The use of air source heat pumps is an efficient method to provide heat for space heating and domestic hot water in residential buildings, which cover roughly one third of the German domestic energy use. Capacity controlled heat pumps are gaining increased market share and provide high flexibility in operation. The possibility to use thermal storage to decouple thermal production and electric load from the heat pump can be used for operation strategies, hereby increasing the possibility to integrate electricity production from renewable energy sources. In the work presented, a range of operational strategies for capacity controlled heat pumps connected to a thermal storage in German multifamily houses are introduced and evaluated. The use cases include maximization of energy performance, cost minimization and utilization of on-site photovoltaic production. For optimal storage operation a model predictive control (MPC) approach using quadratic programming is presented together with simplified models of the multi-family house, a thermal storage and a capacity controlled air-to-water heat pump, the MPC creates a control signal to the heat pump. The resulting control signal is then applied to a detailed heat pump model to investigate the impact on the efficiency of the heat pump unit and thereby its electric energy consumption with different storage options.Results show that the MPC strategy is able to adapt to different objectives. One of the most important findings is that changing the objective towards a variable day-ahead-price-based operation leads to decreased heat pump efficiency but increases revenue. The sensitivity analysis towards storage size shows little influence in the range of sizes investigated.