Modelica.Magnetic.FluxTubes.Basic

Package Content

Name	Description
Ground	Zero magnetic potential
ElectroMagneticConverter	Electro-magnetic energy conversion
ConstantReluctance	Constant reluctance
LeakageWithCoefficient	Leakage reluctance with respect to the reluctance of a useful flux path (not for dynamic simulation of actuators)
EddyCurrent	For modelling of eddy current in a conductive magnetic flux tube

Modelica.Magnetic.FluxTubes.Basic.Ground

Information

The magnetic potential at the magnetic ground node is zero. Every magnetic network model must contain at least one magnetic ground object.

Connectors

Type	Name	Description
PositiveMagneticPort	port

Modelica definition

model Ground "Zero magnetic potential"

  Modelica.Magnetic.FluxTubes.Interfaces.PositiveMagneticPort port;
equation 
  port.V_m = 0;
end Ground;

Modelica.Magnetic.FluxTubes.Basic.ElectroMagneticConverter

Information

The electro-magnetic energy conversion is given by Ampere's law and Faraday's law respectively:

    V_m = i * N
    N * dΦ/dt = -v

V_m is the magnetomotive force that is supplied to the connected magnetic circuit, Φ is the magnetic flux through the associated branch of this magnetic circuit. The negative sign of the induced voltage v is due to Lenz's law.

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).

Parameters

Type	Name	Default	Description
Real	N		Number of turns

Connectors

Type	Name	Description
PositiveMagneticPort	port_p	Positive magnetic port
NegativeMagneticPort	port_n	Negative magnetic port
PositivePin	p	Positive electric pin
NegativePin	n	Negative electric pin

Modelica definition

model ElectroMagneticConverter "Electro-magnetic energy conversion"

  Modelica.Magnetic.FluxTubes.Interfaces.PositiveMagneticPort port_p 
    "Positive magnetic port";
  Modelica.Magnetic.FluxTubes.Interfaces.NegativeMagneticPort port_n 
    "Negative magnetic port";
  Modelica.Electrical.Analog.Interfaces.PositivePin p "Positive electric pin";
  Modelica.Electrical.Analog.Interfaces.NegativePin n "Negative electric pin";
  SI.Voltage v "Voltage";
  SI.Current i(start = 0, stateSelect=StateSelect.prefer) "Current";
  SI.MagneticPotentialDifference V_m "Magnetic potential difference";
  SI.MagneticFlux Phi "Magnetic flux coupled into magnetic circuit";

  parameter Real N(start = 1) "Number of turns";

  //for information only:
  SI.MagneticFlux Psi "Flux linkage for information only";
  SI.Inductance L_stat "Static inductance abs(Psi/i) for information only";

protected 
  Real eps = 100*Modelica.Constants.eps;
equation 
  v = p.v - n.v;
  0 = p.i + n.i;
  i = p.i;

  V_m = port_p.V_m - port_n.V_m;
  0 = port_p.Phi + port_n.Phi;
  Phi = port_p.Phi;

  //converter equations:
  V_m = i * N;   // Ampere's law
  N * der(Phi) = -v;   // Faraday's law

  //for information only:
  Psi = N * Phi;
  //use of abs() for positive results; due to Modelica sign conventions for flow into connectors:
  L_stat = noEvent(if abs(i) > eps then abs(Psi/i) else abs(Psi/eps));

end ElectroMagneticConverter;

Modelica.Magnetic.FluxTubes.Basic.ConstantReluctance

Information

This constant reluctance is provided for test purposes and simple magnetic network models. The reluctance is not calculated from geometry and permeability of a flux tube, but is provided as a parameter.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialTwoPorts (Partial component with magnetic potential difference between two magnetic ports p and n and magnetic flux Phi from p to n).

