  Most of the power-to-heat and thermal energy storage technologies are mature
and impact the European energy transition. However, detailed models of these
technologies are usually very complex, making it challenging to implement them
in large-scale energy models, where simplicity, e.g., linearity and appropriate
accuracy, are desirable due to computational limitations. In the literature,
the main power-to-heat and thermal energy storage technologies across all
sectors have not been clearly identified and characterized. Their potential
roles have not been fully discussed from the European perspective, and their
mathematical modeling equations have not been presented in a compiled form.
This paper contributes to the research gap in three main parts. First, it
identifies and classifies the major power-to-heat and thermal energy storage
technologies that are climate-neutral, efficient, and technologically matured
to supplement or substitute the current fossil fuel-based heating. The second
part presents the technology readiness levels of the identified technologies
and discusses their potential role in a sustainable European energy system. The
third part presents the mathematical modeling equations for the technologies in
large-scale optimization energy models. We identified electric heat pumps,
electric boilers, electric resistance heaters, and hybrid heating systems as
the most promising power-to-heat options. We grouped the most promising thermal
energy storage technologies under four major categories. Low-temperature
electric heat pumps, electric boilers, electric resistance heaters, and
sensible and latent heat storage show high technology readiness levels to
facilitate a large share of the heat demand. Finally, the mathematical
formulations capture the main effects of the identified technologies.
