Hybrid Vehicles Performances Analysis-Feed

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Hybrid Vehicles Performances Analysis: FeedForward Dynamic Approach

2010-01-1443 Published 05/05/2010

S. Brusca, Brusca, A A.T. .T. Ga Galvagno, lvagno, R. Lanzafame and M. Me Messina ssina Univ. of Catania Copyright © 2010 SAE International

ABSTRACT The continuous increase of pollutants and fine particulates is mainly caused by cars circulating worldwide. Therefore, it is necessary to replace internal combustion engines with the cleanest electric motors. The short term solution is represented by Hybrid Electric Vehicles (HEVs) due to its environmental and efficiency characteristics. In the present  paper a dynamic feed-forward mathematical model for a hybrid vehicle performance analysis is proposed. Torque and  power, pollutant emission, fuel consumption, battery pack  state of charge, as well as speed and acceleration have been evaluated by means of simulation of United State and Japanese standard driving cycles. In order to carry out simulations on a real hybrid configuration, the model has  been based on the powertrain installed on the Toyota Prius (Toyota Hybrid System - THS). A mathematical sub-model of each vehicle component has been implemented to simulate the real vehicle behavior in all possible running conditions. To do so, a rule-based control strategy was also implemented to manage the energy flows during vehicle motions taking into account battery pack state of charge, vehicle speed, engine and motor torques, as well as power generation in regenerative breaking condition. In order to assess the effectiveness and accuracy of the implemented mathematical model, different simulations on standard driving cycles have  been carried out, and results have been compared with experimental data found in scientific literature. The comparison shows a well evident agreement between simulated and experimental data in different running conditions. Furthermore, in an acceleration test from 0 km/h to 100 km/h, the response of the simulated vehicle has been evaluated, and results showed a good agreement between simulated and experimental data. The developed mathematical model is a powerful tool to study the dynamics of powertrain system and the interaction between components. It is also possible to try out new control

strategies able to reduce fuel consumption and pollutants emissions maintaining at the same time the required  performance.

INTRODUCTION Today, evermore stringent anti-pollution laws and the  pressing need for energy saving are driving the technological development of increasingly efficient propulsion [1]. Hybrid propulsion systems are nowadays a short-medium term solution for obtaining higher efficiency targets and lower pollutant emissions thanks to the interconnection of  two propulsion systems. At present the most common solution is the combination of an internal combustion engine and an electric motor. Both industrial and scientific research have given great impetus to such technology. As regards the car industry, in 1997 Toyota Motor Corp. marketed their first hybrid vehicle, the Prius, first in Japan and then worldwide in 2001. Honda followed suit with their  Insight, marketed in 2000. Since then, Toyota has been working on several THS (Toyota Hybrid System) propulsion versions, which will be marketed in Europe from 2010, all  based on a hybrid Series/Parallel Series/Parallel configuration. configuration. The research community has mainly focused on energy-flow optimization and overall vehicle-propulsion management, so as to further reduce fuel consumption and pollutants. So, to optimize these flows and performance, there are two main approaches: experimental and numerical modeling. This latter approach is preferred, especially by the scientific community, because mathematical models ensure fast technological low-cost development which can then be tested experimentally for optimized solutions.

 

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Mathematical models [2], depending on level of accuracy, are divided into three main categories: static, quasi-static and dynamic. The first two [3 and 4], feature a backward vehicle simulation, while the last is a forward one. In the first case, the simulation starts from the cycle-imposed speed which, with backward calculations, is able to determine the consumption of the fuel needed to run the imposed cycle. In forward models, the simulated vehicle speed is controlled by the driver, as in reality, to follow the imposed cycle; this  provides actual fuel consumption, pollutant emissions and  predicts vehicle vehicle perfor mance. mance. The main advantages of using a static or quasi-static model lie in simpler implementation of the model and quicker  computations, but this also entails less accurate results in dynamic simulations and inadequacy in simulating vehicle  performance. By contrast, dynamic models, being more complex to accomplish and requiring more computing time, obtain more accurate results in dynamic simulations as well as predicting the real performance of simulated vehicles. Besides, these models best lend themselves to the study and development of control strategies for engines and the generation and storage of electricity. The present work deals with the study of a hybrid vehicle, by implementing a dynamic mathematical model to simulate the Toyota Prius Prius THS THS performance.  performance.

