An Optimization Approach to Hybrid Electric Propulsion System Design

Transcription

1 An Optimization Approach to Hybrid Electric Propulsion System Design D. Assanis, G. Delagrammatikas, R. Fellini, Z. Filipi, J. Liedtke, N. Michelena, P. Papalambros, D. Reyes, D. Rosenbaum, A. Sales, M. Sasena Automotive Research Center College of Engineering The University of Michigan Ann Arbor, Michigan, ABSTRACT Environmentally friendly ground vehicles with range and performance capabilities surpassing those of conventional ones require a careful balance among competing goals for fuel efficiency, performance, and emissions. One research activity at the Automotive Research Center is to integrate hybrid electric vehicle simulations with high-fidelity engine modules to increase the accuracy of predictions and to allow design studies in the concept evaluation stage. This article describes a method4ology for integrating vehicle and engine simulations. The feed-forward model of the engine simulation is modified to allow its linking with the vehicle model, and an engine component scaling routine is added to facilitate system sizing studies. A design optimization framework is then used to find the best overall engine size, battery pack, and motor combination for minimum fuel consumption within proposed US government performance criteria. I. INTRODUCTION Much of the present motivation for environmentally conscious vehicle designs derives from government regulations and corporate recognition of public consciousness. The Partnership for the Next Generation of Vehicles (PNGV) is a joint effort by US government and major automotive manufacturers in the country. The automotive industry is recognizing that widespread use of alternative powertrains will be inevitable at some point in the future. The development and evaluation of new technologies for high-mileage, non-polluting vehicles is expensive and time-consuming. Using rigorous physically-based computer simulations to evaluate how such technologies may affect overall vehicle design is an attractive approach for product development. Under the auspices of the PNGV several design requirements have been agreed upon as vehicle design targets. Simulation models can be coupled with mathematical optimization techniques to explore the design space under the PNGV constraints. Mathematical optima discovered in this way can provide valuable guidance for further system improvement (see, e.g., Papalambros and Wilde, 1991). The present article describes the early stages of such an effort. Conventional internal combustion (IC) engine-driven powertrains have several disadvantages that negatively affect fuel economy and emissions. Specifically, IC engines are typically be over-designed by roughly ten times to meet performance targets, such as acceleration and starting gradeability (Moore, 1996). Oversizing the engine moves the cruising operating point away from the optimal operation point (Gao et al., 1997). Moreover, an engine cannot be optimized for all the speed and load ranges under which it must operate (Moore, 1996). One viable solution to these problems is the use of a hybrid electric powertrain that decouples the IC engine from peak requirements, thus reducing the demands on the engine map.

2 A hybrid electric vehicle (HEV) is a vehicle that has at least two sources of propulsion or energy conversion, one of them being electric. The most popular designs have an electric motor, energy storage and/or peaking device, and a power controller in combination with one or more of the following power units: diesel engine, spark-ignition engine, sterling engine or fuel cell. Once the components have been chosen, they can be arranged according to several configurations. These arrangements are classified as being either series or parallel, as shown in Figure 1 for engine-based hybrids. In a series hybrid, the electric motor is the only source that powers the wheels while the engine is used solely for battery recharging. A parallel HEV allows the engine and the motor to drive the wheels simultaneously or independently. In the latter configuration, the engine can also recharge the batteries depending on the control strategy implemented. The design process requires a system engineering approach, where the design of each component must be evaluated through the component s contribution to the overall system performance. The design process typically starts with evaluation of trade-offs associated with component sizes for a targeted fuel economy and performance. Successful optimization depends on the quality and flexibility of the system simulation, as well as on an effective optimization algorithm. Series Hybrid ENGINE GENERATOR BATTERIES FUEL TANK POWER ELECTRONICS MOTOR Mechanical Connection Electrical Connection BATTERIES Parallel Hybrid FUEL TANK ENGINE POWER ELECTRONICS MOTOR/ GENERATOR Figure 1 Typical series and parallel hybrid powertrain configurations Design optimization studies found in the open literature focus mostly on conventional powertrains. Work on hybrid powertrains has been directed mainly to parametric studies to assess component sizes and energy management strategies using a variety of models and simulations. Moore (1996) uses a set of five linked spreadsheets to size powertrain components based on continuous and peak demand for power and torque. He concludes that component sizes are mostly determined by starting and cruising gradeability, acceleration, and regenerative braking requirements. Cumulative energy throughputs over torque and speed plots are suggested to match an electric motor to a given combination of

