Deep and machine learning models to forecast photovoltaic power generation

The integration and management of distributed energy resources (DERs), including residential photovoltaic (PV) production, coupled with the widespread use of enabling technologies such as artificial intelligence, have led to the emergence of new tools, market models, and business opportunities. The...

Full description

Autores:
Cantillo Luna, Sergio Alejandro
Moreno Chuquen, Ricardo
Celeita, David
George, Anders
Tipo de recurso:
Article of investigation
Fecha de publicación:
2023
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/15884
Acceso en línea:
https://hdl.handle.net/10614/15884
https://doi.org/10.3390/en16104097
https://red.uao.edu.co/
Palabra clave:
Deep learning
Machine learning
PV power forecasting
Time-series analysis
Rights
openAccess
License
Derechos reservados - MDPI, 2023
id REPOUAO2_2559b0170ff72962cd3b636b8df7fb34
oai_identifier_str oai:red.uao.edu.co:10614/15884
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Deep and machine learning models to forecast photovoltaic power generation
title Deep and machine learning models to forecast photovoltaic power generation
spellingShingle Deep and machine learning models to forecast photovoltaic power generation
Deep learning
Machine learning
PV power forecasting
Time-series analysis
title_short Deep and machine learning models to forecast photovoltaic power generation
title_full Deep and machine learning models to forecast photovoltaic power generation
title_fullStr Deep and machine learning models to forecast photovoltaic power generation
title_full_unstemmed Deep and machine learning models to forecast photovoltaic power generation
title_sort Deep and machine learning models to forecast photovoltaic power generation
dc.creator.fl_str_mv Cantillo Luna, Sergio Alejandro
Moreno Chuquen, Ricardo
Celeita, David
George, Anders
dc.contributor.author.none.fl_str_mv Cantillo Luna, Sergio Alejandro
Moreno Chuquen, Ricardo
Celeita, David
George, Anders
dc.contributor.corporatename.spa.fl_str_mv MDPI
dc.subject.proposal.eng.fl_str_mv Deep learning
Machine learning
PV power forecasting
Time-series analysis
topic Deep learning
Machine learning
PV power forecasting
Time-series analysis
description The integration and management of distributed energy resources (DERs), including residential photovoltaic (PV) production, coupled with the widespread use of enabling technologies such as artificial intelligence, have led to the emergence of new tools, market models, and business opportunities. The accurate forecasting of these resources has become crucial to decision making, despite data availability and reliability issues in some parts of the world. To address these challenges, this paper proposes a deep and machine learning-based methodology for PV power forecasting, which includes XGBoost, random forest, support vector regressor, multi-layer perceptron, and LSTM-based tuned models, and introduces the ConvLSTM1D approach for this task. These models were evaluated on the univariate time-series prediction of low-volume residential PV production data across various forecast horizons. The proposed benchmarking and analysis approach considers technical and economic impacts, which can provide valuable insights for decision-making tools with these resources. The results indicate that the random forest and ConvLSTM1D model approaches yielded the most accurate forecasting performance, as demonstrated by the lowest RMSE, MAPE, and MAE across the different scenarios proposed
publishDate 2023
dc.date.issued.none.fl_str_mv 2023
dc.date.accessioned.none.fl_str_mv 2024-11-12T14:44:02Z
dc.date.available.none.fl_str_mv 2024-11-12T14:44:02Z
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.eng.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.content.eng.fl_str_mv Text
dc.type.driver.eng.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.eng.fl_str_mv http://purl.org/redcol/resource_type/ART
dc.type.version.eng.fl_str_mv info:eu-repo/semantics/publishedVersion
format http://purl.org/coar/resource_type/c_2df8fbb1
status_str publishedVersion
dc.identifier.citation.eng.fl_str_mv Cantillo Luna, S.; Moreno-Chuquen, R.; Celeita, D. y Anders, G. (2023). Deep and Machine Learning Models to Forecast Photovoltaic Power Generation. Energies. 16(10). 24 p. https://doi.org/10.3390/en16104097
dc.identifier.issn.spa.fl_str_mv 19961073
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10614/15884
dc.identifier.doi.spa.fl_str_mv https://doi.org/10.3390/en16104097
dc.identifier.instname.spa.fl_str_mv Universidad Autónoma de Occidente
dc.identifier.reponame.spa.fl_str_mv Respositorio Educativo Digital UAO
dc.identifier.repourl.none.fl_str_mv https://red.uao.edu.co/
identifier_str_mv Cantillo Luna, S.; Moreno-Chuquen, R.; Celeita, D. y Anders, G. (2023). Deep and Machine Learning Models to Forecast Photovoltaic Power Generation. Energies. 16(10). 24 p. https://doi.org/10.3390/en16104097
19961073
Universidad Autónoma de Occidente
Respositorio Educativo Digital UAO
url https://hdl.handle.net/10614/15884
https://doi.org/10.3390/en16104097
https://red.uao.edu.co/
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationendpage.spa.fl_str_mv 24
dc.relation.citationissue.spa.fl_str_mv 10
dc.relation.citationstartpage.spa.fl_str_mv 1
dc.relation.citationvolume.spa.fl_str_mv 16
dc.relation.ispartofjournal.eng.fl_str_mv Energies
dc.relation.references.none.fl_str_mv 1. Restrepo-Trujillo, J.; Moreno-Chuquen, R.; Jiménez-García, F.; Chamorro, H.R. Scenario Analysis of an Electric Power System in Colombia Considering the El Niño Phenomenon and the Inclusion of Renewable Energies. Energies 2022, 15, 6690. [CrossRef]
2. Ufa, R.; Malkova, Y.; Rudnik, V.; Andreev, M.; Borisov, V. A review on distributed generation impacts on electric power system. Int. J. Hydrogen Energy 2022, 47, 20347–20361. [CrossRef]
3. Cantillo-Luna, S.; Moreno-Chuquen, R.; Chamorro, H.R.; Sood, V.K.; Badsha, S.; Konstantinou, C. Blockchain for Distributed Energy Resources Management and Integration. IEEE Access 2022, 10, 68598–68617. [CrossRef]
4. Burger, S.P.; Luke, M. Business models for distributed energy resources: A review and empirical analysis. Energy Policy 2017, 109, 230–248. [CrossRef]
5. Zaouali, K.; Rekik, R.; Bouallegue, R. Deep learning forecasting based on auto-lstm model for home solar power systems. In Proceedings of the 2018 IEEE 20th International Conference on High Performance Computing and Communications, IEEE 16th International Conference on Smart City; IEEE 4th International Conference on Data science and Systems (HPCC/SmartCity/DSS), Exeter, UK, 28–30 June 2018; pp. 235–242.
