Ideal Core

Ideal transformer with three windings

The Ideal Core component models an ideal transformer with three windings. The connections to the windings are vectored signals; each vector has $m$ components, with $m$ a parameter of the model.

 ${i}_{m\left[k\right]}=0$ ${v}_{1\left[k\right]}={n}_{12}\cdot {v}_{2\left[k\right]}$ ${v}_{1\left[k\right]}={n}_{13}\cdot {v}_{3\left[k\right]}$ ${i}_{\mathrm{p1}\left[k\right]}+{i}_{\mathrm{n1}\left[k\right]}=0$ ${i}_{\mathrm{p2}\left[k\right]}+{i}_{\mathrm{n2}\left[k\right]}=0$ ${i}_{\mathrm{p3}\left[k\right]}+{i}_{\mathrm{n3}\left[k\right]}=0$ ${v}_{1\left[k\right]}={v}_{\mathrm{p1}\left[k\right]}-{v}_{\mathrm{n1}\left[k\right]}$ ${v}_{2\left[k\right]}={v}_{\mathrm{p2}\left[k\right]}-{v}_{\mathrm{n2}\left[k\right]}$ ${v}_{3\left[k\right]}={v}_{\mathrm{p3}\left[k\right]}-{v}_{\mathrm{n3}\left[k\right]}$

Connections

 Name Description ${\mathrm{plug}}_{\mathrm{px}}$ positive terminal of winding $x$ ${\mathrm{plug}}_{\mathrm{nx}}$ negative terminal of winding $x$

Variables

 Symbol Units Description ${i}_{\mathrm{px}\left[k\right]}$ $A$ Current flowing into pin ${\mathrm{plug}}_{\mathrm{px}\left[k\right]}$, , ${i}_{\mathrm{px}\left[k\right]}$ $A$ Current flowing into pin ${\mathrm{plug}}_{\mathrm{px}\left[k\right]}$, , ${i}_{m\left[k\right]}$ $A$ Magnetization current associated with $k$ ${v}_{\mathrm{px}\left[k\right]}$ $V$ Voltage at pin ${\mathrm{plug}}_{\mathrm{px}\left[k\right]}$, , ${v}_{\mathrm{nx}\left[k\right]}$ $V$ Voltage at pin ${\mathrm{plug}}_{\mathrm{nx}\left[k\right]}$, ,

Parameters

 Symbol Default Units Description Modelica ID $m$ 3 integer number of phases m ${n}_{12}$ 1 $-$ turns ratio, 1:2 n12 ${n}_{13}$ 1 $-$ turns ratio, 1:3 n12

Initial Conditions

 Symbol Units Description ${v}_{\mathrm{k0}}$ $V$ Initial voltages for winding $k$, ${i}_{\mathrm{k0}}$ $A$ Initial currents for winding $k$,

The initial values can be scalars or vectors of size $m$.  If a scalar, then all components get that value.