Modelica.Electrical.Analog.Basic

Information

This package contains basic analog electrical components:

• Ground
• Resistor
• HeatingResistor
• Conductor
• Capacitor
• Inductor
• SaturatingInductor
• Transformer
• Gyrator
• EMF (Electroc-Motoric-Force)
• Linear controlled sources (VCV, VCC, CCV, CCC)
• OpAmp
• VariableResistor, VariableConductor, VariableCapacitor, VariableInductor

Name	Description
Ground	Ground node
Resistor	Ideal linear electrical resistor
HeatingResistor	Temperature dependent electrical resistor
Conductor	Ideal linear electrical conductor
Capacitor	Ideal linear electrical capacitor
Inductor	Ideal linear electrical inductor
SaturatingInductor	Simple model of an inductor with saturation
Transformer	Transformer with two ports
Gyrator	Gyrator
EMF	Electromotoric force (electric/mechanic transformer)
VCV	Linear voltage-controlled voltage source
VCC	Linear voltage-controlled current source
CCV	Linear current-controlled voltage source
CCC	Linear current-controlled current source
OpAmp	Simple nonideal model of an OpAmp with limitation
VariableResistor	Ideal linear electrical resistor with variable resistance
VariableConductor	Ideal linear electrical conductor with variable conductance
VariableCapacitor	Ideal linear electrical capacitor with variable capacitance
VariableInductor	Ideal linear electrical inductor with variable inductance

Modelica.Electrical.Analog.Basic.Ground

Information

Ground of an electrical circuit. The potential at the ground node is zero. Every electrical circuit has to contain at least one ground object.

Modelica definition

model Ground "Ground node" 
  Interfaces.Pin p;
equation 
  p.v = 0;
end Ground;

Modelica.Electrical.Analog.Basic.Resistor

Information

The linear resistor connects the branch voltage v with the branch current i by i*R = v. The Resistance R is allowed to be positive, zero, or negative.

Parameters

Name	Default	Description
R	1	Resistance [Ohm]

Modelica definition

model Resistor "Ideal linear electrical resistor" 
  extends Interfaces.OnePort;
  parameter SI.Resistance R =      1 "Resistance";
equation 
  R*i = v;
end Resistor;

Modelica.Electrical.Analog.Basic.HeatingResistor

Information

This is a model for an electrical resistor where the generated heat is dissipated to the environment via connector heatPort and where the resistance R is temperature dependent according to the following equation:

    R = R_ref*(1 + alpha*(heatPort.T - T_ref))

alpha is the temperature coefficient of resistance, which is often abbreviated as TCR. In resistor catalogues, it is usually defined as X [ppm/K] (parts per million, similarly to per centage) meaning X*1.e-6 [1/K]. Resistors are available for 1 .. 7000 ppm/K, i.e., alpha = 1e-6 .. 7e-3 1/K;

When connector heatPort is not connected, the temperature dependent behaviour is switched off by setting heatPort.T = T_ref. Additionally, the equation heatPort.Q_dot = 0 is implicitly present due to a special rule in Modelica that flow variables of not connected connectors are set to zero.

Parameters

Name	Default	Description
R_ref		Resistance at temperature T_ref [Ohm]
T_ref	300	Reference temperature [K]
alpha	0	Temperature coefficient of resistance [1/K]

Modelica definition

model HeatingResistor "Temperature dependent electrical resistor" 
  extends Interfaces.OnePort;
  
  parameter SI.Resistance R_ref "Resistance at temperature T_ref";
  parameter SI.Temperature T_ref =      300 "Reference temperature";
  parameter Real alpha(unit="1/K") = 0 "Temperature coefficient of resistance";
  
  SI.Resistance R "Resistance = R_ref*(1 + alpha*(heatPort.T - T_ref));";
  
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort;
equation 
  v = R*i;
  
  if cardinality(heatPort) > 0 then
    R = R_ref*(1 + alpha*(heatPort.T - T_ref));
    heatPort.Q_dot = -v*i;
  else
    /* heatPort is not connected resulting in the
         implicit equation 'heatPort.Q_dot = 0'
      */
    R = R_ref;
    heatPort.T = T_ref;
  end if;
end HeatingResistor;

Modelica.Electrical.Analog.Basic.Conductor

Information

The linear conductor connects the branch voltage v with the branch current i by i = v*G. The Conductance G is allowed to be positive, zero, or negative.

Parameters

Name	Default	Description
G	1	Conductance [S]

Modelica definition

model Conductor "Ideal linear electrical conductor" 
  extends Interfaces.OnePort;
  parameter SI.Conductance G =      1 "Conductance";
equation 
  i = G*v;
end Conductor;

Modelica.Electrical.Analog.Basic.Capacitor

Information

The linear capacitor connects the branch voltage v with the branch current i by i = C * dv/dt. The Capacitance C is allowed to be positive, zero, or negative.

