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

In the context of decarbonizing the electricity generation of French non-interconnected territories, the knowledge of future electricity demand, in particular annual and peak demand in the long-term, is crucial to design new renewable energy infrastructures. So far, these territories, mainly islands located in the Pacific and Indian ocean, relies mainly on fossil fuels powered facilities. Energy policies envision to widely develop renewable energies to move towards a low-carbon electricity mix by 2028.  This thesis focuses on the long-term forecasting of hourly electricity demand. A methodology is developed to design and select a model able to fit accurately historical data and to forecast future demand in these particular territories. Historical data are first analyzed through a clustering analysis to identify trends and patterns, based on a k-means clustering algorithm. Specific calendar inputs are then designed to consider these first observations. External inputs, such as weather data, economic and demographic variables, are also included.  Forecasting algorithms are selected based on the literature and they are than tested and compared on different input datasets. These input datasets, besides the calendar and external variables mentioned, include different number of lagged values, from zero to three. The combination of model and input dataset which gives the most accurate results on the testing set is selected to forecast future electricity demand. The inclusion of lagged values leads to considerable improvements in accuracy. Although gradient boosting regression features the lowest errors, it is not able to detect peaks of electricity demand correctly. On the contrary, artificial neural network (ANN) demonstrates a great ability to fit historical data and demonstrates a good accuracy on the testing set, as well as for peak demand prediction. Generalized additive model, a relatively new model in the energy forecasting field, gives promising results as its performances are close to the one of ANN and represent an interesting model for future research.  Based on the future values of inputs, the electricity demand in 2028 in Réunion was forecasted using ANN. The electricity demand is expected to reach more than 2.3 GWh and the peak demand about 485 MW. This represents a growth of 12.7% and 14.6% respectively compared to 2019 levels. / I samband med utfasningen av fossila källor för elproduktion i franska icke-sammankopplade territorier är kunskapen om framtida elbehov, särskilt årlig förbrukning och topplast på lång sikt, avgörande för att utforma ny infrastruktur för förnybar energi. Hittills är dessa territorier, främst öar som ligger i Stilla havet och Indiska oceanen, beroende av anläggningar med fossila bränslen. Energipolitiken planerar att på bred front utveckla förnybar energi för att gå mot en koldioxidsnål elmix till 2028.  Denna avhandling fokuserar på den långsiktiga prognosen för elbehov per timme. En metod är utvecklad för att utforma och välja en modell som kan passa korrekt historisk data och för att förutsäga framtida efterfrågan inom dessa specifika områden. Historiska data analyseras först genom en klusteranalys för att identifiera trender och mönster, baserat på en k-means klusteralgoritm. Specifika kalenderinmatningar utformas sedan för att beakta dessa första observationer. Externa inmatningar, såsom väderdata, ekonomiska och demografiska variabler, ingår också.  Prognosalgoritmer väljs utifrån litteraturen och de testas och jämförs på olika inmatade dataset. Dessa inmatade dataset, förutom den nämnda kalenderdatan och externa variabler, innehåller olika antal fördröjda värden, från noll till tre. Kombinationen av modell och inmatat dataset som ger de mest exakta resultaten på testdvärdena väljs för att förutsäga framtida elbehov. Införandet av fördröjda värden leder till betydande förbättringar i exakthet. Även om gradientförstärkande regression har de lägsta felen kan den inte upptäcka toppar av elbehov korrekt. Tvärtom, visar artificiella neurala nätverk (ANN) en stor förmåga att passa historiska data och visar en god noggrannhet på testuppsättningen, liksom för förutsägelse av toppefterfrågan. En generaliserad tillsatsmodell, en relativt ny modell inom energiprognosfältet, ger lovande resultat eftersom dess prestanda ligger nära den för ANN och representerar en intressant modell för framtida forskning.  Baserat på de framtida värdena på indata, prognostiserades elbehovet 2028 i Réunion med ANN. Elbehovet förväntas nå mer än 2,3 GWh och toppbehovet cirka 485 MW. Detta motsvarar en tillväxt på 12,7% respektive 14,6% jämfört med 2019 års nivåer.