Power for traction characterized by normal distributions

Most studies on power train design rely on deterministic driving cycles to define the vehicles longitudinal speed. Especially simulations on hybrid propulsion systems use driving cycles to define the speed sequence of the vehicle and backwards calculate the power for traction. Disadvantages of this deterministic approach are the limited value of one driving cycle to represent real-life conditions and the possibility of ’cycle beating’ in optimizations. Observations suggest that the distribution of the power for traction is more easily characterized than the distribution of the speed, as it tends to a bell-shaped curve. This study proposes to approximate the bell-shaped distribution with a normal (Gaussian) distribution when considering sizing hybrid electric propulsion system with a fixed gear ratio. This proposal is motivated from simulations, chassis dynamometer experiments and real-world data. In addition, mean and variance of the normal distribution are linked to the parameters of the vehicle and the properties of the driving cycle under consideration. The resulting characterization of the power for traction with a normal distribution provides a more generic specification for the vehicles power demand than deterministic driving cycles. This simplifies decisions on the sizing power train components and the engineering of the energy management system, as results not only hold for one driving cycle but for all driving conditions that match the same statistical distribution of the power for traction.