PRIUS GEN IV 1.8L PERFORMANCE SIMULATION

Transcription

1 PRIUS GEN IV 1.8L PERFORMANCE SIMULATION Macro Model of Hybrid Vehicle Performance: Prius T.icem2Procedure: First model the Prius Internal Combustion Engine's (ICE and the motor's, torque and power. Define vehicle and road parameters. MG1 Starter and Controller Acceleration Protocol: MG1 is the battery initiated starter for the ICE. "Simulate" MG1's spin startup, Ω1init m2 and Ω1init ice, as a ramp from to its maximum speed, along with the motor M2 and ICE, respectively, which are also driven by the Prius Controller to ramp up. Refer to Startup Curves on bottom of page 6. This is an arbitrary set of conditions just to start the generator turning. Note that this startup is not a function of time, but of corresponding rotations. This startup condition simulates a low gear mode for the ICE. Evaluate two different Prius Control Strategies: Max Acceleration and Nonal. See curves on page 4. During acceleration, the largest torque is from motor/generator MG2, which is geared to the axle. The axle deternes the vehicle speed. Use the MG2 rotation, ω m2, as our control variable. During acceleration, supply peak electrical power to MG2 from both the battery (peak battery power for seconds and from MG1, which is now run as a generator at it's max speed and is mechanically driven by the ICE. As MG2 speeds up and demands increasing power, throttle back it's peak drive/torque by liting the MG2's electrical power input to the peak Inverter Output, i.e. the sum of the battery's and MG1 generator's peak power. Refer to the curve of M2 Torque vs.ω m2 on page 3. Peak acceleration and - mph is programmed by setting the MG1 max speed: Ωmax m1 Use equations for vehicle dynacs to calculate the time to mph. Plot performance simulation curves. Calculate All Electric Range, AER, les from a single charge of the battery. Calculate AER using various EPA driving modes. Compare Prius Performance to GM Volt. Basic Description of Prius Modeling and Simulation of Serial Parallel Hybrid EV Description and Design of Synergy (Planetary Gear Drive Patent:US MG1 ICE GR m Motor M2 Grear Reduction MG2 Sun Planet Ring Prius Split Hybrid Drive Gear Rotation Speed Varibles: MG1, MG2, and Engine: ωm1, ωm2, and ωice. Power Efficiencies: Inverter, axle to tire, engine to MG1, reduction gear, and engine to axle efficiencies ηinv, ηaxle, ηeng_m1, ηred, and ηaeng_axle

2 Prius Gen III ICE Performance Curves k TIII ice ( w if w > 5, TIII ice ( 5, TIII ice ( w Scale Up to Gen IV Specs: Torque (N m T icee ( w Scale the Power and Torque Models for Toyota Atkinson Gen III 1.5L ICE to Gen IV 1.8L PIII ice ( w if w < Ω idle,, P idle + P slope w Ω idle Prius 1.8L Atkinson ICE Torque Model Match Model Parameters to: Specifications for Different Prius Models Generation III Torque and Power Models: T idle 85 Ω idle X P w Engine Speed (RPM 142 X T 115 TIII ice ( w if w < Ω idle,, P idle + T slope w Ω idle k 2 π w PIII ice ( w if w > 5, PIII ice ( 5, PIII ice ( w Power (kw P ice ( w PIII ice ( w X P P ice ( w 2 π Ω idle P idle T idle k 57 P idle P slope T icee ( w TIII ice ( w X T Prius 1.8L Atkinson ICE Model (kw w Engine Speed (RPM.23 P idle T slope Model Equations for the Driveshaft, ICE, and Planetary Gears Simulation of a Series Hybrid Electric Vehicle based on Energetic Macroscopic Representation W. Lhomme1, A. Bouscayrol1, Member, P. Barrade2 d J t Ω shaft + f Ω shaft = T ice T dcg d P ice = m ice k ice Ω shaft T ice = m ice k ice dgas η ρ P c k ice = Ω ice_max ω mg ω mg2 = 3.6ω ice J, f, and Ωshaft are the moment of inertia, friction coefficient, and speed of the shaft. Tice and Tdcg are the ICE and generator torques. The ICE pressure, Pice, results from the flow of gasoline. η is the ICE efficiency, ρ the density of gasoline, Pc the calorific value of gasoline and Ωice_max the maximum rotation speed of the engine. The control of the machine is ensured by the ce ratio, which defines the actual flow of gasoline, dgas, through a specific actuator. The relation for the shaft rotational velocities ωice, ωmg1, and ωmg2 describes the action of the Hybrid Synergy Drive Planetary Gear (shown in the above illustration.

