Operational control strategies for the heating system and "smart" utilization of energy storage were developed and analyzed in a simulation based case study of a single-family house with exhaust air heat pump and photovoltaic system. Rule based control algorithms that can easily be implemented into modern heat pump controllers were developed with the aim to minimize final energy and maximize self-consumption by the use of the thermal storage of the building, the hot water tank and electrical storage. Short-term weather and electricity price forecasts are used in some of the algorithms. Heat supply from an exhaust air heat pump is limited by the ventilation flow rate fixed by building codes, and compact systems employ an electric heater as backup for both space heating and hot water. This heater plays an important role in the energy balance of the system. A typical system designed for new detached houses in Sweden was chosen for the study. This system, together with an independent photovoltaic system, was used as a base case and all results are compared to those for this base case system. TRNSYS 17 was used to model the building and system as well as the control algorithms, and special care was taken to model the use of the backup electric heater as this impacts significantly on final energy use. Results show that the developed algorithms can reduce final energy by 5-31% and the annual net cost for the end user by 3-26%, with the larger values being for systems with a battery storage. Moreover, the annual use of the backup electric heater can be decreased by 13-30% using the carefully designed algorithms.