6. Wang, K.; Qi, X.; Liu, H. A comparison of day-ahead photovoltaic power forecasting models based on deep learning neural network. Appl. Energy 2019, 251, 113315. [CrossRef]
7. Akhter, M.N.; Mekhilef, S.; Mokhlis, H.; Mohamed Shah, N. Review on forecasting of photovoltaic power generation based on machine learning and metaheuristic techniques. IET Renew. Power Gener. 2019, 13, 1009–1023. [CrossRef]
8. Hafiz, F.; Awal, M.; de Queiroz, A.R.; Husain, I. Real-time stochastic optimization of energy storage management using deep learning-based forecasts for residential PV applications. IEEE Trans. Ind. Appl. 2020, 56, 2216–2226. [CrossRef]
9. Rajagukguk, R.A.; Ramadhan, R.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. [CrossRef]
10. Santhosh, M.; Venkaiah, C.; Vinod Kumar, D. Current advances and approaches in wind speed and wind power forecasting for improved renewable energy integration: A review. Eng. Rep. 2020, 2, e12178. [CrossRef]
11. Gupta, P.; Singh, R. PV power forecasting based on data-driven models: A review. Int. J. Sustain. Eng. 2021, 14, 1733–1755. [CrossRef]
12. Massaoudi, M.; Chihi, I.; Abu-Rub, H.; Refaat, S.S.; Oueslati, F.S. Convergence of photovoltaic power forecasting and deep learning: State-of-art review. IEEE Access 2021, 9, 136593–136615. [CrossRef]
13. Tina, G.M.; Ventura, C.; Ferlito, S.; De Vito, S. A state-of-art-review on machine-learning based methods for PV. Appl. Sci. 2021, 11, 7550. [CrossRef]
14. Costa, R.L.D.C. Convolutional-LSTM networks and generalization in forecasting of household photovoltaic generation. Eng. Appl. Artif. Intell. 2022, 116, 105458. [CrossRef]
15. Essam, Y.; Ahmed, A.N.; Ramli, R.; Chau, K.W.; Idris Ibrahim, M.S.; Sherif, M.; Sefelnasr, A.; El-Shafie, A. Investigating photovoltaic solar power output forecasting using machine learning algorithms. Eng. Appl. Comput. Fluid Mech. 2022, 16, 2002–2034. [CrossRef]
16. Gaviria, J.F.; Narváez, G.; Guillen, C.; Giraldo, L.F.; Bressan, M. Machine learning in photovoltaic systems: A review. Renew. Energy 2022, 196, 298–318. [CrossRef]
17. Zhao, E.; Sun, S.;Wang, S. New developments in wind energy forecasting with artificial intelligence and big data: A scientometric insight. Data Sci. Manag. 2022, 5, 84–95. [CrossRef]
18. Markovics, D.; Mayer, M.J. Comparison of machine learning methods for photovoltaic power forecasting based on numerical weather prediction. Renew. Sustain. Energy Rev. 2022, 161, 112364. [CrossRef]
19. Shabbir, N.; Kütt, L.; Raja, H.A.; Jawad, M.; Allik, A.; Husev, O. Techno-economic analysis and energy forecasting study of domestic and commercial photovoltaic system installations in Estonia. Energy 2022, 253, 124156. [CrossRef]
20. Luo, Z.; Peng, J.; Tan, Y.; Yin, R.; Zou, B.; Hu, M.; Yan, J. A novel forecast-based operation strategy for residential PV-battery-flexible loads systems considering the flexibility of battery and loads. Energy Convers. Manag. 2023, 278, 116705. [CrossRef]
21. Phinikarides, A.; Makrides, G.; Kindyni, N.; Kyprianou, A.; Georghiou, G.E. ARIMA modeling of the performance of different photovoltaic technologies. In Proceedings of the 2013 IEEE 39th Photovoltaic Specialists Conference (PVSC), Tampa, FL, USA, 16–21 June 2013; pp. 797–801.
