throbber
Fundamentals, Theory, and Design
`
`Mehrdad Ehsani ! f " H
`
`.
`
`l
`
`1
`
`Modern Electric,
`Hybrid Electric, and
`Fuel Cell Vehicles
`
`
`
`Yimin Gao ,/
`
`SebaS’fi/en E. Gay #‘W 7,.
`
`.-
`
`(m Em?i
`
`.
`
`.4,
`
`'I
`
`PAICE 2020
`BMW v. Paice
`|PR2020-00994
`
`PAICE 2020
`BMW v. Paice
`IPR2020-00994
`
`1
`
`

`

`Modern Electric,
`Hybrid Electric, and
`Fuel Cell Vehicles
`
`Fundamentals, Theory, and Design
`
`2
`
`

`

`P O W E R E L E C T R O N I C S A N D
`A P P L I C A T I O N S S E R I E S
`Muhammad H. Rashid, Series Editor
`University of West Florida
`
`PUBLISHED TITLES
`
`Complex Behavior of Switching Power Converters
`Chi Kong Tse
`
`DSP-Based Electromechanical Motion Control
`Hamid A. Toliyat and Steven Campbell
`
`Advanced DC/DC Converters
`Fang Lin Luo and Hong Ye
`
`Renewable Energy Systems: Design and Analysis with
`Induction Generators
`M. Godoy Sim~oes and Felix A. Farret
`
`Uninterruptible Power Supplies and Active Filters
`Ali Emadi, Abdolhosein Nasiri, and Stoyan B. Bekiarov
`
`Electric Energy: An Introduction
`Mohamed El-Sharkawi
`
`3
`
`

`

`Modern Electric,
`Hybrid Electric, and
`Fuel Cell Vehicles
`
`Fundamentals, Theory, and Design
`
`Mehrdad Ehsani, Texas A&M University
`
`Yimin Gao, Texas A&M University
`
`Sebastien E. Gay, Texas A&M University
`
`Ali Emadi, Illinois Institute of Technology
`
`CRC PR E S S
`Boca Raton London New York Washington, D.C.
`
`4
`
`

`

`Library of Congress Cataloging-in-Publication Data
`
`Modern electric, hybrid electric, and fuel cell vehicles: fundamentals,
`theory, and design/Mehrdad Ehsani ... [et al.].
`p. cm. – (Power electronics and applications series)
`Includes bibliographical references and index.
`ISBN 0-8493-3154-4 (alk. paper)
`1. Hybrid electric vehicles. 2. Fuel cells. I. Ehsani, Mehrdad. II. Title. III. Series.
`
`TL221.15.G39 2004
`629.22’93—dc22
`
`2004054249
`
`This book contains information obtained from authentic and highly regarded sources.
`Reprinted material is quoted with permission, and sources are indicated. A wide variety of ref-
`erences are listed. Reasonable efforts have been made to publish reliable data and information,
`but the author and the publisher cannot assume responsibility for the validity of all materials
`or for the consequences of their use.
`
`Neither this book nor any part may be reproduced or transmitted in any form or by any means,
`electronic or mechanical, including photocopying, microfilming, and recording, or by any infor-
`mation storage or retrieval system, without prior permission in writing from the publisher.
`
`The consent of CRC Press LLC does not extend to copying for general distribution, for promo-
`tion, for creating new works, or for resale. Specific permission must be obtained in writing from
`CRC Press LLC for such copying.
`
`Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.
`
`Trademark Notice: Product or corporate names may be trademarks or registered trademarks,
`and are used only for identification and explanation, without intent to infringe.
`
`Visit the CRC Press Web site at www.crcpress.com
`
`© 2005 by CRC Press LLC
`No claim to original U.S. Government works
`
`International Standard Book Number 0-8493-3154-4
`Library of Congress Card Number 2004054249
`Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
`Printed on acid-free paper
`
`5
`
`