DYNAMIC MODEL A feed-forward mathematical model was studied and implemented for a vehicle with hybrid Series/Parallel  propulsion. Figure 1 shows the Simulink® environment/mathematical model of the Toyota Prius THS, listing all the main elements:

• Driver  • Control Unit (CU) • Internal Combustion Engine (ICE) • Electric Motor (MG1) • Electric Power generator (MG2) • Power Split Device (PSD) • Battery • Wheel and vehicle Dynamics (See Figure 1 after last section of paper) This model is a feedback model, where the control parameter  is the simulated vehicle component is given below.speed. A brief description of each  

DRIVER  In the Driver subsystem, driving-cycle imposed speed and feedback simulated speed are compared. The comparison error is managed by two PID controllers, one for the accelerator, the other for the brake, the function of which is to control the related variable, in this case the vehicle simulated speed so as to follow, as faithfully as possible, the reference variable which is the driving-cycle imposed speed. Within the PID controller, equation 1 is solved:

(1) where Kp, Ki and Kd respectively are the gains from  proportional, integrative and derivative effects of the controller, e(t ) is error and u(t) is controller response. The controller response corresponds to a signal proportional to the  pressure exerted by the driver on the accelerator and brake  pedals. Controllers calibration was done using the Ziegler-Nichols methodology [5]. The output signal of the Driver subsystem ranges from 0 to 1, which correspond correspond to the two pedal end-strokes. These signals are used as input signals for the Control Unit subsystem.

CONTROL UNIT The Control Unit, together with the Power Split Device, is the most important part of the THS system. All the signals from other subsystems converge in this subsystem, allowing interaction between propulsion, generation and storage components. THS has five possible operational modes which vary according to the power and speed requirements imposed by the driving cycle. The control unit receives as input the accelerator and the brake signals, the state of charge (later  SOC) of the storage system and the generated and required  power from electrical electrical machines. Taking into account al alll these signals, the control unit activates one of the five possible operational modes. In the first mode (Fully Electric), only the electric motor  (MG1) propels the vehicle, while the ICE remains off. This condition occurs during starting and low-speed drives and requires at the same time vehicle speeds lower than 45 km/h and battery SOC over 50%. If these two conditions are not simultaneously verified, the control unit activates the second operational mode. The second mode applies when vehicle speed is over 45 km/ h, and when the power generate by MG2 (moved from ICE) is greater than power required from MG1. In this mode, the

 

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ICE and MG1 together generate the torque necessary to set the vehicle in motion. In this operational mode the Control Unit evaluates if the motor MG2 can provide the power  required by the motor MG1 (delta_P=(C  (delta_P=( C   MG1  MG 1 − C   MG2  MG 2) <0), if  so it active activess both the ICE to MG1. If the vehicle speed is over 45 km/h, the power generate by MG2 is lower than power required from MG1 and the SOC is greater than 50%, the CU activates the third mode. In this case, the MG1, besides to uses MG2 energy, also drains energy from the storage system. The fourth mode is activated during vehicle deceleration and  braking. In this this case MG1 becomes an electric power  generator and recharges the storage system. system. The fifth mode is activated when the vehicle stops and the SOC is less than 50%. Then, the ICE works at its maximum efficiency point, allowing the MG2 to increase the SOC of  the storage system.

