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Discussion in 'Model 3: Battery & Charging' started by jebinc, Sep 12, 2019.
I believe I did in an earlier post above. Thanks!
Power divided by power is efficiency, and that's in the chart already linked. E vs P.
Power or Efficiency vs SoC looks flat with a taper (the ASCII chart I already drew above, e.g. ---------\)
Power added vs Power supplied is just a straight line sloping up at 45 degrees, for 250 W overhead, it is y = x - 0.25
[EDIT: Sorry, it's y = 0.95x - 0.25. Forgot about the ~5% loss in the charger, so slope is less than 45 degrees! Still a line though]
Sorry, not trying to be an ass here, but I don't understand this. How much power is needed to go from 50 to 51%?
1% is a fixed* kWh depending on your battery size. Say 75 kWh, so 1% is 0.75 kWh or 750 Wh.
How much power is need to go from X to X + 750 Wh? ... any amount of (net) power greater than zero, multiplied by enough time. Net power = input power x efficiency - overhead (~250 W).
e.g. 11 kW at 93% efficiency minus 250 W overhead delivers 9.98 kW to the battery. 11 kW will deliver this same 9.98kW to the battery at 0% or 20% or 55% or 90%. The chart is a flat line. After ~96% it tapers down.
What is T? Or what is it you want here?
Do you want how much energy is needed to add 1%?
*Not really fixed because it can change due to miscalibration, degradation, etc... but let's just go with 'fixed' here.
I think we should be able to take the model equation from @darth_vad3r, which is efficiency as a function of input power E(p). We can then plug in another function p(%). Input power as a function of state of charge %.
So you’ll have E(p(%)).
This would be better than per % because it would be continuous. You could integrate and average over each % if you really want average efficiency per %.
We have a good idea of E(p), and we can just make up a function for p(%) for now, parameterized. Once the empirical values are known they can be plugged in.
Since using %, you’re assuming a battery with no degradation.
Finally, if you want to convert that final function to actual energy and loss, each mile added (after all losses) is 245Wh for AWD. And each % is 3.1 miles. So 760Wh. You can take the efficiency formula and create another formula in terms of energy if you want.
It’s really just a matter of knowing the parameters. That’s the more time-consuming part. All the equation stuff is super easy - high school math; maybe a little calculus if you want.
Wait, this one? It's asking for something different:
x-axis is power in kW (e.g. 1kW, 2kW, ... 11kW)
y-axis is battery gain (in % or range) ... this is essentially energy, kWh.
To get a chart of kWh vs kW, you need to specify a time variable T to multiply by ... do you want 1 minute? 5 minutes?
This is what I *think* you asked for added to the existing efficiency vs charging power chart (with a new right y-axis for power delivered to the battery) ... but I don't think it's actually what you want (at least I don't think it's what you actually want )
The blue squares reflect how much of the input power makes it to the battery at any given power level.
If you want the axis to read %, miles, or energy instead, you need to multiply by some time T, and since that would be the same for all input levels in one chart, the line would look identical, just the axis would be relabelled. Is this what you meant when you said you don't care about T?
Maybe this is what you want after all ...
I was sitting at the table eating lunch thinking about this thread and my wife asked what I was thinking about. My typical answer is sex since it is one word, requires no explanation, and is correct about 80% of the time. Instead I described this thread. Should be a good long time before she asks again.
Here's another chart ... right y-axis is now % delivered to a 310-mile battery per 30 minutes (sorry I forgot the 'per 30' in the axis title)...
ps. I have all this data just sitting in a sheet and can easily add new columns. If these aren't what you are looking for, just let me know.
It's not very interesting to me because it's just a line, but maybe that's what you were after.
Thanks, all! Crazy day here... I will review all above later today. Would be great to have the equation for the P v. C curve, that way I could do some differentiation at various P/C points to determine rate of change, etc. Thanks again!
P vs C is a line. The derivative is the slope, 0.95. I gave the line formula above, y = 0.95x - 0.25.
This is a model. It fits empirical measurements half-decently or better. 5% loss in the charger, then 250 W of fixed overhead from the car being on. All values aprox. Use at your own risk.
To convert power (y) to kWh, I multiplied by 0.5 for my per-30-minute chart.
