Package with models for AC/AC and AC/DC conversion
Information
This package contains models for AC/AC and AC/DC conversion.
Extends from Modelica.Icons.Package (Icon for standard packages).
Package Content
AC AC converter single phase systems
Information
This is an AC/AC converter, based on a power balance between both circuit sides.
The paramater conversionFactor defines the ratio between the RMS voltages
as
V2 = conversionFactor V1
where V1 and V2 are the RMS voltages
at the primary and secondary sides of the transformer, i.e., the
connector N and P, respectively.
The loss of the converter is proportional to the power transmitted.
The parameter eta is the efficiency of the transfer.
The loss is computed as
Ploss = (1-η) Ptr,
where Ptr is the power transmitted. The model is bi-directional
and the power can flow from the primary to the secondary side and vice-versa.
Furthermore, reactive power on both side are set to zero.
Note:
This model is derived from
Modelica.Electrical.QuasiStationary.SinglePhase.Utilities.IdealACDCConverter.
Extends from Buildings.Electrical.Icons.RefAngleConversion (Icon that represents if the angle symble should be displayed or not), Buildings.Electrical.Interfaces.PartialConversion (Model representing a generic two port system for conversion).
Parameters
| Type | Name | Default | Description |
|---|
| replaceable package PhaseSystem_p | PartialPhaseSystem | Phase system of terminal p |
| replaceable package PhaseSystem_n | PartialPhaseSystem | Phase system of terminal n |
| Real | conversionFactor | | Ratio of QS rms voltage on side 2 / QS rms voltage on side 1 |
| Real | eta | | Converter efficiency, pLoss = (1-eta) * Ptr |
| Ground |
| side 1 |
| Boolean | ground_1 | false | If true, connect side 1 of converter to ground |
| side 2 |
| Boolean | ground_2 | true | If true, connect side 2 of converter to ground |
Connectors
| Type | Name | Description |
|---|
| replaceable package PhaseSystem_p | Phase system of terminal p |
| replaceable package PhaseSystem_n | Phase system of terminal n |
Modelica definition
model ACACConverter
"AC AC converter single phase systems"
extends Buildings.Electrical.Icons.RefAngleConversion;
extends Buildings.Electrical.Interfaces.PartialConversion(
redeclare package PhaseSystem_p =
PhaseSystems.OnePhase,
redeclare package PhaseSystem_n =
PhaseSystems.OnePhase,
redeclare Interfaces.Terminal_n terminal_n(
i(start =
zeros(PhaseSystem_n.n),
each stateSelect = StateSelect.prefer)),
redeclare Interfaces.Terminal_p terminal_p(
i(start =
zeros(PhaseSystem_p.n),
each stateSelect = StateSelect.prefer)));
parameter Real conversionFactor(min = Modelica.Constants.eps)
"Ratio of QS rms voltage on side 2 / QS rms voltage on side 1";
parameter Real eta(min=0, max=1)
"Converter efficiency, pLoss = (1-eta) * Ptr";
parameter Boolean ground_1 = false
"If true, connect side 1 of converter to ground";
parameter Boolean ground_2 = true
"If true, connect side 2 of converter to ground";
Modelica.SIunits.Power LossPower[2]
"Loss power";
protected
Modelica.SIunits.Power P_p[2] =
PhaseSystem_p.phasePowers_vi(terminal_p.v, terminal_p.i)
"Power transmitted at pin p";
Modelica.SIunits.Power P_n[2] =
PhaseSystem_n.phasePowers_vi(terminal_n.v, terminal_n.i)
"Power transmitted at pin n";
equation
// Ideal transformation
terminal_p.v = conversionFactor*terminal_n.v;
// Power loss term
terminal_p.i[1] = terminal_n.i[1]/conversionFactor*
Buildings.Utilities.Math.Functions.spliceFunction(eta-2, 1/(eta-2), P_p[1], deltax=0.1);
terminal_p.i[2] = terminal_n.i[2]/conversionFactor*
Buildings.Utilities.Math.Functions.spliceFunction(eta-2, 1/(eta-2), P_p[1], deltax=0.1);
LossPower = P_p + P_n;
// The two sides have the same reference angle
terminal_p.theta = terminal_n.theta;
if ground_1
then
Connections.potentialRoot(terminal_n.theta);
end if;
if ground_2
then
Connections.root(terminal_p.theta);
end if;
end ACACConverter;
AC AC transformer simplified equivalent circuit
Information
This is a simplified equivalent transformer model.
