In my previous analysis of data from our CZero I did not take the storage degradation of the battery into account. In the 2008 Yuasa technical report on the LEV50 cell figure 8 shows Yuasa’s measurements of this degradation. With some minor modifications I’ve reproduced this figure here.
Figure 1 Battery capacity as a function of storage time at two temperatures (Yuasa 2008).
Yuasa found that a model relating the degradation to the squire root of days fit well with their measurements. This means that degradation slows as the battery ages. At the same time temperature has a large effect on the rate of degradation. As the battery is not in use or under charge the temperature in this case is the air temperature around the battery.
Yuasa released a second technical report in 2012 on the LEV50N cell. This has a lower rate of storage degradation than the LEV50. However I’m fairly sure that my battery uses the LEV50. If anyone wants a graph for the LEV50N similar to figure 1 please let me know.
Appling this squire root model to my data I get the result shown in the next figure. The process of data collection and analysis is described in an earlier post on this forum.
Figure 2 Capacity degradation for my battery as a function of the square root of days since the battery was made
My car is a 2012 model, which I bought as its first owner in June 2014, almost two years after it was imported in this country in Sept. 2012. The car only had about 2000 km when I drove it off of the dealer’s lot. By June 2019 the mileage was 89,000 km.
The first measurements shown in figure 2 are from July 2014 and the most recent are from June 2019. Unfortunately, I don’t know when the battery was made. For the age of the battery shown in figure 2 I just assumed a manufacturing date of Jan. 1 2012. Within limits the choice of a manufacturing date has little effect on the slope of the line in figure 2 namely 0.15 (Ah/sqrt(days)). This is the rate of degradation since I bought the car.
The rate of degradation for my battery is about half the rate at 25oC measured by Yuasa and shown in figure 1. We can use the rates shown in figure 1 to compute the temperature that gives the rate shown in figure 2.
Figure 3 The rate of battery storage degradation as a function of the temperature
Figure 3 shows the two rates measured by Yuasa with a line showing the rate as an exponential function of temperature. I chose an exponential function because I assume that this is a typical chemical reaction. Among other things an exponential function won’t predict a rate less than zero no matter how cold the battery gets. Using the inverse of the function in figure 3 and the rate of 0.15 I get a temperature of 10 oC, which is a degree or 2 above the average air temperature here in Denmark. If this analysis is correct then all of the degradation of the battery since I bought our car can be explained by the storage degradation. Charge and use cycles appear to be of little consequence.
The choice of a date for the manufacture of the battery does affect the predicted original capacity of the battery of 44 Ah shown in figure 2. The further back the manufacture date the greater the predicted original capacity. However to reach the specified capacity of 50 Ah at the present rate of degradation I would have to assume that my battery was manufactured in 2008. This seems unlikely. It’s more likely that the battery deteriorated at a greater rate before I bought it, maybe because it was in the dealers showroom and therefore warmer than it would have been if kept outdoors. Another explanation is that the true rate of degradation is greater than that I have seen so far. We know that the battery temperature is 5 to 10 oC greater than the air temperature when the battery is in use or while charging so the average battery temperature over the whole day must be greater than 10oC. I suspect that as I collect more data a new analysis will show a greater rate of degradation.
The most obvious implication here is that the buyer will never get a battery with the specified capacity. This explains the observation made by others on this forum that the battery capacity of a new car is always less than 50Ah. Storage degradation also means that the car should be kept as cold as possible both before and after sale. I’m not sure that air-conditioning the garage is a good idea but heating it certainly isn’t. Lastly it appears that within limits how we use and charge the battery has less effect on the rate of degradation than the average air temperature.
There is a lot of variation in the data for my battery shown in figure 2. Some of this is due to temperature but random errors in measurements also play a role. Therefore I will continue to treat my battery with care.