Research Papers

Efficient Exhaustive Search of Power-Split Hybrid Powertrains With Multiple Planetary Gears and Clutches

[+] Author and Article Information
Xiaowu Zhang

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: xiaowuz@umich.edu

Shengbo Eben Li

State Key Laboratory of Automotive
Safety and Energy,
Tsinghua University,
Beijing 100084, China;
Department of Mechanical Engineering,
University of California, Berkeley,
Berkeley, CA 94720

Huei Peng

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109;
State Key Laboratory of Automotive
Safety and Energy,
Tsinghua University,
Beijing 100084, China

Jing Sun

Department of Naval Architecture
and Marine Engineering,
University of Michigan,
Ann Arbor, MI 48109

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 5, 2015; final manuscript received August 21, 2015; published online September 23, 2015. Assoc. Editor: Junmin Wang.

J. Dyn. Sys., Meas., Control 137(12), 121006 (Sep 23, 2015) (12 pages) Paper No: DS-15-1007; doi: 10.1115/1.4031533 History: Received January 05, 2015; Revised August 21, 2015

Planetary gear (PG) power-split hybrid powertrains have been used in producing hybrid and plug-in hybrid vehicles from the Toyota, General Motor, and Ford for years. Some of the most recent designs use clutches to enable multiple operating modes to improve launching performance and/or fuel economy. Adding clutches and multiple operating modes, however, also increases production cost and design complexity. To enable an exhaustive but fast search for optimal designs among a large number of hardware configurations, clutch locations, and mode selections, an automated modeling and screening process is developed in this paper. Combining this process with the power-weighted efficiency analysis for rapid sizing method (PEARS), an optimal and computationally efficient energy management strategy, the extremely large design space of configuration, component sizing, and control becomes feasible to search through. This methodology to identify optimal designs has yet to be reported in the literature. A case study to evaluate the proposed methodology uses the configuration adopted in the Toyota Hybrid Synergy (THS-II) system used in the Prius model year 2010 and the Hybrid Camry. Two designs are investigated to compare with the simulated Prius design: one uses all possible operating modes; and the other uses a suboptimal design that limits the number of clutches to three.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


