Comparison between Time- and Observation-Based Gaussian Process Regression Models for Global Horizontal Irradiance Forecasting
Abstract
:1. Introduction
- What input should be chosen, time or past GHI observations?
- For each of those inputs, what is most appropriate kernel?
- What are the advantages and disadvantages of multi-horizon GPR models and horizon-specific GPR models?
2. Description of the Forecasting Models Included in This Study
2.1. Scaled Persistence Model
- t is the time;
- is the solar zenith angle;
- is the extraterrestrial solar irradiance: the solar irradiance incident on the outer limit of the Earth’s atmosphere, considering the whole solar spectrum;
- m is the relative optical air mass, defined as the ratio of the optical path length of the solar beam through the atmosphere to the optical path through a standard atmosphere at sea level with the Sun at the zenith; it is calculated here by the Kasten and Young’s formula [37], widely used by the scientific community:
- is the Linke turbidity coefficient [38], defined as the number of atmospheres without aerosols or water vapor necessary to produce the observed attenuation of the solar extraterrestrial irradiance;
- , , , and are parameters given by:
2.2. Gaussian Processes
2.2.1. Definition
2.2.2. Gaussian Process Regression
2.2.3. Training a GPR Model
2.2.4. Kernels Used with Time-Based GPR Models
- The hyperparameter was initialized to the variance of the training data;
- The period P was set to a day, indicating the daily periodicity of GHI;
- The remaining hyperparameters were randomly drawn from an uniform distribution .
- The hyperparameters and were initialized to the variance of the training data;
- The periods and were, respectively, set to one day and 365 days, indicating the daily and annual periodicity of GHI, respectively;
- The remaining hyperparameters were randomly drawn from a uniform distribution .
2.2.5. Kernels Used with Observation-Based GPR Models
3. Description of Training and Test Datasets
4. Results and Discussion
4.1. Performance Criteria
4.1.1. Normalized Root-Mean-Square Error
4.1.2. Dynamic Mean Absolute Error
4.1.3. Skill Score
4.1.4. Interval Score
4.2. Forecasting Results
- The scaled persistence model;
- The time-based multi-horizon GPR models, with kernels and ;
- The observation-based multi-horizon GPR models (obtained by iterating one-step-ahead forecasting models until the desired forecast horizon is reached), with kernels , , , , and ;
- The observation-based horizon-specific GPR models, with kernels , , , , and .
4.2.1. Multi-Horizon GPR Models: Time or Past Observations as Input?
4.2.2. Multi-Horizon or Horizon-Specific GPR Models?
4.2.3. Contribution of the Annual Periodic Kernel
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ANN | Artificial neural network |
ARD | Automatic relevance determination |
CPU | Central processing unit |
DMAE | Dynamic mean absolute error |
DHI | Diffuse horizontal irradiance |
DNI | Direct normal irradiance |
GHI | Global horizontal irradiance |
Clear-sky global horizontal irradiance | |
GP | Gaussian process |
GPML | Gaussian Processes for Machine Learning (Matlab toolbox) |
GPR | Gaussian process regression |
IS | Interval score |
kNN | k-nearest neighbours |
(n)MAE | (Normalised) mean absolute error |
Matérn (kernel) of degree | |
NWP | Numerical weather prediction |
PV | Photovoltaic |
Per | Periodic (kernel) |
(n)RMSE | (Normalised) root mean square error |
RQ | Rational quadratic (kernel) |
SE | Squared exponential (kernel) |
SS | Skill score |
SVR | Support vector regression |
UVA | Ultraviolet A |
UVB | Ultraviolet B |
References
- Syranidou, C.; Linssen, J.; Stolten, D.; Robinius, M. Integration of Large-Scale Variable Renewable Energy Sources into the Future European Power System: On the Curtailment Challenge. Energies 2020, 13, 5490. [Google Scholar] [CrossRef]
- Erdiwansyah, M.; Husin, H.; Nasaruddin, M.Z.; Muhibbuddin. A critical review of the integration of renewable energy sources with various technologies. Prot. Control Mod. Power Syst. 2021, 6, 3. [Google Scholar] [CrossRef]