PROPULSION AND GENERATION SYSTEMS The propulsion

systems, ICE and MG1, and the power  generation system MG2, are complex structures in which thermo-chemical and electro-mechanical transformations take  place. These These systems systems have been simulated through the use of  their characteristic curves that allow to link torques and  power to rotational rotational speed of moving moving parts. For ICE, MG1, and MG2 the torque can be evaluated by equation 2:

(2) where stands for maximum torque at the rotational speed considered, is system pulsation, α  represents the accelerator pedal position,  J   is the total polar moment of  inertia and  P aux  is the power absorbed by any accessories, assumed constant as rotational speed varies. The C max can be deduced from the characteristic curves for  ICE, MG1, and MG2. In Figure 2, the ICE characteristic curves [6] is shown as an example. (See Figure 2 after last section of paper) Within the ICE subsystem there is a further submodel which determines the specific fuel consumption and pollutant emissions. The fuel flow rate is calculated from power balance equation 3:

(3) where  P   IC   E   is the power output of ICE subsystem, η ICE  represents ICE efficiency which varies as supplied power and rotational speed vary (see Figure 2), Hi is the lower heating value of the fuel and ṁcomb is the fuel flow rate. Solving equation 3 and integrating over time, the fuel consumption is obtained for the chosen driving cycle. To evaluate the CO2 production, equation 4 is applied [4]:

(4) where mcomb is fuel mass used, mmC  is carbon molar mass, mmO  is oxygen molar mass, mm H   is hydrogen molar mass and H_C is the hydrogen/carbon fuel ratio.

PSD (POWER SPLIT DEVICE)

Figure 3 shows the Power Split Device used to connect the two power sources and the THS system generator. It is an epicyclic train composed of a sun gear, a ring gear and a  planetary   carrier, to  planetary to which the generator, the motor and the ICE are connected. On the shaft connecting the ring gear and the MG1 there is a gearing which transfers the enginegenerated torque to the wheels via a silent chain. ICE-generated power is conveyed to the wheels (mechanically) and generator (electrically). The former  consists in transferring power from the planetary carrier to the ring gear, the latter in power transfer from the planetary carrier to the PSD sun gear, to which the generator is connected. The energy transferred to it is turned into electricity which is stored in the batteries or sent to the MG1. To calculate the torque and rotation speed of each PSD component, the power equilibrium between the various shafts and the ratios of torques to rotation speeds have been examined and solved. In order not to complicate the model, the inertial PSD torques were deliberately overlooked entailing a slight fuel saving.

 

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and τ   stands for the transmission ratio related to all components between the PSD and the drive wheels.

ELECTRIC STORAGE SYSTEM The subsystem dealing with electric power storage [8] features equations used to obtain the state of charge (SOC) of  the storage batteries: 38 modules of 7.2 V nominal. This subsystem solves equation 9:

(9) where SOC 0 stands for the initial storage battery charge, and within the integral:

Figure 3. Power Split Device

(10) From calculations made in the other subsystems, the PSD input variables are known: C   ICE   the torque supplied by the ICE,

the MG1 rotation speed and C   MG1  MG 1, the MG1

torque. From these inputs, the output variables were defined  by solving equations equations 5, 6 and 7 [7] [7]::

where  I batt   is the charge/discharge current, and C batt   is the system storage capacity; from equation 10 it follows that if  the the I   I   is negative the storage system is discharged and vice batt  versa for charging. The power supplied or absorbed from the storage system ( P   P batt ), can be evaluated by equation 11:

(5) (11)

(6)

where V oc  and  Rbatt  indicate idle voltage and power storage internal resistance, the latter being different in charge and discharge phases,  both functio functions of   SOC, as reported in Figure 4 [9].

