The net zero energy-building (Net-ZEB) concept promotes buildings that use the grid as the virtual energy storage medium. They exchange a large amount of energy with the grid and rely heavily on these energy exchanges to fulfill their yearly zero balance. Nevertheless, grid hosting capacities are limited and they can only accept a limited spread of such buildings. Large scale application of Net-ZEBs in the building stock can only be realized if well-designed energy solutions are in place. As current market trends shows strong growth in heat pump and photovoltaic applications, this article investigates the flexibility of such combinations that they could offer to the grid. For the purpose, two different hydraulic configurations of heat pump with thermal energy storage and four different control strategies are analyzed. Results shows that with a proper control: self-consumption of the building could be improved by almost 40%, the annual import bills could be reduced by 20% and hours of peak exchanges with the grid could be reduced by 30%. However, it is observed that the objectives are mostly contradictory, and optimizing one objective degrades the other. Overall, significant flexibility in Net-ZEBs is found achievable if a proper control is in place. (C) 2013 Elsevier B.V. All rights reserved.