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.