22. Dong, Z.; Yang, D.; Reindl, T.; Walsh, W.M. Short-term solar irradiance forecasting using exponential smoothing state space model. Energy 2013, 55, 1104–1113. [CrossRef]
23. Li, Y.; Su, Y.; Shu, L. An ARMAX model for forecasting the power output of a grid connected photovoltaic system. Renew. Energy 2014, 66, 78–89. [CrossRef]
24. Raza, M.Q.; Nadarajah, M.; Ekanayake, C. On recent advances in PV output power forecast. Sol. Energy 2016, 136, 125–144. [CrossRef]
25. Sobri, S.; Koohi-Kamali, S.; Rahim, N.A. Solar photovoltaic generation forecasting methods: A review. Energy Convers. Manag. 2018, 156, 459–497. [CrossRef]
26. Atique, S.; Noureen, S.; Roy, V.; Subburaj, V.; Bayne, S.; Macfie, J. Forecasting of total daily solar energy generation using ARIMA: A case study. In Proceedings of the 2019 IEEE 9th annual computing and communication workshop and conference (CCWC), Las Vegas, NV, USA, 7–9 January 2019; pp. 114–119.
27. Assouline, D.; Mohajeri, N.; Scartezzini, J.L. Quantifying rooftop photovoltaic solar energy potential: A machine learning approach. Sol. Energy 2017, 141, 278–296. [CrossRef]
28. Preda, S.; Oprea, S.V.; Bâra, A.; Belciu, A. PV forecasting using support vector machine learning in a big data analytics context. Symmetry 2018, 10, 748. [CrossRef]
29. Ahmad, M.W.; Mourshed, M.; Rezgui, Y. Tree-based ensemble methods for predicting PV power generation and their comparison with support vector regression. Energy 2018, 164, 465–474. [CrossRef]
30. Huertas Tato, J.; Centeno Brito, M. Using smart persistence and random forests to predict photovoltaic energy production. Energies 2018, 12, 100. [CrossRef]
31. Zhu, R.; Guo,W.; Gong, X. Short-term photovoltaic power output prediction based on k-fold cross-validation and an ensemble model. Energies 2019, 12, 1220. [CrossRef]
32. Munawar, U.; Wang, Z. A framework of using machine learning approaches for short-term solar power forecasting. J. Electr. Eng. Technol. 2020, 15, 561–569. [CrossRef]
33. Phan, Q.T.; Wu, Y.K.; Phan, Q.D. Short-term Solar Power Forecasting Using XGBoost with Numerical Weather Prediction. In Proceedings of the 2021 IEEE International Future Energy Electronics Conference (IFEEC), Taipei, Taiwan, 16–19 November 2021. [CrossRef]
34. Wang, Y.; Liao,W.; Chang, Y. Gated recurrent unit network-based short-term photovoltaic forecasting. Energies 2018, 11, 2163. [CrossRef]
35. Lee, D.; Jeong, J.; Yoon, S.H.; Chae, Y.T. Improvement of short-term BIPV power predictions using feature engineering and a recurrent neural network. Energies 2019, 12, 3247. [CrossRef]
36. Hossain, M.S.; Mahmood, H. Short-term photovoltaic power forecasting using an LSTM neural network and synthetic weather forecast. IEEE Access 2020, 8, 172524–172533. [CrossRef]
37. Ahn, H.K.; Park, N. Deep RNN-based photovoltaic power short-term forecast using power IoT sensors. Energies 2021, 14, 436. [CrossRef]
38. Khan, W.; Walker, S.; Zeiler, W. Improved solar photovoltaic energy generation forecast using deep learning-based ensemble stacking approach. Energy 2022, 240, 122812. [CrossRef]
39. Ghimire, S.; Deo, R.C.; Raj, N.; Mi, J. Deep solar radiation forecasting with convolutional neural network and long short-term memory network algorithms. Appl. Energy 2019, 253, 113541. [CrossRef]
40. Suresh, V.; Janik, P.; Rezmer, J.; Leonowicz, Z. Forecasting solar PV output using convolutional neural networks with a sliding window algorithm. Energies 2020, 13, 723. [CrossRef]
41. Tovar, M.; Robles, M.; Rashid, F. PV power prediction, using CNN-LSTM hybrid neural network model. Case of study: Temixco-Morelos, México. Energies 2020, 13, 6512. [CrossRef]
42. Agga, A.; Abbou, A.; Labbadi, M.; El Houm, Y.; Ali, I.H.O. CNN-LSTM: An efficient hybrid deep learning architecture for predicting short-term photovoltaic power production. Electr. Power Syst. Res. 2022, 208, 107908. [CrossRef]
43. Zhou, H.; Zhang, Y.; Yang, L.; Liu, Q.; Yan, K.; Du, Y. Short-term photovoltaic power forecasting based on long short term memory neural network and attention mechanism. IEEE Access 2019, 7, 78063–78074. [CrossRef]
44. Wang, F.; Zhang, Z.; Liu, C.; Yu, Y.; Pang, S.; Dui´c, N.; Shafie-Khah, M.; Catalao, J.P. Generative adversarial networks and convolutional neural networks based weather classification model for day ahead short-term photovoltaic power forecasting. Energy Convers. Manag. 2019, 181, 443–462. [CrossRef]
45. Perera, M.; De Hoog, J.; Bandara, K.; Halgamuge, S. Multi-resolution, multi-horizon distributed solar PV power forecasting with forecast combinations. Expert Syst. Appl. 2022, 205, 117690. [CrossRef]
46. Grzebyk, D.; Alcañiz, A.; Donker, J.C.; Zeman, M.; Ziar, H.; Isabella, O. Individual yield nowcasting for residential PV systems. Sol. Energy 2023, 251, 325–336. [CrossRef]
47. Chen, T.; Guestrin, C. Xgboost: A scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13–17 August 2016; pp. 785–794.
