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Heat pumps are a vital element for reaching the greenhouse gas (GHG) reduction targets in the heating sector, but their system integration requires smart control approaches. In this paper, we first offer a comprehensive literature review and definition of the term control for the described context. Additionally, we present a control approach, which consists of an optimal scheduling module coupled with a detailed energy system simulation module. The aim of this integrated two part control approach is to improve the performance of an energy system equipped with a heat pump, while recognizing the technical boundaries of the energy system in full detail. By applying this control to a typical family household situation, we illustrate that this integrated approach results in a more realistic heat pump operation and thus a more realistic assessment of the control performance, while still achieving lower operational costs.