Modelica_Magnetic.Sources

Sources of different complexity of magnetomotive force and magnetic flux

Information


This package contains sources of magnetic potential difference:

Package Content

NameDescription
Modelica_Magnetic.Sources.ConstantMMF ConstantMMF Constant magnetomotive force
Modelica_Magnetic.Sources.SignalMMF SignalMMF Signal-controlled magnetomotive force
Modelica_Magnetic.Sources.ElectroMagneticConverter ElectroMagneticConverter Electro-magnetic energy conversion
Modelica_Magnetic.Sources.ConstantFlux ConstantFlux Source of constant magnetic flux
Modelica_Magnetic.Sources.SignalFlux SignalFlux Signal-controlled magnetic flux source
Modelica_Magnetic.Sources.CoilDesign CoilDesign Calculation of winding parameters (wire diameter, number of turns et al.) and recalculation with optionally chosen parameters; to be adapted to particular design tasks


Modelica_Magnetic.Sources.ConstantMMF Modelica_Magnetic.Sources.ConstantMMF

Constant magnetomotive force

Modelica_Magnetic.Sources.ConstantMMF

Information


Magnetic circuits under steady-state conditions, i.e. with stationary magnetic fields (change of magnetic flux dΦ/dt=0) can be described with constant sources of a magnetomotive force (mmf). Constant mmf's are imposed by

For modelling of reluctance actuators with constant mmf sources it is assumed that the armature is fixed so that no motion-induced flux change dΦ/dt can occur.


Parameters

TypeNameDefaultDescription
MagnetomotiveForcetheta Magnetomotive force [A]

Connectors

TypeNameDescription
PositiveMagneticPortpPositive magnetic port
NegativeMagneticPortnNegative magnetic port

Modelica definition

model ConstantMMF "Constant magnetomotive force" 
  
  extends Modelica_Magnetic.Interfaces.TwoPortComponent;
  parameter SI.MagnetomotiveForce theta "Magnetomotive force";
  
equation 
  V_mag = theta;
end ConstantMMF;

Modelica_Magnetic.Sources.SignalMMF Modelica_Magnetic.Sources.SignalMMF

Signal-controlled magnetomotive force

Modelica_Magnetic.Sources.SignalMMF

Information


In electromagnetic devices, a change of a coil's magnetic flux linkage Ψ reacts on the electrical subsystem in that a voltage v is induced due to Faraday's law:

    v = - dΨ/dt
This reaction can possibly be neglected for In these cases, the magnetomotive force (mmf) imposed by a coil can easily be modelled with a signal-controlled mmf source. Except for the neglected dynamics, steady-state actuator forces will be calculated properly in actuator models based on these sources.


Connectors

TypeNameDescription
PositiveMagneticPortpPositive magnetic port
NegativeMagneticPortnNegative magnetic port
input RealInputthetaMagnetomotive force

Modelica definition

model SignalMMF "Signal-controlled magnetomotive force" 
  
  extends Modelica_Magnetic.Interfaces.TwoPortComponent;
  Modelica.Blocks.Interfaces.RealInput theta "Magnetomotive force";
  
equation 
  V_mag = theta;
end SignalMMF;

Modelica_Magnetic.Sources.ElectroMagneticConverter Modelica_Magnetic.Sources.ElectroMagneticConverter

Electro-magnetic energy conversion

Modelica_Magnetic.Sources.ElectroMagneticConverter

Information


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

 
    V_mag = c_coupl * i*w
    w * der(Φ) =  -c_coupl * v
V_mag 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 coupling coefficient c_coupl denotes leakage: Only a portion of the coil's flux linkage Ψ contributes to the useful magnetic flux Φ in the magnetic circuit. The influence of c_coupl can be interpreted as a leakage inductance connected in series with the inductance that is effective in the magnetic circuit.

The flux linkage Ψ and the static inductance L_stat = Ψ/i are calculated for information only. Note that L_stat is set to zero in case of zero current.

The variability of the number of turns w and the coupling coefficient c_coupl is not restricted to parameter, although both variables can be defined as parameters in many modelling cases. The extended variability allows for calculation of w from other variables (i.e. from non-parameters) in a model or for a variable coupling coefficient, e.g. a position-dependent one in an actuator model.


