked in a insulated garage at night. This could explain some of the differences in the model vs reality as my car never cools much during the night. I think at least 2 degrees Celsius should be added in the average battery temperature for cars parked at night in insulated garages. Since the Leaf battery App (now Leaf Spy) has the battery temperature I have been recording the data 2 times per day (morning and night) so in 10 months I will have a complete year of average battery temperatures that could be used to calibrate the model.

 

[Stoaty]

I don't have the P3227 update. Sorry, I'd love to add a data point.

If you look at my initial results, you will see that I have a section called "No P3227 update". It is for 2013 Leafs where it isn't applicable, and 2012 Leafs that haven't had the update. Even though I won't use the data for the calibration, it is still interesting to look at. So feel free to post your readings (and hopefully post again in a few months when you have had the update).

 

[opencar]

given we are in year 2+, nobody knows what the loss curve is for our particular batteries- linear, polynomial, whatever (hence Stoaty's empirical work is great). at his point, our situation is like looking at past stock market performance and predicting future performance. conversely, the point that i attempted to make is that in any nonlinear extrapolation, a small delta early on results in a big delta further out in time.

Before we get to conclusions, I remember you wanted to collect substantially more responses to be statistically meaningful. Also, the prediction model has a rate of loss that tapers over time; if the loss is instead linear over time, then the small difference between predicted vs actual in year 1 and 2 becomes a much bigger amount in year 5-10.

Loss is not linear. Don't make that assumption/conclusion. Assuming linear loss would be like trusting the GOM on a mountain drive.

I don't have the P3227 update. Sorry, I'd love to add a data point.

+1 on waiting for more data. We know more now than we did a year ago, and will know more in a year than we do now.

 

[TomT]

I think that problem with the tapering loss theory is that it does not take in to account the fact that, with a limited battery size to begin with, as the battery ages and capacity decreases, one has to use more of the available capacity to maintain the needed range (a deeper DOD) AND subject the pack to more charge cycles (a cycle being the equivalent of one charge from 0 to 100% of capacity)... This may negate any tapering of degradation...

Before we get to conclusions, I remember you wanted to collect substantially more responses to be statistically meaningful. Also, the prediction model has a rate of loss that tapers over time; if the loss is instead linear over time, then the small difference between predicted vs actual in year 1 and 2 becomes a much bigger amount in year 5-10.

 

[opencar]

I agree that the dynamic you describe below initiates a vicious cycle that i think is ignored by the model. Since losing my first bar recently, I can attest to a change from daily 80% to daily 100% charging that imposes higher average battery temperature from this point on as compared to my first 2 years of usage. This one factor alone means that the ambient temperature of my location increases over the ownership period.

I think that problem with the tapering loss theory is that it does not take in to account the fact that, with a limited battery size to begin with, as the battery ages and capacity decreases, one has to use more of the available capacity to maintain the needed range (a deeper DOD) AND subject the pack to more charge cycles (a cycle being the equivalent of one charge from 0 to 100% of capacity)... This may negate any tapering of degradation...

Before we get to conclusions, I remember you wanted to collect substantially more responses to be statistically meaningful. Also, the prediction model has a rate of loss that tapers over time; if the loss is instead linear over time, then the small difference between predicted vs actual in year 1 and 2 becomes a much bigger amount in year 5-10.

 

[Stoaty]

One factor not considered is the fact that most of the Leafs we have data on have a battery that is 2.25-2.5 years old. This means the battery has been through 3 summers, but hasn't had 3 full years of service. I would expect that the difference between actual capacity and predicted capacity will go down as the Leafs add another 6 months or so of service with relatively little effect on battery capacity during the cooler months. It is why we really want to get anniversary readings, as close to the date of manufacture (I arbitrarily picked the 15th of the month for this) as possible. That will get rid of the seasonality problem we have with fractional year readings.

 

[RegGuheert]

However, the research paper cited in the Wiki uses the same assumption (that calendar loss is proportional to the square root of time), so I think it is reasonable to infer that this has been seen in previous studies:

http://www.nec.com/en/global/techrep/journal/g12/n01/pdf/120112.pdf" onclick="window.open(this.href);return false;

As previously noted, calendar losses are only proportional to the square root of time at the very biginning of the cell's life. After that, the calendar loss of capacity becomes linear with time with the slope affected by temperature. This effect can be seen in the four papers on long-term calendar losses which have been posted on this forum, including one that you yourself posted. You can find those papers easily by looking at the five links I porvided on point 2 in this post.

In some tests, calendar losses accumulated faster than linear at higher temperatures. The researchers surmised that some unknown mechanism was causing the increasing rate of loss of capacity.

 

[surfingslovak]

I think that problem with the tapering loss theory is that it does not take in to account the fact that, with a limited battery size to begin with, as the battery ages and capacity decreases, one has to use more of the available capacity to maintain the needed range (a deeper DOD) AND subject the pack to more charge cycles (a cycle being the equivalent of one charge from 0 to 100% of capacity)... This may negate any tapering of degradation...

