Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Featured in Physics
  • Open Access

Complexity and Persistence of Price Time Series of the European Electricity Spot Market

Chengyuan Han1,2, Hannes Hilger2, Eva Mix2, Philipp C. Böttcher1, Mark Reyers3, Christian Beck4,5, Dirk Witthaut1,2, and Leonardo Rydin Gorjão1,2,6,7,*

  • 1Forschungszentrum Jülich, Institute for Energy and Climate Research - Systems Analysis and Technology Evaluation (IEK-STE), Jülich 52428, Germany
  • 2Institute for Theoretical Physics, University of Cologne, Köln 50937, Germany
  • 3Institute for Geophysics and Meteorology, University of Cologne, Köln 50937, Germany
  • 4School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
  • 5Alan Turing Institute, London NW1 2DB, United Kingdom
  • 6German Aerospace Center (DLR), Institute of Networked Energy Systems, Oldenburg, Germany
  • 7Department of Computer Science, OsloMet – Oslo Metropolitan University, Oslo N-0130, Norway

  • *Corresponding author: leonardo.rydin@gmail.com

PRX Energy 1, 013002 – Published 7 April, 2022

DOI: https://doi.org/10.1103/PRXEnergy.1.013002

Abstract

The large variability of renewable power sources is a central challenge in the transition to a sustainable energy system. Electricity markets are central for the coordination of electric power generation. These markets rely evermore on short-term trading to facilitate the balancing of power generation and demand and to enable systems integration of small producers. Electricity prices in these spot markets show pronounced fluctuations, featuring extreme peaks as well as occasional negative prices. In this article, we analyze electricity price time series from the European Power Exchange market, in particular the hourly day-ahead, hourly intraday, and 15-min intraday market prices. We quantify the fluctuations, correlations, and extreme events and reveal different time scales in the dynamics of the market. The short-term fluctuations show remarkably different characteristics for time scales below and above 12 h. Fluctuations are strongly correlated and persistent below 12 h, which contributes to extreme price events and a strong multifractal behavior. On longer time scales, they get anticorrelated and price time series revert to their mean, witnessed by a stark decrease of the Hurst coefficient after 12 h. The long-term behavior is strongly influenced by the evolution of a large-scale weather pattern with a typical time scale of four days. We elucidate this dependence in detail using a classification into circulation weather types. The separation in time scales enables a superstatistical treatment, which confirms the characteristic time scale of four days, and motivates the use of q-Gaussian distributions as the best fit to the empiric distribution of electricity prices.

View figure in article

Physics Subject Headings (PhySH)

synopsis

Predicting Fickle Electricity Markets

Published 7 April, 2022

Identifying and explaining patterns in volatile electricity prices could help small-scale wind and solar producers to integrate with the power grid.

See more in Physics

Popular Summary

Article Text

References (95)