48. Nielsen, D. Tree Boosting with Xgboost-Why Does Xgboost Win “Every” Machine Learning Competition? Master’s Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 2016.
49. Xu, S.; An, X.; Qiao, X.; Zhu, L.; Li, L. Multi-output least-squares support vector regression machines. Pattern Recognit. Lett. 2013, 34, 1078–1084. . [CrossRef]
50. Ahmad, W.; Ayub, N.; Ali, T.; Irfan, M.; Awais, M.; Shiraz, M.; Glowacz, A. Towards Short Term Electricity Load Forecasting Using Improved Support Vector Machine and Extreme Learning Machine. Energies 2020, 13, 2907. [CrossRef]
51. Das, U.K.; Tey, K.S.; Seyedmahmoudian, M.; Idna Idris, M.Y.; Mekhilef, S.; Horan, B.; Stojcevski, A. SVR-based model to forecast PV power generation under different weather conditions. Energies 2017, 10, 876. [CrossRef]
52. Cantillo-Luna, S.; Moreno-Chuquen, R.; Chamorro, H.R.; Riquelme-Dominguez, J.M.; Gonzalez-Longatt, F. Locational Marginal Price Forecasting Using SVR-Based Multi-Output Regression in Electricity Markets. Energies 2022, 15, 293. [CrossRef]
53. Hong, W.C.; Fan, G.F. Hybrid Empirical Mode Decomposition with Support Vector Regression Model for Short Term Load Forecasting. Energies 2019. 12, 1093. [CrossRef]
54. Fu, T.; Zhang, S.; Wang, C. Application and research for electricity price forecasting system based on multi-objective optimization and sub-models selection strategy. Soft Comput. 2020, 24, 15611–15637. [CrossRef]
55. Majidpour, M.; Nazaripouya, H.; Chu, P.; Pota, H.R.; Gadh, R. Fast univariate time series prediction of solar power for real-time control of energy storage system. Forecasting 2018, 1, 107–120. [CrossRef]
56. Wang, J.; Li, P.; Ran, R.; Che, Y.; Zhou, Y. A short-term photovoltaic power prediction model based on the gradient boost decision tree. Appl. Sci. 2018, 8, 689. [CrossRef]
57. Hornik, K.; Stinchcombe, M.; White, H. Multilayer feedforward networks are universal approximators. Neural Netw. 1989, 2, 359–366. [CrossRef]
58. Haykin, S. Neural Networks and Learning Machines, 3/E; Pearson Education: Noida, India, 2009.
59. Wang, F.; Xuan, Z.; Zhen, Z.; Li, K.;Wang, T.; Shi, M. A day-ahead PV power forecasting method based on LSTM-RNN model and time correlation modification under partial daily pattern prediction framework. Energy Convers. Manag. 2020, 212, 112766. [CrossRef]
60. Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput. 1997, 9, 1735–1780. [CrossRef]
61. Liu, Y.; Guan, L.; Hou, C.; Han, H.; Liu, Z.; Sun, Y.; Zheng, M. Wind power short-term prediction based on LSTM and discrete wavelet transform. Appl. Sci. 2019, 9, 1108. [CrossRef]
62. Pourdaryaei, A.; Mokhlis, H.; Illias, H.A.; Kaboli, S.H.A.; Ahmad, S.; Ang, S.P. Hybrid ANN and Artificial Cooperative Search Algorithm to Forecast Short-Term Electricity Price in De-Regulated Electricity Market. IEEE Access 2019, 7, 125369–125386. [CrossRef]
63. Azam, M.F.; Younis, S. Multi-Horizon Electricity Load and Price Forecasting using an Interpretable Multi-Head Self-Attention and EEMD-Based Framework. IEEE Access 2021, 9, 85918–85932. [CrossRef]
64. A˘gbulut, Ü.; Gürel, A.E.; Ergün, A.; Ceylan, ˙I. Performance assessment of a V-Trough photovoltaic system and prediction of power output with different machine learning algorithms. J. Clean. Prod. 2020, 268, 122269. [CrossRef]
65. Jiang, L.; Hu, G. A Review on Short-Term Electricity Price Forecasting Techniques for Energy Markets. In Proceedings of the 15th International Conference on Control, Automation, Robotics and Vision (ICARCV), Singapore, 18–21 November 2018. [CrossRef]
66. Hong, Y.Y.; Taylar, J.V.; Fajardo, A.C. Locational marginal price forecasting in a day-ahead power market using spatiotemporal deep learning network. Sustain. Energy Grids Netw. 2020, 24, 100406. [CrossRef]
67. Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine Learning in Python. J. Mach. Learn. Res. 2011, 12, 2825–2830.