Parameters

Name	Default	Description
C	1	Capacitance [F]

Modelica definition

model Capacitor "Ideal linear electrical capacitor" 
  extends Interfaces.OnePort;
  parameter SI.Capacitance C =      1 "Capacitance";
equation 
  i = C*der(v);
end Capacitor;

Modelica.Electrical.Analog.Basic.Inductor

Information

The linear inductor connects the branch voltage v with the branch current i by v = L * di/dt. The Inductance L is allowed to be positive, zero, or negative.

Parameters

Name	Default	Description
L	1	Inductance [H]

Modelica definition

model Inductor "Ideal linear electrical inductor" 
  extends Interfaces.OnePort;
  parameter SI.Inductance L =      1 "Inductance";
equation 
  L*der(i) = v;
end Inductor;

Modelica.Electrical.Analog.Basic.SaturatingInductor

Information

This model approximates the behaviour of an inductor with the influence of saturation, i.e. the value of the inductance depends on the current flowing through the inductor. The inductance decreases as current increases.
The parameters are:

• Inom...nominal current
• Lnom...nominal inductance at nominal current
• Lzer...inductance near current = 0; Lzer has to be greater than Lnom
• Linf...inductance at large currents; Linf has to be less than Lnom

Parameters

Name	Default	Description
Inom	1	Nominal current [A]
Lnom	1	Nominal inductance at Nominal current [H]
Lzer	2*Lnom	Inductance near current=0 [H]
Linf	Lnom/2	Inductance at large currents [H]

Modelica definition

model SaturatingInductor 
  "Simple model of an inductor with saturation" 
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  parameter Modelica.SIunits.Current Inom =      1 "Nominal current";
  parameter Modelica.SIunits.Inductance Lnom =      1 
    "Nominal inductance at Nominal current";
  parameter Modelica.SIunits.Inductance Lzer =      2*Lnom "Inductance near current=0";
  parameter Modelica.SIunits.Inductance Linf =      Lnom/2 
    "Inductance at large currents";
protected 
  Modelica.SIunits.Inductance Lact(
                                   start=Lzer);
  Modelica.SIunits.MagneticFlux Psi;
  parameter Modelica.SIunits.Current Ipar(       start=Inom/10, fixed=false);
initial equation 
  (Lnom - Linf) = (Lzer - Linf)*Ipar/Inom*(Modelica.Constants.pi/2-arctan(Ipar/Inom));
equation 
  assert(Lzer > Lnom+Modelica.Constants.eps,
         "Lzer (= " + String(Lzer) + ") has to be > Lnom (= " + String(Lnom) + ")");
  assert(Linf < Lnom-Modelica.Constants.eps,
         "Linf (= " + String(Linf) + ") has to be < Lnom (= " + String(Lnom) + ")");
  (Lact - Linf)*i/Ipar = (Lzer - Linf)*noEvent(arctan(i/Ipar));
  Psi = Lact*i;
  v = der(Psi);
end SaturatingInductor;

Modelica.Electrical.Analog.Basic.Transformer

Information

The transformer is a two port. The left port voltage v1, left port current i1, right port voltage v2 and right port current i2 are connected by the following relation:

         | v1 |         | L1   M  |  | i1' |
         |    |    =    |         |  |     |
         | v2 |         | M    L2 |  | i2' |

L1, L2, and M are the primary, secondary, and coupling inductances respectively.

Parameters

Name	Default	Description
L1	1	Primary inductance [H]
L2	1	Secondary inductance [H]
M	1	Coupling inductance [H]

Modelica definition

model Transformer "Transformer with two ports" 
  extends Interfaces.TwoPort;
  parameter SI.Inductance L1 =      1 "Primary inductance";
  parameter SI.Inductance L2 =      1 "Secondary inductance";
  parameter SI.Inductance M =      1 "Coupling inductance";
equation 
  v1 = L1*der(i1) + M*der(i2);
  v2 = M*der(i1) + L2*der(i2);
end Transformer;

Modelica.Electrical.Analog.Basic.Gyrator

Information

A gyrator is a two-port element defined by the following equations:

    i1 =  G2 * v2
    i2 = -G1 * v1

where the constants G1, G2 are called the gyration conductance.