3 vehicle characteristics and driving cycle. Zoelch and Schroeder (1998) use dynamic optimization to calculate optimal electric motor torque, engine torque, and CVT gear ratios for a parallel HEV under a simple charge-neutral driving cycle. Bumby and Forster (1986) employ a direct search technique to obtain a minimum energy path through the driving cycle. The control variables are the torque split (between IC engine and electric motor) and gear ratio. This process leads to the definition of an energy management control algorithm. Parametric studies are then conducted to optimize component size and further improve vehicle performance. In this article we present a methodology for hybrid electric vehicle design that can be used to study and optimize a variety of vehicle and powertrain configurations. Since practical experience with such configurations is limited and hardware prototypes are expensive, the methodology uses mathematical models and simulations to represent components and subsystems considered in the preliminary design stage. Optimization algorithms are used to drive design iterations in search of the best possible design according to specified design criteria and constraints. A general overview of the optimization methodology in the context of environmental design was given in Fellini et al. (1999). A detailed description of the design framework used in the present study is given in Michelena et al. (1999). The vehicle simulation program ADVISOR (Cuddy and Wipke, 1997; Senger, 1997), developed at the U.S. National Renewable Energy Laboratory (NREL), was selected as the hybrid-electric system simulation model. ADVISOR allows easy reconfiguration of the vehicle and integration of new component modules. To enhance the predictive ability of the engine module, a high-fidelity turbocharged diesel engine simulation code (TDES) originally developed by Assanis and Heywood (1986) is integrated with the ADVISOR simulation model. The integrated ADVISOR+TDES simulation is then coupled with optimization algorithms to create the desired system design tool. This tool is used to study the effect of component sizing on fuel economy and performance. In the early studies presented here the design variables are simply the diesel engine displacement, battery pack capacity, and power rating of the motor. Design objective and performance constraints are those set by the Partnership for the Next Generation of Vehicles (PNGV). Engine scaling techniques based on TDES were developed to enhance the flexibility and predictive ability of the HEV simulation. Hence, rather then relying on a simple scaling of a baseline engine map, the conceptual engine itself is scaled first and then simulated by TDES to generate a new look-up table. The actual implementation relies on a distributed computing environment to speed up the generation of individual tables. The outline of the article is as follows. First the engine and vehicle models used in the simulation are described in some detail. This includes an overview of the HEV simulation tool ADVISOR, an overview of the turbocharged diesel engine simulation TDES, a description of the conversion of TDES to feed-backward simulation, the engine scaling technique, and the integration of TDES and ADVISOR. Then the optimization methodology and some results are presented, followed by concluding remarks. II. ENGINE AND VEHICLE MODELS FOR HEV SYSTEM SIMULATION A. HEV Simulation - ADVISOR Various computer programs exist for the simulation of hybrid electric powertrains and vehicles. Depending on the way they are configured, these simulations can be categorized as either feed-backward or feed-forward. In the feed-backward configuration, the flow of control begins with the torque required at the tire and ends at the driver pedal position and, consequently, with the fuel supplied to the engine. The feed-forward configuration closely resembles the real-life situation, where a driver acts on the pedal in order to get the

4 required torque to achieve a desired speed. That is, the flow of information starts with driver demand and ends with torque delivered to the wheels. As a result, the simulation must iterate on driver demand at each time step to achieve a torque at the wheels sufficient to meet the demands of the cycle. Feed-forward is the traditional way of configuring engine simulations, where engine output is predicted for a given fuel input and engine operating speed. Some of the better-known feed-backward software tools include SIMPLEV, CarSim, HVEC, CSM HEV, V-Elph, and ADVISOR (Senger, 1997). The U.S. government under the PNGV initiative has sponsored the development of the System Analysis Toolkit (PNGVSAT), a comprehensive feed-forward hybrid electric system simulation developed by USCAR, a consortium of three U.S. automotive manufacturers. In addition, each major automotive company has its own specialized, proprietary modeling software. ADVISOR is a MATLAB/Simulink-based, feed-backward simulation of hybrid electric propulsion systems. A schematic of the top level of the SIMULINK model is shown in Figure 2. ADVISOR allows quick analysis of the performance, emissions, and fuel economy of conventional, electric, and hybrid vehicles. Most of the component models in ADVISOR are empirical, relying on input/output relations for existing components derived from data measured in the laboratory. The engine model, for example, appears in the form of look-up tables, generated by collecting point-by-point data during steady-state tests. Electric motor modules contain efficiency maps over a range of speeds and torques (both positive and negative). Battery modules contain functional relationships for charge and discharge efficiencies at various state of charge. Provisions are made to take into account dynamics and the rotational inertia of drivetrain components, thus allowing estimation of transient effects on the vehicle system. Figure 2 MATLAB/Simulink block diagram of the HEV simulation ADVISOR The block diagram in Figure 2 starts on the far left with data regarding the actual cycle through which the vehicle is to be driven. The driving cycle data include the road grade and the required vehicle speed at each discrete time step. Next, vehicle velocity is passed to a load-calculating block that finds the total load on the vehicle based on inertial effects due to acceleration, grade, and aerodynamic and rolling resistance. Then, the proceeding blocks calculate the load and speed that the engine and motor must provide as output in order to meet the cycle demands. The fuel used block calculates the amount of fuel needed for specific engine speed/load points from a brake specific fuel consumption (BSFC) map. A

