How much energy at least would be consumed driving through a given route ahead conditioned on the current and possible future traffic states, and which factor would contribute most to the energy consumption? Answers to these problems are necessary for route and velocity planning for automated and connected vehicles. In this paper, considering the efficiency of powertrain components and the restriction of control strategy on their operation points, the mechanism-based tank-to-traffic energy consumption model is developed by integrating the energy dissipation within powertrains and the macroscopic traffic states. With Sobol global sensitivity analysis, the acceleration is identified as the most significant contributor to energy consumption within road segments rather than the control variable. Therefore, the summation of optimal segmental energy consumption (OSEC) is utilized as the estimator of the global optimal accumulative energy consumption (GOAEC) over the entire route, which is validated by correlation analysis between the sequences of OSEC and GOAEC. The validation result suggests that the maximum COR is as high as 0.97 and 0.90 for free and congested traffic condition, respectively, while even in the case of minimum COR, the sequences share a similar shape. The effective estimator for GOAEC provides the quantified evidence supporting decisions on route and velocity planning.