Cost-Optimal Charging of Plug-In Hybrid Electric Vehicles Under Time-Varying Electricity Price Signals

This paper develops a convex quadratic programming (QP) framework for the charge pattern optimization of plug-in hybrid electric vehicles (PHEVs) under time-varying electricity price signals. The work is motivated by the need for a computationally efficient PHEV charging model in the bidirectional vehicle-to-grid (V2G) integration studies, accounting for the hybrid powertrain dynamics and battery energy losses of the PHEVs. We adopt a previously developed PHEV power management system and construct a simplified model for the convex optimization problem. We use an equivalent circuit battery model to compute battery energy losses during grid charging and discharging. We then derive the total fuel and electricity cost of the PHEV as a quadratic function of battery state of charge and use a standard QP solver to minimize it for a few sample trips obtained from the National Household Travel Survey data set. Using a quad-core computer, the daily PHEV charging trajectory with 5-min time resolution can be optimized in less than tenth of a second. Through several examples, we show the application of the proposed method in various V2G-related problems, such as obtaining the aggregate load patterns of PHEVs, analyzing the potential impacts of large-scale bidirectional V2G integration, benchmarking the fuel economy of PHEVs, and determining the sensitivity of V2G load to abrupt price variations.