With the development of variable-frequency converter drives during the 1990s, totally enclosed fan-cooled (TEFC) alternating-current (AC) induction motors became viable options in the replacement of direct-current (DC) motors of all types in industrial applications. The torque/speed characteristics of this drive/motor combination matched requirements for most fans and blowers, as well as the vast majority of pumps.

In applications requiring constant torque (e.g., many compressors, as well as positive-displacement, screw, reciprocating, and peristaltic pumps), however, an inherent problem was identified: Under constant-load conditions, as the speed of a motor decreased, so did the cooling provided by the integral fan mounted on the motor shaft. If the increase in internal heat exceeded the motor insulation's thermal class, the motor would have to be de-rated. Additionally, an 18°F increase in operating temperature was found to decrease a motor's useful life by half.

Motor manufacturers responded by developing a number of techniques that came to be known as “inverter-class solutions.” Many manufacturers suggested oversizing motors to ensure they would be able to produce the torque needed to drive a constant load while operating below temperatures that might threaten or prematurely age insulation. Other manufacturers provided external fans or blowers to ensure proper ventilation no matter the speed at which a motor was driving a load. While both techniques work, they significantly increase the size, cost, and energy consumption of installations.


Three major types of losses contribute to heat rise in TEFC induction motors under variable-speed constant-torque conditions:

  • Iron losses, including both hysteresis losses and eddy-current (Foucault) losses, which depend on magnetic induction or flux density, as well as the frequency of the source voltage and the quality of the magnetic material.

  • Losses resulting from the Joule effect, which depend on the current flowing through the stator winding and rotor bars.

  • Mechanical losses attributed to the cooling system (the fan coupled to the motor shaft) and friction, both of which are affected by speed.

Using the Faraday-Lenz law of induction, magnetic flux is shown to be directly proportional to the ratio of electromotive force (V) applied to a motor and the frequency (f) of that force.1,2,3,4 In a constant-torque application, as the frequency of the force is decreased to reduce speed, magnetic flux increases significantly, leading to lower iron losses. At the same time, the fundamental theory of electric machines shows that torque provided by an induction motor is directly proportional to the product of magnetic flux and electric current.5,6 For constant torque to be maintained, flux can be increased as current is decreased (and vice versa). With Joule losses inversely proportional to the square of motor current, these losses can be considered to be inversely proportional to the square of the magnetic flux.7

As the frequency — and, consequently, the rotation — of a variable-speed motor/drive is reduced, mechanical losses decrease in proportion to the cube of the frequency (f3).8,9 These mechanical losses do not affect iron losses, but do act as an additional load on the motor shaft, requiring that torque beyond the rated torque be available to maintain speed under constant-load conditions. The reduction of torque to overcome mechanical losses as motor speed decreases implies a reduction of current required by the motor to maintain constant torque, as well as a reduction of Joule losses within the motor.

In constant-torque inverter-class applications for compressors and specialty pumps, the currently accepted control strategy is to maintain a constant flux (V/f ratio) over the entire motor-speed range. Mathematically modeling a typical induction-motor/variable-frequency-drive (VFD) combination demonstrates that by varying the V/f ratio within a converter, motor losses can be minimized across the entire operating-frequency range while constant torque is maintained and the motor is kept within its insulation-class thermal limits.10

V/f can be calculated, allowing the optimal flux level at various motor speeds to be determined (Figure 1). These values can be stored in a variable-frequency converter to ensure minimum loss levels across the speed range.

Figure 2 shows the loss reduction that can be achieved for a three-phase, 30-kw four-pole motor over a normalized frequency range of 0.1 to 1.0. At all frequencies, the motor powered at the optimal level exhibited lower total losses than the same motor powered using a constant-flux scheme.

Varying V/f ratio to produce optimal flux results in thermal performance significantly better than that achieved under constant-flux conditions (Figure 3). This has been confirmed experimentally with a wide range of NEMA (National Electrical Manufacturers Association) high-efficiency, NEMA premium-efficiency (NPE), and European Union EFF1 motors ranging from 5 to 150 hp.


The combination of a standard off-the-shelf NPE induction motor and a VFD with variable-V/f capabilities delivers several benefits to the user. First and foremost, TEFC NPE motors driven using optimal-flux techniques run significantly cooler than inverter-class solutions using traditional constant-flux drive strategies and, thus, last much longer. Typically, for every 18°F of operating-temperature reduction, motor life doubles. Motors of all sizes and types driven using optimal-flux techniques run at least 11-percent cooler over their entire speed range than comparable motors driven using traditional constant-flux techniques. Longer motor life can translate to extended warranties and lead to reduced motor-maintenance costs, less down time, and lower spares inventory and related costs.


  1. Kaczmarek, R., Amar, M., & Protat, F. (1996). Iron loss under PWM voltage supply on Epstein frame and in induction motor core. IEEE Transactions on Magnetics, 32, 189-194.

  2. Boglietti, A., Ferraris, P., Lazzari, M., & Profumo, F. (1991). Iron losses in magnetic materials with six-step and PWM inverter supply. IEEE Transactions on Magnetics, 27, 5334-5336.

  3. Mthombeni, L.T., & Pillay, P. (2004). Core losses in motor laminations exposed to high-frequency or nonsinusoidal excitation. IEEE Transactions on Industry Applications, 40, 1325-1332.

  4. Lancarotte, M.S., Goldemberg, C., & Penteado Jr., A.A. (2005). Estimation of FeSi core losses under PWM or DC bias ripple voltage excitations. IEEE Transactions on Energy Conversion, 20, 367-372.

  5. Moses, A.J., & Tutkun, N. (1997). Investigation of power loss in wound toroidal cores under PWM excitation. IEEE Transactions on Magnetics, 33, 3763-3765.

  6. Boglietti, A., Ferraris, P., Lazzari, M., & Pastorelli, M. (1997). About the possibility of defining a standard method for iron loss measurement in soft magnetic materials with inverter supply. IEEE Transactions on Industry Applications, 33, 1273-1282.

  7. Cester, C., Kedous-Lebouc, A., & Cornut, B. (1997). Iron loss under practical working conditions of a PWM powered induction motor. IEEE Transactions on Magnetics, 33, 3766-3768.

  8. Ruderman, A., & Welch Jr., R. (2005). Electrical machine PWM loss evaluation basics. Proceedings of the 4th International Conference on Energy Efficiency in Motor Driven Systems (EEMODS), Heidelberg, Germany, vol. 1, pp. 58-68.

  9. Sokola, M., Vuckovic, V., & Levi, E. (1995). Measurement of iron losses in PWM inverter fed induction machines. Proceedings of the 30th Universities Power Engineering Conference (UPEC), London, pp. 371-374.

  10. Nau, S.L., & Sobrinho, A.P. (2002). Optimal voltage/frequency curve for inverter-fed motor. Proceedings of the 3rd International Conference on Energy Efficiency in Motor Driven Systems (EEMODS), Treviso, Italy, vol. 1, pp. 46-50.

For past HPAC Engineering feature articles, visit www.hpac.com.

Hugo G.G. Mello is the head of, and Waldiberto L. Pires is a researcher in, the Technology of Product Section of the Research and Development of Product Department of WEG Electric Motors Corp., working in the area of electrical machines, mainly the application of induction motors fed by frequency converters.