Room Energy Balance & Room States

Overview

In the simulation, every room of the building model is represented as a zone with a well-mixed air node. Two models work together:

• The room balance model sums up all heat flows (and, when the moisture balance is enabled, all moisture flows) into the zone at each computation step and passes the time derivative of the balanced quantities to the integrator.
• The room state model converts the zone’s energy (and moisture mass), as advanced by the integrator, back into the state variables room air temperature, relative humidity, vapor pressure and absolute humidity.

Energy balance

The balanced conserved quantity is the energy of the room air in joules. The balance equation reads

$$\frac{du_R}{dt} \;=\; \sum \dot{Q} \;=\; \dot{Q}_{\mathrm{construction}} + \dot{Q}_{\mathrm{window,U}} + \dot{Q}_{\mathrm{window,solar}} + \dot{Q}_{\mathrm{ventilation}} + \dot{Q}_{\mathrm{persons}} + \dot{Q}_{\mathrm{equipment}} + \dot{Q}_{\mathrm{lighting}} + \dot{Q}_{\mathrm{heating}} - \dot{Q}_{\mathrm{cooling}} + \dot{Q}_{\mathrm{network}}$$

with the terms (each defined positive into the zone):

Contribution	Result quantity	Origin
Heat conduction of all room-enclosing construction surfaces	ConstructionHeatConductionLoad	Construction model
Heat conduction through windows	WindowHeatConductionLoad	Window model
Solar gains (room-node share)	WindowSolarRadiationLoad	Window loads × room-node share from the solar distribution model
Ventilation/infiltration	VentilationHeatLoad	Ventilation model
Convective internal loads (equipment, persons, lighting)	ConvectiveEquipmentHeatLoad, ConvectivePersonHeatLoad, ConvectiveLightingHeatLoad	Internal loads model
Ideal heating/cooling load	IdealHeatingLoad, IdealCoolingLoad (cooling load defined positive, enters negatively)	Ideal heating/cooling
Heat input from network components	NetworkHeatLoad	hydraulic network (district)

All terms are individually available as output quantities, as is the total sum CompleteThermalLoad and the electrical powers EquipmentElectricalPower, LightingElectricalPower and TotalElectricalPower.

Back-calculation to the air temperature

Without a moisture balance, the linear relationship between balanced energy and room air temperature is

$$u_R = \left(\rho_{\mathrm{air}}\, c_{\mathrm{air}}\, V + C_{\mathrm{extra}}\right) \cdot T_{\mathrm{room}}$$

with the zone volume $V$ in [m³] and the additional heat capacity $C_{\mathrm{extra}}$ in [J/K], which lumps the thermal mass of furnishings and lightweight fixtures (room parameter, see room properties). The initial value is the project’s initial temperature.

Moisture balance

If the option Enable moisture balancing is set on the Dynamic Simulation page, a second conserved quantity is balanced per zone — the water vapor mass $m_v$ in [kg]:

$$\frac{dm_v}{dt} = \dot{m}_{v,\mathrm{ventilation}} + \dot{m}_{v,\mathrm{persons}}$$

The energy balance additionally receives the enthalpy flow of the moisture sources (sensible + latent). The back-calculation to the temperature then accounts for the heat capacity and evaporation enthalpy of the water vapor:

$$T_{\mathrm{room}} = \frac{u_R - h_{\mathrm{evap}}\, m_v}{\rho_{\mathrm{air}} c_{\mathrm{air}} V + m_v\, c_{\mathrm{vapor}} + C_{\mathrm{extra}}}$$

As result quantities, the state model provides per zone AirTemperature [C], RelativeHumidity [%], VaporPressure [Pa] and AbsoluteHumidity [kg/m³]; the sum of the moisture flows is available as CompleteMoistureLoad [kg/s].

Operative temperature

The comfort model additionally computes the operative temperature (OperativeTemperature) per zone from the room air temperature and the area-weighted surface temperatures of the enclosing building components. It is part of the standard building outputs and can be selected in the usage profile as the reference variable of the thermostat.