Global Optimization of Plug-In Hybrid Vehicle Design and Allocation to Minimize Life Cycle Greenhouse Gas Emissions

We pose a reformulated model for optimal design and allocation of conventional (CV), hybrid electric (HEV), and plug-in hybrid electric (PHEV) vehicles to obtain global solutions that minimize life cycle greenhouse gas (GHG) emissions of the fleet. The reformulation is a twice-differentiable, factorable, nonconvex mixed-integer nonlinear programming (MINLP) model that can be solved globally using a convexification-based branch-and-reduce algorithm. We compare results to a randomized multistart local-search approach for the original formulation and find that local-search algorithms locate global solutions in 59% of trials for the two-segment case and 18% of trials for the three-segment case. The results indicate that minimum GHG emissions are achieved with a mix of PHEVs sized for 25–45 miles of electric travel. Larger battery packs allow longer travel on electrical energy, but production and weight of underutilized batteries result in higher GHG emissions. Under the current average U.S. grid mix, PHEVs offer a nearly 50% reduction in life cycle GHG emissions relative to equivalent conventional vehicles and about 5% improvement over HEVs when driven on the standard urban driving cycle. Optimal allocation of different PHEVs to different drivers turns out to be of second order importance for minimizing net life cycle GHGs.