Optimal Powertrain Dimensioning and Potential Assessment of Hybrid Electric Vehicles

Hybrid electric vehicles (HEVs), compared to conventional vehicles, complement the traditional combustion engine with one, or several electric motors and an energy buffer, typically a battery and/or an ultracapacitor. This gives the vehicle an additional degree of freedom that allows for a more efficient operation, by e.g. recuperating braking energy, or operating the engine at higher efficiency. In order to be cost effective, the HEV may need to include a downsized engine and a carefully selected energy buffer. The optimal size of the powertrain components depends on the powertrain configuration, ability to draw electric energy from the grid, charging infrastructure, drive patterns, varying fuel, electricity and energy buffer prices and on how well adapted is the buffer energy management to driving conditions. This thesis provides two main contributions for optimal dimensioning of HEV powertrains while optimally controlling the energy use of the buffer on prescribed routes. The first contribution is described by a methodology and a tool for potential assessment of HEV powertrains. The tool minimizes the need for interaction from the user by automizing the processes of powertrain simplification and optimization. The HEV powertrain models are simplified by removing unnecessary dynamics in order to speed up computation time and allow Dynamic Programming to be used to optimize the energy management. The tool makes it possible to work with non-transparent models, e.g. models which are compiled, or hidden for intellectual property reasons. The second contribution describes modeling steps to reformulate the powertrain dimensioning and control problem as a convex optimization problem. The method considers quadratic losses for the powertrain components and the resulting problem is a semidefinite convex program. The optimization is time efficient with computation time that does not increase exponentially with the number of states. This makes it possible to include more accurate models in the optimization, e.g. powertrain components with thermal properties.

[1]  Theo Hofman,et al.  Framework for combined control and design optimization of hybrid vehicle propulsion systems , 2007 .

[2]  Ji‐Guang Zhang,et al.  Ambient operation of Li/Air batteries , 2010 .

[3]  Bruce Edsall Seely,et al.  The Electric Vehicle and the Burden of History , 2002 .

[4]  Jonas Fredriksson,et al.  A methodology and a tool for evaluating hybrid electric powertrain configurations , 2011 .

[5]  Nikolce Murgovski,et al.  Automatic Simplification of Hybrid Powertrain Models for Use in Optimization , 2010 .

[6]  Nikolce Murgovski,et al.  Hybrid powertrain concept evaluation using optimization , 2010 .

[7]  Olivier Hayat,et al.  Powertrain Driveability Evaluation: Analysis and Simplification of Dynamic Models , 2003 .

[8]  Xiaolin Hu,et al.  Multi-Objective Optimization of HEV Fuel Economy and Emissions using Evolutionary Computation , 2004 .

[9]  Olle Sundström,et al.  A generic dynamic programming Matlab function , 2009, 2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC).

[10]  J. R. Bumby,et al.  Computer modelling of the automotive energy requirements for internal combustion engine and battery electric-powered vehicles , 1985 .

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  Petter Krus,et al.  Evaluating hybrid electric and fuel cell vehicles using the capsim simulation environment , 2006 .

[13]  Hosam K. Fathy,et al.  Tradeoffs between battery energy capacity and stochastic optimal power management in plug-in hybrid electric vehicles , 2010 .

[14]  Yair Ein-Eli,et al.  Review on Liair batteriesOpportunities, limitations and perspective , 2011 .

[15]  T. C. Moore HEV control strategy: implications of performance criteria, system configuration and design, and component selection , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[16]  Henrik Sandberg,et al.  Modelling and Control of Series HEVs Including Resistive Losses and Varying Engine Efficiency , 2009 .

[17]  Huei Peng,et al.  Power management strategy for a parallel hybrid electric truck , 2003, IEEE Trans. Control. Syst. Technol..

[18]  Judy Anderson,et al.  Electric and Hybrid Cars: A History , 2004 .

[19]  M Maarten Steinbuch,et al.  Hybrid component specification optimisation for a medium-duty hybrid electric truck , 2008 .

[20]  J. Gover,et al.  Optimizing the Hybridization Factor for a Parallel Hybrid Electric Small Car , 2006, 2006 IEEE Vehicle Power and Propulsion Conference.