Parameters

Name	Default	Description
G1	1	Gyration conductance [S]
G2	1	Gyration conductance [S]

Modelica definition

model Gyrator "Gyrator" 
  extends Interfaces.TwoPort;
  parameter SI.Conductance G1 =      1 "Gyration conductance";
  parameter SI.Conductance G2 =      1 "Gyration conductance";
equation 
  i1 = G2*v2;
  i2 = -G1*v1;
end Gyrator;

Modelica.Electrical.Analog.Basic.EMF

Information

EMF transforms electrical energy into rotational mechanical energy. It is used as basic building block of an electrical motor. The mechanical connector flange_b can be connected to elements of the Modelica.Mechanics.Rotational library. flange_b.tau is the cut-torque, flange_b.phi is the angle at the rotational connection.

Parameters

Name	Default	Description
k	1	Transformation coefficient [N.m/A]

Modelica definition

model EMF "Electromotoric force (electric/mechanic transformer)" 
  parameter Real k(final unit="N.m/A") = 1 "Transformation coefficient";
  
  SI.Voltage v "Voltage drop between the two pins";
  SI.Current i "Current flowing from positive to negative pin";
  SI.AngularVelocity w "Angular velocity of flange_b";
  Interfaces.PositivePin p;
  Interfaces.NegativePin n;
  Modelica.Mechanics.Rotational.Interfaces.Flange_b flange_b;
equation 
  v = p.v - n.v;
  0 = p.i + n.i;
  i = p.i;
  
  w = der(flange_b.phi);
  k*w = v;
  flange_b.tau = -k*i;
end EMF;

Modelica.Electrical.Analog.Basic.VCV

Information

The linear voltage-controlled voltage source is a TwoPort. The right port voltage v2 is controlled by the left port voltage v1 via

    v2 = v1 * gain.

The left port current is zero. Any voltage gain can be chosen.

Parameters

Name	Default	Description
gain	1	Voltage gain

Modelica definition

model VCV "Linear voltage-controlled voltage source" 
  extends Interfaces.TwoPort;
  parameter Real gain=1 "Voltage gain";
equation 
  v2 = v1*gain;
  i1 = 0;
end VCV;

Modelica.Electrical.Analog.Basic.VCC

Information

The linear voltage-controlled current source is a TwoPort. The right port current i2 is controlled by the left port voltage v1 via

    i2 = v1 * transConductance.

The left port current is zero. Any transConductance can be chosen.

Parameters

Name	Default	Description
transConductance	1	Transconductance [S]

Modelica definition

model VCC "Linear voltage-controlled current source" 
  extends Interfaces.TwoPort;
  parameter SI.Conductance transConductance =      1 "Transconductance";
equation 
  i2 = v1*transConductance;
  i1 = 0;
end VCC;

Modelica.Electrical.Analog.Basic.CCV

Information

The linear current-controlled voltage source is a TwoPort. The right port voltage v2 is controlled by the left port current i1 via

    v2 = i1 * transResistance.

The left port voltage is zero. Any transResistance can be chosen.

Parameters

Name	Default	Description
transResistance	1	Transresistance [Ohm]

Modelica definition

model CCV "Linear current-controlled voltage source" 
  extends Interfaces.TwoPort;
  
  parameter SI.Resistance transResistance =      1 "Transresistance";
equation 
  v2 = i1*transResistance;
  v1 = 0;
end CCV;

Modelica.Electrical.Analog.Basic.CCC

Information

The linear current-controlled current source is a TwoPort. The right port current i2 is controlled by the left port current i1 via

    i2 = i1 * gain.

The left port voltage is zero. Any current gain can be chosen.

Parameters

Name	Default	Description
gain	1	Current gain

Modelica definition

model CCC "Linear current-controlled current source" 
  extends Interfaces.TwoPort;
  parameter Real gain=1 "Current gain";
equation 
  i2 = i1*gain;
  v1 = 0;
end CCC;

Modelica.Electrical.Analog.Basic.OpAmp

Information

The OpAmp is a simle nonideal model with a smooth out.v = f(vin) characteristic, where "vin = in_p.v - in_n.v". The characteristic is limited by VMax.v and VMin.v. Its slope at vin=0 is the parameter Slope, which must be positive. (Therefore, the absolute value of Slope is taken into calculation.)

