Proceedings of the American Control Conference Albuquerque, New Mexico June 1997 0-7803-3832-4197/$10.00 0 1997 AACC

Modeling and Simulation of a Hybrid-Electric Vehicle Drivetrain

Gregory A. Hubbard Graduate Student, Massachusetts Institute of Technology Control Systems Development Engineer Allison Transmission Division of General Motors Corporation

Kamal Youcef-Toumi Associate Professor of Mechanical Engineering Massachusetts Institute of Technology

ABSTRACT including maximum fuel capacity, oil, batteries, and all other The drivetrain of a hybrid-electric vehicle is modeled and equipment needed for operation without passengers or driver, of simulated @om a system level approach. The need for accurate 9525 kg (21,000 Ib.). The bus is capable of seating 31 people, at an dynamic models for developing control algorithms is motivated. assumed average weight of 68 kg (150 Ib.) each. The gross vehicle Detailed models capable of describing both transient and weight (GVW) includes the wet weight plus the maximum amount of steady-state operation of each of the key drivetrain components are passengers and cargo the bus can carry. For this vehicle, the GVW is constructed. Bond graphs are the tool of choice for modeling 13,600 kg (30,000 Ib.). The bus has a frontal cross-sectional area because they focus on mechanisms of energy generation, storage, which is 2.74 m (9 ft) high and 2.44 m (8 ft) wide for an area of 6.69 and dissipation. Further, they permit integration of submodels, give m2 (72 ft2). The aerodynamic dimensionless drag coefficient for the insight into component interaction, and allow straighrfonvard modemly styled bus is 0.50. The tire radius is 0.475 m (18.7 in). derivation of governing equations. The following component models The hybrid-electric drivetrain is now described. The drivetrain are presented: transmission, vehicle chassis/bodys three-phase AC is that described by Mayrhofer, Kriegler, and Albrecht and presented induction motor, lead-acid battery, and four cycle, four stroke, spark in Figure 1 [2]. Each N represents an independent angular velocity. ignited internal combustion engine. Simulation results for these The C’s are clutches used to achieve multiple powertrain components are presented. configurations. Pure electric, series hybrid, and parallel hybrid are possible. This study is limited to the case where the planetary INTRODUCTION geartrain operates as a continuously-variable transmission (CVT), As problems of air pollution and dependency on fossil fuels with clutches C1 and C2 locked and C3 and C4 open. persist, the need for modes of transportation that alleviate these The advantage of CVT operation lies in allowing the internal concems grows. The hybrid-electric vehicle (HEV) offers combustion (IC) engine, linked to the sun gear, to operate at a speed improvements over conventional vehicles with today’s technologies. that is independent of the velocity of the transmission output. This The HEV blends energy generating, energy storing, and energy operation is permits the IC engine to always operate at the speed that distributing components to achieve performance in fuel economy, gives either the highest efficiency, lowest exhaust emissions, or a emissions, acceleration, maximum speed, and range that no single compromise of these two for a given operating load. Electric motor 1 element drivetrain can yet match. An HEV matching reliability and adds the additional benefit of permitting the IC engine to operate at cost of conventional vehicles could capture significant market share. the speed and load combination that consumes the least fuel or Simply connecting components together does not necessarily produces the fewest emissions. result in an improved vehicle drivetrain. Thorough characterization The planetary gear train functions as a CVT by permitting each of each component’s idiosyncrasies is required if an optimal component, sun gear, ring gear, and carrier, to be free to rotate. CVT drivetrain is to be configured. Furthermore, supervisory control that operation is possible because the planetary set is, in control systems interprets the driver’s tractive effort request and manages the power terms, a two input system. Kinematically, it is a two degree of flow between the components is needed. Dynamic models are used to freedom system. Here, the sun gear operates at constant speed, while design component and supervisory control algorithms [ 11. the ring gear velocity achieves the correct transmission ratio from The bond graph tool is well-suited for describing the dynamic sun input to carrier output. Motor 2 attains the ring gear velocity vehicle processes. A bond graph is a pictorial representation of the commanded by the supervisory controller. power and energy phenomena in a physical system. A key benefit of the bond graph is that it describes analogous energy processes in COMPONENT MODELING different energy domains identically. This permits the HEV engineer Bond graph models for each of the drivetrain components were to focus on general energy terms rather than the particular constructed and integrated to produce the complete vehicle model. constitutive laws of a specific technology when characterizing First the model for the internal combustion engine is described. physical behavior. Bond graphs of each component may be linked to Then, models for the transmission, vehicle chassishody, electric others, permitting analysis of the interaction between subsystems. motors, and lead-acid batteries are summarized. Each component dynamic model captures the energy storage, dissipation, and VEHICLE CONFIGURATION generation characteristics during both steady-state and transient The vehicle under examination is a nine meter (30 ft) long operation. Pertinent simulation results are discussed. urban transit bus. The bus has a wet weight, the weight of the vehicle