- ElNozahy, M.S.; Salama, M.M.A. Technical impacts of grid-connected photovoltaic systems on electrical networks—A review. J. Renew. Sustain. Energy 2013, 5, 032702. [Google Scholar] [CrossRef]
- Dkhili, N.; Eynard, J.; Thil, S.; Grieu, S. A survey of modelling and smart management tools for power grids with prolific distributed generation. Sustain. Energy Grids Netw. 2020, 21, 100284. [Google Scholar] [CrossRef]
- Sobri, S.; Koohi-Kamali, S.; Rahim, N.A. Solar photovoltaic generation forecasting methods: A review. Energy Convers. Manag. 2018, 156, 459–497. [Google Scholar] [CrossRef]
- Mellit, A.; Massi Pavan, A.; Ogliari, E.; Leva, S.; Lughi, V. Advanced Methods for Photovoltaic Output Power Forecasting: A Review. Appl. Sci. 2020, 10, 487. [Google Scholar] [CrossRef] [Green Version]
- Chu, Y.; Pedro, H.T.C.; Li, M.; Coimbra, C.F.M. Real-time forecasting of solar irradiance ramps with smart image processing. Sol. Energy 2015, 114, 91–104. [Google Scholar] [CrossRef]
- Schmidt, T.; Kalisch, J.; Lorenz, E.; Heinemann, D. Evaluating the spatio-temporal performance of sky-imager-based solar irradiance analysis and forecasts. Atmos. Chem. Phys. 2016, 16, 3399–3412. [Google Scholar] [CrossRef] [Green Version]
- Nou, J.; Chauvin, R.; Eynard, J.; Thil, S.; Grieu, S. Towards the intrahour forecasting of direct normal irradiance using sky-imaging data. Heliyon 2018, 4, e00598. [Google Scholar] [CrossRef] [Green Version]
- Lauret, P.; Voyant, C.; Soubdhan, T.; David, M.; Poggi, P. A benchmarking of machine learning techniques for solar radiation forecasting in an insular context. Sol. Energy 2015, 112, 446–457. [Google Scholar] [CrossRef]
- Gbémou, S.; Eynard, J.; Thil, S.; Guillot, E.; Grieu, S. A Comparative Study of Machine Learning-Based Methods for Global Horizontal Irradiance Forecasting. Energies 2021, 14, 3192. [Google Scholar] [CrossRef]
- Wang, P.; van Westrhenen, R.; Meirink, J.F.; van der Veen, S.; Knap, W. Surface solar radiation forecasts by advecting cloud physical properties derived from Meteosat Second Generation observations. Sol. Energy 2019, 177, 47–58. [Google Scholar] [CrossRef]
- Kallio-Myers, V.; Riihelä, A.; Lahtinen, P.; Lindfors, A. Global horizontal irradiance forecast for Finland based on geostationary weather satellite data. Sol. Energy 2020, 198, 68–80. [Google Scholar] [CrossRef]
- Diagne, M.; David, M.; Lauret, P.; Boland, J.; Schmutz, N. Review of solar irradiance forecasting methods and a proposition for small-scale insular grids. Renew. Sustain. Energy Rev. 2013, 27, 65–76. [Google Scholar] [CrossRef] [Green Version]
- Mathiesen, P.; Collier, C.; Kleissl, J. A high-resolution, cloud-assimilating numerical weather prediction model for solar irradiance forecasting. Sol. Energy 2013, 92, 47–61. [Google Scholar] [CrossRef] [Green Version]
- Sharifzadeh, M.; Sikinioti-Lock, A.; Shah, N. Machine-learning methods for integrated renewable power generation: A comparative study of artificial neural networks, support vector regression, and Gaussian process regression. Renew. Sustain. Energy Rev. 2019, 108, 513–538. [Google Scholar] [CrossRef]
- Rajagukguk, R.A.; Ramadhan, R.A.A.; Lee, H.J. A Review on Deep Learning Models for Forecasting Time Series Data of Solar Irradiance and Photovoltaic Power. Energies 2020, 13, 6623. [Google Scholar] [CrossRef]
- Voyant, C.; Paoli, C.; Muselli, M.; Nivet, M.L. Multi-horizon solar radiation forecasting for Mediterranean locations using time series models. Renew. Sustain. Energy Rev. 2013, 28, 44–52. [Google Scholar] [CrossRef] [Green Version]
- Fouilloy, A.; Voyant, C.; Notton, G.; Motte, F.; Paoli, C.; Nivet, M.L.; Guillot, E.; Duchaud, J.L. Solar irradiation prediction with machine learning: Forecasting models selection method depending on weather variability. Energy 2018, 165, 620–629. [Google Scholar] [CrossRef]
- Pedro, H.T.C.; Coimbra, C.F.M. Nearest-neighbor methodology for prediction of intra-hour global horizontal and direct normal irradiances. Renew. Energy 2015, 80, 770–782. [Google Scholar] [CrossRef]
- Benali, L.; Notton, G.; Fouilloy, A.; Voyant, C.; Dizene, R. Solar radiation forecasting using artificial neural network and random forest methods: Application to normal beam, horizontal diffuse and global components. Renew. Energy 2019, 132, 871–884. [Google Scholar] [CrossRef]
