Estimation of extreme inter-day changes to peak electricity demand using Markov chain analysis: A comparative analysis with extreme value theory
Keywords:Daily peak electricity demand, discrete time Markov chain, mean return time, transition matrix
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.
Agyeman, K.A., Han, S. and Han, S. Real-time recognition non-intrusive electrical appliance monitoring algorithm for a residential building energy management system. Energies, 2015, 8: 9029–9048.
Ardakanian, O., Keshav, S. and Rosenberg, C. Markovian models for home electricity consumption, Proceedings of the 2nd ACM SIGCOMM workshop on Green networking, 2011: 31–36.
Beirlant, J., Goedgebeur, Y., Segers, J. and Teugels, J. Statistics of extremes: Theory and applications, 2004, London, UK: Wiley.
Feres, R. Notes for Math 450 Matlab listings for Markov chains, 2007. [online] http://www.math.wustl.edu/ ~feres/Math450Lect04.pdf (accessed 13 August 2016).
Ferro, C.A.T. and Segers, J. Inference for clusters of extreme values. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 2003, 65(2): 545–556.
Haider, M.K., Ismail, A.K. and Qazi, I.A. Markovian models for electrical load prediction in smart buildings. In: Huang T., Zeng Z., Li C., Leung C.S. (eds) Neural information processing. ICONIP 2012. Lecture notes in computer science, 2012, Vol. 7664. Springer, Berlin, Heidelberg.
Hyndman RJ, Fan S. Density forecasting for long-term peak electricity demand. Institute of Electrical and Electronics Engineers Transactions on Power Systems, 2010, 25(2):1142–1153.
Kulkarni, V.G. Introduction to modelling and analysis of stochastic systems, 2011, Second edition, Springer, New York.
McLoughlin, F., Duffy, A. and Conlon, M. The generation of domestic electricity load profiles through Markov chain modelling: 3rd International Scientific Conference on Energy and Climate Change; Conference proceedings: Athens, Greece, 2010, 18–27.
Munoz, A., Sanchez-Ubeda, E.F., Cruz, A. and Marin, J. Short-term forecasting in power systems: a guided tour. Energy Systems, 2010, 2:129–160.
Scarrott, C. J., Hu, Y. Evmix: Extreme value mixture modelling, threshold estimation and boundary corrected kernel density estimation, 2017. [online] http:// www.math.canterbury.ac.nz/~c.scarrott/evmix (accessed 7 February 2016).
Sigauke, C., Verster, A., Chikobvu, D. Tail quantile estimation of heteroskedastic intraday increases in peak electricity demand. Open Journal of Statistics, 2012: 435–442.
Sigauke, C., Verster, A. and Chikobvu, D. Extreme daily increases in peak electricity demand: Tail-quantile estimation. Energy Policy, 2013, 53:90–96.
Smith, L.R. Statistics of extremes, with applications in environment, insurance and finance, 2003. [online] http://www.stat.unc.edu/postscript/rs/semstatrls.pdf (accessed 16 March 2016).
Spedicato, G.A., Kang, T.S and Yalamanchi, S.B. R package markovchain, version 0.4.3: 2015. [online] https://cran.r-project.org/web/packages/markovchain/ markovchain.pdf (accessed 2 February 2016).
Sun, Z. and Li, L. Potential capability estimation for real-time electricity demand response of sustainable manufacturing systems using Markov decision process. Journal of Cleaner Production, 2014, 65: 184–193.
Verster, A., Chikobvu, D.and Sigauke, C. Analysis of the same day of the week increases in peak electricity demand in South Africa. ORiON, 2013, 29 (2): 125–136.
Wide ́n, J. and Wa ̈ckelga ̇rd, E. A high-resolution stochastic model of domestic activity patterns and electricity demand. Applied Energy, 2010, 87: 1880–1892.
How to Cite
Copyright remains with the author(s).
Publishing rights remain with the author(s)
All articles published in JESA can be re-used under the following CC license: CC BY-SA Creative Commons Attribution-ShareAlike 4.0 International License.