3 Gen III NHW MG2 Motor Performance Curves Toyoto Prius Gen IV 1.8L-Vehicle, Motor and Road Parameters: Specifications for Different Prius Models Gear Ratio and Efficiencies: GR η inv.9 η eng_axle.95 η axle.95 η eng_m1.95 η red.95 Max Motor Power: Max Motor Torque: Max Motor Speeds: Pmax m2 kw η axle Tmax m2 7ft lbf Max. Acceleration Mode==> Pmax m1 37 kw η eng_m1 Pmax m1 = hp Tmax m1 7 ft lbf η eng_m1 GR m2 η axle r tire.287 m Ωmax m1 9 RPM Pmax ice 73 kw η eng_m1 Pmax ice = 93 hp Tmax ice 142 N m η eng_m1 RPM n 1 Ωmax ice 5 RPM Redline Ωmax ice n Tmax m1 Ωmax m1 Tmax m2 = = kw N m Note MG1's power is speed (6 rpm lited Set Pmaxbat to for Extremum Energy bat 6.5 kw hr Pmax bat 27 kw Average Wind Velocity: Shape Correction Factor: Drag Coeff: Cross Wind Drag Coff: Air Density: Road Rolling Resist: Rotational Inertia Coeff: Gross Weight: Chasis and Environmental Parameters Vw Cd.25 Cd cw.14 ρ mph SCF gm liter RR road.2 k m 1.8 M gross M curb + Passengers2 Frontal Area*: Frontal Area Corrected: Rolling Resistance Per Tire: (Average % road grade Average Cross Wind: Curb Weight: Passenger Weight: M gross = lb Afg 2.33 m 2 Af RR tire.7 θ atan(. V cw M curb M batt Afg SCF mph 42 lb Passengers2 68 kg Af = 1.98 m 2 θ (radians: 1 lb Vehicle Dynacs Equations - Find Velocity and Time for Maximum Acceleration Road Resistance, Fr: cos( θ Aerodynac Loss, Fa: Opposing Force, Fo: Fr( v M gross g RR tire + RR road + sin θ Fa( v.5 ρ Af ( v + Vw 2 Cd + Cd cw.5 v + V cw Fo( v Fa( v + Fr( v 2 Fo( mph = N Fr( mph = N Fa( mph = N Fo( mph = N M2rpm_at_mph( s Velocity vs Shaft (MG2 Rotaional Speed and Hybrid Synergy Gearing GR s 2 π r tire RPM velmg2_at_rpm( w 2 π r tire w RPM GR v_r( w 2 π r tire w RPM GR mph

