Lower tail estimation with Chernoff bound and its application for balancing electricity load by storage admission

Rajmund Drenyovszki, Lorant Kovacs, Kalman Tornai, Andras Olah and Istvan Pinter


In this paper we investigate the applicability of the Chernoff in- equality in finding an upper bound on the probability of the lower tail of the aggregate load. The importance of Demand Side Man- agement (DSM) programs in power networks has increased re- cently, especially because of the new challenges like intensive use of renewable energy sources (wind, photovoltaic) and the ex- pected high penetration of Electric Vehicles (EV). We show that Chernoff bound has the potential to be incorporated in DSM algo- rithms to integrate energy storage (e.g. batteries) elements into the power grid and facilitate load shifting.


Keywords: Large Deviation Theory, Chernoff bound, valley filling, smart grid, Demand Side Management,


[1] Goran Strbac, Demand side management: Benefits and challenges, Energy Policy, vol. 36, Issue12, pp. 4419-4426, Dec. 2008.
[2] L. G. Swan, V. I. Ugursal, "Modeling of end-use energy consumption in the residential sector: Areview of modeling techniques," Renewable and Sustainable Energy Reviews, vol. 13, Issue 8,pp. 1819-1835, October 2009.
[3] I. Hadjipaschalis, A. Poullikkas, V. Efthimiou, "Overview of current and future energy storagetechnologies for electric power applications," Renewable and Sustainable Energy Reviews, vol.13, Issues 6-7, pp. 1513-1522, 2009.
[4] X. Luo, J. Wang, M. Dooner, J. Clarke, "Overview of current development in electrical energystorage technologies and the application potential in power system operation," Applied Energy,vol. 137., pp. 511-536, 1 Jan. 2015.
[5] G. Pasaoglu, D. Fiorello, A. Martino, G. Scarcella, A. Alemanno, A. Zubaryeva, C. Thiel,"Driving and parking patterns of European car drivers - a mobility survey", EuropeanCommission, DG JRC, Institute for Energy and Transport, Petten, the Netherlands, 2012,
[6] L. Kovacs, J. Levendovszky, A. Olah, R. Drenyovszki, D. Tisza, K. Tornai and I. Pinter: "Aprobabilistic approach for admission control of smart appliances in Smart Grids," Proceedingsof 5th International Scientific and Expert Conference TEAM 2013, pp. 18-21, Presov, Slovakia,November 4-6, 2013.
[7] M. Y.i Suberu, M. W. Mustafa, N. Bashir, "Energy storage systems for renewable energy powersector integration and mitigation of intermittency," Renewable and Sustainable Energy Reviews,vol 35., pp. 499-514, 2014.
[8] T. R. Ayodele, A. S. O. Ogunjuyigbe, "Mitigation of wind power intermittency: Storage technologyapproach," Renewable and Sustainable Energy Reviews, vol. 44, pp. 447-456, 2015.
[9] S. Babrowski, H.i Heinrichs, P. Jochem, W. Fichtner, "Load shift potential of electric vehicles inEurope," Journal of Power Sources, vol. 255, pp. 283-293, 2014.
[10] G. Haines, A. McGordon, P. A. Jennings, N. Butcher, "The simulation of vehicle-to-home systems- using electric vehicle battery storage to smooth domestic electricity demand", Proceedings ofthe International Conference on Ecologic Vehicles and Renewable Energies, 2009.
[11] P. Mesaric, S. Krajcar, "Home demand side management integrated with electric vehicles andrenewable energy sources, " Energy and Buildings, vol. 108, pp. 1-9, 2015.
[12] Z. Lin, Z. Bai, "Probability inequalities," Springerverlag Berlin Heidelberg, 2010.
[13] H. Chernoff, "A measure of asymptotic efficiency for tests of a hypothesis based on the sum ofobservations," The Annals of Mathematical Statistics, vol 23, sz 4, o 493-507, 1952.
[14] P. Massart, "Concentration inequalities and model selection," Ecole d’Eté de Probabilités deSaint-Flour 2003. Lecture Notes in Mathematics 1896, Springer Berlin/Heidelberg. 2007.
[15] L. Kovacs, R. Drenyovszki, A. Olah, J. Levendovszky, K. Tornai, I. Pinter, "A proba-bilistic demand side management approach by consumption admission control," ArXiv e-printsarXiv:1608.00546.
[16] R. Drenyovszki, L. Kovacs, I. Pinter, A. Olah, K. Tornai, J. Levendovszky: "Power system reliabil-ity assessment for the residential sector based on Large Deviation Theory bounds," Proceedingsof EnergyCon 2016, IEEE International Energy Conference, Leuven, Belgium, April 4-8. 2016.
[17] D.L. Evans, L.M. Leemis, "Algorithms for computing the distributions of sums of discrete randomvariables," Mathematical and Computer Modelling, vol. 40, Issue 13, pp. 1429-1452, 2004.

Copyright (c) 2020 Gradus