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International Journal of Automotive Technology

, Volume 20, Issue 1, pp 37–49 | Cite as

Power Management Strategy for the 48 V Mild Hybrid Electric Vehicle Based on the Charge-Sustaining Control

  • Jeongwon Sohn
  • Myoungho Sunwoo
  • Kyunghan Min
  • Jaewook Shin
  • Manbae HanEmail author
Article
  • 1 Downloads

Abstract

To enhance the 48 V mild hybrid electric vehicle performance using a smaller capacity and lower voltage battery than the full hybrid electric vehicle, a novel power management strategy needs to be established that considers the characteristics and limitations of the components. This paper proposes a charge-sustaining control strategy as a ground principle of the 48 V hybrid electric vehicle control for managing the battery state-of-charge (SOC) to stay near the most efficient regime. The base efficiency characteristics of the component models including engine, motor/generator, and battery are determined in the form of efficiency maps using the powertrain analysis tool. Then the control strategy is formulated as a nonlinear optimal regulation problem that meets two conflicting control objectives, such as fuel efficiency improvement and state-of-charge maintenance. The optimal regulation problem implements a discrete-time Hamilton-Jacobi-Bellman approach. The proposed strategy is evaluated by comparing with the reference strategy applying the Dynamic Programming (DP), i.e. a global optimal result, under urban dynamometer driving schedule and worldwide harmonized light duty test cycle. Through the evaluation, the fuel efficiency of the proposed strategy with three different electrical loads is slightly deteriorated at most by 5.03 % from the DP results with staying within a desirable SOC. This suggests that the proposed strategy is operating very closely to global optimal performances.

Key words

48 V mild hybrid electric vehicle Charge-sustaining control Hamilton-Jacobi-Bellman Optimal regulation problem Power management strategy 

Nomenclature

BSFC

engine, brake specific fuel consumption, g/kWh

fbat,int.c

battery, function for internal charge resistance

fbat,int.d

battery, function for internal discharge resistance

fbat,oc

battery, function for open circuit voltage

feng,fuel

engine, function for fuel efficiency

fmge

M/G, function for electric power efficiency

fmgm

M/G, function for mechanical power efficiency

H(·)

Hamiltonian function

Ibat,int,c

battery, internal charge current, A

Ibat,int,d

battery, internal discharge current, A

Ibat,t

battery, internal temperature, A

J(·)

cost function

mfuel

engine, fuel consumption rate, kg/sec

nbat,cell

battery, the number of cell

p

lyapunov coefficient

Pbat12

battery, power 12 V, W

Pbat48

battery, power 48 V, W

Pbat,max

battery, maximum power, W

Pdc12

DC/DC converter, outlet power (12 V power-net), W

Pdc48

DC/DC converter, inlet power (48 V power-net), W

Pdt

drivetrain, power, W

Pel

electric loads, consumed power, W

Pel12

electric loads, consumed power (12 V power-net), W

Pel48

electric loads, consumed power (48 V power-net), W

Peng

engine, power, W

Pma

mechanical accessary, power, W

Pmg

M/G, power, W

Pmgm

M/G, mechanical power, W

Pmge

M/G, electrical power, W

Qbat

battery, cell capacity, Ah

Rbat,int,c

battery, internal charge resistance, Ω

Rbat,int,d

battery, internal discharge resistance, Ω

SOC

SOC

SOC0

battery, SOC initial value

SOCe

battery, SOC error between current and target SOC

SOCinit

battery, initial SOC

SOCtgt

battery target SOC

Ts

calculation interval, sec

tbat,int

battery, internal temperature, °C

uτ

control input = τmg,dmd / τdrv,dmd

V(·)

