The 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 by means of three cardinal points: the short-circuit point
( 0 , I sc ) , the open-circuit point ( V oc , 0 ) , and the maximum
power point ( V mp , I mp ) . 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 cardinal points must satisfy the following
inequalities V oc / 2 < V mp < V oc and I sc / 2
< I mp < I sc . Then, it is possible to implicitly
represent the SDM by means of one single parameter in a thoroughly
chosen coordinate space. Based on these theoretical results, a fast
computational algorithm for calculating the SDM parameters limits is
proposed. 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 a practical application, the California Energy Commission
database is analyzed using the proposed algorithm.