5 two-dimensional linear interpolation scheme is used for look-up tables. Also, charge and discharge energies to and from the batteries are accounted for in order to monitor the state of charge and provide a correction for the total amount of fuel consumed during a test. ADVISOR offers a selection of component modules that can be used to build a vehicle system. These include a number of existing fuel converters, generators, motors, transmissions, energy storage devices, controllers, and vehicle parameters. Having a fixed list of components may cause some difficulties for the design engineer who desires to evaluate the impact of using a different, non-existing component or wants to continuously vary component sizes in search of an optimum combination. The developers of ADVISOR, aware of this need, have included routines that allow variation of component size through scaling of maps. Component look-up tables can be scaled linearly with respect to the required size or capacity (e.g., rated power). If the sizes of these components are kept close to their nominal values, the scaled experimental data can be used as a reasonably good estimate. Unfortunately, powertrain components do not scale well outside a narrow range, as many processes in the engine are non-linear in nature. For this reason, the engine block in ADVISOR and linear scaling routines were replaced with the predictions of the diesel engine simulation TDES. Hence, a procedure was developed to use a comprehensive turbocharged diesel engine simulation to generate a new set of engine characteristics for every change in engine size or design. B. TDES Turbocharged Diesel Engine Simulation TDES is a modified version of the turbocharged diesel engine simulation developed by Assanis and Heywood (1986). The thermodynamic model combines quasi-steady flow models of the compressor, turbine, manifolds, and intercooler with a zero-dimensional, multi-cylinder diesel reciprocator model to enable simulation of the complete engine system. A wastegate valve model (Filipi and Assanis, 1991) has been implemented since the present work focuses on a high-speed passenger car type diesel engine system, which typically includes a boost pressure control device. The parent code provides a great deal of flexibility regarding engine size and auxiliary engine subsystems. This code has been validated for engine systems ranging in size from a typical truck engine (Assanis and Heywood, 1986) to a large locomotive engine (Poola et al., 1996). The diesel four-stroke cycle is treated as a sequence of continuous processes: intake, compression, combustion (including expansion), and exhaust. Quasi-steady, adiabatic, onedimensional flow equations are used to predict mass flows past the intake and exhaust valves. Combustion is modeled as a uniformly distributed heat release process, using Watson s correlation (Watson et al., 1980). Convective heat transfer in the combustion chamber is modeled using a Nusselt number correlation based on turbulent flow in pipes and the characteristic velocity concept (Assanis and Heywood, 1986) for evaluating turbulent Reynolds number in the cylinder. The characteristic velocity and length scales required by these correlations are obtained from an energy cascade zero-dimensional turbulence model (Tennekes, 1972). Radiative heat transfer is added during combustion (Assanis and Heywood, 1986). The combustion chamber surface temperatures of the piston, cylinder head, and liner can be either specified or calculated from a specification of the wall structure. A friction sub-model based on the Millington s and Hartles correlation (1968) is used to predict the engine friction losses and convert indicated to brake quantities. The interaction between the master cylinder model and the other components is accounted for in the manifolds modeled as separate control volumes. There is instantaneous mixing of all mass flows that enter the intake manifold with the gases in the manifold. To complete the system, a compressor is connected to the inlet side of the intake manifold and a turbine is connected to the outlet side of the exhaust manifold. Turbomachinery performance is

6 defined by maps that interrelate efficiency, pressure ratio, mass flow rate and shaft speed for each component. At a particular step in the cycle simulation, the tables are interpolated in a two-dimensional fashion to calculate two unknown map variables (i.e., mass flow rate and efficiency) from the two known variables (i.e., pressure ratio and rotor speed) provided as solutions in a previous simulation step. The turbocharger turbine and compressor are on a common shaft; hence, turbocharger dynamics are controlled by the balance of the turbine and compressor torque, rotor inertia and damping. The wastegate valve is boost pressure controlled as shown in Figure 3. Valve dynamics take into account the pressure and spring force acting on the actuator diaphragm as well as pressure difference acting on the valve head (Filipi and Assanis, 1991). Hence: m&& z + bz& + Sz = ( p p ) A + ( p p ) A exman back v contr atm dfgm F preload (1) where z is the wastegate valve lift, m is the mass, b is damping constant, S is spring stiffness, p s are pressures at locations defined by subscripts, A v is valve head diameter, A dfgm is diaphragm diameter and F prel is spring pre-load force. Once the boost pressure reaches a high enough value and the valve opens, the flow is predicted using compressible flow routines otherwise applied to engine valves. Spring P atm Diaphragm P BACK P control (boost) P EXMAN TURBINE INLET SIDE Figure 3 Schematic of the wastegate valve As a first step the input data file was configured for a baseline engine, the 1.9 L Volkswagen TDI diesel (Neumann et al., 1992). This engine was among the limited group available in the ADVISOR library of engines. The turbocharger manufacturer, AlliedSignal, supplied turbine and compressor maps. Instead of using data from the literature, the authors were able to obtain actual baseline engine test data from the Michigan Automotive Research Company (MARCO). The data were then used for validation purposes of the engine simulation. The predictions of the system parameters, i.e., manifold pressures and temperatures, were validated first an indication that the cycle simulation is using accurate values of parameters having most impact on the process in the cylinder. The friction correlation was then calibrated for correct conversion of indicated to brake quantities. Results of the validation of engine performance are shown in Figure 4. The agreement is very good throughout the range of operating speeds.