`

`Contents
`
`1. Environmental Impact and History of Modern Transportation ..............1
`1.1 Air Pollution ............................................................................................2
`1.1.1 Nitrogen Oxides ..........................................................................2
`1.1.2 Carbon Monoxide ........................................................................3
`1.1.3 Unburned Hydrocarbons ..........................................................3
`1.1.4 Other Pollutants ..........................................................................3
`1.2 Global Warming ......................................................................................4
`1.3 Petroleum Resources ..............................................................................5
`1.4 Induced Costs ..........................................................................................7
`1.5 Importance of Different Transportation Development
`Strategies to Future Oil Supply ............................................................9
`1.6 History of Electric Vehicles ..................................................................13
`1.7 History of Hybrid Electric Vehicles ....................................................15
`1.8 History of Fuel Cell Vehicles ..............................................................17
`References........................................................................................................19
`
`2. Vehicle Fundamentals....................................................................................21
`2.1 General Description of Vehicle Movement ......................................22
`2.2 Vehicle Resistance ................................................................................23
`2.2.1 Rolling Resistance ....................................................................23
`2.2.2 Aerodynamic Drag ..................................................................25
`2.2.3 Grading Resistance ..................................................................26
`2.3 Dynamic Equation ................................................................................27
`2.4 Tire–Ground Adhesion and Maximum Tractive Effort ..................29
`2.5 Power Train Tractive Effort and Vehicle Speed ..............................31
`2.6 Vehicle Power Plant and Transmission Characteristics ..................33
`2.6.1 Power Plant Characteristics ....................................................34
`2.6.2 Transmission Characteristics ..................................................36
`2.6.2.1 Gear Transmission ....................................................37
`2.6.2.2 Hydrodynamic Transmission ..................................39
`2.6.2.3 Continuously Variable Transmission ......................43
`2.7 Vehicle Performance ............................................................................44
`2.7.1 Maximum Speed of a Vehicle ................................................45
`2.7.2 Gradeability ..............................................................................46
`2.7.3 Acceleration Performance ......................................................46
`
`6
`
`

`

`2.8 Operating Fuel Economy ....................................................................49
`2.8.1 Fuel Economy Characteristics of Internal
`Combustion Engines ........................................................................49
`2.8.2 Calculation of Vehicle Fuel Economy ....................................50
`2.8.3 Basic Techniques to Improve Vehicle Fuel Economy ..........52
`2.9 Braking Performance ..........................................................................54
`2.9.1 Braking Force ............................................................................54
`2.9.2 Braking Distribution on Front and Rear Axles ....................55
`References ......................................................................................................60
`
`3. Internal Combustion Engines ......................................................................61
`3.1 4S, Spark-Ignited IC Engines ..............................................................62
`3.1.1 Operating Principles..................................................................62
`3.1.2 Operation Parameters ..............................................................64
`3.1.2.1 Rating Values of Engines ..........................................64
`3.1.2.2
`Indicated Work per Cycles and Mean Effective
`Pressure ........................................................................64
`3.1.2.3 Mechanical Efficiency ................................................66
`3.1.2.4 Specific Fuel Consumption and Efficiency ............67
`3.1.2.5
`Specific Emissions ......................................................68
`3.1.2.6 Fuel/Air and Air/Fuel Ratio......................................68
`3.1.2.7 Volumetric Efficiency ................................................69
`3.1.3 Relationships between Operation and Performance
`Parameters ................................................................................69
`3.1.4 Engine Operation Characteristics............................................70
`3.1.4.1 Engine Performance Parameters ..............................70
`3.1.4.2
`Indicated and Brake Power and Torque ................71
`3.1.4.3 Fuel Consumption Characteristics ..........................72
`3.1.5 Operating Variables Affecting SI Engine Performance,
`Efficiency, and Emissions Characteristics ..............................74
`3.1.5.1
`Spark Timing ..............................................................74
`3.1.5.2 Fuel/Air Equivalent Ratio ........................................74
`3.1.6 Emission Control ......................................................................77
`3.1.7 Basic Technique to Improve Performance, Efficiency, and
`Emission Characteristics ..........................................................78
`3.2 4S, Compression-Ignition IC Engines ................................................81
`3.3 Two-Stroke Engines ..............................................................................82
`3.4 Wankel Rotary Engines ........................................................................86
`3.5 Stirling Engines......................................................................................89
`3.6 Gas Turbine Engines ............................................................................94
`3.7 Quasi-Isothermal Brayton Cycle Engines..........................................97
`References........................................................................................................98
`
`4. Electric Vehicles ..............................................................................................99
`4.1 Configurations of Electric Vehicles ....................................................99
`
`7
`
`

