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
References:
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[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).

[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)., (2012).

[8]

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

[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. doi: 10.1109/TEC.2003.822305.

[10]

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

[11]

J. Cruise, L. C. Flatley and S. Zachary, Impact of Storage Competition on Energy Markets,, working paper, (2016).

[12]

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

[13]

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

[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.

[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.

[16]

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

[17]

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

[18]

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

show all references

References:
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[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).

[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)., (2012).

[8]

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

[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. doi: 10.1109/TEC.2003.822305.

[10]

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

[11]

J. Cruise, L. C. Flatley and S. Zachary, Impact of Storage Competition on Energy Markets,, working paper, (2016).

[12]

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

[13]

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

[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.

[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.

[16]

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

[17]

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

[18]

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

[1]

Jian-Wu Xue, Xiao-Kun Xu, Feng Zhang. Big data dynamic compressive sensing system architecture and optimization algorithm for internet of things. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1401-1414. doi: 10.3934/dcdss.2015.8.1401

[2]

Ali Fuat Alkaya, Dindar Oz. An optimal algorithm for the obstacle neutralization problem. Journal of Industrial & Management Optimization, 2017, 13 (2) : 835-856. doi: 10.3934/jimo.2016049

[3]

Xiangyu Gao, Yong Sun. A new heuristic algorithm for laser antimissile strategy optimization. Journal of Industrial & Management Optimization, 2012, 8 (2) : 457-468. doi: 10.3934/jimo.2012.8.457

[4]

M. Montaz Ali. A recursive topographical differential evolution algorithm for potential energy minimization. Journal of Industrial & Management Optimization, 2010, 6 (1) : 29-46. doi: 10.3934/jimo.2010.6.29

[5]

Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1

[6]

M. Delgado Pineda, E. A. Galperin, P. Jiménez Guerra. MAPLE code of the cubic algorithm for multiobjective optimization with box constraints. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 407-424. doi: 10.3934/naco.2013.3.407

[7]

Lipu Zhang, Yinghong Xu, Zhengjing Jin. An efficient algorithm for convex quadratic semi-definite optimization. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 129-144. doi: 10.3934/naco.2012.2.129

[8]

Paul B. Hermanns, Nguyen Van Thoai. Global optimization algorithm for solving bilevel programming problems with quadratic lower levels. Journal of Industrial & Management Optimization, 2010, 6 (1) : 177-196. doi: 10.3934/jimo.2010.6.177

[9]

Chunlin Hao, Xinwei Liu. Global convergence of an SQP algorithm for nonlinear optimization with overdetermined constraints. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 19-29. doi: 10.3934/naco.2012.2.19

[10]

Chia-Huang Wu, Kuo-Hsiung Wang, Jau-Chuan Ke, Jyh-Bin Ke. A heuristic algorithm for the optimization of M/M/$s$ queue with multiple working vacations. Journal of Industrial & Management Optimization, 2012, 8 (1) : 1-17. doi: 10.3934/jimo.2012.8.1

[11]

Xin Zhang, Jie Wen, Qin Ni. Subspace trust-region algorithm with conic model for unconstrained optimization. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 223-234. doi: 10.3934/naco.2013.3.223

[12]

Nguyen Van Thoai. Decomposition branch and bound algorithm for optimization problems over efficient sets. Journal of Industrial & Management Optimization, 2008, 4 (4) : 647-660. doi: 10.3934/jimo.2008.4.647

[13]

Lianshuan Shi, Enmin Feng, Huanchun Sun, Zhaosheng Feng. A two-step algorithm for layout optimization of structures with discrete variables. Journal of Industrial & Management Optimization, 2007, 3 (3) : 543-552. doi: 10.3934/jimo.2007.3.543

[14]

Tran Ngoc Thang, Nguyen Thi Bach Kim. Outcome space algorithm for generalized multiplicative problems and optimization over the efficient set. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1417-1433. doi: 10.3934/jimo.2016.12.1417

[15]

Behrouz Kheirfam, Morteza Moslemi. On the extension of an arc-search interior-point algorithm for semidefinite optimization. Numerical Algebra, Control & Optimization, 2018, 8 (2) : 261-275. doi: 10.3934/naco.2018015

[16]

Bopeng Rao. Optimal energy decay rate in a damped Rayleigh beam. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 721-734. doi: 10.3934/dcds.1998.4.721

[17]

Bruce D. Craven, Sardar M. N. Islam. Dynamic optimization models in finance: Some extensions to the framework, models, and computation. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1129-1146. doi: 10.3934/jimo.2014.10.1129

[18]

Antonio Greco, Giovanni Porru. Optimization problems for the energy integral of p-Laplace equations. Conference Publications, 2013, 2013 (special) : 301-310. doi: 10.3934/proc.2013.2013.301

[19]

Jean-Paul Arnaout, Georges Arnaout, John El Khoury. Simulation and optimization of ant colony optimization algorithm for the stochastic uncapacitated location-allocation problem. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1215-1225. doi: 10.3934/jimo.2016.12.1215

[20]

Enkhbat Rentsen, J. Zhou, K. L. Teo. A global optimization approach to fractional optimal control. Journal of Industrial & Management Optimization, 2016, 12 (1) : 73-82. doi: 10.3934/jimo.2016.12.73

 Impact Factor: 

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (3)

[Back to Top]