The Impact of Regenerative Braking on the Powertrain-Delivered Energy Required for Vehicle Propulsion. 2011-01-0891
Driving schedules prescribed for fuel-economy regulation are composed of two generic modes: (1) accelerations and constant-speed travel, requiring a positive tractive force at a vehicle's driving wheels; (2) decelerations, requiring a negative or braking force at those wheels. In the first mode, a total tractive energy, ETR, is required to overcome a vehicle's tire rolling resistance, aerodynamic drag, and the inertia of its mass. In the second mode, all the kinetic energy that a vehicle's mass acquired in the first mode has to be removed. The inherent rolling resistance and aerodynamic drag remove some of it. The remainder, EBR, has to be removed by a wheel-braking force.
In vehicles with conventional braking the wheel-braking force is frictional, and so all of EBR is dissipated. However, if this force is not inherently frictional some of EBR can be captured, stored, and subsequently used to provide part of the ETR required for propulsion. This reduces EPT, the powertrain's responsibility for ETR, leading to reduced fuel consumption. The magnitude of the reduced responsibility is dependent on: (1) the magnitude of EBR relative to ETR; (2) the overall
braking-wheels to driving-wheels effectiveness, ξ, with which the regenerative-braking system converts EBR into recycled energy delivered to the driving wheels.
For the EPA Urban and Highway driving schedules, simple algebraic correlations have previously been developed for quantifying ETR and EBR. These are used to generate a plot of EBR/ETR for broad ranges of vehicle mass, tire rolling resistance, and aerodynamic drag. As an example of the results, a representative Midsize vehicle has an EBR that is 45% of ETR on the Urban schedule. This is the "carrot" for regenerative braking, and it increases significantly with increasing vehicle size.
For any given vehicle/driving schedule combination, regeneration-system effectiveness, ξ, determines the reduction in required powertrain-delivered energy. If that vehicle had conventional braking, an equal reduction in powertrain responsibility would require an equal reduction in its ETR. The
greatest and most important contributor to that energy is vehicle mass, M. Consequently, the benefit of increasing ξ in regenerative braking can be equivalated to the benefit of decreasing M in the vehicle configuration with conventional braking. Equations for this equivalence are developed using the correlations for ETR and EBR.
Example Tables are generated to quantify the equivalence for the representative Midsize vehicle. Since regenerative braking adds mass to a vehicle, several percentage increases are considered. The equivalent mass reduction increases rapidly with increasing ξ. At ξ = 70%, the mass reduction is 39% on the Urban schedule for a system that doesn't add mass, decreasing to 36% for a system that increases it by 5%. The corresponding values for the Highway schedule are smaller, 15% and 11%, but still substantial. In the limiting case of ξ=100%, the corresponding Urban values are 56% and 54%, respectively, while the Highway value are 21% and 18%. The Tables also suggest that efforts to increase ξ need not be limited to ones that do not increase the mass of the regenerative-braking system.
The impact of reduction in the actual mass of a hybrid vehicle on the required powertrain-delivered energy, EPT, is examined. Such reduction influences both tire rolling resistance and vehicle kinetic energy. A sensitivity factor relating percentage reduction in mass to the resultant percentage reduction in EPT is derived for each. Their variation with ξ is tabulated for the Midsize vehicle. As ξ increases from zero the kinetic-energy sensitivity decreases, while the rolling-resistance one increases. The former reduces to zero at ξ = 1.0, leaving only the rolling-resistance sensitivity. Consequently, at this limiting condition a reduction in tire coefficient r₀ is as effective in reducing EPT as reduction in vehicle mass, M.
Since large values of ξ are equivalent to large reductions in vehicle mass, even when a regeneration system adds mass to a vehicle, they suggest that development effort to achieve them warrants comparable effort to that expended for reducing baseline vehicle mass. In addition, high values can reduce the incentive to downsize vehicles for fuel-economy improvement, thereby avoiding reductions in consumer choice, and reduced occupant safety in vehicle collisions.