`

`4.2 Performance of Electric Vehicles ......................................................102
`4.2.1 Traction Motor Characteristics ..............................................103
`4.2.2 Tractive Effort and Transmission Requirement ..................104
`4.2.3 Vehicle Performance................................................................105
`4.3 Tractive Effort in Normal Driving ....................................................109
`4.4 Energy Consumption ..........................................................................114
`References ....................................................................................................116
`
`5. Hybrid Electric Vehicles ..............................................................................117
`5.1 Concept of Hybrid Electric Drive Trains ........................................118
`5.2 Architectures of Hybrid Electric Drive Trains ................................120
`5.2.1 Series Hybrid Electric Drive Trains ......................................121
`5.2.2 Parallel Hybrid Electric Drive Trains....................................123
`5.2.2.1 Torque-Coupling Parallel Hybrid Electric
`Drive Trains ..............................................................124
`5.2.2.2 Speed-Coupling Parallel Hybrid Electric
`Drive Trains ..............................................................130
`5.2.2.3 Torque-Coupling and Speed-Coupling
`Parallel Hybrid Electric Drive Trains ....................133
`References......................................................................................................136
`
`6. Electric Propulsion Systems ......................................................................137
`6.1 DC Motor Drives ................................................................................142
`6.1.1 Principle of Operation and Performance ............................142
`6.1.2 Combined Armature Voltage and Field Control ................146
`6.1.3 Chopper Control of DC Motors ............................................146
`6.1.4 Multiquadrant Control of Chopper-Fed DC Motor
`Drives ........................................................................................151
`6.1.4.1 Two-Quadrant Control of Forward Motoring
`and Regenerative Braking ......................................151
`6.1.4.1.1 Single Chopper with a Reverse
`Switch ......................................................151
`6.1.4.1.2 Class C Two-Quadrant Chopper..........152
`6.1.4.2 Four-Quadrant Operation ......................................154
`6.2 Induction Motor Drives......................................................................155
`6.2.1 Basic Operation Principles of Induction Motors ................156
`6.2.2 Steady-State Performance ......................................................159
`6.2.3 Constant Volt/Hertz Control ................................................162
`6.2.4 Power Electronic Control........................................................163
`6.2.5 Field Orientation Control ......................................................166
`6.2.5.1 Field Orientation Principles....................................166
`6.2.5.2 Control........................................................................173
`6.2.5.3 Direction Rotor Flux Orientation Scheme ............175
`6.2.5.4
`Indirect Rotor Flux Orientation Scheme ..............178
`
`8
`
`

`

`6.2.6 Voltage Source Inverter for FOC ..........................................180
`6.2.6.1 Voltage Control in Voltage Source Inverter ..........182
`6.2.6.2 Current Control in Voltage Source Inverter ........185
`6.3 Permanent Magnetic Brush-Less DC Motor Drives ......................187
`6.3.1 Basic Principles of BLDC Motor Drives ..............................190
`6.3.2 BLDC Machine Construction and Classification ................190
`6.3.3 Properties of PM Materials ....................................................193
`6.3.3.1 Alnico ........................................................................194
`6.3.3.2 Ferrites........................................................................195
`6.3.3.3 Rare-Earth PMs ........................................................195
`6.3.4 Performance Analysis and Control of BLDC Machines ....196
`6.3.4.1 Performance Analysis ..............................................196
`6.3.4.2 Control of BLDC Motor Drives ..............................198
`6.3.5 Extension of Speed Technology ............................................199
`6.3.6 Sensorless Techniques ............................................................200
`6.3.6.1 Methods Using Measurables and Math................201
`6.3.6.2 Methods Using Observers ......................................201
`6.3.6.3 Methods Using Back EMF Sensing........................202
`6.3.6.4 Unique Sensorless Techniques................................203
`6.4 Switched Reluctance Motor Drives ..................................................204
`6.4.1 Basic Magnetic Structure ........................................................204
`6.4.2 Torque Production ..................................................................207
`6.4.3 SRM Drive Converter..............................................................210
`6.4.4 Modes of Operation ................................................................213
`6.4.5 Generating Mode of Operation (Regenerative Braking) ..214
`6.4.6 Sensorless Control ..................................................................216
`6.4.6.1 Phase Flux Linkage-Based Method........................218
`6.4.6.2 Phase Inductance-Based Method ..........................218
`6.4.6.2.1 Sensorless Control Based on
`Phase Bulk Inductance ..........................218
`6.4.6.2.2 Sensorless Control Based on
`Phase Incremental Inductance..............219
`6.4.6.3 Modulated Signal Injection Methods ....................220
`6.4.6.3.1 Frequency Modulation Method ..........220
`6.4.6.3.2 AM and PM Methods ............................221
`6.4.6.3.3 Diagnostic Pulse-Based Method ..........221
`6.4.6.4 Mutually Induced Voltage-Based Method............222
`6.4.6.5 Observer-Based Methods ........................................222
`6.4.7 Self-Tuning Techniques of SRM Drives................................222
`6.4.7.1 Self-Tuning with the Arithmetic Method..............223
`6.4.7.1.1 Optimization with Balanced
`Inductance Profiles ................................223
`6.4.7.1.2 Optimization in the Presence of
`Parameter Variations..............................224
`6.4.7.2 Self-Tuning Using an Artificial Neural
`Network ....................................................................224
`
`9
`
`

