With the development of variablefrequency converter drives during the 1990s, totally enclosed fancooled (TEFC) alternatingcurrent (AC) induction motors became viable options in the replacement of directcurrent (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 positivedisplacement, screw, reciprocating, and peristaltic pumps), however, an inherent problem was identified: Under constantload 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 derated. 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 “inverterclass 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.
UNDERSTANDING LOSSES IN TEFC INDUCTION MOTORS
Three major types of losses contribute to heat rise in TEFC induction motors under variablespeed constanttorque conditions:

Iron losses, including both hysteresis losses and eddycurrent (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 FaradayLenz 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 constanttorque 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 variablespeed motor/drive is reduced, mechanical losses decrease in proportion to the cube of the frequency (f^{3}).^{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 constantload 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 constanttorque inverterclass applications for compressors and specialty pumps, the currently accepted control strategy is to maintain a constant flux (V/f ratio) over the entire motorspeed range. Mathematically modeling a typical inductionmotor/variablefrequencydrive (VFD) combination demonstrates that by varying the V/f ratio within a converter, motor losses can be minimized across the entire operatingfrequency range while constant torque is maintained and the motor is kept within its insulationclass 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 variablefrequency converter to ensure minimum loss levels across the speed range.
Figure 2 shows the loss reduction that can be achieved for a threephase, 30kw fourpole 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 constantflux scheme.
Varying V/f ratio to produce optimal flux results in thermal performance significantly better than that achieved under constantflux conditions (Figure 3). This has been confirmed experimentally with a wide range of NEMA (National Electrical Manufacturers Association) highefficiency, NEMA premiumefficiency (NPE), and European Union EFF1 motors ranging from 5 to 150 hp.
OPTIMALFLUX CONTROL
The combination of a standard offtheshelf NPE induction motor and a VFD with variableV/f capabilities delivers several benefits to the user. First and foremost, TEFC NPE motors driven using optimalflux techniques run significantly cooler than inverterclass solutions using traditional constantflux drive strategies and, thus, last much longer. Typically, for every 18°F of operatingtemperature reduction, motor life doubles. Motors of all sizes and types driven using optimalflux techniques run at least 11percent cooler over their entire speed range than comparable motors driven using traditional constantflux techniques. Longer motor life can translate to extended warranties and lead to reduced motormaintenance costs, less down time, and lower spares inventory and related costs.
REFERENCES

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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.