This paper presents the effect which the utilization of excess power in Power-to-Heat units has on an energy system which is fully supplied by renewables. For this, a possible future German integrated energy system consisting of the power, heat and gas sectors is modeled using the TransiEnt Library in Modelica R. The first system contains electric energy storage units, Power-toGas as well as Gas-to-Power plants and hot water storage units as energy storage technologies. The heat supply does not use excess power, and an option to curtail renewable power generation is added. The system costs are optimized by using simplified models in MATLAB R and designed in Modelica afterwards to include the dynamic effects. In a second system, excess power can also be used in existing electric heat pumps and in a third system as well in existing electric heating rods installed in the hot water storage tanks instead of curtailing renewable energy generation. This reduces the component sizes and thus the cost of the system because only control has to be added to enable this behavior.