`

`6.4.8 Vibration and Acoustic Noise in SRM..................................226
`6.4.9 SRM Design ..............................................................................228
`6.4.9.1 Number of Stator and Rotor Poles ........................228
`6.4.9.2
`Stator Outer Diameter..............................................229
`6.4.9.3 Rotor Outer Diameter ..............................................230
`6.4.9.4 Air gap........................................................................230
`6.4.9.5
`Stator Arc ..................................................................231
`6.4.9.6
`Stator Back-Iron ........................................................231
`6.4.9.7 Performance Prediction ..........................................231
`References......................................................................................................232
`
`7. Series Hybrid Electric Drive Train Design ..............................................239
`7.1 Operation Patterns ..............................................................................240
`7.2 Control Strategies ................................................................................242
`7.2.1 Max. SOC-of-PPS Control Strategy ......................................243
`7.2.2 Thermostat Control Strategy (Engine-On–Off) ..................244
`7.3 Sizing of the Major Components ......................................................246
`7.3.1 Power Rating Design of the Traction Motor........................246
`7.3.2 Power Rating Design of the Engine/Generator..................247
`7.3.3 Design of PPS ..........................................................................249
`7.3.3.1 Power Capacity of PPS ............................................249
`7.3.3.2 Energy Capacity of PPS ..........................................250
`7.4 Design Example ..................................................................................251
`7.4.1 Design of Traction Motor Size ..............................................251
`7.4.2 Design of the Gear Ratio ........................................................251
`7.4.3 Verification of Acceleration Performance ............................252
`7.4.4 Verification of Gradeability ....................................................253
`7.4.5 Design of Engine/Generator Size ........................................254
`7.4.6 Design of the Power Capacity of PPS ..................................255
`7.4.7 Design of the Energy Capacity of PPS ................................255
`7.4.8 Fuel Consumption ..................................................................256
`References......................................................................................................257
`
`8. Parallel Hybrid Electric Drive Train Design ............................................259
`8.1 Control Strategies of Parallel Hybrid Drive Train..........................261
`8.1.1 Maximum State-of-Charge of Peaking
`Power Source (Max. SOC-of-PPS) Control Strategy ..........262
`8.1.2 Engine Turn-On and Turn-Off (Engine-On–Off)
`Control Strategy ......................................................................265
`8.2 Design of Drive Train Parameters ....................................................266
`8.2.1 Design of Engine Power Capacity ........................................266
`8.2.2 Design of Electric Motor Drive Power Capacity ................268
`8.2.3 Transmission Design ..............................................................271
`8.2.4 Energy Storage Design............................................................272
`
`10
`
`