68. Chollet, F. Keras. 2015. Available online: https://github.com/fchollet/keras (accessed on 25 January 2023).
69. Gulli, A.; Pal, S. Deep Learning with Keras; Packt Publishing Ltd.: Birmingham, UK, 2017.
70. Rachmatullah, M.I.C.; Santoso, J.; Surendro, K. A novel approach in determining neural networks architecture to classify data with large number of attributes. IEEE Access 2020, 8, 204728–204743. [CrossRef]
dc.rights.spa.fl_str_mv Derechos reservados - MDPI, 2023
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.uri.eng.fl_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.eng.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.creativecommons.spa.fl_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
rights_invalid_str_mv Derechos reservados - MDPI, 2023
https://creativecommons.org/licenses/by-nc-nd/4.0/
Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv 24 páginas
dc.format.mimetype.none.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv MDPI
dc.publisher.place.eng.fl_str_mv Basel, Switzerland
institution Universidad Autónoma de Occidente
bitstream.url.fl_str_mv https://red.uao.edu.co/bitstreams/5db182c5-82e8-4119-a1fb-253c036ae95a/download
https://red.uao.edu.co/bitstreams/1bf63b39-3189-4d1e-8dc6-c60aea6a6ff9/download
https://red.uao.edu.co/bitstreams/9585db9d-b7ad-47b9-bef4-6a3cd3dce45d/download
https://red.uao.edu.co/bitstreams/30381695-1009-4f6f-9140-4876e6820d85/download
bitstream.checksum.fl_str_mv 55529df48a637ae0d457b4de51aed687
6987b791264a2b5525252450f99b10d1
cc982345501d75a9cadef5a47c831ac0
a41ef466d0abd98e29d59eeab3bfd063
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Digital Universidad Autonoma de Occidente
repository.mail.fl_str_mv repositorio@uao.edu.co
_version_ 1831928571860353024
spelling Cantillo Luna, Sergio AlejandroMoreno Chuquen, RicardoCeleita, DavidGeorge, AndersMDPI2024-11-12T14:44:02Z2024-11-12T14:44:02Z2023Cantillo Luna, S.; Moreno-Chuquen, R.; Celeita, D. y Anders, G. (2023). Deep and Machine Learning Models to Forecast Photovoltaic Power Generation. Energies. 16(10). 24 p. https://doi.org/10.3390/en1610409719961073https://hdl.handle.net/10614/15884https://doi.org/10.3390/en16104097Universidad Autónoma de OccidenteRespositorio Educativo Digital UAOhttps://red.uao.edu.co/The integration and management of distributed energy resources (DERs), including residential photovoltaic (PV) production, coupled with the widespread use of enabling technologies such as artificial intelligence, have led to the emergence of new tools, market models, and business opportunities. The accurate forecasting of these resources has become crucial to decision making, despite data availability and reliability issues in some parts of the world. To address these challenges, this paper proposes a deep and machine learning-based methodology for PV power forecasting, which includes XGBoost, random forest, support vector regressor, multi-layer perceptron, and LSTM-based tuned models, and introduces the ConvLSTM1D approach for this task. These models were evaluated on the univariate time-series prediction of low-volume residential PV production data across various forecast horizons. The proposed benchmarking and analysis approach considers technical and economic impacts, which can provide valuable insights for decision-making tools with these resources. The results indicate that the random forest and ConvLSTM1D model approaches yielded the most accurate forecasting performance, as demonstrated by the lowest RMSE, MAPE, and MAE across the different scenarios proposed24 páginasapplication/pdfengMDPIBasel, SwitzerlandDerechos reservados - MDPI, 2023https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2Deep and machine learning models to forecast photovoltaic power generationArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a852410116Energies1. Restrepo-Trujillo, J.; Moreno-Chuquen, R.; Jiménez-García, F.; Chamorro, H.R. Scenario Analysis of an Electric Power System in Colombia Considering the El Niño Phenomenon and the Inclusion of Renewable Energies. Energies 2022, 15, 6690. [CrossRef]2. Ufa, R.; Malkova, Y.; Rudnik, V.; Andreev, M.; Borisov, V. A review on distributed generation impacts on electric power system. Int. J. Hydrogen Energy 2022, 47, 20347–20361. [CrossRef]3. Cantillo-Luna, S.; Moreno-Chuquen, R.; Chamorro, H.R.; Sood, V.K.; Badsha, S.; Konstantinou, C. Blockchain for Distributed Energy Resources Management and Integration. IEEE Access 2022, 10, 68598–68617. [CrossRef]4. Burger, S.P.; Luke, M. Business models for distributed energy resources: A review and empirical analysis. Energy Policy 2017, 109, 230–248. [CrossRef]5. Zaouali, K.; Rekik, R.; Bouallegue, R. Deep learning forecasting based on auto-lstm model for home solar power systems. In Proceedings of the 2018 IEEE 20th International Conference on High Performance Computing and Communications, IEEE 16th International Conference on Smart City; IEEE 4th International Conference on Data science and Systems (HPCC/SmartCity/DSS), Exeter, UK, 28–30 June 2018; pp. 235–242.6. Wang, K.; Qi, X.; Liu, H. A comparison of day-ahead photovoltaic power forecasting models based on deep learning neural network. Appl. Energy 2019, 251, 113315. [CrossRef]7. Akhter, M.N.; Mekhilef, S.; Mokhlis, H.; Mohamed Shah, N. Review on forecasting of photovoltaic power generation based on machine learning and metaheuristic techniques. IET Renew. Power Gener. 