Vq/Vd ratio of different motors and consequences

Hello,

I've designed a FOC controller which runs in sensorless mode to drive different kind of ebike hub motors (geared and direct drive), and I'm wondering where does the difference in Vd required to maintain an Id near zero comes from ?

Some motors, typically geared ones, have a quite low Vd/Vq ratio (absolute value of about 1/6), but other ones have a much higher ratio, with some times Vd higher than Vq (in absolute value). In this case, there is a strange phenomenon : If we increase Iq ref, the speed becomes lower and motor consumes more (unloaded test). I think it's because of the circle limitation : we ask more Iq but as the Vd cannot go further (sqrt(Vq²+Vd²) = max output voltage), Id is increasing, hence motor going slower (contrary of flux weakening).

An other observation is that when I try to drive the motor in regeneration mode, motors which require an high vd have a very poor efficiency (most of the time, they provide a braking torque, but the regenerated power is close to zero, even close to nominal speed).

Anyway, has someone any idea of what makes some motor requires an higher Vd to maintain Id to 0 ? Is it related to motor saliency (I think ebike motor are only surface type PMSM, not IPMSM, so saliency should be very limited).

If you have any experience or explanation about this Vd/Vq ratio and its consequences on motor driving, don't hesitate to share them !

Thanks a lot,
Theophile

You're correct that this phenomenon is related to saliency and flux weakening.

In general for a permanent magnet motor, there is flux on the D axis due to the permanent magnets, and there is flux on both the D and Q axis due to the currents through the coils.

Mathematically (neglecting motor resistance):
λd = Øm + Ld*Id
λq = Lq*Iq

Øm is permanent magnet flux

Now assume the rotor is rotating at a constant speed ω. The currents in the stator do not rotate with the rotor, the flux in the D axis rotates into Q and the flux in the Q axis rotates into the D axis.

We can differentiate the equations to get the axis EMFs

Vd = ω*Iq*Lq
Vq = ω*Øm + ω*Id*Ld

We can see that a current in the Q axis will induce an EMF on the D axis.
If we assume, as you have, that this is an SPMSM and we don't want any current on the D axis, we get

Vd = ω*Iq*Lq
Vq = ω*Øm

Vd/Vq = (Lq/Øm) * Iq

Hence, lower inductance motors will have less EMF on the D axis and will have a better power factor. This is desireable, but the low inductance is not, so different manufacturers will make different tradeoffs in this respect. Creating a salient motor allows you to partially offset this effect, and is part of the reason IPMs are preferred for applications with a wide speed range.