Forecasting medium-term electricity demand in a South African electric power supply system

The paper discusses an application of generalised additive models (GAMs) in predicting medium-term hourly electricity demand using South African data for 2009 to 2013. Variable selection was done using least absolute shrinkage and selection operator (Lasso) via hierarchical interactions, resulting in a model called GAM-Lasso. The GAM-Lasso model was then extended by including tensor product interactions to yield a second model, called GAM- -Lasso. Comparative analyses of these two models were done with a gradient-boosting model to act as a benchmark model and the third model. The forecasts from the three models were combined using a forecast combination algorithm where the average loss suffered by the models was based on the pinball loss function. The results showed significantly improved accuracy of forecasts, making this study a useful tool for decision-makers and system operators in power utility companies, particularly in maintenance planning including medium-term risk assessment. A major contribution of this paper is the inclusion of a nonlinear trend. Another contribution is the inclusion of temperature based on two thermal regions of South Africa

Robust modelling framework for short-term forecasting of global horizontal irradiance

The increasing demand for electricity and the need for clean energy sources have increased solar energy use. Accurate forecasts of solar energy are required for easy management of the grid. This paper compares the accuracy of two Gaussian Process Regression (GPR) models combined with Additive Quantile Regression (AQR) and Bayesian Structural Time Series (BSTS) models in the 2-day ahead forecasting of global horizontal irradiance using data from the University of Pretoria from July 2020 to August 2021. Four methods were adopted for variable selection, Lasso, ElasticNet, Boruta, and GBR (Gradient Boosting Regression). The variables selected using GBR were used because they produced the lowest MAE (Minimum Absolute Errors) value. A comparison of seven models GPR (Gaussian Process Regression), Two-layer DGPR (Two-layer Deep Gaussian Process Regression), bstslong (Bayesian Structural Time Series long), AQRA (Additive Quantile Regression Averaging), QRNN(Quantile Regression Neural Network), PLAQR(Partial Linear additive Quantile Regression), and Opera(Online Prediction by ExpRt Aggregation) was made. The evaluation metrics used to select the best model were the MAE (Mean Absolute Error) and RMSE (Root Mean Square Error). Further evaluations were done using proper scoring rules and Murphy diagrams. The best individual model was found to be the GPR. The best forecast combination was AQRA ((AQR Averaging) based on MAE. However, based on RMSE, GPNN was the best forecast combination method. Companies such as Eskom could use the methods adopted in this study to control and manage the power grid. The results will promote economic development and sustainability of energy resources.Comment: 25 pages, 12 figures and 7 table

Short-term forecasting of confirmed daily COVID-19 cases in the Southern African Development Community region

Background: The coronavirus pandemic has resulted in complex challenges worldwide, and the Southern African Development Community (SADC) region has not been spared. The region has become the epicentre for coronavirus in the African continent. Combining forecasting techniques can help capture other attributes of the series, thus providing crucial information to address the problem. Objective: To formulate an effective model that timely predicts the spread of COVID-19 in the SADC region. Methods: Using the Quantile regression approaches; linear quantile regression averaging (LQRA), monotone composite quantile regression neural network (MCQRNN), partial additive quantile regression averaging (PAQRA), among others, we combine point forecasts from four candidate models namely, the ARIMA (p, d, q) model, TBATS, Generalized additive model (GAM) and a Gradient Boosting machine (GBM). Results: Among the single forecast models, the GAM provides the best model for predicting the spread of COVID-19 in the SADC region. However, it did not perform well in some periods. Combined forecasts models performed significantly better with the MCQRNN being the best (Theil’s U statistic=0.000000278). Conclusion: The findings present an insightful approach in monitoring the spread of COVID-19 in the SADC region. The spread of COVID-19 can best be predicted using combined forecasts models, particularly the MCQRNN approach. Keywords: Combined Forecasts; LQRA; PLAQR; OPERA; Quantile Regression Neural Networks; COVID-19

Estimation of extreme inter-day changes to peak electricity demand using Markov chain analysis: A comparative analysis with extreme value theory

Uncertainty in electricity demand is caused by many factors. Large changes are usually attributed to extreme weather conditions and the general random usage of electricity by consumers. More understanding requires a detailed analysis using a stochastic process approach. This paper presents a Markov chain analysis to determine stationary distributions (steady state probabilities) of large daily changes in peak electricity demand. Such large changes pose challenges to system operators in the scheduling and dispatching of electrical energy to consumers. The analysis used on South African daily peak electricity demand data from 2000 to 2011 and on a simple two-state discrete-time Markov chain modelling framework was adopted to estimate steady-state probabilities of two states: positive inter-day changes (increases) and negative inter-day changes (decreases). This was extended to a three-state Markov chain by distinguishing small positive changes and extreme large positive changes. For the negative changes, a decrease state was defined. Empirical results showed that the steady state probability for an increase was 0.4022 for the two-state problem, giving a return period of 2.5 days. For the three state problem, the steady state probability of an extreme increase was 0.0234 with a return period of 43 days, giving approximately nine days in a year that experience extreme inter-day increases in electricity demand. Such an analysis was found to be important for planning, load shifting, load flow analysis and scheduling of electricity, particularly during peak periods

