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A linear function submission-based double auction (LFS-DA) mechanism for a regional electricity network is proposed in this paper. Each agent in the network is equipped with a battery and a generator. Each agent simultaneously becomes a producer and consumer of electricity, i.e., a prosumer, and trades electricity in the regional market at a variable price. In the LFS-DA, each agent uses linear demand and supply functions when they submit bids and asks to an auctioneer in the regional market. The LFS-DA can achieve an exact balance between electricity demand and supply for each time slot throughout the learning phase and was shown capable of solving the primal problem of maximizing the social welfare of the network without any central price setter, e.g., a utility or a large electricity company, in contrast with conventional real-time pricing (RTP). This paper presents a clarification of the relationship between the RTP algorithm derived on the basis of a dual decomposition framework and LFS-DA. Specifically, we proved that the changes in the price profile of the Energies 2015, 8 7382 LFS-DA mechanism are equal to those achieved by the RTP mechanism derived from the dual decomposition framework, except for a constant factor.

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