MSc (Statistics) / Department of Statistics / Generally, short term load forecasting is essential for any power generating utility. In this dissertation the main objective was to develop short term load forecasting models for the peak demand periods (i.e. from 18:00 to 20:00 hours) in South Africa using. Quantile semi-parametric additive models were proposed and used to forecast electricity demand during peak hours. In addition to this, forecasts obtained were then used to nd an optimal number of generating units to commit (switch on or o ) daily in order to produce the required electricity demand at minimal costs. A mixed integer linear programming technique was used to nd an optimal number of units to commit. Driving factors such as calendar e ects, temperature, etc. were used as predictors in building these models. Variable selection was done using the least absolute shrinkage and selection operator (Lasso). A feasible solution to the unit commitment problem will help utilities meet the demand at minimal costs. This information will be helpful to South Africa's national power utility, Eskom. / NRF

This study estimates the price and income elasticity coefficients of electricity demand in the mining sector of South Africa for the period ranging from April 2006 to March 2019. A time varying parameter (TVP) model with the Kalman filter is applied to monitor the evolution of the elasticity estimates. The TVP model can provide a robust estimation of elasticities and can detect any outliers and structural breaks. The results indicate that income and price elasticity coefficients of electricity demand are lower than unit. The income elasticity of demand has a positive sign and it is statistically significant. This indicates that mining production – used as a proxy for mining income – is a significant determinant of electricity consumption in the mining sector. In its final state income elasticity is estimated at 0.15 per cent. On the contrary, price does not play a significant role in explaining electricity demand. In fact, the price elasticity coefficient was found to be positive which is contrary to normal economic convention. This lack of response is attributed mainly to the mining sector’s inability to respond, rather than an unwillingness to do so. A fixed coefficient model in a form of Ordinary Least Squares (OLS) is used as a benchmark model to estimate average price and income elasticity coefficients for the period. The results of the OLS regression model confirm that price does not play a significant role in explaining electricity consumption in the mining sector. An average price elasticity coefficient of -0.007 has been estimated. Income elasticity was estimated at 0.11 for the period under review. The CUSUM of squares test indicate that parameters of the model are unstable. The Chow test confirms 2009 as a breakpoint in the data series. This means that elasticity coefficients of electricity demand in the mining sector are time variant. Thus the OLS results cannot be relied upon for inference purposes. The Kalman filter results are superior. This study cautions policy makers not to interpret the seeming lack of response to price changes as an indication that further prices increases could be implemented without hampering electricity consumption in the sector. Furthermore, it recommends that the electricity pricing policy should take into account both the negative impacts of rapid price increases and the need to invest in long-term electricity infrastructure in order to improve the security of energy supply. A long term electricity price path should be introduced in order to provide certainty and predictability in the price trajectory. This would allow all sectors of the economy sufficient time and space to make investment and operational decisions that would have the least adverse effects on economic growth and job creation. / Economics / M. Com. (Economics)

MSc (Statistics) / Department of Statistics / Short-term load forecasting in South Africa using machine learning and statistical models is discussed in this study. The research is focused on carrying out a comparative analysis in forecasting hourly electricity demand. This study was carried out using South Africa’s aggregated hourly load data from Eskom. The comparison is carried out in this study using support vector regression (SVR), stochastic gradient boosting (SGB), artificial neural networks (NN) with generalized additive model (GAM) as a benchmark model in forecasting hourly electricity demand. In both modelling frameworks, variable selection is done using least absolute shrinkage and selection operator (Lasso). The SGB model yielded the least root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) on testing data. SGB model also yielded the least RMSE, MAE and MAPE on training data. Forecast combination of the models’ forecasts is done using convex combination and quantile regres- sion averaging (QRA). The QRA was found to be the best forecast combination model ibased on the RMSE, MAE and MAPE. / NRF

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