Battery internal resistance losses

Battery internal resistance losses

I was wondering why I am getting quite widely different kWHr usage on my daily commute over HW 17 Santa Cruz, where the main variables are temperature and driving speed. I've seen variations between 280WHr/mile to 350WHr per mile (I have a 60kWHr battery). Since the speed mostly below 60mph, aerodynamic losses probably do not account for the whole variability. I took a look at the losses due to battery internal resistance, and came to the conclusion that losses due to (high) acceleration and hill climbing at different speeds are significant, accounting for about a 10% variation. If you are interested in the details you can follow the link to a google spreadsheet that shows an estimate of the effective battery efficiency at various output powers for all three battery sizes.

jat | 17/02/2013

Aren't you conflating internal resistance in the battery with losses elsewhere in the system, particularly the inverter and the motor itself, or do you have a way of measuring just the battery?

In particular, the efficiency of an AC induction motor drops substantially at high torque.

mal42north | 17/02/2013

No I believe the internal resistance losses are to first order independent of the losses in the rest of the drive system. So to get the total losses you have to add the internal resistance losses to the losses in the inverter the motor and the drive train. However since we don't know the design of the inverter its not really possible to calculate its efficiency. I would expect the inverter efficiency to peak somewhere near its maximum drive capability, so its efficiency variation will somewhat level the efficiency variation of the battery.

lph | 17/02/2013

Disclaimer: I am not an electronics engineer.
It does seem plausible that resistance (producing heat) is to be expected. When I use my laptop with low demand the battery stays cool, however when playing a movie with the CD running and sound it gets really hot. This indicates that it maybe a trait of the lithium battery to give more resistance under demand.
Guessing here but maybe in really cold weather and when starting in the morning trip in slightly warmer climes there is not much disadvantage to mashing the accelerator because under this scenario it would help warm the battery and in its sweet spot.

mal42north | 17/02/2013

To first order the resistance is just a function of temperature, but the power loss due to the resistance is dependent on the square of the current I^2R. So as your current draw increases the loss due to internal resistance increases quite rapidly.

eq1 | 18/02/2013