The Optimal Control of Storage for Arbitrage and Buffering, with Energy Applications

  • James Cruise
  • Stan ZacharyEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 254)


We study the optimal control of storage which is used for both arbitrage and buffering against unexpected events (shocks), with particular applications to the control of energy systems in a stochastic and typically time-heterogeneous environment. Our philosophy is that of viewing the problem as being formally one of stochastic dynamic programming (SDP), but of recasting the SDP recursion in terms of functions which, if known, would reduce the associated optimisation problem to one which is deterministic, except that it must be re-solved at times when shocks occur. In the case of a perfectly efficient store facing linear buying and selling costs the functions required for this approach may be determined exactly; otherwise they may typically be estimated to good approximation. We provide characterisations of optimal control policies. We consider also the associated deterministic optimisation problem, outlining an approach to its solution which is both computationally tractable and—through the identification of a running forecast horizon—suitable for the management of systems over indefinitely extended periods of time. We give examples based on Great Britain electricity price data.


Storage Buffering Optimisation Control 



The authors acknowledge the support of the Engineering and Physical Sciences Research Council for the programme (EPSRC grant EP/I017054/1) under which the present research is carried out. They also acknowledge the benefit of very helpful discussions with numerous colleagues, notably: Janusz Bialek, Chris Dent, Lisa Flatley, Richard Gibbens, Frank Kelly and Phil Taylor. They are further most grateful to the referees for many insightful comments and suggestions which have considerably improved the exposition of the paper.


