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Tellinen Soft

Generic flux tube with soft magnetic hysteresis based on the Tellinen model and simple tanh functions  Description The Tellinen Soft component is a flux tube element of fixed length and cross-sectional area for modeling soft magnetic materials with ferromagnetic and dynamic hysteresis (eddy currents). The ferromagnetic hysteresis behavior is defined by the Tellinen hysteresis model. The shape of the limiting hysteresis loop (see Fig. 1) is described by simple hyperbolic tangent functions with four parameters. The hysteresis shape is limited but the parameterization of the model is simple and the model is relatively fast and robust. The rising (${\mathrm{hyst}}_{R}$) and falling (${\mathrm{hyst}}_{F}$) branches of the limiting hysteresis loop are defined by the following equations: ${\mathrm{hyst}}_{R}={J}_{s}\mathrm{tanh}\left(\left({H}_{\mathrm{stat}}M-{H}_{0}\right)\right)+{K}_{{\mathrm{\mu }}_{0}}{H}_{\mathrm{stat}}$ ${\mathrm{hyst}}_{F}={J}_{s}\mathrm{tanh}\left(\left({H}_{\mathrm{stat}}M+{H}_{0}\right)\right)+{K}_{{\mathrm{\mu }}_{0}}{H}_{\mathrm{stat}}$ ${H}_{0}=\frac{1}{2}\mathrm{log}\left(\frac{1+\frac{{B}_{r}}{{J}_{s}}}{1-\frac{{B}_{r}}{{J}_{s}}}\right)$ $M=\frac{{H}_{0}}{{H}_{c}}$ Fig. 1: Hyperbolic tangent functions define the shape of the ferromagnetic (static) hysteresis  Equations $\mathrm{\Phi }={\mathrm{\Phi }}_{p}=-{\mathrm{\Phi }}_{n}=BA$ ${V}_{m}={V}_{{m}_{p}}-{V}_{{m}_{n}}$ $H=\frac{{V}_{m}}{\ell }={H}_{\mathrm{stat}}+{H}_{\mathrm{eddy}}$ ${H}_{\mathrm{eddy}}=\left\{\begin{array}{cc}\frac{\mathrm{\sigma }{d}^{2}}{12}\frac{\mathrm{dB}}{\mathrm{dt}}& \mathrm{Include eddy currents}\\ 0& \mathrm{otherwise}\end{array}$ ${H}_{0}=\frac{1}{2}\mathrm{log}\left(\frac{1+\frac{{B}_{r}}{{J}_{s}}}{1-\frac{{B}_{r}}{{J}_{s}}}\right)$ ${\mathrm{hyst}}_{F}={J}_{s}\mathrm{tanh}\left(\frac{{H}_{\mathrm{stat}}M+{H}_{0}}{{H}_{\mathrm{unit}}}\right)+{\mathrm{\mu }}_{0}{H}_{\mathrm{stat}}+\frac{1}{2}\mathrm{eps}$ ${\mathrm{hyst}}_{R}={J}_{s}\mathrm{tanh}\left(\frac{{H}_{\mathrm{stat}}M-{H}_{0}}{{H}_{\mathrm{unit}}}\right)+{\mathrm{\mu }}_{0}{H}_{\mathrm{stat}}-\frac{1}{2}\mathrm{eps}$ $\left\{\begin{array}{cc}\left\{\mathrm{dHyst}=0,k=\frac{1}{100}\right\}& \mathrm{initial}\\ \left\{\mathrm{dHyst}=\frac{d}{\mathrm{dt}}\left(-{H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+{\mathrm{hyst}}_{R}\right),k=\mathrm{max}\left(\frac{1}{100},\frac{{\mathrm{hyst}}_{F}-B}{\Delta \mathrm{hyst}}\right)\right\}& 0<\frac{{\mathrm{dH}}_{\mathrm{stat}}}{\mathrm{dt}}\\ \left\{\mathrm{dHyst}=\frac{d}{\mathrm{dt}}\left(-{H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+{\mathrm{hyst}}_{F}\right),k=\mathrm{max}\left(\frac{1}{100},\frac{B-{\mathrm{hyst}}_{R}}{\Delta \mathrm{hyst}}\right)\right\}& \mathrm{otherwise}\end{array}$ $\mathrm{LossPower}={\mathrm{LossPower}}_{\mathrm{stat}}+{\mathrm{LossPower}}_{\mathrm{eddy}}$ ${\mathrm{LossPower}}_{\mathrm{eddy}}={H}_{\mathrm{eddy}}\frac{\mathrm{dB}}{\mathrm{dt}}V$ ${\mathrm{LossPower}}_{\mathrm{stat}}={H}_{\mathrm{stat}}\frac{\mathrm{dB}}{\mathrm{dt}}V$ $\Delta \mathrm{hyst}={\mathrm{hyst}}_{F}-{\mathrm{hyst}}_{R}$ $\frac{\mathrm{dB}}{\mathrm{dt}}=k\mathrm{dHyst}+{\mathrm{\mu }}_{0}\frac{d{H}_{\mathrm{stat}}}{\mathrm{dt}}$ $\frac{\mathrm{dMagRel}}{\mathrm{dt}}=0$ ${T}_{\mathrm{hp}}=\left\{\begin{array}{cc}{T}_{\mathrm{heatPort}}& \mathrm{Use Heat Port}\\ T& \mathrm{otherwise}\end{array}$ Variables

