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 applies 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 BH or HB curve for a material, starting from its BH or HB curve.
Effective Nonlinear Magnetic Curves Calculator: Application Library path ACDC_Module/Applications/effective_nonlinear_magnetic_curves