The model accounts for winding Joule losses and leakage reactances
that are represented by a series of a resistance R and an
inductance L. The resistance and the inductance represent both the
effects of the secondary and primary side of the transformer.
The model is parameterized using the following parameters
VHigh - RMS voltage at primary side,VLow - RMS voltage at secondary side,VABase - apparent nominal power of the transformer,XoverR - ratio between reactance and resistance, andZperc - the short circuit impedance.
Given the nominal conditions,the model computes the values of the resistance and the inductance.
Extends from Buildings.Electrical.Icons.RefAngleConversion (Icon that represents if the angle symble should be displayed or not), Buildings.Electrical.Interfaces.PartialConversion (Model representing a generic two port system for conversion).
Parameters
| Type | Name | Default | Description |
|---|
| replaceable package PhaseSystem_p | PartialPhaseSystem | Phase system of terminal p |
| replaceable package PhaseSystem_n | PartialPhaseSystem | Phase system of terminal n |
| Voltage | VHigh | | Rms voltage on side 1 of the transformer (primary side) [V] |
| Voltage | VLow | | Rms voltage on side 2 of the transformer (secondary side) [V] |
| ApparentPower | VABase | | Nominal power of the transformer [VA] |
| Real | XoverR | | Ratio between the complex and real components of the impedance (XL/R) |
| Real | Zperc | | Short circuit impedance |
| Ground |
| side 1 |
| Boolean | ground_1 | false | If true, connect side 1 of converter to ground |
| side 2 |
| Boolean | ground_2 | true | If true, connect side 2 of converter to ground |
| Initialization |
| Angle | phi_1 | 0 | Angle of the voltage side 1 at initialization [rad] |
| Angle | phi_2 | phi_1 | Angle of the voltage side 2 at initialization [rad] |
Connectors
| Type | Name | Description |
|---|
| replaceable package PhaseSystem_p | Phase system of terminal p |
| replaceable package PhaseSystem_n | Phase system of terminal n |
Modelica definition
model ACACTransformer
"AC AC transformer simplified equivalent circuit"
extends Buildings.Electrical.Icons.RefAngleConversion;
extends Buildings.Electrical.Interfaces.PartialConversion(
redeclare package PhaseSystem_p =
PhaseSystems.OnePhase,
redeclare package PhaseSystem_n =
PhaseSystems.OnePhase,
redeclare Interfaces.Terminal_n terminal_n(
i(start =
zeros(PhaseSystem_n.n),
each stateSelect = StateSelect.prefer)),
redeclare Interfaces.Terminal_p terminal_p(
i(start =
zeros(PhaseSystem_p.n),
each stateSelect = StateSelect.prefer)));
parameter Modelica.SIunits.Voltage VHigh
"Rms voltage on side 1 of the transformer (primary side)";
parameter Modelica.SIunits.Voltage VLow
"Rms voltage on side 2 of the transformer (secondary side)";
parameter Modelica.SIunits.ApparentPower VABase
"Nominal power of the transformer";
parameter Real XoverR
"Ratio between the complex and real components of the impedance (XL/R)";
parameter Real Zperc
"Short circuit impedance";
parameter Boolean ground_1 = false
"If true, connect side 1 of converter to ground";
parameter Boolean ground_2 = true
"If true, connect side 2 of converter to ground";
parameter Modelica.SIunits.Angle phi_1 = 0
"Angle of the voltage side 1 at initialization";
parameter Modelica.SIunits.Angle phi_2 = phi_1
"Angle of the voltage side 2 at initialization";
Modelica.SIunits.Efficiency eta
"Efficiency";
Modelica.SIunits.Power PLoss[2]
"Loss power";
protected
Real N = VHigh/VLow
"Winding ratio";
Modelica.SIunits.Current IHigh = VABase/VHigh
"Nominal current on primary side";
Modelica.SIunits.Current ILow = VABase/VLow
"Nominal current on secondary side";
