Buildings.Electrical.DC.Loads

Package with models for DC electrical loads

Information

This package contains models that represent different types of DC loads.

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
Conductor	Model of a generic DC load
Resistor	Ideal linear electrical resistor
Examples	Package with example models

Buildings.Electrical.DC.Loads.Conductor

Model of a generic DC load

Buildings.Electrical.DC.Loads.Conductor

Information

Model of a generic DC load. The load can be either constant or variable depending on the value of the parameter mode. See the model Buildings.Electrical.Interfaces.Load for more information.

The model computes the current drawn from the load as

P = V i,

where P is the power, V is the voltage and i is the current.
If the component consumes power, then P < 0. If it feeds power into the electrical grid, then P > 0.

Linearization

Consider the simple DC circuit shown in the figure below

where V_S is a constant voltage source, and R is the line resistance. The load has a voltage V across its electrical pins and a current i is flowing through it. If the power consumption drawn by the load is prescribed by the variable P_LOAD, the equation that describes the circuit is

V_S - R i - P_LOAD/i = 0

The unknown variable i appears in a nonlinear equation. This means that in order to compute the current that is drawn by the load, a nonlinear equation has to be solved. If the number of loads increases (as typically happens in real case examples) the number of nonlinear equations to be solved increases too, and the resulting system of nonlinear equations can slow down the simulation. It is possible to avoid such a problem by introducing a linearized model.

The first step to linearize the load model is to define its nominal voltage conditions V_nom, around which the equations will be linearized.
The constitutive equation of the load can be linearized around the nominal voltage condition V_nom as

i = P_LOAD/V = P_LOAD/V_nom + (V - V_nom)[∂ (P_LOAD/V)/ ∂V ]_{V = V_nom} + ₒ((V - V_nom)²),

which leads to the linearized formulation

i ≃ P_LOAD (2/V_nom - V/V_nom²).

The linearized formulation approximates the load power consumption (or production), with the approximation error being proportional to (V - V_nom)². A further approximation has been introduced to improve the approximation of the linearized model even if the voltage is far from the nominal condition. This piecewise linearized approximation instead of approximating the model just in the neighborhood of the nominal voltage V_nom introduces two new points where the model is approximated. The points are at 0.8 V_nom and 1.2 V_nom.

Equation	Condition
i ≃ P_LOAD (2/(0.8 V_nom) - V/(0.8 V_nom²))	V < 8/9⋅ V_nom
i ≃ P_LOAD (2/(1.2 V_nom) - V/(1.2 V_nom²))	V ≥ 12/11⋅ V_nom
i ≃ P_LOAD (2/V_nom - V/V_nom²)	Otherwise

Extends from Buildings.Electrical.Interfaces.ResistiveLoad (Partial model of a resistive load).

Parameters

Type	Name	Default	Description
replaceable package PhaseSystem		PartialPhaseSystem	Phase system
Modeling assumption
Boolean	linearized	false	If true, the load model is linearized
Load	mode	Buildings.Electrical.Types.L...	Type of load model (e.g., steady state, dynamic, prescribed power consumption, etc.)
Nominal conditions
Power	P_nominal	0	Nominal power (negative if consumed, positive if generated). Used if mode <> Buildings.Electrical.Types.Load.VariableZ_P_input [W]
Voltage	V_nominal		Nominal voltage (V_nominal >= 0) [V]
Initialization
Current	i.start[:]	0	Current vector [A]
Power	P.start	0	Power of the load (negative if consumed, positive if fed into the electrical grid) [W]
Initialization
InitMode	initMode	Buildings.Electrical.Types.I...	Initialization mode for homotopy operator

Connectors

Type	Name	Description
replaceable package PhaseSystem		Phase system
input RealInput	y	Fraction of the nominal power consumed [1]
input RealInput	Pow	Power consumed [W]
Terminal_n	terminal	Generalized electric terminal