- Zendehboudi, A.; Baseer, M.A.; Saidur, R. Application of support vector machine models for forecasting solar and wind energy resources: A review. J. Clean. Prod. 2018, 199, 272–285. [Google Scholar] [CrossRef]
- Rohani, A.; Taki, M.; Abdollahpour, M. A novel soft computing model (Gaussian process regression with K-fold cross validation) for daily and monthly solar radiation forecasting (Part: I). Renew. Energy 2018, 115, 411–422. [Google Scholar] [CrossRef]
- Tolba, H.; Dkhili, N.; Nou, J.; Eynard, J.; Thil, S.; Grieu, S. Multi-Horizon Forecasting of Global Horizontal Irradiance Using Online Gaussian Process Regression: A Kernel Study. Energies 2020, 13, 4184. [Google Scholar] [CrossRef]
- Lubbe, F.; Maritz, J.; Harms, T. Evaluating the Potential of Gaussian Process Regression for Solar Radiation Forecasting: A Case Study. Energies 2020, 13, 5509. [Google Scholar] [CrossRef]
- Guermoui, M.; Melgani, F.; Gairaa, K.; Mekhalfi, M.L. A comprehensive review of hybrid models for solar radiation forecasting. J. Clean. Prod. 2020, 258, 120357. [Google Scholar] [CrossRef]
- Inman, R.H.; Pedro, H.T.C.; Coimbra, C.F.M. Solar forecasting methods for renewable energy integration. Prog. Energy Combust. Sci. 2013, 39, 535–576. [Google Scholar] [CrossRef]
- Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning; MIT Press: Cambridge, MA, USA, 2006. [Google Scholar]
- Gbémou, S.; Tolba, H.; Thil, S.; Grieu, S. Global horizontal irradiance forecasting using online sparse Gaussian process regression based on quasiperiodic kernels. In Proceedings of the 2019 IEEE International Conference on Environment and Electrical Engineering and 2019 IEEE Industrial and Commercial Power Systems Europe (EEEIC/ICPS Europe), Genova, Italy, 11–14 June 2019; pp. 1–6. [Google Scholar]
- Guermoui, M.; Gairaa, K.; Rabehi, A.; Djelloul, D.; Benkaciali, S. Estimation of the daily global solar radiation based on the Gaussian process regression methodology in the Saharan climate. Eur. Phys. J. Plus 2018, 133, 211. [Google Scholar] [CrossRef]
- Huang, C.; Zhang, Z.; Bensoussan, A. Forecasting of daily global solar radiation using wavelet transform-coupled Gaussian process regression: Case study in Spain. In Proceedings of the 2016 IEEE Innovative Smart Grid Technologies—Asia (ISGT-Asia), Melbourne, VIC, Australia, 28 November–1 December 2016; pp. 799–804. [Google Scholar] [CrossRef]
- Salcedo-Sanz, S.; Casanova-Mateo, C.; Muñoz-Marí, J.; Camps-Valls, G. Prediction of Daily Global Solar Irradiation Using Temporal Gaussian Processes. IEEE Geosci. Remote Sens. Lett. 2014, 11, 1936–1940. [Google Scholar] [CrossRef]
- Notton, G.; Voyant, C. Chapter 3—Forecasting of Intermittent Solar Energy Resource. In Advances in Renewable Energies and Power Technologies; Yahyaoui, I., Ed.; Elsevier: Amsterdam, The Netherlands, 2018; pp. 77–114. [Google Scholar] [CrossRef]
- Antonanzas-Torres, F.; Urraca, R.; Polo, J.; Perpiñán-Lamigueiro, O.; Escobar, R. Clear sky solar irradiance models: A review of seventy models. Renew. Sustain. Energy Rev. 2019, 107, 374–387. [Google Scholar] [CrossRef]
- Chauvin, R.; Nou, J.; Eynard, J.; Thil, S.; Grieu, S. A new approach to the real-time assessment and intraday forecasting of clear-sky direct normal irradiance. Sol. Energy 2018, 167, 35–51. [Google Scholar] [CrossRef]
- Ineichen, P.; Perez, R. A new airmass independent formulation for the Linke turbidity coefficient. Sol. Energy 2002, 73, 151–157. [Google Scholar] [CrossRef] [Green Version]
- Kasten, F.; Young, A.T. Revised optical air mass tables and approximation formula. Appl. Opt. 1989, 28, 4735–4738. [Google Scholar] [CrossRef] [PubMed]
- Linke, F. Transmisions-Koeffizient und Trübungsfaktor. Beiträge Zur Phys. Der Atmosphäre 1922, 10, 91–103. [Google Scholar]
- Neal, R.M. Bayesian Learning for Neural Networks; Lecture Notes in Statistics; Springer Science + Business Media: Berlin/Heidelberg, Germany, 1996. [Google Scholar]
