Abstract
We discuss the application of classical variational methods to optimal charging/discharging strategies for a prosumer or storage supplier, where the price of electrical power is known in advance. We outline how a classical calculus of variations approach can be applied to two related problems: (i) how can a prosumer minimise the cost of charging/discharging a battery, when the price of electrical power is known throughout the charging/discharging period? and (ii) how can an electricity supplier incentivise desired prosumer/storage supplier behaviour by adjusting the price?
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Binding, C., Sundström, O.: A simulation environment for vehicle-to-grid integration studies. In: Proceedings of the 2011 Summer Computer Simulation Conference (SCSC ’11), pp. 14–21 (2011)
Bompard, E., Connors, S., Full, G., Han, B., Masera, M., Mengolini, A., Nuttall, W.J.: Smart Energy Grids and Complexity Science. Joint Research Centre-Institute for Energy and Transport, European Union (2012)
Ceraolo, M.: New dynamical models of lead-acid batteries. IEEE Trans. Power Syst. 15(4), 1184–1190 (2000)
Cruise, J.R., Gibbens, R.J., Zachary, S.: Optimal control of storage for arbitrage, with applications to energy systems. In: 48th Annual Conference on Information Sciences and Systems (CISS 2014), pp. 1–6 (2014). doi:10.1109/CISS.2014.6814090
The future role and challenges of energy storage. DG ENER Working Paper, European Union. https://ec.europa.eu/energy/sites/ener/files/energy_storage.pdf (2013). Accessed 15 July 2016
Guzzella, L., Sciarretta, A.: Vehicle Propulsion Systems: Introduction to Modeling and Optimization. Springer, Berlin, New York (2005)
Kleiwegt, E., Lukszo, Z.: Grid impact analysis of electric mobility on a local electricity grid. In: 9th IEEE International Conference on Networking, Sensing and Control (ICNSC 2012), pp. 316–321 (2012)
Li, Y., Lukszo, Z., Weijnen, M.P.C.: The potential of electric vehicles to facilitate a high wind power penetration. In: 10th IEEE International Conference on Networking, Sensing and Control (ICNSC 2013), pp. 901–906 (2013)
Energy storage: the missing link in the UK’s energy commitments. Institution of Mechanical Engineers. https://www.imeche.org/docs/default-source/reports/imeche-energy-storage-report.pdf (2014). Accessed 15 July 2016
Rockafellar, R.T.: Convex analysis in the calculus of variations. In: Advances in Convex Analysis and Global Optimization (Pythagorion, 2000), Nonconvex Optim. Appl., vol 54, Kluwer Academic Publishers, Dordrecht, pp. 135–151 (2001)
Seaman, A., Dao, T.S., McPhee, J.: A survey of mathematics-based equivalent-circuit and electrochemical battery models for hybrid and electric vehicle simulation. J. Power Sour. 256, 410–423 (2014)
Tippmann, S., Walper, D., Balboa, L., Spier, B., Bessler, W.G.: Low-temperature charging of lithium-ion cells part I. Electrochemical modeling and experimental investigation of degradation behavior. J. Power Sour. 252, 305–316 (2014)
Verzijlbergh, R.A., Lukszo, Z.: System impacts of electric vehicle charging in an evolving market environment. In: 8th IEEE International Conference on Networking, Sensing and Control (ICNSC 2011), pp. 20–25 (2011)
Verzijlbergh, R.A., Grond, M.O.W., Lukszo, Z., Slootweg, J.G., Ilic, M.D.: Network impacts and cost savings of controlled EV charging. In: 9th IEEE International Conference on Networking, Sensing and Control (ICNSC 2012) pp. 1203–1212 (2012)
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I would like to express my thanks to the referees for their helpful suggestions to improve the manuscript.
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Mestel, B.D. Optimal battery charge/discharge strategies for prosumers and suppliers. Energy Syst 8, 511–523 (2017). https://doi.org/10.1007/s12667-016-0211-y
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DOI: https://doi.org/10.1007/s12667-016-0211-y