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# Electric Machine With Boosted Inductance to Stabilize Current Control

- Created on Sunday, 01 December 2013
- Lyndon B. Johnson Space Center, Houston, Texas

High-powered motors typically have very low resistance and inductance (*R* and *L*) in their windings. This makes the pulse-width modulated (PWM) control of the current very difficult, especially when the bus voltage (*V*) is high. These *R* and *L* values are dictated by the motor size, torque (K_{t}), and back-emf (K_{b}) constants. These constants are in turn set by the voltage and the actuation torque-speed requirements. This problem is often addressed by placing inductive chokes within the controller. This approach is undesirable in that space is taken and heat is added to the controller.

By keeping the same motor frame, reducing the wire size, and placing a correspondingly larger number of turns in each slot, the resistance, inductance, torque constant, and back-emf constant are all increased. The increased inductance aids the current control but ruins the K_{t} and K_{b} selections. If, however, a fraction of the turns is moved from their “correct slot” to an “incorrect slot,” the increased *R* and *L* values are retained, but the K_{t} and K_{b} values are restored to the desired values. This approach assumes that increased resistance is acceptable to a degree. In effect, the heat allocated to the added inductance has been moved from the controller to the motor body, which in some cases is preferred.

The slew-rate of the current is calculated as *V/L* and can easily be 250,000 A/s. With a pulse width resolution of 10 μs, for example, the current could slew 2.5 A, which in some cases may exceed the resolution needed for the current control loop. If *L* is increased, the problem is proportionately improved. Consider a certain motor size and gear train selection where the back-emf constant has been selected to meet a required output speed. The corresponding K_{t} and *L*, however, produce an uncontrollable current regulator. If the wire size is decreased by three gauges, for example, and the slots arc filled with twice as many turns (the slots will be full in this example), then the *R* and *L* will increase by a factor of four, while the K_{t} and K_{b} will increase by a factor of two. If the slots are only filled 67 percent in the correct fashion and the other 33 percent of the windings are placed in incorrect slots, then the K_{t} and K_{b} are reduced to their original levels.

The fourfold benefit of the inductance increase assists the current control. The resistance increase will cause more heating since the current level is unchanged in this example. If this is a problem, the motor thermal mass can be increased as a solution.

*This work was done by Steve Abel of Honeywell Aerospace for Johnson Space Center. For further information, contact the JSC Innovation Partnerships Office at (281) 483- 3809. MSC-24906-1*