Solar power poses challenges to the management of grid energy due to its intermittency. To have an optimal integration of solar power on the electricity grid it is important to have accurate forecasts. This study discusses the comparative analysis of semi-parametric extremal mixture (SPEM), generalised additive extreme value (GAEV) or quantile regression via asymmetric Laplace distribution (QR-ALD), additive quantile regression (AQR-1), additive quantile regression with temperature variable (AQR-2) and penalised cubic regression smoothing spline (benchmark) models for probabilistic forecasting of hourly global horizontal irradiance (GHI) at extremely high quantiles (τ = 0.95, 0.97, 0.99, 0.999 and 0.9999). The data used are from the University of Venda radiometric in South Africa and are from the period 1 January 2020 to 31 December 2020. Empirical results from the study showed that the AQR-2 is the best fitting model and gives the most accurate prediction of quantiles at τ = 0.95, 0.97, 0.99 and 0.999, while at 0.9999-quantile the GAEV model has the most accurate predictions. Based on these results it is recommended that the AQR-2 and GAEV models be used for predicting extremely high quantiles of hourly GHI in South Africa. The predictions from this study are valuable to power utility decision-makers and system operators when making highrisk decisions and regulatory frameworks that require high-security levels. This is the first application to conduct a comparative analysis of the proposed models using South African solar irradiance data, to the best of our knowledge.
Power utility companies rely on forecasting for the operation of electricity demand. This presents an applicationof linear quantile regression, non-linear quantile regression, and additive quantile regression models for forecasting extreme electricity demand at peak hours such as 18:00, 19:00, 20:00 and 21:00 using Northern Cape data for the period 01 January 2000 to 31 March 2014. The selection of variables was done using the least absolute shrinkage and selection operator. Additive quantile regression models were found to be the best fitting models for hours 18:00, and 19:00, whereas linear quantile regression models were found to be the best fitting models for hours 20:00, and 21:00. Out of sample forecasts for seven days (01 to 07 April 2014) were used to solve the unit commitment problem using mixed-integer programming. The unit commitment problem results showed that it is less costly to use all the generating units such as hydroelectric, wind power, concentrated solar power and solar photovoltaic. The main contribution of this study is in the development of models for forecasting hourly extreme peak electricity demand. These results could be useful to system operators in the energy sector who have to maintain the minimum cost by scheduling and dispatching electricity during peak hours when the grid is constrained due to peak load demand.
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