Clear-sky index space-time trajectories from probabilistic solar forecasts: Comparing promising copulas

Short-term probabilistic solar forecasts are an important tool in decision-making processes in which uncertainty plays a non-negligible role. Purely statistical models that produce temporal or spatiotemporal probabilistic solar forecasts are generally trained individually, and the combined forecasts therefore lack the temporal or spatiotemporal correlation present in the data. To recover the spatiotemporal dependence structure, a copula can be employed, which constructs a multivariate distribution from which spatially and temporally correlated uniform random numbers can be sampled, which in turn can be used to generate the so-called space-time trajectories via the inverse probability integral transform. In this study, we employ the recently introduced ultra-fast preselection algorithm to leverage the spatiotemporal information present in a pyranometer network and compare its accuracy to that of quantile regression forecasts that only consider temporal information. We show that the preselection algorithm i...

[1]  Georgios Giasemidis,et al.  A hybrid model of kernel density estimation and quantile regression for GEFCom2014 probabilistic load forecasting , 2016, 1610.05183.

[2]  Leonard A. Smith,et al.  Increasing the Reliability of Reliability Diagrams , 2007 .

[3]  Robin Girard,et al.  Short-Term Spatio-Temporal Forecasting of Photovoltaic Power Production , 2018, IEEE Transactions on Sustainable Energy.

[4]  Mathieu David,et al.  Probabilistic Solar Forecasting Using Quantile Regression Models , 2017 .

[5]  Laura M. Hinkelman,et al.  Differences between along-wind and cross-wind solar irradiance variability on small spatial scales , 2013 .

[6]  John Bjørnar Bremnes,et al.  Probabilistic wind power forecasts using local quantile regression , 2004 .

[7]  Vladimiro Miranda,et al.  Probabilistic solar power forecasting in smart grids using distributed information , 2015 .

[8]  Shanlin Yang,et al.  Short-term power load probability density forecasting based on quantile regression neural network and triangle kernel function , 2016 .

[9]  Jean-François Toubeau,et al.  Deep Learning-Based Multivariate Probabilistic Forecasting for Short-Term Scheduling in Power Markets , 2019, IEEE Transactions on Power Systems.

[10]  Thomas Reindl,et al.  Solar irradiance forecasting using spatio-temporal empirical kriging and vector autoregressive models with parameter shrinkage , 2014 .

[11]  Jan Kleissl,et al.  Spatiotemporal interpolation and forecast of irradiance data using Kriging , 2017 .

[12]  Fotios Petropoulos,et al.  Exploring the sources of uncertainty: Why does bagging for time series forecasting work? , 2018, Eur. J. Oper. Res..

[13]  Luca Delle Monache,et al.  Post-processing techniques and principal component analysis for regional wind power and solar irradiance forecasting , 2016 .

[14]  Akin Tascikaraoglu,et al.  Evaluation of spatio-temporal forecasting methods in various smart city applications , 2018 .

[15]  Carlos F.M. Coimbra,et al.  History and trends in solar irradiance and PV power forecasting: A preliminary assessment and review using text mining , 2018, Solar Energy.

[16]  Pierre Pinson,et al.  Verification of solar irradiance probabilistic forecasts , 2019 .

[17]  Florian Ziel,et al.  Lasso estimation for GEFCom2014 probabilistic electric load forecasting , 2016, 1603.01376.

[18]  G. Nagy,et al.  GEFCom2014: Probabilistic solar and wind power forecasting using a generalized additive tree ensemble approach , 2016 .

[19]  L. D. Monache,et al.  An analog ensemble for short-term probabilistic solar power forecast , 2015 .

[20]  Dipti Srinivasan,et al.  Automatic hourly solar forecasting using machine learning models , 2019, Renewable and Sustainable Energy Reviews.

[21]  Dazhi Yang,et al.  Ultra-fast preselection in lasso-type spatio-temporal solar forecasting problems , 2018, Solar Energy.

[22]  Ilias Bilionis,et al.  Model predictive control under forecast uncertainty for optimal operation of buildings with integrated solar systems , 2018, Solar Energy.

[23]  N. Cressie,et al.  Fixed rank kriging for very large spatial data sets , 2008 .

[24]  Pierre Pinson,et al.  Wind Energy: Forecasting Challenges for Its Operational Management , 2013, 1312.6471.

[25]  L. Held,et al.  Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds , 2008 .

[26]  David Moser,et al.  Photovoltaic generation forecast for power transmission scheduling: A real case study , 2018, Solar Energy.

[27]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[28]  Dazhi Yang,et al.  A universal benchmarking method for probabilistic solar irradiance forecasting , 2019, Solar Energy.

[29]  J. Widén,et al.  On the properties of aggregate clear-sky index distributions and an improved model for spatially correlated instantaneous solar irradiance , 2017 .

[30]  Hadrien Verbois,et al.  Probabilistic forecasting of day-ahead solar irradiance using quantile gradient boosting , 2018, Solar Energy.

[31]  Noel A Cressie,et al.  Statistics for Spatio-Temporal Data , 2011 .

[32]  Yoshiyasu Tamura,et al.  Using the ensemble Kalman filter for electricity load forecasting and analysis , 2016 .

[33]  Rob J. Hyndman,et al.  Forecasting Uncertainty in Electricity Smart Meter Data by Boosting Additive Quantile Regression , 2016, IEEE Transactions on Smart Grid.

[34]  Henrik Madsen,et al.  Multi-site solar power forecasting using gradient boosted regression trees , 2017 .

[35]  J. Widén,et al.  An autocorrelation-based copula model for generating realistic clear-sky index time-series , 2017 .

[36]  H. Hersbach.  Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems , 2000 .

[37]  Joakim Widén,et al.  Review on probabilistic forecasting of photovoltaic power production and electricity consumption , 2018 .

[38]  P. Pinson,et al.  Generation and evaluation of space–time trajectories of photovoltaic power , 2016, 1603.06649.

[39]  Nicolai Meinshausen,et al.  Quantile Regression Forests , 2006, J. Mach. Learn. Res..

[40]  O. Perpiñán,et al.  PV power forecast using a nonparametric PV model , 2015 .

[41]  Alex J. Cannon.  Quantile regression neural networks: Implementation in R and application to precipitation downscaling , 2011, Comput. Geosci..

[42]  A. Raftery,et al.  Space-time modeling with long-memory dependence: assessing Ireland's wind-power resource. Technical report , 1987 .

[43]  T. Thorarinsdottir,et al.  Assessing the Calibration of High-Dimensional Ensemble Forecasts Using Rank Histograms , 2013, 1310.0236.

[44]  Henrik Ohlsson,et al.  A multiple quantile regression approach to the wind, solar, and price tracks of GEFCom2014 , 2016 .

[45]  Ralf Mikut,et al.  On the use of probabilistic forecasts in scheduling of renewable energy sources coupled to storages , 2018 .

[46]  A. McNeil,et al.  The t Copula and Related Copulas , 2005 .

[47]  L. Wald,et al.  McClear: a new model estimating downwelling solar radiation at ground level in clear-sky conditions , 2013 .

[48]  Dazhi Yang,et al.  Very short term irradiance forecasting using the lasso , 2015 .

[49]  H. Madsen,et al.  Reliability diagrams for non‐parametric density forecasts of continuous variables: Accounting for serial correlation , 2010 .

[50]  Peter Tzscheutschler,et al.  Impact of probabilistic small-scale photovoltaic generation forecast on energy management systems , 2018 .

[51]  Matteo De Felice,et al.  Data-driven upscaling methods for regional photovoltaic power estimation and forecast using satellite and numerical weather prediction data , 2017 .