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

MSc (Statistics) / Department of Statistics / Daily peak electricity data from ESKOM, South African power utility company for the period, January 1997 to December 2013 consisting of 6209 observations were used in this dissertation. Since 1994, the increased electricity demand has led to sustainability issues in South Africa. In addition, the electricity demand continues to rise everyday due to a variety of driving factors. Considering this, if the electricity generating capacity in South Africa does not show potential signs of meeting the country’s demands in the subsequent years, this may have a significant impact on the national grid causing it to operate in a risky and vulnerable state, leading to disturbances, such as load shedding as experienced during the past few years. In particular, it is of greater interest to have sufficient information about the extreme value of the stochastic load process in time for proper planning, designing the generation and distribution system, and the storage devices as these would ensure efficiency in the electrical energy in order to maintain discipline in the grid systems. More importantly, electricity is an important commodity used mainly as a source of energy in industrial, residential and commercial sectors. Effective monitoring of electricity demand is of great importance because demand that exceeds maximum power generated will lead to power outage and load shedding. It is in the light of this that the study seeks to assess the frequency of occurrence of extreme peak electricity demand in order to come up with a full electricity demand distribution capable of managing uncertainties in the grid system. In order to achieve stationarity in the daily peak electricity demand (DPED), we apply a penalized regression cubic smoothing spline to ensure the data is non-linearly detrended. The R package “evmix” is used to estimate the thresholds using the bounded corrected kernel density plot. The non-linear detrended datasets were divided into summer, spring, winter and autumn according to the calender dates in the Southern Hemisphere for frequency analysis. The data is declustered using Ferro and Segers automatic declustering method. The cluster maxima is extracted using the R package “evd”. We fit Poisson GPD and stationary point process to the cluster maxima and the intensity function of the point process which measures the frequency of occurrence of the daily peak electricity demand per year is calculated for each dataset. The formal goodness-of-fit test based on Cramer-Von Mises statistics and Anderson-Darling statistics supported the null hypothesis that each dataset follow Poisson GPD (σ, ξ) at 5 percent level of significance. The modelling framework, which is easily extensible to other peak load parameters, is based on the assumption that peak power follows a Poisson process. The parameters of the developed i models were estimated using the Maximum Likelihood. The usual asymptotic properties underlying the Poisson GPD were satisfied by the model. / NRF

Abstracts in English, Southern Sotho and Afrikaans / The purpose of the study was to explore and describe the perceptions of electricity stakeholders (referred to for the purposes of the study as electricity customers) regarding their communication with Lesotho Electricity and Water Authority (LEWA) during electricity tariff reviews in 2016 and 2017. LEWA is the electricity regulator, while Lesotho Electricity Company (LEC) is the national power distributor in Lesotho. The electricity customers participated in the review process. The study was framed within development communication, with particular focus on its derivative, participatory communication. The principles of stakeholder theory were also considered. The study combined both quantitative and qualitative research approaches for data collection. The findings of the study were triangulated using an online self-administered questionnaire, a focus group moderator’s guide and a qualitative document analysis. The results were interpreted in line with the proposed practical guidelines. The finding of the study is that although LEWA endeavoured to collaborate with electricity customers during