Efficient Auction Games pp 139-171 | Cite as

# Economic Operations of Microgrid Systems Under Auction Games

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## Abstract

This chapter studies the economic operations of the microgrid in a distributed way such that the operational schedule of each of units, like generators, load units, storage units, etc., in a microgrid system is implemented by autonomous agents. In this problem, the divisible resource is electricity resource in the system and we apply the progressive second price (PSP) auction mechanism to efficiently allocate the resource. Considering the economic operation for the microgrid systems, the generators play as sellers to supply energy and the load units play as the buyers to consume energy, while a storage unit, like battery, supercapacitor, etc., may transit between buyer and seller, such that it is a buyer when it charges and becomes a seller when it discharges. This problem is different from the double-sided auction game specified in Chap. 3 due to the existence of the storage units. Furthermore, when the microgrid is in a connected mode, each individual unit competes against not only the other individual units in the microgrid but also the exogenous main grid possessing fixed electricity price and infinite trade capacity; that is to say, the auctioneer assigns the electricity among all individual units and the main grid with respect to the submitted bid strategies of all individual units in the microgrid in an economic way. Due to these distinct characteristics, the underlying auction games are distinct from those studied in the literature. We show that under mild conditions, the efficient economic operation strategy is a Nash equilibrium (NE) for the PSP auction games, and propose a distributed algorithm under which the system can converge to a NE. We also show that the performance of worst NE can be bounded with respect to the system parameters, say the energy trading price with the main grid, and based upon that, the implemented NE is unique and efficient under some conditions.

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