The influence of different control strategies and boundary conditions on heat pump system performance are investigated in this study and the trade-off between complexity and performance of different controllers is addressed. For this purpose five different control approaches for a variable speed air source heat pump in a multi family house are compared for three different use-cases. The used controls differ in complexity and the use of external input data like price and weather forecasts. The use-cases are: Constant electricity prices, time variable electricity prices and PV self-consumption. Four different rule-based controllers are compared to a convex MPC approach, presented in this work. Results show that the MPC approach reduces annual operating cost by 6-11% for constant electricity prices and 6-16% in the case of variable electricity prices. Rule-based approaches lead to cost reductions of 2-4%. MPC could increases PV self-consumption from 56% to 58% up to 64-71%. The rule base approaches are found computationally less demanding and easier to design. However fine-tuning has been considerable work and with changing boundary conditions rules had to be readjusted. It showed that increasing thermal storage without MPC is not beneficial and optimised controls are a prerequisite to benefit from increased storage sizes. (C) 2017 Elsevier Ltd. All rights reserved.