# 3. Multi-zone building modeling¶

In this chapter the application of the BuildingSystems library for multi-zone building modeling is demonstrated.

For this purpose, a thermal building model of the Thermal Model House (http://www.thermisches-modellhaus.de) with two thermal zones shall be created:

The Thermal Model House (TMH) is a portable experimental test facility with a simple geometry and a compact size of approximately 1 m length, 0.5 m depth and 0.5 m height. This small thermal box is able to reproduce different phenomena of building climatization within physical experiments. Due to its manifold configuration options, it is possible to do experiments about the energy balance of rooms, about the heat and air transport processes within rooms, about ventilation, heating and cooling of buildings as well as about building control. The TMH is being developed at the Institute of Architecture and Urban Planning at UdK Berlin. It is used for the education of architecture and engineering students and also for research.

One configuration of the TMH works with a inner partition wall, which divides the air volume of the box into two different thermal zones. These zones can be separately heated or cooled using individual heating surfaces on the bottom and cooling surfaces on the ceiling. Exactly this configuration shall be modelled in the present case.

The modelling and simulation process is described using the Modelica simulation environment, Dymola (version Dymola 2018 FD01). First of all the Modelica library BuildingSystems has to be loaded into Dymola. After that, the library will occur in the library tree in addition to the other present Modelica libraries.

The creation and configuration of a new thermal building model takes place in the following steps:

• Configuration of the building model structure (topology of the construction of the buildings model)
• Definition of the building model parameters (building geometry and physical parameters of the construction elements)
• Definition of the boundary conditions of the system model (climate conditions of the building ambient, set temperatures for heating and cooling for each thermal zone)

## 3.1. Set up the building model structure¶

1. Create a new package for your simulation experiment.
• Open dialog: File -> New -> Package and fill in the field Name of new package: “ThermalModelHouse” and click OK
• Mark the new package ThermalModelHouse in the package browser and save it with File -> Save in the file ThermalModelHouse.mo in a folder of your choice.
1. Create a new building model based on the template model class BuildingTemplate. That means you insert a new building model into the previously defined package as follows:
• Open dialog: File -> New -> Model and fill in the field Name of new model: “Building”. Then click on the button to the right of the field Extends (optional): and navigate to the model class BuildingSystems.Buildings.BaseClasses.BuildingTemplate and click OK. Further click on the button right of the field Insert in Package (optional): and navigate to the package ThermalModelHouse on the top level and click OK (compare the Dymola screenshoot above).

As a result you can see now the inner structure (the Diagram view in Dymola) of the empty building model. On the left side you see the interfaces to the building ambient, below the interfaces to the ground of the building and on the right side the input signals for the set temperatures for heating and cooling of each zone and the interfaces of the air paths to the ambient.

1. Instantiate two thermal zones, which shall represent the left and right part of the TMH.

For this purpose drag and drop a component model from the class BuildingSystems.Buildings.Zones.ZoneTemplateAirvolumeMixed into the building model and rename it to zone1. Add zone2 in the same manner:

1. Instantiate construction elements.

For the opaque constructions (walls, bottoms, ceilings etc.) use the model class BuildingSystems.Buildings.Constructions.Walls.WallThermal1DNodes and for the transparent constructions (windows) the model class BuildingSystems.Buildings.Constructions.Windows.Window.

Notice, that each component comes with a blue line (which indicates side 1) and has the connector toSurfacePort_1. The other unmarked side 2 owns the connector toSurfacePort_2. The blue line helps you to distinguish both component sides, e.g. if you want to define single layers of a construction in a certain order. In our case we bring all component models in a position, that all blue lines show to the zones respectively in the case of the partition wall to zone1 and to the adjacent zone2.

In our case we have to instantiate seven walls (wall1 to wall7), two bottoms (bottom1 and bottom2), two ceilings (ceiling1 and ceiling2) and two windows models (window1 and window2).

1. Connect construction elements.

Now connect the connectors of all “blue sides” with the zone models as in the following picture:

Here each zone model offers you six different positions for connections to the construction elements (toConstructionPorts1 to toConstructionPorts6) to enable a simplification of the graphical diagram.

In a further step connect the connectors of the other sides of all construction elements to the construction connector of the building model (toConstructionPorts on the left side).

Finally connect the input values of T_setHeating and T_setCooling (four connections) and the output values Q_flow_heating and Q_flow_cooling (again four connections) from the building model to both zone models. Now your topology of your building model is completely specified:

## 3.2. Define the building model parameters¶

Now the building model has to be completed with parameters, which exactly describe the problem. The first type are geometrical parameters, e.g. the size of the construction elements or the volumes of the zones. The second type are physical parameters which define the building constructions (e.g. the heat conductivity or specific heat capacity of the used materials).

1. Geometrical parameters

The TMH has a strongly simplified geometry. In our problem each thermal zone describes one half of the TMH, which has in total an inner dimension of 1.0 m x 0.5 m x 0.5 m. So each opaque construction element (walls, bottoms and ceilings) has a height of 0.5 m and a width of 0.5 m. Double-click on each component and fill in these values in the General tab in the Geometry group.

Both thermal zones have an air volume of 0.5 m x 0.5 m x 0.5 m = 0.125 m3. The height of the zone is 0.5 m. Fill in these values into the zone model’s zone1 and zone2.

Each of the windows of the TMH has a width of 0.378 m and a height of 0.33 m, which leads to a window area of approx. 0.125 m2. The thickness of the window pane is 0.003 m. Assign these three values to both window models.

