Battery current vs. phase current --- is it always MC x 1.73?


100 W
Jan 21, 2020
Supposedly phase current (if it has to stay theoretical and cannot be adjusted on the controller) is motor current x 1.73 (square root of 3). I know the actual equation to get to that point is more complicated but on a practical level, do all controllers with 3 phase lines have this already built in, and which controllers can adjust phase current out of proportion to battery current?

I'm also seeing a lot of controllers (ebike or not) with phase currents either calculated or 'set' at 2.5 times the battery current for some reason, instead of 1.73.

If a controller is rated at 30A, that means it's 30A max for the battery current and 52A for the phase current --- or the other way around? So if the latter, then 30A labelled max on the controller is for the phase current; that would be a max 17.3A for the current draw from the battery?

The reason I'm asking is that on the Grin Motor Simulator, the difference between the battery and phase current can determine huge torque and watt changes to the both curves. We are talking between 40-120 Nm which is a large difference, all other variables being held equal.

For example, on my mid-drive if I put 17.3A max battery current limit and 30A phase current limit, the torque peak starts dropping at 51 Nm @550W, around 8 mph.

If however it's a 30A max battery current limit and 52A phase current limit, peak torque before the drop is 90 Nm @800W, around 7.5 mph. That's a big difference. Keep in mind again that this controller (in the mail) is current limited at would that be 30A total limiting (for phase current) or 30A just battery draw?

Considering that my rated 500W geared hub drive has a claimed torque peak of 48 Nm and the 450W rated mid-drive's is 139 Nm, I'm thinking the phase current goes 1.73x above the max battery current that is labelled on the controller. Yes or no?

Messing around with the parameters, the mid-drive (strangely) came with a triple chainring 28T, 34T, 44T. If inputing 34T and they are assuming I'd use an 8-speed 34T cog for the granny gear, all other variables equal to the above torque outcome of 90 nM (including 30A battery / 52A phase to motor), then the peak torque is 139 Nm, exactly the same as the manufacturer's rating. Yes, I of course had to mess around to get that number but it's realistic. A lot of riders do use a 34/36T chainring and have a 34T max cog in the back. So it really does point to the phase current being 1.73x higher than the labelled max current on the controller. Correct? And if not, where did I go wrong in these motor simulation calcs?

If you were wondering, the Geared Hub Motor with the current set at 30/52 has a peak torque point of 59 Nm @1000w, about 14 mph. (It does now have a 30A max controller). Setting the max battery current A to 22 with the original controller it came with 43 Nm peak torque @850W, around 13 mph. Remember peak torque is claimed by Bafang on this geared hub drive to be 48 Nm, so 43 is pretty close. Calculations 'seem' correct for phase current to be 1.73x the labelled max controller current.

If limiting current set at 17.3 from battery / & 30 max phase current to motor = 34 peak torque @650W, 15 mph. Torque was almost cut in half from the 59 Nm above (with the 30A max controller, not from the 22A one). Torque would be cut even more on the 22A max controller if phase current set at 22 instead of battery current.