Rotor Saliency Air Gap - MapleSim Help
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Fundamental Wave Rotor Saliency Air Gap

Air gap model with rotor saliency

 Description The Fundamental Wave Rotor Saliency Air Gap (or Rotor Saliency Air Gap) component can be used for machines with uniform air gaps and for machines with rotor saliencies. The air gap model is not symmetrical between stator and rotor because it is assumed the saliency always refers to the rotor. The saliency of the air gap is represented by a main field inductance in the d- and q-axis. For the mechanical interaction of the air gap model with the stator and the rotor it is equipped with two rotational connectors. The torques acting on the connectors are equal but opposite. The difference between the stator and the rotor angle, $\mathrm{\gamma }$, is required for the transformation of the magnetic stator quantities to the rotor side. The air gap model has two magnetic stator ports and two magnetic rotor ports. The magnetic potential difference and the magnetic flux of the stator are transformed to the rotor fixed reference frame. The effective reluctances of the main field with respect to the d- and q-axis are considered in the balance equations.
 Equations $\mathrm{\gamma }=p\left({\mathrm{\phi }}_{a}-{\mathrm{\phi }}_{\mathrm{supp}}\right)$ $\Gamma =\mathrm{exp}\left(j\mathrm{\gamma }\right)$ ${\stackrel{^}{R}}_{m}={\stackrel{^}{R}}_{{m}_{d}}+j{\stackrel{^}{R}}_{{m}_{q}}=\frac{1}{{L}_{{0}_{d}}}+j\frac{1}{{L}_{{0}_{q}}}$ ${\mathrm{\Phi }}_{\mathrm{sr}}={\mathrm{\Phi }}_{\mathrm{rr}}={\stackrel{^}{\mathrm{\Phi }}}_{\mathrm{rp}}=-{\stackrel{^}{\mathrm{\Phi }}}_{\mathrm{rn}}={\mathrm{\Phi }}_{\mathrm{ss}}\stackrel{&conjugate0;}{\Gamma }$ ${\stackrel{^}{\mathrm{\Phi }}}_{\mathrm{ss}}={\stackrel{^}{\mathrm{\Phi }}}_{\mathrm{sp}}=-{\stackrel{^}{\mathrm{\Phi }}}_{\mathrm{sn}}$ ${\stackrel{^}{V}}_{{m}_{\mathrm{rr}}}={\stackrel{^}{V}}_{{m}_{\mathrm{rp}}}-{\stackrel{^}{V}}_{{m}_{\mathrm{rn}}}$ ${\stackrel{^}{V}}_{{m}_{\mathrm{ss}}}={\stackrel{^}{V}}_{{m}_{\mathrm{sp}}}-{\stackrel{^}{V}}_{{m}_{\mathrm{sn}}}$ ${\stackrel{^}{V}}_{{m}_{\mathrm{sr}}}={\stackrel{^}{V}}_{{m}_{\mathrm{ss}}}\stackrel{&conjugate0;}{\Gamma }$ $\frac{\mathrm{\pi }}{2}\left({\stackrel{^}{V}}_{{m}_{\mathrm{rr}}}+{\stackrel{^}{V}}_{{m}_{\mathrm{sr}}}\right)=\Re \left({\stackrel{^}{R}}_{m}\stackrel{&conjugate0;}{{\stackrel{^}{\mathrm{\Phi }}}_{\mathrm{rr}}}\right)$ $-{\mathrm{\tau }}_{a}={\mathrm{\tau }}_{\mathrm{elec}}={\mathrm{\tau }}_{\mathrm{supp}}=\Im \left({\stackrel{^}{V}}_{{m}_{\mathrm{ss}}}\stackrel{&conjugate0;}{{\stackrel{^}{\mathrm{\Phi }}}_{\mathrm{ss}}}\right)$

Variables

 Name Units Description Modelica ID ${V}_{\mathrm{mss}}$ $\frac{1}{A}$ Complex magnetic potential difference of stator w.r.t. stator reference frame V_mss ${V}_{\mathrm{msr}}$ $\frac{1}{A}$ Complex magnetic potential difference of stator w.r.t. rotor reference frame V_msr ${V}_{\mathrm{mrr}}$ $\frac{1}{A}$ Complex magnetic potential difference of rotor w.r.t. rotor reference frame V_mrr ${\mathrm{\Phi }}_{\mathrm{ss}}$ $\mathrm{Wb}$ Complex magnetic flux of stator w.r.t. stator reference frame Phi_ss ${\mathrm{\Phi }}_{\mathrm{sr}}$ $\mathrm{Wb}$ Complex magnetic flux of stator w.r.t. rotor reference frame Phi_sr ${\mathrm{\Phi }}_{\mathrm{rr}}$ $\mathrm{Wb}$ Complex magnetic flux of rotor w.r.t. rotor reference frame Phi_rr ${\mathrm{\tau }}_{\mathrm{elec}}$ $Nm$ Electrical torque tauElectrical $\mathrm{\gamma }$ $\mathrm{rad}$ Electrical angle between rotor and stator gamma $\Gamma$ Equivalent vector representation of orientation rotator

Connections

 Name Description Modelica ID ${\mathrm{port}}_{\mathrm{sp}}$ Positive complex magnetic stator port port_sp ${\mathrm{port}}_{\mathrm{sn}}$ Negative complex magnetic stator port port_sn ${\mathrm{port}}_{\mathrm{rp}}$ Positive complex magnetic rotor port port_rp ${\mathrm{port}}_{\mathrm{rn}}$ Negative complex magnetic rotor port port_rn ${\mathrm{flange}}_{a}$ Flange of the rotor flange_a $\mathrm{support}$ Support at which the reaction torque is acting support

Parameters

 Name Default Units Description Modelica ID $p$ $1$ Number of pole pairs p ${L}_{{0}_{d}}$ $H$ Salient inductance, direct-axis component L0d ${L}_{{0}_{q}}$ $H$ Salient inductance, quadrature-axis component L0q

 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.