Recently, decentralized household photovoltaic (PV) systems have become more affordable and there is a tendency to decrease subsidies for the PV excess electricity fed into the grid. Therefore, there is growing interest in methods to increase the self-consumption (SC), which is the part of the electricity produced by PV and directly consumed on buildings. It has been found that battery storage is an effective way to achieve this. When there is a heat pump system installed, thermal energy storage using the thermal mass of the building or hot water tanks, can also be used to increase the household self-sufficiency and minimize the final energy use. The main aim of this thesis is to develop operational control strategies for the heating system of a single-family house with an exhaust air heat pump, a photovoltaic system and energy storage. In order to accomplish this a detailed system model was developed in TRNSYS 17, which includes a six-zone building model and the heat pump control. Moreover, these control strategies include short-term weather and price forecast services.  Another objective is to evaluate the impact on the benefit of these control strategies in terms of energy use and economic performance for a wide range of boundary conditions (country/climate, electricity prices, occupancy and appliance loads).  Results show that the control using a forecast of dynamic electricity price in most locations leads to greater final energy savings than those due to the control using thermal storage for excess PV production. The exception is Sweden, where the result is the opposite. Moreover, the addition of battery storage leads to greater decreases in final energy than the use of the thermal storage (TH mode), which is limited to the thermal mass of the building and small hot water tank of the compact heat pump. As far as the impact of the advanced control (combined use of TH and PRICE) on cost savings is concerned, savings (up to 175 €) are possible in Spain and in Germany. The design of the TH and PRICE mode show low computational complexity that can be easily implemented in existing heat pump controllers. Additionally, the PRICE mode should have no capital and running cost for the end user while the TH mode might require an external electricity meter. Another yet implication with the TH mode is the need to activate the room thermostatic valve.