On a typical application for a variable speed centrifugal pump, at which percentage speed setting will the VFD dissipate the most heat, in other words have the highest losses?
Since the torque required to drive a centrifugal pump is approximately proportional to to the square of speed and the power is approximately proportional to the cube of speed, the VFD will almost certainly dissipate the most heat at the maximum speed.
Most VFDs that are available today are essentially a 3-phase rectifier supplying a constant DC voltage input to a 3-phase PWM inverter.
The output current of a VFD is approximately proportional to motor torque. The losses due to forward voltage drop in the switching devices is proportional to current. The switching losses are proportional to speed unless the VFD has a design feature that changes the PWM strategy over the operating range. The input current of a VFD is proportional to output power. The losses due to forward drop in the input rectifier will therefore be proportional to output power.
The many VFD designs that are available or have been available in the past have different loss characteristics over their operating ranges, but it is very likely that all of them will experience the highest losses when driving a centrifugal pump at maximum speed as compared to any lower speed.