Will a 3HP motor ever use less electricity (power) than a 1.5HP
For most motors sold for general purpose use or purchased by manufacturers for use products, the motor manufacturer will provide reasonably complete performance data. That would generally include input power or efficiency at 1/4, 1/2. 3/4 and full rated load torque. For many motors, manufacturers will provide performance curves that include a continuous plot of efficiency or power vs. load torque. The efficiency curve shows zero efficiency at no load, rising rapidly as load increases and then leveling of somewhat above 1/2 load. Peak efficiency often occurs at or slightly above rated load, but sometimes occurs closer to 1/2 load.

If you have a 1.5 Hp load, you really should use a 2 Hp motor if there is any chance at all that the load might actually be more than 1.5 Hp or might increase as the machine ages or the process changes. There will probably not be very much wasted power. You should not use a 3 Hp motor unless you absolutely can not be confident that the load is less than 2 Hp even then, you should consider replacing the motor if you later find it is larger than necessary.

Since higher power motors are generally have a higher peak efficiency than lower power motors, there is a possibility that a higher power motor will use a little less power than a lower power motor at some load, but that would rarely be the case and the difference would be quite small.

Here is an example of a motor data table that provides the information needed for this type of comparison:



Note that the table and the above discussion assumes a 3-phase induction motor, the type of motor usually used for fixed-speed motors 1-1/2 Hp and larger.