Decentralized Charging Coordination of Large-scale Plug-in Electric Vehicles in Power Systems pp 59-108 | Cite as

# Decentralized Charging Coordination with Battery Degradation Cost

## Abstract

In Chap. 2, the decentralized charging method has been designed to effectively coordinate the charging behaviors of large-scale PEVs, like the valley-filling strategy, to minimize their impacts on the power grid. However high charging rates under the valley-filling strategy may result in high battery degradation cost. Consequently in this chapter, it formulates a class of PEV charging coordination problems which deals with the tradeoff between total generation cost and the accumulated battery degradation cost of PEV populations. Due to the autonomy of individual PEVs and the computational complexity of the system with large-scale PEVs, it is impractical to implement the solution in a centralized way. Alternatively in this part a decentralized method is proposed such that all of the individual PEVs simultaneously update their own best charging behaviors with respect to a common electricity price curve, which is updated as the generation marginal cost with respect to the aggregated charging behaviors of the PEV populations implemented at last step. The iteration procedure terminates in case the price curve does not update any longer. It has been shown that, by applying the proposed decentralized method and under certain mild conditions, the system can converge to a unique charging strategy which is nearly socially optimal or efficient. Simulation examples are studied to illustrate the results developed in this chapter.

## References

- 1.S. Bashash, S.J. Moura, J.C. Forman, H.K. Fathy, Plug-in hybrid electric vehicle charge pattern optimization for energy cost and battery longevity. J. Power Sour.
**196**, 541–549 (2011)Google Scholar - 2.J. Wang, P. Liu, J. Hicks-Garner, E. Sherman, S. Soukiazian, M. Verbrugge, H. Tataria, J. Musser, P. Finamore, Cycle-life model for graphite-LiFePO4 cells. J. Power Sour.
**194**(8), 3942–3948 (2011)Google Scholar - 3.L. Gan, U. Topcu, S.H. Low, Stochastic distributed protocol for electric vehicle charging with discrete charging rate, in
*IEEE Power and Energy Society General Meeting*(2012), pp. 1–8Google Scholar - 4.K.W.E. Cheng, B.P. Divakar, H. Wu, K. Ding, H.F. Ho, Battery-management system (BMS) and SOC development for electrical vehicles. IEEE Trans. Veh. Technol.
**60**(1), 76–88 (2011)Google Scholar - 5.J. Forman, J. Stein, H. Fathy, Optimization of dynamic battery paramter characterization experiments via differential evolution. In
*American Control Conference (ACC)*, pp. 867–874, Washington, DC, USA, 17–19 June 2013Google Scholar - 6.J. Forman, S. Moura, J. Stein, H. Fathy, Optimal experimental design for modeling battery degradation, in
*Proceedings of Dynamic Systems and Control Conference*(2012), pp. 309–318Google Scholar - 7.S. Moura, J. Forman, S. Bashash, J. Stein, H. Fathy, Optimal control of film growth in lithium-ion battery packs via relay switches. IEEE Trans. Ind. Electr.
**58**(8), 3555–3566 (2011)Google Scholar - 8.D. Callaway, I. Hiskens, Achieving controllability of electric loads. Proc. IEEE
**99–1**, 184–199 (2011)Google Scholar - 9.A.-H. Mohsenian-Rad, A. Leon-Garcia, Optimal residential load control with price prediction in real-time electricity pricing environments. IEEE Trans. Smart Grid
**1**(2), 120–133 (2010)Google Scholar - 10.P. Samadi, A. Mohsenian-Rad, R. Schober, V. Wong, J. Jatskevich, Optimal real-time pricing algorithm based on utility maximization for smart grid, in
*Proceedings of 1st IEEE International Conference on Smart Grid Communications*, Gaithersburg, 4–6 Oct 2010Google Scholar - 11.R.A. Waraich, M. Galus, C. Dobler, M. Balmer, G. Andersson, K. Axhausen, Plug-in hybrid electric vehicles and smart grid: investigations based on a micro-simulation. Technical Report 10.3929/ethza-005916811 (Institute for Transport Planning and Systems, ETH Zurich, 2009)Google Scholar
- 12.C. Wu, H. Mohsenian-Rad, J. Huang, Vehicle-to-aggregator interaction game. IEEE Trans. Smart Grid