7 60 50 Power Torque Predicted Measured Engine Speed (RPM) Figure 4 Comparison of predicted and measured VW 1.9L TDI engine performance Calibration and validation was performed with the original TDES code that has a feedforward structure. As mentioned previously, this is the traditional way of configuring engine simulations, where it is assumed that the user requires a prediction of engine output for a given fuel input and engine operating speed. However, ADVISOR has a feed-backward structure, where the main inputs are the driving conditions, i.e., vehicle speed as a function of time. The vehicle simulation determines engine speed/torque histories necessary to achieve these conditions. For every speed/torque point, the fuel mass supplied to the engine is evaluated from a look-up table and the integrated value allows calculation of the fuel consumption associated with the specific driving cycle. Therefore, TDES had to be modified to act as a feed-backward simulation in order to enable its integration with ADVISOR. C. Conversion to Feed-Backward Simulation The integration of TDES and ADVISOR required developing two routines for automatic generation of the data used by the system simulation. One routine produces maximum torque values as a function of speed, and the other generates the map of fueling rate as a function of speed and output torque. The speed range considered for maximum torque calculations was from 1000 RPM to 4500 RPM. The peak torque at each point is constrained by the amount of fuel that can be burned without exceeding the smoke limit. It was estimated that the smoke limit of a modern highspeed DI engine corresponds to an overall fuel-air equivalence ratio of 0.7. A modified Newton-Raphson technique was used to assess iteratively the amount of fuel needed to achieve an overall equivalence ratio of 0.7. Once this is accomplished the output torque is recorded as a maximum value within the smoke limit constraint. The automated routine then starts the calculation for the next speed value and proceeds with the calculations until the vector of peak torque values vs. speed is complete. The second routine is then applied to generate a map of fueling rates in the complete engine speed/torque range. For every speed the torque range is uniformly split into a number of segments. Then, for every specific speed point, the modified Newton-Raphson technique is used to vary the fuel input to TDES in an iterative loop until the desired torque value is 50

8 matched. Once the correct value of required torque is found, the fueling rate used at that point is indexed with the respective speed and torque. A plot of a typical fueling rate map generated for the 1.9 L diesel engine is shown in Figure 5. All data are stored in a file with the format expected by the ADVISOR. This technique allows the user to generate data for different engine designs. D. Engine System Scaling Techniques Figure 5 Sample fuel table used by ADVISOR One of the objectives of this study was to replace the linear scaling of experimentally obtained engine look-up tables with a high-fidelity simulation capable of predicting the effects of engine geometry on processes in the cylinder and external engine components. The fidelity of physical models built into TDES guaranties realistic accounting for nonlinear effects, such as changes in heat losses due to cylinder size. The scaling methodology considers engine geometry first, e.g., bore, stroke, connecting rod length, valve diameters, and nominal valve lift. Any change in engine size will have a direct impact on mass and enthalpy flows through the engine, so a technique for scaling the turbocharging system components is also needed. Variations of any of the geometric data independently of the others would inevitable lead to engine designs that are not plausible, thereby creating design space discontinuity problems for design optimization schemes. Instead, for a given engine configuration with a fixed bore-to-stroke ratio, it is possible to derive relationships between any of the geometric parameters and engine bore. These ratios are to be preserved when the bore is increased or decreased, and this will depend on the desired engine size, i.e., power level. The scaled bore size for the desired displacement is found using the following equation: B scaled = ( B baseline S baseline 4 Π V I )1/3 (2) where I is the number of cylinders in the baseline engine, B is the bore, S is the stroke, and V is the desired displacement corresponding to a specified power level. The scaled values of

9 other engine geometric parameters are then determined by multiplying the baseline values with ratios with respect to bore. These values are inserted in the TDES input file for the scaled engine. The manifolds are scaled such that their volumes change in direct proportion to the change of engine displacement. Scaling of the turbine and compressor implies creation of new maps representing machines with flow characteristics matched to the scaled engine. As a starting point, it is assumed that the percentage change in the nominal mass flow rate corresponds directly to the change in engine displacement. Maps are then scaled using scaling laws that take into account increase or decrease of the nominal mass flow rate and evaluate a new wheel diameter based on the assumption that the rotor tip velocity will remain the same (Watson, 1982, Filipi et al., 1998). Hence, the wheel diameter varies directly, while the wheel map speed varies inversely, with the square of the mass flow ratio of the original and the scaled machine. The wastegate valve geometric area and actuator diaphragm area are scaled linearly with the change in engine displacement. The scaling technique was implemented for engines between 1.0 and 1.9 liters. Baseline data were those of the VW 1.9 L TDI diesel engine. The behavior of the turbocharging system was very consistent. Intake manifold pressure increased gradually with engine speed up to about 2000 RPM and remained at bars after that point regardless of engine size (see Figure 6 (a)). The exhaust manifold pressure given in Figure 6 (b) shows similar trends; however, there are some differences in pressure levels after the wastegate valve opens. The largest engine system has highest pressures ahead of the turbine, and the difference between the largest and the smallest pressures is on the order of 5%. This is a consequence of the inherent non-linearity of processes affecting overall pressure and temperature difference across the engine. The effects of physical engine scaling vs. linear scaling of engine output maps (standard in ADVISOR) are illustrated in Figures 7 and 8. The top line in Figure 7 is the baseline 1.9 L engine torque as a function of speed, while the other two lines represent predicted torques for the small, 1.0 L engine L 1.8L 1.7 L 1.6L 1.5L 1.4 L 1.3L 1.2 L 1.1 L 1.0L L 1.8 L 1.7 L 1.6 L 1.5 L 1.4 L 1.3 L 1.2 L 1.1 L 1.0 L Engine Speed (RPM) Engine Speed (RPM) (a) (b) Figure 6 Predicted (a) intake and (b) exhaust manifold pressures for engines of varying size

