This intelligent thermostat, which I worked on under the supervision of Prof. Alex Rogers at the University of Southampton, is able to:

- learn the thermal characteristics of the house in which it is deployed
- predict the carbon intensity of the electricity grid and air temperature
- optimally control the heater such that the carbon intensity and cost are minimised.

Here is a software simulation of the thermostat.

Electricity is generated using a mix of different types of fuel, each of which accounting for a different amount of generation at any given point. This means that the carbon intensity of the grid (i.e. the quantity of CO2 produced for 1 kWh of electricity consumed) varies throughout the day. Therefore, by figuring out the off-peak times and shifting the load, one can reduce its use of carbon intensive electricity. The following **live** plots show how much each fuel has contributed to the electricity that has been generated in the UK over the past 24 hours, as well as the corresponding overall carbon intensity.

The following **live** plot shows the past and the forecast of future demand.

Since the supply (i.e., generation) should precisely match the demand, the carbon intensity is strongly correlated with the demand. This linear relationship can be seen in the plot below, which shows the demand and carbon intensity observations over one week in the summer of 2010.

There are different methods to predict the carbon intensity, such as a linear regression or a standard Gaussian process. However, exploiting the correlation between the demand and carbon intensity can significantly improve this naive approach.

At first glance, given the almost linear relationship between the two variables, perhaps a good choice to exploit the correlation might be the linear regression. However, in my master's project I showed that a multi-output Gaussian process can predict about 42% more accurately than a linear regression. For this Gaussian process I developed a special covariance function that would also factor in the cross correlation between the demand and carbon intensity.

To further evaluate this approach, the same technique was applied to external air temperature prediction. The data was collected using a temperature logger deployed on the Highfield campus, and also the Weather Channel service which provided current and forecast hourly temperature data for Southampton. In the experiments, the root mean-squared error of the Gaussian proceess prediction over January 2010 was 2.2 Celcius degrees, which was 22% more accurate than the Weather Channel forecasts for Southampton.

Using the discussed prediction methods, I developed an intelligent thermostat that controls a heater (or cooler) in a way that the carbon intensity is minimised while the temperature preferences are also satisifed. The working of the thermostat is as follows.

The thermostat has a thermal model of a house which includes such parameters as the thermal leakage of the building and the output power of the heater. Using this model, and the predicted external temperature, it works out the evolution of internal temperature over the next day.

By discretising the time, solving a binary program, the thermostat determines the time intervals during which the heater should be on in order to meet the internal temperature preference constraint while minimising the cost and the corresponding carbon intensity.