The increasing number of prosumers and the accompanying greater use of decentralised energy resources (DERs) bring new opportunities and challenges for the traditional electricity systems and the electricity markets. Microgrids, virtual power plants (VPPs), peer-to-peer (P2P) trading and federated power plants (FPPs) propose different schemes for prosumer coordination and have the potential of becoming the new paradigm of electricity market and power system operation. This paper proposes a P2P trading scheme for energy communities that negotiates power flows between participating prosumers with insufficient renewable power supply and prosumers with surplus supply in such a way that the community welfare is maximized while avoiding critical grid conditions. For this purpose, the proposed scheme is based on an Optimal Power Flow (OPF) problem with a Multi-Bilateral Economic Dispatch (MBED) formulation as an objective function. The solution is realized in a fully decentralized manner on the basis of the Relaxed Consensus + Innovations (RCI) algorithm. Network security is ensured by a tariff-based system organized by a network agent that makes use of product differentiation capabilities of the RCI algorithm. It is found that the proposed mechanism accurately finds and prevents hazardous network operations, such as over-voltage in grid buses, while successfully providing economic value to prosumers’ renewable generation within the scope of a P2P, free market.