Smart grids are components of future clean energy systems. They create new challenges and opportunities for the efficient and reliable management of the electricity system. The aggregate behaviour of groups of electricity users, such as the magnitude and timing of peak demand are important factors in determining the required capacity of the Low Voltage (LV) distribution network in the context of a transition to low carbon heat and transport. In this paper we use smart meter data from consumer behaviour trials in Ireland to create Reference Load Profiles (RLPs), and to model peak residential electricity demand. We find differences in the peak demand and profile by day type, and that Burr, and Weibull models are useful to estimate peak demand.