.Buildings.DHC.Loads.BaseClasses.SimpleRoomODE

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 = Q̇_{heating, nom} + G (T_{out, heating, nom} - T_{ind, heating, nom}).

Note that for model representativeness, it is important for Q̇_{heating, 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) Q̇_{heat_cool, req} corresponds to a steady-state control error equal to zero,

0 = Q̇_{heat_cool, req} + G (T_out - T_{ind, set}) + Q̇_various,

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

C ∂T_ind / ∂t = Q̇_{heat_cool, act} + G (T_out - T_ind) + Q̇_various,

where Q̇_{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 ∂T_ind / ∂t = (Q̇_{heat_cool, act} - Q̇_{heat_cool, req}) / G - T_ind + T_{ind, set},

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

Revisions

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