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:

${\mathrm{hyst}}_R\=J_s\tanh \left(\left(H_{\mathrm{stat}}M-H_0\right)\right)\+K_{{\mathrm{\mu }}_0}{H}_{\mathrm{stat}}$

${\mathrm{hyst}}_F\=J_s\tanh \left(\left(H_{\mathrm{stat}}M\+H_0\right)\right)\+K_{{\mathrm{\mu }}_0}{H}_{\mathrm{stat}}$

$H_0\=\frac{1}{2}\log \left(\frac{1\+\frac{B_r}{J_s}}{1-\frac{B_r}{J_s}}\right)$

$M\=\frac{H_0}{H_c}$

Fig. 1: Hyperbolic tangent functions define the shape of the ferromagnetic (static) hysteresis

$\mathrm{\Phi }\={\mathrm{\Phi }}_p\=-{\mathrm{\Phi }}_n\=BA$

$V_m\=V_{m_p}-V_{m_n}$

$H\=\frac{V_m}{\ell }\=H_{\mathrm{stat}}\+H_{\mathrm{eddy}}$

$H_{\mathrm{eddy}}\=\{\begin{array}{cc}\frac{\mathrm{\sigma }{d}^2}{12}\frac{\mathrm{dB}}{\mathrm{dt}}& \mathrm{Include\; eddy\; currents}\\ 0& \mathrm{otherwise}\end{array}$

$H_0\=\frac{1}{2}\log \left(\frac{1\+\frac{B_r}{J_s}}{1-\frac{B_r}{J_s}}\right)$

${\mathrm{hyst}}_F\=J_s\tanh \left(\frac{H_{\mathrm{stat}}M\+H_0}{H_{\mathrm{unit}}}\right)\+{\mathrm{\mu }}_0{H}_{\mathrm{stat}}\+\frac{1}{2}\mathrm{eps}$

${\mathrm{hyst}}_R\=J_s\tanh \left(\frac{H_{\mathrm{stat}}M-H_0}{H_{\mathrm{unit}}}\right)\+{\mathrm{\mu }}_0{H}_{\mathrm{stat}}-\frac{1}{2}\mathrm{eps}$

$\{\begin{array}{cc}\left\{\mathrm{dHyst}\&equals;0\&comma;k\&equals;\frac{1}{100}\right\}& \mathrm{initial}\\ \left\{\mathrm{dHyst}\&equals;\frac{d}{\mathrm{dt}}\left(-H_{\mathrm{stat}}{\mathrm{\mu }}_0\&plus;{\mathrm{hyst}}_R\right)\&comma;k\&equals;\max \left(\frac{1}{100}\&comma;\frac{{\mathrm{hyst}}_F-B}{\Delta \mathrm{hyst}}\right)\right\}& 0<\frac{{\mathrm{dH}}_{\mathrm{stat}}}{\mathrm{dt}}\\ \left\{\mathrm{dHyst}\&equals;\frac{d}{\mathrm{dt}}\left(-H_{\mathrm{stat}}{\mathrm{\mu }}_0\&plus;{\mathrm{hyst}}_F\right)\&comma;k\&equals;\max \left(\frac{1}{100}\&comma;\frac{B-{\mathrm{hyst}}_R}{\Delta \mathrm{hyst}}\right)\right\}& \mathrm{otherwise}\end{array}$

$\mathrm{LossPower}\&equals;{\mathrm{LossPower}}_{\mathrm{stat}}\&plus;{\mathrm{LossPower}}_{\mathrm{eddy}}$

${\mathrm{LossPower}}_{\mathrm{eddy}}\&equals;H_{\mathrm{eddy}}\frac{\mathrm{dB}}{\mathrm{dt}}V$

${\mathrm{LossPower}}_{\mathrm{stat}}\&equals;H_{\mathrm{stat}}\frac{\mathrm{dB}}{\mathrm{dt}}V$

$\Delta \mathrm{hyst}\&equals;{\mathrm{hyst}}_F-{\mathrm{hyst}}_R$

$\frac{\mathrm{dB}}{\mathrm{dt}}\&equals;k\mathrm{dHyst}\&plus;{\mathrm{\mu }}_0\frac{d{H}_{\mathrm{stat}}}{\mathrm{dt}}$

$\frac{\mathrm{dMagRel}}{\mathrm{dt}}\&equals;0$

$T_{\mathrm{hp}}\&equals;\{\begin{array}{cc}{T}_{\mathrm{heatPort}}& \mathrm{Use\; Heat\; Port}\\ T& \mathrm{otherwise}\end{array}$

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.