Prediction Intervals for Day-Ahead Photovoltaic Power Forecasts with Non-Parametric and Parametric Distributions

  • Fonseca, Joao Gari da Silva Junior (The University of Tokyo, Institute of Industrial Science) ;
  • Ohtake, Hideaki (National Institute of Advanced Industrial Science and Technology, Research Center for Photovoltaics) ;
  • Oozeki, Takashi (National Institute of Advanced Industrial Science and Technology, Research Center for Photovoltaics) ;
  • Ogimoto, Kazuhiko (The University of Tokyo, Institute of Industrial Science)
  • Received : 2017.04.27
  • Accepted : 2017.12.14
  • Published : 2018.07.01


The objective of this study is to compare the suitability of a non-parametric and 3 parametric distributions in the characterization of prediction intervals of photovoltaic power forecasts with high confidence levels. The prediction intervals of the forecasts are calculated using a method based on recent past data similar to the target forecast input data, and on a distribution assumption for the forecast error. To compare the suitability of the distributions, prediction intervals were calculated using the proposed method and each of the 4 distributions. The calculations were done for one year of day-ahead forecasts of hourly power generation of 432 PV systems. The systems have different sizes and specifications, and are installed in different locations in Japan. The results show that, in general, the non-parametric distribution assumption for the forecast error yielded the best prediction intervals. For example, with a confidence level of 85% the use of the non-parametric distribution assumption yielded a median annual forecast error coverage of 86.9%. This result was close to the one obtained with the Laplacian distribution assumption (87.8% of coverage for the same confidence level). Contrasting with that, using a Gaussian and Hyperbolic distributions yielded median annual forecast error coverage of 89.5% and 90.5%.


Photovoltaic power;Day-ahead forecasting;Forecast error;Prediction intervals;Maximum likelihood estimation;Parametric versus non-parametric distributions


Grant : Research and Development of PV Performance and Reliability Characterization Technologies

Supported by : NEDO


  1. S. Pelland, G. Galanis, and G. Kallos, "Solar and photovoltaic forecasting through post-processing of the Global Environmental Multiscale numerical weather prediction model," Prog. Photovolt: Res. Appl., vol. 21, no. 3, pp. 284-296, May 2013.
  2. E. Ogliari, A. Dolara, G. Manzolini, and S. Leva, "Physical and hybrid methods comparison for the day ahead PV output power forecast," Renewable Energy, vol. 113, no. Supplement C, pp. 11-21, Dec. 2017.
  3. M. Pierro et al., "Multi-Model Ensemble for day ahead prediction of photovoltaic power generation," Solar Energy, vol. 134, no. Supplement C, pp. 132- 146, Sep. 2016.
  4. E. Lorenz, J. Hurka, D. Heinemann, and H. G. Beyer, "Irradiance Forecasting for the Power Prediction of Grid-Connected Photovoltaic Systems," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 2, no. 1, pp. 2-10, Mar. 2009.
  5. P. Bacher, H. Madsen, and H. A. Nielsen, "Online short-term solar power forecasting," Sol. Energy, vol. 83, n 10, pp. 1772-1783, Oct. 2009.
  6. R. Marquez and C. F. M. Coimbra, "Forecasting of global and direct solar irradiance using stochastic learning methods, ground experiments and the NWS database," Sol. Energy, vol. 85, no. 5, pp. 746-756, May 2011.
  7. J. G. da S. Fonseca Jr., T. Oozeki, H. Ohtake, T. Takashima, and O. Kazuhiko, "On the Use of Maximum Likelihood Estimation and Data Similarity to Obtain Prediction Intervals for Forecasts of Photovoltaic Power Generation," Proceeding of the International Conference on Electric Engineering 2014, Jeju, South Korea, 2014.
  8. J. G. da S. Fonseca Jr., H. Ohtake, T. Oozeki, and O. Kazuhiko, "Comparison of 3 Distributions to Characterize Prediction Intervals for Photovoltaic Power Forecasts - A Study with 432 PV Systems," Proceedings of the International Conference on Electrical Engineering 2016, Okinawa, Japan, 2016.
  9. J. G. da S. Fonseca Jr., T. Oozeki, H. Ohtake, K. Shimose, T. Takashima, and K. Ogimoto, "A Comprehensive Study of Photovoltaic Power Generation Forecasts in Multiple Locations in Japan," in Proceedings of the 28th European Photovoltaic Solar Energy Conference and Exhibition, Paris, France, 2013, pp. 3601-3606.
  10. J. G. da S. Fonseca, T. Oozeki, T. Takashima, G. Koshimizu, Y. Uchida, and K. Ogimoto, "Use of support vector regression and numerically predicted cloudiness to forecast power output of a photovoltaic power plant in Kitakyushu, Japan," Prog. Photovolt. Res. Appl., vol. 20, no. 7, pp. 874-882, 2012.
  11. Y. Hirata, T. Yamada, J. Takahashi, K. Aihara, and H. Suzuki, "Online multi-step prediction for wind speeds and solar irradiation: Evaluation of prediction errors," Renewable Energy, vol. 67, pp. 35-39, Jul. 2014.
  12. H. Ohtake, J. G. da S. F. Jr, T. Takashima, T. Oozeki, and Y. Yamada, "Estimation of Confidence Intervals of Global Horizontal Irradiance Obtained from a Weather Prediction Model," Energy Procedia, vol. 59, no. Supplement C, pp. 278-284, Jan. 2014.