Methodology, or How do I Log All of This Data and Stay Sane?
After my nearly-out-of-charge experience driving home from the Rochester dealership to Madison, I figured I wanted to know how the battery would behave in this new electric car over a long period of time and a wide range of driving conditions. I immediately started a mileage log where I recorded the number of miles on the GOM post-charge, the high and low temperature as measured by the car's thermometer during the trips between charges, and the number of miles on the GOM and the odometer right before plugging in. Since my commute to work is slightly more than 11 miles, and I use the Leaf primarily for that commute, most of the trips between charges are either 22 miles in the winter or 45 miles in the summer. In the summer I can safely do two commutes on an 80% charge, but in the winter I don't chance it.
One of the issues with taking the data this way is that the temperatures associated with the driven miles are not very accurate. For each set of trips between charges, I end up with a single high and low temperature. In the summer when I do two commutes on a charge, there can be a lot of variation in temperature between the two commutes, and that is not captured well in the data. If I had it to do over again, I would have recorded a temperature for each trip and calculated a weighted average temperature for each charge cycle. In fact, I've started doing that now, so in a few months I should have some more accurate temperature data to compare to what I already have. As it is, I calculate an average temperature from the high and low temperatures.
The other major issue is that I am fully depending on the car's measurements and representation of the battery charge level. The Leaf's miles-to-empty readout is called a Guess-O-Meter for a reason. It moves around a lot, and in my experience, it is always optimistic - more so in ECO mode. I could have invested in a GID meter that reads the battery's charge level directly off of the Leaf's CANbus, but I didn't do this for two reasons. First, I didn't know about this meter early on, and I didn't want to invalidate the data I had already taken by changing my methodology. Second, I wanted this to be a real-world test of what an average Leaf owner will experience over the long term. The average person is not going to buy a meter and measure their battery everyday. They're going to depend on the Leaf's telematics, so I thought it best to do the same.
Data in the Raw
After entering all of the data into a Google spreadsheet, I did some quick data corrections. On a handful of charges, I charged to 100% instead of 80%, so I scaled the GOM readings for those charges to 80% to make later comparisons easier. Then I took the midpoint of each high and low temperature set to have an average temperature value for each charge cycle. Here's what the post-charge GOM and temperature data looks like as a time series (click to enlarge).
Conveniently, the GOM miles and temperature are on the same scale. Immediately, you can see that there is a correlation between these two series, although it's far from perfect. In a number of places, big changes in temperature do not correspond to big changes in the GOM readout. A couple other observations come out here. One is that the GOM readout changes markedly near the end. That is because of the software upgrade I had done on June 28th, and you can see that it reduced the GOM's optimism somewhat. The second is that 2012 was warmer overall than 2013 so far. The early winter months were milder and warmed up much faster than 2013, and the summer spent much more time over an average temperature of 75℉. That will be significant later on.
One other thing I changed during the data collection was when I drove in ECO mode or D(rive) mode. At first I always drove in ECO mode, but in the end of May this year I switched to D mode on the beltline because I wondered if the regenerative braking was being too aggressive when I was going 55mph. I thought I might get better mileage in D mode, but it turned out to make absolutely no difference and no change is noticeable in the data. I did learn that ECO mode adds a flat 10% to the GOM. That may be a good estimate for city driving, but at constant freeway speeds ECO mode and D mode are basically equivalent unless you're running the climate control. There is no mileage benefit to one or the other so I'm switching back to ECO mode because I like the accelerator behavior more in that mode. For the purposes of this data analysis, everything is converted to ECO mode values to keep calculations consistent.
Estimating the Battery's Capacity from the GOM
There's not much more we can deduce from the raw time series, so let's try putting it into a more useful form. The obvious thing to do is plot the post-charge GOM reading against temperature, so here's a scatter plot of that.
I plotted the data for 2012 and 2013 in different colors so that you can see how they differ. The 2012 data has a lot more samples in the 50-60 degree range and above 80 degrees. The 2013 data has more samples clustered below 30 degrees with a near void in the 50-60 degree range. The data is certainly noisy, but there is a definite correlation between GOM miles and temperature. That trend seems to peak right around 75 degrees and then starts to tail off at hotter temperatures, but at a much slower rate than it does at freezing temperatures. It's a bit hard to draw more conclusions from the higher temperatures because of a lack of samples up there.