Because window1 is enclosed in wall6 and window2 in wall5 the area of the window models has to be communicated from the window to the wall models. Double-click on wall6 and fill in the parameter field nInnSur 1 and in the field AInnSur using the Edit Text option

AInnSur=window1.ASur


Do the same with wall5 and window2.

Finally add the parameter values for the orientation of each construction elements, which face to the ambient by setting the azimuth angle and the tilt angle. The default values for each construction element (walls and windows are 90.0 degree for the tilt angle and 0.0 degree for the azimuth angle. North is defined by an azimuth angle of 180 degree, east by -90 degree and west by + 90 degree:

element angleAzi angleTil element angleAzi angleTil
wall1 90.0 90.0 bottom1 0.0 180.0
wall2 180.0 90.0 bottom2 0.0 180.0
wall3 180.0 90.0 ceiling1 0.0 0.0
wall4 -90.0 90.0 ceiling2 0.0 0.0
wall5 0.0 90.0 window1 0.0 90.0
wall6 0.0 90.0 window2 0.0 90.0
wall7 default default
2. Construction parameters

All the opaque construction elements except the partition element wall7 share the same construction. For this reason a common construction type shall be configured, which will be later assigned to each individual construction.

• Definition of a construction type

Extend a child record from the general parent record for opaque constructions BuildingSystems.Buildings.Data.Constructions.OpaqueThermalConstruction and rename it to Construction1TMH. Then include it in the package ThermalModelHouse.

The Construction1TMH shall have three layers. The materials of the three layers are 0.006 m wood, 0.030 m insulation and again 0.009 m wood. The layer order is counted from inside (zone) to outside (building ambient). The BuildingSystems library contains in the package BuildingSystems.HAM.Data.MaterialProperties a database with pre-defined thermal and hygro-thermal material property sets.

Now double-click on the construction type record Construction1TMH left in the package browser and adapt the parameterization of the construction direct in the Modelica source code editor of Dymola with the help of the pre-defined materials:

record Construction1TMH
"Outer constructions of the TMH"
extends BuildingSystems.Buildings.Data.Constructions.OpaqueThermalConstruction(
nLayers=3,
thickness={0.006,0.030,0.009},
material={BuildingSystems.HAM.Data.MaterialProperties.Thermal.Wood(),
BuildingSystems.HAM.Data.MaterialProperties.Thermal.Insulation(),
BuildingSystems.HAM.Data.MaterialProperties.Thermal.Wood()});
end Construction1TMH;

• Assignment of an construction type

Now you can assign this common construction type to all the opaque construction elements by inserting component references using the component parameter dialog of Dymola:

The generated code, for example for wall1 shall look now like:

BuildingSystems.Buildings.Constructions.Walls.WallThermal1DNodes wall1(
redeclare Construction1TMH constructionData,
width=0.5,
height=0.5,
angleDegAzi=90.0,
angleDegTil=90.0);

• Create in the same manner for the partition wall a second construction2TMH, which only consists in one layer of wood with a thickness of 0.009 m and assign it afterwards to wall7.

## 3.3. Configure the system model and set its boundary conditions¶

1. Create a new model with the name SystemModel and insert it into the package ThermalModelHouse.

2. Instantiate the previous defined building model within the system model and rename it to building.

3. Instantiate an ambient model BuildingSystems.Buildings.Ambient within the system model and set the climate data (parameter weatherDataFile) to USA_SanFrancisco_Meteonorm_NetCDF.

4. Assign the parameter nSurfaces of the ambient model to the number of surfaces of the building, which are in contact with the building environment:

nSurfaces={building.nSurfacesAmbient)

5. Connect the ambient model and the building model regarding to their blue interfaces (boundary conditions of the facade surfaces to the air) and their green interfaces (boundary conditions of the facade surfaces to the solar irradiation and other enclosing surfaces)

6. Connect the output variable ambient.TAirRef and the input variable building.TAirAmb (ambient temperature at a reference height of 10 m) and also ambient.xAirRef and building.xAirAmb (ambient absolute moisture).

7. Add six constant sources of the type Modelica.Blocks.Sources.Constant for the definition of the set temperatures for heating and cooling as well as the air change for both thermal zones:

..
Modelica.Blocks.Sources.Constant TSetHeatingZone1(k=273.15 + 22.0);
Modelica.Blocks.Sources.Constant TSetCoolingZone2(k=273.15 + 20.0);
Modelica.Blocks.Sources.Constant TSetHeatingZone1(k=273.15 + 26.0);
Modelica.Blocks.Sources.Constant TSetCoolingZone2(k=273.15 + 24.0);
Modelica.Blocks.Sources.Constant airchangeZone1(k=0.5);
Modelica.Blocks.Sources.Constant airchangeZone2(k=0.5);


and connect them to the input signals of the building model.

Caused by this definition of the set temperatures zone1 will have a higher temperature level than zone2 during the simulation experiment.

The Modelica code of the described example of this chapter can be found under

## 3.4. Simulate the system model¶

• Perform a simulation with the system model over 10 days (start time = 0.0 s end time = 60 s/h x 24 h/d * 10 d = 864000 s).

The following diagrams illustrate selected results of the simulation experiment:

1. The yearly air temperature for zone1 and zone2 and the outside air temperature (1st to 3rd line).
2. The corresponding ideal heating and cooling load for zone 1 (4th and 5th line).
3. The corresponding ideal heating and cooling load for zone 2 (6th and 7th line).
4. The heat flow by heat transmittance through both surfaces of wall7 between both zones (8th and 9th line).