Abstract
Conventional developed component matching methods for a series type hybrid electric vehicle have a high computational burden or component alternation researches have considered only a few parts without the weight variation of each component. To address such problems, this study presents a novel component matching method with nonlinear programming (NLP) for a series hybrid electric bus. The fuel consumption minimization problem is discretized in time and multistarting points are used with the variations of each component. The proposed matching method suggests to use novel initial standards for component matching such that both the computational efficiency and accuracy could be achieved simultaneously. As a result, the most fuel efficient component combination among 8 components could be found, where the results were verified with those of dynamic programming (DP).
Similar content being viewed by others
Abbreviations
- a :
-
vehicle acceleration
- A :
-
frontal area
- B eff :
-
battery efficiency
- c d :
-
air drag coefficient
- DP:
-
dynamic programming
- fc total :
-
total fuel consumption
- g :
-
gravitational acceleration
- g e :
-
gear ratio between the engine and the generator
- I b :
-
battery current
- m :
-
gross weight
- NLP:
-
nonlinear programming
- OOP:
-
optimal operating point
- P e :
-
engine output power
- P f :
-
engine fuel power
- P g :
-
generator output power
- P m :
-
mechanical power in the traction motor
- P r :
-
required electric power in the traction motor
- Q :
-
total battery capacity
- r g :
-
reduction gear ratio
- R i :
-
total battery internal resistance
- r t :
-
tire radius
- SOC :
-
state of charge
- t r :
-
tractive resistance
- v s :
-
vehicle speed
- V bus :
-
bus voltage
- V o :
-
open circuit voltage
- w e :
-
engine output speed
- w e,max :
-
maximum engine speed
- w g :
-
generator speed
- w m :
-
traction motor speed
- ΔSOC :
-
variation of SOC
- η e :
-
combustion efficiency
- η g :
-
efficiency of the reduction gear
- η g :
-
efficiency of the generator
- η m :
-
efficiency of the motor
- θ :
-
slope angle
- μ :
-
rolling resistance coefficient
- ρ :
-
air density
- τ e :
-
engine output torque
- τ e,max :
-
maximum engine torque
- τ g :
-
generator torque
- τ m :
-
mechanical torque of the traction motor
References
Lee, D., Kim, N., Jeong, J., Park, Y., and Cha, S., “Component Sizing and Engine Optimal Operation Line Analysis for a Plug-In Hybrid Electric Transit Bus,” International Journal of Automotive Technology, Vol. 14, No. 3, pp. 459–469, 2013.
Chau, K. and Wong, Y., “Overview of Power Management in Hybrid Electric Vehicles,” Energy Conversion and Management, Vol. 43, No. 15, pp. 1953–1968, 2002.
Madanipour, V., Montazeri-Gh, M., and Mahmoodi-k, M., “Optimization of the Component Sizing for a Plug-In Hybrid Electric Vehicle Using a Genetic Algorithm,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 230, No. 5, pp. 692–708, 2016.
Ao, G.-Q., Qiang, J.-X., Zhong, H., Yang, L., and Zhuo, B., “Exploring the Fuel Economy Potential of ISG Hybrid Electric Vehicles through Dynamic Programming,” International Journal of Automotive Technology, Vol. 8, No. 6, pp. 781–790, 2007.
Pourabdollah, M., Silvas, E., Murgovski, N., Steinbuch, M., and Egardt, B., “Optimal Sizing of a Series PHEV: Comparison between Convex Optimization and Particle Swarm Optimization,” IFACPapersOnLine, Vol. 48, No. 15, pp. 16–22, 2015.
Bayindir, K. Ç., Gözüküçük, M. A., and Teke, A., “A Comprehensive Overview of Hybrid Electric Vehicle: Powertrain Configurations, Powertrain Control Techniques and Electronic Control Units,” Energy Conversion and Management, Vol. 52, No. 2, pp. 1305–1313, 2011.
Salmasi, F. R., “Control Strategies for Hybrid Electric Vehicles: Evolution, Classification, Comparison, and Future Trends,” IEEE Transactions on Vehicular Technology, Vol. 56, No. 5, pp. 2393–2404, 2007.
Gao, J., Zhu, G. G., Strangas, E. G., and Sun, F., “Equivalent Fuel Consumption Optimal Control of a Series Hybrid Electric Vehicle,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 223, No. 8, pp. 1003–1018, 2009.
Johri, R. and Filipi, Z., “Low-Cost Pathway to Ultra Efficient City Car: Series Hydraulic Hybrid System with Optimized Supervisory Control,” SAE International Journal of Engines, Vol. 2, No. 2009-24-0065, pp. 505–520, 2009.