Modelica.SIunits.Current IscHigh = IHigh/Zperc
"Short circuit current on primary side";
Modelica.SIunits.Current IscLow = ILow/Zperc
"Short circuit current on secondary side";
Modelica.SIunits.Impedance Zp = VHigh/IscHigh
"Impedance of the primary side (module)";
Modelica.SIunits.Impedance Z1[2]=
{Zp*
cos(
atan(XoverR)), Zp*
sin(
atan(XoverR))}
"Impedance of the primary side of the transformer";
Modelica.SIunits.Impedance Zs = VLow/IscLow
"Impedance of the secondary side (module)";
Modelica.SIunits.Impedance Z2[2]=
{Zs*
cos(
atan(XoverR)), Zs*
sin(
atan(XoverR))}
"Impedance of the secondary side of the transformer";
Modelica.SIunits.Voltage V1[2](
start =
PhaseSystem_n.phaseVoltages(VHigh, phi_1))
"Voltage at the winding - primary side";
Modelica.SIunits.Voltage V2[2](
start =
PhaseSystem_p.phaseVoltages(VLow, phi_2))
"Voltage at the winding - secondary side";
Modelica.SIunits.Power P_p[2]=
PhaseSystem_p.phasePowers_vi(terminal_p.v, terminal_p.i)
"Power transmitted at pin p (secondary)";
Modelica.SIunits.Power P_n[2]=
PhaseSystem_n.phasePowers_vi(terminal_n.v, terminal_n.i)
"Power transmitted at pin n (primary)";
Modelica.SIunits.Power S_p =
Modelica.Fluid.Utilities.regRoot(P_p[1]^2 + P_p[2]^2, delta=0.1)
"Apparent power at terminal p";
Modelica.SIunits.Power S_n =
Modelica.Fluid.Utilities.regRoot(P_n[1]^2 + P_n[2]^2, delta=0.1)
"Apparent power at terminal n";
equation
// Efficiency
eta =
Buildings.Utilities.Math.Functions.smoothMin(
x1=
Modelica.Fluid.Utilities.regRoot(P_p[1]^2 + P_p[2]^2, delta=0.01)/
Modelica.Fluid.Utilities.regRoot(P_n[1]^2 + P_n[2]^2 + 1e-6, delta=0.01),
x2=
Modelica.Fluid.Utilities.regRoot(P_n[1]^2 + P_n[2]^2, delta=0.01)/
Modelica.Fluid.Utilities.regRoot(P_p[1]^2 + P_p[2]^2 + 1e-6, delta=0.01),
deltaX= 0.01);
// Ideal transformation
V2 = V1/N;
terminal_p.i[1] + terminal_n.i[1]*N = 0;
terminal_p.i[2] + terminal_n.i[2]*N = 0;
// Losses due to the impedance
terminal_n.v = V1 +
Buildings.Electrical.PhaseSystems.OnePhase.product(
terminal_n.i, Z1);
V2 = terminal_p.v;
// Loss of power
PLoss = P_p + P_n;
// The two sides have the same reference angle
terminal_p.theta = terminal_n.theta;
if ground_1
then
Connections.potentialRoot(terminal_n.theta);
end if;
if ground_2
then
Connections.root(terminal_p.theta);
end if;
end ACACTransformer;
AC AC transformer with detailed equivalent circuit
Information
This is a detailed transformer model that takes into account the winding Joule losses
and the leakage reactances on both primary and secondary side. The model also describes
the core or iron losses and the losses due to magnetization effects.
The losses are represented by a series of resistances R1, R2,
Rm and inductances L1, L2, and
Lm.
The model is parameterized using the following parameters
VHigh - RMS voltage at primary side,VLow - RMS voltage at secondary side,VABase - apparent nominal power of the transformer,f - frequency,R_1, L_1 - resistance and inductance at primary side (per unit),R_2, L_2 - resistance and inductance at secondary side (per unit), andR_m, L_m - resistance and inductance for magnetization effects (per unit).
Given the nominal conditions, the model computes the values of the nominal impedances
at both primary and secondary side. Given these values, the per unit values are transformed into
the actual values of the resistances and inductances.
The magnetization losses can be enabled or disabled using the boolean flag magEffects.
Extends from Buildings.Electrical.Icons.RefAngleConversion (Icon that represents if the angle symble should be displayed or not), Buildings.Electrical.Interfaces.PartialConversion (Model representing a generic two port system for conversion).