4 Control Strategies (Hybrid Synergy Drive Speed Relationships: Develop an MG1 Profile and then Find Speed Relationships of MG2(ICE and ICE(MG2 Hybrid Synergy Drive MG1 Control Stategy: Max MG1 Rotation Ωmax m1 Initial M2 Spinup ( Ωm1, ICE and MG2 Rotation Profiles From MG1 Profiles Ω1Prfl1m1 (Enabled or Ω1Pffl2m1 (Disabled : Ω ice ( ω mg2 Ω ice ( ω mg2 Ω1init m2 ω mg2 and Driving Profiles, Ω1Prfl m1, Ω1Prfl2 m1 Vel rev_up Calculate Control Point: Ω icevel ω Rev up ICE from Cruise at mg2 Vehicle Velocity Vel rev_up Ω1Prfl2 m1 ω mg2 See Plot Lower Right Max Acceleration Control Strategy P1: Turn on ICE at 15 mph (See Control Plot Apply maxium MG1 power/speed Ωmax m1 = 8 RPM from Generator MG1 to MG2. Ω1init m2 ω mg2 Ω1init ice ω ice Ω1Prfl m1 ω mg2 Ω ice_vel vel 7 Ω1Prfl2 vm1 ( v if v <, 6 v, + ( v ( Ω1Prfl m1 ( ω mg ω mg2 3.6 ( Ω1Prfl2 vm1 ( v_r( ω mg ω mg2 3.6 ( 2.6 ω mg2 Ω1Prfl Ω icep1 ( ω mg2 m1 ω mg Ω ice ( M2rpm_at_mph( 1 mph = Ω1init m2 ( ω mg2 Nonal Control Strategy P2: Constant ICE (rpm= to mph, then ramp up. Profile 2- Ω1Prfl2 m1 Use just Ω ice_vel ( vel to find resultant relation between MG1 and Velocity, i.e. MG2 if vel < Vel rev_up,, + ( vel Vel rev_up velmg2_at_rpm( ω mg2 Ω ice_vel 3.6 Ω icevel ( ω mg2 Exanation of above then gives us the form of Ω1Prfl2 vm1 ( v if ω mg2 if ω ice Ωmax m1 ω ice < Pmax bat > 1 kw, +, Ωmax m1 n 19 RPM Ωmax m1 ω mg2 < Pmax bat > 1 kw, +, Ωmax m1 n 8 RPM root xm2 Ω mg2 ω ice root xm2 Ω mg2 ω ice 2.6ω mg2 Use these expressions Just for generating plots at bottom of page Ω icep2 ( ω mg2 ( Ω1Prfl2 vm1 ( v_r( ω mg ω mg2 Control Stategy Plots: Max Acceleration and Nonal Cruise Profiles Plot Colors: MG2 Shaft Rotational Speed (Red, ICE RPM (Blue, and MG1 Rotor (Green. Note Max Accel Plot: ICE does not turn on until MG2 propels Vehicle Speed up to 15 mph mph Ω icevel ( = ω ice 3.6 ω ice 3.6 Vel rev_up Ω1Prfl2 vm1 ( v_r( xm2 3.6 Ω1Prfl m1 ( xm xm2, xm2, xm2 Rotational Speeds (rpm 1. 4 Control Strategy: Max Acceleration Vehicle Velocity (mph Rotational Speeds (rpm Control Strategy: Nom ICE Idle Profile MG1 Motor Vehicle Velocity (mph

5 Torque, ICE: Torque,MG1: Given Control Acceleration Stategy Ω1Prfl1m1: Calculate Power and Torque T icee ( Ω ice ( ω mg2 N T icem2 ω mg2 T m1 ω mg2 m Ω1Prfl m1 ( = 9 3 T icem2 ( ω mg2 PinvA m2 ω mg η eng_m1 η inv ( Pmax bat T m1 ( ω mg2 2 π Ωmax m1 MG2 Inverter Power, Pinv: Pinv m2 ω mg2 Tractive Road Force, Total: Plot Terms: PinvB m2 ω mg2 if ( PinvA m2 ( ω mg2 Pmax m2 η inv, Pmax m2 η inv, PinvA m2 ( ω mg2 Max Power to Inverter: < P2max, P1max + Pbatmax and Pm1< P1max and Pice x 2.6/3.6 if ( T m1 ( Ω1init m2 ( ω mg2 2 π Ωmax m1 Torque MG2 Power Lited Break Point, ω inv Torque, MG2: Tractive Torq, Total: Problem, Find ω inv such that: (Tmax m2 ω inv = Pinv m2 (ω inv if ω mg2 ω inv T m2 ω mg2 T tot ω mg2 Tractive Road Force, Total: Ftω( ω mg2 GR T tot ω mg2 r tire > Pmax m1, Pmax bat + Pmax m1, PinvB m2 ω mg2 η red η inv T tot ( M2rpm_at_mph( v GR η red F tot ( v P M2 ( ω r tire P tot ( v F tot ( v v P tot ( mph = hp P m2 ( Ω mg2 ( ω kw Guess for winv, wx: wx if Pmax bat < 1 kw, 8, Solution (rpm: Pinv m2 ( wx ω inv root Tmax m2, wx ( 2 πwx + 1 ω inv = RPM Pinv m2 ω mg2, Tmax m2, T m2 ω inv 2 π ω mg2 RPM T m2 ( ω mg2 + T icem2 ( ω mg η eng_axle P m2 ω 3.6 π ω inv RPM T m2 ( ω 2 = kw π ω RPM Applying maximum motor torque, find the velocity and time starting from initial velocity = mph. Third Law of Motion: (dv/dt is acceleration accel( t Time Given End d dt v( t F tot ( v( t Fo( v( t = v( = velocity Odesolve( t, End k m M gross F tot ( velocity( t Fo( velocity( t sec time v k m M gross T tot ( ω m2 2 P t ω m2 Prius Spec is 9.8 sec root( v velocity( Time, Time time( mph = s Passing to mph: Passing time( mph time( mph Passing = s π ω m2 RPM kw 1