[21]  H. Chandler Practical , 1982, Digital Transformation of the Laboratory.

[22]  Anders Grauers,et al.  Optimal Sizing of a Parallel PHEV Powertrain , 2013, IEEE Transactions on Vehicular Technology.

[23]  Huei Peng,et al.  Power management and design optimization of fuel cell/battery hybrid vehicles , 2007 .

[24]  William Rowan Hamilton Second Essay on a General Method in Dynamics. [Abstract] , 1830 .

[25]  Ilya V. Kolmanovsky,et al.  Ultracapacitor Assisted Powertrains: Modeling, Control, Sizing, and the Impact on Fuel Economy , 2011, IEEE Transactions on Control Systems Technology.

[26]  Kim-Chuan Toh,et al.  On the Implementation and Usage of SDPT3 – A Matlab Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0 , 2012 .

[27]  Lino Guzzella,et al.  Vehicle Propulsion Systems: Introduction to Modeling and Optimization , 2005 .

[28]  Vadim I. Utkin,et al.  Model-Based Fuel Optimal Control of Hybrid Electric Vehicle Using Variable Structure Control Systems , 2004 .

[29]  Srdjan M. Lukic,et al.  Effects of drivetrain hybridization on fuel economy and dynamic performance of parallel hybrid electric vehicles , 2004, IEEE Transactions on Vehicular Technology.

[30]  Huei Peng,et al.  Automated Modelling of Power-Split Hybrid Vehicles , 2008 .

[31]  Lars Johannesson Predictive Control of Hybrid Electric Vehicles on Prescribed Routes , 2009 .

[32]  Alois Amstutz,et al.  CAE tools for quasi-static modeling and optimization of hybrid powertrains , 1999 .

[33]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[34]  Mehrdad Ehsani,et al.  A Matlab-based modeling and simulation package for electric and hybrid electric vehicle design , 1999 .

[35]  Michael Johansson,et al.  Feasability study of dual-mode buses in Gothenburg´s public transport , 2011 .

[36]  G. Maggetto,et al.  VEHICLE SIMULATION PROGRAM : A TOOL TO EVALUATE HYBRID POWER MANAGEMENT STRATEGIES BASED ON AN INNOVATIVE ITERATION , 2001 .

[37]  U Zoelch,et al.  Dynamic optimization method for design and rating of the components of a hybrid vehicle , 2014 .

[38]  Nikolce Murgovski,et al.  Convex optimization of charging infrastructure design and component sizing of a plug-in series HEV powertrain , 2011 .

[39]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[40]  E. J. McShane On Multipliers for Lagrange Problems , 1939 .

[41]  Lino Guzzella,et al.  Introduction to Modeling and Control of Internal Combustion Engine Systems , 2004 .

[42]  Dimitri Peaucelle,et al.  SEDUMI INTERFACE 1.02: a tool for solving LMI problems with SEDUMI , 2002, Proceedings. IEEE International Symposium on Computer Aided Control System Design.

[43]  A. Burke Ultracapacitors: why, how, and where is the technology , 2000 .

[44]  Olle Sundstrom,et al.  Optimal control and design of hybrid-electric vehicles , 2009 .

[45]  L. Triger,et al.  Hybrid vehicle engine size optimization , 1993 .

[46]  E. Blum,et al.  The Mathematical Theory of Optimal Processes. , 1963 .

[47]  Huei Peng,et al.  Combined control/plant optimization of fuel cell hybrid vehicles , 2006, 2006 American Control Conference.

[48]  J.M. Miller,et al.  Ultracapacitor Plus Battery Energy Storage System Sizing Methodology for HEV Power Split Electronic CVT's , 2005, Proceedings of the IEEE International Symposium on Industrial Electronics, 2005. ISIE 2005..

[49]  Alfredo Vaccaro,et al.  A genetic-based methodology for hybrid electric vehicles sizing , 2001, Soft Comput..

[50]  L. Gaines,et al.  COSTS OF LITHIUM-ION BATTERIES FOR VEHICLES , 2000 .