Parameters
| Type | Name | Default | Description |
|---|
| replaceable package PhaseSystem_p | PartialPhaseSystem | Phase system of terminal p |
| replaceable package PhaseSystem_n | PartialPhaseSystem | Phase system of terminal n |
| Voltage | VHigh | | RMS voltage on side 1 of the transformer (primary side) [V] |
| Voltage | VLow | | RMS voltage on side 2 of the transformer (secondary side) [V] |
| ApparentPower | VABase | | Nominal power of the transformer [VA] |
| Frequency | f | | Nominal frequency [Hz] |
| PerUnit | R1 | | Resistance on side 1 of the transformer (pu) [1] |
| PerUnit | L1 | | Inductance on side 1 of the transformer (pu) [1] |
| PerUnit | R2 | | Resistance on side 2 of the transformer (pu) [1] |
| PerUnit | L2 | | Inductance on side 2 of the transformer (pu) [1] |
| Magnetization |
| Boolean | magEffects | false | If true, introduce magnetization effects |
| PerUnit | Rm | | Magnetization resistance (pu) [1] |
| PerUnit | Lm | | Magnetization inductance (pu) [1] |
| Ground |
| side 1 |
| Boolean | ground_1 | false | Connect side 1 of converter to ground |
| side 2 |
| Boolean | ground_2 | true | Connect side 2 of converter to ground |
| Initialization |
| Angle | phi_1 | 0 | Angle of the voltage side 1 at initialization [rad] |
| Angle | phi_2 | phi_1 | Angle of the voltage side 2 at initialization [rad] |
Connectors
| Type | Name | Description |
|---|
| replaceable package PhaseSystem_p | Phase system of terminal p |
| replaceable package PhaseSystem_n | Phase system of terminal n |
Modelica definition
model ACACTransformerFull
"AC AC transformer with detailed equivalent circuit"
extends Buildings.Electrical.Icons.RefAngleConversion;
extends Buildings.Electrical.Interfaces.PartialConversion(
redeclare package PhaseSystem_p =
PhaseSystems.OnePhase,
redeclare package PhaseSystem_n =
PhaseSystems.OnePhase,
redeclare Interfaces.Terminal_n terminal_n(
i(start =
zeros(PhaseSystem_n.n),
each stateSelect = StateSelect.prefer)),
redeclare Interfaces.Terminal_p terminal_p(
i(start =
zeros(PhaseSystem_p.n),
each stateSelect = StateSelect.prefer)));
parameter Modelica.SIunits.Voltage VHigh
"RMS voltage on side 1 of the transformer (primary side)";
parameter Modelica.SIunits.Voltage VLow
"RMS voltage on side 2 of the transformer (secondary side)";
parameter Modelica.SIunits.ApparentPower VABase
"Nominal power of the transformer";
parameter Modelica.SIunits.Frequency f(start=60)
"Nominal frequency";
parameter Buildings.Electrical.Types.PerUnit R1(min=0)
"Resistance on side 1 of the transformer (pu)";
parameter Buildings.Electrical.Types.PerUnit L1(min=0)
"Inductance on side 1 of the transformer (pu)";
parameter Buildings.Electrical.Types.PerUnit R2(min=0)
"Resistance on side 2 of the transformer (pu)";
parameter Buildings.Electrical.Types.PerUnit L2(min=0)
"Inductance on side 2 of the transformer (pu)";
parameter Boolean magEffects = false
"If true, introduce magnetization effects";
parameter Buildings.Electrical.Types.PerUnit Rm(min=0)
"Magnetization resistance (pu)";
parameter Buildings.Electrical.Types.PerUnit Lm(min=0)
"Magnetization inductance (pu)";
parameter Boolean ground_1 = false
"Connect side 1 of converter to ground";
parameter Boolean ground_2 = true
"Connect side 2 of converter to ground";
parameter Modelica.SIunits.Angle phi_1 = 0
"Angle of the voltage side 1 at initialization";
parameter Modelica.SIunits.Angle phi_2 = phi_1