  1. 1.
    M. Arnold, G. Andersson, Model predictive control of energy storage including uncertain forecasts, in Proceedings of the 17th Power Systems Computation Conference (2011)Google Scholar
  2. 2.
    J.P. Barton, D.G. Infield, Energy storage and its use with intermittent renewable energy. IEEE Trans. Energy Convers. 19(2), 441–448 (2004)CrossRefGoogle Scholar
  3. 3.
    J.P. Barton, D.G. Infield, A probabilistic method for calculating the usefulness of a store with finite energy capacity for smoothing electricity generation from wind and solar power. J. Power Sources 162, 943–948 (2006)CrossRefGoogle Scholar
  4. 4.
    A.I. Bejan, R.J. Gibbens, F.P. Kelly, Statistical aspects of storage systems modelling in energy networks, in 46th Annual Conference on Information Sciences and Systems (invited session on Optimization of Communication Networks), Princeton University, USA, 2012Google Scholar
  5. 5.
    R. Bellman, On the theory of dynamic programming–a warehousing problem. Manag. Sci. 2(3), 272–275 (1956)MathSciNetCrossRefGoogle Scholar
  6. 6.
    A. Bernstein, L. Reyes-Chamorro, J.-Y. Le Boudec, M. Paolone, A composable method for real-time control of active distribution networks with explicit power setpoints. Part I: Framework. Electr. Power Syst. Res. 125, 254–264 (2015)CrossRefGoogle Scholar
  7. 7.
    R. Billinton, R.N. Allan, Reliability Evaluation of Power Systems, 2nd edn. (Springer, Berlin, 1996)CrossRefGoogle Scholar
  8. 8.
    A.S. Cahn, The warehouse problem. Bull. Am. Math. Soc. 54(11), 1073–1073 (1948)Google Scholar
  9. 9.
    E.D. Castronuovo, J.A. Peças Lopes, Optimal operation and hydro storage sizing of a wind power plant. Int. J. Electr. Power Energy Syst. 26(10), 771–778 (2004)CrossRefGoogle Scholar
  10. 10.
    J.R. Cruise, L.C. Flatley, R.J. Gibbens, S. Zachary, Control of energy storage with market impact: Lagrangian approach and horizons. Oper. Res. (2018). To appearGoogle Scholar
  11. 11.
    J.R. Cruise, L.C. Flatley, S. Zachary, Impact of storage competition on energy markets. Eur. J. Oper. Res. (2018). To appearGoogle Scholar
  12. 12.
    P. Denholm, R. Sioshansi, The value of compressed air energy storage with wind in transmission-constrained electric power systems. Energy Policy 37(8), 3149–3158 (2009)CrossRefGoogle Scholar
  13. 13.
  14. 14.
    S.E. Dreyfus, An analytic solution of the warehouse problem. Manag. Sci. 4(1), 99–104 (1957)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Electricity balancing services, National Audit Office Briefing, May 2014,
  16. 16.
    N.G. Gast, D.-C. Tomozei, J.-Y. Le Boudec, Optimal storage policies with wind forecast uncertainties, in Greenmetrics 2012, Imperial College, London, UK, 2012CrossRefGoogle Scholar
  17. 17.
    P. Harsha, M. Dahleh, Optimal management and sizing of energy storage under dynamic pricing for the efficient integration of renewable Energy. IEEE Trans. Power Syst. 30(3), 1164–1181 (2015)CrossRefGoogle Scholar
  18. 18.
    S.D. Howell, P.W. Duck, A. Hazel, P.V. Johnson, H. Pinto, G. Strbac, N. Proudlove, M. Black, A partial differential equation system for modelling stochastic storage in physical systems with applications to wind power generation. IMA J. Manag. Math. 22, 231–252 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Y. Huang, S. Mao, R.M. Nelms, Adaptive electricity scheduling in microgrids, in Proceedings of IEEE INFOCOM, Turin, Italy, 2013Google Scholar
  20. 20.
    M. Korpaas, A.T. Holen, R. Hildrum, Operation and sizing of energy storage for wind power plants in a market system. Int. J. Electr. Power Energy Syst. 25(8), 599–606 (2003)CrossRefGoogle Scholar
  21. 21.
    I. Koutsopoulos, V. Hatzi, L. Tassiulas, Optimal energy storage control policies for the smart power grid, in Proceedings of IEEE SmartGridComm (2011), pp. 475–480Google Scholar
  22. 22.
    G. Lai, F. Margot, N. Secomandi, An approximate dynamic programming approach to benchmark practice-based heuristics for natural gas storage valuation. Oper. Res. 58(3), 564–582 (2010)MathSciNetCrossRefGoogle Scholar
  23. 23.
    O. Megel, J.L. Mathieu, G. Andersson, Maximizing the potential of energy storage to provide fast frequency control, in IEEE PES ISGT Europe 2013 (IEEE, 2013), pp. 1–5Google Scholar
  24. 24.
    A. Oudalov, D. Chartouni, C. Ohler, Optimizing a battery energy storage system for primary frequency control. IEEE Trans. Power Syst. 22(3), 1259–1266 (2007)CrossRefGoogle Scholar
  25. 25.
    D. Pudjianto, M. Aunedi, P. Djapic, G. Strbac, Whole-systems assessment of the value of energy storage in low-carbon electricity systems. IEEE Trans. Smart Grid 5, 1098–1109 (2014)CrossRefGoogle Scholar
  26. 26.
    N. Richmond, P. Jacko, A.M. Makowski, Optimal planning of slow-ramping power production in energy systems with renewables forecasts and limited storage, in 2014 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS) (IEEE, 2014), pp. 1–6Google Scholar
  27. 27.
    N. Secomandi, Optimal commodity trading with a capacitated storage asset. Manag. Sci. 56(3), 449–467 (2010)MathSciNetCrossRefGoogle Scholar
  28. 28.
    N. Secomandi, Merchant commodity storage practice revisited. Oper. Res. 63(5), 1131–1143 (2015)MathSciNetCrossRefGoogle Scholar
  29. 29.
    R. Sioshansi, P. Denholm, T. Jenkin, J. Weiss, Estimating the value of electricity storage in PJM: arbitrage and some welfare effects. Energy Econ. 31(2), 269–277 (2009)CrossRefGoogle Scholar
  30. 30.
    F. Teng, J. Miles, A. Thomson, G. Strbac, N. Brandon, D. Pudjianto, Potential value of energy storage in the UK electricity system. Proc. ICE Energy 168(2), 107–117 (2015)Google Scholar
  31. 31.
  32. 32.
    A. Tuohy, M. O’Malley, Impact of pumped storage on power systems with increasing wind penetration, in 2009 IEEE Power & Energy Society General Meeting (IEEE, 2009), pp. 1–8Google Scholar
  33. 33.
    P.M. van de Ven, N. Hegde, L. Massoulié, T. Salonidis, Optimal control of end-user energy storage. IEEE Trans. Smart Grid 4, 789–797 (2013)CrossRefGoogle Scholar
  34. 34.
    R. Walawalkar, J. Apt, R. Mancini, Economics of electric energy storage for energy arbitrage and regulation in New York. Energy Policy 35(4), 2558–2568 (2007)CrossRefGoogle Scholar
  35. 35.
    J.C. Williams, B.D. Wright, Storage and Commodity Markets (Cambridge University Press, Cambridge, 2005)Google Scholar
  36. 36.
    O.Q. Wu, D.D. Wang, Z. Qin, Seasonal energy storage operations with limited flexibility: the price-adjusted rolling intrinsic policy. Manuf. Serv. Oper. Manag. 14(3), 455–471 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mathematical and Computer SciencesHeriot-Watt UniversityEdinburghUK

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