Moments of power: Statistical analysis of the primary energy consumption of a vehicle

The energy consumption of a vehicle is typically determined either by testing or in simulation. While both approaches are valid, they only work for a specific drive cycle, they are time intensive, and they do not directly result in a closed-form relationship between key parameters and consumption. This paper presents an alternative approach that determines the consumption based on a simple analytical model of the vehicle and statistical parameters of the drive cycle, specifically the moments of the velocity. This results in a closed-form solution that can be used for analysis or synthesis.

The drive cycle is quantified via its moments, specifically the average speed, the standard deviation of the speed as well as the higher order moments skewness, and the kurtosis. A mixed quadratic term is added to account for acceleration or aggressiveness, but it is noticeably distinct from the conventional metric of positive kinetic energy (PKE). The vehicle is quantified using a polynomial model of the traction force and of the primary energy consumption of the powertrain. This model form fits both conventional and electrified powertrains, including all the component efficiencies.

Through a statistical analysis of the model, the primary energy consumption can be related to both the model parameters and the statistical properties of the drive cycle. This result can be useful for the analysis of a drive cycle, for the analysis of a powertrain, for economy optimization, and for control purposes. An example of a Nissan LEAF powertrain is presented over different cycles.