# Advanced Optimization of an IPM Machine

Motors and generators with MagNetThis example looks at the optimization of a 3-phase, 4-pole single-barrier IPM (interior permanent magnet) using the combined power of MagNet (as the core solution engine) and OptiNet (as the optimizer). The goal is to optimize the motor's performance with respect to a reasonably realistic and complex objective function by changing a few simple geometric parameters (the size and position of the permanent magnets) and the advance angle (angle between the d-axis and the stator field).

The purpose is to reduce the torque ripple while ensuring adequate running torque, and simultaneously ensuring that the back EMF at 1800 RPM does not exceed the peak supply voltage of 41.5 V.

Although this is a relatively complex task from the viewpoint of optimization, OptiNet and Magnet allow for the simple setup of such a model using its rich library of built-in constraints and objective functions, full parameterization of models and close coupling between both packages.

### METHODS and RESULTS

## GEOMETRY of the PERMANENT MAGNET

Of the four design parameters considered for this optimization, the first three relate to the geometry of the permanent magnet (the magnet height, width and depth) as shown in this figure. The magnet is a NdFeB (neodymium iron boron) material. The geometry of the magnet can have a significant effect on the magnitude of torque ripple and cogging torque.

View larger image

## TORQUE ABOUT ORIGIN

Using MagNet's parameterization feature, the motor model is solved for 30 positions of the rotor, at a spacing of one degree mechanical between each. The periodicity of the torque ripple was calculated to be 30 degrees. The average running torque is 0.547 N-m and the peak torque ripple is 0.109 N-m, or nearly 20%.

View larger image

## VARYING the MAGNET GEOMETRY and ADVANCE ANGLE

OptiNet is then charged with the task of reducing the torque ripple, by varying the magnet geometry and advance angle. Minimum and maximum values are set for these four parameters. In addition, the running torque (average torque over 30 degree sweep) must be at least 0.475 N-m for the design to be considered acceptable.

View larger image

## CHANGES IN GEOMETRY PRODUCED BY OPTINET

This is set as a "Should Be" constraint in OptiNet, so it is possible that a design with slightly less than 0.475 N-m would be selected, although it would be penalized when compared with an alternate design. The relative weights of these constraints can be set by the user. This figure shows the changes in geometry produced by OptiNet in search for a better design.

View larger image

## AN IMPROVED SOLUTION

After 111 iterations, OptiNet has found an improved solution. The torque ripple has been reduced from almost 20% to 13.6%. The running torque has been maintained at 0.475 N-m as required by the constraints. The back EMF is kept at 19.26 V (well below our maximum voltage of 41.25 V). Simple Visual Basic script files are used to calculate more complex quantities like back EMF across all the coils, however OptiNet built-in objectives and constraints include options like torque ripple and average torque.

View larger image