The Fixed Route Electric Vehicle Charging Problem with nonlinear energy management and variable vehicle speed.

The problem of an individual who wants to plan a long route in an electric vehicle where charging decisions are needed can be modeled as an instance of the Fixed Route Electric Vehicle Charging Problem (FRVCP). We developed a mixed-integer programming model that optimally solves a new variant of the FRVCP, the FRVCP with nonlinear energy management (FRVCP-NLEM). It considers charging times as a nonlinear function and allows to decide at which speed to drive on each segment of the route while considering the non-linearity of energy consumption functions. The non-linearity of all functions has been solved using multiple linear approximations. The proposed model is tested using an electric vehicle trip planner called PlaniCharge that uses realistic energy consumption and charging functions that take into account external factors such as temperature and road topology. The model is tested under different road types such as urban or highway routes. The proposed model is able to optimally solve most test instances within seconds. Results show that varying the vehicle speed is an important factor to consider under low temperatures and for long-range routes as it can reduce total route duration. Some routes cannot be completed at maximum speed and require varying driving speed on segment to be able to reach the destination.