2019, 13, 1009–1023. [CrossRef]8. Hafiz, F.; Awal, M.; de Queiroz, A.R.; Husain, I. Real-time stochastic optimization of energy storage management using deep learning-based forecasts for residential PV applications. IEEE Trans. Ind. Appl. 2020, 56, 2216–2226. [CrossRef]9. Rajagukguk, R.A.; Ramadhan, R.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. [CrossRef]10. Santhosh, M.; Venkaiah, C.; Vinod Kumar, D. Current advances and approaches in wind speed and wind power forecasting for improved renewable energy integration: A review. Eng. Rep. 2020, 2, e12178. [CrossRef]11. Gupta, P.; Singh, R. PV power forecasting based on data-driven models: A review. Int. J. Sustain. Eng. 2021, 14, 1733–1755. [CrossRef]12. Massaoudi, M.; Chihi, I.; Abu-Rub, H.; Refaat, S.S.; Oueslati, F.S. Convergence of photovoltaic power forecasting and deep learning: State-of-art review. IEEE Access 2021, 9, 136593–136615. [CrossRef]13. Tina, G.M.; Ventura, C.; Ferlito, S.; De Vito, S. A state-of-art-review on machine-learning based methods for PV. Appl. Sci. 2021, 11, 7550. [CrossRef]14. Costa, R.L.D.C. Convolutional-LSTM networks and generalization in forecasting of household photovoltaic generation. Eng. Appl. Artif. Intell. 2022, 116, 105458. [CrossRef]15. Essam, Y.; Ahmed, A.N.; Ramli, R.; Chau, K.W.; Idris Ibrahim, M.S.; Sherif, M.; Sefelnasr, A.; El-Shafie, A. Investigating photovoltaic solar power output forecasting using machine learning algorithms. Eng. Appl. Comput. Fluid Mech. 2022, 16, 2002–2034. [CrossRef]16. Gaviria, J.F.; Narváez, G.; Guillen, C.; Giraldo, L.F.; Bressan, M. Machine learning in photovoltaic systems: A review. Renew. Energy 2022, 196, 298–318. [CrossRef]17. Zhao, E.; Sun, S.;Wang, S. New developments in wind energy forecasting with artificial intelligence and big data: A scientometric insight. Data Sci. Manag. 2022, 5, 84–95. [CrossRef]18. Markovics, D.; Mayer, M.J. Comparison of machine learning methods for photovoltaic power forecasting based on numerical weather prediction. Renew. Sustain. Energy Rev. 2022, 161, 112364. [CrossRef]19. Shabbir, N.; Kütt, L.; Raja, H.A.; Jawad, M.; Allik, A.; Husev, O. Techno-economic analysis and energy forecasting study of domestic and commercial photovoltaic system installations in Estonia. Energy 2022, 253, 124156. [CrossRef]20. Luo, Z.; Peng, J.; Tan, Y.; Yin, R.; Zou, B.; Hu, M.; Yan, J. A novel forecast-based operation strategy for residential PV-battery-flexible loads systems considering the flexibility of battery and loads. Energy Convers. Manag. 2023, 278, 116705. [CrossRef]21. Phinikarides, A.; Makrides, G.; Kindyni, N.; Kyprianou, A.; Georghiou, G.E. ARIMA modeling of the performance of different photovoltaic technologies. In Proceedings of the 2013 IEEE 39th Photovoltaic Specialists Conference (PVSC), Tampa, FL, USA, 16–21 June 2013; pp. 797–801.22. Dong, Z.; Yang, D.; Reindl, T.; Walsh, W.M. Short-term solar irradiance forecasting using exponential smoothing state space model. Energy 2013, 55, 1104–1113. [CrossRef]23. Li, Y.; Su, Y.; Shu, L. An ARMAX model for forecasting the power output of a grid connected photovoltaic system. Renew. Energy 2014, 66, 78–89. [CrossRef]24. Raza, M.Q.; Nadarajah, M.; Ekanayake, C. On recent advances in PV output power forecast. Sol. Energy 2016, 136, 125–144. [CrossRef]25. Sobri, S.; Koohi-Kamali, S.; Rahim, N.A. Solar photovoltaic generation forecasting methods: A review. Energy Convers. Manag. 