American Institute of Mathematical Sciences

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

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

Lisa C Flatley 1, , Robert S MacKay 1, and  Michael Waterson 2,

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 $[t,t_k]\subset[t,T].$
Keywords: energy storage, Dynamic optimization, optimal localized algorithm..
Mathematics Subject Classification: Primary: 49K30; Secondary: 93C1.
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
References:
[1]

, Compressed Air Energy Storage Power Plants,, BINE Informationsdienst projektinfo 05/07., ().   Google Scholar

[2]

, ADELE - Adiabatic Compressed-Air Energy Storage for Electricity Supply,, RWE Power., ().   Google Scholar

[3]

, \url{https://www.elexonportal.co.uk/}, ().   Google Scholar

[4]

, Energy Storage and Management Study,, AEA, (2010).   Google Scholar

[5]

, Options for low-carbon power sector flexibility to 2050 - a report to the Committee on Climate Change,, Pöyry, (2010).   Google Scholar

[6]

, Study of Compressed Air Energy Storage with Grid and Photovoltaic Energy Generation, Draft Final Report - for Arizona Public Service Company,, Arizona Research Institute for Solar Energy (AZTISE), (2010).   Google Scholar

[7]

M. Aunedi, N. Brandon, D. Jackravut, D. Predrag, D. Pujianto, R. Sansom, G. Strbac, A. Sturt, F. Teng and V. Yufit, Strategic Assessment of the Role and Value of Energy Storage Systems in the UK Low Carbon Energy Future - Report for Carbon Trust, (2012). Google Scholar

[8]

M. Black and G. Strbac, Value of bulk energy storage for managing wind power fluctuations, IEEE Transactions on Energy Conversion, 22 (2007), 197-205. doi: 10.1109/TEC.2006.889619.  Google Scholar

[9]

J. P. Barton and D. G. Infield, Energy storage and its use with intermittent renewable energy, IEEE Transactions on Energy Conversion, 19 (2004), 441-448. doi: 10.1109/TEC.2003.822305.  Google Scholar

[10]

J. Cruise, L. C. Flatley, R. Gibbens and S. Zachary, Optimal Control of Storage Incorporating Market Impact and with Energy Applications, (2015), arXiv:1406.3653v2. Google Scholar

[11]

J. Cruise, L. C. Flatley and S. Zachary, Impact of Storage Competition on Energy Markets, working paper, (2016), https://arxiv.org/abs/1606.05361. Google Scholar

[12]

A. K. Dixit and R. S. Pindyck, Investment Under Uncertainty, Princeton UP, (1994). Google Scholar

[13]

M. Giulietti, L. Grossi and M. Waterson, Price transmission in the UK electricity market: Was NETA beneficial?, Energy Economics, 32 (2010), 1165-1174. doi: 10.1016/j.eneco.2010.01.008.  Google Scholar

[14]

P. Grünewald, T. Cockerill, M. Contestabile and P. Pearson, The role of large scale storage in a GB low carbon energy future: Issues and policy challenges, Energy Policy, 39 (2011), 4807-4815. Google Scholar

[15]

N. Löhndorf and S. Minner, Optimal day-ahead trading and storage of renewable energies - an approximate dynamic programming approach, Energy Syst., 1 (2010), 61-77. Google Scholar

[16]

D. J. C. MacKay, Sustainable Energy - without the hot air, Am. J. Phys., 78 (2010), p222. doi: 10.1119/1.3273852.  Google Scholar

[17]

R. S. MacKay, S. Slijepčević and J. Stark, Optimal scheduling in a periodic environment, Nonlinearity, 13 (2000), 257-297. doi: 10.1088/0951-7715/13/1/313.  Google Scholar

[18]

A. J. Pimm and S. D. Garvey, The economics of hybrid energy storage plant, International Journal of Environmental Studies, (2014), 787-795. doi: 10.1080/00207233.2014.948321.  Google Scholar

show all references

References:
[1]

, Compressed Air Energy Storage Power Plants,, BINE Informationsdienst projektinfo 05/07., ().   Google Scholar

[2]

, ADELE - Adiabatic Compressed-Air Energy Storage for Electricity Supply,, RWE Power., ().   Google Scholar

[3]

, \url{https://www.elexonportal.co.uk/}, ().   Google Scholar

[4]

, Energy Storage and Management Study,, AEA, (2010).   Google Scholar

[5]

, Options for low-carbon power sector flexibility to 2050 - a report to the Committee on Climate Change,, Pöyry, (2010).   Google Scholar

[6]

, Study of Compressed Air Energy Storage with Grid and Photovoltaic Energy Generation, Draft Final Report - for Arizona Public Service Company,, Arizona Research Institute for Solar Energy (AZTISE), (2010).   Google Scholar

[7]

M. Aunedi, N. Brandon, D. Jackravut, D. Predrag, D. Pujianto, R. Sansom, G. Strbac, A. Sturt, F. Teng and V. Yufit, Strategic Assessment of the Role and Value of Energy Storage Systems in the UK Low Carbon Energy Future - Report for Carbon Trust, (2012). Google Scholar

[8]

M. Black and G. Strbac, Value of bulk energy storage for managing wind power fluctuations, IEEE Transactions on Energy Conversion, 22 (2007), 197-205. doi: 10.1109/TEC.2006.889619.  Google Scholar

[9]

J. P. Barton and D. G. Infield, Energy storage and its use with intermittent renewable energy, IEEE Transactions on Energy Conversion, 19 (2004), 441-448. doi: 10.1109/TEC.2003.822305.  Google Scholar

[10]

J. Cruise, L. C. Flatley, R. Gibbens and S. Zachary, Optimal Control of Storage Incorporating Market Impact and with Energy Applications, (2015), arXiv:1406.3653v2. Google Scholar

[11]

J. Cruise, L. C. Flatley and S. Zachary, Impact of Storage Competition on Energy Markets, working paper, (2016), https://arxiv.org/abs/1606.05361. Google Scholar

[12]

A. K. Dixit and R. S. Pindyck, Investment Under Uncertainty, Princeton UP, (1994). Google Scholar

[13]

M. Giulietti, L. Grossi and M. Waterson, Price transmission in the UK electricity market: Was NETA beneficial?, Energy Economics, 32 (2010), 1165-1174. doi: 10.1016/j.eneco.2010.01.008.  Google Scholar

[14]

P. Grünewald, T. Cockerill, M. Contestabile and P. Pearson, The role of large scale storage in a GB low carbon energy future: Issues and policy challenges, Energy Policy, 39 (2011), 4807-4815. Google Scholar

[15]

N. Löhndorf and S. Minner, Optimal day-ahead trading and storage of renewable energies - an approximate dynamic programming approach, Energy Syst., 1 (2010), 61-77. Google Scholar

[16]

D. J. C. MacKay, Sustainable Energy - without the hot air, Am. J. Phys., 78 (2010), p222. doi: 10.1119/1.3273852.  Google Scholar

[17]

R. S. MacKay, S. Slijepčević and J. Stark, Optimal scheduling in a periodic environment, Nonlinearity, 13 (2000), 257-297. doi: 10.1088/0951-7715/13/1/313.  Google Scholar

[18]

A. J. Pimm and S. D. Garvey, The economics of hybrid energy storage plant, International Journal of Environmental Studies, (2014), 787-795. doi: 10.1080/00207233.2014.948321.  Google Scholar

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