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Performance Analysis of Second Order Semi-Markov Chains: An Application to Wind Energy Production

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Abstract

In this paper a general second order semi-Markov reward model is presented. Equations for the higher order moments of the reward process are presented for the first time and applied to wind energy production. The application is executed by considering a database, freely available from the web, that includes wind speed data taken from L.S.I. - Lastem station (Italy) and sampled every 10 minutes. We compute the expectation, the variance, the skewness and the kurtosis of the total energy produced by using the commercial blade Aircon HAWT - 10 kW.

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References

  • Barbu V, Boussemart M, Limnios N (2004) Discrete time semi-Markov model for reliability and survival analysis. Commun Stat Theory Methods 33(11):2833–2868

    Article  MathSciNet  MATH  Google Scholar 

  • Ciardo G, Raymonf MA, Sericola B, Trivedi KS (1990) Performability analysis using semi-Markov reward processes. IEEE Trans Comput 39(10):1251–1264

    Article  Google Scholar 

  • D’Amico G, Guillen M, Manca R (2013) Semi-Markov disability insurance models. Commun Stat Theory Methods 42(16):2172–2188

    MathSciNet  Google Scholar 

  • D’Amico G, Petroni F (2012) A semi-Markov model for price returns. Physica A 391:4867–4876

    Article  MathSciNet  Google Scholar 

  • D’Amico G, Petroni F, Prattico F (2013a) First and second order semi-Markov chains for wind speed modeling. Physica A 392(5):1194–1201

    Article  MathSciNet  Google Scholar 

  • D’Amico G, Petroni F, Prattico F (2013b) Reliability measures of second order semi-Markov chain with application to wind energy production. J Renew Energy 2013(368940)

  • De Dominicis R, Manca R (1985) Some new results on the transient behavior of semi-Markov reward processes. Methods Oper Res 54:387–397

    Google Scholar 

  • Howard RA (1971) Dynamic probabilistic systems: semi-Markov and decision processes, vol II. Dover

  • Janssen J, Manca R (2007) Semi-Markov risk models for finance insurance and reliability. Springer, New York

    MATH  Google Scholar 

  • Limnios N, Oprişan G (2003) An introduction to Semi-Markov processes with application to reliability. In: Shanbhag DN, Rao CR (eds) Handbook of Statistics, vol 21, pp 515–556

  • Papadopoulou AA, Tsaklidis G (2007) Some reward paths in semi-Markov models with stochastic selection of the transition probabilities. Methodol Comput Appl Probab 9(3):399–411

    Article  MathSciNet  MATH  Google Scholar 

  • Papadopoulou AA, Tsaklidis G, McClean S, Garg L (2012) On the moments and the distribution of the cost of a semi-Markov model for healthcare systems. Methodol Comput Appl Probab 14(3):717–737

    Article  MathSciNet  MATH  Google Scholar 

  • Papadopoulou AA (2013) Some results on modeling biological sequences and web navigation with a semi-Markov chain. Commun Stat Theory Methods 42(16):2153–2171

    Article  MathSciNet  Google Scholar 

  • Soltani AR, Khorshidian K (1998) Reward Processes for semi-Markov processes: asymptotic behaviour. J Appl Probab 35:833–842

    Article  MathSciNet  MATH  Google Scholar 

  • Stenberg F, Manca R, Silvestrov D (2006) Semi Markov reward models for disability insurance. Theory Stoch Proces 12(28):239–254

    MathSciNet  Google Scholar 

  • Stenberg F, Manca R, Silvestrov D (2007) An algorithmic approach to discrete time non-homogeneous backward semi-Markov reward processes with an application to disability insurance. Methodol Comput Appl Probab 9:497–519

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Guglielmo D’Amico.

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D’Amico, G., Petroni, F. & Prattico, F. Performance Analysis of Second Order Semi-Markov Chains: An Application to Wind Energy Production. Methodol Comput Appl Probab 17, 781–794 (2015). https://doi.org/10.1007/s11009-013-9394-z

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  • DOI: https://doi.org/10.1007/s11009-013-9394-z

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