Day Ahead Hourly Global Horizontal Irradiance Forecasting—Application to South African Data

Due to its variability, solar power generation poses challenges to grid energy management. In order to ensure an economic operation of a national grid, including its stability, it is important to have accurate forecasts of solar power. The current paper discusses probabilistic forecasting of twenty-four hours ahead of global horizontal irradiance (GHI) using data from the Tellerie radiometric station in South Africa for the period August 2009 to April 2010. Variables are selected using a least absolute shrinkage and selection operator (Lasso) via hierarchical interactions and the parameters of the developed models are estimated using the Barrodale and Roberts’s algorithm. Two forecast combination methods are used in this study. The first is a convex forecast combination algorithm where the average loss suffered by the models is based on the pinball loss function. A second forecast combination method, which is quantile regression averaging (QRA), is also used. The best set of forecasts is selected based on the prediction interval coverage probability (PICP), prediction interval normalised average width (PINAW) and prediction interval normalised average deviation (PINAD). The results demonstrate that QRA gives more robust prediction intervals than the other models. A comparative analysis is done with two machine learning methods—stochastic gradient boosting and support vector regression—which are used as benchmark models. Empirical results show that the QRA model yields the most accurate forecasts compared to the machine learning methods based on the probabilistic error measures. Results on combining prediction interval limits show that the PMis the best prediction limits combination method as it gives a hit rate of 0.955 which is very close to the target of 0.95. This modelling approach is expected to help in optimising the integration of solar power in the national grid.

[1]  Gang Zhang,et al.  A Hybrid Forecasting Method for Solar Output Power Based on Variational Mode Decomposition, Deep Belief Networks and Auto-Regressive Moving Average , 2018, Applied Sciences.

[2]  Jie Li,et al.  Wavelet Decomposition and Convolutional LSTM Networks Based Improved Deep Learning Model for Solar Irradiance Forecasting , 2018, Applied Sciences.

[3]  R. Tibshirani,et al.  A LASSO FOR HIERARCHICAL INTERACTIONS. , 2012, Annals of statistics.

[4]  Mohamed Abuella,et al.  Solar power probabilistic forecasting by using multiple linear regression analysis , 2015, SoutheastCon 2015.

[5]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[6]  Adam Maidman.  Partially Linear Additive Quantile Regression , 2015 .

[7]  Caston Sigauke,et al.  Forecasting medium-term electricity demand in a South African electric power supply system , 2017 .

[8]  Tadao Hoshino,et al.  Quantile regression estimation of partially linear additive models , 2014 .

[9]  Yannig Goude,et al.  Forecasting Electricity Consumption by Aggregating Experts; How to Design a Good Set of Experts , 2015 .

[10]  Paola Sebastiani,et al.  Coherent dispersion criteria for optimal experimental design , 1999 .

[11]  J. Tait,et al.  Challenges and opportunities. , 1996, Journal of psychiatric and mental health nursing.

[12]  E. Zhandire,et al.  Predicting clear-sky global horizontal irradiance at eight locations in South Africa using four models , 2017 .

[13]  J. Friedman.  Stochastic gradient boosting , 2002 .

[14]  George Athanasopoulos,et al.  Forecasting: principles and practice , 2013 .

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

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

[17]  John Boland,et al.  Nonparametric short-term probabilistic forecasting for solar radiation , 2016 .

[18]  T. Hastie,et al.  Learning Interactions via Hierarchical Group-Lasso Regularization , 2015, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[19]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .

[20]  N. Rahim,et al.  Solar photovoltaic generation forecasting methods: A review , 2018 .

[21]  Fei Wang,et al.  Comparative Study on KNN and SVM Based Weather Classification Models for Day Ahead Short Term Solar PV Power Forecasting , 2017 .

[22]  Dilhani Marasinghe,et al.  QUANTILE REGRESSION FOR CLIMATE DATA , 2014 .

[23]  J. Ludden,et al.  Principles and Practice , 1998, Community-based Learning and Social Movements.

[24]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[25]  Luca Massidda,et al.  Quantile Regression Post-Processing of Weather Forecast for Short-Term Solar Power Probabilistic Forecasting , 2018, Energies.

[26]  R. Urraca,et al.  Review of photovoltaic power forecasting , 2016 .

[27]  Jakub Nowotarski,et al.  Computing electricity spot price prediction intervals using quantile regression and forecast averaging , 2015, Comput. Stat..

[28]  Heng Lian,et al.  Bayesian quantile regression for partially linear additive models , 2013, Stat. Comput..

[29]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[30]  Cristina Davino,et al.  Quantile Regression: Theory and Applications , 2013 .

[31]  R. Koenker,et al.  Regression Quantiles , 2007 .

[32]  Robert L. Winkler,et al.  Combining Interval Forecasts , 2016 .

[33]  Xueying Sun,et al.  Prediction Interval Construction for Byproduct Gas Flow Forecasting Using Optimized Twin Extreme Learning Machine , 2017 .

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

[35]  R. Koenker.  Quantile Regression: Fundamentals of Quantile Regression , 2005 .

[36]  Liyang Xie,et al.  The Influence of Rotating Direction on the Tribological Behavior of Grey Cast Iron with Curve Distributed Pit Textured Surface , 2017 .

[37]  J. M. Bates,et al.  The Combination of Forecasts , 1969 .

[38]  Jing Huang,et al.  A semi-empirical approach using gradient boosting and k-nearest neighbors regression for GEFCom2014 probabilistic solar power forecasting , 2016 .

[39]  Zeyar Aung,et al.  Probabilistic Forecasting of Solar Power: An Ensemble Learning Approach , 2017, KES-IDT.

[40]  Chris Chatfield,et al.  Calculating Interval Forecasts , 1993 .

[41]  Zita Vale,et al.  Decision Support Application for Energy Consumption Forecasting , 2019, Applied Sciences.

[42]  Muhammad Khalid,et al.  A review on the selected applications of forecasting models in renewable power systems , 2019, Renewable and Sustainable Energy Reviews.