value function in Hamilton-Jacobi-Bellman equation

Vbat,oc

battery, open circuit voltage, V

Vbat,t

battery, internal temperature, V

Vdc

DC/DC converter target voltage, V

Vveh

vehicle speed, km/h

ηbat,c

battery, charge efficiency, %

ηbat,d

battery, discharge efficiency, %

τdrv,dmd

driver, torque demand, Nm

τeng

engine, torque, Nm

τeng,dmd

engine, torque demand, Nm

τeng,max

engine, maximum permissible torque, Nm

τeng,min

engine, minimum permissible torque, Nm

τmg

M/G, torque, Nm

τmg,dmd

M/G, torque demand, Nm

τmg,max

M/G, maximum permissible torque, Nm

τmg,min

M/G, minimum permissible torque, Nm

ωeng

engine, rotational speed, rad/s

ωmg

M/G, rotational speed, rad/s

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References

  1. Abu-Khalaf, M. and Lewis, F. L. (2005). Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica 415, 779–791.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Al-Tamimi, A., Lewis, F. L. and Abu-Khalaf, M. (2008). Discrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proof. IEEE Trans. Systems, Man, and Cybernetics, Part B (Cybernetics) 38, 4, 943–949.CrossRefGoogle Scholar
  3. Anderman, M. (2013). Assessing the Future of Hybrid and Electric Vehicles: The 2014 xEV Industry Insider Report Based on Private Onsite Interviews with Leading Technologists and Executives. 2014 Edition.Google Scholar
  4. Argonne (2009). Autonomie v1210. UChicago Argonne, LLC.Google Scholar
  5. Argonne (2007). PSAT v6.2, Argonne National Laboratory.Google Scholar
  6. Bellman, R. E. and Dreyfus, S. E. (1962). Applied Dynamic Programming. Princeton University Press. Princeton, New Jersey, USA.CrossRefzbMATHGoogle Scholar
  7. Benchetrite, D. (2013). Hybrid4all: A low voltage, low cost, mass-market hybrid solution. Proc. Int. Conf. Automotive 48 V Power Supply Systems, Berlin, Germany.Google Scholar
  8. Buchmann, I. (2014). Lithium-based Batteries. Battery University; Cadex Electronics Inc. http://batteryuniversity.com/learn/article/lithium_based_batteries Google Scholar
  9. Chen, Z. and Jagannathan, S. (2008). Generalized Hamilton-Jacobi-Bellman formulation -based neural network control of affine nonlinear discrete-time systems. IEEE Trans. Neural Networks 19, 1, 90–106.CrossRefGoogle Scholar
  10. Haddad, W. M., Chellaboina, V.-S., Fausz, J. L. and Abdallah, C. (1998). Optimal discrete-time control for non-linear cascade systems. J. Franklin Institute 335, 5, 827–839.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Hou, C., Ouyang, M., Xu, L. and Wang, H. (2014). Approximate Pontryagin’s minimum principle applied to the energy management of plug-in hybrid electric vehicles. Applied Energy, 115, 174–189.CrossRefGoogle Scholar
  12. Kim, C. S., Park, K., Kim, H., Lee, G., Lee, K., Yang, H. J., Cho, H., Song, M. and Son, Y. (2013). 48 V power assist recuperation system (PARS) with a permanent magnet motor, inverter and DC-DC converter. Proc. IEEE Int. Future Energy Electronics Conf. (IFEEC), Tainan, Taiwan.Google Scholar
  13. Kim, N., Cha, S. and Peng, H. (2011). Optimal control of hybrid electric vehicles based on pontryagin's minimum principle. IEEE Trans. Control Systems Technology 19, 5, 1279–1287.CrossRefGoogle Scholar
  14. Kim, N., Cha, S. and Peng, H. (2012). Optimal equivalent fuel consumption for hybrid electric vehicles. IEEE Trans. Control Systems Technology 20, 3, 817–825.CrossRefGoogle Scholar
  15. Kirk, D. E. (2004). Optimal Control Theory: An Introduction. Dover Publications. Mineola, New York, USA.Google Scholar
  16. Lewis, F. L., Vrabie, D. L. and Syrmos, V. L. (2012). Optimal Control. 3rd edn. John Wiley & Sons. Hoboken, New Jersey, USA.CrossRefzbMATHGoogle Scholar
  17. Liu, W. (2013). Introduction to Hybrid Vehicle System Modeling and Control. John Wiley & Sons. Hoboken, New Jersey, USA.CrossRefGoogle Scholar
  18. Mate, J.-L. (2013). 48 V eco-hybrid systems. Proc. European Conf. Nanoelectronics and Embedded Systems for Electric Mobility Toulouse, Toulouse, France.Google Scholar
  19. Naidu, D. S. (2002). Optimal Control Systems. Taylor & Francis. Boca Raton, Florida, USA.CrossRefGoogle Scholar
  20. Ornelas, F., Sanchez, E. N. and Loukianov, A. G. (2011). Discrete-time nonlinear systems inverse optimal control: A control Lyapunov function approach. Proc. IEEE Int. Conf. Control Applications (CCA), Denver, Colorado, USA.Google Scholar
  21. Pang, S., Farrell, J., Jie, D. and Barth, M. (2001). Battery state-of-charge estimation. Proc. IEEE American Control Conf., Arlington, Virginia, USA.Google Scholar
  22. Robert Bosch GmbH (2007). Bosch Automotive Handbook. John Wiley & Sons. Hoboken, New Jersey, USA.Google Scholar
  23. SAE International (2014). Hybrid Electric Vehicle (HEV) and Electric Vehicle (EV) Terminology. Surface Vehicle Information Report. J1715_201410.Google Scholar
  24. Sampathnarayanan, B., Onori, S. and Yurkovich, S. (2012). An optimal regulation strategy for energy management of hybrid electric vehicles. Proc. IEEE Conf. Decision and Control (CDC), Maui, Hawaii, USA.Google Scholar
  25. Saridis, G. N. and Lee, C.-S. G. (1979). An approximation theory of optimal control for trainable manipulators. IEEE Trans. Systems, Man, and Cybernetics 9, 3, 152–159.MathSciNetCrossRefzbMATHGoogle Scholar
  26. Sohn, J. (2015). Electric Power Management Strategy for 48V Mild Hybrid Electric Vehicles Based on a Chargesustaining Control Applying Hamilton-Jacobi-Bellman Approach. Ph. D. Dissertation. Hanyang University. Seoul, Korea.Google Scholar

Copyright information

© The Korean Society of Automotive Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jeongwon Sohn
    • 1
  • Myoungho Sunwoo
    • 2
  • Kyunghan Min
    • 2
  • Jaewook Shin
    • 2
  • Manbae Han
    • 3
    Email author
  1. 1.VC Green Controller SW Team, LG Electronics Inc.Seo-gu, IncheonKorea
  2. 2.Department of Automotive EngineeringHanyang UniversitySeoulKorea
  3. 3.Department of Mechanical and Automotive EngineeringKeimyung UniversityDaeguKorea

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