What we can do is calculate a regression line to get a linear estimation of the GOM-Temperature relationship. I ran regressions for all of the data and 2012 and 2013 separately, and here is what came out:
All
|
2012
|
2013
| |
slope
|
0.219
|
0.189
|
0.237
|
slope-sigma
|
0.0119
|
0.0154
|
0.0164
|
intercept
|
68.8
|
71.6
|
66.4
|
intercept-sigma
|
0.62
|
0.82
|
0.84
|
r^2
|
0.541
|
0.484
|
0.622
|
The regression coefficient, which is a measure of how closely the data fits the regression line with 1.0 being a perfect fit, is pretty good considering the GOM data is so noisy. It's a bit worse for the 2012 data and a bit better for the 2013 data. To get a better idea of what this data is telling us, we can plot the estimated miles-to-empty value for a given temperature using the slope and intercept values. Let's do that for the 2012 and 2013 regressions between 0 degrees and 75 degrees, and I'll include 3-sigma error lines above and below the main regression lines. I'll also scale the lines so that the 2012 75 degree point represents 100% of full capacity. I stop at 75 degrees because it's unclear from the data what the trend is above that temperature.
Now this is interesting. It looks like the Leaf's battery loses about 15-25% of its capacity in temperatures below 15℉. The 2013 line is probably pulled lower because there is a lot more data at low temperatures for that year, but overall, that agrees with what I was experiencing on the road. It also looks like my battery lost a bit less than 2% of its capacity over 18 months. That seems pretty good to me. If loss continues at that rate, my battery wouldn't go below 70% capacity for more than 20 years, and it would still be useable to me at that point!
I bet charging to 80% and not ever using quick charge stations has helped keep the battery healthy. It's nice to see that taking good care of the battery is having a positive effect. I just hope that the charge loss in years to come stays linear. Of course, with taking into account the error bands, the real capacity loss could be higher or lower than 2%. It would be nice if Nissan would give you a capacity loss value in percent during the annual battery checks, but they only report the number of bars of capacity out of twelve that the Leaf's display already gives you.
How About Calculating Battery Capacity Another Way
Instead of using the Leaf's GOM to estimate battery capacity directly, we can calculate an estimated range for each charge cycle and look at the charge loss between 2012 and 2013 from that data. The range can be estimated by calculating the ratio between the number of miles traveled and the difference in the GOM readings for each charge cycle and multiplying that by the post-charge GOM reading scaled to 100% charge, i.e.
Range = Charged_GOM/0.8 * miles/(Charged_GOM - Post_Trip_GOM)Plotting these ranges against the average temperature for each trip gives us the following scatter plot:
Whoa, that is some noisy data! I plotted the first five months of data in yellow to show that there was even more variation in the beginning. It seems that the Leaf goes through a pretty long learning period of about 2500 miles. Even with those points removed, this data is quite diffuse, and the regression coefficient is only 0.28. Also, the regression lines for the 2012 and 2013 data cross, which doesn't seem right at all. However, if we take the average of all of these ranges, we get 75.5 miles. That is really close to the EPA's estimation of a 73 mile range for the 2012 Leaf, so we're probably on the right track.
One of the problems with using the Leaf's GOM reading to calculate range is that after a charge it is estimating the miles-to-empty using the data from the previous charge cycle to attempt to predict the future. Since we already know the future temperature for each trip that the GOM is trying to predict, we can plug that average temperature into the linear estimation formula to get a better estimate of the starting miles-to-empty for each charge. Then we can plug that number into the equation above for calculating the range. Here is the plot that we get from that exercise:
All
|
2012
|
2013
| |
slope
|
0.237
|
0.215
|
0.222
|
slope-sigma
|
0.0215
|
0.034
|
0.028
|
intercept
|
61.1
|
64.3
|
60.5
|
intercept-sigma
|
1.18
|
2.06
|
1.43
|
r^2
|
0.371
|
0.34
|
0.334
|
The overall regression coefficient improved considerably, and the regression coefficients for the individual years aren't much worse. However, there is considerably more uncertainty in all of the coefficients than there were for the battery capacity estimates. It is still informative to plot the regression lines, but the 3-sigma error lines are much wider.
Note that for the estimated range, the slopes for the two years are almost identical, possibly because the data during the learning period was removed. The range varies from a minimum of about 55 miles in extreme cold to more than 85 miles in pleasantly warm temperatures, or more than 20% variation over this temperature range. The difference in the two lines equates to approximately a 4% loss of range, but with the large error bands, it's quite possible that the real loss would be higher or lower. A 4% loss would still be respectable, and it would take more than 11 years to hit 70% of full range.