Johri, R. and Filipi, Z., “Self-Learning Neural Controller for Hybrid Power Management Using Neuro-Dynamic Programming,” SAE Technical Paper, No. 2011-24-0081, Presented at ICE2011 Conference, 2011.
Johri, R., Salvi, A., and Filipi, Z., “Optimal Energy Management for a Hybrid Vehicle Using Neuro-Dynamic Programming to Consider Transient Engine Operation,” Proc. of ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Paper No. DSCC2011-6138, pp. 279–286 2011.
Jeong, J., Lee, D., Kim, N., Zheng, C., Park, Y.-I., and Cha, S. W., “Development of PMP-Based Power Management Strategy for a Parallel Hybrid Electric Bus,” Int. J. Precis. Eng. Manuf., Vol. 15, No. 2, pp. 345–353, 2014.
Paganelli, G., Delprat, S., Guerra, T.-M., Rimaux, J., and Santin, J.-J., “Equivalent Consumption Minimization Strategy for Parallel Hybrid Powertrains,” Proc. of IEEE 55th Vehicular Technology Conference, pp. 2076–2081 2002.
Pérez, L. V. and Pilotta, E. A., “Optimal Power Split in a Hybrid Electric Vehicle Using Direct Transcription of an Optimal Control Problem,” Mathematics and Computers in Simulation, Vol. 79, No. 6, pp. 1959–1970, 2009.
Pourabdollah, M., Murgovski, N., Grauers, A., and Egardt, B., “Optimal Sizing of a Parallel Phev Powertrain,” IEEE Transactions on Vehicular Technology, Vol. 62, No. 6, pp. 2469–2480, 2013.
Hu, X., Johannesson, L., Murgovski, N., and Egardt, B., “Longevity-Conscious Dimensioning and Power Management of the Hybrid Energy Storage System in a Fuel Cell Hybrid Electric Bus,” Applied Energy, Vol. 137, pp. 913–924, 2015.
Pisu, P. and Rizzoni, G., “A Comparative Study of Supervisory Control Strategies for Hybrid Electric Vehicles,” IEEE Transactions on Control Systems Technology, Vol. 15, No. 3, pp. 506–518, 2007.
Luján, J. M., Guardiola, C., Pla, B., and Reig, A., “Cost of Ownership-Efficient Hybrid Electric Vehicle Powertrain Sizing for Multi-Scenario Driving Cycles,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 230, No. 3, pp. 382–394, 2016.
Sundstrom, O., Guzzella, L., and Soltic, P., “Torque-Assist Hybrid Electric Powertrain Sizing: From Optimal Control towards a Sizing Law,” IEEE Transactions on Control Systems Technology, Vol. 18, No. 4, pp. 837–849, 2010.
Liao, Y. G. and Quail, A. M., “Component Sizing of Traction Motor in Hybrid Powertrains,” Proc. of Vehicle Power and Propulsion Conference (VPPC), pp. 1–6 2011.
Thibault, L., Grondin, O., Querel, C., and Corde, G., “Energy Management Strategy and Optimal Hybridization Level for a Diesel HEV,” SAE International Journal of Alternative Powertrains, Vol. 1, No. 1, pp. 260–271, 2012.
Guzzella, L. and Sciarretta, A., “Vehicle Propulsion Systems,” Springer, 2007.
Liu, X., Wu, Y., and Duan, J., “Optimal Sizing of a Series Hybrid Electric Vehicle Using a Hybrid Genetic Algorithm,” Proc. of IEEE International Conference on Automation and Logistics, pp. 1125–1129 2007.
Desai, C., Berthold, F., and Williamson, S.S., “Optimal Drivetrain Component Sizing for a Plug-In Hybrid Electric Transit Bus Using Multi-Objective Genetic Algorithm,” Proc. of Electric Power and Energy Conference (EPEC), pp. 1–5 2010.
Jeong, J., Lee, D., Shin, C., Jeong, D., Min, K., Cha, S. W., and Park, Y.-I., “Comparison of the Fuel Economy of Series and Parallel Hybrid Bus System Using Dynamic Programming,” Transactions of the Korean Society of Automotive Engineers, Vol. 21, No. 1, pp. 92–98, 2013.
Jeong, J.-R., Lee, D.-H., Shin, C.-W., Lim, W.-S., Park, Y.-I., and Cha, S.-W., “Analysis of Correlation of Fuel Efficiency and Cost Depending on Component Size of Heavy-Duty Parallel Hybrid System,” Transactions of the Korean Society of Automotive Engineers, Vol. 19, No. 3, pp. 73–82, 2011.
