ringo wrote:
Internal resistance also drops with increased temperature.
Sorry Ringo, are you are sure about this?
Supra conductivity is normaly achieved at 0K.
It is correct, that a battery looses performance when it is cold, because you need a minimum temperatue/energy for the chemical reaction to take place, but the resistance of most materials increases with temperature.
As WB pointed out the internal resistance of the battery means it will heat up during charging/discharging. As lower the internal resistance of a battery as lower the temperature involved and as lower the voltage drop.
R= U/I and P=U*I
which means for a know restitance and current you can calculate the voltage drop and then the power (loss) which get´s turned into heat.
To achieve the charging rates WB is looking for we need:
4000KJ (4MJ) / 12s = 333KJ (kW/s)
at an voltage of 305V that makes 333000W/305V = 1092A /3 (because we have 3 cells in parallel)= 364A
Now, we need to know the internal resitance of an A123 cell (I will do some calcs later), but for now I will use the 140mOhm claimed in one of the KERS papers I have posted earlier.
This would mean 364A*0.14Ohm= 50.96V (this is the voltage drop at the battery)
50.96V*364A= ~18550W or 18.5kW
As Xpensive would say, that´s a lot of toasters, and would require some massive cooling.
This energy is a "loss" so you would need to account for it, when calculating your havesting&release rate.
For fun you could calculate the cable diameter required for 1092A (from the MGU to the accu).
An acceptable voltage droop for such an application is normally 0.25V.
(this means 1092A*0.25V=273W your cable gets pretty warm as well, but its managable)
Let´s assume we have 1m distance and two cables (+/-) that makes 2 meter and we use silver cable (which is common for these applications).
Silver cable has a specific resistance of ~0,0161Ohm*m/mm^2.
With this you can calculate the area (mm^2) needed for your cable, and then, assuming it´s a round cable, the diameter needed.
We talk about some pretty serious installations here.
Just think about the electronics to control 333kW!!! and the connectors involved.