Domain

• energy conversion device

Intended application (including scale and resolution)

Modelling of spatial aspects

• lumped (single device)

Model dynamics

• dynamic
• The component models the dynamic response using a first order differential equation. The model is able to capture flow reversals and zero flow.

Model of computation

• time-continuous
• The model avoids the use of events if possible (see, e.g., the noEvent- or smooth-operator described in the Modelica standard).

Functional representation

• explicit
• other, please specify: acausal modelling. The fluid ports (port_a and port_b) use Modelica’s acausal modelling paradigm. Thus, no strict classification of input/output variables is possible. Instead a design flow direction from port_a to port_b is used for this classification. An additional note is added to these variables for clarification. Moreover, Modelica ports are not restricted to single variables. The fluid ports used here define a mix of multiple variables, i.e., enthalpy (stream), mass flow (flow) and pressure (potential). For more details see the Modelica Specification and the respective fluid port model Modelica.Fluid.Interfaces.FluidPort.

Input variables (name, type, unit, description)

• Real m_flow_set: mass flow setpoint for pump [kg/s]
• Modelica.Fluid.Interfaces.FluidPort port_a (acausal): fluid port at return side

Output variables (name, type, unit, description)

• Real P: current electric load [W]
• Modelica.Fluid.Interfaces.FluidPort port_b (acausal): fluid port at supply side

Parameters (name, type, unit, description)

• Real Q_flow_nominal: nominal heat flow [W]
• Real TemSup_nominal: nominal supply temperature [K]
• Real TemRet_nominal: nominal return temperature [K]
• Real eff: power-to-heat efficiency [-]

Internal variables (name, type, unit, description)

• Real m_flow_nominal: nominal mass flow calculated based on parameter values [kg/s]
• Real c_p: heat capacity of water [J/K*kg]

Model equations

Governing equations

m_flow_nominal = Q_flow_nominal / (c_p*(TemSup_nominal - TemRet_nominal)) See Modelica models:

• Heater: IBPSA.Fluid.HeatExchangers.Heater_T
• Pump: IBPSA.Fluid.Movers.FlowControlled_m_flow

Constitutive equations

See Modelica models:

• Medium: IBPSA.Media.Water

Initial conditions

Boundary conditions

Optional: graphical representation (schematic diagram, state transition diagram, etc.)

Model Validation

Narrative

Test system configuration

Inputs and parameters

Inputs:

• m_flow_set
• port_a: connected to fluid boundary with a fixed temperature of 30 °C

• port_b: connected to fluid boundary

• Q_flow_nominal = 10 kW
• TemSup_nominal = 70 K
• TemRet_nominal = 30 K
• eff = 1
• m_flow_nominal (internal) = 0.06 kg/s

Control function (optional)

Initial system state

Temporal resolution

Evolution of system state

The electric heater takes water from the cold source (corresponding to the nominal return temperature value of the electric heater TemRet_nominal). The mass flow is set by the pump which is controlled through a ramping function. The heater increases the temperature of the fluid. In case the mass flow is below the nominal mass flow, the fluid temperature equals the nominal temperature TemSup_nominal. In case the mass flow is higher the heater is operating with full capacity Q_flow_nominal but is not able to reach the nominal temperature TemSup_nominal.

Results

Model harmonization

Narrative

Test system configuration

Inputs and parameters

Initial system state

Temporal resolution

Evolution of system state

Results

  Mean weighted temperature:

  Where ????? is the mass flow and ??????? the supply temperature.
  Total electric power consumption:

  Where ? is the electric power consumed.