APPROACH TO MODELING PHOTOVOLTAIC ENERGY YIELD USING CHEBYSHEV POLYNOMIALS: APPROACH TO MODELING PHOTOVOLTAIC ENERGY YIELD USING CHEBYSHEV POLYNOMIALS

Iliyana Ivanova; Donika Dimanova

doi:10.46687/jsar.v31i1.500

Authors

Iliyana Ivanova Department of Communication and Computer Engineering and Security Technologies, Faculty of Technical Sciences, Konstantin Preslavsky University of Shumen, Shumen 9712, 115 Universitetska St., e-mail: i.s.ivanova@shu.bg
Donika Dimanova Department of Communication and Computer Engineering and Security Technologies, Konstantin Preslavsky University of Shumen, Shumen 9712, 115 Universitetska St., e-mail: d.dimanova@shu.bg

DOI:

https://doi.org/10.46687/jsar.v31i1.500

Keywords:

Photovoltaic systems, Photovoltaic energy yield, Chebyshev polynomials, Solar irradiance, Temperature, Mathematical modeling

Abstract

Photovoltaic energy yield varies in response to changes in meteorological conditions. The main factors affecting the amount of electricity generated include solar irradiance and air temperature, as well as seasonal and daily variations. This paper examines the relationships between these factors and photovoltaic energy yield and presents an approach to modeling those using orthogonal Chebyshev polynomials. The main input variables, data-preprocessing steps, and structure of the approximation model are defined.

Author Biographies

Iliyana Ivanova, Department of Communication and Computer Engineering and Security Technologies, Faculty of Technical Sciences, Konstantin Preslavsky University of Shumen, Shumen 9712, 115 Universitetska St., e-mail: i.s.ivanova@shu.bg

Department of Communication and Computer Engineering and Security Technologies, Faculty of Technical Sciences, Konstantin Preslavsky University of Shumen, Shumen 9712, 115 Universitetska St., e-mail: i.s.ivanova@shu.bg

Donika Dimanova, Department of Communication and Computer Engineering and Security Technologies, Konstantin Preslavsky University of Shumen, Shumen 9712, 115 Universitetska St., e-mail: d.dimanova@shu.bg

Department of Communication and Computer Engineering and Security Technologies, Konstantin Preslavsky University of Shumen, Shumen 9712, 115 Universitetska St., e-mail: d.dimanova@shu.bg

References

Iheanetu K. J. Solar Photovoltaic Power Forecasting: A Review. Sustainability, Vol. 14, No. 24, 2022, Article 17005, ISSN 2071-1050. DOI: https://doi.org/10.3390/su142417005.

Diagne M., David M., Lauret P., Boland J., Schmutz N. Review of Solar Irradiance Forecasting Methods and a Proposition for Small-Scale Insular Grids. Renewable and Sustainable Energy Reviews, Vol. 27, 2013, pp. 65–76, ISSN 1364-0321. DOI: https://doi.org/10.1016/j.rser.2013.06.042.

Antonanzas J., Osorio N., Escobar R., Urraca R., Martinez-de-Pison F. J., Antonanzas-Torres F. Review of Photovoltaic Power Forecasting. Solar Energy, Vol. 136, 2016, pp. 78–111, ISSN 0038-092X. DOI: https://doi.org/10.1016/j.solener.2016.06.069.

Mellit A., Massi Pavan A., Ogliari E., Leva S., Lughi V. Advanced Methods for Photovoltaic Output Power Forecasting: A Review. Applied Sciences, Vol. 10, No. 2, 2020, Article 487, ISSN 2076-3417. DOI: https://doi.org/10.3390/app10020487.

Simeonova, I. Improving Administrative Security in Municipal Administrations: A Comprehensive Approach Using the Monte Carlo Model. Yearbook of Konstantin Preslavski University of Shumen, Vol. XIII E, Faculty of Technical Sciences, 2023, pp. 219–223, ISSN 1311-834.

Trifonov T. Modeling and Calculation of Passive Audio Crossovers. Annual of Konstantin Preslavski University of Shumen, Vol. IX E, Technical Sciences, 2019, pp. 182–189, ISSN 1311-834X. Available at: http://annuals.ftn.shu.bg/files/godishnik_ftn_2019.pdf.

Al-Dahidi S., Madhiarasan M., Al-Ghussain L., Abubaker A. M., Ahmad A. D., Alrbai M., Aghaei M., Alahmer H., Alahmer A., Baraldi P., Zio E. Forecasting Solar Photovoltaic Power Production: A Comprehensive Review and Innovative Data-Driven Modeling Framework. Energies, Vol. 17, No. 16, 2024, Article 4145, ISSN 1996-1073. DOI: https://doi.org/10.3390/en17164145.

