# Modeling Reluctance-Assisted PM Motors

## Abstract

This report contains a derivation of the fundamental equations used to calculate the base speed, torque delivery, and power output of a reluctance-assisted PM motor which has a saliency ratio greater than 1 as a function of its terminal voltage, current, voltage-phase angle, and current-phase angle. The equations are applied to model Motor X using symbolically-oriented methods with the computer tool Mathematica to determine: (1) the values of current-phase angle and voltage-phase angle that are uniquely determined once a base speed has been selected; (2) the attainable current in the voltage-limited region above base speed as a function of terminal voltage, speed, and current-phase angle; (3) the attainable current in the voltage-limited region above base speed as a function of terminal voltage, speed, and voltage-phase angle; (4) the maximum-power output in the voltage-limited region above base speed as a function of speed; (5) the optimal voltage-phase angle in the voltage-limited region above base speed required to obtain maximum-power output; (6) the maximum-power speed curve which was linear from rest to base speed in the current limited region below base speed; (7) the current angle as a function of saliency ratio in the current-limited region below base speed; and (8) themore »

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 885945

- Report Number(s):
- ORNL/TM-2005/185

TRN: US200617%%261

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; COMPUTERS; EFFICIENCY; INCLINATION; MAGNETS; MOTORS; OPTIMIZATION; PERFORMANCE; SIMULATION; TORQUE; VELOCITY

### Citation Formats

```
Otaduy, P J.
```*Modeling Reluctance-Assisted PM Motors*. United States: N. p., 2006.
Web. doi:10.2172/885945.

```
Otaduy, P J.
```*Modeling Reluctance-Assisted PM Motors*. United States. https://doi.org/10.2172/885945

```
Otaduy, P J. 2006.
"Modeling Reluctance-Assisted PM Motors". United States. https://doi.org/10.2172/885945. https://www.osti.gov/servlets/purl/885945.
```

```
@article{osti_885945,
```

title = {Modeling Reluctance-Assisted PM Motors},

author = {Otaduy, P J},

abstractNote = {This report contains a derivation of the fundamental equations used to calculate the base speed, torque delivery, and power output of a reluctance-assisted PM motor which has a saliency ratio greater than 1 as a function of its terminal voltage, current, voltage-phase angle, and current-phase angle. The equations are applied to model Motor X using symbolically-oriented methods with the computer tool Mathematica to determine: (1) the values of current-phase angle and voltage-phase angle that are uniquely determined once a base speed has been selected; (2) the attainable current in the voltage-limited region above base speed as a function of terminal voltage, speed, and current-phase angle; (3) the attainable current in the voltage-limited region above base speed as a function of terminal voltage, speed, and voltage-phase angle; (4) the maximum-power output in the voltage-limited region above base speed as a function of speed; (5) the optimal voltage-phase angle in the voltage-limited region above base speed required to obtain maximum-power output; (6) the maximum-power speed curve which was linear from rest to base speed in the current limited region below base speed; (7) the current angle as a function of saliency ratio in the current-limited region below base speed; and (8) the torque as a function of saliency ratio which is almost linear in the current-limited region below base speed. The equations were applied to model Motor X using numerically-oriented methods with the computer tool LabVIEW. The equations were solved iteratively to find optimal current and voltage angles that yield maximum power and maximum efficiency from rest through the current-limited region to base speed and then through the voltage-limited region to high-rotational speeds. Currents, voltages, and reluctance factors were all calculated and external loops were employed to perform additional optimization with respect to PM pitch angle (magnet fraction) and with respect to magnet strength. The conclusion was that the optimal-magnet fraction for Motor X is 0.72 which corresponds to a PM pitch angle of 130{sup o}, a value close to the maximum-saliency ratio in a plot of saliency ratio versus PM pitch angle. Further, the strength of Motor X magnets may be lowered to 80% of full strength without significantly impacting motor performance for PM pitch angles between the peak saliency (130{sup o}) and peak-characteristic current (160{sup o}). It is recommended that future research involve maximizing a driving-cycle-weighted efficiency based on the Federal Urban Driving Cycle and the Federal Highway Driving Cycle as criteria for selecting the final optimal-PM fraction and magnet strength for this inset PM motor. Results of this study indicate that the reduction in PM torque due to reduced-magnet fraction will be more than compensated by the reluctance torque resulting from the higher saliency ratio. It seems likely that the best overall performance will require saliency; consequently, we think the best motor will be a reluctance-assisted PM motor. This should be explored for use with other types of PM motors, such as fractional-slot motors with concentrated windings.},

doi = {10.2172/885945},

url = {https://www.osti.gov/biblio/885945},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2006},

month = {1}

}