Ideal Heating, Thermostat & Surface Heating

Overview

The heat and cooling delivery to the zones is modeled via a control chain: the thermostat model generates normalized control signals from the setpoint and actual temperature, which the delivery models — ideal heating/cooling, ideal surface heating or ideal pipe register — convert into powers. All models are parameterized via the usage profile or the surface-heating assignment.

Thermostat

The thermostat model provides per zone the control signals HeatingControlValue and CoolingControlValue (each 0…1) as well as the current setpoints ThermostatHeatingSetpoint and ThermostatCoolingSetpoint [C]. Properties:

• Setpoints — constant or schedule-controlled (heating and cooling setpoint separately).
• Reference variable — room air temperature (AirTemperature) or operative temperature (OperativeTemperature).
• Controller type —
  • Analog (P controller): the signal rises proportionally to the control deviation; the tolerance (TemperatureTolerance [K]) determines the steepness ($k_P = 1/\mathrm{tolerance}$). At 0.1 K tolerance, the signal is fully modulated 0.1 K below the setpoint.
  • Digital (two-position controller with hysteresis): switches with the hysteresis band TemperatureBand [K] around the setpoint.

Ideal heating/cooling (convective)

The model converts the thermostat signals into an ideal convective heating or cooling load of the zone, limited by the maximum powers per floor area:

$$\dot{Q}_{\mathrm{heat}} = \min\!\big(1,\; \max(0,\; k_P\,x_H + k_I\!\textstyle\int x_H\,dt)\big)\cdot q_{\mathrm{heat,max}} \cdot A$$

with the heating control signal $x_H$, the zone floor area $A$ and MaxHeatingPowerPerArea or MaxCoolingPowerPerArea [W/m²]. Optionally, an I component acts in addition to the P component (Kp/Ki parameters, PI controller; the integral component does not accumulate any negative control deviation). The limitation to 0…1 prevents “cooling by the heater” and exceeding the maximum power. Results: IdealHeatingLoad and IdealCoolingLoad [W] (cooling load defined positive), which are accounted for in the room energy balance. A zone without a cooling setpoint receives no cooling load (and vice versa).

Ideal surface heating (active layer)

The ideal surface heating delivers the power not to the room air, but directly into the active layer of a construction (see construction heat conduction):

$$\dot{Q}_{\mathrm{active}} = x_H \cdot q_{\mathrm{heat,max}} \cdot A_{\mathrm{construction}} \;-\; x_C \cdot q_{\mathrm{cool,max}} \cdot A_{\mathrm{construction}}$$

The control signals $x_H$, $x_C$ come from the thermostat of the assigned control zone — which can also be a different zone than the one in which the surface is located. The heat reaches the room only via the component layers, whereby the inertia of a floor or ceiling heating system is physically modeled. Result: ActiveLayerThermalLoad [W].

Ideal pipe register

The pipe register is the more detailed surface-heating model: instead of a power, a mass flow through a pipe register in the active layer is controlled.

• The mass flow follows the thermostat signal: $\dot{m} = x \cdot \dot{m}_{\mathrm{max}}$ (MaxMassFlux [kg/s]).
• The supply temperature is constant (SupplyTemperature [C]) or schedule-controlled (e.g. from a heating curve via the supply system).
• The heat delivery to the layer follows the analytical solution of a pipe in a constant ambient temperature:

$$\dot{Q} = \dot{m}\, c_p \left(1 - e^{-\,UA/(\dot{m}_{\parallel}\, c_p)}\right)\left(T_{\mathrm{supply}} - T_{\mathrm{layer}}\right)$$

The UA value is formed from the pipe length, inner diameter, length-related U-value of the pipe wall (UValuePipeWall [W/mK]) and the inner-side heat transfer; the latter is computed flow-dependently via Reynolds, Prandtl and Nusselt correlations from the fluid properties. $\dot{m}_{\parallel}$ is the mass flow per parallel pipe strand. A simultaneous heating and cooling signal is not permitted (runtime error).

Results per active layer: MassFlux [kg/s], ActiveLayerThermalLoad [W] and ReturnTemperature [C] — the return temperature results from the supply temperature and the delivered power.