10 Figure 7 Comparison of maximum torque using ADVISOR default scaling and TDES code. (Solid line corresponds to the baseline 1.9 L engine.) BSFC (g/kw-h) All Displacements BSFC (gm/kw/hr) Displacement=1.9L Displacement=1.5L Displacement=1.0L Engine Speed (RPM) Engine Speed (RPM) (a) (b) Figure 8 Comparison of BSFC results obtained for engines of different sizes using (a) ADVISOR default linear scaling and (b) TDES predictions for the engine composed of scaled components. The linear scaling of engine characteristics is clearly overestimating the engine performance at low and medium speeds. Nonlinear scaling of a turbocharged engine ultimately affects the engine fuel economy a key characteristic for HEV applications. Figure 8 illustrates the difference in brake specific fuel consumption (BSFC) between a linearly scaled baseline engine and the simulated physically scaled engine. Whereas the BSFC curves remains virtually unchanged after linear scaling of the baseline, Figure 8 (a), the predicted BSFC curves of engines having displacements 1.0, 1.5 and 1.9 liters show significant discrepancies, Figure 8 (b). At speeds below 2000 RPM the specific fuel consumption increases inversely proportional to engine size, primarily because of the adverse effects of small size on relative heat and mechanical losses. BSFC curves cross each other at about 2000 RPM, whereas larger engines demonstrate increased relative fuel consumption at speeds above 2000 RPM. This can be attributed to the negative effect of the increased exhaust manifold pressure on pumping work and cycle efficiency, Figure 6 (b). It is believed that such results will allow more realistic predictions of fuel economy when vehicles having engines of different sizes are driven in varying road conditions.

11 E. Integrating TDES and ADVISOR: ADVISOR+TDES ADVISOR is capable of scaling the engine, motor, and battery pack maps within a small range (Cuddy and Wipke, 1997; Senger 1997). Alternatively, it has been shown above that the high-fidelity turbocharged diesel engine simulation TDES can be modified for simulating geometrically similar engines within a wide range of sizes. A next step in preparing the vehicle simulation for optimization studies is to replace the built-in engine look-up tables within ADVISOR with those produced by TDES. To accomplish this, TDES was modified to produce the fuel consumption tables and maximum torque vs. RPM vectors, which ADVISOR requires for calculating fuel economy and performance. Graphical interpretation of the integration technique is given in Figure 9. ATMOSPHERE C T INTER- COOLER I M E M FUEL SYSTEM 4CYL ENGINE Ẇ TURBOCHARGED DIESEL ENGINE SIMULATION ADVISOR Figure 9 Integration of ADVISOR with the engine system simulation TDES In addition, TDES is now able to accept a desired engine displacement as input and automatically scale all engine components. Consequently, after every change in engine size or, generally speaking, in engine design, ADVISOR executes the modified TDES code to generate a new engine look-up table on-line. This integrated version of the HEV simulation is referred to as ADVISOR+TDES in this article. To illustrate the effect of the increased fidelity of the new tool on engine characteristics, Figure 10 shows the relative difference between fuel consumption maps created for the smallest engine, i.e., the 1.0 L engine. This 3-D surface was generated through direct comparison of maps of the same type as the one given in Figure 4, one being calculated using a standard ADVISOR linear scaling routine and the other generated by the TDES code.

12 Figure 10 Relative error between linearly scaled and TDES-generated 32.6 kw engine fuel consumption maps The error is in general increasing with the increase of engine speed and decrease of engine load. At high speeds and very low loads the error is above 10%, while at medium speeds and moderate loads the error is mostly below 5%. Since the medium speed/part load conditions are predominant in standard driving cycles, the overall effect on vehicle fuel consumption should correlate with the latter error value. Figure 11 shows contour plots of fuel consumption with maximum torque curves overlaid. Operating points of the engine at each time step of the urban driving schedule are shown on the plot of Figure 11(a). Similar plot is given for the highway cycle on Figure 11(b). The plots show that indeed the engine operates at mid-range speed and load conditions most of the time, in particular for the highway cycle. (a) (b) Figure 11 Operating points of the engine at each time step of the (a) urban and (b) highway driving schedules ADVISOR+TDES offers several benefits. First, it allows a designer to change an engine module on-the-fly without the prohibitive costs and lengthy lead times necessary to

13 develop a prototype and produce the experimental data needed by ADVISOR. If an engine is scaled within a wide range of sizes, the simulation output includes scaled dimensions of major engine components that can be used to evaluate the feasibility of the new design or as a starting point in the design of a prototype engine. It is also possible to add or remove certain auxiliary systems, such as power turbines or superchargers, as well as to study control issues, e.g., injection system or variable valve strategies. The following section describes the design optimization methodology for HEVs developed around the ADVISOR+TDES simulation. III. OPTIMAL DESIGN OF HYBRID ELECTRIC PROPULSION SYSTEMS A generic CORBA-based, object-oriented design framework was used in the present design study of a parallel hybrid electric propulsion system. As described in Michelena et al., (1999), the framework supports distributed and heterogeneous computer resources, custom and existing simulation codes, a variety of optimization algorithms, and easy reconfigurability of the design problem. Figure 12 Pre-optimality response surface study A preliminary study was performed on a baseline design using ADVISOR and its default scaling routine in order to gain some basic understanding of the effects of component sizing on overall vehicle performance and fuel economy. The simulations essentially act as implicit mathematical functions relating these quantities. The nature of such functions has a major impact on the quality of the optimization results. The graphs of these functions, sometimes referred to as response surfaces, are shown in Figure 12. The effects of fuel economy,

