Effective Nonlinear Magnetic Constitutive Relations
The effective constitutive relations can be used to approximate the behavior of a nonlinear magnetic material, such as a saturable material, in a (linear) Frequency Domain study.
The approach consists in replacing the nonlinear material with an inhomogeneous linear material — a material described by a magnetic permeability constant in time but which can be space dependent. The local magnetic permeability is chosen using an approximation criterion, such as, for example, that the cycle-average energy stored must be equal to the nonlinear case. As a consequence, the permeability may depend on the amplitude of the magnetic field and the nonlinear solver is invoked during the solution.
The formulation still uses the assumption of harmonic time dependency of the fields (which are still described as phasors): the fields still oscillate at the given frequency; higher-order harmonic effects, or other similar effects due to the nonlinearity, are not accounted for.
Using this constitutive relation provides a better approximation of the behavior of a nonlinear material in the frequency domain than linearizing the material properties, still avoiding the computational cost of a full transient analysis.
The application Effective Nonlinear Magnetic Curves Calculator in the AC/DC Module Application Library can be used to compute the effective B-H curve for a material, starting from its B-H curve.
Effective Nonlinear Magnetic Curves Calculator: Application Library path ACDC_Module/Applications/effective_nonlinear_magnetic_curves
An Effective BH Curve generated with the Effective Nonlinear Magnetic Curves Calculator with the Average energy method selected leads to accurate evaluation of cycle-average quantities such as the cycle-average magnetic energy and the cycle-average magnetic coenergy. The chosen averaging method affects which quantities can be considered “accurate” in postprocessing and which ones will deviate. Usually, the loss and the energy are of main interest, while the field strength is considered of secondary importance.