**3**(1), 434–442 (2012)Google Scholar - 13.Z. Fan, A distributed demand response algorithm and its application to PHEV charging in smart grids. IEEE Trans. Smart Grid
**3**(3), 1280–1290 (2012)Google Scholar - 14.L. Gan, N. Chen, A. Wierman, U. Topcu, S.H. Low, Real-time deferrable load control: handling the uncertainties of renewable generation, in
*Fourth International Conference on Future Energy Systems*, ACM (2013)Google Scholar - 15.Z. Ma, D. Callaway, I. Hiskens, Decentralized charging control of large populations of plug-in electric vehicles. IEEE Trans. Control Syst. Technol.
**21**(1), 67–78 (2013)CrossRefGoogle Scholar - 16.L. Gan, U. Topcu, S. Low, Optimal decentralized protocol for electric vehicle charging. IEEE Trans. Power Syst.
**28**(2), 940–951 (2013)Google Scholar - 17.F. Kelly, A. Maulloo, D. Tan, Rate control for communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc.
**49**(3), 237–252 (1998)Google Scholar - 18.T. Lee, Z. Bareket, T. Gordon, Stochastic modeling for studies of real-world PHEV usage: driving schedule and daily temporal distributions. IEEE Trans. Veh. Technol.
**61**(4), 1493–1502 (2012)CrossRefGoogle Scholar - 19.P. Denholm, W. Short, An evaluation of utility system impacts and benefits of optimally dispatched plug-in hybrid electric vehicles. Technical Report NREL/TP-620-40293 (National Renewable Energy Laboratory, 2006)Google Scholar
- 20.P. Prosini, Modeling the voltage profile for LiFePO4. J. Electrochem. Soc.
**152**(10), A1925–A1929 (2005)CrossRefGoogle Scholar - 21.J. Kim, G.-S. Seo, C. Chun, B.-H. Cho, S. Lee, OCV hysteresis effect-based SOC estimation in extended Kalman filter algorithm for an LiFePO4/C cell, in
*IEEE International Electric Vehicle Conference (IEVC)*, pp. 1–5, Greenville, SC, 4–8 March 2012Google Scholar - 22.A. Singh, A. Izadian, S. Anwar, Fault diagnosis of li-ion batteries using multiple-model adaptive estimation, in
*39th Annual Conference of the IEEE Industrial Electronics Society (IECON)*, pp. 3524–3529, Vienna, 10–13 November 2013Google Scholar - 23.M.D. Galus, G. Andersson. Demand management of grid connected plug-in hybrid electric vehicles (PHEV), in
*IEEE Energy 2030*, Atlanta, Georgia, 17–18 Nov 2008Google Scholar - 24.Y. He, B. Venkatesh, L. Guan, Optimal scheduling for charging and discharging of electric vehicles. IEEE Trans. Smart Grid
**3**(3), 1095–1105 (2012)Google Scholar - 25.E. Bompard, Y. Ma, R. Napoli, G. Abrate, The demand elasticity impacts on the strategic bidding behavior of the electricity producers. IEEE Trans. Power Syst.
**22**(1), 188–197 (2007)CrossRefGoogle Scholar - 26.V.P. Gountis, A.G. Bakirtzis, Bidding strategies for electricity producers in a competitive electricity marketplace. IEEE Trans. Power Syst.
**19**(1), 356–365 (2004)CrossRefGoogle Scholar - 27.F.S. Wen, A.K. David, Strategic bidding for electricity supply in a day-ahead energy market. Electr. Power Syst. Res.
**59**, 197–206 (2001)CrossRefGoogle Scholar - 28.S. Boyd, L. Vandenberghe,
*Convex Optimization*(Cambridge University Press, Cambridge, 2004)CrossRefGoogle Scholar - 29.O. Sundstrom, C. Binding, Planning electric-drive vehicle charging under constrained grid conditions. Technical Report (IBM - Zurich, Switzerland, 2010)Google Scholar
- 30.D.R. Smart,
*Fixed Point Theorems*(Cambridge University Press, London, 1974)Google Scholar - 31.Z. Luo, Z. Hu, Y. Song, Z. Xu, H. Lu, Optimal coordination of plug-in electric vehicles in power grids with cost-benefit analysis - part I: enabling techniques. IEEE Trans. Power Syst.
**28**(4), 3546–3555 (2013)Google Scholar - 32.Z. Luo, Z. Hu, Y. Song, Z. Xu, H. Lu, Optimal coordination of plug-in electric vehicles in power grids with cost-benefit analysis - part II: a case study in China. IEEE Trans. Power Syst.
**28**(4), 3556–3565 (2013)CrossRefGoogle Scholar - 33.R. Deliso, Understanding peak demand charges. EnerNOC EnergySMART (2013)Google Scholar
- 34.S. Han, S. Han, K. Sezaki, Development of an optimal vehicle-to-grid aggregrator for frequency regulation. IEEE Trans. Smart Grid
**1**(1), 65–72 (2010)CrossRefGoogle Scholar - 35.S. Grammatico, F. Parise, M. Colombino, J. Lygeros. Decentralized convergence to Nash equilibria in constrained deterministic mean field control. IEEE Trans. Autom. Control (cond. accepted) (2015), arXiv:1410.4421v2
- 36.V. Berinde,
*Iterative Approximation of Fixed Points*(Springer, Berlin, 2007)zbMATHGoogle Scholar