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The main challenge when driving heat pumps by PV-electricity is balancing differing electrical and thermal demands. In this article, a heuristic method for optimal operation of a heat pump driven by a maximum share of PV-electricity is presented. For this purpose, the (DHW) are activated in order shift the operation of the heat pump to times of PV-generation. The system under consideration refers to thermal and electrical demands of a single family house. It consists of a heat pump, a thermal energy storage for DHW and of grid connected heating and generation of domestic hot water, the heat pump runs with two different supply temperatures and thereby achieving a maximum overall COP. Within the algorithm for optimization a set of heuristic rules is developed in a way that the operational characteristics of the heat pump in terms of minimum running and stopping times are met as well as the limiting constraints of upper and lower limits of room temperature and energy content of electricity generated, a varying number of heat pump schedules fulfilling the bundary conditions are created. Finally, the schedule offering the maximum on-site utilization of PV-electricity with a minimum number of starts of the heat pump, which serves as secondary condition, is selected. Yearly simulations of this combination have been carried out. Initial results of this method indicate a significant rise in on-site consumption of the PV-electricity and heating demand fulfilment by renewable electricity with no need for a massive TES for the heating system in terms of a big water tank.