14 passing time, and distance covered under acceleration are depicted against motor and battery power levels. These surfaces show basic tradeoffs of system responses and contribution of various design variables. Since a priori knowledge of numerical noise inherent to the simulation is not available, such a preliminary study allows us to determine proper finite difference step sizes for gradient approximations needed by optimization algorithms. Figure 13 shows a zoom-in to a region of the fuel economy response surface depicting an average level of numerical noise. This type of noise is most likely due to numerical round-off, interpolation inaccuracy or discrete events within the system. The choice was made to use a finite difference step of 0.2 kw to allow the gradient-based algorithms to sample the functions better mph Time (s) Motor Size (kw) Motor Size (kw) Figure 13 Numerical noise in ADVISOR performance metric A. Optimization Methodology 1. Optimization Problem Formulation PNGV passenger car performance constraints were used for the design models presented in this article. The design problem was formulated as a component sizing problem. The design variables include engine, motor, and battery rated power. Simple bounds were imposed on these design variables based on engineering judgement, in order to adhere to packaging limitations imposed by the size of the powertrain compartment. Two design optimization problem formulations were chosen for the study. The first formulation attempts to maximize fuel economy subject to performance constraints. The optimization problem statement is shown in Table 1. A second problem formulation was devised to minimize the 0 to 60 mph acceleration time while maintaining a relatively high fuel economy and satisfying other performance constraints. The idea behind this formulation is to design a high performance vehicle without substantial loss in fuel economy. The optimization problem statement for the second formulation is shown in Table 2.

15 Table 1 Optimization Problem Statement Maximize: f(x AD VISOR, x TDES ) = mpg x AD VI SOR = {motor size, battery size} x TDES = {engine size} Subject to: 0-60 time < 12 seconds (passing time) < 5.3 seconds maximum speed > 85 mph 0-85 time < 23.4 seconds 5 second distance > 140 feet maximum acceleration > 0.5 gõs cruising (55 mph) grade > 6.5% Table 2 Alternative Problem Statement Maximize: f(x AD VISOR, x TDES ) = 0-60 mph time x AD VI SOR = {motor size, battery size} x TDES = {engine size} Subject to: Fuel Economy > 45 mpg (passing time) < 5.3 seconds maximum speed > 85 mph 0-85 time < 23.4 seconds 5 second distance > 140 feet maximum acceleration > 0.5 gõs cruising (55 mph) grade > 6.5% The driving schedule selected to evaluate the fuel economy of the hybrid propulsion system was the SAE Cycle J1711. This cycle runs the vehicle through two urban and two highway schedules starting at a high state of charge (SOC) of the storage device (i.e., the batteries). This set of schedules is then repeated starting at a low SOC. The goal here is to account for the energy being supplied by the batteries as measured by the overall change in SOC. A linear interpolation is performed to estimate a charge-neutral fuel economy, namely, the fuel consumption corresponding to a cycle with no variation in SOC. The two portions of the driving cycle that were employed in this study are the Federal Urban Driving Schedule (FUDS) and the Federal Highway Driving Schedule (FHDS), Figure 14. The SAE method is one of the first attempts to estimate the equivalent fuel used to have a charge-neutral end state. Other methods being explored are algorithms that iterate on the initial SOC, until the final SOC is within some tolerance of the initial one.

16 Figure 14 SAE Driving Cycle J1711: (a) urban and (b) highway 2. Optimization Procedure Figure 15 illustrates the optimization loop implemented using the design framework. The schematic indicates the linking of the optimization routine that traverses the design space and the HEV simulations that evaluate design objective and constraint functions at each new design point generated by an optimization iteration. YES ENGINE CHANGE? TDES FIND MAX TORQUE CURVE NO MAP A RPM MAP B 1250 Ð 2000 RPM ADVISOR + TDES COMPLETE MAP AND MAX TORQUE ADVISOR MAP D RPM MAP C RPM ADVISOR SQP OPTIMIZATION ROUTINE Figure 15 Optimization loop showing distributed map generation

