# Core Loss and Efficiency Calculations

Motors and generators with MagNetMagnetic losses (also known as iron losses or core losses) are an area of growing interest in fields such as advanced electric machines and transformers. Traditionally, losses have been specified and calculated using empirical loss curves provided by manufacturers, which specify the power loss per unit mass at a given frequency as a function of the maximum magnetic flux density.

However, in the case of modern permanent magnet machines, there often exist regions of high magnetic saturation that remain relatively constant with time. Therefore, the previous model of core losses would haves given erroneous results for such a device.

To address this issue, Infolytica's products have adopted an advanced core loss model. This can be used to accurately determine the efficiency of a permanent magnet machine, or when coupled with ThermNet, provide a better simulation of temperature changes in a permanent magnet voice coil.

### METHODS and RESULTS

## FREQUENCY-DEPENDENT LOSS MODEL

The interior permanent magnet motor offers efficiency advantages over a number of other machine designs. However, in order to calculate the losses properly, the standard frequency-dependent loss model (depending only on maximum **B**) is not valid, as although the rotor is heavily saturated, this field remains relatively constant as the rotor turns, and therefore does not contribute to iron losses.

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## HIGH LOSSES near the SURFACE of the ROTOR

The plot here shows high losses near the surface of the rotor, where the flux changes rapidly due to interactions with the stator. In the interior region just above the magnet, the flux density is high but constant, and therefore the losses are much lower.

Please note the units in this plot and the one below are different, and the colors in the plots have been scaled accordingly.

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## AVERAGED IRON LOSSES and CORRESPONDING MAXIMUM B for the IPM STATOR

For a more accurate model of iron losses, the vector difference between minimum and maximum B is used, to ensure that areas which see strong, but relatively constant, magnetic fields do not exhibit large core losses, and that areas that see magnetic fields of constant magnitude but significant changes in direction would also model losses correctly.

In addition, the time-averaged losses can be calculated over a number of parameterized solutions or time instants, to allow for a faster thermal solution. The averaged iron losses and corresponding maximum B for the IPM stator is shown.

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## EXPLOITING CORE LOSS CALCULATIONS using OPTINET

The core loss calculations can be exploited with OptiNet as well. An IPM machine is optimized to reduce torque ripple while constraining the efficiency to be at least 80%. This efficiency calculation includes core losses, eddy current losses in conducting parts and ohmic losses in the windings.

The low efficiency of one of OptiNet's solutions is worth explaining. It illustrates the ability of OptiNet to explore a wide search space. As OptiNet converges to a final solution, this inefficient solution is ignored and OptiNet returns to search out a more efficient solution.

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