Battery Pack configuration & Estimations

Mr_funnypuns

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Rivian has annonounced that their battery modules will contain 864 2170 cells and deliver 15 kWh. According to published data, the LG 21700 can deliver about 18 WH, so the math matches, at a module capacity of 15.6 kWH.

Factoring the 864 batteries it seems to me that the configuration could be 8 x 108 - eight strings of 108 2170 cells. This means each string would have a peak voltage of 108 * 3.6V = 388V and have an internal resistance of 108*0.025 ohms = 2.7 ohms, 8 modules has a resistance of 2.7 ohms / 8 = 337 milliohms. Rivian has published a 0-96 kPH time of 3s. This means 26.7 m/2 * 26.7 m/s * 1/2 * 2670 kg = 951.7 kJ over 3s, or an average power output of 317 kW from 12 modules, with each module delivering 26 kw. Applying a little algebra, this works out to about 71 amps per module, or 8.8 amps per string and cell, making the dissipation for each cell right about 1.9W.

1.9W per cell means each module is dissipating 1.7 kW while delivering 26 kW, and operates at an electrical efficiency of about 93%. The entire pack is generating about 20 kW of heat, which means the thermal conductivity of the cooling system needs to be around 667 Watts per degree C if the pack is kept to 30C, or 400 watts per degree C at 50C.

The point of all this math? It’s fun!!! Well that, and, by known the configuration and some of the implications of that configuration allow us to make other estimations about the Rivian. One of the more interesting things is that the pack seems to be be designed in such a way that when the truck is used around town at much modest loads, say 0-60 in 15 seconds, the pack might last a very long time indeed.

Working out the math for that next.
 
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ajdelange

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Consumption is probably going to be 400 - 500 Wh/mi. For an errand involving 20 mi of driving that's 8 - 10 kWh. At 90% overall efficiency that means 0.8 - 1 kWh of heat dissipated in the battery, inverter, and motors. If the average speed in town is 30 mpH then going 20 miles means 2/3 hr drive time for power consumption of about 12 - 15 kW and waste heat generation at 1.2 - 1.5 kW. This is just about enough to heat the cabin on a reasonably cold day. On the highway the consumption may be a bit better but using the same range at 60 mpH would imply 1/3 hr for 20 mi and average power consumption of 24 - 30 kW with waste heat of 2.4 - 3 kW.

These numbers aren't too far distant from what I observe in a Tesla MX100D which consumes about 300 Wh/mi for 18 kW consumption at around 60 mph and about 1.8 kW waste heat assuming 90% efficiency.
 

ajdelange

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1.9W per cell means each module is dissipating 1.7 kW while delivering 26 kW, and operates at an electrical efficiency of about 93%. The entire pack is generating about 20 kW of heat, which means the thermal conductivity of the cooling system needs to be around 667 Watts per degree C if the pack is kept to 30C, or 400 watts per degree C at 50C.
Let's take a stab at a ROM number for thermal mass of the battery by assuming that the 4 kW battery heater in the Tesla X can warm it 20 K in 10 minutes. That gives a thermal mass of 4000*600/20 = 120000 J•K^-1. We know the Rivian battery is going to be about 1.8 times bigger than the battery in an X so lets call the thermal mass 216000 J•K^-1. Now hit that with 10% of 951.7 kJ and you' have a rise of 95170/216000 = 0.4 K for the acceleration from 0 to 60. It's going to be more than that because more energy is expended in going from 0 to 60 than just the kinetic energy delivered to the car i.e. drag and rolling resistance also have to be overcome. But certainly less than 1 K. More interesting is in cruise where power consumption would be more like 30 kW with 3 kW waste heat assuming 90% efficiency. That's 10.2 BTU/h which may sound like a lot but is only 0.85 ton. In winter we want to retain a large part of this heat to keep the battery warm (it's enough to raise the temperature of a 216000 J•K^-1 battery 50 degrees in an hour) but in summer we need to shed it. In hot weather the usual rule of thumb is 1 HP per ton so that the cooling load would be about 750 W. This is of the same order of magnitude as the heating load for cold weather operation. Very rough numbers these but instructive nonetheless.
 
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Mr_funnypuns

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Y'all are good at math.

Break it down for me on a 100 degree summer day here in TX.
sure. We start by assuming the battery works. Then, using physics, work backwards to deduce how it works.

I’d neglected to consider thermal mass.
Math is fun!
 

ajdelange

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Break it down for me on a 100 degree summer day here in TX.
The numbers I gave are very rough rule of thumb and so we can't say what's going to happen with the Rivians especially as we don't know any of the design details - even at the most sketchy level. What we do know is that some of the Teslas will seize some or all of the cabin cooling capacity to keep the battery cool if the battery needs it and, I suppose, limit the draw from the battery in other ways under such circumstances. Several people have reported miserable trips in the California desert as a result of this. The same will happen with a Rivian, of course, unless its cooling system is designed with more capacity than that in the Tesla. This is, of course, a design trade. Modern compressors can be modulated using the same control techniques that modulate traction motor output but we can be sure that a 4 ton (4 HP) capacity compressor running at 25% of capacity most of the time will be heavier, more expensive and less efficient than a 1 ton compressor running at 100%.
 
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electruck

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Several people have reported miserable trips in the California desert as a result of this. The same will happen with a Rivian, of course, unless its cooling system is designed with more capacity than that in the Tesla. This is, of course, a design trade.
I would/will be pretty pissed if my high dollar vehicle can't keep me comfortably chilled on a 110 degree Texas summer afternoon. It's fear of this very scenario that may drive me toward the metal roof option instead of one of the glass options.
 

ajdelange

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It is something to be aware of.
 

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As far as I know, the cabin cooling issue on Tesla's was on the S/X years ago and has since been resolved. I know of one owner that called tech support mid trip and they fixed the issue "over the air". This was in his Model X very shortly after they were released.

I have zero concerns that the AC will not be able to cool both the battery and cabin.
 

ajdelange

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As far as I know, the cabin cooling issue on Tesla's was on the S/X years ago and has since been resolved.
This is the result of a design trade off. There simply is not enough cooling capacity to handle the battery and have any left over for the cabin. This is pointed out in the owners manuual.

I know of one owner that called tech support mid trip and they fixed the issue "over the air". This was in his Model X very shortly after they were released.
There are some problems that are fixable OTA and some that aren't. Inadequate cooling capacity is one of the latter. The manual warns that drivers may find themselves in this situation.

I have zero concerns that the AC will not be able to cool both the battery and cabin.
That's nice but a prudent buyer would ask about this when talking to the Rivian people. Clearly it happens at some level of power consumption, at some ambient and at some cabin SP. One should find out what those numbers are if he lives in or anticipates operating in a hot climate.
 
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