 Name Units Description Modelica ID $B$ $T$ Magnetic flux density B $\mathrm{dHyst}$ $\frac{T}{s}$ Slope of the limiting hysteresis branch dHyst $H$ $\frac{A}{m}$ Magnetic field strength H ${H}_{\mathrm{eddy}}$ $\frac{A}{m}$ Dynamic (eddy currents) portion of the magnetic field strength Heddy ${H}_{\mathrm{stat}}$ $\frac{A}{m}$ Static (ferromagnetic) portion of the magnetic field strength Hstat $\mathrm{LossPower}$ $W$ Loss power leaving component via HeatPort LossPower ${\mathrm{LossPower}}_{\mathrm{eddy}}$ $W$ Eddy current losses (dynamic hysteresis losses) LossPowerEddy ${\mathrm{LossPower}}_{\mathrm{stat}}$ $W$ Ferromagnetic (static) hysteresis losses LossPowerStat $\mathrm{MagRel}$ $1$ Relative magnetization at initialization (-1..1) MagRel $\mathrm{\Phi }$ $\mathrm{Wb}$ Magnetic flux from port_p to port_n Phi ${T}_{\mathrm{heatPort}}$ $K$ Temperature of HeatPort T_heatPort ${V}_{m}$ $A$ Magnetic potential difference between both ports V_m Connections

 Name Description Modelica ID ${\mathrm{port}}_{p}$ Positive magnetic port port_p ${\mathrm{port}}_{n}$ Negative magnetic port port_n $\mathrm{heatPort}$ heatPort Parameters Hystersis

 Name Default Units Description Modelica ID ${B}_{r}$ $0.9$ $T$ Remanence Br ${H}_{c}$ $120$ $\frac{A}{m}$ Coercitivity Hc ${J}_{s}$ $1.8$ $T$ Saturation polarization Js $K$ $1$ $1$ ${\mathrm{\mu }}_{0}$ multiplier K Fixed Geometry

 Name Default Units Description Modelica ID $\ell$ $0.1$ $m$ Length in direction of flux l $A$ $1·{10}^{-4}$ ${m}^{2}$ Area of cross section A Losses And Heat Parameters

 Name Default Units Description Modelica ID Use Heat Port $\mathrm{false}$ True (checked) enables heat port useHeatPort Include Eddy Currents $\mathrm{false}$ True (checked) enables eddy current losses includeEddyCurrents $\mathrm{\sigma }$ $1·{10}^{7}$ $\frac{S}{m}$ Conductivity of core material sigma $d$ $5·{10}^{-4}$ $m$ Thickness of lamination d Modelica Standard Library The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.