An efficient game for vehicle-to-grid coordination problems in smart grids

Abstract

Emerging plug-in electric vehicles (PEVs), as distributed energy sources, are promising to provide vehicle-to-grid (V2G) services for power grids, like frequency and voltage regulations, by coordinating their active and reactive power rates. However, due to the autonomy of PEVs, it is challenging how to efficiently schedule the coordination behaviours among these units in a distributed way. In this paper, we formulate the underlying coordination problems as a novel class of Vickrey–Clarke–Groves style (VCG-style) auction games where players, power grids and PEVs do not report a full cost or valuation function but only a multidimensional bid signal: the maximum active and reactive power quantities that a power grid wants and the maximum per unit prices it is willing to pay, and the maximum active and reactive power quantities that a PEV can provide and the minimum per unit prices it asks for. We show the existence of the efficient Nash equilibrium (NE) for the underlying auction games, though there may exist other inefficient NEs. In order to deal with large-scale PEVs, we design games with aggregator players each of which submits bid profiles representing the overall utility for a collection of PEVs, and extend the so-called quantised-progressive second price mechanism to the underlying auction games to implement the efficient NE.

Keywords:

• plug-in electric vehicles
• vehicle-to-grid
• frequency and voltage regulations
• progressive second price auction
• non-cooperative game
• Nash equilibrium

Acknowledgements

This work is supported by the National Natural Science Foundation (NNSF) of China under Grant 61174091, the Program for Changjiang Scholars and Innovative Research Team in University under Grant IRT1208 and the Excellent Young Scholars Research Fund of Beijing Institute of Technology (BIT).

Additional information

Notes on contributors

Xingyu Shi

Xingyu Shi was born in Hunan Province, China, in 1989. He received his BEng degree from Beijing Institute of Technology, Beijing, China, in 2011. Currently, he is pursing his MEng degree at the School of Automation at Beijing Institute of Technology. His research interests lie in the design, optimisation and game-theoretic analysis of smart grids.

Zhongjing Ma

Zhongjing Ma received his BEng degree from Nankai University, Tianjin, China, in 1997, and MEng and PhD degrees from McGill University, Montreal, QC, Canada, in 2005 and 2009, respectively, all in the area of systems and control. After a period as a postdoctoral research fellow with the Center of Sustainable Systems, University of Michigan, Ann Arbor, he joined Beijing Institute of Technology, Beijing, China, in 2010, where he is currently an associate professor. He was an engineer with the Institute of Automation Research, Shanxi, China. His research interests lie in the areas of optimal control, stochastic systems, and applications in the power and microgrid systems.