Modelling influence of temperature on daily peak electricity demand in South Africa

The paper discusses the modelling of the influence of temperature on average daily electricity demand in South Africa using a piecewise linear regression model and the generalized extreme value theory approach for the period - 2000 to 2010. Empirical results show that electricity demand in South Africa is highly sensitive to cold temperatures. Extreme low average daily temperatures of the order of 8.20C are very rare in South Africa. They only occur about 8 times in a year and result in huge increases in electricity demand

Regression-SARIMA modelling of daily peak electricity demand in South Africa

In this paper, seasonal autoregressive integrated moving average (SARIMA) and regression with SARIMA errors (regression-SARIMA) models are developed to predict daily peak electricity demand in South Africa using data for the period 1996 to 2009. The performance of the developed models is evaluated by comparing them with Winter’s triple exponential smoothing model. Empirical results from the study show that the SARIMA model produces more accurate short-term forecasts. The regression-SARIMA modelling framework captures important drivers of electricity demand. These results are important to decision makers, load forecasters and systems operators in load flow analysis and scheduling of electricity

Regression-SARIMA modelling of daily peak electricity demand in South Africa

In this paper, seasonal autoregressive integrated moving average (SARIMA) and regression with SARIMA errors (regression-SARIMA) models are developed to predict daily peak electricity demand in South Africa using data for the period 1996 to 2009. The performance of the developed models is evaluated by comparing them with Winter’s triple exponential smoothing model. Empirical results from the study show that the SARIMA model produces more accurate short-term forecasts. The regression-SARIMA modelling framework captures important drivers of electricity demand. These results are important to decision makers, load forecasters and systems operators in load flow analysis and scheduling of electricity

Entrepreneurship gaps framework model: An early-stage business diagnostic tool

Background: In South Africa, entrepreneurship literature demonstrates that three out of four businesses collapse within 3 years of their inception. A plethora of research effort identifies factors such as the lack of finance and access to markets as the leading causes for the high attrition rates amongst emerging businesses. This study finds the narrative to be limiting and inadequate as it does not address the possible gap between entrepreneurs’ expectations and their realities of managing their businesses. Aim: To present the entrepreneurship gaps framework (EGF), an early-stage business diagnostic tool that seeks to assess entrepreneurs’ preparedness. Setting: This study focused on emerging entrepreneurs operating within the limits of developing economies. The framework can be used by emerging entrepreneurs, capacity development institutions and lenders. Methods: A descriptive research design supported by a mixed-method research approach was employed. This was coupled by a two-phase data collection procedure which took place within Limpopo province with 215 participants. Explorative data analysis based on discrete choice models was further implemented. Results: Findings on the EGF illustrated the ability of the framework to act as a more comprehensive diagnostic mechanism that improves early-stage entrepreneurship survival. Conclusion: Entrepreneurship gaps framework is a decision-making tool that can be used by lenders and capacity development institutions to evaluate the emerging entrepreneur with respect to specific areas of business. This results in the necessary support for improving entrepreneur preparedness being provided to entrepreneurs. Secondly, entrepreneurs are likely to benefit from the EGF, if used as a self-diagnostic tool to measure their business preparedness and experience

Micro-perspective lens on entrepreneurs in the early stage of business: Expectations vis-à-vis realities

In the early stage of business, which is where most new ventures fail, many entrepreneurs experience discrepancies between their entrepreneurial expectations and business realities. These discrepancies referred to by this paper as an entrepreneurial gap (EG) are, therefore, among other factors, professed to be responsible for the high attrition rate of emerging ventures in South Africa. An oversight in this area of EG, despite the provision of most required resources, may still lead to business failure. This paper argues that there is more yet to be comprehended regarding early-stage business success, concerning the entrepreneur component. The purpose of this paper was to recognize and classify factors responsible for establishing entrepreneurial gaps with the intent to improve the level of preparedness among emerging entrepreneurs. A qualitative approach with in-depth interviews was employed in the data collection. ATLAS ti 8 was used to unpack factors that instigate entrepreneurial gaps while posing challenges to emerging entrepreneurs in the early stage of business. The groups identified were: entrepreneur management, familism and personal management. The findings provide information that is credible to improving the level of preparedness among emerging entrepreneurs, and could be used by mentors, coaches and relevant support structures

Regularisation in discrete survival models: A comparison of lasso and gradient boosting

We present the results of a simulation study performed to compare the accuracy of a lassotype penalization method and gradient boosting in estimating the baseline hazard function and covariate parameters in discrete survival models. The mean square error results reveal that the lasso-type algorithm performs better in recovering the baseline hazard and covariate parameters. In particular, gradient boosting underestimates the sizes of the parameters and also has a high false positive rate. Similar results are obtained in an application to real-life data