PHEV powertrain co-design with vehicle performance considerations using MDSDO

  • Saeed AzadEmail author
  • Mohammad Behtash
  • Arian Houshmand
  • Michael J. Alexander-Ramos
Research Paper


The complexity of plug-in hybrid-electric vehicles (PHEVs) motivates the simultaneous integration of component design and supervisory control strategy decisions. Methods from combined optimal design and control (co-design) are generally used to manage such integrated system design decisions. Although several studies have investigated the PHEV powertrain co-design problem, the impact of key vehicle performance criteria such as 0–60 mph acceleration time and all-electric-range (AER) has rarely been explicitly included in such system co-design problems. This is problematic as these vehicle performance criteria strongly affect component sizing and control strategy in a way that a non-performance-based co-design solution could become sub-optimal. Therefore, this study addresses this issue by formulating and solving a PHEV powertrain co-design problem that explicitly includes vehicle-level performance constraints. In particular, a three-phase, PHEV powertrain co-design problem is solved to simultaneously identify the optimal supervisory control strategies during the acceleration performance and standard duty cycle phases, along with the optimal component designs spanning all phases (acceleration performance, standard duty cycle, and AER performance) such that the vehicle powertrain cost is minimized. A relatively new, balanced co-design approach known as multidisciplinary dynamic system design optimization (MDSDO) is used to solve the problem. The optimal design and standard duty cycle supervisory control trajectories are compared to the solution of a non-performance-based co-design problem. The results indicate that the formal inclusion of vehicle performance criteria in a co-design problem significantly affects component design and supervisory control strategies.


PHEV powertrains Co-design Vehicle performance criteria MDSDO 


Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflicts of interest.


