The city of Stockholm is close to hitting the capacity limits of its power grid. As an additional challenge, electricity has been identified as a key resource to help the city to meet its environmental targets. This has pushed citizens to prefer power-based technologies, like heat pumps and electric vehicles, thus endangering the stability of the grid. The focus of this paper is on the district of Hammarby Sjöstad. Here, plans are set to switch from district heating to heat pumps. A previous study verified that this choice will cause overloadings on the electricity distribution grid. The present paper tackles this problem by proposing a new energy storage option. By considering the increasing share of electric vehicles, the potential of using the electricity stored in their batteries to support the grid is explored through technical performance simulations. The objective was to enable a bi-directional flow and use the electric vehicles’ (EVs)’ discharging to shave the peak demand caused by the heat pumps. It was found that this solution can eliminate overloadings up to 50%, with a 100% EV penetration. To overcome the mismatch between the availability of EVs and the overloadings’ occurrence, the minimum state of charge for discharging should be lower than 70%.