I should stress that these linear estimates are just that - estimates. The range values were calculated from a linear estimation, and I have never driven my Leaf from a 100% charge to "turtle" mode, where the car limits the speed to a crawl to conserve charge and protect the battery from completely discharging. Thus, I don't actually know what the real range is at any temperature, let alone over a range of temperatures. What these plots do show quite well is that even if you did drive the Leaf until it's near empty, there's a lot of variation from one charge cycle to the next, and you won't have a good idea of its overall range unless you do a lot of those measurements. Treating the battery that harshly is not recommended, and would accelerate the capacity loss, so I prefer to play with estimation techniques.
We're Not Done Yet
So far we have seen that the GOM data I'm working with is highly variable. I'm going to speculate that the variation is actually due to the comparatively short range of the Leaf, and that if its range was about four times larger, it would be at least as accurate as the mileage estimators on normal ICE cars. To model this assumption, I took the data from the previous plots and summed every five samples of the post-charge GOM, post-trip GOM and trip miles, and I did a five-sample running average of the temperature data that was weighted by the trip miles. If I then run this data through the range estimation equation, I get a set of estimated ranges for a 300-mile range Leaf with the assumption that I'm charging it to 80% and driving it almost to empty.
Now that data looks much more correlated to temperature. I removed the first five months of data again for this plot, and I combined all of the rest into one color since comparing the two years isn't useful with the modifications that were done to the data. The regression coefficient on this set of samples is now 0.72, showing much more predictive accuracy versus temperature.
Some may quibble with the fact that it looks like I'm just running the data through a running average, and of course the data will look tighter after I do that. But that is entirely the point. If the Leaf had a 300 mile range instead of 75 miles, the telematics would have many more miles of range and the associated driving conditions to make a good estimate and adjust it. Like so many other issues with EVs, the issues with highly variable range and what appears to be an inaccurate GOM would evaporate with a much bigger range.
A 300-mile Leaf would likely have an even more accurate trip computer than this plot portrays because the data it would be processing would be much less disjointed. (Also, remember that my temperature data could have been taken in a more accurate way.) The current job of the GOM is practically impossible because it's working with only tens of miles between charges, and it's trying to predict the range on a charged battery for as yet unknown driving conditions based primarily on the previous cycle's driving conditions. No wonder it's a Guess-O-Meter. Increasing the range in future EVs will certainly improve the GOM's ability to estimate range.
And Finally We Come to the Issue of Miles/kWh
I'm quite pleased to see that my Leaf's battery has probably only lost 2% of its charge in 18 months. It is also nice to see that the huge variations in range estimation are likely due to the simple fact that the Leaf has a much shorter range than a normal ICE car. What about that other number that the Leaf's telematics display so prominently: the miles/kWh? My Leaf has varied from 4.0 miles/kWh to 5.1 miles/kWh between winter and summer. Does that agree with all of this data?
If I assume that the battery is at a full capacity of 24 kWh in the summer, my range estimate of 80.5 miles equates to 3.4 miles/kWh, which is a far cry from 5.1 miles/kWh. The battery appears to be at about 80% of full capacity, or 19.2 kWh in the winter, so my range estimate of 64.3 miles equates to the same 3.4 miles/kWh. The Leaf must be estimating based on a fixed kWh number, so if we assume it's 24 kWh, that results in 2.7 miles/kWh. The average of 2.7 and 3.4 is 3.05 miles/kWh, which is really close to the EPA's estimate of 2.94 miles/kWh.
Why is the Leaf over-reporting this number? It's possible that it's using a lower value for the usable capacity of the battery and that the battery is more efficient in the 80%-20% range that I have been using it. But if we assume that the Leaf's measurement is accurate, then there would only be 16 kWh of usable energy in the battery. That seems a bit too low. Without knowing more about the battery measurement system design, I'm suspecting that it's a combination of usable capacity, optimal efficiency range, and over-reporting.
I'm not too pleased about that last reason. The miles/kWh is a critical measure of the efficiency of the car, and Leaf owners would benefit much more from an accurate reporting of this measurement for fuel savings calculations than the happy-but-ignorant feeling that comes from an inflated value. I hope that Nissan corrects this measurement in the future, or that the EPA can force more accurate reporting.
Other than that one issue, I'm quite happy with how this analysis has turned out. It appears that I have a healthy battery that will serve me well for many years to come, and the range is more than enough for my daily driving needs, even if it's a little variable. I'm definitely sold on the idea of EVs and believe that they are a solid, reliable alternative to ICE cars in the right circumstances with even more potential in the future.
Next week I'd like to shift from thinking about the past year and a half of Leaf ownership to thinking about the future of EVs.
The Rest of the Leaf Series:
Part 1: The Acquisition
Part 2: The Summer Drive
Part 3: The Winter Drive
Part 4: Frills and Maintenance
Part 5: The Data
Part 6: The Future
Part 7: The Energy Efficiency Meter
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