Gradus
VOL 3, NO 2 (2016): AUTUMN (NOVEMBER)
Lower tail estimation with Chernoff bound and its application for balancing electricity load by storage admission
Abstract
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
Keywords: Large Deviation Theory, Chernoff bound, valley filling, smart grid, Demand Side Management,
References
| [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,http://publications.jrc.ec.europa.eu/repository/handle/JRC77079 |
| [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. |