(7) where

is MG2 rotation speed and C  MG  MG2 2  is MG2

torque, is the ICE rotation speed, and z is the number  of teeth of the sun and ring gear. Knowing the ICE and MG1 torques which propel the vehicle, the torque from the shaft connected to the PSD ring gear  which is transferred to the wheels through a system made up of a silent train and a series of cogwheels was calculated as  per equation 8:

(See Figure 4 after last section of paper)

WHEEL AND VEHICLE DYNAMICS Within these two subsystems, the simulated vehicle speed is defined by solving the unidimensional equation of motion. In this model it is assumed that vehicle motion is rectilinear and that the wheels do not skid either during braking or  acceleration; this simplifies the equations but produces lower  fuel consumption. The Wheel subsystem calculates the horizontal component traction force  F t   which provides vehicle acceleration or  deceleration through equation 11:

(8) where C   prop  is the torque generated by the PSD subsystem resulting from the torques supplied by both power sources

(12)

 

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where C   prop  is the torque generated by the PSD subsystem resulting from the torques supplied by both engines, C braking  is braking system torque proportional to the brake pedal  position, C inertia  the torque inertia at the wheels and  Rwheel  the wheel radius. In the Vehicle Dynamics subsystem, the motion equation is solved along the vehicle's trajectory.

Figure 5 a) shows also the threshold of 45 km/h. The ICE is activated when the vehicle speed overcomes this threshold (see Figure 5 b). For each SOC starting value, during UDDS cycle, the THS Control Unit manages power sources in or  in  or der der to obtain a final SOC value of about 60%. This THS strategy is designed to optimized the fuel consumption [12]. (See Figure 5 after last section of paper)

(13) where F  where F  projection of the gravitational force along the  p is the projection vehicle's trajectory,  F r   is the friction generated by the tire rolling along the asphalt, due to the rolling friction coefficient,  F a  is the aerodynamic friction caused by the vehicle impacting the air, mv is the vehicle mass and v ̇vehicle is the vehicle acceleration. Integrating and solving equation 12 in relation to speed, we get the feedback signal which allows the subsystem Driver, once the difference between cycle-imposed speed and actual vehicle speed is known, to send the most suitable acceleration or braking inputs to obtain a f aaithful ithful reproduction of the imposed cycle.

SIMULATIONS AND DISCUSSION OF RESULTS All parameters concerning the system's components were put into the mathematical model in order to carry out simulations and evaluate the effectiveness of the model. As stated above, up to now two versions of Prius are on the market, the THS and the 2nd generation called THS-II. Basing on data from the two versions [10], it has been noticed that the improvements in the second series mainly consist in a more efficient ICE, a larger motor and generator, and some small details in the control system such as extending the generator's range. Apart from that, nothing has changed in changed in the dynamic equations which govern the vehicle. The simulation regarded the THS model.

Figure 5 b) and c) shown the ICE and MG1 torques respectively. respectiv ely. The ICE is activated when vehicle speed overcomes the threshold of 45 km/h, while the electrical motor (MG1) is activated when vehicle acceleration is greater  than zero and vehicle is moving (vvehicle > 0 km/h) Table 1 shows a comparison between the simulation results of the proposed model, experimental data [13] and ADVISOR 2002, related to the UDDS driving cycle. They confirm the effectiveness of the proposed model, with limited errors, both in terms of fuel consumption and pollutant emissions. (See Table 1 after last section of of p paper) aper) Being a dynamic model, the simulated vehicle's performance can be assessed. Figure 6 shows the model's response to an acceleration test using a driving cycle from 0 km/h to 100 km/h. Table 2 compares the simulation results with the experimental data [14]. Since the experimental test refers to an acceleration test from 0 to 60 mph, it also was used to validate the numerical simulation. (See Figure 6 after last section of paper) Table 2. Performance Comparison

All vehicle characteristics, efficiency maps and characteristic curves, were obtained from official Toyota Motor Corp., from the ADVISOR 2002 and from scientific literature [11]. Figure 5 a) shows the response of proposed model to the UDDS standard cycle (Urban Dynamometer Driving Schedule) in terms of speed and state of charge of the power  storage system (SOC at the cycle beginning equal to 70%; SOC at the cycle end equal to 62 %). The model closely

