# Bidirectional Energy Management for Plug-in Hybrid Electric Vehicles via Vehicle-to-Grid

## Abstract

As a paradigm of the incoming smart grid, vehicle-to-grid (V2G) has been proposed as a solution to increase the adoption rate of plug-in hybrid electric vehicles (PHEVs). In this paper, we investigate the bidirectional energy management for PHEVs via V2G system. We formulate the energy management problem through dynamic programming, aiming at flattening the grid peak load and minimizing the daily energy cost. However, the “well-known” complexity in solving dynamic programming poses a computational challenge even for a small *N*. Therefore, we prove that a ( *s*, *S*, *s′*, *S′*) feedback policy is optimal for PHEV battery charging/discharging based on inventory storage theory. Simulation results verified the validity of the proposed algorithm. The theoretical analysis and proofs are instrumental to the future large-scale PHEV adoption in smart grid.

### Keywords

Plug-in hybrid electric vehicles Vehicle-to-grid Battery charging Dynamic programming Stochastic inventory## Notes

### Acknowledgements

This work was supported by U.S. National Science Foundation under Grant CNS-1116749.

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