*Pumps & Systems*, June 2008

Following the development of variable frequency converter drives during the 1990s, totally enclosed fan-cooled (TEFC) AC induction motors became viable options for replacing DC motors in pumping applications. The torque and speed characteristics of these motors are a close match to those required for centrifugal pumps.

However, since positive displacement pumps require constant torque, an inherent problem was identified. As a TEFC motor's speed decreased under constant load conditions, the cooling provided by the integral fan mounted on the motor shaft also decreased significantly, so the motor would run hotter as speed decreased. If the increase in internal heat exceeded the motor's insulation thermal class, the motor's life would be reduced. A 10-deg C increase in motor operating temperature actually decreases the motor's useful service life by half.

Motor makers responded to this ventilation challenge by developing a number of techniques called inverter class solutions. Many suggested over-sizing the pump motor to ensure it will always produce the needed torque to drive the constant load, but still operate below temperatures that might threaten or prematurely age the insulation. Others provided external fans or blowers to ensure proper ventilation no matter what speed the pump motor was driving the load. While both of these techniques work, they also significantly increase the size of the induction motor/pump installation and the cost and energy consumption of the combination.

## Understanding Losses in TEFC Induction Motors

There are three major types of losses that contribute to heat rise in TEFC induction motors. These include:

- Iron losses, including both hysteresis losses and eddy current (Foucault) losses, which depend on magnetic induction or flux density as well as the operation frequency and the quality of magnetic material
- Joule losses, which depend on the current flowing through the stator winding and the rotor bars
- Mechanical losses due to the cooling system (the fan coupled to the motor shaft) and friction, both of which depend on speed

The Faraday-Lenz law of induction demonstrates that magnetic flux in a motor is directly proportional to the ratio of electromotive force applied to the motor (V) and the frequency (f) of that source. In a variable speed pumping application, as the frequency of the source decreases to decrease speed, iron losses are significantly reduced. 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 the electric current. To maintain a constant torque in a pumping application, if the flux increases, the current can decrease (and vice versa). As Joule losses are inversely proportional to the square of the motor current, these losses can be considered inversely proportional to the square of the magnetic flux.

Concerning mechanical losses, as the frequency of a variable speed motor/drive, and consequently the rotation, is reduced, the mechanical losses decrease in proportion to the cube of the frequency (f3). The mechanical losses do not affect the iron losses but do act as an additional load on the motor shaft, so they require some torque over the rated torque be available to maintain speed under constant load conditions. The reduction of mechanical losses as motor speed decreases does imply a reduction of current, as well as a subsequent reduction in the Joule losses within the motor conductors.

In constant torque inverter class applications for positive displacement pumps, the currently accepted control strategy has been to maintain a constant flux (V/f ratio) over the entire motor speed range. Mathematically modeling a typical induction motor/variable frequency drive combination demonstrates that by varying the V/f ratio within the 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.

The values of V/f that minimize losses at each operational frequency (Figure 1) can be calculated, determining the OptimalFluxTM level required to drive the motor at minimum loss levels at each speed. These values can then be stored in the variable frequency converter so as to power the motor/pump combination at minimum loss levels across the speed range.

**Figure 1. V/f vs. frequency (f) curve for the minimization of losses**

Figure 2 presents an example of the loss reduction that can be achieved for a 3-phase, 30-kW 4-pole motor over a normalized frequency range from 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 drive scheme.

**Figure 2. Total losses vs. frequency for induction motors, comparing constant flux and optimal operation**