Major changes are under way in our power grids. Until very recently, a few hundred, very large, dependable fossil-fuelled power stations were supplying power to consumers whose only role was to use energy whenever they wanted. Today we have wind farms, solar farms, solar panels on millions of roofs, smart metering. Electric vehicles are on the rise and storage technologies are developing rapidly. Achieving a low-carbon, affordable, and secure electricity system, the so-called `energy trilemma,’ presents many challenges and opportunities. As energy becomes more dependent on volatile resources such as the wind and sun, flexibility will become increasingly important for maintaining system security at palatable costs. One new source of flexibility could come from domestic appliances. Thermostatically-controlled loads (TCLs), such as fridges, freezers, air-conditioners and hot-water tanks are effectively energy stores that can be adapted to meet the needs of the grid with negligible impact on consumers. By allowing their operating set points to vary (a little) according to the electricity frequency, they could provide a valuable resource to the grid. However, a thorough understanding of their potential to exhibit synchronisation will be needed to understand and mitigate against the potential risks of a decentralised response provider.
In this thesis I outline the operation of the electricity grid in Great Britain and describe the existing research into using TCLs for demand-side response. I present a new continuum model for a population of deterministic frequency-sensitive TCLs that is sufficiently tractable to allow for our stability analysis. I also solve for the long-term behaviour of a fully synchronised group of TCLs and analyse its stability to splitting into two groups, and hypothesise about the stability of N groups. Using system data from National Grid, the operation of the GB electricity system is simulated over ten-day periods with, and without, a population of fridges providing frequency response to determine their impact. I find that synchronisation issues should always be expected when the fridge population is identical, but with even very low levels of parameter diversity, such issues are eradicated in our simulations. Given the inherent diversity in a population of TCLs, this research shows that decentralised, deterministic control schemes are a viable option for using TCLs for frequency response, and that such a scheme could provide a valuable resource.