modelSimpleRoomODE

Simplified model for assessing room air temperature variations around a set point

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Information

This is a first order ODE model assessing the indoor air temperature variations around a set point, based on the difference between the required and actual heating or cooling heat flow rate and a minimum set of parameters at nominal conditions.

The lumped thermal conductance G representing all heat transfer mechanisms that depend on the temperature difference with the outside (transmission, infiltration and ventilation) is assessed from the steady-state energy balance at heating nominal conditions as

0 = Q̇heating, nom + G (Tout, heating, nom - Tind, heating, nom).

Note that for model representativeness, it is important for Q̇heating, nom to be evaluated in close to steady-state conditions with no internal heat gains and no solar heat gains.

The lumped thermal conductance G is then considered constant for all operating conditions.

The required heating or cooling heat flow rate (i.e. the space load) heat_cool, req corresponds to a steady-state control error equal to zero,

0 = Q̇heat_cool, req + G (Tout - Tind, set) + Q̇various,

where various represents the miscellaneous heat gains. The indoor temperature variation rate due to an unmet load is given by

C ∂Tind / ∂t = Q̇heat_cool, act + G (Tout - Tind) + Q̇various,

where heat_cool, act is the actual heating or cooling heat flow rate and C is the thermal capacitance of the indoor volume. The two previous equations yield

τ ∂Tind / ∂t = (Q̇heat_cool, act - Q̇heat_cool, req) / G - Tind + Tind, set,

where τ = C / G is the time constant of the indoor temperature.

Parameters

TypeNameDefaultDescription
Modelica.Units.SI.Timetau1800Time constant of the indoor temperature
Nominal condition
Modelica.Units.SI.TemperatureDifferencedTEnv_nominalDesign temperature difference at which envelope heat loss is QEnv_flow_nominal
Modelica.Units.SI.TemperatureTAir_startInitial air temperature
Modelica.Units.SI.HeatFlowRateQEnv_flow_nominalEnvelope heat loss at temperature difference of dTEnv_nominal (with no internal gains, no solar radiation)
Initialization
BooleansteadyStateInitialfalsetrue initializes T with dT(0)/dt=0, false initializes T with T(0)=TIndHea_nominal

Connectors

TypeNameDefaultDescription
Modelica.Blocks.Interfaces.RealInputTSetTemperature set point for heating or cooling
Modelica.Blocks.Interfaces.RealInputQReq_flowRequired heat flow rate to meet temperature set point (>=0 for heating)
Modelica.Blocks.Interfaces.RealInputQAct_flowActual heating or cooling heat flow rate (>=0 for heating)
Modelica.Blocks.Interfaces.RealOutputTAirRoom air temperature

Revisions

  • January 26, 2023, by Michael Wetter:
    Updated parameters for clarity if used for cooling.
  • February 21, 2020, by Antoine Gautier:
    First implementation.