Energy consumption estimation integrated into the Electric Vehicle Routing Problem

When planning routes for fleets of electric commercial vehicles, it is necessary to precisely predict the energy required to drive and plan for charging whenever needed, in order to manage their driving range limitations. Although there are several energy estimation models available in the literature, so far integration with Vehicle Routing Problems has been limited and without demonstrated accuracy. This paper introduces the Two-stage Electric Vehicle Routing Problem (2sEVRP) that incorporates improved energy consumption estimation by considering detailed topography and speed profiles. First, a method to calculate energy cost coefficients for the road network is outlined. Since the driving cycle is unknown, the model generates an approximation based on a linear function of mass, as the latter is only determined while routing. These coefficients embed information about topography, speed, powertrain efficiency and the effect of acceleration and braking at traffic lights and intersections. Secondly, an integrated two-stage approach is described, which finds the best paths between pairs of destinations and then finds the best routes including battery and time-window constraints. Energy consumption is used as objective function including payload and auxiliary systems. The road cost coefficients are aggregated to generate the path cost coefficients that are used in the routing problem. In this way it is possible to get a proper approximation of the complete driving cycle for the routes and accurate energy consumption estimation. Lastly, numerical experiments are shown based on the road network from Gothenburg Sweden. Energy estimation is compared with real consumption data from an all-electric bus from a public transport route and with high-fidelity vehicle simulations. Routing experiments focus on trucks for urban distribution of goods. The results indicate that time and energy estimations are significantly more precise than existing methods. Consequently the planned routes are expected to be feasible in terms of energy demand and that charging stops are properly included when necessary.