A Computationally Efficient Framework for Modelling Energy Consumption of ICE and Electric Vehicles

Working out how much energy a truck uses on a stretch of road is well understood: integrate the equations of motion over the drive cycle, the speed and gradient profile of the journey, with the vehicle’s mass, drag and rolling resistance. The difficulty is cost. Done the conventional way the calculation is too slow to sit inside anything that has to evaluate it thousands of times a second, and a route optimiser is exactly that.

Madhusudhanan, Na and Cebon, at the University of Cambridge Department of Engineering, set out a way round it. The energy for a leg is split into two parts: a vector that describes the drive cycle (the speed profile, the elevation, the timing) and a vector that describes the vehicle (its mass including payload, its drag, its rolling resistance). Energy use becomes a multiplication of the two. The drive-cycle part can be computed once per leg and the vehicle part changes with the load, so the question “how much energy does this vehicle, carrying this much, use on this leg starting at this time” is cheap to ask repeatedly.

The paper validates the framework against a conventional model for two vehicles, an electric bus and a diesel truck. The mean error against that model is under 2 percent, its standard deviation under 5 percent, and the mean computation time is under 20 milliseconds, two orders of magnitude faster than the conventional model. Those error figures are a measure of how closely the fast model tracks the slow one, not of either against metered consumption on the road; the paper is clear about that and so are we.

This is the basis of Optrak’s EV modelling. For each leg between two sites Optrak builds the energy use as a function of start time (because congestion changes the drive cycle) and of vehicle mass (because the load changes through the route), and that sits in the same matrix layer as distance and journey time, so the optimiser reads energy for every candidate move rather than checking range afterwards. It is also what makes in-route charging tractable: the energy either side of a proposed charging stop has to be cheap to evaluate, or the search cannot afford to consider the stop at all.

Read the paper: doi.org/10.3390/en14072031 (open access)

Published in Energies, volume 14, article 2031 (MDPI, 2021). This is not Optrak’s research. It is work from Cambridge Engineering that the product is built on; Optrak is a member of the Centre for Sustainable Road Freight, the industry and academic consortium that Cambridge Engineering anchors, which is how the collaboration came about.