A Fluid Model of an Electric Vehicle Charging Network

References

• Ardakanian O, Rosenberg C, Keshav S (2013) Distributed control of electric vehicle charging. Ardakanian O, Rosenberg C, Keshav S, eds. Proc. 4th Internat. Conf. Future Energy Systems (Berkeley, CA), 101–112.Google Scholar
• Arif A, Babar M, Ahamed TI, Al-Ammar E, Nguyen P, Kamphuis IR, Malik N (2016) Online scheduling of plug-in vehicles in dynamic pricing schemes. Sustainable Energy. Grids Networks 7:25–36.Google Scholar
• Aveklouris A (2020) Layered stochastic networks with limited resources. PhD thesis, Eindhoven University of Technology, Eindhoven, Netherlands.Google Scholar
• Aveklouris A, Vlasiou M, Zwart B (2019) A stochastic resource-sharing network for electric vehicle charging. IEEE Trans. Control Network System 6(3):1050–1061.Google Scholar
• Baran M, Wu FF (1989) Optimal sizing of capacitors placed on a radial distribution system. IEEE Trans. Power Delivery 4(1):735–743.Google Scholar
• Bienstock D (2015) Electrical Transmission System Cascades and Vulnerability: An Operations Research Viewpoint (SIAM, Philadelphia).Google Scholar
• Billingsley P (1995) Probability and Measure. Wiley Series in Probability and Mathematical Statistics, 3rd ed. (Wiley, New York).Google Scholar
• Billingsley P (1999) Convergence of Probability Measures, 2nd ed. (Wiley, New York).Google Scholar
• Bonald T, Proutiere A (2003) Insensitive bandwidth sharing in data networks. Queueing Systems 44(1):69–100.Google Scholar
• Bonald T, Massoulié L, Proutiere A, Virtamo J (2006) A queueing analysis of max-min fairness, proportional fairness and balanced fairness. Queueing Systems 53(1):65–84.Google Scholar
• Borst S, Egorova R, Zwart B (2014) Fluid limits for bandwidth-sharing networks in overload. Math. Oper. Res. 39(2):533–560.Link, Google Scholar
• Carvalho R, Buzna L, Gibbens R, Kelly F (2015) Critical behaviour in charging of electric vehicles. New J. Physics 17(9):095001.Google Scholar
• Chen H, Yao D (2001) Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization, vol. 46 (Springer-Verlag, New York).Google Scholar
• Dörfler F, Chertkov M, Bullo F (2013) Synchronization in complex oscillator networks and smart grids. Proc. National Acad. Sci. USA 110(6):2005–2010.Google Scholar
• Dvijotham K, Mallada E, Simpson-Porco J (2017) High-voltage solution in radial power networks: Existence, properties, and equivalent algorithms. IEEE Control Systems Lett. 1(2):322–327.Google Scholar
• Fan Z (2012) A distributed demand response algorithm and its application to phev charging in smart grids. IEEE Trans. Smart Grid 3(3):1280–1290.Google Scholar
• Gan L, Li N, Topcu U, Low S (2015) Exact convex relaxation of optimal power flow in radial networks. IEEE Trans. Automated Control 60(1):72–87.Google Scholar
• Gromoll C, Williams R (2009) Fluid limits for networks with bandwidth sharing and general document size distributions. Ann. Appl. Probabilities 19(1):243–280.Google Scholar
• Gromoll C, Robert P, Zwart B (2008) Fluid limits for processor-sharing queues with impatience. Math. Oper. Res. 33(2):375–402.Link, Google Scholar
• Hiskens I, Davy R (2001) Exploring the power flow solution space boundary. IEEE Trans. Power Systems 16(3):389–395.Google Scholar
• Hoogsteen G, Molderink A, Hurink JL, Smit GJ, Kootstra B, Schuring F (2017) Charging electric vehicles, baking pizzas, and melting a fuse in lochem. CIRED Open Access Proc. J. 2017(1):1629–1633.Google Scholar
• Kang W (2015) Fluid limits of many-server retrial queues with nonpersistent customers. Queueing Systems 79(2):183–219.Google Scholar
