Currently, the use of air-source heat pumps (ASHP) in combination with a photovoltaic (PV) installation is a very promising option for a necessary and urgent energy transformation in European countries. It is extremely important to develop solutions that will help maximize the use of energy generated from renewable energy sources. Such issues include the problem of insufficient use of generated electricity in PV on-grid microinstallations in residential buildings. This paper’s aim is to analyse the results of a one-year-round operation of a PV array grid-connected hybrid installation with ASHP for domestic hot water preparation in a residential building in Cracow, Poland, in the context of increasing self-consumption of PV energy. Models of systems are built and simulated in the Transient System Simulation software in release 18.05.0001. Simulations were carried out for different scenarios involving different building electricity consumption profiles, PV system capacity and specified runtime management of ASHP. The novelty of this study lies in the evaluation of the impact of a certain range of conditions on the energy performance of the system and in particular on increasing self-consumption. The results showed that the use of ASHP, with specified runtime management, results in an increase in monthly self-consumption values from 7% to 18%, and annual values up to 13%. Moreover, determining the appropriate size of the used PV system depending on whether it is present ASHP in the installation is crucial to increasing the value of this parameter. Overall, this study provides valuable insights into the potential benefits of PV panels and ASHP operating together, particularly on self-consumption values.