We consider an electricity consumer equipped with a perfect battery, who needs to satisfy a non-elastic load, subject to external control signals. The control imposes a time-varying upper-bound on the instantaneous energy consumption (this is called “Demand-Response via quantity”). The consumer defines a charging schedule for the battery. We say that a schedule is feasible if it successfully absorbs the effects of service reduction and achieves the satisfiability of the load (making use of the battery). Our contribution is twofold. (1) We provide explicit necessary and sufficient conditions for the load, the control, and the battery, which ensure the existence of a feasible battery charging schedule. Furthermore, we show that whenever a feasible schedule exists, we can explicitly define an online (causal) feasible schedule. (2) For a given arrival curve characterizing the load and a given service curve characterizing the control, we compute a sufficient battery size that ensures existence of an online feasible schedule. For an arrival curve determined from a real measured trace, we numerically characterize the sufficient battery size for various types of service curves.


Control Signal Feasible Schedule Maximal Solution Battery Capacity Online Schedule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    CAISO and GE Consulting. Integration of renewable resources. Operational requirements and generation fleet capability at 20% RPS. Technical report, CAISO (August 2010)Google Scholar
  2. 2.
    Cho, I., Meyn, S.: Efficiency and marginal cost pricing in dynamic competitive markets with friction. Theoretical Economics 5, 215–239 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Fan, X., Weber, W.-D., Barroso, L.A.: Power provisioning for a warehouse-sized computer. In: Proceedings of ISCA (2007)Google Scholar
  4. 4.
    Thiran, P., Le Boudec, J.-Y.: Network Calculus. LNCS, vol. 2050, pp. 3–81. Springer, Heidelberg (2001), CrossRefzbMATHGoogle Scholar
  5. 5.
    Le Boudec, J.-Y., Tomozei, D.-C.: Demand response using service curves. In: Proceedings of PES ISGT - Europe. IEEE (2011) (to appear)Google Scholar
  6. 6.
    Li, N., Chen, L., Low, S.H.: Optimal demand response based on utility maximization in power networks. In: 2011 IEEE Power and Energy Society General Meeting, pp. 1–8 (July 2011)Google Scholar
  7. 7.
    Linden, D., Reddy, T.: Handbook of Batteries, 3rd edn. McGraw-Hill (2002)Google Scholar
  8. 8.
    Peaksaver. Peaksaver,
  9. 9.
    Qureshi, A., Weber, R., Balakrishnan, H., Guttag, J., Maggs, B.: Cutting the electric bill for internet-scale systems. In: Proceedings of the ACM SIGCOMM 2009, pp. 123–134. ACM, New York (2009)CrossRefGoogle Scholar
  10. 10.
    SPEC. Design document SSJ workload (2011),
  11. 11.
    Voltalis. Bluepod,

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jean-Yves Le Boudec
    • 1
  • Dan-Cristian Tomozei
    • 1
  1. 1.EPFL - LCA2LausanneSwitzerland

Personalised recommendations