Parameters

Type	Name	Default	Description
Reluctance	R_m		Magnetic reluctance [H-1]

Connectors

Type	Name	Description
PositiveMagneticPort	port_p	Positive magnetic port
NegativeMagneticPort	port_n	Negative magnetic port

Modelica definition

model ConstantReluctance "Constant reluctance"

  extends Modelica.Magnetic.FluxTubes.Interfaces.PartialTwoPorts;

  parameter SI.Reluctance R_m(start = 1) "Magnetic reluctance";

equation 
  V_m = Phi * R_m;

end ConstantReluctance;

Modelica.Magnetic.FluxTubes.Basic.LeakageWithCoefficient

Information

Differently from the flux tube elements of package Shapes.Leakage that are calculated from their geometry, this leakage reluctance is calculated with reference to the total reluctance of a useful flux path. Please refer to the Parameters section for an illustration of the resulting magnetic network. Exploiting Kirchhoff's generalized current law, the leakage reluctance is calculated by means of a coupling coefficient c_usefulFlux.

Attention:

This element must not be used for dynamic simulation of electro-magneto-mechanical actuators, where the shape of at least one flux tube element with reluctance force generation in the useful flux path changes with armature motion (e.g. air gap). This change results in a non-zero derivative dG_m/dx of those elements permeance G_m with respect to armature position x, which in turn will lead to a non-zero derivative of the leakage permeance with respect to armature position. This would generate a reluctance force in the leakage element that is not accounted for properly. Shapes.Force.LeakageAroundPoles provides a simple leakage reluctance with force generation.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

Type	Name	Default	Description
CouplingCoefficient	c_usefulFlux		Ratio useful flux/(leakage flux + useful flux) = useful flux/total flux [1]
Reference reluctance
Reluctance	R_mUsefulTot		Total reluctance of useful flux path as reference [H-1]

Connectors

Type	Name	Description
PositiveMagneticPort	port_p	Positive magnetic port
NegativeMagneticPort	port_n	Negative magnetic port

Modelica definition

model LeakageWithCoefficient 
  "Leakage reluctance with respect to the reluctance of a useful flux path (not for dynamic simulation of actuators)"

  extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage;

  parameter SI.CouplingCoefficient c_usefulFlux( start = 0.7) 
    "Ratio useful flux/(leakage flux + useful flux) = useful flux/total flux";

  input SI.Reluctance R_mUsefulTot 
    "Total reluctance of useful flux path as reference";
equation 
  (1 - c_usefulFlux) * R_m = c_usefulFlux * R_mUsefulTot;   // Generalized Kirchhoff's current law

end LeakageWithCoefficient;

Modelica.Magnetic.FluxTubes.Basic.EddyCurrent

Information

Eddy currents are induced in a conductive magnetic flux tube when the flux changes with time. This causes a magnetic voltage drop in addition to the voltage drop that is due to the reluctance of this flux tube. The eddy current component can be thought of as a short-circuited secundary winding of a transformer with only one turn. Its resistance is calculated from the geometry and resistivity of the eddy current path.

Partitioning of a solid conductive cylinder or prism into several hollow cylinders or separate nested prisms and modelling of each of these flux tubes connected in parallel with a series connection of a reluctance element and an eddy current component can model the delayed buildup of the magnetic field in the complete flux tube from the outer to the inner sections. Please refer to [Ka08] for an illustration.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialTwoPorts (Partial component with magnetic potential difference between two magnetic ports p and n and magnetic flux Phi from p to n).

Parameters

Type	Name	Default	Description
Resistivity	rho		Resistivity of flux tube material (default: Iron at 20degC) [Ohm.m]
Length	l		Average length of eddy current path [m]
Area	A		Cross sectional area of eddy current path [m2]

Connectors

Type	Name	Description
PositiveMagneticPort	port_p	Positive magnetic port
NegativeMagneticPort	port_n	Negative magnetic port

Modelica definition

model EddyCurrent 
  "For modelling of eddy current in a conductive magnetic flux tube"

  extends Modelica.Magnetic.FluxTubes.Interfaces.PartialTwoPorts;

  parameter SI.Resistivity rho( start = 0.098e-6) 
    "Resistivity of flux tube material (default: Iron at 20degC)";
  parameter SI.Length l(start = 1) "Average length of eddy current path";
  parameter SI.Area A(start = 1) "Cross sectional area of eddy current path";

  final parameter SI.Resistance R = rho * l /A 
    "Electrical resistance of eddy current path";

equation 
  V_m = 1/R * der(Phi); //Magnetic voltage drop in magnetic network due to eddy current

end EddyCurrent;