This content is not included in your SAE MOBILUS subscription, or you are not logged in.
Willans Line Bidirectional Power Flow Model for Energy Consumption of Electric Vehicles
ISSN: 0148-7191, e-ISSN: 2688-3627
Published March 29, 2022 by SAE International in United States
Annotation ability available
A new and unique electric vehicle powertrain model based on bidirectional power flow for propel and regenerative brake power capture is developed and applied to production battery electric vehicles. The model is based on a Willans line model to relate power input from the battery and power output to tractive effort, with one set of parameters (marginal efficiency and an offset loss) for the bidirectional power flow through the powertrain. An electric accessory load is included for the propel, brake and idle phases of vehicle operation. In addition, regenerative brake energy capture is limited with a regen fraction (where the balance goes to friction braking), a power limit, and a low-speed cutoff limit. The purpose of the model is to predict energy consumption and range using only tractive effort based on EPA published road load and test mass (test car list data) and vehicle powertrain parameters derived from EPA reported unadjusted UDDS and HWFET energy consumption. The model can then be applied for other drive cycles, road grades, and parasitic accessory loads due to cabin or battery heating, air conditioning/cooling, or additional ADAS and autonomy loads (cameras and radar sensors, and compute and actuation hardware). The modeled battery net energy consumption is within 1% error for the UDDS and HWFET data used for fitting the powertrain parameters, as expected. The model is then applied to a vehicle that also has US06 data available, and predicts the US06 energy consumption to within 4%, validating the model parameterization method. The proposed modeling method is applied to a range of current and past EVs with very accurate results. A sensitivity study provides insight into the model parameters and similarities of electric powertrain efficiency among different classes of vehicles.
CitationHarvey, D. and Nelson, D., "Willans Line Bidirectional Power Flow Model for Energy Consumption of Electric Vehicles," SAE Technical Paper 2022-01-0531, 2022.
- Willans , P.W. Economy Trials of a Non-Condensing Steam Engine—Simple, Compound, and Triple Scientific American 25 647 1888 10331 10333 https://doi.org/10.1038/scientificamerican05261888-10331bsupp
- Phlips , P. Analytic Engine and Transmission Models for Vehicle Fuel Consumption Estimation SAE Int. J. Fuels Lubr. 8 2 2015 423 440 https://doi.org/10.4271/2015-01-0981
- Phlips , P. , Ruona , W. , Megli , T. , and Orpe , M. Unified Power-Based Vehicle Fuel Consumption Model Covering a Range of Conditions SAE Int. J. Adv. & Curr. Prac. in Mobility 2 4 2020 2320 2336 https://doi.org/10.4271/2020-01-1278
- Thomas , J. Drive Cycle Powertrain Efficiencies and Trends Derived from EPA Vehicle Dynamometer Results SAE Int. J. Passeng. Cars - Mech. Syst. 7 4 2014 1374 1384 https://doi.org/10.4271/2014-01-2562
- Brooker , A. , Gonder , J. , Wang , L. , Wood , E. et al. FASTSim: A Model to Estimate Vehicle Efficiency, Cost and Performance SAE Technical Paper 2015-01-0973 2015 https://doi.org/10.4271/2015-01-0973
- Holden , J. , Reinicke , N. , and Cappellucci , J. RouteE: A Vehicle Energy Consumption Prediction Engine SAE Int. J. Adv. & Curr. Prac. in Mobility 2 5 2020 2760 2767 https://doi.org/10.4271/2020-01-0939
- Environmental Protection Agency 2021 https://www.epa.gov/compliance-and-fuel-economy-data/data-cars-used-testing-fuel-economy
- Environmental Protection Agency 2021 https://www.epa.gov/vehicle-and-fuel-emissions-testing/dynamometer-drive-schedules
- Environmental Protection Agency 2021 https://iaspub.epa.gov/otaqpub/pubadvsearch.jsp
- Sovran , G. and Blaser , D. A Contribution to Understanding Automotive Fuel Economy and Its Limits SAE Technical Paper 2003-01-2070 2003 https://doi.org/10.4271/2003-01-2070
- www.fueleconomy.gov 2021 https://www.fueleconomy.gov/
- Light Duty Vehicle Performance and Economy Measure Committee n.d. https://doi.org/10.4271/j1634_202104
- Rask , E. , Santini , D. , and Lohse-Busch , H. Analysis of Input Power, Energy Availability, and Efficiency during Deceleration for X-Ev Vehicles SAE Int. J. Alt. Power. 2 2 2013 350 361 https://doi.org/10.4271/2013-01-1473
- Nakamura , E. , Soga , M. , Sakai , A. , Otomo , A. et al. Development of Electronically Controlled Brake System for Hybrid Vehicle SAE Technical Paper 2002-01-0300 2002 https://doi.org/10.4271/2002-01-0300