Photovoltaic single-diode model parametrization. An application to the calculus of the Euclidean distance to an I–V curve
Photovoltaic single-diode model parametrization. An application to the calculus of the Euclidean distance to an I–V curve
In this paper we provide a new parametrization of the characteristic curve (I-V curve) associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates the voltage with the current, through a transcendental equation with five parameters to be determined. There are many methodologies to extract the SDM parameters and some of them are based on obtaining the best fit of the SDM model on a voltage–current dataset through the ordinary least squares method. However, the fact that errors affect not only the current but also the voltage indicates that the maximum likelihood estimation (MLE) of the parameters is obtained by the total least squares method, also called orthogonal distance regression (ODR). The main difficulty in performing ODR lies in obtaining the Euclidean distance from a point to the SDM I-V curve which is in general a hard mathematical problem; in our particular case it is noticeably more difficult due to the implicit nature of the SDM equation and the fact that solution candidates might not be unique. This paper proposes a new parametrization that allows reduction of the calculus of the Euclidean distance from any point to the I-V curve to solving a single-variable equation. An in-depth mathematical analysis determines the number of possible candidates where the Euclidean distance can be attained. Moreover, a full casuistry alongside a geometrical study based on the curvature of the I-V curve and the Maximum Curvature Point, permits identification and classification of all these candidates. This enables for the first time a complete algorithm to compute the Euclidean distance from a point to an I-V curve at any condition and, thus, to perform a reliable ODR to obtain the MLE of the SDM parameters. Using the obtained theoretical background, it is demonstrated that two existing methodologies to compute the Euclidean distance fail in some cases, whereas the proposed algorithm is execution-proof and runs faster.
Euclidean distance, orthogonal distance regression, parametrization, photovoltaics, single-diode model, total least squares
Toledo, F. Javier
72ef6fd0-9d57-4b45-8a7b-bc99688520ac
Galiano, Vicente
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Blanes, Jose M.
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Herranz, Victoria
de716d36-30b2-4bd7-a3f0-efebc92a1932
Batzelis, Efstratios
2a85086e-e403-443c-81a6-e3b4ee16ae5e
9 January 2023
Toledo, F. Javier
72ef6fd0-9d57-4b45-8a7b-bc99688520ac
Galiano, Vicente
241d4b06-7a9a-4153-9398-98f0b969e01d
Blanes, Jose M.
a67c9dda-7676-4514-802a-1cb9b024aee1
Herranz, Victoria
de716d36-30b2-4bd7-a3f0-efebc92a1932
Batzelis, Efstratios
2a85086e-e403-443c-81a6-e3b4ee16ae5e
Toledo, F. Javier, Galiano, Vicente, Blanes, Jose M., Herranz, Victoria and Batzelis, Efstratios
(2023)
Photovoltaic single-diode model parametrization. An application to the calculus of the Euclidean distance to an I–V curve.
Mathematics and Computers in Simulation.
(doi:10.1016/j.matcom.2023.01.005).
Abstract
In this paper we provide a new parametrization of the characteristic curve (I-V curve) associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates the voltage with the current, through a transcendental equation with five parameters to be determined. There are many methodologies to extract the SDM parameters and some of them are based on obtaining the best fit of the SDM model on a voltage–current dataset through the ordinary least squares method. However, the fact that errors affect not only the current but also the voltage indicates that the maximum likelihood estimation (MLE) of the parameters is obtained by the total least squares method, also called orthogonal distance regression (ODR). The main difficulty in performing ODR lies in obtaining the Euclidean distance from a point to the SDM I-V curve which is in general a hard mathematical problem; in our particular case it is noticeably more difficult due to the implicit nature of the SDM equation and the fact that solution candidates might not be unique. This paper proposes a new parametrization that allows reduction of the calculus of the Euclidean distance from any point to the I-V curve to solving a single-variable equation. An in-depth mathematical analysis determines the number of possible candidates where the Euclidean distance can be attained. Moreover, a full casuistry alongside a geometrical study based on the curvature of the I-V curve and the Maximum Curvature Point, permits identification and classification of all these candidates. This enables for the first time a complete algorithm to compute the Euclidean distance from a point to an I-V curve at any condition and, thus, to perform a reliable ODR to obtain the MLE of the SDM parameters. Using the obtained theoretical background, it is demonstrated that two existing methodologies to compute the Euclidean distance fail in some cases, whereas the proposed algorithm is execution-proof and runs faster.
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More information
Accepted/In Press date: 3 January 2023
e-pub ahead of print date: 9 January 2023
Published date: 9 January 2023
Additional Information:
Funding Information:
Dr. F. Javier Toledo, Dr. V. Galiano, Dr. Victoria Herranz and Dr. José M. Blanes have received funding from grant TED2021-130025B-I00 funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR . Dr. F. Javier Toledo’s work has received funding from the Ministerio de Ciencia e Innovación of Spain ( PGC2018-097960-B-C21 ), the government of the Valencian Community ( PROMETEO/2021/063 ) and the European Union (ERDF, ”A way to make Europe”). Dr. V. Galiano’s work has received funding from the Valencian Ministry of Innovation, Universities, Science and Digital Society (Generalitat Valenciana) under Grant CIAICO/2021/278 and from Grant PID2021-123627OB-C55 funded by MCIN/AEI/ 10.13039/501100011033 and, by “ ERDF A way of making Europe ”. Dr. E. Batzelis’ work has received funding from the Royal Academy of Engineering under the Engineering for Development Research Fellowship scheme (number RF/201819/18/86 ).
Keywords:
Euclidean distance, orthogonal distance regression, parametrization, photovoltaics, single-diode model, total least squares
Identifiers
Local EPrints ID: 480552
URI: http://eprints.soton.ac.uk/id/eprint/480552
ISSN: 0378-4754
PURE UUID: 0a0a9cf1-92c6-4f9f-888d-faa2652e2dcf
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Date deposited: 04 Aug 2023 16:46
Last modified: 06 Jun 2024 02:10
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Contributors
Author:
F. Javier Toledo
Author:
Vicente Galiano
Author:
Jose M. Blanes
Author:
Victoria Herranz
Author:
Efstratios Batzelis
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