636 Internal Combustion Engine The flow rate through the exhalust valve is shown in Figure 5. The General Motors Quad 4 engine was chosen for analysis Because the effective exhaust manifold outlet area and the because its power range matches the HEV mean power demand and atmospheric pressure are assumed constant, the flow rate variation is because detailed design information for it is available in the public a result of pressure and temperature fluctuations in the exhaust domain [3]. The dynamic model for the internal combustion engine manifold. The exhaust manifold pressure oscillates with the entry of builds on the work of Heywood and Moskwa [4,5]. The engine bumed gas products from the cylinders. The cylinder pressure result model is subdivided into mechanical and thermodynamic sections. is given in Figure 6. The peak pressure magnitude near 3500 kpa The mechanical model assumes a rigid crankshaft, an empirical agrees with the load conditions from the intake manifold pressure energy dissipation tinction for cam losses from Armstrong and and the quantity of fuel burned [9]. It is shown that these results may Buuck, and an empirical energy dissipation function for bearing be extended to compute instantaneous IC engine efficiency [8]. losses from Bishop and Heywood [6,7,4]. One state equation describing the flywheel velocity incorporates all significant inertias Transmission and Vehicle Chassis/Body reflected via slider-crank kinematic equations to the flywheel. The transmission directs energy between the drivetrain The thermodynamic section of the engine model is a zero components. The bond graph model shown in Figure 7 is described dimensional model employing the filling and emptying method for below. Descriptions of energy dissipation for bearings by Shipley engine plenums. The combustion chamber consists of two zones: a and for gear meshes by dzguven and Houser are included [10,1 I]. bumed and an unbumed region. All gas mixtures are assumed to be Eight independent states in the transmission and one independent ideal gases. Separate control volumes are considered for the state in the vehicle chassishody are contributed to the system. following: intake manifold, unbumed and bumed combustion In this HEV configuration, the IC engine operates at a constant chamber regions, and the exhaust manifold. nominal speed,f,,, and supplies a constant torque, e2, consistent with A bond graph is constructed for the thermodynamic processes the engine's minimum brake-specific fuel consumption (BSFC) and is presented in Figure 2. The throttle valve, intake manifold, point. The minimum BSFC point is the engine's peak steady state exhaust manifold, intake valve, unburned cylinder zone, burned efficiency operating point. The first electric motor (bond 10) is zone, and exhaust valve for one cylinder are included. The R-fields responsible for maintaining the desired constant engine operating represent flow through restrictions: valves modeled as isentropic mode and operates at speed, fs, which is directly proportional to A, nozzles. The input to each R-field is the effective discharge area, through the transformer, gear mesh TF,,. It must balance any torque C,A (m2). The input for the throttle valve comes from the engine debit or credit in the shaft represented by el> The second electric low-level controller. Between the R-fields are zero junctions, one for motor (bond 26) elicits the desired vehicle velocity by determining the temperature and one for the pressure of each plenum. A C-field the velocity of the ring geae,f,,, through the gear mesh TF,,,. The with thermal and hydraulic bonds captures the energy conservation ring structure denotes the planetary gear kinematic constraint of each plenum. Heywood derives the following formula for the time described in the VEHICLE CONFIGURATION section. rate of change of temperature in the control volume: AC Induction Motors The three-phase AC induction motors transmit energy between the battery-fed inverter and the transmission. The field-orientation principle is used in motor control simulations for optimal torque where h is the specific enthalpy of the gas, 9 is the time rate of production. In 1959, Kovacs and Racz introduced the concept of change of the plenum volume, Vis the volume of the plenum, 6 is vector quantities in AC machines [12]. Trzynadlowski described a the time rate of change of the fueYair equivalence ratio, and p is the dynamic model founded on Kovacs and Racz [13]. This dynamic gas density. A', B', and C' are parameters describing partial model permits analysis with nonsinusoidal currents. The model is derivatives of the gas properties. Specific assumptions for the based on a fictitious two phase, two pole motor. It is termed the &- computation of these parameters for the control volumes in the model for its orthogonal axes: the direct, d, and quadrature, q. engine model are described by Hubbard [8]. The bond graph model describing the transformation of energy In the center of the bond graph, the Wiebe heat release model from the electrical domain through the magnetic domain to the determines the heat from combustion and the rate of mass buming mechanical domain is shown in Figure 8. In the bond graph, vqs and from the unbumed to the bumed zone as a function of crank angle v, are the stator voltages driven by the battery fed inverter. Energy is [4]. Figure 3 depicts this Wiebe function for a spark advance of 30" stored in inductances: Lb the leakage inductance in the stator, L,,, the BTDC, and combustion duration of 80°.The cylinder models include leakage in the rotor, and Lm,the magnetizing inductance. The copper a flow source for the PdV work done on the piston by the gas. The losses in the stator are given by R,; those in the rotor are R,. The flux pressure acting on the piston drives the engine's mechanical model. linkages are designated by kh and Aqr The state equations from the Simulation results for the IC engine bond graph model are bond graph are equivalent to those given by Trzynadlowski: presented in Figures 4, 5, and 6. The engine operates at 4000 rpm and is driving a 187 N-m load. Figure 4 shows the mass flow rate of air into the combustion chamber from the intake manifold through the inlet valve. The characteristics of the simulated flow agree with empirical data for a similar engine[4]. When air mass begins to flow through the opening intake valve, it is flowing from the high pressure combustion cylinder to the lower pressure intake manifold. The air flow depends not only on the pressures in the cylinder and exhaust manifold but also the effective intake valve area as a function of lift.