[51]  Ilya Kolmanovsky,et al.  Approximate dynamic programming solutions for lean burn engine aftertreatment , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[52]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[53]  Jonas Sjöberg,et al.  A tool for generating optimal control laws for hybrid electric powertrains , 2010 .

[54]  Jing Sun,et al.  Optimal control-based powertrain feasibility assessment: A software implementation perspective , 2005, Proceedings of the 2005, American Control Conference, 2005..

[55]  Lino Guzzella,et al.  Optimal Hybridization in Two Parallel Hybrid Electric Vehicles using Dynamic Programming , 2008 .

[56]  S. J. Pachernegg,et al.  A Closer Look at the Willans-Line , 1969 .

[57]  K. B. Wipke,et al.  ADVISOR 2.1: a user-friendly advanced powertrain simulation using a combined backward/forward approach , 1999 .

[58]  Lino Guzzella,et al.  Implementation of Dynamic Programming for $n$-Dimensional Optimal Control Problems With Final State Constraints , 2013, IEEE Transactions on Control Systems Technology.

[59]  J Van Mierlo,et al.  Technical Note: Vehicle simulation program: A tool to evaluate hybrid power management strategies based on an innovative iteration algorithm , 2001 .

[60]  Olle Sundström,et al.  Torque-Assist Hybrid Electric Powertrain Sizing: From Optimal Control Towards a Sizing Law , 2010, IEEE Transactions on Control Systems Technology.

[61]  Pierluigi Pisu,et al.  A Comparative Study Of Supervisory Control Strategies for Hybrid Electric Vehicles , 2007, IEEE Transactions on Control Systems Technology.

[62]  L. Guzzella,et al.  Control of hybrid electric vehicles , 2007, IEEE Control Systems.

[63]  C. Sadarangani,et al.  The four-quadrant energy transducer , 2002, Conference Record of the 2002 IEEE Industry Applications Conference. 37th IAS Annual Meeting (Cat. No.02CH37344).

[64]  Andrew F. Burke,et al.  Batteries and Ultracapacitors for Electric, Hybrid, and Fuel Cell Vehicles , 2007, Proceedings of the IEEE.

[65]  Bo Egardt,et al.  Assessing the Potential of Predictive Control for Hybrid Vehicle Powertrains Using Stochastic Dynamic Programming , 2005, IEEE Transactions on Intelligent Transportation Systems.

[66]  Alberto Bemporad,et al.  HYSDEL-a tool for generating computational hybrid models for analysis and synthesis problems , 2004, IEEE Transactions on Control Systems Technology.

[67]  Giorgio Rizzoni,et al.  Unified modeling of hybrid electric vehicle drivetrains , 1999 .

[68]  G. H. Cole,et al.  SIMPLEV: A simple electric vehicle simulation program, Version 1.0 , 1991 .

[69]  Keith Wipke,et al.  ANALYSIS OF THE FUEL ECONOMY BENEFIT OF DRIVETRAIN HYBRIDIZATION , 1997 .

[70]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[71]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[72]  Gilbert Ames Bliss The Problem of Lagrange in the Calculus of Variations , 1930 .

[73]  M Maarten Steinbuch,et al.  Parametric modeling of components for selection and specification of hybrid vehicle drivetrains , 2007 .

[74]  Lino Guzzella,et al.  Vehicle Propulsion Systems , 2013 .

[75]  Lino Guzzella,et al.  Explicit optimal control policy and its practical application for hybrid electric powertrains , 2010 .

[76]  Tony Markel,et al.  ADVISOR: A SYSTEMS ANALYSIS TOOL FOR ADVANCED VEHICLE MODELING , 2002 .

[77]  H. Witsenhausen A class of hybrid-state continuous-time dynamic systems , 1966 .

[78]  Stephen P. Boyd,et al.  Finding Ultimate Limits of Performance for Hybrid Electric Vehicles , 2000 .

[79]  Thierry-Marie Guerra,et al.  Control of a parallel hybrid powertrain: optimal control , 2004, IEEE Transactions on Vehicular Technology.

[80]  Lino Guzzella,et al.  On Implementation of Dynamic Programming for Optimal Control Problems with Final State Constraints , 2010 .