modelVariableImpedance

Polyphase variable impedance

Extends from Interfaces.TwoPlug (Two plugs with pin-adapter, reference connection and declaration of voltage and current), Modelica.Electrical.Polyphase.Interfaces.ConditionalHeatPort (Partial model to include conditional HeatPorts in order to describe the power loss via a thermal network).

Information

The impedance model represents a series connection of a resistor and either an inductor or capacitor in each phase.

The linear impedance connects the complex voltage v with the complex current i by i*Z = v in each phase, using m variable single-phase impedances. The impedances Z_ref = R_ref + j*X_ref are given as complex input signals, representing the resistive and reactive components of the input impedances. The resistive components are modeled temperature dependent, so the real part R_actual = real(Z) are determined from the actual operating temperatures and the reference input resistances real(Z_ref). Conditional heat ports are considered. The reactive components X_actual = imag(Z) are equal to imag(Z_ref) if frequencyDependent = false. Frequency dependency is considered by frequencyDependent = true, distinguishing two cases:

(a) imag(Z_ref) > 0: inductive case
The actual reactances X_actual are proportional to f/f_ref
(b) imag(Z_ref) < 0: capacitive case
The actual reactances X_actual are proportional to f_ref/f

Note

Zero crossings of the real or imaginary parts of the impedance signals Z_ref could cause singularities due to the actual structure of the connected network.

See also

VariableResistor, Resistor, Conductor, Capacitor, Inductor, Impedance, Admittance, Variable conductor, Variable capacitor, Variable inductor Variable admittance

Parameters

TypeNameDefaultDescription
Integerm (from TwoPlugElementary)3Number of phases
SI.Temperature[m]T_reffill(293.15, m)Reference temperatures
SI.LinearTemperatureCoefficient[m]alpha_refzeros(m)Temperature coefficient of resistance (R_actual = R_ref*(1 + alpha_ref*(heatPort.T - T_ref)))
Integermh (from ConditionalHeatPort)3Number of heatPorts=number of phases
BooleanuseHeatPort (from ConditionalHeatPort)false= true, if all heat ports are enabled
SI.Temperature[mh]T (from ConditionalHeatPort)fill(293.15, mh)Fixed device temperatures if useHeatPort = false
BooleanfrequencyDependentfalseConsider frequency dependency, if true
SI.Frequencyf_ref1Reference frequency, if frequency dependency is considered

Connectors

TypeNameDefaultDescription
PositivePlugplug_p (from TwoPlugElementary)Positive quasi-static polyphase plug
NegativePlugplug_n (from TwoPlugElementary)Negative quasi-static polyphase plug
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a[mh]heatPort (from ConditionalHeatPort)Conditional heat ports
Modelica.ComplexBlocks.Interfaces.ComplexInput[m]Z_refVariable complex impedances

Components

TypeNameDefaultDescription
SI.AngularVelocityomega (from TwoPlugElementary)Angular velocity of reference frame
Basic.PlugToPins_pplugToPins_p (from TwoPlugElementary)
Basic.PlugToPins_nplugToPins_n (from TwoPlugElementary)
SI.ComplexVoltage[m]v (from TwoPlug)Complex voltage
SI.Voltage[m]abs_v (from TwoPlug)Modelica.ComplexMath.abs(v)Magnitude of complex voltage
SI.Angle[m]arg_v (from TwoPlug)Modelica.ComplexMath.arg(v)Argument of complex voltage
SI.ComplexCurrent[m]i (from TwoPlug)Complex current
SI.Current[m]abs_i (from TwoPlug)Modelica.ComplexMath.abs(i)Magnitude of complex current
SI.Angle[m]arg_i (from TwoPlug)Modelica.ComplexMath.arg(i)Argument of complex current
SI.ActivePower[m]P (from TwoPlug){Modelica.ComplexMath.real(v[k]*Modelica.ComplexMath.conj(i[k])) for k in 1:m}Active power
SI.ActivePowerP_total (from TwoPlug)sum(P)Total active power
SI.ReactivePower[m]Q (from TwoPlug){Modelica.ComplexMath.imag(v[k]*Modelica.ComplexMath.conj(i[k])) for k in 1:m}Reactive power
SI.ReactivePowerQ_total (from TwoPlug)sum(Q)Total reactive power
SI.ApparentPower[m]S (from TwoPlug){Modelica.ComplexMath.abs(v[k]*Modelica.ComplexMath.conj(i[k])) for k in 1:m}Magnitude of complex apparent power
SI.ApparentPowerS_total (from TwoPlug)sqrt(P_total^2 + Q_total^2)Magnitude of total complex apparent power
Real[m]pf (from TwoPlug){cos(Modelica.ComplexMath.arg(Complex(P[k], Q[k]))) for k in 1:m}Power factor
SinglePhase.Basic.VariableImpedance[m]variableImpedance