  1. U.S. Energy Information Administration, Annual Energy Outlook 2021 (2021), accessed August, 2021, https://www.eia.gov/outlooks/aeo/pdf/AEO_Narrative_2021.pdf.
  2. REN21 Secretariat: Renewables 2021 Global Status Report (REN21, 2021), https://www.ren21.net/gsr-2021/.
  3. R. J. Green and D. M. Newbery, Competition in the British electricity spot market, J. Polit. Econ. 100, 929 (1992).
  4. D. M. Newbery, Competition, contracts, and entry in the electricity spot market, RAND J. Econ. 29, 726 (1998).
  5. C. K. Woo, I. Horowitz, J. Moore, and A. Pacheco, Impact of wind generation on the electricity spot-market price level and variance: The Texas experience, Energ. Policy 39, 3939 (2011).
  6. J. Cludius, H. Hermann, F. C. Matthes, V. Graichen, The merit order effect of wind and photovoltaic electricity generation in Germany 2008–2016: Estimation and distributional implications, Energy Econ. 44, 302 (2014).
  7. K. Mayer and S. Trück, Electricity markets around the world, J. Commod. Mark. 9, 77 (2018).
  8. D. Infield and L. Freris, Renewable Energy in Power Systems (John Wiley & Sons, Wiltshire, UK, 2020), 2nded.
  9. C. Koch and L. Hirth, Short-term electricity trading for system balancing: An empirical analysis of the role of intraday trading in balancing Germany’s electricity system, Renew. Sust. Energ. Rev. 113, 109275 (2019).
  10. O. Edenhofer, L. Hirth, B. Knopf, M. Pahle, S. Schlömer, E. Schmid, and F. Ueckerdt, On the economics of renewable energy sources, Energy Econ. 40, S12 (2013).
  11. D. P. Macedo, A. C. Marques, and O. Damette, The impact of the integration of renewable energy sources in the electricity price formation: Is the merit-order effect occurring in Portugal?, Util. Policy 66, 101080 (2020).
  12. J. Rodríguez-Molina, M. Martínez-Núñez, J.-F. Martínez, and W. Pérez-Aguiar, Business models in the smart grid: Challenges, opportunities and proposals for prosumer profitability, Energies 7, 6142 (2014).
  13. European Power Exchange (EPEX SPOT) (2021), Market data https://www.epexspot.com/en/market-data.
  14. P. Spodniak, K. Ollikka, and S. Honkapuro, Impact of wind power and electricity demand on the relevance of different short-term electricity markets: The Nordic case, Appl. Energ. 283, 116063 (2021).
  15. M. Narajewski and F. Ziel, Estimation and simulation of the transaction arrival process in intraday electricity markets, Energies 12, 4518 (2019).
  16. E. S. Mix, Persistence Statistics of Electricity Price Time Series, B.Sc. Thesis, school University of Cologne (2020).
  17. F. Ocker and K.-M. Ehrhart, The “German Paradox” in the balancing power markets, Renew. Sust. Energ. Rev. 67, 892 (2017).
  18. I. Oksuz and U. Ugurlu, Neural network based model comparison for intraday electricity price forecasting, Energies 12, 4557 (2019).
  19. T. Janke and F. Steinke, Forecasting the price distribution of continuous intraday electricity trading, Energies 12, 4262 (2019).
  20. G. Marcjasz, B. Uniejewski, and R. Weron, Beating the naïve–combining LASSO with naïve intraday electricity price forecasts, Energies 13, 1667 (2020).
  21. E. Abramova and D. Bunn, Forecasting the intra-day spread densities of electricity prices, Energies 13, 687 (2020).
  22. C. Kath, W. Nitka, T. Serafin, T. Weron, P. Zaleski, and R. Weron, Balancing generation from renewable energy sources: Profitability of an energy trader, Energies 13, 205 (2020).
  23. H. Geman and A. Roncoroni, Understanding the fine structure of electricity prices, J. Bus. 79, 1225 (2006).
  24. C. Beck and F. Schögl, Thermodynamics of Chaotic Systems: An Introduction, Cambridge Nonlinear Science Series (Cambridge University Press, 1993), 1st ed.
