Significant installations of individual heat pumps are expected in future energy systems due to their economic competitiveness. This case study of the Danish energy system in 2020 with 50% wind power shows that individual heat pumps and heat storages can contribute to the integration of wind power. Heat accumulation tanks and passive heat storage in the construction are investigated as two alternative storage options in terms of their ability to increase wind power utilisation and to provide cost-effective fuel savings. Results show that passive heat storage can enable equivalent to larger reductions in excess electricity production and fuel consumption than heat accumulation tanks. Moreover, passive heat storage is found to be significantly more cost-effective than heat accumulation tanks. In terms of reducing fuel consumption of the energy system, the installation of heat pumps is the most important step. Adding heat storages only moderately reduces the fuel consumption. Model development has been made to facilitate a technical optimisation of individual heat pumps and heat storages in integration with the energy system.