Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic Curves
To effectively represent photovoltaic (PV) modules while considering their dependency on changing environmental conditions, three novel mathematical and empirical formulations are proposed in this study to model PV curves with minimum effort and short timing. The three approaches rely on distinct ma...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/21/4417 |
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| author | Othman A. M. Omar Ahmed O. Badr Ibrahim Mohamed Diaaeldin |
| author_facet | Othman A. M. Omar Ahmed O. Badr Ibrahim Mohamed Diaaeldin |
| author_sort | Othman A. M. Omar |
| collection | DOAJ |
| description | To effectively represent photovoltaic (PV) modules while considering their dependency on changing environmental conditions, three novel mathematical and empirical formulations are proposed in this study to model PV curves with minimum effort and short timing. The three approaches rely on distinct mathematical techniques and definitions to formulate PV curves using function representations. We develop our models through fractional derivatives and stochastic white noise. The first empirical model is proposed using a fractional regression tool driven by the Liouville-Caputo fractional derivative and then implemented by the Mittag-Leffler function representation. Further, the fractional-order stochastic ordinary differential equation (ODE) tool is employed to generate two effective generic models. In this work, multiple commercial PV modules are modeled using the proposed fractional and stochastic formulations. Using the experimental data of the studied PV panels at different climatic conditions, we evaluate the proposed models’ accuracy using two effective statistical indices: the root mean squares error (RMSE) and the determination coefficient (R<sup>2</sup>). Finally, the proposed approaches are compared to several integer-order models in the literature where the proposed models’ precisely follow the real PV curves with a higher R<sup>2</sup> and lower RMSE values at different irradiance levels lower than 800 w/m<sup>2</sup>, and module temperature levels higher than 50 °C. |
| first_indexed | 2024-03-11T11:25:13Z |
| format | Article |
| id | doaj.art-487835d63ae449d388db044c503a1ea5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T11:25:13Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-487835d63ae449d388db044c503a1ea52023-11-10T15:07:49ZengMDPI AGMathematics2227-73902023-10-011121441710.3390/math11214417Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic CurvesOthman A. M. Omar0Ahmed O. Badr1Ibrahim Mohamed Diaaeldin2Engineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University, Cairo 11517, EgyptElectric Power and Machines Department, Faculty of Engineering, Ain Shams University, Cairo 11517, EgyptEngineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University, Cairo 11517, EgyptTo effectively represent photovoltaic (PV) modules while considering their dependency on changing environmental conditions, three novel mathematical and empirical formulations are proposed in this study to model PV curves with minimum effort and short timing. The three approaches rely on distinct mathematical techniques and definitions to formulate PV curves using function representations. We develop our models through fractional derivatives and stochastic white noise. The first empirical model is proposed using a fractional regression tool driven by the Liouville-Caputo fractional derivative and then implemented by the Mittag-Leffler function representation. Further, the fractional-order stochastic ordinary differential equation (ODE) tool is employed to generate two effective generic models. In this work, multiple commercial PV modules are modeled using the proposed fractional and stochastic formulations. Using the experimental data of the studied PV panels at different climatic conditions, we evaluate the proposed models’ accuracy using two effective statistical indices: the root mean squares error (RMSE) and the determination coefficient (R<sup>2</sup>). Finally, the proposed approaches are compared to several integer-order models in the literature where the proposed models’ precisely follow the real PV curves with a higher R<sup>2</sup> and lower RMSE values at different irradiance levels lower than 800 w/m<sup>2</sup>, and module temperature levels higher than 50 °C.https://www.mdpi.com/2227-7390/11/21/4417fractional order derivativesstochastic modelingrenewable energy imitationphotovoltaic curves formulationmathematical modeling |
| spellingShingle | Othman A. M. Omar Ahmed O. Badr Ibrahim Mohamed Diaaeldin Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic Curves Mathematics fractional order derivatives stochastic modeling renewable energy imitation photovoltaic curves formulation mathematical modeling |
| title | Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic Curves |
| title_full | Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic Curves |
| title_fullStr | Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic Curves |
| title_full_unstemmed | Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic Curves |
| title_short | Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic Curves |
| title_sort | novel fractional order and stochastic formulations for the precise prediction of commercial photovoltaic curves |
| topic | fractional order derivatives stochastic modeling renewable energy imitation photovoltaic curves formulation mathematical modeling |
| url | https://www.mdpi.com/2227-7390/11/21/4417 |
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