  25. C. Tsallis, Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World (Springer Science & Business Media, New York, 2009), 1st ed.
  26. S. Voronin, J. Partanen, and T. Kauranne, A hybrid electricity price forecasting model for the Nordic electricity spot market, Int. Trans. Electr. Energ. Syst. 24, 736 (2014).
  27. J. Kwapień and S. Drożdż, Physical approach to complex systems, Phys. Rep. 515, 115 (2012).
  28. Q. Fan and D. Li, Multifractal cross-correlation analysis in electricity spot market, Phys. A: Stat. Mech. Appl. 429, 17 (2015).
  29. P. Norouzzadeh, W. Dullaert, and B. Rahmani, Anti-correlation and multifractal features of Spain electricity spot market, Phys. A: Stat. Mech. Appl. 380, 333 (2007).
  30. J. Alvarez-Ramirez and R. Escarela-Perez, Time-dependent correlations in electricity markets, Energy Econ. 32, 269 (2010).
  31. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. A: Math. Phys. Eng. Sci. 454, 903 (1998).
  32. C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Mosaic organization of DNA nucleotides, Phys. Rev. E 49, 1685 (1994).
  33. C. Peng, S. Havlin, H. E. Stanley, and A. L. Goldberger, Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos 5, 82 (1995).
  34. J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series, Phys. A: Stat. Mech. Appl. 316, 87 (2002).
  35. S. Drożdż and P. Oświcimka, Detecting and interpreting distortions in hierarchical organization of complex time series, Phys. Rev. E 91, 030902 (2015).
  36. L. Rydin Gorjão, G. Hassan, J. Kurths, and D. Witthaut, MFDFA: Efficient multifractal detrended fluctuation analysis in python, Comput. Phys. Commun. 273, 108254 (2022).
  37. F. Wang, G. Liao, J. Li, X. Li, and T. Zhou, Multifractal detrended fluctuation analysis for clustering structures of electricity price periods, Phys. A: Stat. Mech. Appl. 392, 5723 (2013).
  38. F. Wang, G.-p. Liao, X.-y. Zhou, and W. Shi, Multifractal detrended cross-correlation analysis for power markets, Nonlinear Dyn. 72, 353 (2013).
  39. C. Beck, Dynamical Foundations of Nonextensive Statistical Mechanics, Phys. Rev. Lett. 87, 180601 (2001).
  40. C. Beck and E. G. D. Cohen, Superstatistics, Phys. A: Stat. Mech. Appl. 322, 267 (2003).
  41. R. Rak, S. Drożdż, and J. Kwapień, Nonextensive statistical features of the Polish stock market fluctuations, Phys. A: Stat. Mech. Appl. 374, 315 (2007).
  42. P. Gopikrishnan, V. Plerou, L. A. Nunes Amaral, M. Meyer, and H. E. Stanley, Scaling of the distribution of fluctuations of financial market indices, Phys. Rev. E 60, 5305 (1999).
  43. R. Cont, Empirical properties of asset returns: Stylized facts and statistical issues, Quant. Finance 1, 223 (2001).
  44. S. M. D. Queirós and C. Tsallis, On the connection between financial processes with stochastic volatility and nonextensive statistical mechanics, Eur. Phys. J. B. 48, 139 (2005).
  45. S. M. D. Queirós, On the emergence of a generalised Gamma distribution. application to traded volume in financial markets, Europhys. Lett. (EPL) 71, 339 (2005).
  46. L. Borland, Option Pricing Formulas Based on a non-Gaussian Stock Price Model, Phys. Rev. Lett. 89, 098701 (2002).
  47. L. Borland, Exploring the dynamics of financial markets: From stock prices to strategy returns, Chaos Solit. Fractals 88, 59 (2016).
  48. P. Zhao, B. Zhou, and J. Wang, Non-Gaussian closed form solutions for geometric average Asian options in the framework of non-extensive statistical mechanics, Entropy 20, 71 (2018).
  49. P. Jones, M. Hulme, and K. Briffa, A comparison of Lamb circulation types with an objective classification scheme, Int. J. Climatol. 13, 655 (1993).
