The net zero energy-building (Net-ZEB) concept promotes buildings that use the grid as the virtual energystorage medium. They exchange a large amount of energy with the grid and rely heavily on these energyexchanges to fulfill their yearly zero balance. Nevertheless, grid hosting capacities are limited and theycan only accept a limited spread of such buildings. Large scale application of Net-ZEBs in the buildingstock can only be realized if well-designed energy solutions are in place. As current market trends showsstrong growth in heat pump and photovoltaic applications, this article investigates the flexibility of suchcombinations that they could offer to the grid. For the purpose, two different hydraulic configurations ofheat pump with thermal energy storage and four different control strategies are analyzed. Results showsthat with a proper control: self-consumption of the building could be improved by almost 40%, the annualimport bills could be reduced by 20% and hours of peak exchanges with the grid could be reduced by30%. However, it is observed that the objectives are mostly contradictory, and optimizing one objectivedegrades the other. Overall, significant flexibility in Net-ZEBs is found achievable if a proper control is inplace.