Nonlinear Inductor Characteristics

Open Model

This example shows a comparison of nonlinear inductor behavior for different parameterizations. Starting with fundamental parameter values, the parameters for linear and nonlinear representations are derived. These parameters are then used in a Simscape™ model and the simulation outputs compared.

Specification of Parameters

Fundamental parameter values used as the basis for subsequent calculations:

Permeability of free space, $\mu_0, \rm{H/m}$
Relative permeability of core, $\mu_r$
Number of winding turns,
Effective magnetic core length, $l_e, \rm{m}$
Effective magnetic core cross-sectional area, $A_e, \rm{m^2}$
Core saturation begins, $B_{sat_{begin}}, \rm{T}$
Core fully saturated, $B_{sat}, \rm{T}$

Calculate Magnetic Flux Density and Magnetic Field Strength Data

Where:

Magnetic flux density, $B, \rm{T}$
Magnetic field strength, $H, \rm{A/m}$

Linear representation:

$B = \mu_0 \mu_r H$

Nonlinear representation (including coefficient, a):

$B = B_{sat} \tanh(a.H)$

Display Magnetic Flux Density Versus Magnetic Field Strength

The linear and nonlinear representations can be overlaid.

Calculate Magnetic Flux and Current Data

Where:

Magnetic flux, $\phi, \rm{Wb}$
Current, $I, \rm{A}$

Linear representation:

$L = \mu_0 \mu_r A_e N_w^2/l_e$

$\phi = I L/N_w$

Nonlinear representation:

$\phi = B A_e$

Display Magnetic Flux Versus Current

The linear and nonlinear representations can be overlaid.

Use Parameters in Simscape Model

The parameters calculated can now be used in a Simscape model. Once simulated, the model is set to create a Simscape logging variable, simlog.

Conclusion

The state variable for all representations is magnetic flux, $\phi$ . Current, I, and magnetic flux, $\phi$ , can be obtained from the Simscape logging variable, simlog, for each representation. Overlaying the simulation results from the representations permits direct comparison.