I'm surprised to see that the model is holding up reasonably well. If the batteries are declining faster than anticipated in hot climates, we should see a proportionally faster decline in cooler locales. Personally, I'm ready to embrace a more linear decline, since that's what some of the owners who had gone through a pack replacement have seen. That said, the leveling off built into the model is based on an NREL paper, and others. I believe that Stoaty used the graph TickTock drew after a meeting with a Nissan engineer, among other things, to verify the calibration. While cycling will increase with diminishing battery capacity, cycling losses apparently still make out a minority of capacity loss. You might want to look up a prior discussion on this.

Capacity fade models typically assume diminishing caledar losses and linear cycling losses, as evidenced by this NREL study as well. Since the majority of the capacity fade in the LEAF will be due to calendar life degradation, we can expect this process to slow down over time. This is typically modelled with square root of time, which means that calendar life degradation seen in the second year will be about 41% of the loss seen in the first year of ownership. This diminishes to 32% in the third year, and 27% in the fourth year, and so forth.

Stoaty's model incorporates this assumption as well, and so far it has been pretty accurate, considering the field data we have collected so far. Linear cycling losses assume similar and constant charging and driving habits over time. If you have to start quick charging every day to make your commute, much like TaylorSFguy lately, or charge more often on a daily basis, then these losses could accelerate instead of remaining steady. However, since they will likely make out a smaller portion of the total degradation figure, the net effect of more agressive charging could be somewhat contained. Overall, there is a good chance that we will see the leveling off Andy mentioned in his interview.

Below is what the model from the Wiki predicts for Dallas, TX. Assumptions made: 12.5K miles annually, 4.2 m/kWh average economy, 5 days a week in the sun, 100% charging with 1 hour spent sitting at full charge.

(Many thanks to Stoaty for all the hard work that went into this).

 

[TomT]

Yep, I am often forced to do a 100% charge now when an 80% charge would have been plenty before...

I agree that the dynamic you describe below initiates a vicious cycle that i think is ignored by the model. Since losing my first bar recently, I can attest to a change from daily 80% to daily 100% charging that imposes higher average battery temperature from this point on as compared to my first 2 years of usage. This one factor alone means that the ambient temperature of my location increases over the ownership period.

 

[surfingslovak]

As previously noted, calendar losses are only proportional to the square root of time at the very biginning of the cell's life. After that, the calendar loss of capacity becomes linear with time with the slope affected by temperature. This effect can be seen in the four papers on long-term calendar losses which have been posted on this forum, including one that you yourself posted. You can find those papers easily by looking at the five links I porvided on point 2 in this post.

There appear to be two schools of thought on this, but most capacity loss curves and predictions I have seen are not linear. I think this particular behavior is supposedly based on the fact that the cathode material becomes more heat resistant as it ages. I would have to look up that quote somewhere, but that's what I remember.

 

[surfingslovak]

Yep, I am often forced to do a 100% charge now when an 80% charge would have been plenty before...

I agree that the dynamic you describe below initiates a vicious cycle that i think is ignored by the model. Since losing my first bar recently, I can attest to a change from daily 80% to daily 100% charging that imposes higher average battery temperature from this point on as compared to my first 2 years of usage. This one factor alone means that the ambient temperature of my location increases over the ownership period.

What if the cycling loss only made out 20% or 30% of the total capacity loss? Even with 100% charging and more cycles towards the end of the life of the battery, the impact on the overall decline should be fairly modest, and might add "only" a few percentage points. I think the model could be tweaked to include rising number of cycles for cover the same mileage. I think the factor to multiply the line item with would be 1/(remaining capacity). An owner who has lost 15% of battery capacity will consequently need to cycle the battery 17% more to achieve the same number of annual miles.

 

[RegGuheert]

There appear to be two schools of thought on this, but most capacity loss curves and predictions I have seen are not linear. I think this particular behavior is supposedly based on the fact that the cathode material becomes more heat resistant as it ages. I would have to look up that quote somewhere, but that's what I remember.

There are several mechanisms which affect loss. I do not dispute that some of the mechanisms result in a loss which is a function of the square root of time. But other mechanisms result in a linear loss of capacity over time. Logically, the linear loss mechanisms will dominate when long times are observed.

To my knowledge, we have uncovered four papers showing calendar losses for long term tests. ALL of them show linear or faster degradation (sometimes following a period where the other type of degradation is apparent). I have asked before for someone to produce a paper showing MEASURED data of long-term calendar losses that indicated less than linear degradation. So far, I do not recall seeing any such measured data.

 

[Stoaty]

Below is what the model from the Wiki predicts for Dallas, TX. Assumptions made: 12.5K miles annually, 4.2 m/kWh average economy, 5 days a week in the sun, 100% charging with 1 hour spent sitting at full charge.

One correction to your post: after 5 years in Dallas with the above assumptions the distribution will look like this (you may have forgotten to fill in the appropriate numbers under the fractional year section). Still, calendar loss is the major portion of the loss.