Main Content

Thermal Model of a House

Open Model

This example shows how to use Simulink® to create the thermal model of a house. This system models the outdoor environment, the thermal characteristics of the house, and the house heating system.

The sldemo_househeat_data.m file initializes data in the model workspace. To make changes, you can edit the model workspace directly or edit the file and reload the model workspace. To view the model workspace, from the Simulink Editor, on the Modeling tab, in the Design section, click Model Explorer.

Open the sldemo_househeat model.

mdl='sldemo_househeat';
open_system(mdl);

Initialize Model

This model calculates heating costs for a generic house. Opening the model loads the information about the house from the sldemo_househeat_data.m file. The file:

  • Defines the house geometry: size and number of windows

  • Specifies the thermal properties of house materials

  • Calculates the thermal resistance of the house

  • Provides the heater characteristics: hot air temperature and flow-rate

  • Defines the cost of electricity: $0.09/kWhr

  • Specifies the initial room temperature: 20 ºC = 68 ºF

Model Components

Set Point

The Set Point is a Constant block that specifies the temperature that must be maintained indoors. By default, it is 70 ºF. Temperatures are given in ºF. The model converts the temperature to ºC.

Thermostat

The Thermostat subsystem contains a Relay block. The thermostat allows fluctuations of 5 ºF above or below the desired room temperature. If air temperature drops below 65 ºF, the thermostat turns on the heater.

Open the Thermostat subsystem.

open_system([mdl,'/Thermostat']);

Heater

The Heater subsystem models a constant air flow rate, Mdot, is specified in the sldemo_househeat_data.m file. The thermostat signal turns the heater on or off. When the heater is on, it blows hot air at temperature THeater (50 ºC = 122 ºF by default) at a constant flow rate of Mdot (1kg/sec = 3600kg/hr by default). This equation expresses the heat flow into the room.

$$\frac{dQ}{dt}=\left( T_{heater} - T_{room} \right) \cdot Mdot \cdot c$$

$$\frac{dQ}{dt} = \mbox{ heat flow from the heater into the room}$$

$$c = \mbox{ heat capacity of air at constant pressure}$$

$$Mdot = \mbox{ air mass flow rate through heater (kg/hr)}$$

$$T_{heater} = \mbox{ temperature of hot air from heater}$$

$$T_{room} = \mbox{ current room air temperature}$$

Open the Heater subsystem.

open_system([mdl,'/Heater']);

Cost Calculator

The Cost Calculator is a Gain block that integrates the heat flow over time and multiplies it by the energy cost. The model plots the heating cost in the PlotResults scope.

House

The House is a subsystem that calculates room temperature variations. It takes into consideration the heat flow from the heater and heat losses to the environment. This equation expresses the heat losses and the temperature time derivative.

$$\left( \frac{dQ}{dt} \right) _{losses} = \frac{T_{room}-T_{out}}{R_{eq}}$$

$$\frac{dT_{room}}{dt} = \frac{1}{M_{air} \cdot c} \cdot \left( \frac{dQ_{heater}}{dt} - \frac{dQ_{losses}}{dt} \right) $$

$$M_{air} = \mbox{ mass of air inside the house}$$

$$R_{eq} = \mbox{ equivalent thermal resistance of the house}$$

Open the House subsystem.

open_system([mdl,'/House']);

Environment Model

To simulate the environment, the model uses a heat sink with infinite heat capacity and time varying temperature, Tout. The Constant block Avg Outdoor Temp specifies the average air temperature outdoors. The block named Daily Temp Variation Sine Wave generates daily outdoor temperature fluctuations. You can vary these parameters to see how they affect the heating costs.

Run Simulation and Visualize Results

Run the simulation. Use the PlotResults scope to visualize the results. The scope plots the heat cost and indoor versus outdoor temperatures. The temperature outdoors, Toutdoors, varies sinusoidally. The temperature indoors, Tindoors, remains within 5 ºC of the Set Point. The time axis is in seconds.

evalc('sim(mdl)');
open_system([mdl '/PlotResults']),

According to this model, heating the house for two days would cost about $30. Try varying the parameters and observing the system response.

Modify Model

This model calculates the heating costs only. If the temperature of the outside air is higher than the room temperature, the room temperature will exceed the desired Set Point.

You can modify this model to include an air conditioner. You can implement the air conditioner as a modified heater. To do this, add parameters like these to sldemo_househeat_data.m:

  • Cold air output

  • Temperature of the stream from the air conditioner

  • Air conditioner efficiency

To control both the air conditioner and the heater, modify the thermostat.

See Also

|

Related Topics