Parameters

Name	Default	Description
Slope	1	Slope of the out.v/vin characteristic at vin=0

Modelica definition

model OpAmp "Simple nonideal model of an OpAmp with limitation" 
  parameter Real Slope=1 "Slope of the out.v/vin characteristic at vin=0";
  Modelica.Electrical.Analog.Interfaces.PositivePin in_p 
    "Positive pin of the input port";
  Modelica.Electrical.Analog.Interfaces.NegativePin in_n 
    "Negative pin of the input port";
  Modelica.Electrical.Analog.Interfaces.PositivePin out "Output pin";
  Modelica.Electrical.Analog.Interfaces.PositivePin VMax 
    "Positive output voltage limitation";
  Modelica.Electrical.Analog.Interfaces.NegativePin VMin 
    "Negative output voltage limitation";
  SI.Voltage vin "input voltagae";
protected 
  Real f "auxiliary variable";
  Real absSlope;
equation 
  in_p.i = 0;
  in_n.i = 0;
  VMax.i = 0;
  VMin.i = 0;
  vin = in_p.v - in_n.v;
  f = 2/(VMax.v - VMin.v);
  absSlope = if (Slope < 0) then -Slope else Slope;
  out.v = (VMax.v + VMin.v)/2 + absSlope*vin/(1 + absSlope*noEvent(if (f*vin
     < 0) then -f*vin else f*vin));
end OpAmp;

Modelica.Electrical.Analog.Basic.VariableResistor

Information

The linear resistor connects the branch voltage v with the branch current i by

i*R = v

The Resistance R is defined by the R_Port signal.

Attention!!!
It is recomended that the R_Port signal should not cross the zero value. Otherwise depending on the surrounding circuit the probability of singularities is high.

Modelica definition

model VariableResistor 
  "Ideal linear electrical resistor with variable resistance" 
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  Modelica.Blocks.Interfaces.InPort R_Port(
                                           final n=1);
protected 
  Modelica.SIunits.Resistance R;
equation 
  R = R_Port.signal[1];
  v = R*i;
end VariableResistor;

Modelica.Electrical.Analog.Basic.VariableConductor

Information

The linear conductor connects the branch voltage v with the branch current i by

i = G*v

The Conductance G is defined by the G_Port signal.

Attention!!!
It is recomended that the G_Port signal should not cross the zero value. Otherwise depending on the surrounding circuit the probability of singularities is high.

Modelica definition

model VariableConductor 
  "Ideal linear electrical conductor with variable conductance" 
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  Modelica.Blocks.Interfaces.InPort G_Port(
                                           final n=1);
protected 
  Modelica.SIunits.Conductance G "Conductance";
equation 
  G = G_Port.signal[1];
  i = G*v;
end VariableConductor;

Modelica.Electrical.Analog.Basic.VariableCapacitor

Information

The linear capacitor connects the branch voltage v with the branch current i by

i = dQ/dt with Q = C * v .

The capacitance C is defined by the C_Port signal.

It is required that C_Port.signal ≥ 0, otherwise an assertion is raised. To avoid a variable index system,
C = Cmin, if 0 ≤ C_Port.signal < Cmin, where Cmin is a parameter with default value Modelica.Constants.eps.

Parameters

Name	Default	Description
Cmin	Modelica.Constants.eps	[F]

Modelica definition

model VariableCapacitor 
  "Ideal linear electrical capacitor with variable capacitance" 
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  Modelica.Blocks.Interfaces.InPort C_Port(
                                           final n=1);
  parameter Modelica.SIunits.Capacitance Cmin =      Modelica.Constants.eps;
  Modelica.SIunits.ElectricCharge Q;
protected 
  Modelica.SIunits.Capacitance C;
equation 
  assert(C_Port.signal[1]>=0,"Capacitance C_Port.signal[1] (= " +
                             String(C_Port.signal[1]) + ") has to be >= 0!");
  // protect solver from index change
  C = noEvent(max(C_Port.signal[1],Cmin));
  Q = C*v;
  i = der(Q);
end VariableCapacitor;

Modelica.Electrical.Analog.Basic.VariableInductor

Information

The linear inductor connects the branch voltage v with the branch current i by

v = d Psi/dt with Psi = L * i .

The inductance L is defined by the L_Port signal.

It is required that L_Port.signal ≥ 0, otherwise an assertion is raised. To avoid a variable index system,
L = Lmin, if 0 ≤ L_Port.signal < Lmin, where Lmin is a parameter with default value Modelica.Constants.eps.

Parameters

Name	Default	Description
Lmin	Modelica.Constants.eps	[H]

Modelica definition

model VariableInductor 
  "Ideal linear electrical inductor with variable inductance" 
  
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  Modelica.Blocks.Interfaces.InPort L_Port(
                                           final n=1);
  Modelica.SIunits.MagneticFlux Psi;
  parameter Modelica.SIunits.Inductance Lmin =      Modelica.Constants.eps;
protected 
  Modelica.SIunits.Inductance L;
equation 
  assert(L_Port.signal[1]>=0,"Inductance L_Port.signal[1] (= " +
                             String(L_Port.signal[1]) + ") has to be >= 0!");
  // protect solver from index change
  L = noEvent(max(L_Port.signal[1],Lmin));
  Psi = L*i;
  v = der(Psi);
end VariableInductor;