Kim, M., Jung, D., Kang, H., and Min, K., “Series-Type Hybrid Electric Bus Fuel Economy Increase with Optimal Component Sizing and Real-Time Control Strategy,” Transactions of the Korean Society of Mechanical Engineers B, Vol. 37, No. 3, pp. 307–312, 2013.
Zou, Y., Li, D.-G., and Hu, X.-S., “Optimal Sizing and Control Strategy Design for Heavy Hybrid Electric Truck,” Mathematical Problems in Engineering, Vol. 2012, Article ID: 404073, 2012.
Wu, X., Cao, B., Wen, J., and Wang, Z., “Application of Particle Swarm Optimization for Component Sizes in Parallel Hybrid Electric Vehicles,” Proc. of IEEE Congress on Evolutionary Computation, pp. 2874–2878 2008.
Nüesch, T., Ott, T., Ebbesen, S., and Guzzella, L., “Cost and Fuel-Optimal Selection of HEV Topologies Using Particle Swarm Optimization and Dynamic Programming,” Proc. of American Control Conference (ACC), pp. 1302–1307 2012.
Williamson, S. S., Wirasingha, S. G., and Emadi, A., “Comparative Investigation of Series and Parallel Hybrid Electric Drive Trains for Heavy-Duty Transit Bus Applications,” Proc. of Vehicle Power and Propulsion Conference, pp. 1–10 2006.
Wirasingha, S. G., Schofield, N., and Emadi, A., “Feasibility Analysis of Converting a Chicago Transit Authority (CTA) Transit Bus to a Plug-In Hybrid Electric Vehicle,” Proc. of Vehicle Power and Propulsion Conference, pp. 1–7 2008.
Nüesch, T., Elbert, P., Flankl, M., Onder, C., and Guzzella, L., “Convex Optimization for the Energy Management of Hybrid Electric Vehicles Considering Engine Start and Gearshift Costs,” Energies, Vol. 7, No. 2, pp. 834–856, 2014.
Verdonck, N., Chasse, A., Pognant-Gros, P., and Sciarretta, A., “Automated Model Generation for Hybrid Vehicles Optimization and Control,” Oil & Gas Science and Technology-Revue de l’Institut Français du Pétrole, Vol. 65, No. 1, pp. 115–132, 2010.
Gao, J., Sun, F., He, H., Zhu, G. G., and Strangas, E. G., “A Comparative Study of Supervisory Control Strategies for a Series Hybrid Electric Vehicle,” Proc. of Power and Energy Engineering Conference, pp. 1–7 2009.
Barsali, S., Miulli, C., and Possenti, A., “A Control Strategy to Minimize Fuel Consumption of Series Hybrid Electric Vehicles,” IEEE Transactions on Energy Conversion, Vol. 19, No. 1, pp. 187–195, 2004.
Xiong, W., Zhang, Y., and Yin, C., “Optimal Energy Management for a Series-Parallel Hybrid Electric Bus,” Energy Conversion and Management, Vol. 50, No. 7, pp. 1730–1738, 2009.
Kim, M., Jung, D., and Min, K., “Hybrid Thermostat Strategy for Enhancing Fuel Economy of Series Hybrid Intracity Bus,” IEEE Transactions on Vehicular Technology, Vol. 63, No. 8, pp. 3569–3579, 2014.
Zhu, Q., Wang, Q., and Chen, Q., “Component Sizing For Compound Hybrid Excavators,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 230, No. 7, pp. 969–982, 2016.
Enang, W., Bannister, C., Brace, C., and Vagg, C., “Modelling and Heuristic Control of a Parallel Hybrid Electric Vehicle,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 229, No. 11, pp. 1494–1513, 2015.
Pérez, L. and García, G., “State Constrained Optimal Control Applied to Supervisory Control in HEVs,” Oil & Gas Science and Technology-Revue de l’Institut Français du Pétrole, Vol. 65, No. 1, pp. 191–201, 2010.
Dosthosseini, R., Kouzani, A., and Sheikholeslam, F., “Direct Method for Optimal Power Management in Hybrid Electric Vehicles,” International Journal of Automotive Technology, Vol. 12, No. 6, pp. 943–950, 2011.
Sundström, O., Guzzella, L., and Soltic, P., “Optimal Hybridization in Two Parallel Hybrid Electric Vehicles Using Dynamic Programming,” IFAC Proceedings Volumes, Vol. 41, No. 2, pp. 4642–4647, 2008.
Zhang, C. and Vahidi, A., “Route Preview in Energy Management of Plug-in Hybrid Vehicles,” IEEE Transactions on Control Systems Technology, Vol. 20, No. 2, pp. 546–553, 2012.