Parameters

TypeNameDefaultDescription
Variables
Realw1Number of turns
CouplingCoefficientc_coupl1Ratio of coil's complete flux linkage to flux linked with the magnetic circuit; 0 < c_coupl <= 1; 1...complete flux linked with magnetic circuit [1]

Connectors

TypeNameDescription
PositiveMagneticPortp_mag 
NegativeMagneticPortn_mag 
PositivePinp_el 
NegativePinn_el 

Modelica definition

model ElectroMagneticConverter "Electro-magnetic energy conversion" 
  
  Interfaces.PositiveMagneticPort p_mag;
  Interfaces.NegativeMagneticPort n_mag;
  Modelica.Electrical.Analog.Interfaces.PositivePin p_el;
  Modelica.Electrical.Analog.Interfaces.NegativePin n_el;
  SI.Voltage v "Voltage";
  SI.Current i "Current";
  SI.MagneticPotentialDifference V_mag "Magnetomotive force";
  SI.MagneticFlux Phi "Magnetic flux coupled into magnetic circuit";
  
  Real w = 1 "Number of turns";
  SI.CouplingCoefficient c_coupl = 1 
    "Ratio of coil's complete flux linkage to flux linked with the magnetic circuit; 0 < c_coupl <= 1; 1...complete flux linked with magnetic circuit";
  
  //for information only:
  SI.MagneticFlux Psi "Flux linkage for information only";
  SI.Inductance L_stat 
    "Static inductance abs(Psi/i) for information only (Caution: L(i=0) set to zero!)";
  
  
equation 
  v = p_el.v - n_el.v;
  0 = p_el.i + n_el.i;
  i = p_el.i;
  
  V_mag = p_mag.V_mag - n_mag.V_mag;
  0 = p_mag.Phi + n_mag.Phi;
  Phi = p_mag.Phi;
  
  assert(c_coupl>0 and c_coupl<=1, "c_coupl out of allowed range 0 <= c_coupl <= 1");
  
  //converter equations:
  V_mag = c_coupl * i*w;   // Ampere's law
  w*der(Phi) = - c_coupl * v;   // Faraday's law
  
  //for information only:
  Psi = w * Phi / c_coupl;
  //use of abs() for positive results; due to Modelica sign conventions for flow into connectors:
  L_stat = if i>0 or i<0 then abs(Psi/i) else 0;
  
end ElectroMagneticConverter;

Modelica_Magnetic.Sources.ConstantFlux Modelica_Magnetic.Sources.ConstantFlux

Source of constant magnetic flux

Modelica_Magnetic.Sources.ConstantFlux

Information


Sources of a constant magnetic flux are useful for modelling of permanent magnets with Norton's magnetic equivalent circuit.


Parameters

TypeNameDefaultDescription
MagneticFluxPhi_source1Magnetic source flux [Wb]

Connectors

TypeNameDescription
PositiveMagneticPortpPositive magnetic port
NegativeMagneticPortnNegative magnetic port

Modelica definition

model ConstantFlux "Source of constant magnetic flux" 
  
  extends Modelica_Magnetic.Interfaces.TwoPortComponent;
  parameter SI.MagneticFlux Phi_source = 1 "Magnetic source flux";
  
equation 
  Phi = Phi_source;
end ConstantFlux;

Modelica_Magnetic.Sources.SignalFlux Modelica_Magnetic.Sources.SignalFlux

Signal-controlled magnetic flux source

Modelica_Magnetic.Sources.SignalFlux

Information


This source of a magnetic flux is intended for test purposes, e.g. for simulation and subsequent plotting of a softmagnetic material's magnetisation characteristics if used together with a nonlinear reluctance element.


Connectors

TypeNameDescription
PositiveMagneticPortpPositive magnetic port
NegativeMagneticPortnNegative magnetic port
input RealInputPhi_sourceImposed magnetic flux

Modelica definition

model SignalFlux "Signal-controlled magnetic flux source" 
  
  extends Modelica_Magnetic.Interfaces.TwoPortComponent;
  Modelica.Blocks.Interfaces.RealInput Phi_source "Imposed magnetic flux";
  
equation 
  Phi = Phi_source;
end SignalFlux;

Modelica_Magnetic.Sources.CoilDesign Modelica_Magnetic.Sources.CoilDesign

Calculation of winding parameters (wire diameter, number of turns et al.) and recalculation with optionally chosen parameters; to be adapted to particular design tasks

Information


This model exemplarily shows dimensioning of a winding (wire diameter, number of turns) based on desired operating conditions (voltage, temperature, current density, conductor filling factor) for a given cross-section area of the winding. It can be modified according to the parameters given and sought after for a particular design project.

The calculated winding resistance and number of turns can be used as input parameters to the electrical subsystem of a device to be modelled. Operating voltage U can be minimum, nominal and maximum voltage respectively as specified for a particular design project. In conjunction with the setting of the operating temperature T_opCelsius, this enables for analysis of the device under worst-case conditions (e.g. minimum required magnetomotive force, maximum allowed ohmic losses, minimum and maximum force respectively).

