Distributed energy resources (DERs) can provide flexibility and promote controllability for distribution networks. However, there are still some obstacles in the management of the small-capacity DERs. In this paper, an aggregated operation model of various heterogeneous DERs in peer-to-peer (P2P) energy trading is proposed. First, a supervised-learning assisted aggregation model of DERs is presented, which aims at estimating the aggregated parameters of heterogeneous DERs. Second, a P2P trading model is proposed for the aggregated DERs. The aggregators can trade with each other in a distributed manner so that privacy can be protected. Third, the fast alternating direction method of multipliers (F-ADMM) is utilized to accelerate the iteration process between the aggregators. Therefore, a quick decision can be made, and less information exchange is required between aggregators, which can reduce the communication burden. The effectiveness of the proposed methodology is verified in case studies.