modelSimpleRoomODE
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) Q̇heat_cool, req corresponds to a steady-state control error equal to zero,
0 = Q̇heat_cool, req + G (Tout - Tind, set) + Q̇various,
where Q̇various 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 Q̇heat_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
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Units.SI.Time | tau | 1800 | Time constant of the indoor temperature |
| Nominal condition | |||
| Modelica.Units.SI.TemperatureDifference | dTEnv_nominal | Design temperature difference at which envelope heat loss is QEnv_flow_nominal | |
| Modelica.Units.SI.Temperature | TAir_start | Initial air temperature | |
| Modelica.Units.SI.HeatFlowRate | QEnv_flow_nominal | Envelope heat loss at temperature difference of dTEnv_nominal (with no internal gains, no solar radiation) | |
| Initialization | |||
| Boolean | steadyStateInitial | false | true initializes T with dT(0)/dt=0, false initializes T with T(0)=TIndHea_nominal |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Blocks.Interfaces.RealInput | TSet | Temperature set point for heating or cooling | |
| Modelica.Blocks.Interfaces.RealInput | QReq_flow | Required heat flow rate to meet temperature set point (>=0 for heating) | |
| Modelica.Blocks.Interfaces.RealInput | QAct_flow | Actual heating or cooling heat flow rate (>=0 for heating) | |
| Modelica.Blocks.Interfaces.RealOutput | TAir | Room 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.