  Efficient residential sector coupling plays a key role in supporting the
energy transition. In this study, we analyze the structural properties
associated with the optimal control of a home energy management system and the
effects of common technological configurations and objectives. We conduct this
study by modeling a representative building with a modulating air-sourced heat
pump, a photovoltaic (PV) system, a battery, and thermal storage systems for
floor heating and hot-water supply. In addition, we allow grid feed-in by
assuming fixed feed-in tariffs and consider user comfort. In our numerical
analysis, we find that the battery, naturally, is the essential building block
for improving self-sufficiency. However, in order to use the PV surplus
efficiently grid feed-in is necessary. The commonly considered objective of
maximizing self-consumption is not economically viable under the given tariff
structure; however, close-to-optimal performance and significant reduction in
solution times can be achieved by maximizing self-sufficiency. Based on optimal
control and considering seasonal effects, the dominant order of PV distribution
and the target states of charge of the storage systems can be derived. Using a
rolling horizon approach, the solution time can be reduced to less than 1 min
(achieving a time resolution of 1 h per year). By evaluating the value of
information, we find that the common value of 24 h for the prediction and
control horizons results in unintended but avoidable end-of-horizon effects.
Our input data and mixed-integer linear model developed using the Julia JuMP
programming language are available in an open-source manner.
