On the parameters domain of the single-diode model

Abstract

The current-voltage (I-V) curves of solar photovoltaic (PV) systems have been widely used as a tool to determine their electrical operation. Usually, I-V curves are described employing three cardinal points: the short-circuit point $\left(0,I_\mathrm{sc}\right)$, the open-circuit point $\left(V_\mathrm{oc},0\right)$, and the maximum power point $\left(V_\mathrm{mp},I_\mathrm{mp} \right)$. In this context, to study the I-V curves, the single-diode model (SDM) is often used. In this manuscript, we present a practical approach for determining the parameters domain of the SDM given a set of cardinal points. An in-depth mathematical analysis showed that the SDM must satisfy the following inequalities $\frac{V_\mathrm{oc}}{2} < V_\mathrm{mp} &lt; V_\mathrm{oc}$ and $\frac{I_\mathrm{sc}}{2} < I_\mathrm{mp} < I_\mathrm{sc}$. Then, it is possible to implicitly represent the SDM by a single parameter and, consequently, to determine its domain. For this purpose, a fast open-source computational algorithm for the single parameter domain of the SDM is presented. The algorithm has been computer-tested using $40\,000$ synthetically generated maximum power points which are processed in about one minute of the CPU time on a standard laptop computer. Moreover, as practical applications, the databases from the California Energy Commission and the NREL are analyzed using the presented algorithm.

Keywords

Bibliographic record

BibTeX Citation

@article{CrdenasBravo2024parametersdomain,
  author = {Cárdenas-Bravo, C. and Dutykh, D. and Lespinats, S.},
  title = {On the parameters domain of the single-diode model},
  journal = {Solar Energy},
  year = {2024},
  volume = {277},
  pages = {112718},
  doi = {10.1016/j.solener.2024.112718},
  abstract = {The current-voltage (I-V) curves of solar photovoltaic (PV) systems have been widely used as a tool to determine their electrical operation. Usually, I-V curves are described employing three cardinal points: the short-circuit point $\left(0,I_\mathrm{sc}\right)$, the open-circuit point $\left(V_\mathrm{oc},0\right)$, and the maximum power point $\left(V_\mathrm{mp},I_\mathrm{mp} \right)$. In this context, to study the I-V curves, the single-diode model (SDM) is often used. In this manuscript, we present a practical approach for determining the parameters domain of the SDM given a set of cardinal points. An in-depth mathematical analysis showed that the SDM must satisfy the following inequalities $\frac{V_\mathrm{oc}}{2} < V_\mathrm{mp} &lt; V_\mathrm{oc}$ and $\frac{I_\mathrm{sc}}{2} < I_\mathrm{mp} < I_\mathrm{sc}$. Then, it is possible to implicitly represent the SDM by a single parameter and, consequently, to determine its domain. For this purpose, a fast open-source computational algorithm for the single parameter domain of the SDM is presented. The algorithm has been computer-tested using $40\,000$ synthetically generated maximum power points which are processed in about one minute of the CPU time on a standard laptop computer. Moreover, as practical applications, the databases from the California Energy Commission and the NREL are analyzed using the presented algorithm.},
  keywords = {solar photovoltaic (PV) systems, open-circuit point, current-voltage (I-V) curves, single-diode model (SDM), computational algorithm, Mathematical analysis, Photovoltaic single-diode model (SDM), cardinal points, parameter domain, NREL, Photovoltaic systems, California Energy Commission, mathematical analysis, maximum power point, short-circuit point}
}