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For low saturation cases a linear time-harmonic analysis can be run with assumed constant permeability properties. For moderate to high saturation conditions a nonlinear time-harmonic or time-transient ("2-D Transient Magnetic Analysis") solution should be considered.

In moderate to high saturation cases, an analyst is often most interested in obtaining global electromagnetic force, torque and power losses in a magnetic device under sinusoidal steady state excitation, but less concerned with the actual flux density waveform. Under such circumstances, an approximate nonlinear time-harmonic analysis procedure may be pursued. This procedure can predict the time-averaged torque and power losses with good accuracy, and yet at much reduced computational cost compared to a transient time-stepping procedure.

The basic principle of the nonlinear time-harmonic analysis is to replace the DC B-H curve with a fictitious or effective B-H curve based on an energy equivalence method.

With the effective B-H curve, a nonlinear transient problem can be effectively reduced to a nonlinear time-harmonic one. In this nonlinear analysis, all field quantities are all sinusoidal at a given frequency, similar to the linear harmonic analysis, except that a nonlinear solution is computed.

It should be emphasized that in a nonlinear transient analysis, given a sinusoidal power source, the magnetic flux density B has a non-sinusoidal waveform. While in the nonlinear harmonic analysis, B is assumed sinusoidal. Therefore, it is not the true waveform, but rather represents an approximation to the fundamental time harmonic of the true flux density waveform. The time-averaged global force, torque and loss, which are determined by the approximated fundamental harmonics of fields, are then subsequent approximations to the true values.