2018, 156, 459–497. [CrossRef]26. Atique, S.; Noureen, S.; Roy, V.; Subburaj, V.; Bayne, S.; Macfie, J. Forecasting of total daily solar energy generation using ARIMA: A case study. In Proceedings of the 2019 IEEE 9th annual computing and communication workshop and conference (CCWC), Las Vegas, NV, USA, 7–9 January 2019; pp. 114–119.27. Assouline, D.; Mohajeri, N.; Scartezzini, J.L. Quantifying rooftop photovoltaic solar energy potential: A machine learning approach. Sol. Energy 2017, 141, 278–296. [CrossRef]28. Preda, S.; Oprea, S.V.; Bâra, A.; Belciu, A. PV forecasting using support vector machine learning in a big data analytics context. Symmetry 2018, 10, 748. [CrossRef]29. Ahmad, M.W.; Mourshed, M.; Rezgui, Y. Tree-based ensemble methods for predicting PV power generation and their comparison with support vector regression. Energy 2018, 164, 465–474. [CrossRef]30. Huertas Tato, J.; Centeno Brito, M. Using smart persistence and random forests to predict photovoltaic energy production. Energies 2018, 12, 100. [CrossRef]31. Zhu, R.; Guo,W.; Gong, X. Short-term photovoltaic power output prediction based on k-fold cross-validation and an ensemble model. Energies 2019, 12, 1220. [CrossRef]32. Munawar, U.; Wang, Z. A framework of using machine learning approaches for short-term solar power forecasting. J. Electr. Eng. Technol. 2020, 15, 561–569. [CrossRef]33. Phan, Q.T.; Wu, Y.K.; Phan, Q.D. Short-term Solar Power Forecasting Using XGBoost with Numerical Weather Prediction. In Proceedings of the 2021 IEEE International Future Energy Electronics Conference (IFEEC), Taipei, Taiwan, 16–19 November 2021. [CrossRef]34. Wang, Y.; Liao,W.; Chang, Y. Gated recurrent unit network-based short-term photovoltaic forecasting. Energies 2018, 11, 2163. [CrossRef]35. Lee, D.; Jeong, J.; Yoon, S.H.; Chae, Y.T. Improvement of short-term BIPV power predictions using feature engineering and a recurrent neural network. Energies 2019, 12, 3247. [CrossRef]36. Hossain, M.S.; Mahmood, H. Short-term photovoltaic power forecasting using an LSTM neural network and synthetic weather forecast. IEEE Access 2020, 8, 172524–172533. [CrossRef]37. Ahn, H.K.; Park, N. Deep RNN-based photovoltaic power short-term forecast using power IoT sensors. Energies 2021, 14, 436. [CrossRef]38. Khan, W.; Walker, S.; Zeiler, W. Improved solar photovoltaic energy generation forecast using deep learning-based ensemble stacking approach. Energy 2022, 240, 122812. [CrossRef]39. Ghimire, S.; Deo, R.C.; Raj, N.; Mi, J. Deep solar radiation forecasting with convolutional neural network and long short-term memory network algorithms. Appl. Energy 2019, 253, 113541. [CrossRef]40. Suresh, V.; Janik, P.; Rezmer, J.; Leonowicz, Z. Forecasting solar PV output using convolutional neural networks with a sliding window algorithm. Energies 2020, 13, 723. [CrossRef]41. Tovar, M.; Robles, M.; Rashid, F. PV power prediction, using CNN-LSTM hybrid neural network model. Case of study: Temixco-Morelos, México. Energies 2020, 13, 6512. [CrossRef]42. Agga, A.; Abbou, A.; Labbadi, M.; El Houm, Y.; Ali, I.H.O. CNN-LSTM: An efficient hybrid deep learning architecture for predicting short-term photovoltaic power production. Electr. Power Syst. Res. 2022, 208, 107908. [CrossRef]43. Zhou, H.; Zhang, Y.; Yang, L.; Liu, Q.; Yan, K.; Du, Y. Short-term photovoltaic power forecasting based on long short term memory neural network and attention mechanism. IEEE Access 2019, 7, 78063–78074. [CrossRef]44. Wang, F.; Zhang, Z.; Liu, C.; Yu, Y.; Pang, S.; Dui´c, N.; Shafie-Khah, M.; Catalao, J.P. Generative adversarial networks and convolutional neural networks based weather classification model for day ahead short-term photovoltaic power forecasting. Energy Convers. Manag. 2019, 181, 443–462. [CrossRef]45. Perera, M.; De Hoog, J.; Bandara, K.; Halgamuge, S. Multi-resolution, multi-horizon distributed solar PV power forecasting with forecast combinations. Expert Syst. Appl. 2022, 205, 117690. [CrossRef]46. Grzebyk, D.; Alcañiz, A.; Donker, J.C.; Zeman, M.; Ziar, H.; Isabella, O. Individual yield nowcasting for residential PV systems. Sol. Energy 2023, 251, 325–336. [CrossRef]47. Chen, T.; Guestrin, C. Xgboost: A scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13–17 August 2016; pp. 785–794.48. Nielsen, D. Tree Boosting with Xgboost-Why Does Xgboost Win “Every” Machine Learning Competition? Master’s Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 2016.49. Xu, S.; An, X.; Qiao, X.; Zhu, L.; Li, L. Multi-output least-squares support vector regression machines. Pattern Recognit. Lett. 2013, 34, 1078–1084. . [CrossRef]50. Ahmad, W.; Ayub, N.; Ali, T.; Irfan, M.; Awais, M.; Shiraz, M.; Glowacz, A. Towards Short Term Electricity Load Forecasting Using Improved Support Vector Machine and Extreme Learning Machine. Energies 2020, 13, 2907. [CrossRef]51. Das, U.K.; Tey, K.S.; Seyedmahmoudian, M.; Idna Idris, M.Y.; Mekhilef, S.; Horan, B.; Stojcevski, A. SVR-based model to forecast PV power generation under different weather conditions. Energies 2017, 10, 876. [CrossRef]52. Cantillo-Luna, S.; Moreno-Chuquen, R.; Chamorro, H.R.; Riquelme-Dominguez, J.M.; Gonzalez-Longatt, F. Locational Marginal Price Forecasting Using SVR-Based Multi-Output Regression in Electricity Markets. Energies 2022, 15, 293. [CrossRef]53. Hong, W.C.; Fan, G.F. Hybrid Empirical Mode Decomposition with Support Vector Regression Model for Short Term Load Forecasting. Energies 2019. 