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This paper studies the optimal clearing problem for prosumers in peer-to-peer(P2P) energy markets. It is proved that if no trade weights are enforced andthe communication structure between successfully traded peers is connected,then the optimal clearing price and total traded powers in P2P market are thesame with that in the pool-based market. However, if such communicationstructure is unconnected, then the P2P market is clustered into smaller P2Pmarkets. If the trade weights are imposed, then the derived P2P marketsolutions can be significantly changed. Next, a novel decentralizedoptimization approach is proposed to derive a trading mechanism for P2Pmarkets, based on the alternating direction method of multipliers (ADMM) whichnaturally fits into the bidirectional trading in P2P energy systems andconverges reasonably fast. Analytical formulas of variable updates revealinsightful relations for each pair of prosumers on their individually tradedprices and powers with their total traded powers. Further, based on thoseformulas, decentralized learning schemes for tuning parameters of prosumerscost functions are proposed to attain successful trading with total tradedpower amount as desired. Case studies on a synthetic system and the IEEEEuropean Low Voltage Test Feeder are then carried out to verify the proposedapproaches.

Optimal Solution Analysis and Decentralized Mechanisms for Peer-to-Peer Energy Markets