This information is part of the Modelica Standard Library maintained by the Modelica Association.

The electromagnetic energy conversion is given by Ampere's law and Faraday's law respectively:

Vm = N * i
N * dΦ/dt = -v

V_m is the magnetic potential difference applied to the magnetic circuit due to the current i through the coil (Ampere's law). There exists a left-hand assignment between the current i (Put your hand around the coil, fingers pointing in the direction of current flow.) and the magnetic potential difference V_m (thumb).
Note: There exists a right-hand assignment between the current through the coil i (fingers) and the magnetomotive force mmf. The mmf has the opposite direction compared with V_m, it is not used in Modelica.

For the complete magnetic circuit the sum of all magnetic potential differences counted with the correct sign in a reference direction is equal to zero: sum(V_m) = 0.
The magnetic flux Φ in each passive component is related to the magnetic potential difference V_m by the equivalent of Ohms' law: V_m = R_m * Φ
Note: The magnetic resistance R_m depends on geometry and material properties. For ferromagnetic materials R_m is not constant due to saturation.

Therefore the sign (actual direction) of Φ (magnetic flux through the converter) depends on the associated branch of the magnetic circuit.
v is the induced voltage in the coil due to the derivative of magnetic flux Φ (Faraday's law).
Note: The negative sign of the induced voltage v is due to Lenz's law.

Note: The image shows a coil wound counter-clockwise (positive mathematical direction). If a coil wound clockwise has to be modeled instead, the parameter N (Number of turns) can be set to a negative value.

The flux linkage Ψ and the static inductance L_stat = |Ψ/i| are calculated for information only. Note that L_stat is set to |Ψ/eps| if |i| < eps (= 100*Modelica.Constants.eps).