electricity tariff review processes, its implementation of participatory communication was inadequate. Furthermore, electricity customers have not yet fully embraced the importance of participating in electricity tariff review processes, because they perceive such endeavours not to be useful. As a result, the findings of the study encapsulate revised practical guidelines to fit an electricity review setting, which could serve as a heuristic for similar organisations as well as provide insights into the benefits of participatory communication in the various aspects of their work. / Morero wa phuputso ena e ne e le ho hlahloba le ho hlalosa maikutlo a ba nang le seabo motlakaseng (ba boletsweng e le bareki ba motlakase molemong wa phuputso) mabapi le puisano ya bona le Lekgotla la Taolo ya Motlakase le Metsi Lesotho (LEWA) nakong ya ditlhahlobo tsa ditefiso tsa motlakase ka selemo sa 2016 le 2017. LEWA ke molaodi wa motlakase, athe Khampani ya Motlakase ya Lesotho (LEC) ke yona moabi wa matla wa naha ya Lesotho. Bareki ba motlakase ba nkile karolo tshebetsong ya tlhahlobo. Phuputso e hlophisitswe kahara puisano ya ntshetsopele, e shebane haholo le puisano ya yona eo eseng ya pele, le ya bonkakarolo. Ditekanyetso tsa dikgopolo tsa ba amehang le tsona di ile tsa hlokomelwa. Phuputso e kopantse mekgwa ya dipatlisiso ya bongata le boleng ka bobedi bakeng sa pokello ya datha. Diphumano tsa phuputso di ne di arotswe ka dikgutlo-tharo ka tshebediso ya lethathamo la dipotso le fumanehang inthaneteng, tataiso ya motho ya lekanyang wa sehlopha seo ho tsepamisitsweng maikutlo ho sona le manollo ya tokomane ya boleng. Diphetho di ile tsa hlaloswa ka tumellano le ditataiso tse sebetsang. Phumano ya phuputso ke hore leha e le hore LEWA e ne e leka ho sebedisana le bareki ba motlakase nakong ya ditshebetso tsa tlhahlobo ya ditefiso, ho kenngwa tshebetso ha yona ha dipuisano tsa bonkakarolo ho ne ho sa lekana. Ntle le moo, bareki ba motlakase ha ba so ka ba amohela bohlokwa ba ho nka karolo ditshebetsong tsa tlhahlobo ya ditefiso tsa motlakase, hobane ba bona boiteko bo jwalo bo sena thuso. Ka lebaka leo, diphumano tsa phuputso di akarelletsa ditataiso tse ntlafaditsweng tse sebetsang bakeng sa ho nepahala boemong ba tlhahlobo ya motlakase, bo ka sebetsang e le tharollo bakeng sa mekgatlo e tshwanang hammoho le ho fana ka lesedi la melemo ya puisano ya bonkakarolo dikarolong tse fapaneng tsa mosebetsi wa yona. / Die doel van hierdie studie was om die persepsies van elektrisiteitsbelanghebbers (waarna vir die doel van die studie verwys word as elektrisiteitskliënte) rakende hul kommunikasie met die Lesotho Electricity and Water Authority (LEWA) gedurende elektrisiteitstariefhersienings in 2016 en 2017, te ondersoek en te beskryf. LEWA is die elektrisiteitsreguleerder, terwyl die Lesotho Electricity Company (LEC) die nasionale kragverspreider in Lesotho is. Die elektrisiteitskliënte het aan die hersieningsproses deelgeneem. Die studie het in die konteks van ontwikkelingskommunikasie geskied, met spesifieke fokus op die afleiding, deelnemende kommunikasie. Die beginsels van belanghebberteorie is ook in ag geneem. Die studie het kwantitatiewe en kwalitatiewe navorsingsbenaderings tot data-insameling gekombineer. Die bevindings van die studie is getrianguleer met behulp van ʼn aanlyn selfgeadministreerde vraelys, ʼn fokusgroepmoderatorsgids en ʼn kwalitatiewe dokumentontleding. Die resultate is geïՙnterpreteer ooreenkomstig die voorgestelde praktiese riglyne. Die gevolgtrekking van die studie is dat hoewel LEWA probeer het om met elektrisiteitskliënte saam te werk gedurende elektrisiteitstariefhersieningsprosesse, hul implementering van deelnemende kommunikasie ontoereikend was. Verder besef elektrisiteitskliënte nog nie ten volle die belangrikheid van deelname aan elektrisiteitstariefhersieningsprosesse nie, omdat hulle sodanige pogings nie as nuttig ervaar nie. Gevolglik is die bevindings van die studie ʼn samevatting van hersiene praktiese riglyne om by ʼn elektrisiteitshersieningskonteks te pas, en dit kan dien as heuristiek vir soortgelyke organisasies en kan ook insig gee in die voordele van deelnemende kommunikasie in die verskillende aspekte van hul werk. / Communication Science / M.A. (Communication)