Das U. K., Tey K. S., Seyedmahmoudian M., Mekhilef S., Idris M. Y. I., Van Deventer W., Horan B., Stojcevski A. Solar Photovoltaic Generation Forecasting Methods: A Review. Energy Conversion and Management, Vol. 156, 2018, pp. 459–497, ISSN 0196-8904. DOI: https://doi.org/10.1016/j.enconman.2017.11.019.

Chodakowska E., Nazarko J., Nazarko Ł., Rabayah H. S. Solar Radiation Forecasting: A Systematic Meta-Review of Current Methods and Emerging Trends. Energies, Vol. 17, No. 13, 2024, Article 3156, ISSN 1996-1073. DOI: https://doi.org/10.3390/en17133156.

Voyant C., Notton G., Kalogirou S. A., Nivet M. L., Paoli C., Motte F., Fouilloy A. Machine Learning Methods for Solar Radiation Forecasting: A Review. Renewable Energy, Vol. 105, 2017, pp. 569–582, ISSN 0960-1481. DOI: https://doi.org/10.1016/j.renene.2016.12.095.

Dubey S., Sarvaiya J. N., Seshadri B. Temperature Dependent Photovoltaic (PV) Efficiency and Its Effect on PV Production in the World – A Review. Energy Procedia, Vol. 33, 2013, pp. 311–321, ISSN 1876-6102. DOI: https://doi.org/10.1016/j.egypro.2013.05.072.

Skoplaki E., Palyvos J. A. On the Temperature Dependence of Photovoltaic Module Electrical Performance: A Review of Efficiency/Power Correlations. Solar Energy, Vol. 83, No. 5, 2009, pp. 614–624, ISSN 0038-092X. DOI: https://doi.org/10.1016/j.solener.2008.10.008.

Mohamad Radzi P. N. L., Akhter M. N., Mekhilef S., Mohamed Shah N. Review on the Application of Photovoltaic Forecasting Using Machine Learning for Very Short- to Long-Term Forecasting. Sustainability, Vol. 15, No. 4, 2023, Article 2942, ISSN 2071-1050. https://doi.org/10.3390/su15042942.

Inman R. H., Pedro H. T. C., Coimbra C. F. M. Solar Forecasting Methods for Renewable Energy Integration. Progress in Energy and Combustion Science, Vol. 39, No. 6, 2013, pp. 535–576, ISSN 0360-1285. https://doi.org/10.1016/j.pecs.2013.06.002.

Xu K. The Chebyshev Points of the First Kind. Applied Numerical Mathematics, Vol. 102, 2016, pp. 17–30, ISSN 0168-9274. DOI: https://doi.org/10.1016/j.apnum.2015.12.002.

Niu C., Liao H., Ma H., Wu H. Approximation Properties of Chebyshev Polynomials in the Legendre Norm. Mathematics, Vol. 9, No. 24, 2021, Article 3271, ISSN 2227-7390. DOI: https://doi.org/10.3390/math9243271.

Hyndman R. J., Koehler A. B. Another Look at Measures of Forecast Accuracy. International Journal of Forecasting, Vol. 22, No. 4, 2006, pp. 679–688, ISSN 0169-2070. DOI: https://doi.org/10.1016/j.ijforecast.2006.03.001.

Chai T., Draxler R. R. Root Mean Square Error (RMSE) or Mean Absolute Error (MAE)? – Arguments Against Avoiding RMSE in the Literature. Geoscientific Model Development, Vol. 7, No. 3, 2014, pp. 1247–1250, ISSN 1991-9603. DOI: https://doi.org/10.5194/gmd-7-1247-2014.

Hodson T. O. Root-Mean-Square Error (RMSE) or Mean Absolute Error (MAE): When to Use Them or Not. Geoscientific Model Development, Vol. 15, No. 14, 2022, pp. 5481–5487, ISSN 1991-9603. DOI: https://doi.org/10.5194/gmd-15-5481-2022.

Di Leo P., Ciocia A., Malgaroli G., Spertino F. Advancements and Challenges in Photovoltaic Power Forecasting: A Comprehensive Review. Energies, Vol. 18, No. 8, 2025, Article 2108, ISSN 1996-1073. DOI: https://doi.org/10.3390/en18082108.

APPROACH TO MODELING PHOTOVOLTAIC ENERGY YIELD USING CHEBYSHEV POLYNOMIALS