I am looking to properly understand the impact of battery specification, both voltage, and peak current, on the performance of a Tesla small drive unit, and the vehicle it is installed in. I discussed this briefly, but want to go into some more detail. While writing this post, I think I've answered pretty much all my own questions, but I'm going to post it anyway for information / discussion / corrections.
My basic understanding, assuming throttle is at 100% is as follows:
- 100% of battery voltage is always used, only current varies (directly proportional to power)
- The inverter attempts to provide the motor with 600A regardless of RPM for 100% torque
- The voltage required across the motor to achieve this 600A is (somewhat) proportional to the rotational speed
- The power drawn from the battery is (basically) the same as the power consumed by the motor
- At low RPM, the motor can have its 600A (and constant torque) at low motor voltage, and hence low battery current.
- Eventually a point will be reached where 600A is drawn and motor voltage is equal to battery voltage, so peak 600A is drawn from the battery.
- As RPM rises further, the motor voltage required to achieve 600A exceeds battery voltage. The inverter continues to apply full battery voltage to the motor, but current (and torque) falls as RPM rises. Power remains constant.
- Eventually the reducing torque and increasing air resistance are equal, hence top speed.
I'm fairly confident that this is how an induction motor works, but I have two big questions:
* With the Tesla Small Drive Unit, at what RPM will I run out of voltage for a 200V, 300V 400V battery? ie if I have a 200V or a 300V battery, at what RPM will i reach peak power and start to experience reduced torque? (this question is potentially answered later in the post)
* If I use a battery pack that cannot actually supply 600A peak, is the correct solution to reduce the maximum output power of the inverter accordingly, so for a 300V 400A battery pack, limit the inverter power to 120kW? This would seemingly have exactly the same affect as a lower voltage battery, the only difference being that the inverter is artificially limiting battery voltage.
It seems to me that if one can't fit a fully sized 96S 600A battery pack, one would get exactly the same reduction in performance, at all speed/rpm, using a 400A 96S pack, or using a 600A 64S pack. Both would deliver full torque up to some RPM limit, and then constant power (146kW) beyond that. Am I missing any benefits of one option over the other, or am I completely misunderstanding anything?
I found a graph that implies that constant power (reducing torque) begins at 40mph in the Model S (pretty much regardless of which model). I suppose we can assume this is correct for Tesla's wheel size and standard gearing at 96S. Will this reduce somewhat linearly with reduced power, approx 30mph if one were to reduce voltage 25% (ie to 72S)?
The final question I'd have to answer would be how the car actually feels
overtaking at 30mph vs 50mph vs 70mph, but I fear no amount of maths will be able to do that, as aerodynamics will have considerable impact.
Thanks for reading my ramblings. Please tell me if I'm missing anything important.