"Angle of the voltage side 2 at initialization";
Modelica.SIunits.Efficiency eta
"Efficiency";
Modelica.SIunits.Power PLoss[2]
"Loss power";
protected
parameter Modelica.SIunits.AngularVelocity omega_n = 2*Modelica.Constants.pi*f;
parameter Real N = VHigh/VLow
"Winding ratio";
parameter Modelica.SIunits.Resistance RBaseHigh = VHigh^2/VABase
"Base impedance of the primary side";
parameter Modelica.SIunits.Resistance RBaseLow = VLow^2/VABase
"Base impedance of the secondary side";
Modelica.SIunits.Impedance Z1[2] = {RBaseHigh*R1, omega*L1*RBaseHigh/omega_n}
"Impedance of the primary side of the transformer";
Modelica.SIunits.Impedance Z2[2] = {RBaseLow*R2, omega*L2*RBaseLow/omega_n}
"Impedance of the secondary side of the transformer";
Modelica.SIunits.Impedance Zrm[2] = {RBaseHigh*Rm, 0}
"Magnetization impedance - resistance";
Modelica.SIunits.Impedance Zlm[2] = {0, omega*Lm*RBaseHigh/omega_n}
"Magnetization impedance - impedence";
Modelica.SIunits.Voltage V1[2](start =
PhaseSystem_n.phaseVoltages(VHigh, phi_1))
"Voltage at the winding - primary side";
Modelica.SIunits.Voltage V2[2](start =
PhaseSystem_n.phaseVoltages(VLow, phi_2))
"Voltage at the winding - secondary side";
Modelica.SIunits.Power P_p[2] =
PhaseSystem_p.phasePowers_vi(terminal_p.v, terminal_p.i)
"Power transmitted at pin p (secondary)";
Modelica.SIunits.Power P_n[2] =
PhaseSystem_n.phasePowers_vi(terminal_n.v, terminal_n.i)
"Power transmitted at pin n (primary)";
Modelica.SIunits.Power S_p =
Modelica.Fluid.Utilities.regRoot(P_p[1]^2 + P_p[2]^2, delta=0.1)
"Apparent power at terminal p";
Modelica.SIunits.Power S_n =
Modelica.Fluid.Utilities.regRoot(P_n[1]^2 + P_n[2]^2, delta=0.1)
"Apparent power at terminal n";
Modelica.SIunits.AngularVelocity omega
"Angular velocity";
Modelica.SIunits.Current Im[2]
"Magnetization current";
equation
assert(
sqrt(P_p[1]^2 + P_p[2]^2) <= VABase*1.01,
"The load power of the transformer is higher than VABase");
// Angular velocity
omega =
der(
PhaseSystem_p.thetaRef(terminal_p.theta));
// Efficiency
eta =
Buildings.Utilities.Math.Functions.smoothMin(
x1=
Modelica.Fluid.Utilities.regRoot(P_p[1]^2 + P_p[2]^2, delta=0.01)/
Modelica.Fluid.Utilities.regRoot(P_n[1]^2 + P_n[2]^2 + 1e-6, delta=0.01),
x2=
Modelica.Fluid.Utilities.regRoot(P_n[1]^2 + P_n[2]^2, delta=0.01)/
Modelica.Fluid.Utilities.regRoot(P_p[1]^2 + P_p[2]^2 + 1e-6, delta=0.01),
deltaX= 0.01);
// Ideal transformation
V2 = V1/N;
terminal_p.i[1] + (terminal_n.i[1] - Im[1])*N = 0;
terminal_p.i[2] + (terminal_n.i[2] - Im[2])*N = 0;
// Magnetization current
if magEffects
then
Im =
Buildings.Electrical.PhaseSystems.OnePhase.divide(V1, Zrm) +
Buildings.Electrical.PhaseSystems.OnePhase.divide(V1, Zlm);
else
Im =
zeros(2);
end if;
// Losses due to the impedance - primary side
terminal_n.v = V1 +
Buildings.Electrical.PhaseSystems.OnePhase.product(
terminal_n.i, Z1);
// Losses due to the impedance - secondary side
terminal_p.v = V2 +
Buildings.Electrical.PhaseSystems.OnePhase.product(
terminal_p.i, Z2);
// Loss of power
PLoss = P_p + P_n;
// The two sides have the same reference angle
terminal_p.theta = terminal_n.theta;
if ground_1
then
Connections.potentialRoot(terminal_n.theta);
end if;
if ground_2
then
Connections.root(terminal_p.theta);
end if;
end ACACTransformerFull;
AC DC converter
Information
This is an AC/DC converter, based on a power balance between both circuit sides.