  1. Allison JT, Herber DR (2014) Special section on multidisciplinary design optimization: multidisciplinary design optimization of dynamic engineering systems. AIAA JournalGoogle Scholar
  2. Allison JT, Guo T, Han Z (2014) Co-design of an active suspension using simultaneous dynamic optimization. J Mech Des 136(8):081,003CrossRefGoogle Scholar
  3. Azad S, Alexander-Ramos MJ (2018) Robust mdsdo for co-design of stochastic dynamic systems. In: ASME 2018 international design engineering technical conferences and computers and information in engineering conference, american society of mechanical engineers, pp V02AT03A002–V02AT03A002Google Scholar
  4. Azad S, Behtash M, Houshmand A, Alexander-Ramos M (2017) Comprehensive PHEV powertrain co-design performance studies using MDSDO. In: World congress of structural and multidisciplinary optimisation. Springer, pp 83–97Google Scholar
  5. Bayrak AE, Kang N, Papalambros PY (2016) Decomposition-based design optimization of hybrid electric powertrain architectures: Simultaneous configuration and sizing design. J Mech Des 138(7):071,405CrossRefGoogle Scholar
  6. Behtash M, Alexander-Ramos MJ (2018) Decomposition-based MDSDO For co-design of large-scale dynamic systems. In: ASME 2018 international design engineering technical conferences and computers and information in engineering conferenceGoogle Scholar
  7. Brooker AD, Ward J, Wang L (2013) Lightweighting impacts on fuel economy, cost, and component losses. Tech rep, SAE technical paperGoogle Scholar
  8. Burress T, Coomer C, Campbell S, Seiber L, Marlino LD, Staunton R, Cunningham J (2008) Evaluation of the 2007 toyota camry hybrid synergy drive system. Tech rep, Oak Ridge National Laboratory (ORNL)Google Scholar
  9. Burress TA, Campbell SL, Coomer C, Ayers CW, Wereszczak AA, Cunningham JP, Marlino LD, Seiber LE, Lin HT (2011) Evaluation of the 2010 toyota prius hybrid synergy drive system. Tech rep, Oak Ridge National Laboratory (ORNL); Power electronics and electric machinery research facilityGoogle Scholar
  10. Cluzel C, Douglas C, et al. (2012) Cost and performance of EV batteries. Element energy, final report for the committee on climate changeGoogle Scholar
  11. Contestabile M, Offer G, Slade R, Jaeger F, Thoennes M (2011) Battery electric vehicles, hydrogen fuel cells and biofuels. which will be the winner? Energ Environ Sci 4(10):3754–3772CrossRefGoogle Scholar
  12. Deshmukh AP, Allison JT (2016) Multidisciplinary dynamic optimization of horizontal axis wind turbine design. Struct Multidiscip Optim 53(1):15–27MathSciNetCrossRefGoogle Scholar
  13. Duleep G, van Essen H, Kampman B, Grünig M (2011) Impacts of electric vehicles - deliverable 2, assessment of electric vehicle and battery technology. Tech rep, CE Delft, ICF, EcologicGoogle Scholar
  14. Egardt B, Murgovski N, Pourabdollah M, Mardh LJ (2014) Electromobility studies based on convex optimization: design and control issues regarding vehicle electrification. IEEE Control Syst 34(2):32–49MathSciNetCrossRefGoogle Scholar
  15. Fathy HK, Reyer JA, Papalambros PY, Ulsov A (2001) On the coupling between the plant and controller optimization problems. In: Proceedings of American control conference, 2001, vol 3. IEEE, pp 1864–1869Google Scholar
  16. Fathy HK, Papalambros PY, Ulsoy AG, Hrovat D (2003) Nested plant/controller optimization with application to combined passive/active automotive suspensions. In: Proceedings of the 2003 American control conference, 2003, vol 4. IEEE, pp 3375–3380Google Scholar
  17. Geng B, Mills J, Sun D (2014) Combined power management/design optimization for a fuel cell/battery plug-in hybrid electric vehicle using multi-objective particle swarm optimization. Int J Automot Technol 15(4):645–654CrossRefGoogle Scholar
  18. Herber DR, Allison JT (2017) Nested and simultaneous solution strategies for general combined plant and controller design problems. In: ASME 2017 international design engineering technical conferences and computers and information in engineering conference. ASME, pp V02AT03A002–V02AT03A002Google Scholar
  19. Heywood JB, et al. (1988) Internal combustion engine fundamentals. Mcgraw-hill, New YorkGoogle Scholar
  20. Houshmand A (2016) Multidisciplinary dynamic system design optimization of hybrid electric vehicle powertrains. PhD thesis, University of CincinnatiGoogle Scholar
  21. Hu X, Murgovski N, Johannesson LM, 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):1193–1205CrossRefGoogle Scholar
  22. Hu X, Moura SJ, Murgovski N, Egardt B, Cao D (2016) Integrated optimization of battery sizing, charging, and power management in plug-in hybrid electric vehicles. IEEE Trans Control Syst Technol 24(3):1036–1043CrossRefGoogle Scholar
  23. Le Berr F, Abdelli A, Postariu DM, Benlamine R (2012) Design and optimization of future hybrid and electric propulsion systems: an advanced tool integrated in a complete workflow to study electric devices. Oil Gas Sci Technol 67(4):547–562CrossRefGoogle Scholar
  24. Li L, Zhang Y, Yang C, Jiao X, Zhang L, Song J (2015) Hybrid genetic algorithm-based optimization of powertrain and control parameters of plug-in hybrid electric bus. J Frankl Inst 352(3):776–801zbMATHCrossRefGoogle Scholar
  25. Liu J, Peng H (2008) Modeling and control of a power-split hybrid vehicle. IEEE Trans Control Syst Technol 16(6):1242–1251CrossRefGoogle Scholar