Koot, M., Kessels, J. T., de Jager, B., Heemels, W., Van den Bosch, P., and Steinbuch, M., “Energy Management Strategies for Vehicular Electric Power Systems,” IEEE Transactions on Vehicular Technology, Vol. 54, No. 3, pp. 771–782, 2005.
Hargraves, C. R. and Paris, S. W., “Direct Trajectory Optimization Using Nonlinear Programming and Collocation,” Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, pp. 338–342, 1987.
Von Stryk, D. M. O., “Numerical Solution of Optimal Control Problems by Direct Collocation,” in: Optimal Control, Bulirsch, R., Miele, A., Stoer, J., Well, K., (Eds.), Springer, pp. 129–143, 1993.
Von Stryk, O. and Bulirsch, R., “Direct and Indirect Methods for Trajectory Optimization,” Annals of Operations Research, Vol. 37, No. 1, pp. 357–373, 1992.
Betts, J. T., “Practical Methods for Optimal Control and Estimation Using Nonlinear Programming,” SIAM, 2010.
Gill, P. E., Murray, W., and Saunders, M. A., “User’s Guide for SNOPT Version 7: Software for Large-Scale Nonlinear Programming,” http://web.stanford.edu/group/SOL/guides/sndoc7.pdf (Accessed 2 MAR 2017)
Kessels, J. T., Koot, M., de Jager, B., van den Bosch, P. P., Aneke, N., and Kok, D. B., “Energy Management for the Electric Powernet in Vehicles with a Conventional Drivetrain,” IEEE Transactions on Control Systems Technology, Vol. 15, No. 3, pp. 494–505, 2007.
Xuan, D., Kim, J., and Kim, Y., “Optimal Operation Strategy Development for Fuel Cell Hybrid Vehicle,” Journal of Mechanical Science and Technology, Vol. 25, No. 1, pp. 183–192, 2011.
Betts, J. T., “A Direct Approach to Solving Optimal Control Problems,” Computing in Science & Engineering, Vol. 1, No. 3, pp. 73–75, 1999.
Kleimaier, A. and Schroder, D., “Optimization Strategy for Design and Control of a Hybrid Vehicle,” Proc. of 6th International Workshop on Advanced Motion Control, pp. 459–464 2000.
Bäuml, B., Wimbö ck, T., and Hirzinger, G., “Kinematically Optimal Catching a Flying Ball with a Hand-Arm-System,” Proc. of IEEE/ RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2592–2599 2010.
Yan, F., Wang, J., and Huang, K., “Hybrid Electric Vehicle Model Predictive Control Torque-Split Strategy Incorporating Engine Transient Characteristics,” IEEE Transactions on Vehicular Technology, Vol. 61, No. 6, pp. 2458–2467, 2012.
Kermani, S., Delprat, S., Guerra, T.-M., Trigui, R., and Jeanneret, B., “Predictive Energy Management for Hybrid Vehicle,” Control Engineering Practice, Vol. 20, No. 4, pp. 408–420, 2012.
Guemri, M., Caux, S., Ngueveu, S. U., and Messine, F., “Heuristics and Lower Bound for Energy Management in Hybrid-Electric Vehicles,” Proceedings of MOSIM’12, 2012. https://hal.archivesouvertes. fr/hal-00728563 (Accessed 2 MAR 2017)
Guemri, M., Caux, S., and Ngueveu, S. U., “Using Quasi-Newton Method for Energy Management in Electrical Multi Source Systems,” Proc. of 11th International Conference on Environment and Electrical Engineering (EEEIC), pp. 194–199 2012.
Kim, M., Jung, D., and Min, K., “Hybrid Thermostat Strategy for Enhancing Fuel Economy of Series Hybrid Intracity Bus,” IEEE Transactions on Vehicular Technology, Vol. 63, No. 8, pp. 3569–3579, 2014.
He, H., Xiong, R., Guo, H., and Li, S., “Comparison Study on the Battery Models Used for the Energy Management of Batteries in Electric Vehicles,” Energy Conversion and Management, Vol. 64, No. pp. 113–121, 2012.
Murgovski, N., Johannesson, L., Sjöberg, J., and Egardt, B., “Component Sizing of a Plug-In Hybrid Electric Powertrain via Convex Optimization,” Mechatronics, Vol. 22, No. 1, pp. 106–120, 2012.
Tate, E. D. and Boyd, S. P., “Finding Ultimate Limits of Performance for Hybrid Electric Vehicles,” SAE Technical Paper, No. 2000-01-3099, 2000.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, M. Component matching of a series hybrid electric bus using nonlinear programming. Int. J. Precis. Eng. Manuf. 18, 1043–1056 (2017). https://doi.org/10.1007/s12541-017-0123-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12541-017-0123-3