The paramater conversionFactor defines the ratio between the RMS voltages
as
VDC = conversionFactor VAC,
where VDC is the voltage of the DC circuit and VAC
is the RMS voltage at the primary side of the transformer.
The loss of the converter is proportional to the power transmitted.
The parameter eta is the efficiency of the transfer.
The loss is computed as
Ploss = (1-η) Ptr
where Ptr is the power transmitted. The model is bi-directional
and the power can flow from both the primary to the secondary side and vice-versa.
Furthermore, reactive power on both side are set to 0.
Note:
This model is derived from
Modelica.Electrical.QuasiStationary.SinglePhase.Utilities.IdealACDCConverter.
Extends from Buildings.Electrical.Interfaces.PartialConversion (Model representing a generic two port system for conversion).
Parameters
| Type | Name | Default | Description |
|---|
| replaceable package PhaseSystem_p | PartialPhaseSystem | Phase system of terminal p |
| replaceable package PhaseSystem_n | PartialPhaseSystem | Phase system of terminal n |
| Real | conversionFactor | | Ratio of DC voltage / AC RMS voltage |
| Real | eta | | Converter efficiency, pLoss = (1-eta) * Ptr |
| Ground |
| AC side |
| Boolean | ground_AC | false | Connect AC side of converter to ground |
| DC side |
| Boolean | ground_DC | true | Connect DC side of converter to ground |
Connectors
| Type | Name | Description |
|---|
| replaceable package PhaseSystem_p | Phase system of terminal p |
| replaceable package PhaseSystem_n | Phase system of terminal n |
Modelica definition
model ACDCConverter
"AC DC converter"
extends Buildings.Electrical.Interfaces.PartialConversion(
redeclare package PhaseSystem_p =
PhaseSystems.TwoConductor,
redeclare package PhaseSystem_n =
PhaseSystems.OnePhase,
redeclare Interfaces.Terminal_n terminal_n(
i(start =
zeros(PhaseSystem_n.n),
each stateSelect = StateSelect.prefer)),
redeclare DC.Interfaces.Terminal_p terminal_p(
i(start =
zeros(PhaseSystem_p.n),
each stateSelect = StateSelect.prefer)));
parameter Real conversionFactor(min = Modelica.Constants.eps)
"Ratio of DC voltage / AC RMS voltage";
parameter Real eta(min=0, max=1)
"Converter efficiency, pLoss = (1-eta) * Ptr";
Modelica.SIunits.Power PLoss
"Loss power";
parameter Boolean ground_AC = false
"Connect AC side of converter to ground";
parameter Boolean ground_DC = true
"Connect DC side of converter to ground";
protected
PhaseSystem_p.Current i_dc
"DC current";
PhaseSystem_p.Voltage v_dc
"DC voltage";
Modelica.SIunits.Power P_p[2] =
PhaseSystem_p.phasePowers_vi(terminal_p.v, terminal_p.i)
"Power transmitted at pin p (secondary)";
Modelica.SIunits.Power P_n[2] =
PhaseSystem_n.phasePowers_vi(terminal_n.v, terminal_n.i)
"Power transmitted at pin n (primary)";
equation
//voltage relation
v_p = v_n*conversionFactor;
// Power losses
PLoss = (1-eta)*
Buildings.Utilities.Math.Functions.spliceFunction(P_p[1], P_n[1], i_p, deltax=0.1);
P_n + P_p = {PLoss, 0};
if ground_AC
then
Connections.potentialRoot(terminal_n.theta);
end if;
if ground_DC
then
v_dc = 0;
Connections.root(terminal_p.theta);
else
i_dc = 0;
Connections.potentialRoot(terminal_p.theta);
end if;
v_dc = terminal_p.v[2];
sum(terminal_p.i) + i_dc = 0;
end ACDCConverter;
Automatically generated Mon May 4 10:18:40 2015.
ACACConverter
ACACTransformer
ACACTransformerFull
ACDCConverter
Examples
Buildings.Electrical.AC.OnePhase.Conversion.ACACConverter
Buildings.Electrical.AC.OnePhase.Conversion.ACACTransformer
Buildings.Electrical.AC.OnePhase.Conversion.ACACTransformerFull
Buildings.Electrical.AC.OnePhase.Conversion.ACDCConverter