Modelica definition

model Conductor "Model of a generic DC load" extends Buildings.Electrical.Interfaces.ResistiveLoad( redeclare package PhaseSystem = PhaseSystems.TwoConductor, redeclare Interfaces.Terminal_n terminal); protected Modelica.Units.SI.Voltage absDV "Absolute value of the voltage difference between the two conductors (used by the linearized model)"; equation absDV = abs(terminal.v[1]-terminal.v[2]); if linearized then // Linearized version of the model if absDV <= (8/9)*V_nominal then terminal.i[1] + P*(2/(0.8*V_nominal) - (terminal.v[1]-terminal.v[2])/(0.8*V_nominal)^2) = 0; elseif absDV >= (12/11)*V_nominal then terminal.i[1] + P*(2/(1.2*V_nominal) - (terminal.v[1]-terminal.v[2])/(1.2*V_nominal)^2) = 0; else terminal.i[1] + P*(2/V_nominal - (terminal.v[1]-terminal.v[2])/V_nominal^2) = 0; end if; else // Full nonlinear version of the model // PhaseSystem.activePower(terminal.v, terminal.i) + P = 0; if initMode == Buildings.Electrical.Types.InitMode.zero_current then i[1] = - homotopy(actual= P/(v[1] - v[2]), simplified= 0); else i[1] = - homotopy(actual= P/(v[1] - v[2]), simplified= P*(2/V_nominal - (v[1]-v[2])/V_nominal^2)); end if; end if; // Since the connector is a two conductor, the sum of the currents at the terminal // is null sum(i) = 0; end Conductor;

Buildings.Electrical.DC.Loads.Resistor

Ideal linear electrical resistor

Buildings.Electrical.DC.Loads.Resistor

Information

Model of a linear DC resistor that can vary with respect to temperature.

The model implements the Ohm's law

V = R(T) i.

The resistance R(T) varies depending on the temperature T as

R(T) = R (1 + α (T - T_ref)),

where the resistance R is the reference value of the resistance, α is the linear temperature coefficient, and T_ref is the reference temperature. The temperature T is the temperature of the heat port if useHeatPort = true.

Extends from Buildings.Electrical.Interfaces.ResistiveLoad (Partial model of a resistive load), Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
replaceable package PhaseSystem		PartialPhaseSystem	Phase system
Boolean	useHeatPort	false	= true, if heatPort is enabled
Temperature	T	T_ref	Fixed device temperature if useHeatPort = false [K]
Resistance	R		Resistance at temperature T_ref [Ohm]
Temperature	T_ref	300.15	Reference temperature [K]
LinearTemperatureCoefficient	alpha	0	Temperature coefficient of resistance (R_actual = R(1 + alpha(T_heatPort - T_ref)) [1/K]
Modeling assumption
Boolean	linearized	false	If true, the load model is linearized
Load	mode	Buildings.Electrical.Types.L...	Type of load model (e.g., steady state, dynamic, prescribed power consumption, etc.)
Nominal conditions
Power	P_nominal	V_nominal^2/max(R, Modelica....	Nominal power (negative if consumed, positive if generated). Used if mode <> Buildings.Electrical.Types.Load.VariableZ_P_input [W]
Voltage	V_nominal		Nominal voltage (V_nominal >= 0) [V]
Initialization
Current	i.start[:]	0	Current vector [A]
Power	P.start	0	Power of the load (negative if consumed, positive if fed into the electrical grid) [W]
Initialization
InitMode	initMode	Buildings.Electrical.Types.I...	Initialization mode for homotopy operator

Connectors

Type	Name	Description
replaceable package PhaseSystem		Phase system
input RealInput	y	Fraction of the nominal power consumed [1]
input RealInput	Pow	Power consumed [W]
Terminal_n	terminal	Generalized electric terminal
HeatPort_a	heatPort	Conditional heat port

Modelica definition

model Resistor "Ideal linear electrical resistor" extends Buildings.Electrical.Interfaces.ResistiveLoad( redeclare package PhaseSystem = PhaseSystems.TwoConductor, redeclare Interfaces.Terminal_n terminal, final mode=Buildings.Electrical.Types.Load.FixedZ_steady_state, final P_nominal=V_nominal^2/max(R, Modelica.Constants.small)); extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(T = T_ref); parameter Modelica.Units.SI.Resistance R(start=1) "Resistance at temperature T_ref"; parameter Modelica.Units.SI.Temperature T_ref=300.15 "Reference temperature"; parameter Modelica.Units.SI.LinearTemperatureCoefficient alpha=0 "Temperature coefficient of resistance (R_actual = R*(1 + alpha*(T_heatPort - T_ref))"; Modelica.Units.SI.Resistance R_actual "Actual resistance = R*(1 + alpha*(T_heatPort - T_ref))"; equation assert((1 + alpha*(T_heatPort - T_ref)) >= Modelica.Constants.eps, "Temperature outside of scope of model"); R_actual = R*(1 + alpha*(T_heatPort - T_ref)); PhaseSystem.systemVoltage(v) = R_actual*PhaseSystem.systemCurrent(i); LossPower = PhaseSystem.activePower(v,i); sum(i) = 0; end Resistor;