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Tellinen Everett Flux Tube

Generic flux tube with ferromagnetic hysteresis based on the Tellinen model and the Everett function

 Description The Tellinen Everett component is a flux tube of fixed length and cross-sectional area that models ferromagnetic hysteresis based on the Tellinen model and the Everett function. The hysteresis curve is static and is determined by the parameters of the Everett function used by the magnetic material. The Hysteresis Material parameter specifies a record of parameter values, it should be the instance name of a magnetic material from the palette Magnetic > Material > Hysteresis > Parameter Based. See Magnetic Material with Parameter-based Hysteresis. The Use default material boolean parameter, when true, sets the Hysteresis Material parameter to hysteresisParameterMaterial1, which corresponds to the default name assigned to a record of the appropriate class. To use a different name, uncheck the box and enter the name for the parameter that appears.
 Equations $\left\{\left({T}_{\mathrm{heatPort}}=T;¬\mathrm{useHeatPort}\right)$ $\left\{\begin{array}{cc}\left\{\mathrm{dHyst}=0,k=\frac{1}{100}\right\}& \mathrm{initial}\left(\right)\\ \left\{\mathrm{dHyst}=\frac{d\left(-{H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+\mathrm{hystR}\right)}{\mathrm{dt}},k=\mathrm{max}\left(\frac{1}{100},\frac{\mathrm{hystF}-B}{\mathrm{diffHyst}}\right)\right\}& \mathrm{asc}\\ \left\{\mathrm{dHyst}=\frac{d\left(-{H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+\mathrm{hystF}\right)}{\mathrm{dt}},k=\mathrm{max}\left(\frac{1}{100},\frac{B-\mathrm{hystR}}{\mathrm{diffHyst}}\right)\right\}& \mathrm{otherwise}\end{array}$ $H=\frac{{V}_{m}}{l}$ $H={H}_{\mathrm{stat}}+{H}_{\mathrm{eddy}}$ ${H}_{2}={H}_{\mathrm{lim}}-{H}_{c\left(\mathrm{mat}\right)}$ ${H}_{3}=-{H}_{\mathrm{lim}}-{H}_{c\left(\mathrm{mat}\right)}$ ${H}_{\mathrm{lim}}=\left\{\begin{array}{cc}-{H}_{\mathrm{sat}\left(\mathrm{mat}\right)}& {H}_{\mathrm{stat}}<-{H}_{\mathrm{sat}\left(\mathrm{mat}\right)}\\ {H}_{\mathrm{sat}\left(\mathrm{mat}\right)}& {H}_{\mathrm{sat}\left(\mathrm{mat}\right)}<{H}_{\mathrm{stat}}\\ {H}_{\mathrm{stat}}& \mathrm{otherwise}\end{array}$ ${H}_{\mathrm{eddy}}=\left\{\begin{array}{cc}\mathrm{eddyCurrentFactor}\frac{\mathrm{dB}}{\mathrm{dt}}& \mathrm{includeEddyCurrents}\\ 0& \mathrm{otherwise}\end{array}$ ${P}_{2}={M}_{\mathrm{mat}}{r}_{\mathrm{mat}}\left(\frac{2}{\mathrm{\pi }}\mathrm{arctan}\left({q}_{\mathrm{mat}}{H}_{2}\right)+1\right)+2{M}_{\mathrm{mat}}\frac{1-{r}_{\mathrm{mat}}}{1+\frac{1}{2}\mathrm{exp}\left(-{\mathrm{p1}}_{\mathrm{mat}}{H}_{2}\right)+\frac{1}{2}\mathrm{exp}\left(-{\mathrm{p2}}_{\mathrm{mat}}{H}_{2}\right)}$ ${P}_{3}={M}_{\mathrm{mat}}{r}_{\mathrm{mat}}\left(\frac{2}{\mathrm{\pi }}\mathrm{arctan}\left({q}_{\mathrm{mat}}{H}_{3}\right)+1\right)+2{M}_{\mathrm{mat}}\frac{1-{r}_{\mathrm{mat}}}{1+\frac{1}{2}\mathrm{exp}\left(-{\mathrm{p1}}_{\mathrm{mat}}{H}_{3}\right)+\frac{1}{2}\mathrm{exp}\left(-{\mathrm{p2}}_{\mathrm{mat}}{H}_{3}\right)}$ $\mathrm{\Phi }=BA={\mathrm{\Phi }}_{p}=-{\mathrm{\Phi }}_{n}$ ${V}_{m}={V}_{{m}_{p}}-{V}_{{m}_{n}}$ $\mathrm{asc}=0<\frac{{\mathrm{dH}}_{\mathrm{stat}}}{\mathrm{dt}}$ $\mathrm{hystF}={J}_{s}+\mathrm{unitT}\left(-{P}_{1}{P}_{3}+{P}_{2}{P}_{4}\right)+{\mathrm{\mu }}_{0}{H}_{\mathrm{stat}}+\frac{1}{2}\mathrm{eps}$ $\mathrm{hystR}=-{J}_{s}+\mathrm{unitT}\left({P}_{1}{P}_{2}-{P}_{3}{P}_{4}\right)+{\mathrm{\mu }}_{0}{H}_{\mathrm{stat}}-\frac{1}{2}\mathrm{eps}$ $\mathrm{LossPower}=\mathrm{LossPowerStat}+\mathrm{LossPowerEddy}$ $\mathrm{LossPowerEddy}={H}_{\mathrm{eddy}}\frac{\mathrm{dB}}{\mathrm{dt}}V$ $\mathrm{LossPowerStat}={H}_{\mathrm{stat}}\frac{\mathrm{dB}}{\mathrm{dt}}V$ $\mathrm{diffHyst}=\mathrm{hystF}-\mathrm{hystR}$ $\frac{\mathrm{dB}}{\mathrm{dt}}=k\mathrm{dHyst}+{\mathrm{\mu }}_{0}\frac{{\mathrm{dH}}_{\mathrm{stat}}}{\mathrm{dt}}$ $\frac{\mathrm{dMagRel}}{\mathrm{dt}}=0$

