Motor Connection with VFD, Delta or Wye?

For induction motors if you run the motor at a high flux level the winding flux magnetizing current has a significant third harmonic content that can flow around the Delta winding without appearing in the lines to the VFD.

This is good for the flux waveform but it is not seen by the VFD internal current sensors so you can over-flux and get high motor winding currents giving motor overheating with no indication in the VFD. So with Delta I recommend winding current sensors but this is extra complications.

With Wye all harmonics are seen by the inverter which stops over-heating but the inverter can not supply the third harmonics on a normal 3 wire design.

I prefer to have a Wye connection in the case of getting a grounded neutral to have a clear path to ground for the high frequency noise of the inverter system regardless of the motor, but that may not be of concern to you if the other connections around the system are not noise sensitive then using a delta connection can save you on the cost of copper wire if you are running over a long distance from the VFD. Then you can ground the Shell of the Motor. We have to consider the motor design as well. Is the motor an inverter duty motor or a direct online motor? What voltages are the windings set for and does it have a wiring diagram for delta or a wye?

Let me describe one special case of motor connection.
It's a variant, how to get more mechanical power from the motor comparing to direct on-line operation.
Conditions:

1. Mains supply to VFD is higher, then motor rated voltage
   (example: VFD's input 3x400 V, Motor is connected in Delta 3x230 V 50 Hz)
2. Rated VFD output current not less than motor current in Delta connection.
3. Set in VFD parameters motor data as follows:
   Motor rated voltage 400 V, Motor rated frequency 87 Hz.

Results:

1. V/f line comes through rated motor point 230V 50 Hz to maximum point 400 V 87 Hz with correct ratio.
2. Motor develop constant (rated) torque from low frequency to the maximum one on 87 Hz.
3. According to formula Power = Torque * Rotational speed, on 87 Hz motor can provide mechanical power 1,7 times higher, comparing to the direct connection to the mains.
   (Ratio 87 / 50 Hz is equal to ratio 400 / 230 V, or square root of 3)