  26. Liu J, Peng H, Filipi Z (2005) Modeling and analysis of the toyota hybrid system. TIc 200:3Google Scholar
  27. Lucidi S, Rinaldi F (2010) Exact penalty functions for nonlinear integer programming problems. J Optim Theory Appl 145(3):479–488MathSciNetzbMATHCrossRefGoogle Scholar
  28. Maples JM (2013) Vehicle choice modeling and projections for the annual energy outlook., Accessed 10-June-2018
  29. McKinsey (2014) Electric vehicles in europe: gearing up for a new phase? Tech rep, Amsterdam Roundtable Foundation and McKinsey & CompanyGoogle Scholar
  30. Moura SJ (2011) Techniques for battery health conscious power management via electrochemical modeling and optimal control. PhD thesis, University of MichiganGoogle Scholar
  31. Moura SJ, Callaway DS, Fathy HK, Stein JL (2010) Tradeoffs between battery energy capacity and stochastic optimal power management in plug-in hybrid electric vehicles. J Power Sources 195(9):2979–2988CrossRefGoogle Scholar
  32. Moura SJ, Fathy HK, Callaway DS, Stein JL (2011) A stochastic optimal control approach for power management in plug-in hybrid electric vehicles. IEEE Trans Control Syst Technol 19(3):545–555CrossRefGoogle Scholar
  33. Murgovski N, Johannesson L, Sjöberg J, Egardt B (2012) Component sizing of a plug-in hybrid electric powertrain via convex optimization. Mechatronics 22(1):106–120CrossRefGoogle Scholar
  34. Murgovski N, Hu X, Johannesson L, Egardt B (2014a) Combined design and control optimization of hybrid vehicles. Handbook of clean energy systemsGoogle Scholar
  35. Murgovski N, Johannesson LM, Egardt B (2014b) Optimal battery dimensioning and control of a cvt phev powertrain. IEEE Trans Veh Technol 63(5):2151–2161CrossRefGoogle Scholar
  36. Nam EK, Giannelli R (2005) Fuel consumption modeling of conventional and advanced technology vehicles in the physical emission rate estimator (pere). US environmental protection agencyGoogle Scholar
  37. Patil RM (2012) Combined design and control optimization: application to optimal PHEV design and control for multiple objectives. PhD thesis, University of MichiganGoogle Scholar
  38. Patterson MA, Rao AV (2014) Gpops-II: a matlab software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans Math Softw (TOMS) 41(1):1MathSciNetzbMATHCrossRefGoogle Scholar
  39. Peters DL, Papalambros PY, Ulsoy AG (2009) On measures of coupling between the artifact and controller optimal design problems. In: Proceedings of the 2009 ASME design engineering technical conferenceGoogle Scholar
  40. Peters DL, Papalambros P, Ulsoy A (2011) Control proxy functions for sequential design and control optimization. J Mech Des 133(9):091,007CrossRefGoogle Scholar
  41. Plotkin S, Singh M, et al. (2009) Multi-path transportation futures study: vehicle characterization and scenario analyses. Tech rep, Argonne National Laboratory (ANL)Google Scholar
  42. Pourabdollah M, Murgovski N, Grauers A, Egardt B (2013) Optimal sizing of a parallel phev powertrain. IEEE Trans Veh Technol 62(6):2469–2480CrossRefGoogle Scholar
  43. Raghavachari M (1969) On connections between zero-one integer programming and concave programming under linear constraints. Oper Res 17(4):680–684MathSciNetzbMATHCrossRefGoogle Scholar
  44. Reyer JA (2000) Combined embodiment design and control optimization: effects of cross-disciplinary coupling. PhD thesis, The University of MichiganGoogle Scholar
  45. Reyer JA, Papalambros PY (2002) Combined optimal design and control with application to an electric dc motor. J Mech Des 124(2):183–191CrossRefGoogle Scholar
  46. Rousseau A, Shidore N, Carlson R, Freyermuth V, et al. (2007) Research on phev battery requirements and evaluation of early prototypes. In: 7th advanced automotive battery conference, pp 16–18Google Scholar
  47. Silvas E, Hofman T, Murgovski N, Etman LP, Steinbuch M (2017) Review of optimization strategies for system-level design in hybrid electric vehicles. IEEE Trans Veh Technol 66(1):57–70Google Scholar
  48. Simpson A (2006) Cost-benefit analysis of plug-in hybrid electric vehicle technology. In: Presented at the 22nd international battery, hybrid and fuel cell electric vehicle symposium and exhibition, Yokohama, JapanGoogle Scholar
  49. Soong WL (1993) Design and modeling of axially-laminated interior permanent magnet motor drives for field-weakening applications. PhD thesis, University of GlasgowGoogle Scholar
  50. Sovacool BK, Hirsh RF (2009) Beyond batteries: an examination of the benefits and barriers to plug-in hybrid electric vehicles (phevs) and a vehicle-to-grid (v2g) transition. Energy Policy 37(3):1095–1103CrossRefGoogle Scholar
  51. Van Mierlo J, Van den Bossche P, Maggetto G (2004) Models of energy sources for ev and hev: fuel cells, batteries, ultracapacitors, flywheels and engine-generators. J Power Sources 128(1):76–89CrossRefGoogle Scholar
  52. Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106(1):25–57MathSciNetzbMATHCrossRefGoogle Scholar
  53. Wu L, Wang Y, Yuan X, Chen Z (2011) Multiobjective optimization of HEV fuel economy and emissions using the self-adaptive differential evolution algorithm. IEEE Trans Veh Technol 60(6):2458–2470CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, College of Engineering and Applied SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Boston UniversityBostonUSA

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