A Model for Joint Probabilistic Forecast of Solar Photovoltaic Power and Outdoor Temperature

Andrey Bernstein, Raksha Ramakrishna, Anna Scaglione, Vijay Vittal, Emiliano Dall'Anese

Research output: Contribution to journalArticlepeer-review

28 Scopus Citations


In this paper, a stochastic model is proposed for a joint statistical description of solar photovoltaic (PV) power and outdoor temperature. The underlying correlation emerges from solar irradiance that is responsible in part for both the variability in solar PV power and temperature. The proposed model can be used to capture the uncertainty in solar PV power and its correlation with the electric power consumption of thermostatically controlled loads. First, a model for solar PV power that explicitly incorporates the stochasticity due to clouds via a regime-switching process between the three classes of sunny, overcast and partly cloudy is proposed. Then, the relationship between temperature and solar power is postulated using a second-order Volterra model. This joint modeling is leveraged to develop a joint probabilistic forecasting method for solar PV power and temperature. Real-world datasets that include solar PV power and temperature measurements in California are analyzed and the effectiveness of the joint model in providing probabilistic forecasts is verified. The proposed forecasting methodology outperforms several reference methods thus portraying that the underlying correlation between temperature and solar PV power is well defined and only requires a simple lower-complexity sampling space.

Original languageAmerican English
Article number8910466
Pages (from-to)6368-6383
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number24
StatePublished - 15 Dec 2019

Bibliographical note

Publisher Copyright:
© 1991-2012 IEEE.

NREL Publication Number

  • NREL/JA-5D00-75846


  • Dictionary learning
  • Hidden Markov Models
  • Probabilistic forecast solar power
  • Roof-Top solar panels
  • temperature forecast
  • Volterra system


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