  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 $V_\mathrm{oc}/2
<V_\mathrm{mp}<V_\mathrm{oc}$ and $I_\mathrm{sc}/2
<I_\mathrm{mp}<I_\mathrm{sc}$. 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.
