Modeling, analysis, and optimal control of hybrid electric vehicle powertrains

Pogoni hibridnih električnih vozila sastoje se od dvaju ili više različitih energetskih izvora u svrhu smanjenja potrošnje goriva i emisija štetnih plinova. Zbog složenosti takvih pogona, primjenjuju se prikladni upravljački sustavi, čija se sinteza temelji na opsežnom računalnopodržanom optimiranju i simulacijama koje zahtijevaju točne i računalno efikasne matematičke modele. U radu se predlaže modeliranje kinematike i dinamike hibridnih pogona, te analiza njihovih tokova snage, primjenom grafo-analitičkog postupka veznih dijagrama. Zatim se razmatra globalno optimiranje upravljačkih varijabli pogona električnog vozila proširenog dometa pomoću algoritma dinamičkog programiranja, a rezultati optimiranja dobiveni za razne režime rada pogona se potom koriste u parametriranju i provjeri sustava upravljanja. Konačno, predlaže se postupak višekriterijskog optimiranja dimenzija komponenti električnog vozila proširenog dometa, uz korištenje parametarski optimirane skalabilne strategije upravljanja temeljene na kombiniranju upravljanja zasnovanog na bazi pravila i trenutačne minimizacije ekvivalentne potrošnje goriva.For the last two decades, passenger vehicles have been increasingly equipped with hybrid electric powertrains in order to provide significant gains in fuel economy, and also reductions in greenhouse gases emissions. Due to the fact that the hybrid powertrains consist of two or more different energy sources, the many variants of the powertrains are present, from simpler ones, such as parallel configurations to the more complex series-parallel structures. Currently, the full hybrid systems are mostly based on series-parallel configuration, which consists of an internal combustion engine, two electrical machines, electrochemical battery, one or more planetary gears used as powersplit devices, and possibly the clutches which determine the powertrain operating mode. Such a concept is known as a power-split or electronic continuously variable transmission (e-CVT or electric variator), because it can provide optimal engine speed operation for a wide range of vehicle velocities. The complex structure of HEV powertrains opens many questions in terms of HEV powertrain structure selection, components sizing and energy management control, which all have influence on the powertrain price and efficiency. The power-flow analysis can provide good preliminary insights into HEV powertrain operations, and also its advantages and disadvantages. However, control variables optimization is usually used in order to find minimum possible fuel consumption and optimal control rules for different operating regimes. The optimization problem is to find time responses of control variables, which minimize the fuel consumption, while satisfying physical constraints of the transmission components. Among various control variable optimization methods, the Dynamic Programming (DP) approach is usually used in literature, because of its unique feature to provide the global optimum solution. The control strategy of hybrid electric vehicles consists of low-level and high-level subsystems, where the low-level control subsystem is responsible for providing proper system transient and steady-state behaviours, in order to bring the powertrain components into operating points requested from the high-level (supervisory) controller. The supervisory controller can be of different types such as rule-based controllers, controllers based on instantaneous equivalent fuel consumption minimization strategy (ECMS), fuzzy logic controllers, controllers using the game theory, and self-learning neural network controllers. In order to define optimal hybrid electric vehicle component sizing and optimal control rules with respect to criteria of minimizing the investment cost and the fuel consumption rate (exploitation price), multi-objective optimization approaches have been considered based on applying suitable component sizing parameter optimization algorithms. Thus, for a certain structure of hybrid electric powertrain and for certain driving scenario the optimal configuration and control rules are aimed to be defined. The fundamental problem of this combined approach is its demand for an extensive computational power, particularly if the computationally inefficient DP algorithm is used on the control level. The main goal of this thesis is to develop a systematic approach to modelling of kinematics and dynamics of HEV powertrains, graphical analysis of power flow, and interactive optimization of component sizing parameters and control variables with the aim of minimizing the HEV investment and exploitation cost. Chapter 1 “Introduction” gives an overview of the doctoral thesis, the current state of the art and the main goals and hypotheses of the thesis. Chapter 2 “Modelling of hybrid electric powertrains” presents the use of bond graph modelling approach for modelling the kinematics and dynamics of common series-parallel hybrid electric vehicle (HEV) powertrains. The main advantages of this approach include a straightforward way of transforming the mechanical system structure into a bond graph/mathematical model, modelling modularity, and ease of handling the redundant state variables. The latter results in a minimum-realization state-space dynamics model convenient for efficient computer simulations, and various analysis and controller design studies. The structure of this model is the same for all considered transmissions, while only the parameters are different. Chapter 3 “Powerflow analysis of hybrid electric powertrains” demonstrates that bond graph model provides a unique graphical representation of relations between the torque, speed, and power variables of complex series-parallel HEV transmissions. It, thus, represents a powerful tool for analyzing the power flow in HEV transmissions for different characteristic transmission configurations and operating modes. Various effects such as output torque boost at low vehicle velocities, negative electrical power recirculation in the electric variator configuration, and constraints related to optimal engine operation can readily be visualized and understood by using the bond graph models. Chapter 4 “Control variables optimization of hybrid powertrains” describes a dynamic programming-based approach of optimizing the operating mode selection, generator speed, and engine torque control variables of an Extended Range Electric Vehicle (EREV) transmission for different certification driving cycles. The optimization is based on a simplified (backward-looking) powertrain model with the battery state-of-charge as the only state variable. The optimization goal is to minimize the battery energy consumption in the case of charge depleting mode (CD) or to minimize the fuel consumption for the charge sustaining mode (CS) and the blended mode (BLND), while satisfying transmission components constraints, and the state-of-charge bounds and boundary condition. The optimization results, particularly those related to the operating mode boundary curves and to the state-of-charge trajectory in the BLND mode, can be directly used for designing an appropriate rule-based energy management control strategy. The optimization results can also be used as an "idealized" optimization benchmark for verifying/assessing various control strategies. Chapter 5 “Control system of hybrid electric powertrain” outlines an energy management control strategy for the EREV powertrain. The adopted control strategy takes the complementary advantages of a rule-based+SoC controller and an exact (non-adaptive) instantaneous, equivalent consumption minimization strategy (ECMS). The strategy is designed for the CD mode, and extended with more refined rules and ECMS for the CS mode. The control strategy is verified by computer simulation against the DP-based optimization benchmark. Chapter 6 “Multi-objective optimization of an extended range electric delivery truck component sizing” first describes the virtual conversion of a conventional delivery truck to a fully electric one. For that purpose, a backward-looking model of a diesel engine-propelled mid-size delivery truck is built up and experimentally validated in terms of cumulative fuel consumption prediction for previously experimentally recorded diving cycles. Comparison of the two vehicles, conventional and fully electric ones, in the terms of energy cost and wellwheel CO2 emissions for the constant vehicle velocity mode and realistic driving cycles is presented. The fully electric truck model is then converted into a series-type EREV model with scalable submodels of the battery and the range extender module. The EREV model also includes control strategy from Chapter 5, which has been made scalable with optimized parameters, and verified against the DP global optimum benchmark. Finally the multiobjective optimization of the EREV drivetrain components is conducted, including discussion of the obtained results. Chapter 7 “Conclusion” summarizes the main achievements of the doctoral thesis, which are claimed to include the following original scientific contributions: I) Systematic graphoanalytical approach for a kinematic and dynamic modelling, and power-flow analysis of the hybrid vehicle powertrains based on the bond graph methodology, II) Control variable optimisation of a complex structure of extended range electric vehicle for various operating modes and driving cycles, with clear recommendations for the synthesis of optimal control management system, and III) Numerically efficient procedure for multi-objective optimization of power train component sizing parameters for an extended range electric delivery truck, with an interactive application of sizing parameter search algorithm and the parameteroptimized scalable control strategy