  50. M. Reyers, J. G. Pinto, and J. Moemken, Statistical-dynamical downscaling for wind energy potentials: Evaluation and applications to decadal hindcasts and climate change projections, Int. J. Climatol. 35, 229 (2015).
  51. J. Märkle-Huß, S. Feuerriegel, and D. Neumann, Contract durations in the electricity market: Causal impact of 15 min trading on the EPEX SPOT market, Energy Econ. 69, 367 (2018).
  52. S. Wilkens and J. Wimschulte, The pricing of electricity futures: Evidence from the European energy exchange, J. Futures Mark. 27, 387 (2007).
  53. D. Peters, R. Völker, F. Schuldt, and K. von Maydell, in 2020 17th International Conference on the European Energy Market (EEM) (2020), p. 1.
  54. F. Borggrefe and K. Neuhoff, in DIW Berlin Discussion Paper (2011), p. 1162.
  55. C. Behm, L. Nolting, and A. Praktiknjo, How to model European electricity load profiles using artificial neural networks, Appl. Energ. 277, 115564 (2020).
  56. J. D. Hunter, Matplotlib: A 2D graphics environment, Comput. Sci. Eng. 9, 90 (2007).
  57. European Power Exchange (EPEX SPOT), Annual Report 2019 (2020), https://www.epexspot.com/sites/default/files/download_center_files/Epex-spot-2019_200703_Planche.pdf accessed 17/04/2021.
  58. T. Weissbach and E. Welfonder, Improvement of the performance of scheduled stepwise power programme changes within the European power system, IFAC Proc. Vol. 41, 11972 (2008). 17th IFAC World Congress
  59. L. Rydin Gorjão, M. Anvari, H. Kantz, C. Beck, D. Witthaut, M. Timme, and B. Schäfer, Data-driven model of the power-grid frequency dynamics, IEEE Access 8, 43082 (2020).
  60. J. Kruse, B. Schäfer, and D. Witthaut, Revealing drivers and risks for power grid frequency stability with explainable AI, Patterns 2, 100365 (2021).
  61. F. Sensfuß, M. Ragwitz, and M. Genoese, The merit-order effect: A detailed analysis of the price effect of renewable electricity generation on spot market prices in Germany, Energ. Policy 36, 3086 (2008).
  62. Y. He, M. Hildmann, F. Herzog, and G. Andersson, Modeling the merit order curve of the European Energy Exchange power market in Germany, IEEE Trans. Power Syst. 28, 3155 (2013).
  63. J. Weber, J. Wohland, M. Reyers, J. Moemken, C. Hoppe, J. G. Pinto, and D. Witthaut, Impact of climate change on backup energy and storage needs in wind-dominated power systems in Europe, PLoS ONE 13, 1 (2018).
  64. S. M. Braun and C. Brunner, Price sensitivity of hourly day-ahead and quarter-hourly intraday auctions in Germany, Zeitschrift für Energiewirtschaft 42, 257 (2018).
  65. S. Halbrügge, P. Schott, M. Weibelzahl, H. U. Buhl, G. Fridgen, and M. Schöpf, How did the German and other European electricity systems react to the COVID-19 pandemic?, Appl. Energ. 285, 116370 (2021).
  66. R. Weron, I. Simonsen, and P. Wilman, in The Application of Econophysics, edited by H. Takayasu (Springer Japan, Tokyo, 2004), p. 182.
  67. Z. Wu and N. E. Huang, A study of the characteristics of white noise using the empirical mode decomposition method, Proc. R. Soc. A: Math. Phys. Eng. Sci. 460, 1597 (2004).
  68. S. Lahmiri, Comparing variational and empirical mode decomposition in forecasting day-ahead energy prices, IEEE Syst. J. 11, 1907 (2017).
  69. P. Virtanen, et al., SciPy 1.0 contributors, SciPy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  70. C. R. Harris, et al., Array programming with NumPy, Nature 585, 357 (2020).
  71. B. Mandelbrot, The Pareto–Lévy law and the distribution of income, Int. Econ. Rev. 1, 79 (1960).
  72. C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52, 479 (1988).
