Convex Fuel Consumption Model for Diesel and Hybrid Buses

The concave fuel consumption model may generate unrealistic driving recommendations in a control system; for instance, the model may recommend higher cruise speed to achieve lower fuel consumption levels on steeper roads. To improve the model performance with regard to driving control, the study developed a convex second-order polynomial fuel consumption model for conventional diesel and hybrid-electric buses. The model simultaneously circumvents the bang-bang type of control that implies that drivers would have to accelerate at full throttle or brake at full braking to minimize their fuel consumption levels. Six bus series (four diesel series and two hybrid series), covering a wide range of bus properties, were modeled. The model was developed on the basis of the Virginia Tech comprehensive power fuel-based model (VT-CPFM) framework and, given a lack of readily available data, calibrated by conducting empirical measurements. The model was validated by comparing its estimates against in-field measurements and predictions from the comprehensive modal emissions model, the Motor Vehicle Emissions Simulator model, and the concave VT-CPFM model. The results demonstrate that the convex model generates estimates consistent with field measurements and the predictions of the other models and can provide realistic driving recommendations without significantly sacrificing accuracy relative to the concave model. Optimum fuel economy cruise speed ranges from 39 to 47 km/h for all tested buses on grades ranging from 0% to 8% and decreases with the increase of grade and vehicle load.