There exists a gap between the flexibility needed within the German energy system and the flexibility being actually provided. Heat pumps can be seen to be the core technology to couple the heating and electricity sectors and thereby provide flexibility to the system. We contribute to the scientific discussion by conducting validated simulations of realistic and easily applicable heat pump control methods that are implemented to provide flexibility and not limited to pilot trials. We assess effects on energy efficiency and economic potentials compared to standard reference control algorithms. The flexible control schemes under investigation can be divided into two categories: time-of-use based controls and spot market price based control. We investigate both control types for current market conditions and for future scenarios of the German electricity market in 2030. In our study, we introduce a validated MODELICA simulation model of a ground source heat pump and market models to evaluate financial consequences. Our results indicate that efficiency losses occur for all investigated control methods. Further, financial gains for heat pump owners could not be achieved with current price structures, only distinct future scenarios with high shares of fluctuating renewables and low electricity demand led to enough price fluctuations to allow for electricity cost savings. Thus, we conclude that (1) heat pump owners need to weigh pros and cons of currently applicable, flexible heat pump controls carefully before their implementation, (2) there exists a need for heat pump manufacturers to further develop controllers that are capable of more advanced control schemes on large-scale, (3) policy makers should establish market mechanisms to ensure that heat pump owners are provided with incentives to use flexible controls, and (4) scientific modelers should not only focus on the development of highly elaborated control methods, but also investigate their transferability to large-scale real-world applications in the near future.