# American Institute of Mathematical Sciences

October  2016, 3(4): 371-398. doi: 10.3934/jdg.2016020

## Optimal strategies for operating energy storage in an arbitrage or smoothing market

 1 Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, United Kingdom, United Kingdom 2 Economics Department, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, United Kingdom

Received  March 2016 Revised  September 2016 Published  October 2016

We characterize cost-minimizing operating strategies for an energy store over a given interval of time $[0,T]$. The cost functional here can represent, for example, a traditional economic cost or a penalty for time-variation of the output from a storage-assisted wind farm or more general imbalance between supply and demand. Our analysis allows for leakage, operating inefficiencies and general cost functionals. In the case where the cost of a store depends only on its instantaneous power output (or input), we present an algorithm to determine the optimal strategies. A key feature is that this algorithm is localized in time, in the sense that the action of the store at a time $t\in[0,T]$ requires cost information over only some usually much shorter subinterval of time $[t,t_k]\subset[t,T].$
Citation: Lisa C Flatley, Robert S MacKay, Michael Waterson. Optimal strategies for operating energy storage in an arbitrage or smoothing market. Journal of Dynamics & Games, 2016, 3 (4) : 371-398. doi: 10.3934/jdg.2016020
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##### References:
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