Photovoltaic single-diode model parametrization

In this paper it is provided a new, the first one as far as the authors
knowledge, parametrization of the 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, through a transcendental equation with five parameters to be
determined, the voltage with the current. There are many methodologies
to extract the SDM parameters and, some of them, are based on obtaining
the best fit of a voltage-current data 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 I-V curve which is, in general, a hard
mathematical problem but, 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. The new parametrization
will allow to reduce the calculus of the Euclidean distance from any
point to the I-V curve to solve a single-variable equation. An in-depth
mathematical analysis will determine the number of possible candidates
where the Euclidean distance can be attained. Moreover, a full casuistry
together with a geometrical study based on the curvature of the I-V
curve and the Maximum Curvature Point, will allow to locate and classify
all these candidates, enabling to develop the first complete algorithm
able to compute the Euclidean distance from a point to an I-V curve in
any condition and, as a consequence, to perform a reliable ODR to obtain
the MLE of the SDM parameters. Using the obtained theoretical
background, it will be demonstrated that two existing methodologies to
compute the Euclidean distance fail in some conditions. It will be shown
that the proposed algorithm is even faster than the previous
methodologies despite it needs to verify with casuistry the right
selection of the solution.