Temperature Modeling of a Residential, House using Modelica | Combine

### Temperature Modeling of a Residential, House using Modelica

Ever wondered why it takes your house days to adjust for temperature changes while your car can do it in minutes? By using dynamic modelling, you can adjust different physical parameters and optimize your system performance before building physical objects. Mattias Grundelius has Ph.D. in Controls and has written a blog post on how to model the temperature behavior of a residential house using Modelica.

Modelica is a non-proprietary language for object oriented equation based modeling maintained by the Modelica Association. Using Modelica, complex models can be built by combining components from different domains such as, mechanical, electrical, thermal and hydraulic. There are many libraries, both public and commercial, for modeling various types of system. Modelica models can be built and simulated using a wide range of tools, both commercial and free of charge.

Here a model of a residential house will be built using the public Modelica Buildings Library and the open source modeling and simulation environment Open Modelica.

The house that we are modeling is a one-story gable roof house with a solid ground floor. The model of the house will contain:

• the envelope of the house
• two air volumes, the residential area and the attic, separated by the internal ceiling
• the interior walls of the house lumped into one wall
• a solid ground floor with underfloor heating
• a ventilation system with heat recovery
• a fan coil unit

The heat transfer between the house and the environment is modeled using heat conduction and heat convection. The environment is described by the air temperature, wind speed and wind direction. Since we include the wind direction in the model we need to take the orientation of the

outside walls into consideration and cannot lump all walls into one. So first a model of an exterior wall is created that consist of three models from the Buildings Library:

• HeatTransfer.Convection.Exterior extConv, a model of exterior convection that take windspeed and direction into account
• HeatTransfer.Conduction.MultiLayer cond, a model of conduction through a multi-layer construction
• HeatTransfer.Convection.Interior intConv, a model of interior convection

The input to the model is the outdoor conditions and the interaction with the indoor air is through the heat port, port. The parameters of the model are the area of the wall, the azimuth of the wall and the construction of the wall. The construction of the wall is specified as an instance of Buildings.HeatTransfer.Data.OpaqueConstructions.Generic with the materials of each layer. Each material specifies the layer thickness and the material properties such as density, thermal conductivity and specific heat capacity, also the number of states can be specified in the spatial discretization of each layer. Similar models are created for the roof and interior ceiling.

Now a model of the house can be put together using the created models. First the materials and constructions need to be specified for the different constructions, below is an excerpt of the Modelica code that shows the definition of the exterior wall construction:

constant Buildings.HeatTransfer.Data.Solids.Brick brickWall(x = 0.12);

constant Buildings.HeatTransfer.Data.Solids.InsulationBoard insulationWall(x = 0.10);

constant Buildings.HeatTransfer.Data.Solids.GypsumBoard gypsum(x = 0.013);

constant Buildings.HeatTransfer.Data.OpaqueConstructions.Generic wallLayers(nLay = 3, material = {brickWall, insulationWall, gypsum});

The air in the residential area and the attic are modeled using a Buildings.Fluid.MixingVolumes.MixingVolume which has a heat port and a variable number of fluid ports.

Now the various sub-models can be connected for the envelope and the interior air volumes. The heat ports of the wall, roof and ceiling segments are connected to the air volume that they are facing, and the outdoor conditions are connected to an external input to the house model.

Next the floor with underfloor heating and an input for internal heat load disturbances are added. The underfloor heating is modeled by inserting a prescribed heat flow between two layers of the floor and the internal heat load is modeled by connecteng a prescribed heat flow to the indoor air. The floor is connected to the ground which is set to a prescribed temperature of 10 °C.

The ventilation system that provides the house with fresh air is modeled using an exhaust fan, heat exchanger and a fluid boundary with a variable temperature connected to the outdoor temperature. The exhaust fan is modeled using a Buildings.Fluid.Movers.FlowControlled_m_flow with a constant mass flow rate determined by the specified air replacement time, typically 2 hours. To recover heat from the exhaust air an heat exchanger is used modeled by

Buildings.Fluid.HeatExchangers.ConstantEffectiveness with an efficiency of 80%. The ventilation system is connected to two fluid ports of the indoor air volume.

In a similar way the fan coil unit is modeled using a flow controlled fluid mover but instead of a heat exchanger a Buildings.Fluid.HeatExchangers.HeaterCooler_u is used with a specified max power of 4 kW. The mass flow rate of the fan is set as a function of the requested power starting from ¼ of the max flow at zero requested power to the max flow at the maximum requested power.

Then some temperature sensors and an energy usage calculation and the corresponding outputs are added to the model and the model of the house is complete.

Now we can use the house for simulation. First, we build a model for simulating the open loop responses to different inputs.

To get some understanding on how the house responds to the outdoor conditions and the different heating systems step responses are performed at an operating point when the outdoor temperature is 10 °C, the windspeed is 0 m/s, the wind direction is north, and the indoor temperature is 22 °C. Four step responses are simulated:

• The outdoor temperature is raised to 11 °C
• The wind speed is increased to 10 m/s
• The fan coil power is increased by 200 W
• The floor heating power is increased by 200 W

The figure shows that the all step responses settle in about the same time and reach a steady state in 1000 h, about 42 days.  However, the initial transient of the step is quite different, and it can also be seen that the fan coil unit raises the indoor temperature slightly more than the floor heating at 200 W. To make further comparisons the normalized step responses are plotted in two different time scales.

The plot of the normalized step responses in the 1000 h time scale confirms that the time to reach steady state is about the same. Looking at the plot showing the first 24 h of the step responses it shows that a change in the outdoor temperature or fan coil power initial changes the indoor temperature very quickly. This is due to that they are directly connected to the indoor air volume, that outdoor temperature through the ventilation system and the fan coil power through to the heater that heats the air that is blown through it.

Studying the step responses, the following conclusions can be drawn.

• Heating the house with a fan coil unit is more energy efficient if only the indoor temperature is considered, using floor heating more energy is lost to heat transfer to the ground but a warm floor may give a higher perceived comfort for the occupants of the house.
• If it is desired to keep the indoor temperature close to a specified setpoint at all times this can only be achieved using a fan coil unit.

This model of a house is not modeling all aspects of a real building, for instance there are no windows or doors in the building envelope and radiation heat transfer between the building and the environment is not modeled. This means that absolute energy performance calculations using this model may be inaccurate. However, the model can be used to evaluate different control strategies with respect to control and energy performance.