• Kang W, Ramanan K (2010) Fluid limits of many-server queues with reneging. Ann. Appl. Probabilities 20(6):2204–2260.Google Scholar
• Kang WN, Kelly FP, Lee NH, Williams RJ (2009) State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy. Ann. Appl. Probabilities 19(5):1719–1780.Google Scholar
• Kaspi H, Ramanan K (2011) Law of large numbers limits for many-server queues. Ann. Appl. Probabilities 21(1):33–114.Google Scholar
• Kelly F (1997) Charging and rate control for elastic traffic. Trans. Emerging Telecomm. Tech. 8(1):33–37.Google Scholar
• Kersting W (2012) Distribution System Modeling and Analysis (CRC Press, Boca Raton, FL).Google Scholar
• Lavaei J, Tse D, Zhang B (2014) Geometry of power flows and optimization in distribution networks. IEEE Trans. Power Systems 29(2):572–583.Google Scholar
• Liu Y, Whitt W (2011) A network of time-varying many-server fluid queues with customer abandonment. Oper. Res. 59(4):835–846.Link, Google Scholar
• Low S (2014a) Convex relaxation of optimal power flow: part I: Formulations and equivalence. IEEE Trans. Control Network Systems 1(1):15–27.Google Scholar
• Low S (2014b) Convex relaxation of optimal power flow–part II: Exactness. IEEE Trans. Control Network Systems 1(2):177–189.Google Scholar
• Machowski J, Bialek J, Bumby J (2008) Power System Dynamics: Stability and Control (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Mandelbaum A, Momčilović P (2017) Personalized queues: the customer view, via a fluid model of serving least-patient first. Queueing Systems 87(1):23–53.Google Scholar
• Massoulié L, Roberts J (1999) Bandwidth sharing: Objectives and algorithms. Proc. INFOCOM 3:1395–1403.Google Scholar
• Molzahn D, Mehta D, Niemerg M (2016) Toward topologically based upper bounds on the number of power flow solutions. Proc. Amer. Control Conf., Boston, 5927–5932.Google Scholar
• Pang G, Talreja R, Whitt W (2007) Martingale proofs of many-server heavy-traffic limits for markovian queues. Probability Survey 4:193–267.Google Scholar
• Puha A, Ward RA (2019) Scheduling an overloaded multiclass many-server queue with impatient customers. Tutorials Oper. Res. Oper. Res. Management Sci. Age Analytics, 189–217.Google Scholar
• Reed J (2009) The G/GI/N queue in the halfin–whitt regime. Ann. Appl. Probabilities 19(6):2211–2269.Google Scholar
• Reed J, Zwart B (2014) Limit theorems for markovian bandwidth sharing networks with rate constraints. Oper. Res. 62(6):1453–1466.Link, Google Scholar
• Remerova M, Reed J, Zwart B (2014) Fluid limits for bandwidth-sharing networks with rate constraints. Math. Oper. Res. 39(3):746–774.Link, Google Scholar
• Rudin W (1987) Real and Complex Analysis (Tata McGraw-Hill Education).Google Scholar
• Simpson-Porco J, Dörfler F, Bullo F (2016) Voltage collapse in complex power grids. Nature Comm. 7:10790.Google Scholar
• Vlasiou M, Zhang J, Zwart B (2014) Insensitivity of proportional fairness in critically loaded bandwidth sharing networks. Preprint, submitted June 17, 2015, https://arxiv.org/abs/1411.4841.Google Scholar
• Ye HQ, Yao D (2012) A stochastic network under proportional fair resource control-diffusion limit with multiple bottlenecks. Oper. Res. 60(3):716–738.Link, Google Scholar
• Zhang J (2013) Fluid models of many-server queues with abandonment. Queueing Systems 73(2):147–193.Google Scholar
• Zhang J, Dai J, Zwart B (2009) Law of large number limits of limited processor-sharing queues. Math. Oper. Res. 34(4):937–970.Link, Google Scholar
• Zuñiga AW (2014) Fluid limits of many-server queues with abandonments, general service and continuous patience time distributions. Stochastic Processing Appl. 124(3):1436–1468.Google Scholar