Stochastic Models for Solar Power

  • Dimitra PolitakiEmail author
  • Sara AloufEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10497)


In this work we develop a stochastic model for the solar power at the surface of the earth. We combine a deterministic model of the clear sky irradiance with a stochastic model for the so-called clear sky index to obtain a stochastic model for the actual irradiance hitting the surface of the earth. Our clear sky index model is a 4-state semi-Markov process where state durations and clear sky index values in each state have phase-type distributions. We use per-minute solar irradiance data to tune the model, hence we are able to capture small time scales fluctuations. We compare our model with the on-off power source model developed by Miozzo et al. (2014) for the power generated by photovoltaic panels, and to a modified version that we propose. In our on-off model the output current is frequently resampled instead of being a constant during the duration of the “on” state. Computing the autocorrelation functions for all proposed models, we find that the irradiance model surpasses the on-off models and it is able to capture the multiscale correlations that are inherently present in the solar irradiance. The power spectrum density of generated trajectories matches closely that of measurements. We believe our irradiance model can be used not only in the mathematical analysis of energy harvesting systems but also in their simulation.


Solar power Semi-Markov process Photovoltaic panel 



The authors would like to thank Alain Jean-Marie for fruitful discussions during early stages of this work. This work was partly funded by the French Government (National Research Agency, ANR) through the “Investments for the Future” Program reference #ANR-11-LABX-0031-01.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Université Côte d’Azur, Inria, CNRS, I3SSophia AntipolisFrance
  2. 2.Université Côte d’Azur, InriaSophia AntipolisFrance

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