Analysis of Extreme Peak Loads Using Point Processes: An Application Using South African Data

Abstract

Extreme value modelling of peak load process is critical to the reliable specification of power generation, distribution and maintenance purposes during both peak and off-peak periods. In this study, a frequency assessment of extreme peak electricity demand for the four seasons of the year using South African data for the period, January 1997 to December 2013 is carried out. A point process approach from extreme value theory is proposed as an ingenious extreme value theory approach. The data are made stationary by using a time-varying threshold which has a positive shift factor. The non-linear detrended datasets are then grouped into summer, spring, winter and autumn according to the calendar dates in the Southern Hemisphere. The datasets were declustered to keep the series relatively independent using Ferro and Segers automatic declustering method. A stationary point process model is then fitted to each of the cluster maxima. The modelling framework, which is easily extensible to other peak load parameters, assumes that peak power follows a Poisson point process. The parameters of the developed model are estimated using the maximum likelihood method. Empirical results show that daily peak electricity demand could be experienced approximately 27, 16, 7 and 15 days per year in winter, spring, summer and autumn, respectively. The modelling approach could assist system operators of utility companies in scheduling maintenance of generating units including long term planning.

Keywords

• Extreme value theory
• daily peak electricity demand
• peaks-over threshold
• maximum likelihood estimation
• point process