`

`8.3 Simulations ..........................................................................................274
`References......................................................................................................276
`
`9. Mild Hybrid Electric Drive Train Design ................................................277
`9.1 Energy Consumed in Braking and Transmission ..........................278
`9.2 Parallel Mild Hybrid Electric Drive Train ......................................280
`9.2.1 Configuration ..........................................................................280
`9.2.2 Operating Modes and Control Strategy ..............................281
`9.2.3 Drive Train Design ..................................................................283
`9.2.4 Performance..............................................................................285
`9.3 Series–Parallel Mild Hybrid Electric Drive Train ..........................287
`9.3.1 Configuration of the Drive Train with a
`Planetary Gear Unit ................................................................287
`9.3.2 Operating Modes and Control ..............................................291
`9.3.2.1 Speed-Coupling Operating Mode..........................291
`9.3.2.2 Torque-Coupling Operating Mode ........................293
`9.3.2.3 Engine-Alone Traction Mode..................................294
`9.3.2.4 Regenerative Braking Mode ..................................294
`9.3.2.5 Engine Starting..........................................................295
`9.3.3 Control Strategy ......................................................................295
`9.3.4 Drive Train with Floating-Stator Motor ..............................296
`References......................................................................................................298
`
`10. Energy Storages............................................................................................299
`10.1 Electrochemical Batteries....................................................................300
`10.1.1 Electrochemical Reactions ......................................................302
`10.1.2 Thermodynamic Voltage ........................................................304
`10.1.3 Specific Energy ........................................................................304
`10.1.4 Specific Power ..........................................................................306
`10.1.5 Energy Efficiency ....................................................................309
`10.1.6 Battery Technologies ..............................................................309
`10.1.6.1 Lead-Acid Batteries ..................................................310
`10.1.6.2 Nickel-based Batteries..............................................311
`10.1.6.2.1 Nickel/Iron System ................................311
`10.1.6.2.2 Nickel/Cadmium System......................311
`10.1.6.2.3 Nickel–Metal Hydride (Ni–MH)
`Battery ......................................................312
`10.1.6.3 Lithium-Based Batteries ..........................................313
`10.1.6.3.1 Lithium–Polymer (Li–P) Battery ..........313
`10.1.6.3.2 Lithium-Ion (Li-Ion) Battery ................313
`10.2 Ultracapacitors ....................................................................................314
`10.2.1 Features of Ultracapacitors ....................................................315
`10.2.2 Basic Principles of Ultracapacitors........................................315
`
`11
`
`

`

`10.2.3 Performance of Ultracapacitors ............................................317
`10.2.4 Ultracapacitor Technologies ..................................................320
`10.3 Ultrahigh-Speed Flywheels................................................................322
`10.3.1 Operation Principles of Flywheels........................................322
`10.3.2 Power Capacity of Flywheel Systems ..................................324
`10.3.3 Flywheel Technologies............................................................326
`10.4 Hybridization of Energy Storages ....................................................328
`References......................................................................................................332
`
`11. Fundamentals of Regenerative Braking ..................................................333
`11.1 Energy Consumption in Braking ......................................................334
`11.2 Braking Power and Energy on Front and Rear Wheels ................334
`11.3 Brake System of EVs and HEVs........................................................338
`11.3.1 Series Brake — Optimal Feel ................................................338
`11.3.2 Series Brake — Optimal Energy Recovery ..........................339
`11.3.3 Parallel Brake............................................................................341
`11.4 Antilock Brake System (ABS) ............................................................343
`References......................................................................................................345
`
`12. Fuel Cell Vehicles ........................................................................................347
`12.1 Operating Principles of Fuel Cells....................................................348
`12.2 Electrode Potential and Current–Voltage Curve ............................350
`12.3 Fuel and Oxidant Consumption ......................................................354
`12.4 Fuel Cell System Characteristics ......................................................355
`12.5 Fuel Cell Technologies........................................................................357
`12.5.1 Proton Exchange Membrane Fuel Cells ..............................357
`12.5.2 Alkaline Fuel Cells ..................................................................359
`12.5.3 Phosphoric Acid Fuel Cells1 ..................................................361
`12.5.4 Molten Carbonate Fuel Cells ................................................361
`12.5.5 Solid Oxide Fuel Cells ............................................................362
`12.5.6 Direct Methanol Fuel Cells ....................................................363
`12.6 Fuel Supply ..........................................................................................364
`12.6.1 Hydrogen Storage....................................................................364
`12.6.1.1 Compressed Hydrogen............................................364
`12.6.1.2 Cryogenic Liquid Hydrogen ..................................366
`12.6.1.3 Metal Hydrides ........................................................367
`12.6.2 Hydrogen Production ............................................................368
`12.6.2.1 Steam Reforming ......................................................369
`12.6.2.2 POX Reforming ........................................................370
`12.6.2.3 Autothermal Reforming ..........................................370
`12.6.3 Ammonia as Hydrogen Carrier ............................................371
`12.7 Nonhydrogen Fuel Cells ....................................................................371
`References......................................................................................................372
`
`12
`
`

