MSc (Statistics) / Department of Statistics / Forecasting of electricity peak demand levels is important for decision makers in Eskom. The overall objective of this study was to develop medium term load forecasting models which will help decision makers in Eskom for planning of the operations of the utility company. The frequency table of hourly daily demands was carried out and the results show that most peak loads occur at hours 19:00 and 20:00, over the period 2009 to 2013. The study used generalised additive models with and without tensor product interactions to forecast electricity demand at 19:00 and 20:00 including daily peak electricity demand. Least absolute shrinkage and selection operator (Lasso) and Lasso via hierarchical interactions were used for variable selection to increase the model interpretability by eliminating irrelevant variables that are not associated with the response variable, this way also over tting is reduced. The parameters of the developed models were estimated using restricted maximum likelihood and penalized regression. The best models were selected based on smallest values of the Akaike information criterion (AIC), Bayesian information criterion (BIC) and Generalized cross validation (GCV) along with the highest Adjusted R2. Forecasts from best models with and without tensor product interactions were evaluated using mean absolute percentage error (MAPE), mean absolute error (MAE) and root mean square error (RMSE). Operational forecasting was proposed to forecast the demand at hour 19:00 with unknown predictor variables. Empirical results from this study show that modelling hours individually during the peak period results in more accurate peak forecasts compared to forecasting daily peak electricity demand. The performance of the proposed models for hour 19:00 were compared and the generalized additive model with tensor product interactions was found to be the best tting model. / NRF