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First and second order semi-Markov chains for wind speed modeling

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  • D’Amico, Guglielmo
  • Petroni, Filippo
  • Prattico, Flavio

Abstract

The increasing interest in renewable energy, particularly in wind, has given rise to the necessity of accurate models for the generation of good synthetic wind speed data. Markov chains are often used for this purpose but better models are needed to reproduce the statistical properties of wind speed data. We downloaded a database, freely available from the web, in which are included wind speed data taken from L.S.I. -Lastem station (Italy) and sampled every 10 min. With the aim of reproducing the statistical properties of this data we propose the use of three semi-Markov models. We generate synthetic time series for wind speed by means of Monte Carlo simulations. The time lagged autocorrelation is then used to compare statistical properties of the proposed models with those of real data and also with a synthetic time series generated through a simple Markov chain.

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  • D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2013. "First and second order semi-Markov chains for wind speed modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1194-1201.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:5:p:1194-1201
    DOI: 10.1016/j.physa.2012.11.022
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    13. D'Amico, Guglielmo & Guillen, Montserrat & Manca, Raimondo, 2009. "Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 173-179, October.
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    Cited by:

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    4. Tang, Jie & Brouste, Alexandre & Tsui, Kwok Leung, 2015. "Some improvements of wind speed Markov chain modeling," Renewable Energy, Elsevier, vol. 81(C), pages 52-56.
    5. G. D'Amico & F. Petroni & F. Prattico, 2013. "Semi-Markov Models in High Frequency Finance: A Review," Papers 1312.3894, arXiv.org.
    6. Li, Yanting & Wu, Zhenyu, 2020. "A condition monitoring approach of multi-turbine based on VAR model at farm level," Renewable Energy, Elsevier, vol. 166(C), pages 66-80.
    7. Ma, Jinrui & Fouladirad, Mitra & Grall, Antoine, 2018. "Flexible wind speed generation model: Markov chain with an embedded diffusion process," Energy, Elsevier, vol. 164(C), pages 316-328.
    8. Hui Hwang Goh & Gumeng Peng & Dongdong Zhang & Wei Dai & Tonni Agustiono Kurniawan & Kai Chen Goh & Chin Leei Cham, 2022. "A New Wind Speed Scenario Generation Method Based on Principal Component and R-Vine Copula Theories," Energies, MDPI, vol. 15(7), pages 1-21, April.
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    11. Riccardo De Blasis, 2023. "Weighted-indexed semi-Markov model: calibration and application to financial modeling," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-16, December.
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    13. Guglielmo D'Amico & Filippo Petroni, 2012. "Weighted-indexed semi-Markov models for modeling financial returns," Papers 1205.2551, arXiv.org, revised Jun 2012.
    14. Maegebier, Alexander, 2013. "Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 802-811.
    15. Chia-Hung Wang & Qigen Zhao & Rong Tian, 2023. "Short-Term Wind Power Prediction Based on a Hybrid Markov-Based PSO-BP Neural Network," Energies, MDPI, vol. 16(11), pages 1-24, May.
    16. Dmitrii Silvestrov & Raimondo Manca, 2017. "Reward Algorithms for Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1191-1209, December.
    17. Mavromatidis, Georgios & Orehounig, Kristina & Carmeliet, Jan, 2018. "A review of uncertainty characterisation approaches for the optimal design of distributed energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 88(C), pages 258-277.
    18. Lahmiri, Salim, 2016. "Interest rate next-day variation prediction based on hybrid feedforward neural network, particle swarm optimization, and multiresolution techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 388-396.
    19. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
    20. D׳Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2015. "Reliability measures for indexed semi-Markov chains applied to wind energy production," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 170-177.
    21. 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.
    22. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "New reliability indices for first- and second-order discrete-time aggregated semi-Markov systems with an application to TT&C system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    23. Jónsdóttir, Guðrún Margrét & Milano, Federico, 2019. "Data-based continuous wind speed models with arbitrary probability distribution and autocorrelation," Renewable Energy, Elsevier, vol. 143(C), pages 368-376.

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