For manufacturing of a winding, the obtained wire diameter d_wireCalculated must be rounded to that of an available wire. In order to analyse the influence of this rounding, one can enter the chosen wire diameter d_wireChosen and number of turns w_chosen as optional input. Calculation of the resulting winding parameters enables for comparison with the ones obtained otherwise.


Parameters

TypeNameDefaultDescription
Resistivityrho_200.0178e-6Resistivity of conductor material at 20°C [Ohm.m]
TemperatureCoefficientalpha0.0039Temperature coefficient of conductor material's resistivity [1/K]
CelsiusTemperatureT_opCelsius20Winding's operating temperature [degC]
Heighth_w Height of winding's cross-section [m]
Breadthb_w Breadth of winding's cross-section [m]
Lengthl_avg Average length of one turn [m]
VoltageU Operating voltage (nominal/ minimum/ maximum voltage depending on design objective) [V]
CurrentDensityJ_desired4e6DESIRED current density at operating temperature and voltage resp. [A/m2]
Realc_condFillChosen0.6CHOSEN conductor filling factor = total conductor area without insulation/ total winding area
Chosen feasible parameters (optional)
Diameterd_wireChosend_wireCalculatedCHOSEN available wire diameter (without insulation) [m]
Realw_chosenw_calculatedCHOSEN number of turns

Modelica definition

model CoilDesign 
  "Calculation of winding parameters (wire diameter, number of turns et al.) and recalculation with optionally chosen parameters; to be adapted to particular design tasks" 
  
  parameter SI.Resistivity rho_20 = 0.0178e-6 
    "Resistivity of conductor material at 20°C";   //default material: Copper
  parameter Utilities.TemperatureCoefficient alpha = 0.0039 
    "Temperature coefficient of conductor material's resistivity";   //default material: Copper
  parameter SI.CelsiusTemperature T_opCelsius = 20 
    "Winding's operating temperature";
  
  final parameter SI.Resistivity rho = rho_20 * (1 + alpha *(T_opCelsius - 20)) 
    "Resistivity at operating temperature";
  
  parameter SI.Height h_w "Height of winding's cross-section";
  parameter SI.Breadth b_w "Breadth of winding's cross-section";
  
  final parameter SI.Area A_w = h_w * b_w "Cross-section area of winding";
  
  parameter SI.Length l_avg "Average length of one turn";
  
  parameter SI.Voltage U 
    "Operating voltage (nominal/ minimum/ maximum voltage depending on design objective)";
  
  parameter SI.CurrentDensity J_desired = 4e6 
    "DESIRED current density at operating temperature and voltage resp.";
  
  parameter Real c_condFillChosen = 0.6 
    "CHOSEN conductor filling factor = total conductor area without insulation/ total winding area";
  
  final parameter Real w_calculated = U/ (rho * l_avg * J_desired) 
    "CALCULATED number of turns";
  
  final parameter SI.Diameter d_wireCalculated = sqrt(4 * A_w * c_condFillChosen /(pi * w_calculated)) 
    "CALCULATED wire diameter (without insulation)";
  
  final parameter SI.Area A_wireCalculated = pi * d_wireCalculated^2 / 4 
    "Calculated wire cross-section area";
  
  final parameter SI.Resistance R_calculated = rho * w_calculated * l_avg / A_wireCalculated 
    "Winding resistance at operating temperature and voltage resp. with CALCULATED number of turns and wire diameter";
  
  final parameter SI.Power P_calculated = U^2 / R_calculated 
    "Winding's ohmic losses at operating temperature and voltage resp. with CALCULATED number of turns and wire diameter";
  
  parameter SI.Diameter d_wireChosen = d_wireCalculated 
    "CHOSEN available wire diameter (without insulation)";
  
  parameter Real w_chosen = w_calculated "CHOSEN number of turns";
  
  final parameter SI.Area A_wireChosen = pi * d_wireChosen^2 / 4 
    "Wire cross-section area resulting from CHOSEN wire diameter";
  
  final parameter SI.Resistance R_actual = rho * w_chosen * l_avg / A_wireChosen 
    "Winding resistance at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter";
  
  final parameter SI.Power P_actual = U^2 / R_actual 
    "Winding's ohmic losses at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter";
  
  final parameter SI.CurrentDensity J_actual = U * 4/(R_actual * pi * d_wireChosen^2) 
    "Current density at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter";
  
  final parameter Real c_condFillActual = w_chosen * pi * d_wireChosen^2 /(4 * A_w) 
    "Conductor filling factor resulting from CHOSEN number of turns and wire diameter";
  
  
end CoilDesign;

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