Recharging Probably Keeps Batteries Alive

  • Holger Hermanns
  • Jan Krčál
  • Gilles NiesEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9361)


Battery powered systems are a major area of cyber physical system innovation. This paper develops a kinetic battery model with bounded capacity in the context of piecewise constant yet random charging and discharging. The resulting model enables a faithful time-dependent evaluation of the risk of a mission failure due to battery depletion. This is exemplified in a power dependability study of a nano satellite mission currently in orbit.



The authors are grateful for inspiring discussions with Peter Bak and Morten Bisgaard (GomSpace ApS), Erik R. Wognsen (Aalborg University), and other members of the SENSATION consortium, as well as with Pascal Gilles (ESA Centre for Earth Observation), Xavier Bossoreille (Deutsches Zentrum für Luft- und Raumfahrt) and Marc Bouissou (Électricité de France S.A., École Centrale Paris - LGI).

This work is supported by the EU 7th Framework Programme under grant agreements 295261 (MEALS) and 318490 (SENSATION), by the DFG as part of SFB/TR 14 AVACS, by the Czech Science Foundation under grant agreement P202/12/G061, by the CAS/SAFEA International Partnership Program for Creative Research Teams, and by the CDZ project CAP (GZ 1023).


  1. 1.
    Abate, A., Prandini, M., Lygeros, J., Sastry, S.: Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems. Automatica 44(11), 2724–2734 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Altman, E., Gaitsgory, V.: Asymptotic optimization of a nonlinear hybrid system governed by a markov decision process. SIAM J. Control Optim. 35(6), 2070–2085 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Aydin, H., Mejía-Alvarez, P., Mossé, D., Melhem, R.G.: Dynamic and aggressive scheduling techniques for power-aware real-time systems. IEEE RTSS 2001, 95–105 (2001)Google Scholar
  4. 4.
    Blom, H.A., Lygeros, J., Everdij, M., Loizou, S., Kyriakopoulos, K.: Stochastic Hybrid Systems: Theory and Safety Critical Applications. LNCS, vol. 337. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Boker, U., Henzinger, T.A., Radhakrishna, A.: Battery transition systems. In: POPL, pp. 595–606. ACM (2014)Google Scholar
  6. 6.
    Bujorianu, M.L., Lygeros, J., Bujorianu, M.C.: Bisimulation for general stochastic hybrid systems. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 198–214. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  7. 7.
    Cao, J., Schofield, N., Emadi, A.: Battery balancing methods: a comprehensive review. In: Vehicle Power and Propulsion Conference, VPPC 2008, pp. 1–6. IEEE, September 2008Google Scholar
  8. 8.
    Cloth, L., Jongerden, M.R., Haverkort, B.R.: Computing battery lifetime distributions. In: DSN, pp. 780–789. IEEE Computer Society (2007)Google Scholar
  9. 9.
    Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the lambertW function. Adv. Comput. Math. 5(1), 329–359 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Davis, M.H.: Piecewise-deterministic markov processes: a general class of non-diffusion stochastic models. J. Roy. Stat. Soc. Ser. B (Methodol.) 46, 353–388 (1984)zbMATHGoogle Scholar
  11. 11.
    Esa: Esa cubesat program, October 2014.
  12. 12.
    Soudjani, S.E.Z., Gevaerts, C., Abate, A.: Faust2: formal abstractions of uncountable-state stochastic processes. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 272–286. Springer, Heidelberg (2015)Google Scholar
  13. 13.
    Fox, M., Long, D., Magazzeni, D.: Automatic construction of efficient multiple battery usage policies. In: Walsh, T. (ed.) IJCAI, pp. 2620–2625. IJCAI/AAAI (2011)Google Scholar
  14. 14.
    Fränzle, M., Hahn, E.M., Hermanns, H., Wolovick, N., Zhang, L.: Measurability and safety verification for stochastic hybrid systems. In: HSCC, pp. 43–52. ACM Press, New York, NY, USA (2011)Google Scholar
  15. 15.
    Fränzle, M., Hermanns, H., Teige, T.: Stochastic satisfiability modulo theory: a novel technique for the analysis of probabilistic hybrid systems. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 172–186. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  16. 16.
    Gilles, P.: Private communication (2014)Google Scholar
  17. 17.
    Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22(4), 403–434 (1976)MathSciNetCrossRefGoogle Scholar
  18. 18.
    GomSpace: Gomspace gomx-1, October 2014.
  19. 19.
    Henzinger, T.A.: The theory of hybrid automata. In: Kemal Inan, M., Kurshan, R.P. (eds.) Verification of Digital and Hybrid Systems. NATO ASI Series, vol. 170, pp. 265–292. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  20. 20.
    Henzinger, T.A., Sifakis, J.: The embedded systems design challenge. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 1–15. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  21. 21.
    Hermanns, H., Krcál, J., Nies, G.: Recharging probably keeps batteries alive. CoRR abs/1502.07120 (2015)Google Scholar
  22. 22.
    Jongerden, M., Haverkort, B., Bohnenkamp, H., Katoen, J.: Maximizing system lifetime by battery scheduling. In: DSN, pp. 63–72. IEEE (2009)Google Scholar
  23. 23.
    Jongerden, M.R., Haverkort, B.R.: Which battery model to use? IET Softw. 3(6), 445–457 (2009)CrossRefGoogle Scholar
  24. 24.
    Jongerden, M.R.: Model-based energy analysis of battery powered systems. Ph.d. thesis, Enschede, December 2010Google Scholar
  25. 25.
    Liaw, B.Y., Roth, E.P., Jungst, R.G., Nagasubramanian, G., Case, H.L., Doughty, D.H.: Correlation of arrhenius behaviors in power and capacity fades with cell impedance and heat generation in cylindrical lithium-ion cells. J. Power Sources 119, 874–886 (2003)CrossRefGoogle Scholar
  26. 26.
    Liu, J., Chou, P.H., Bagherzadeh, N., Kurdahi, F.: Power-aware scheduling under timing constraints for mission-critical embedded systems. In: DAC, pp. 840–845. ACM, New York, NY, USA (2001)Google Scholar
  27. 27.
    Manwell, J.F., McGowan, J.G.: Lead acid battery storage model for hybrid energy systems. Sol. Energy 50(5), 399–405 (1993)CrossRefGoogle Scholar
  28. 28.
    Rao, V., Singhal, G., Kumar, A., Navet, N.: Battery model for embedded systems. In: VLSI Design/ES Design, pp. 105–110. IEEE (2005)Google Scholar
  29. 29.
    SENSATION: Sensation, March 2015.
  30. 30.
    Sproston, J.: Decidable model checking of probabilistic hybrid automata. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, p. 31. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  31. 31.
    Villén-Altamirano, M., Villén-Altamirano, J.: Restart: a straightforward method for fast simulation of rare events. In: WSC, pp. 282–289. IEEE (1994)Google Scholar
  32. 32.
    Wognsen, E.R., Hansen, R.R., Larsen, K.G.: Battery-aware scheduling of mixed criticality systems. In: Margaria, T., Steffen, B. (eds.) ISoLA 2014, Part II. LNCS, vol. 8803, pp. 208–222. Springer, Heidelberg (2014) Google Scholar
  33. 33.
    Zhang, L., She, Z., Ratschan, S., Hermanns, H., Hahn, E.M.: Safety verification for probabilistic hybrid systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 196–211. Springer, Heidelberg (2010) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Computer ScienceSaarland UniversitySaarbrückenGermany

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