To verify the reliability of the proposed model versus different imposed cycles, other simulations were performed with different standard cycles. Figure 7 shows the response of  the model to Japanese 10-15 mode standard cycle, made up of three urban cycles (Japanese 10 mode) and an extra-urban one (Japanese 15 mode). Also in this case the model response

follows imposed noticecycle how speed the simulated faithfullythefollows thecycle; reference whereas speed SOC trend is similar to that seen in [12].

follows the imposed cycle perfectly in terms of speed, while the SOC remains nearly constant from start to end.

 

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(See Figure 7 after last section of paper) Table 3 shows a numerical comparison between the experimental data [11], results from ADVISOR 2002 simulations, and results of proposed model simulation. It seems clear how, even with other driving cycles than the one used for setting the model, the model can accurately provide the fuel consumption to complete the cycle.

9. Advisor 2002 program libraries files. 10. Muta, K., Yamazaki, M., and Tokieda, J., “Development of New-Generation Hybrid System THS II - Drastic Improvement of Power Performance and Fuel Economy,” SAE Technical Paper 2004-01-0064, 2004.

11. Rousseau, A., Sharer, P., and Pasquier, M., “Validation Process of a HEV System Analysis Model: PSAT,” SAE Technical Paper 2001-01-0953, 2001.

(See Table 3 after last section of paper)

12. Kelly K. J., Mihalic M. and Zolot M., “Battery Usage

CONCLUSIONS

and Thermal Performance of the Toyota Prius and Honda Insight During During Chassis Dynamometer Testing”, The Seventeenth Annual Battery Conference on Applications and Advances, Long Beach, California, 2002.

In this work, a feed-forward dynamic model of Toyota Hybrid system has been developed. The characteristics of all vehicle components were entered into the model, and a “rule based” control system system   was implemented implemented to manage interaction between vehicle components, making it easy to  predict the general behavior of a real vehicle. The model  performed simulations of the UDDS standard cycle and other  cycles to evaluate the model's response. The results confirm that the model can simulate the actual vehicle accurately and that the control strategy implemented closely follows that of  the first generation Toyota Prius. Compared to previous model studies [15], this one can assess vehicle performance as well as fuel consumption and pollutant emissions. This represents a remarkable target to help popularise hybrid motor vehicles in a market looking for ever better   performance and lower fuel consumption. consumption.

13. Liu J., Peng H. and Filipi Z., “Modeling and Analysis of  the Toyota Hybrid System”, Proceedings of the 2005 IEEE/ ASME Advanced Intelligent Mechatronics Conference, Monterrey, California, 2005.

14. Douba M., “Performance and Emissions of The Toyota Prius”, Prius Data Exchange Workshop, USCAR, Ott. 1999.

15. Fiorenza, S., Lanzafame, R., and Messina, M., “Analysis of Rules-Based Control Strategies for Integrated Starter  Alternator Vehicles,” SAE Technical Paper 2008-01-1314, 2008.

DEFINITIONS/ABBREVIATIONS THS Toyota Hybrid System;

