Electricity management systems are experiencing significant challenges due to the increased penetration of distributed energy resources. Electricity flows in distribution networks are transforming from unidirectional to bi-directional form. Consumers are transitioning to prosumers with different characteristics, where they take more active roles in electricity generation and consumption. Aggregators are vital financial intermediary agents in the power system transitions, as they could aggregate energy profiles of prosumers. The market competition between aggregators and interactions between prosumers and aggregators are complex and dynamic, which requires a holistic framework to model the market competition. This paper proposes an intelligent aggregation framework with edge computing, enabling decentralized competition for multiple aggregators and prosumers, which can be solved with a graph-based consensus algorithm. This study mathematically proves the proposed algorithm's convergence guarantee and convergence rate. In addition, the proposed framework is applied to an open-source dataset to demonstrate its applicability. Lastly, a benchmark analysis is conducted to show that the proposed algorithm has better communication complexity than the benchmark algorithms
