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 (2D 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.