  73. D. Applebaum, Lévy Processes and Stochastic Calculus (Cambridge University Press, Cambridge, 2011), 2nd ed.
  74. S. Umarov, C. Tsallis, and S. Steinberg, On a q-central limit theorem consistent with nonextensive statistical mechanics, Milan J. Math. 76, 307 (2008).
  75. M. Wątorek, J. Kwapień, and S. Drożdż, Financial return distributions: Past, present, and COVID-19, Entropy 23, 884 (2021).
  76. P. Gopikrishnan, M. Meyer, L. A. N. Amaral, and H. E. Stanley, Inverse cubic law for the distribution of stock price variations, Eur. Phys. J. B. 3, 139 (1998).
  77. X. Gabaix, P. Gopikrishnan, V. Plerou, and H. E. Stanley, A theory of power-law distributions in financial market fluctuations, Nature 423, 267 (2003).
  78. B. Podobnik, D. Horvatic, A. M. Petersen, and H. E. Stanley, Cross-correlations between volume change and price change, Proc. Natl. Acad. Sci. U.S.A. 106, 22079 (2009).
  79. M. Wątorek, S. Drożdż, J. Kwapień, L. Minati, P. Oáwicimka, and M. Stanuszek, Multiscale characteristics of the emerging global cryptocurrency market, Phys. Rep. 901, 1 (2021).
  80. H. E. Hurst, Long-term storage capacity of reservoirs, Trans. Am. Soc. Civil Eng. 116, 770 (1951).
  81. R. Weron and B. Przybyłowicz, Hurst analysis of electricity price dynamics, Phys. A: Stat. Mech. Appl. 283, 462 (2000).
  82. E. Ihlen, Introduction to multifractal detrended fluctuation analysis in matlab, Front. Physiol. 3, 141 (2012).
  83. S. Drożdż, J. Kwapień, P. Oświecimka, and R. Rak, Quantitative features of multifractal subtleties in time series, EPL (Europhys. Lett.) 88, 60003 (2009).
  84. L. Borland, A theory of non-Gaussian option pricing, Quant. Finance 2, 415 (2002).
  85. E. Van der Straeten and C. Beck, Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence, Phys. Rev. E 80, 036108 (2009).
  86. C. Beck, Generalised information and entropy measures in physics, Contemp. Phys. 50, 495 (2009).
  87. K. van der Wiel, H. C. Bloomfield, R. W. Lee, L. P. Stoop, R. Blackport, J. A. Screen, and F. M. Selten, The influence of weather regimes on European renewable energy production and demand, Environ. Res. Lett. 14, 094010 (2019).
  88. C. M. Grams, R. Beerli, S. Pfenninger, I. Staffell, and H. Wernli, Balancing Europe’s wind-power output through spatial deployment informed by weather regimes, Nat. Clim. Change 7, 557 (2017).
  89. A. Dalton, B. Bekker, and A. C. Kruger, Wind power variability during the passage of cold fronts across South Africa, J. Energy South. Afr. 30, 52 (2019).
  90. J. Wohland, M. Reyers, C. Märker, and D. Witthaut, Natural wind variability triggered drop in German redispatch volume and costs from 2015 to 2016, PLoS ONE 13, 1 (2018).
  91. J. Weber, M. Reyers, C. Beck, M. Timme, J. G. Pinto, D. Witthaut, and B. Schäfer, Wind power persistence characterized by superstatistics, Sci. Rep. 9, 19971 (2019).
  92. H. Hersbach, B. Bell, P. Berrisford, S. Hirahara, A. Horányi, J. Muñoz-Sabater, J. Nicolas, C. Peubey, R. Radu, D. Schepers, and A. Simmons, The ERA5 global reanalysis, Q. J. R. Meteorol. Soc. 146, 1999 (2000).
  93. W. O. Sosa-Correa, A. M. Ramos, and G. L. Vasconcelos, Investigation of non-Gaussian effects in the Brazilian option market, Phys. A: Stat. Mech. Appl. 496, 525 (2018).
  94. F. Alonso-Marroquin, K. Arias-Calluari, M. Harré, M. N. Najafi, and H. J. Herrmann, $q$-gaussian diffusion in stock markets, Phys. Rev. E 99, 062313 (2019).
  95. H. Bessembinder and M. L. Lemmon, Equilibrium pricing and optimal hedging in electricity forward markets, J. Finance 57, 1347 (2002).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation