2442 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 6, JULY 2012 Topology Optimization for Hybrid Electric Vehicles With Automated Transmissions Theo Hofman, Søren Ebbesen, and Lino Guzzella, Senior Member, IEEE Abstract—Currently, many different topologies are designed with different transmission technologies such as automated man- ual transmission (AMT) and continuously variable transmission (CVT). The choice of topology determines the energy-flow effi- ciency between the hybrid system, the engine, and the vehicle wheels. The optimal topology minimizing fuel consumption is influenced by the transmission technology. Therefore, an AMT (high efficiency) and a push-belt CVT (moderate efficiency), are used in this research for comparison. In addition, a controlled switching topology is introduced as a benchmark, where controlled coupling with additional clutches of the electric machine before or after the transmission minimizing transmission losses and im- proving hybrid performance is investigated. The results showed that a switching topology can significantly improve CO 2 emission reduction (average relative improvements between 2% and 7%), particularly for CVT-based hybrid vehicles. Moreover, in case of an AMT, a precoupled topology is preferable, and in the case of a CVT, a postcoupled is preferable for full-hybrid vehicles. For these cases, selecting the optimal fixed topology can improve the relative CO 2 emission reduction between 2% and 8%. Index Terms—Dynamic programming (DP), energy manage- ment, fuel optimal control, modeling, optimization, road vehicle propulsion, topology, transmission. I. I NTRODUCTION D ESIGNING a hybrid electric drivetrain for a vehicle is a complex task. This multidomain design problem includes finding optimal component sizes, component technology, topol- ogy, and control design [1]. Moreover, all areas of this non- convex nonlinear design problem (see, e.g., [2]) are interlinked and often require a multiobjective design solution, e.g., min- imization of production cost while maximizing measures of environmental and dynamic performance such as CO 2 emission reduction, vehicle acceleration, comfort, and driveability. Many different and new hybrid (electric and mechanical) drivetrain topologies are developed and introduced into the market [3]. A topology is largely defined by the position of the electric machine(s) in the drivetrain, where it may be either pre- or postcoupled to the transmission. In addition, different Manuscript received September 5, 2011; revised January 2, 2012 and February 26, 2012; accepted March 30, 2012. Date of publication April 25, 2012; date of current version July 10, 2012. The review of this paper was coordinated by Dr. C. C. Mi. T. Hofman is with the Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands (e-mail: t.hofman@tue.nl). S. Ebbesen and L. Guzzella are with the Institute of Dynamic Systems and Control, Department of Mechanical and Process Engineering, Swiss Fed- eral Institute of Technology, 8092 Zurich, Switzerland (e-mail: sebbesen@ idsc.mavt.ethz.ch; lguzzella@ethz.ch). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2012.2196299 types of transmission technologies are used. For example, the Mercedes S400 Hybrid uses a seven-speed automated trans- mission (7-AT) in combination with a precoupled electric ma- chine (160-N · m/15-kW) and two clutches [4], and the Honda Civic IMA uses a push-belt continuously variable transmission (CVT) also in combination with a precoupled electric machine (103-N · m/15-kW) yet with a single clutch. In contrast, the Toyota Prius uses an electrical CVT (e-CVT) consisting of two electric machines (30-kW/50-kW) with a planetary gear set [5]. The electric machine at the wheel side (50-kW) is used for electric driving and braking while the engine is off [6]. Since the largest part of the total fuel-saving potential is obtained using these modes (together with engine start/stop at vehicle stand- still), this topology can be seen as a fixed topology, where the electric machine is primarily postcoupled to the transmission. Recently, a new demonstrator vehicle was realized with the electric machine (15-kW) fixed coupled at the posttransmission side in combination with a push-belt CVT realizing fuel savings between 8% and 10% on the New European Driving Cycle (NEDC), compared with the precoupled topology [7]. In this paper, we investigate and compare the potential of three different full-parallel hybrid electric drivetrain topologies: the first topology has a precoupled electric machine, i.e., the location of electric machine is fixed between the engine and the transmission; the second topology has a postcoupled elec- tric machine, i.e., the electric machine is fixed between the transmission and the differential. The third topology allows the energy management system to select the location of the electric machine between pre- and postcoupling, using an appropriate system of clutches. In addition, to have a fair comparison between the different topologies with the maximum potential, we investigate the influence of the choice of topology on the optimal sizing of the electric machine and engine. Moreover, two different transmission technologies are considered, i.e., a six-speed automated manual transmission (AMT) and a push- belt CVT. The potential of each topology is quantified in terms of CO 2 (in grams per kilometers) emissions. Dynamic programming (DP), in combination with prescribed drive cycles, is used to compute the minimum CO 2 emissions of each vehicle con- figuration. This way, the influence of the energy management strategy is removed from the investigation. This paper is organized as follows. In Section II, the three dif- ferent topologies are conceptually presented. In Section III, the topologies are mathematically modeled, where the kinematic constraints are also explained. The model-scaling methods for the main components are explained in Section IV. In Section V, the optimal control problem is formalized, and in Section VI, 0018-9545/$31.00 © 2012 IEEE