With the proliferation of distributed energy resources (DERs), electricity consumers in virtual power plants (VPPs) are transitioning into prosumers and are encouraged to share surplus energy with peers. Nevertheless, large-scale energy sharing among thousands of prosumers may encounter communication-related challenges. Communication network congestion may result in a significant increase in the negotiation waiting time to reach a sharing agreement, and potentially risks exceeding the deadline of negotiation before the market gate closes, rendering energy sharing ineffective. This paper proposes an online partial-update algorithm for the alternating direction method of multipliers (ADMM)-based energy sharing. By restricting the update connection between the VPP and the prosumers, the algorithm selects a subset of the prosumers participating in ADMM updates each round, hence eliminating the excessively long waiting time caused by communication congestion. Considering the delay induced by massive prosumer communication access requests, a method for determining the optimal number of prosumers participating in updates is provided. To fully utilize the limited update opportunities, a fair and efficient prosumer update scheduling policy is designed. The VPP schedules the participation of prosumers in updates such that the convergence-critical prosumers receive higher priority, yet every prosumer is granted sufficient update opportunities. Additionally, the extra computation and communication overheads brought by the prosumer scheduling are minimized, allowing the whole algorithm to be executed in real time. Numerical studies are conducted to validate the effectiveness of the algorithm and its performance in reducing the overall convergence time.@en