`

`13. Fuel Cell Hybrid Electric Drive Train Design..........................................375
`13.1 Configuration ......................................................................................376
`13.2 Control Strategy ..................................................................................377
`13.3 Parametric Design ..............................................................................379
`13.3.1 Motor Power Design ..............................................................379
`13.3.2 Power Design of the Fuel Cell System ................................381
`13.3.3 Design of the Power and Energy Capacity of the PPS ......381
`13.3.3.1 Power Capacity of the PPS......................................381
`13.3.3.2 Energy Capacity of the PPS ....................................381
`13.4 Design Example ..................................................................................383
`References......................................................................................................385
`
`Index ..............................................................................................................387
`
`13
`
`

`

`2 V
`
`ehicle Fundamentals
`
`CONTENTS
`2.1 General Description of Vehicle Movement ............................................22
`2.2 Vehicle Resistance ......................................................................................23
`2.2.1 Rolling Resistance ..........................................................................23
`2.2.2 Aerodynamic Drag ........................................................................25
`2.2.3 Grading Resistance ........................................................................26
`2.3 Dynamic Equation ......................................................................................27
`2.4 Tire–Ground Adhesion and Maximum Tractive Effort ........................29
`2.5 Power Train Tractive Effort and Vehicle Speed ......................................31
`2.6 Vehicle Power Plant and Transmission Characteristics ........................33
`2.6.1 Power Plant Characteristics
`........................................................34
`2.6.2 Transmission Characteristics ........................................................36
`2.6.2.1 Gear Transmission ........................................................37
`2.6.2.2 Hydrodynamic Transmission ......................................39
`2.6.2.3 Continuously Variable Transmission ..........................43
`2.7 Vehicle Performance ..................................................................................44
`2.7.1 Maximum Speed of a Vehicle ......................................................45
`2.7.2 Gradeability ....................................................................................46
`2.7.3 Acceleration Performance ............................................................46
`2.8 Operating Fuel Economy ..........................................................................49
`2.8.1
`Fuel Economy Characteristics of Internal
`Combustion Engines ..............................................................................49
`2.8.2 Calculation of Vehicle Fuel Economy ........................................50
`2.8.3 Basic Techniques to Improve Vehicle Fuel Economy ..............52
`2.9 Braking Performance ..................................................................................54
`2.9.1 Braking Force ..................................................................................54
`2.9.2 Braking Distribution on Front and Rear Axles
`........................55
`References ..............................................................................................................60
`
`Vehicle operation fundamentals mathematically describe vehicle behavior
`based on the general principles of mechanics. A vehicle, consisting of thou-
`sands of components, is a complex system. To describe its behavior fully,
`sophisticated mechanical and mathematical knowledge is needed. A great
`
`21
`
`14
`
`

`

`22
`
`Modern Electric, Hybrid Electric, and Fuel Cell Vehicles
`
`amount of literature of this kind already exists. Since this book proposes to
`discuss electric and hybrid electric power trains, the discussion of vehicle
`fundamentals will be restricted to one-dimensional movement. This chapter
`will therefore focus on vehicle performance speed, gradeability, acceleration,
`fuel consumption, and braking performance.
`
`2.1 General Description of Vehicle Movement
`
`Figure 2.1 shows the forces acting on a vehicle moving up a grade. The trac-
`tive effort, Ft, in the contact area between tires of the driven wheels and the
`road surface propels the vehicle forward. It is produced by the power plant
`torque and is transferred through transmission and final drive to the drive
`wheels. While the vehicle is moving, there is resistance that tries to stop its
`movement. The resistance usually includes tire rolling resistance, aerody-
`namic drag, and uphill resistance. According to Newton’s second law, vehi-
`cle acceleration can be written as
`⫺ΣFtrᎏᎏ
`ΣFt
`dVᎏ
`dt
`δMv
`where V is vehicle speed, ΣFt is the total tractive effort of the vehicle, ΣFtr is
`the total resistance, Mv is the total mass of the vehicle, and δ is the mass fa

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