Optimizing demand response of plug-in hybrid electric vehicles using quadratic programming

This paper develops a convex quadratic programming (QP) formulation for the demand response (DR) 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 DR model that accounts for the ohmic energy losses in PHEV batteries, and is scalable to large-scale vehicle-to-grid (V2G) optimization and control applications. We use a previously-developed power-split PHEV model with an optimal power management strategy to compute the average distance-based PHEV energy consumption characteristics. Moreover, we use an equivalent circuit battery model for the PHEV´s charge and discharge process. We then derive the PHEV´s total fuel and electric energy cost as a quadratic function of battery state-of-charge (SOC), and show that the cost function is convex. Finally, we use a standard QP solver to optimize the PHEV´s demand response for a few sample trips obtained from the U.S. National Household Travel Survey (NHTS) dataset. The achieved optimization time for a 24-hour time window with 5 min. resolution is less than 0.1 s (using a single quad-core computer). The method can hence be easily scaled for large-scale smart grid optimization and control studies.