A variable frequency drive (VFD)[1] controls the speed of an AC induction motor by controlling the power, both voltage and frequency, that supplies the motor. By reducing the motor speed to match the needs of the application, VFDs have the potential to significantly save energy and reduce operating costs for a variety of motor driven applications[2]. Motor systems that should be evaluated for energy savings through the use of VFDs include:

  • Variable load motor systems where output is throttled or damped below full rated speed
  • Centrifugal fan, pump, or blower systems
  • Systems that meet either criteria above that operate frequently, for example, more than 2000h/y

The potential energy savings from reducing motor power to manage its speed are approximated by the Affinity Laws[3]. These engineering laws are used to express the relationship between flow, head, and consumed power and shaft speed for pump and fan applications. It can be summarized as follows:

  • Change in flow is proportional to the change in shaft speed
  • Change in head pressure is proportional to the square of the change in shaft speed
  • Change in power consumed is proportional to the cube of the change in shaft speed

Energy Savings Example

To illustrate the relationship between motor speed and consumed power, assume a 50hp centrifugal pump—95 percent efficiency, operating 4,067 hours per year with a 75 percent load factor, and electric costs at $.07kWh—is using a throttling valve to regulate flow to 70 percent on average. Applying the third affinity law, the yearly electricity cost of the motor running at fully rated 100 percent shaft speed or flow would be:

Annual Energy Cost (Throttling Valve)=
hp/Emotor) * LF * 0.746 kW/hp * (% full rated shaft speed)3 * (annual operating hours) * (cost of electricity)


50hp/0.93 * 0.75 * 0.746 kW/hp * (1.0)3 * 4,067h/y * $.07/kWh = $8,564 per year

The same system is represented below, except with a variable-speed drive at 97 percent efficiency replaces the throttling valve to achieve the same flow regulation by varying the motor rotational speed.

Annual Energy Cost (VSD) =
(hp/Emotor) * LF * 0.746 kW/hp * (% full rated shaft speed)3 * (annual operating hours) * (cost of electricity) * (1/EASD)


50hp/.93 * 0.75% * 0.746kW/hp * (0.7)3 * 4,067h/y * $.07/kWh * 1/0.97 = $3,028 per year

As the scenario above demonstrates, replacing the throttling valve with the VSD can achieve approximately $5,500 in annual energy cost savings. Nearly 65 percent energy cost savings is gained as a result of a 30 percent reduction in shaft speed or flow. In other words, small reductions in speed and flow lead to significant energy cost savings.

For additional summary information, please see CEE Motor Efficiency, Selection, and Management: A Guidebook for Efficiency Programs.

[1] Variable Frequency Drives (VFD) are sometimes referred to as: Adjustable Speed Drives (ASD) or Variable Speed Drives (VSD).† ASD and VSD are more broad categorizations that include mechanical, electromechanical, hydraulic, and VFD controls.† VFDs uniquely control the frequency of the electrical power supplied to a motor.

[2] Actual savings depend on the application. When used in constant speed, high torque, sequencing, and soft start applications, energy costs may not change or actually be higher with a VFD.

[3] Affinity Laws express an ideal relationship and do not take into account energy losses in the motor system, see also this description.