637 From the torque developed by the fictitious two pole, the torque REFERENCES for a real, three-phase motor may be derived: 11 Hubbard, G.A., and Youcef-Toumi,K., “System Level Control of a Hybrid-Electric Vehicle Drivetrain,” WM08-5, Proceedings (3) of ACC97,1997. [2] Mayrhofer, J., Kriegler, W., and Albrechf K., “A Hybrid Drive The two AC induction motors are driven by DC to AC fast Based on a Structure Variable Arrangement,” The 12th switching, low loss IGBT. Switching at 20kHz, the inverter International Electric Vehicle Symposium, Electric Vehicle dynamics are ignored. But a constant resistance voltage drop across Association of the Americas, Vol. 2, pp. 189-200, 1994. the inverter is assumed. A hysteresis current controller is simulated [3] Thomson, M.W., Frelund, A.R., Pallas, M., and Miller, K.D., to determine the voltage switching to elicit the desired current “General Motors 2.3L Quad 4 Engine,” SAE 870353, 1987. waveforms [8]. [4] Heywood, J.B., Internal Combustion Engine Fundamentals, McGraw-Hill Book Company, New York, 1988. Lead-Acid Batteries [5] Moskwa, J.J., “Automotive Engine Modeling for Real Time The battery pack stores or discharges energy based on the motor Control,” Ph.D. thesis, Massachusetts Institute of Technology, requirements. The lead-acid battery model builds on the work Cambridge, MA, 1988. described by the landmark paper by Shepherd and that by Ekdunge [6] Armstrong, W.B., and Buuck, B.A., “Valve Gear Energy [ 14,151. Ekdunge’s model includes detailed descriptions of battery Consumption: Effect of Design and Operation Parameters,” electrochemistry, but simplifies the analysis by using integral mean SAE 810787, 1981. values for parameters such as sulfuric acid concentration. The [7] Bishop, I.N., “Effect of Design Variables on Friction and purpose of the model is to describe the energy dissipation, generation Economy,” SAE Transactions, Vol. 73, pp. 334-358, 1965. and storage characteristics of the lead-acid battery. The bond graph [8] Hubbard, G.A., “Modeling and Control of a Hybrid-Electric in Figure 9 depicts the elements for battery dynamics. The causal Vehicle,” M.S. thesis, Massachusetts Institute of Technology, input to the model is the current from the electric motor models. The Cambridge, MA, 1996. output is the voltage imposed on the motors. [9] Watts, P.A., and Heywood, J.B., “Simulation Studies of the The battery cell voltage is expressed as: Effects of Turbocharging and Reduced Heat Transfer on Spark- Ignition Engine Operation,” SAE 800289, 1980. [lo] Shipley, E.E., “Loaded Gears in Action,” Dudley‘s Gear Handbook, Townsend, D., ed., McGraw-Hill, New York, 1992. where E, is the equilibrium cell potential, I, is the battery current, [l 11 dzguven, H.N., and Houser, D.R., “Mathematical Models Used R,,e,,,,,,,e is the resistance of the electrolyte, and R,,, and R,,- are the in Gear Dynamics--A Review,” Journal Sound and overpotentials at the positive and negative electrodes, respectively. of Vibration, Vol. 121(3), pp. 383-411, 1988. The overpotentials are nonlinear functions of the cell current 1121 Kovacs, K.P., and Racz, “Transient Regimes of AC characterized by Tafel equations described by Ekdunge and Bode I., Machines,” Hungarian Academy Sciences, 1959. [15,16]. Hubbard expands the model to include charging [8] of [ 131 Trzynadlowski, A.M., The Field Orientation Principle in Next, the results of a lead-acid battery simulation are presented. Control Induction Motors, Kluwer Publishers, Boston, 1994. The scenario for the simulation is that the battery is discharged at 60 of [14] Shepherd, C.M., “Design of Primary and Secondary Cells. 11. A for 30 minutes, charged at 60 A for 30 minutes, then left in open An Equation Describing Battery Discharge,” Journal the circuit for one hour. Figure 10 shows the sulfuric acid concentration of Electrochemical Society, Vol. 112, pp. 657-664, 1965. during the simulation. The positive electrode consumes sulfuric acid [15] Ekdunge, P., “A Simplified Model of the LeadAcid Battery,” during discharge and returns it during charge faster than the negative Journal ofpower Sources, Vol. 46, pp. 251-262, 1993. electrode, as explained by diffusion process kinetics equations [ 151. [16] Bode, H., Lead-Acid Batteries, R.J. Brodd and K.V. Kordesch, In open circuit, the acid diffuses from higher concentration regions to those of lower concentration. This lead-acid battery model describes translators, John Wiley & Sons, New York, 1977. I1 transient and steady-state characteristics.