Variables

 Name Units Description Modelica ID ${V}_{m}$ $A$ Magnetic potential difference between both ports V_m $\mathrm{\Phi }$ $\mathrm{Wb}$ Magnetic flux from port_p to port_n Phi $\mathrm{LossPower}$ $W$ Loss power leaving component via HeatPort LossPower ${T}_{\mathrm{heatPort}}$ $K$ Temperature of HeatPort T_heatPort $H$ $\frac{A}{m}$ Magnetic field strength H ${H}_{\mathrm{stat}}$ $\frac{A}{m}$ Static (ferromagnetic) portion of the magnetic field strength Hstat ${H}_{\mathrm{eddy}}$ $\frac{A}{m}$ Dynamic (eddy currents) portion of the magnetic field strength Heddy $B$ $T$ Magnetic flux density B $\mathrm{MagRel}$ $1$ Relative magnetization at initialization (-1..1) MagRel $\mathrm{LossPowerStat}$ $W$ Ferromagnetic (static) hysteresis losses LossPowerStat $\mathrm{LossPowerEddy}$ $W$ Eddy current losses (dynamic hysteresis losses) LossPowerEddy ${\mathrm{derH}}_{\mathrm{stat}}$ $\frac{A}{ms}$ derH_stat $\mathrm{asc}$ True when ${\mathrm{derH}}_{\mathrm{stat}}>0$ asc

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

Material

 Name Default Units Description Modelica ID Hysteresis Material [1] Parameter-based hysteresis material mat Use default material $\mathrm{true}$ True (checked) uses hysteresisParameterMaterial1 as the name for the material parameter useDefaultMaterial

[1] hysteresisTableMaterial1

Fixed Geometry

 Name Default Units Description Modelica ID $\ell$ $\frac{1}{10}$ $m$ 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 $\mathrm{\sigma }$ $\mathrm{mat}\cdot \mathrm{\sigma }$ $\frac{S}{m}$ Conductivity of core material sigma $d$ $5.·{10}^{-4}$ $m$ Thickness of lamination d

Constant Parameters

 Name Default Units Description Modelica ID $V$ $A\ell$ ${m}^{3}$ Volume of FluxTube V $T$ $293.15$ $K$ Fixed device temperature if useHeatPort = false T

Constants

 Name Value Units Description Modelica ID $\mathrm{unitT}$ $1$ $T$ unitT

 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.

 See Also