Accurate modelling of household electricity on a large scale is a cornerstone for demand management and decarbonisation efforts. This paper introduces a data-driven model for South African households. According to the Paris Agreement, a 50 % reduction in global CO2 emissions is required to ensure the global average temperature does not surpass 2 °C above pre-industrial levels. In this context, 26 % of the overall European energy consumption is used by the residential sector and the global energy consumption is estimated to increase by 1.3 % on average per year until 2050. In the last decade, the development and implementation of smart grid technologies have grown to efficiently and cost-effectively meet the electricity demands of the grid and mitigating greenhouse gas emissions. We present a data-driven, enveloped sum of Gaussians-based model and residential household synthesiser that statistically models the household's electricity usage demand based on smart meter data and generates synthetic data that accurately represents the actual demand profile, load peaks, and daily variances for an individual or aggregate group of households. The measured data was gathered over a one year period for 1200 households in South Africa. Our model accounts for temporal variations such as seasonality and the day of week, household uniqueness, and is fully autonomous. Our results show that the root mean square error between the aggregated measured and synthetic electricity profiles is 0.181 A (5.68 %) and the total energy of each profile is 75.9 and 76.3 A·h, respectively.