Stochastic Models for Solar Power

Dimitra Politaki (1, 2) , Sara Alouf (1, 3)

1 NEO - Network Engineering and Operations
2 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis
3 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)

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.

Mots clés: Solar power; Semi-Markov process; Photovoltaic panel

Domaines: Réseaux et télécommunications [cs.NI]; Sciences de l'environnement

Dimitra Politaki, Sara Alouf. Stochastic Models for Solar Power. EPEW 2017 - European Performance Engineering Workshop, Sep 2017, Berlin, Germany. pp.282--297, ⟨10.1007/978-3-319-66583-2_18⟩. ⟨hal-01624419⟩