17 The standard gradient-based optimization algorithm sequential quadratic programming (SQP) was selected as the search engine in the framework. At each iteration the SQP algorithm generates a new point in the design space that improves the objective function while also reducing any existing constraint violations. The iterations continue until the search converges to a local optimum. The algorithm is efficient but it may converge to a local rather than a global optimum. This deficiency of gradient-based algorithms is typically addressed by performed multiple optimization runs starting from different starting points. This multi-start process can identify several local minima and/or give a preponderance of evidence for a global solution. Successful attempts at using other optimization algorithms are described in Fellini (1998) and Sasena (1998). In this study we selected starting points using a basic design of experiments (two-level full factorial) approach, namely, we started at the eight design states corresponding to the upper and lower bounds of the design variables. Two function evaluation schemes were implemented using either ADVISOR or ADVISOR+TDES, as shown in Figure 15. Stand-alone ADVISOR was used to evaluate functions at points that did not require regeneration of the engine map due to a change in engine size. This is the case for estimating partial derivatives with respect to motor and battery size. The ADVISOR default scaling scheme was not used. ADVISOR+TDES was used for all other function evaluations that did require regeneration of the engine map. In each case, the simulation was represented as a black box to the CORBA framework. The framework was also used to distribute map generation onto four workstations for concurrent numerical processing. Care was taken to avoid generating the same engine size map more than once. Simple measures, such as distributed map generation and additional logic to reuse maps, resulted in a four-fold decrease in runtime. B. Optimization Results 1. Fuel economy as design objective As mentioned already, eight starting points were used. The eight sets of values for the initial component sizes are listed in Table 3. Since these combinations include all the extreme possibilities, they allow the optimizer to start working towards the optimum from very different directions. The runs were performed using ADVISOR default scaling techniques, but using as the baseline the 1.9 L diesel engine map generated by TDES. For the baseline motor component, a Westinghouse 75 kw AC induction motor with a maximum torque of 271 N-m was selected. As with the engine, a torque scale factor was used to vary the motor size continuously. The battery modeled was the Electrosource Horizon advanced lead-acid battery pack, model number 12N85. This battery provides a specific energy of 35 W-h/kg and a specific power of 240 W/kg. To vary the battery pack size, the number of battery modules was considered to be a continuous variable. Table 3 Multi-start starting points Run # Motor (kw) Engine (kw) Battery (kw)

18 Table 4 Multi-start results for fuel economy optimization Run # Motor (kw) Battery (kw) Engine (kw) Fuel econ. (mpg) passing time activity (s) The results of this exploratory study are shown in Table 4. Note that the optimizer did identify a configuration with a fuel economy close to or above 49 mpg in five of eight cases, while the other three configurations converged to inferior local minima. Averaging the most efficient combinations produces the following HEV specification: Motor Battery Engine Fuel Economy ~41 kw ~52 kw ~33 kw ~49 mpg The mph passing time constraint was always active see the corresponding column in Table 4 meaning that this design requirement is critical to the location of the optimum. The optimizer found the smallest possible engine that allows the vehicle to meet the passing time requirement eaxctly. The electric motor and battery are sized such that they can assist the engine with enough power during acceleration. Other local minima (runs #2, #3, and #7) have smaller electrical components and larger engines; hence, the performance criteria are still satisfied but fuel economy is inferior, roughly in proportion to the increase in engine size. Next, the optimization iterations were repeated using the ADVISOR+TDES tool. This combination was expected to provide more accuracy due to the higher fidelity of the engine performance predictor, but at the expense of longer computational time. Since the first study with ADVISOR clearly indicated where to expect the optimum, the calculation did not require multiple starts. In addition, the starting point was chosen near the previously found optimum, thereby allowing the code to converge more quickly. The optimum configuration as determined by the ADVISOR+TDES integrated tool was: Motor Battery Engine Fuel Economy 42.1 kw 53.5 kw 32.6 kw 48.5 mpg Comparison between results obtained with the two tools shows small differences. In fact, predicted fuel economy varies by only one percent, while maximum variation in component size is three percent (for the battery). Apparently, the improvement in accuracy hardly justifies the increased computational cost of ADVISOR+TDES. However, part of the reason for this result is the fact that the optimum configuration includes the smallest engine,

19 thus the relative impact of engine characteristics on vehicle performance is small. Also, examination of the engine operating points most frequently visited during the SAE driving cycle (Figure 11) reveals that the engine operates mostly at medium speed and medium to light load. Fuel consumption of the small engine predicted by two different scaling methods varies little for these conditions, hence the small effect on the vehicle fuel economy. 2. Acceleration time as design objective Finding the optimum for an initial problem statement and a set of design specifications is usually a first step in a comprehensive optimization study. Alternative problem statements may be explored, and new optimization runs can be executed with different sets of design specifications referred to as parametric studies. Such additional studies provide the design engineer and the management with insights into alternatives that may be more attractive from a production or marketability point of view, factors not included in performance models explicitly. The solution obtained in the previous subsection indicated a combination of a small engine with relatively large electrical components as the best one for fuel economy. An alternative problem statement was studied whereby the 0-60 mph time was minimized. The other performance constraints were left in the problem statement; however, an additional 45 mpg fuel economy constraint was imposed. This study was intended to show how changing the design goal has a direct impact on the component sizes found. As with the first study, ADVISOR default scaling routine was used first in a multi-start optimization scheme. The same eight points were used as the starting locations, and the resulting solutions are shown in Table 5 below. Once again, several solutions were in the same general area, while the remaining ones were clearly worse. The best solutions have a 0-60 time of 7.9 seconds, but other starting points yielded results of only 10.3 seconds. This reinforces the need for multi-start techniques when using algorithms such as SQP. Table 5 Multi-start result for acceleration time optimization Run # Motor (kw) Battery (kw) Engine (kw) 0-60 mph time (s) 45 mpg activity Note that the optimal designs are quite different from those obtained for fuel economy optimization. The active constraint is now the fuel economy constraint of 45 mpg. Note that the 0-60 constraint in the first problem statement was an upper bound of 12 seconds and was not active. The engines have been sized somewhat larger, which results in worse fuel economy but better performance. It can also be seen that the optimal configurations have battery packs very near the upper bound and correspondingly large motors in order to maximize performance. Averaging the best combinations produces the following HEV specification:

