modelZone

Thermal zone based on 5R1C network

Information

This is a lumped-capacity simplified building model based on the 5R1C network presented in the ISO 13790:2008 Standard. The simplified 5R1C model uses five thermal resistances and one thermal capacity to reproduce the transient thermal behaviour of buildings. The thermal zone is modeled with three temperature nodes, the indoor air temperature TAir, the envelope internal surface temperature TSur and the zone's mass temperature TMas (the heat port is not shown in the figure), and two boundary condition nodes, supply air temperature TSup and the external air temperature TExt. The five resistances are related to heat transfer by ventilation HVen, windows HWin, opaque components (split between HTra and HMas) and heat transfer between the internal surfaces of walls and the air temperature HThe. The thermal capacity Cm includes the thermal capacity of the entire zone. The heating and/or cooling demand is found by calculating the heating and/or cooling power ΦHC that needs to be supplied to, or extracted from, the internal air node to maintain a certain set-point. Internal, Φint , and solar, Φsol, heat gains are input values, which are split in three components.

The ventilation heat transfer coefficient H_ven is calculated using

H_ven = ρ_a c_a ∑_kV̇_k,

where ρ_a is the density of air, c_a is the specific heat capacity of air and V̇_k is the k-th volumetric external air flow rate. The coupling conductance H_the is given by

H_the = h_as A_tot,

where h_as is the heat transfer coefficient between the air node the surface node, with a fixed value of 3.45 W/m²K, and A_tot is the area of all surfaces facing the building zone. The thermal transmission coefficient of windows H_win is calculated using

H_win = ∑_kU_win,kA_win,k,

where U_win,k is the thermal transmittance of window element k of the building envelope and A_k is the area of the window element k of the building envelope. The coupling conductance H_mas is given by

H_mas =h_ms f_ms A_f,

where h_ms is the heat transfer coefficient between the mass node and the surface node, with fixed value of 9.1 W/m²K, f_ms is a correction factor, and A_f is the floor area. The correction factor f_ms can be assumed as 2.5 for light and medium building constructions, and 3 for heavy constructions. The coupling conductance H_tra is calculated using

H_tra = 1 ⁄ (1 ⁄ H_op - 1 ⁄ H_mas),

where H_op is the thermal transmission coefficient of opaque elements. The three heat gains components are calculated using

Φ_air = 0.5 Φ_int,

Φ_sur = (1-f_ms A_f ⁄ A_tot -H_win ⁄ h_ms A_tot)(0.5 Φ_int+ Φ_sol),

Φ_mas = f_ms A_f ⁄ A_tot (0.5Φ_int + Φ_sol).

Tips for parametrization

The parameters AWin, AWal, surTil and surAzi must have the same dimension of nOrientations .
The areas in AWal must account only for the opaque parts of the walls (excluding windows). The floor and roof area is entered through AFlo and ARoo and must not be entered as part of AWal.
If a wall contains only opaque parts, the corresponding window area must be set to 0.
The parameter coeFac is used to vary the g-factor as a function of the incident angle of the surface. Often, the curve can be approximated by a cubic polynomial, as shown in Buildings.ThermalZones.ISO13790.Validation.BESTEST.Case600. When this information is not available, the parameter coeFac must be set to 1.

Parameters

Type	Name	Default	Description
Modelica.Units.SI.Area	AFlo		Net conditioned floor area
Modelica.Units.SI.Volume	VRoo		Volume of room
Modelica.Units.SI.CoefficientOfHeatTransfer	hInt	3.45	Heat transfer coefficient between surface and air nodes
ISO13790.Data.Generic	buiMas		Building mass
Integer	nOrientations	4	Number of orientations for vertical walls
Modelica.Units.SI.Angle[nOrientations]	surTil		Tilt angle of surfaces
Modelica.Units.SI.Angle[nOrientations]	surAzi		Azimuth angle of surfaces
Ventilation
Real	airRat		Air change rate
Windows
Modelica.Units.SI.Area[nOrientations]	AWin		Area of windows
Modelica.Units.SI.CoefficientOfHeatTransfer	UWin		U-value of windows
Real	winFra	0.001	Frame fraction of windows
Real	gFac		Energy transmittance of glazings
Real[:]	coeFac	{1}	Polynomial coefficients for gFac
Real	shaRedFac	1	Shading reduction factor
Opaque constructions
Modelica.Units.SI.Area[nOrientations]	AWal		Area of external walls (only opaque part)
Modelica.Units.SI.Area	ARoo		Area of roof
Modelica.Units.SI.CoefficientOfHeatTransfer	UWal		U-value of external walls
Modelica.Units.SI.CoefficientOfHeatTransfer	URoo		U-value of roof
Modelica.Units.SI.CoefficientOfHeatTransfer	UFlo		U-value of floor
Real	b	0.5	Adjustment factor for ground heat transfer

Connectors

Type	Name	Description
Modelica.Blocks.Interfaces.RealInput	intSenGai	Internal sensible heat gains
Modelica.Blocks.Interfaces.RealOutput	TAir	Room air temperature
Modelica.Blocks.Interfaces.RealOutput	TSur	Average inside surface temperature
Buildings.BoundaryConditions.WeatherData.Bus	weaBus	Weather data bus
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a	heaPorAir	Heat port to air node
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a	heaPorSur	Heat port to surface temperatures

Components

Type	Name	Description
Modelica.Thermal.HeatTransfer.Components.ThermalConductor	HVen	Heat transfer due to ventilation
Modelica.Thermal.HeatTransfer.Components.ThermalConductor	HTra	Heat transfer through opaque elements
Modelica.Thermal.HeatTransfer.Components.ThermalConductor	HWin	Heat transfer through glazed elements
Modelica.Thermal.HeatTransfer.Components.ThermalConductor	HThe	Coupling conductance betwee air and surface nodes
Modelica.Thermal.HeatTransfer.Components.ThermalConductor	HMas	Coupling conductance between surface and mass nodes
Modelica.Thermal.HeatTransfer.Components.HeatCapacitor	capMas	Zone thermal capacity
Buildings.HeatTransfer.Sources.PrescribedTemperature	TExt	External air temperature
Modelica.Blocks.Math.Add	solGai	Total solar heat gains
BaseClasses.GlazedElements	win	Solar heat gains of glazed elements
BaseClasses.OpaqueElements	opa	Solar heat gains of opaque elements
BaseClasses.GainSurface	phiSur	Heat flow injected to surface node
Modelica.Blocks.Math.Gain	phiAir	Heat flow injected to air node
BaseClasses.GainMass	phiMas	Heat flow injected to mass node
Buildings.HeatTransfer.Sources.PrescribedTemperature	TVen	Supply air temperature

Revisions

May 8, 2024, by Michael Wetter:
Removed connection to itself.
Mar 16, 2022, by Alessandro Maccarini:
First implementation.