To get % I divided by the battery capacity.
For a 310-mile LR AWD I ballparked this as 310 mi * 245 Wh/mi = 75.95 kWh*
For some definition of a "kWh" this may even be accurate. We've got wall-kWh, DC kWh into the battery (ikWh) and DC kWh out of the battery (okWh) being 'measured' / estimated by various meters available to us in the car and/or API. "245" is the charge constant for adding "okWh" to an LR AWD.
[EDIT: Or did I mess up the nomenclature already. I think it was oWh and iWh, and then koWh and kiWh ]
I think @jebinc means the power vs. SoC (C?) at the end of the charge (i.e. the taper characteristic). But not sure! Though you also gave a rough model of that above as I recall.
Haven't reviewed anything above yet, but you are correct - Power (P) v. SoC (C)
Edit: I charge using a HPWC at 48 Amps, so power is around 12 kW. Ideally, a chart would cover that range, if it hasn't already been posted above. Later all!
Well that's a totally different chart ... and one that I still don't understand the requirements for.
If someone tells me what "y" is, I can chart it (maybe).
Oh wait, the formula for @Zoomit 's taper? Ask him
ps. I think we should be saying "y vs x", so a taper profile is max power vs SoC.
but earlier C was described as the y-axis I believe ... and P the independent variable ... so... maybe the opposite was meant and I read it the traditional way and misinterpreted things. Or actually I said it backwards at least once myself
Well, no, C was described as %-gained there. So that was delta-C vs P.
A taper chart is max-P vs SoC.
Here is a capture from Chargepoint. This was an 88% to 99% charge. It was a 6kW max charge station.
You can see the taper to below 6kW did not occur until about 97 or 98% (based on area under the curve prior to taper, relative to total area, then using this ratio to scale the 11% added energy). Only 15 minutes of the 1:30 charge had any taper.
For an 11.5kW source it would taper a little sooner, maybe 96-97%?
Really this capture does not have the necessary resolution to generate a full model with decent parameters. Sorry. I played around briefly with a model today; might try again with a time-based model tomorrow. In the end it is not going to be very interesting though - the taper doesn’t matter much, because it just does not last very long.
First, thank you to all who have tried to find or produce the chart I was after. I was looking for a plot that ranged from 0% to 100% SoC, as I figured this plot would largely be linear - until some point near 100% - and then, at a point near 100% the plot would turn somewhat asymptotic (But not really, as you do get to 100%) as power dropped approaching and ultimately achieving 100% SoC. Once this elbow was isolated, I would do a time ("T") v. SoC ("C") plot, starting from just before (say 3%-5% SoC before) the start of the elbow in the P v. C plot, to 100% C. For me, I wanted to first see where the “elbow” of this plot was to determine the optimal cut off for charging, when taking a longer trip. Rather than charging to 100%, I would charge to the optimal point in this “elbow,” for max efficiency and reduced wait time. Based on the data provided this far, that optimal point appears to be somewhere between 95% - 97% SoC.
Please keep the letters and cards coming!
I admire your dedication to efficiency and optimization. Taking it to the next level.
Agreed. Pretty sure no tapering prior to 95%. Though even with battery heating I could see it could maybe happen a little earlier in winter. Or not.
Your optimal charge range is like 10-20% to 50-60% and driving ~200km/hr if you refer to TeslaBjorn's video.
If you don't want to drive that fast, and care about preserving Tesla's electrons, you'll slow down a bit, but your overall trip time efficiency is still going to be best stopping well WELL before 95%. e.g. 2x 10->50, 10->50 is going to be faster than one 10->90.
Another way to look at it is, unless you are going to NOT make it to the last stop, how long is it going to take you to add that 5% from 90 to 95% now, versus adding that same 5% later.
a) You might never need to add that extra 5% if you don't need it.
b) If your next charge is a 20->60% charge, then the extra 5% is going to be 60->65% (this is the case where the 5% is needed down the line, say to get you into a spot where an overnight trickle charge has you starting a morning leg at the SoC you want).
I personally would take into consideration time efficiency not just electrical efficiency. For this you have to consider the entire profile from 0 to 100% from @Zoomit 's excellent charts.
If time is of no concern, and you only want to save electrons, then that's a different matter.