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A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm

Author

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  • Riccardo De Blasis

    (Department of Finance, Management and Technology, LUM University, 70010 Casamassima, Italy)

  • Giovanni Batista Masala

    (Department of Economics and Business Sciences, University of Cagliari, 09124 Cagliari, Italy)

  • Filippo Petroni

    (Department of Management, Università Politecnica delle Marche, 60121 Ancona, Italy)

Abstract

The energy produced by a wind farm in a given location and its associated income depends both on the wind characteristics in that location—i.e., speed and direction—and the dynamics of the electricity spot price. Because of the evidence of cross-correlations between wind speed, direction and price series and their lagged series, we aim to assess the income of a hypothetical wind farm located in central Italy when all interactions are considered. To model these cross and auto-correlations efficiently, we apply a high-order multivariate Markov model which includes dependencies from each time series and from a certain level of past values. Besides this, we used the Raftery Mixture Transition Distribution model (MTD) to reduce the number of parameters to get a more parsimonious model. Using data from the MERRA-2 project and from the electricity market in Italy, we estimate the model parameters and validate them through a Monte Carlo simulation. The results show that the simulated income faithfully reproduces the empirical income and that the multivariate model also closely reproduces the cross-correlations between the variables. Therefore, the model can be used to predict the income generated by a wind farm.

Suggested Citation

  • Riccardo De Blasis & Giovanni Batista Masala & Filippo Petroni, 2021. "A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm," Energies, MDPI, vol. 14(2), pages 1-16, January.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:2:p:388-:d:478903
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    References listed on IDEAS

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    1. Ozgur Danisman & Umay Uzunoglu Kocer, 2019. "Construction of a semi-Markov model for the performance of a football team in the presence of missing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(3), pages 559-576, February.
    2. Rafal Weron & Florian Ziel, 2018. "Electricity price forecasting," HSC Research Reports HSC/18/08, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    3. I. Votsi & A. Brouste, 2019. "Confidence interval for the mean time to failure in semi-Markov models: an application to wind energy production," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(10), pages 1756-1773, July.
    4. Guglielmo D’Amico & Giovanni Masala & Filippo Petroni & Robert Adam Sobolewski, 2020. "Managing Wind Power Generation via Indexed Semi-Markov Model and Copula," Energies, MDPI, vol. 13(16), pages 1-21, August.
    5. Laura Casula & Guglielmo D'Amico & Giovanni Masala & Filippo Petroni, 2020. "Performance estimation of a wind farm with a dependence structure between electricity price and wind speed," The World Economy, Wiley Blackwell, vol. 43(10), pages 2803-2822, October.
    6. Chang, Tian Pau, 2011. "Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application," Applied Energy, Elsevier, vol. 88(1), pages 272-282, January.
    7. Nowotarski, Jakub & Weron, Rafał, 2018. "Recent advances in electricity price forecasting: A review of probabilistic forecasting," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 1548-1568.
    8. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2014. "Wind speed and energy forecasting at different time scales: A nonparametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 59-66.
    9. Fred Espen Benth & Luca Di Persio & Silvia Lavagnini, 2018. "Stochastic Modeling of Wind Derivatives in Energy Markets," Risks, MDPI, vol. 6(2), pages 1-21, May.
    10. Adrian Raftery & Simon Tavaré, 1994. "Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 179-199, March.
    11. Weron, Rafał, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," International Journal of Forecasting, Elsevier, vol. 30(4), pages 1030-1081.
    12. Yuan Song & Insu Paek, 2020. "Prediction and Validation of the Annual Energy Production of a Wind Turbine Using WindSim and a Dynamic Wind Turbine Model," Energies, MDPI, vol. 13(24), pages 1-15, December.
    13. Luis Lopez & Ingrid Oliveros & Luis Torres & Lacides Ripoll & Jose Soto & Giovanny Salazar & Santiago Cantillo, 2020. "Prediction of Wind Speed Using Hybrid Techniques," Energies, MDPI, vol. 13(23), pages 1-13, November.
    14. Riccardo De Blasis, 2020. "The price leadership share: a new measure of price discovery in financial markets," Annals of Finance, Springer, vol. 16(3), pages 381-405, September.
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    1. D’Amico, Guglielmo & De Blasis, Riccardo & Petroni, Filippo, 2023. "The Mixture Transition Distribution approach to networks: Evidence from stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    2. Altaf Hussain Rajpar & Imran Ali & Ahmad E. Eladwi & Mohamed Bashir Ali Bashir, 2021. "Recent Development in the Design of Wind Deflectors for Vertical Axis Wind Turbine: A Review," Energies, MDPI, vol. 14(16), pages 1-23, August.

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