In the context of the energy transition, energy communities are gaining increasing attention all over the world, in recent years. By participating in an energy community, prosumers may take a leading role in the energy transition and improve the self-consumption of renewable energy produced inside the community. Prosumers can carry out energy exchanges inside the energy community and provide ancillary services to the system operators, thus contributing to improve the efficiency and stability of the grid. A novel scalable, privacy-preserving, and real-time distributed parallel optimization is proposed to manage a large-scale energy community, considering energy exchanges inside the community according to the model of virtual self-consumption and the provision of ancillary services. The proposed method preserves the privacy of prosumers and allows the assessment of the impact of energy exchanges on the ancillary services provided by an energy community. Simulation results confirmed that the proposed method is superior in terms of privacy if compared with the equivalent centralized optimization and that it has a convergence rate higher than that of the splitting conic solver (SCS).