Control of Two Energy Storage Units with Market Impact: Lagrangian Approach and Horizons

Miguel F Anjos, Albert Solà Vilalta, James R. Cruise

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Energy storage and demand-side response will play an increasingly important role in the future electricity system. We extend previous results on a single energy storage unit to the management of two energy storage units cooperating for the purpose of price arbitrage. We consider a deterministic dynamic programming model for the cooperative problem, which accounts for market impact. We develop the Lagrangian theory and present a new algorithm to identify pairs of strategies. While we are not able to prove that the algorithm provides optimal strategies, we give strong numerical evidence in favour of it. Furthermore, the Lagrangian approach makes it possible to identify decision and forecast horizons, the latter being a time beyond which it is not necessary to look in order to determine the present optimal action. In practice, this allows for real-time reoptimization, with both horizons being of the order of days.
Index Terms-control, two storage units, arbitrage, pricemaker, market impact, energy, Lagrangian.
Original languageEnglish
Title of host publication2020 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS)
PublisherIEEE Xplore
ISBN (Electronic)978-1-7281-2822-1
ISBN (Print)978-1-7281-2823-8
Publication statusPublished - 1 Sep 2020


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