The frequency of power outages being experienced in Sub-Saharan Africa mean that traditional methods of electricity demand forecasting which rely on directly observed demand data are inadequate for use in projections. Nevertheless, accurate forecasting methods are urgently required to ensure efficient power system operations and expansion planning. To address this gap, we develop a novel method to estimate unsuppressed electricity demand for developing countries. This follows a bottom-up approach based on socioeconomic data and a time-use database developed from a householder survey, which are used to generate household profiles using a Markov Chain approach. These profiles are then converted into electrical load time series by a series of appliance models, using reanalysis weather data to accurately represent ambient conditions for the generation of cooling demand profiles. We apply our method to a Nigerian case study, obtaining the first time series of unsuppressed residential electricity demand for the country using the first Time-of-Use Survey (TUS) for Nigerian households. We validate our model outputs using the results of a small-scale residential metering trial, which yielded a correlation coefficient of 0.97, RMSE of 0.04, and percentage error of 6% between measured and model data. This evidences that our method is a credible and practical tool for electrical demand studies in developing countries. Using the model, the forecasted domestic demand for Abuja Electricity Distribution Company ranges between 345 and 575 MW, while that of Nigeria ranges between 3,829 and 6,605 MW