CONCLUSIONS The need for control algorithms to exploit the components of a hybrid-electric vehicle drivetrain motivates the development of accurate transient and steady-state models. Dynamic models for each of the drivetrain components have been presented, including the ._ internal combustion engine, transmission, vehicle chassislbody, AC induction motors, and lead-acid battery pack. Descriptive simulation I_;_1 results have also been shown. The choice of bond graphs for modeling was instrumental because the bond graph focuses modeling effort on mechanisms of energy generation, storage, dissipation, and transfer, and it provides a map to the governing equations. These dynamic models form the foundation for schemes to size the L I drivetrain components and for low-level and supervisory control I methods [l]. Battery J Figure 1: Universal Hybrid-Electric Drivetrain [2]

638 Figure 2: Bond Graph for Two Zone, Four Stroke, Spark Ignited IC Engine Model

4.05; 4.05; ' 0.01 0.02 0.03 0.04 I limo (S) Figure 3: Wiebe Function for the Fraction of FueVAir Mixture Figure 5: Mass Rate of Air through Cylinder Exhaust Burned Flow Valve, Cylinder 1

0.12, h' 4aoo 1 0.1 1

4.021

4.04' J 0.01 0.02 0.03 0.04 005 Tima (I) Time (5) Figure 4: Air Mass Flow through Intake Valve Figure 6: Cylinder Pressure during IC Engine Simulation

639 R:R,, sC:Beacing IS A" - ...-

TF:TFtu, \I c4,:c '-1 0 I 4-

1/ Tire Radius Beacing 25 se: mTF4w

kG& &,:R VehicleChassis/B& II k:I J 2,,, Figure 7: Transmission and Vehicle ChassidBody Bond Graph Model

R+

i' SUAId 1 ll& .--+ I -y Le& -4-ysI:LDd

v*:se-y 1 1- 0 L:a WRR. /\ JL&c /T'.. k%, k4 se:€.Iw m- *~d.- 0.lrU 4r, 4-b:GY IR:R, I (1) @)

Figure 9: Bond Graph Representations of the Lead-Acid Battery 1I .-I .-I !:I, Cell (a) and Complete Battery (b)

85 1 R.R. 6- - Positive Electrode : GYI' ~PL

u-:Q-y I I-' 0 -1 1 1*'R.R

'L Negative Electrode TT1'14, IC :Lt

lime (5) Figure 8: Bond Graph Representation of AC Induction Motor in Figure 10: Sulfuric Acid Depletion during Discharge, Simplified dq Axes Replenishment during Charge, and Diffusion Process.

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