12, 1093. [CrossRef]54. Fu, T.; Zhang, S.; Wang, C. Application and research for electricity price forecasting system based on multi-objective optimization and sub-models selection strategy. Soft Comput. 2020, 24, 15611–15637. [CrossRef]55. Majidpour, M.; Nazaripouya, H.; Chu, P.; Pota, H.R.; Gadh, R. Fast univariate time series prediction of solar power for real-time control of energy storage system. Forecasting 2018, 1, 107–120. [CrossRef]56. Wang, J.; Li, P.; Ran, R.; Che, Y.; Zhou, Y. A short-term photovoltaic power prediction model based on the gradient boost decision tree. Appl. Sci. 2018, 8, 689. [CrossRef]57. Hornik, K.; Stinchcombe, M.; White, H. Multilayer feedforward networks are universal approximators. Neural Netw. 1989, 2, 359–366. [CrossRef]58. Haykin, S. Neural Networks and Learning Machines, 3/E; Pearson Education: Noida, India, 2009.59. Wang, F.; Xuan, Z.; Zhen, Z.; Li, K.;Wang, T.; Shi, M. A day-ahead PV power forecasting method based on LSTM-RNN model and time correlation modification under partial daily pattern prediction framework. Energy Convers. Manag. 2020, 212, 112766. [CrossRef]60. Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput. 1997, 9, 1735–1780. [CrossRef]61. Liu, Y.; Guan, L.; Hou, C.; Han, H.; Liu, Z.; Sun, Y.; Zheng, M. Wind power short-term prediction based on LSTM and discrete wavelet transform. Appl. Sci. 2019, 9, 1108. [CrossRef]62. Pourdaryaei, A.; Mokhlis, H.; Illias, H.A.; Kaboli, S.H.A.; Ahmad, S.; Ang, S.P. Hybrid ANN and Artificial Cooperative Search Algorithm to Forecast Short-Term Electricity Price in De-Regulated Electricity Market. IEEE Access 2019, 7, 125369–125386. [CrossRef]63. Azam, M.F.; Younis, S. Multi-Horizon Electricity Load and Price Forecasting using an Interpretable Multi-Head Self-Attention and EEMD-Based Framework. IEEE Access 2021, 9, 85918–85932. [CrossRef]64. A˘gbulut, Ü.; Gürel, A.E.; Ergün, A.; Ceylan, ˙I. Performance assessment of a V-Trough photovoltaic system and prediction of power output with different machine learning algorithms. J. Clean. Prod. 2020, 268, 122269. [CrossRef]65. Jiang, L.; Hu, G. A Review on Short-Term Electricity Price Forecasting Techniques for Energy Markets. In Proceedings of the 15th International Conference on Control, Automation, Robotics and Vision (ICARCV), Singapore, 18–21 November 2018. [CrossRef]66. Hong, Y.Y.; Taylar, J.V.; Fajardo, A.C. Locational marginal price forecasting in a day-ahead power market using spatiotemporal deep learning network. Sustain. Energy Grids Netw. 2020, 24, 100406. [CrossRef]67. Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine Learning in Python. J. Mach. Learn. Res. 2011, 12, 2825–2830.68. Chollet, F. Keras. 2015. Available online: https://github.com/fchollet/keras (accessed on 25 January 2023).69. Gulli, A.; Pal, S. Deep Learning with Keras; Packt Publishing Ltd.: Birmingham, UK, 2017.70. Rachmatullah, M.I.C.; Santoso, J.; Surendro, K. A novel approach in determining neural networks architecture to classify data with large number of attributes. IEEE Access 2020, 8, 204728–204743. [CrossRef]Deep learningMachine learningPV power forecastingTime-series analysisComunidad generalPublicationORIGINALDeep_and_Machine_Learning_Models_to_Forecast_Photovoltaic_Power_Generation.pdfDeep_and_Machine_Learning_Models_to_Forecast_Photovoltaic_Power_Generation.pdfArchivo texto completo del artículo de revista, PDFapplication/pdf2641458https://red.uao.edu.co/bitstreams/5db182c5-82e8-4119-a1fb-253c036ae95a/download55529df48a637ae0d457b4de51aed687MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81672https://red.uao.edu.co/bitstreams/1bf63b39-3189-4d1e-8dc6-c60aea6a6ff9/download6987b791264a2b5525252450f99b10d1MD52TEXTDeep_and_Machine_Learning_Models_to_Forecast_Photovoltaic_Power_Generation.pdf.txtDeep_and_Machine_Learning_Models_to_Forecast_Photovoltaic_Power_Generation.pdf.txtExtracted texttext/plain78707https://red.uao.edu.co/bitstreams/9585db9d-b7ad-47b9-bef4-6a3cd3dce45d/downloadcc982345501d75a9cadef5a47c831ac0MD53THUMBNAILDeep_and_Machine_Learning_Models_to_Forecast_Photovoltaic_Power_Generation.pdf.jpgDeep_and_Machine_Learning_Models_to_Forecast_Photovoltaic_Power_Generation.pdf.jpgGenerated Thumbnailimage/jpeg15854https://red.uao.edu.co/bitstreams/30381695-1009-4f6f-9140-4876e6820d85/downloada41ef466d0abd98e29d59eeab3bfd063MD5410614/15884oai:red.uao.edu.co:10614/158842024-11-16 03:00:28.697https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - MDPI, 2023open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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

Publicaciones similares