  This two-part tutorial dives into the field of data-driven power flow
linearization (DPFL), a domain gaining increased attention. DPFL stands out for
its higher approximation accuracy, wide adaptability, and better ability to
implicitly incorporate the latest system attributes. This renders DPFL a
potentially superior option for managing the significant fluctuations from
renewable energy sources, a step towards realizing a more sustainable energy
future, by translating the higher model accuracy into increased economic
efficiency and less energy losses. To conduct a deep and rigorous
reexamination, this tutorial first classifies existing DPFL methods into DPFL
training algorithms and supportive techniques. Their mathematical models,
analytical solutions, capabilities, limitations, and generalizability are
systematically examined, discussed, and summarized. In addition, this tutorial
reviews existing DPFL experiments, examining the settings of test systems, the
fidelity of datasets, and the comparison made among a limited number of DPFL
methods. Further, this tutorial implements extensive numerical comparisons of
all existing DPFL methods (40 methods in total) and four classic physics-driven
approaches, focusing on their generalizability, applicability, accuracy, and
computational efficiency. Through these simulationmethodss, this tutorial aims
to reveal the actual performance of all the methods (including the performances
exposed to data noise or outliers), guiding the selection of appropriate
linearization methods. Furthermore, this tutorial discusses future directions
based on the theoretical and numerical insights gained. As the first part, this
paper reexamines DPFL theories, covering all the training algorithms and
supportive techniques. Capabilities, limitations, and aspects of
generalizability, which were previously unmentioned in the literature, have
been identified.