REFERENCES 1. Chan C. C., “The state of the art of electric and hybrid vehicles”, Proceedings of the IEEE , 90 (2), 247-275, 2002. vehicles”, Proceedings 2. Gao D. W., Mi C. and Emadi A., “Modeling and Simulation of Electric and Hybrid Veicles”, Proceedings Veicles”, Proceedings of  the IEEE , 95 (4), 729-745, 729-745, 2007. 3. Markel T., Brooker A., Hendricks T., Johnson V., Kelly K., Kramer B., Spriktool S., for andadvanced Wipke K.,vehicle “ADVISOR: “ADVISOR : A O'Keefe systems M., analysis modeling”, J. modeling”,  J. Power Sources Sources,, 110 (2), 255-266, 2002. 4. Fiorenza, S., Lanzafame, R., and Messina, M., “Development of a Quasi-Static Backward Code for the Simulation of an Integrated Starter Alternator Vehicle,” SAE Technical Paper 2007-01-4125, 2007. 5. Hwang H., Choi J., Lee W., Kim J., “A Tuning Algorithm for The PID Controller Utilizing Fuzzy Theory”,  International Joint Joint Conference on Neural Networ Networks ks,, 4, 2210-2215, 1999. 6. http://www-personal.engin.umd.umich.edu 7. Sasaki S., “Toyota's “Toyota's newly developed hybrid powertrain”, Proceedings of the 10th International Symposium on Power  Semiconductor Devices and ICs, 1, pp. 17-22, 1998. 8. Liu J., Peng H., “Modeling and Control of a Power-Split Hybrid Vehicle”, IEEE Vehicle”, IEEE Transactions Transactions on Contr Control ol Systems Technology,, 16 (6), 1242-1251, 2008. Technology

ICE Internal combustion engine;

MG1 Electrical Motor;

MG2 Electrical Power generator;

PSD Power Split Device;

u(t) Accelerator/Brake Accelerator/B rake control signal;

Kp Propor ttional ional g gain; ain;

Ki integrative gain;

 

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H_C

e(t )

hydrogen/carbon fuel ratio;

error between imposed cycle speed and simulated speed;

Kd

generator angular pulsation [s^(−1)];

derivative gain;

C

torque [Nm];

internal combustion engine angular pulsation [s^(−1)];

angular pulsation;

electric motor angular pulsation [s^(−1)];  z ring  ring 

α

teeth number of ring gear;

 propulsion system command signal;  z sun sun

J

teeth number of sun gear;

 polar inertial moment [kg*m^2] [kg*m^2];;

P

C   MG 2

 power [W]; η

generator torque [Nm]; C   ICE 

efficiency;

Hi lower heating value [J/kg];

ṁcomb fuel flow rate [kg/s];

mCO2

internal combustion engine torque [Nm]; C   MG 1

electrical motor torque [Nm]; C   prop

tractor torque [Nm]; τ 

CO2 mass produced [kg];

mcomb

gear ratio;

SOC fuel mass used [kg];

mmC

storage system state of charge;  SOC 0

carbon molar mass [g/mol];

mmO

initial state of charge;

SȮC temporary variation of state of charge;

oxygen molar mass [g/mol];

mmH

 I batt  batt 

hydrogen molar mass [g/mol];

current in storage system [A];

 

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V batt 

tension in storage system [V];  P batt 

storage system power [W]; V oc

storage system idle tension [V]; F t 

traction force [N]; C braking   braking torque [Nm]; [Nm]; C inertia

inertial torque [Nm];  Rwheel 

wheel radius [m]; F   p

gravitation force [N]; F rr  

rolling friction force [N]; F a

aerodynamic friction force [N]; mv

vehicle mass [kg];

vvehicle vehicle speed [m/s]

v̇ vehicle vehicle acceleration [m/s^2];

UDDS Urban Dynamometer Driving Schedule.

 

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Figure 1. Toyota Prius THS dynamic model schematization

Figure 2. Maximum torque curve and ICE efficiency map

 

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Figure 4. Power storage internal resistance as charge varies

Figure 5. a) Model response to UDDS cycle; b) ICE torque; c) Electric Motor (MG1) torque

 

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Figure 6. Acceleration test 

Figure 7. Response of model to Japan 10-15 cycle

 

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Table 1. UDDS cycle Consumption / Emission comparison

Table 3. Japan 10-15 Cycle consumption comparison

The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAE's peer review process under the supervision of the session organizer. This process requires a minimum of three (3) reviews by industry experts. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,  photocopying, recording, or otherwise, without the prior written permission of SAE. ISSN 0148-7191 doi:10.4271/2010-01-1443

Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper.

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