2012, “ Part II: Environment Protection Agency,” Federal Register, Vol. 77, pp. 62623–63200.
Mi, C. , Masrur, M. A. , and Gao, D. , 2011, Hybrid Electric Vehicles: Principles and Applications With Practical Perspectives, Wiley Online Library, London.
Ehsani, M. , Gao, Y. , and Emadi, A. , 2009, Modern Electric Hybrid Electric and Fuel Cell Vehicles: Fundamentals, Theory, and Design, 2nd ed., CRC Press, Boca Raton.
Miler, M. , Holmes, A. , Conlon, B. , and Savagian, P. , 2011, “ The GM ‘Voltec’ 4ET50 Multi-Mode Electric Transaxle,” SAE Int., 4(1), pp. 1102–1114.
2010, “ Alternative Fuels and Advanced Vehicles Data Center, Data, Analysis, and Trends: Vehicle—HEV Sales by Model,” Last accessed Sept. 20, 2013, http://www.afdc.energy.gov/afdc/data/vehicles.html
Schmidt, M. R. , 1999, “ Two-Mode, Compound-Split Electro-Mechanical Vehicular,” U.S. Patent No. 5,931,757.
Rahman, K. , and Anwar, M. , 2011, “ The Voltec 4ET50 Electric Drive System,” SAE Int., 4(1), pp. 323–337.
Si, B. , 2011, “ Reconfiguration Hybrid Powertrain,” U.S. Patent No. 0,319,211.
Seo, K. , and Yang, H. , 2012, “ Powertrain for Hybrid Vehicle,” U.S. Patent No. 8,147,367.
Muta, K. , Yamazaki, M. , and Tokieda, J. , 2004, “ Development of New-Generation Hybrid System THS II—Drastic Improvement of Power Performance and Fuel Economy,” SAE Technical Paper No. 2004-01-0064.
Bucknor, N. K. , Hendrickson, J. D. , and Raghavan, M. , 2007, “ Electrically Variable Transmission Having Two Planetary Gear Sets With One Fixed Interconnection,” U.S. Patent No. 7,198,373.
Si, B. , 2011, “ Dual Mode Input Split Compound Split Configuration EPPV Transmission,” U.S. Patent No. 8,075,435.
Zhang, X. , Li, C.-T. , Kum, D. , and Peng, H. , 2012, “ Prius+ and Volt−: Configuration Analysis of Power-Split Hybrid Vehicles With a Single Planetary Gear,” IEEE Trans. Veh. Technol., 61(8), pp. 3544–3552. [CrossRef]
Liu, J. , and Peng, H. , 2010, “ A Systematic Design Approach for Two Planetary Gear Split Hybrid Vehicles,” Veh. Syst. Dyn., 48(11), pp. 1395–1412. [CrossRef]
Li, C.-T. , and Peng, H. , 2010, “ Optimal Configuration Design for Hydraulic Split Hybrid Vehicles,” American Control Conference, Baltimore, MD, pp. 5812–5817.
Hermance, D. , 1999, “ Toyota Hybrid System,” SAE TOPTEC Conference, Albany, NY.
Jalil, N. , Kheir, N. , and Salman, M. , 1997, “ A Rule-Based Energy Management Strategy for a Series Hybrid Vehicle,” American Control Conference, Albuquerque, NM, June 4–6, pp. 689–693.
Pagalelli, G. , Delprat, S. , Guerra, T. , Rimaux, J. , and Santin, J. , 2002, “ Equivalent Consumption Minimization Strategy for Parallel Hybrid Powertrains,” 55th IEEE Vehicular Technology Conference, pp. 2076–2081.
Sciarretta, A. , Back, M. , and Guzzella, L. , 2004, “ Optimal Control of Parallel Hybrid Electric Vehicles,” IEEE Trans. Veh. Technol., 12(3), pp. 352–363.
Delprat, S. , Lauber, J. , Guerra, T. M. , and Rimaux, J. , 2004, “ Control of a Parallel Hybrid Powertrain: Optimal Control,” IEEE Trans. Veh. Technol., 53(3), pp. 872–881. [CrossRef]
Delprat, S. , Guerra, T. M. , and Rimaux, J. , 2002, “ Control Strategies for Hybrid Vehicles: Optimal Control,” 56th IEEE Vehicular Technology Conference, Vancouver, BC, Canada, pp. 1681–1685.
Kim, N. , Cha, S. , and Peng, H. , 2010, “ Optimal Control of Hybrid Electric Vehicles Based on Pontryagin's Minimum Principle,” IEEE Trans. Control Syst. Technol., 19(5), pp. 1279–1287.
Lin, C.-C. , Peng, H. , Grizzle, J. , and Kang, J.-M. , 2003, “ Power Management Strategy for a Parallel Hybrid Electric Truck,” IEEE Trans. Control Syst. Technol., 11(6), pp. 839–849. [CrossRef]
Liu, J. , and Peng, H. , 2006 “ Control Optimization for a Power-Split Hybrid Vehicle,” American Control Conference, Minneapolis, MN, pp. 466–471.
Murgovski, N. , Johannesson, L. , Sjoberg, J. , and Egardt, B. , 2012, “ Component Sizing of a Plug-In Hybrid Electric Powertrain Via Convex Optimization,” Mechatronics, 22(1), pp. 106–120. [CrossRef]
Hu, X. , Murgovski, N. , Johannesson, L. , and Egardt, B. , 2013, “ Energy Efficiency Analysis of a Series Plug-In Hybrid Electric Bus With Different Energy Management Strategies and Battery Sizes,” Appl. Energy, 111, pp. 1001–1009. [CrossRef]
Hu, X. , Murgovski, N. , Johannesson, L. , and Egardt, B. , 2014, “ Comparison of Three Electrochemical Energy Buffers Applied to a Hybrid Bus Powertrain With Simultaneous Optimal Sizing and Energy Management,” IEEE Trans. Intell. Transp. Syst., 15(3), pp. 1193–1205. [CrossRef]
Zhang, X. , Peng, H. , and Sun, J. , 2015, “ A Near-Optimal Energy Management Strategy for Rapid Component Sizing of Multimode Power Split Hybrid Vehicles,” IEEE Trans. Control Syst. Technol., 23(2), pp. 609–618. [CrossRef]
Benford, H. , and Leising, M. , 1981, “ The Lever Analogy: A New Tool in Transmission Analysis,” SAE Paper No. 810102.
Olszewski, M. , 2011, “ Evaluation of the 2010 Toyota Prius Hybrid Synergy Drive System,” Oak Ridge National Laboratory Report.
Kawamoto, N. , Naiki, K. , Kawai, T. , Shikida, T. , and Tomatsuri, M. , 2009, “ Development of New 1.8-Liter Engine for Hybrid Vehicles,” SAE Technical Paper No. 2009-01-1061.


Grahic Jump Location
Fig. 2

All 16 possible clutch locations for a double PG system

Grahic Jump Location
Fig. 1

PG and its lever analogy

Grahic Jump Location
Fig. 6

The PEARS + process

Grahic Jump Location
Fig. 3

The lever diagram of THS-II

Grahic Jump Location
Fig. 5

The simulink diagram of a general multimode HEV powertrain system

Grahic Jump Location
Fig. 10

Trajectories of PEARS+ in the FUDS cycle

Grahic Jump Location
Fig. 8

Lever diagram of the Prius 2010++

Grahic Jump Location
Fig. 9

Trajectories of DP in the FUDS cycle

Grahic Jump Location
Fig. 7

Power flow in the hybrid mode

Grahic Jump Location
Fig. 11

Two types of configurations

Grahic Jump Location
Fig. 12

All feasible and nonredundant modes for the configuration used in Prius 2010, grouped into 14 mode types

Grahic Jump Location
Fig. 13

Optimal modes used in the FUDS and HWFET cycles

Grahic Jump Location
Fig. 14

The mode types and usage frequency (percentage of time each mode type is used) of the Utopian design

Grahic Jump Location
Fig. 16

Optimization results comparing three-clutch designs and the benchmarks

Grahic Jump Location
Fig. 17

Lever diagrams of the two suboptimal designs selected in Fig. 16

Grahic Jump Location
Fig. 18

The mode types and usage frequency of the suboptimal design for fuel economy

Grahic Jump Location
Fig. 19

The mode types and usage frequency of the suboptimal design for drivability

Grahic Jump Location
Fig. 15

The mode shift and acceleration profile of the Utopian design



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In