Do energy efficient motors always cost less to operate?

This is an interesting phenomenon that many times creates a building construction problem.  Energy efficient motors have a higher inrush current simply because they are manufactured with a lower rotor and stator resistance.  This means that many types of energy efficient motors have a higher full load speed than their standard counterparts.  This could be significant when the motors are utilized for continuous centrifugal loads such as in pumping and fan operation. 

In centrifugal loads, speed changes greatly effect the required energy input, since variations in speed effect the required shaft power as the cube of the speed, while the flow of the air or liquid actually varies directly and linearly with the shaft speed.

Therefore an increase in the load of the driven equipment such as the fan or pump, can result in the increase of the kilowatt usage, despite the overall lower losses of the energy efficient motor.

There will actually then be a cost penalty of going to the energy efficient motor, since the equipment may have to operate at a higher full load speed.   This will depend on the type of service the motor is actually utilized for.  For example.  If you are going to utilize the energy efficient motor on a pump which is used to fill a tank or similar usage where the service is more or less a start - stop type, the higher speed at full load will develop a greater flow. This will simply cause the tank to fill faster and cause the pump to be shut down faster.  In this type of usage, the energy efficient motor will generate a cost savings.   Although the input to the motor may be greater, the operating time will be shorter.   This is where the cost savings can be developed.

If however, the motor is utilized in a system where there is continuous operation, as in a cooling or heating system where the extra flow developed by the faster speed is wasted and where it will often be throttled down by the balancing process, the actual system may generate an increase in energy usage by the installation of the energy efficient motor.

For the above reasons, the entire system must be evaluated when considering the installation of an energy efficient motor; not just the motor itself.  Hal Finkelstein's book covers these problems as well as other motor and HVAC problems.
Learn more here