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Stochastic modelling of daily beam irradiation

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  • Callegari, M.
  • Festa, R.
  • Ratto, C.F.

Abstract

A dynamical statistical analysis of the daily sum of the beam irradiation measured, on a horizontal surface, in Genoa, Italy, has been done using a 9-year time series, with two substantially different methods: the Markov chain model and the first order autoregressive model. In the first case, the data range has been divided into five different equiprobable classes or “states”. The sequential characteristics of the obtained discrete time series have been described by four “seasonal” 5 × 5 transition matrices between the states of the process. Yearly series of daily beam irradiation have been simulated by associating suitable values of irradiation to every state of the chain. In the second case, data have been first modified in order to obtain a standard Normal frequency distribution; an autoregressive process of order 1 has been fitted to the transformed series. The autoregressive parameter has been estimated keeping it time invariant. Synthetic sequences of daily solar irradiations have been generated with the fitted model. The reliability both of the Markov chain model and of AR(1) model has been verified by comparing the artificial series to the empirical one. The autoregressive model has shown an appreciable superiority in reproducing the stochastic law of the daily sums of beam irradiation with respect to the Markov chain model.

Suggested Citation

  • Callegari, M. & Festa, R. & Ratto, C.F., 1992. "Stochastic modelling of daily beam irradiation," Renewable Energy, Elsevier, vol. 2(6), pages 611-624.
    • Handle: RePEc:eee:renene:v:2:y:1992:i:6:p:611-624
    DOI: 10.1016/0960-1481(92)90027-Z
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    References listed on IDEAS

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    1. Parzen, Emanuel & Pagano, Marcello, 1979. "An approach to modeling seasonally stationary time series," Journal of Econometrics, Elsevier, vol. 9(1-2), pages 137-153, January.
    2. Festa, R. & Jain, S. & Ratto, C.F., 1992. "Stochastic modelling of daily global irradiation," Renewable Energy, Elsevier, vol. 2(1), pages 23-34.
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    1. Ratto, C.F. & Festa, R., 1993. "A procedure for evaluating the influence of weather Markovianity on the storage behaviour of solar systems," Renewable Energy, Elsevier, vol. 3(8), pages 951-960.
    2. Craggs, C & Conway, E & Pearsall, N.M, 1999. "Stochastic modelling of solar irradiance on horizontal and vertical planes at a northerly location," Renewable Energy, Elsevier, vol. 18(4), pages 445-463.
    3. Festa, R. & Jain, S. & Ratto, C.F., 1992. "Stochastic modelling of daily global irradiation," Renewable Energy, Elsevier, vol. 2(1), pages 23-34.
    4. Maafi, A. & Adane, A., 1998. "Analysis of the performances of the first-order two-state Markov model using solar radiation properties," Renewable Energy, Elsevier, vol. 13(2), pages 175-193.

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