- Duvenaud, D.; Lloyd, J.; Grosse, R.; Tenenbaum, J.; Zoubin, G. Structure Discovery in Nonparametric Regression through Compositional Kernel Search. In Proceedings of the 30th International Conference on Machine Learning, Atlanta, GA, USA, 17–19 June 2013; Dasgupta, S., McAllester, D., Eds.; PMLR: Atlanta, GA, USA, 2013; Volume 28, pp. 1166–1174. [Google Scholar]
- Chen, Z.; Wang, B. How priors of initial hyperparameters affect Gaussian process regression models. Neurocomputing 2018, 275, 1702–1710. [Google Scholar] [CrossRef] [Green Version]
- Tolba, H.; Dkhili, N.; Nou, J.; Eynard, J.; Thil, S.; Grieu, S. GHI forecasting using Gaussian process regression: Kernel study. IFAC-PapersOnLine 2019, 52, 455–460. [Google Scholar] [CrossRef]
- Voyant, C.; Notton, G.; Kalogirou, S.; Nivet, M.L.; Paoli, C.; Motte, F.; Fouilloy, A. Machine learning methods for solar radiation forecasting: A review. Renew. Energy 2017, 105, 569–582. [Google Scholar] [CrossRef]
- Frías-Paredes, L.; Mallor, F.; Gastón-Romeo, M.; León, T. Assessing energy forecasting inaccuracy by simultaneously considering temporal and absolute errors. Energy Convers. Manag. 2017, 142, 533–546. [Google Scholar] [CrossRef]
- Frías-Paredes, L.; Mallor, F.; Gastón-Romeo, M.; León, T. Dynamic mean absolute error as new measure for assessing forecasting errors. Energy Convers. Manag. 2018, 162, 176–188. [Google Scholar] [CrossRef]
- Yang, D. Making reference solar forecasts with climatology, persistence, and their optimal convex combination. Sol. Energy 2019, 193, 981–985. [Google Scholar] [CrossRef]
- Lauret, P.; David, M.; Pinson, P. Verification of solar irradiance probabilistic forecasts. Sol. Energy 2019, 194, 254–271. [Google Scholar] [CrossRef]
Authors | Input Variables When Using GPR | Output Variables | Data Sampling Time | Forecast Horizons | Database |
---|---|---|---|---|---|
Gbémou et al. (2021) [11] | GHI | GHI | 10 min | 10 min to 4 h | Two-year dataset: one year for training and one year for testing |
Lubbe et al. (2020) [25] | GHI, DNI, DHI, UVA, UVB, air temperature, barometric pressure, relative humidity, wind speed, wind direction, standard deviation in wind direction | GHI | 1 h | 1 h | Fourteen-day dataset: nine days for training and five days for testing |
Tolba et al. (2020) [24] | Time | GHI | 30 min | 30 min to 48 h | Two 45-day datasets: 30 days for training and 15 days for testing |
Gbémou et al. (2019) [29] | Time | GHI | 30 min | 30 min to 24 h | Two-year dataset: one year for training and one year for testing |
Sharifzadeh et al. (2019) [16] | PV power generation, temperature, DHI, DNI | PV power generation | 1 h | 1 h to 6 h | From 1985 to 2014 |
Guermoui et al. (2018) [30] | Air temperature, relative humidity, sunshine duration | Clearness index | 24 h | 24 h | From 2005 to 2008 |
Rohani et al. (2018) [23] | Temperature, relative humidity, sea level pressure, sunshine duration, extraterrestrial irradiation | GHI | 24 h | 24 h | From 2009 to 2014 |
Huang et al. (2016) [31] | Clearness index | Clearness index | 24 h | 24 h | Three-year dataset: two years for training and one year for testing |
Lauret et al. (2015) [10] | Clear-sky index | Clear-sky index | 1 h | 1 h to 6 h | Two-year dataset: one year for training and one year for testing, in each of three sites |
Salcedo-Sanz et al. (2014) [32] | Aerosol optical depth, ozone concentration, total precipitable water, NWP data, time | GHI | 24 h | 24 h | Two-year dataset: one year for training and one year for testing |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Gbémou, S.; Eynard, J.; Thil, S.; Grieu, S. Comparison between Time- and Observation-Based Gaussian Process Regression Models for Global Horizontal Irradiance Forecasting. Solar 2022, 2, 445-468. https://doi.org/10.3390/solar2040027
Gbémou S, Eynard J, Thil S, Grieu S. Comparison between Time- and Observation-Based Gaussian Process Regression Models for Global Horizontal Irradiance Forecasting. Solar. 2022; 2(4):445-468. https://doi.org/10.3390/solar2040027
Chicago/Turabian StyleGbémou, Shab, Julien Eynard, Stéphane Thil, and Stéphane Grieu. 2022. "Comparison between Time- and Observation-Based Gaussian Process Regression Models for Global Horizontal Irradiance Forecasting" Solar 2, no. 4: 445-468. https://doi.org/10.3390/solar2040027