20 Motor ~72 kw Battery ~99 kw Engine ~36 kw 0 60 mph time ~7.9 sec It is interesting to have the multi-start results for comparison since the best designs require electric components too large to be practical. This is not true of some of the other local optima. A designer may be willing to give up some performance in order to use smaller motor/battery combinations. For example, the solution from the first multi-start point yielded a design with only a 34.4 and 41.1 kw rating for the motor and battery, respectively, while keeping the engine at 40.6 kw. This design predicts a 0-60 time of 10.1 seconds and a fuel economy of 45.7 mpg. These numbers may be much more appealing to the designer, although optimization algorithms will identify solutions that are mathematically best within the specified problem statement. As with the first formulation, the best solution was chosen as a starting point for a single run of the ADVISOR+TDES problem. The solution converged relatively quickly to the following point: Motor 75.1 kw Battery 97.2 kw Engine 34.2 kw 0 60 mph time 7.9 sec Once again, the solution appears to be relatively close to the solution obtained using ADVISOR default scaling rules. IV. CONCLUSIONS The results of early design optimization studies are usually the starting point for further studies that may provide more insight on the complex relationships present in real engineering systems. In the present study dominant relationships between vehicle subsystems were determined and sensitivity studies were conducted offering a better understanding of variable and parameter interactions. Further studies are currently under way. These include optimization studies for determining subsystem local design variables, such as geometric dimensions, and also for adding control strategy design, since the controller is ultimately a key ingredient in systems that may operate under transient conditions most of the time. Finally, several non-gradient global optimization algorithms are being evaluated for use either as stand alone or in conjunction with SQP. In the present study the primary goal of the integrated simulation tool was not to increase the accuracy of the overall simulation. It was pointed out that the results of both simulations vary only slightly. An important advantage of the coupled ADVISOR+TDES simulation is that it allows easy alterations of the engine module. For instance, the same engine design can be changed slightly (different valve timings, injection timing, type of fuel used, without a turbocharger, and so on) and proceed with system evaluation and design studies without expensive experimentation for collecting new calibration data. An important design requirement that has been completely omitted here is emissions constraints. Emission models are not available within ADVISOR. Researchers in the ARC are currently validating an emissions submodel that has been implemented within TDES. This will be include in future design studies.

21 Acknowledgements This research is partially supported by the U.S. Army Automotive Research Center for Modeling and Simulation of Ground Vehicles. This support is gratefully acknowledged. In addition, the authors would like to thank M. Cuddy and K. Wipke of NREL for their assistance with the ADVISOR model, and M. Salman and T. Weber of General Motors Corporation for their advice on hybrid vehicle models. REFERENCES D. Assanis and J. Heywood, Development and Use of a Computer Simulation of the Turbocompounded Diesel System for Engine Performance and Component Heat Transfer Studies, SAE Paper , J. Bumby and I. Forster, Optimisation and Control of a Hybrid Electric Car, IEE Proceedings, Part D: Control Theory and Applications, Vol. 134, No. 6,1986, pp M. Cuddy and K. Wipke, Analysis of the Fuel Economy Benefit of Drivetrain Hybridization, SAE Paper , R. Fellini, Derivative-Free and Global Search Optimization Algorithms in an Object- Oriented Design Framework, Master of Science Thesis, Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI, R. Fellini, N. Michelena, P. Papalambros, and M. Sasena, Optimal Design of Automotive Hybrid Powertrain Systems, Proceedings of EcoDesign'99: First International Symposium on Environmentally Conscious Design and Inverse Manufacturing, Tokyo, Japan, February 1-3, 1999, pp Z. Filipi and D. Assanis, "Quasi-Dimensional Computer Simulation of the Turbocharged SI Engine and Its Use for 2 and 4 Valve Engine Matching Study", paper presented at the 1991 SAE International Congress & Exposition, SAE Paper , SAE Transactions, Journal of Engines, Sec. 3, Vol. 100, Detroit, Z. Filipi, D. Assanis, D. Jung, G. Delagrammatikas, J. Liedtke, D. Reyes, D. Rosenbaum, A. Sales, Enhancing Flexibility and Transient Capability of the Diesel Engine System Simulation, 4 th ARC Conference on Critical Technologies for Modeling and Simulation of Ground Vehicles, Ann Arbor, May 19-20, Y. Gao, K. Rahman, and M. Ehsani, Parametric Design of the Drive Train of an Electrically Peaking Hybrid (ELPH) Vehicle, SAE Paper , B. W. Millington, E. R. Hartles, Frictional Losses in Diesel Engines, SAE Paper , SAE Transactions, Vol. 77, N. Michelena, C. Scheffer, R. Fellini, and P. Papalambros, A CORBA-Based Framework for Distributed, Object-Oriented System Design, Journal of Mechanics of Structures and Machines, this issue, T. Moore, Tools and Strategies for Hybrid-Electric Drivesystem Optimization, SAE Paper , 1996.