6 P R I U S G E N I V P E F O R M A N C E S I M U L A T I O N C U R V E S Dyno Motor Torque (Nm, Power (hp T tot ( ω m2 T m2 ( ω m2 T icem2 ( ω m2 T m1 ( ω m2 Torque (Total,MG2,ICE,MG2 vs. Speed 9 MG2 Torque/Power is Lited by ICE & Battery Peak Power velocity (mph velocity( t mph accel( t g Velocity & g Acceleration (x Curve ω m2 t MG2 Motor Speed (RPM time (sec Motor Force (N F tot ( v mph N Dyno Road Force (N vs. Velocity (mph v velocity (mph DYNO Power (kw P M2 ω ice P ice ω ice ICE and MG2 Power (kw vs. ICE RPM Redline ω ice ICE Speed (RPM Dyno Power (kw Motor Revs (RPM Pmax.ice P t Ω mg2 ( ω P m2 ( Ω mg2 ( ω ξ P ice ( ω Ω1init m2 ( ω mg2 Ω1init ice ω ice Ω mg2 ω ice Dyno Power vs. ICE RPM ω ICE Speed (RPM Redline 4MG1 and MG2 Startup vs. ICE Spin <===These are an arbirary set of ICE and MG1 initial conditions just to start the MG1 generator turning. ω mg2, ω ice, ω ice Engine Revs (RPM DYNO Motor Torque (Nm Dyno Motor Torque (Nm T tot ( ω T m2 ( ω T icem2 ( ω T tot ( ω 9 T m2 ( Ω mg2 ( ω T icee ( ω Dyno Axle Torque vs. RPM 9 ω Axle (MG2 Speed (RPM Dyno Torque vs. ICE RPM ω ICE Speed (RPM

7 Find the Single Charge = % Cruise Range for a given Velocity Driving Pattern/Profile: Given we cruise at constant speed and Time for start, stop, and regen breaking, Time ssr = every 15 nutes. Drive Train Power Efficiency - Battery Loss to Force Commanded Vehicle Velocity: State of Charge for generator is SOC gen. SOC gen is % for recharge. 1V HV battery idle power is Po. 12V battery gives Accessory Power. The Traction Inverter x motor Efficiency - TInvE, HV Power Electronics at Idle Efficiency - IPEE, and Gear Power Efficiency - GPE are 9%, 95%, and 97%, respectively. Brake Regen efficiency of kinetic energy is deacceleration =.315g. Then the number of starts per hour as a function of velocity, NS, NumStarts(v, Po, is Time ssr n NS o ( v 2 mph v NumStarts v, P o, S floor TInvE.9 Power dissloss ( v, P o 2 Fo( v v TInvE GPE NS v, P o, S IPEE.95 NSo and NS are iterative converging estimates of NumStarts Energy bat ( 1 S NS o ( v Energy bat ( 1 S NS v, P o, S + P o watt IPEE GPE.97 Energy accel ( v TInvE GPE Time ssr Power dissloss v, P o Regen.69 Energy accel ( v TInvE GPE Time ssr Power dissloss v, P o Regen M gross v 2 2 SOC gen.5 USABC Round Trip Battery Energy Efficiency RTEff.92 Energy accel ( v Pmax m2 time( v Regen M gross v 2 2 Cruise_Range v, P o, S Velocity Range v, 2.. Energy bat ( 1 S NumStarts v, P o, S Single Charge Highway Cruise Range Estimate Cruise_Range mph Cruise_Range mph Cruise_Range mph Cruise_Range 55 mph Cruise_Range mph Energy accel ( v TInvE GPE Power dissloss v, P o (,, SOC gen = (,, SOC gen = (,, SOC gen = (,, SOC gen = (,, SOC gen = 17.1 = Cruise_Range 62.5 mph,, SOC gen Regen M gross v 2 2 Cruise_Range( mph,,.5 = v Cruise Range (les Cruise_Range v mph,, SOC gen Cruise_Range v mph,, SOC gen Single Charge Cruise Mileage Range v velocity (mph

8 Cruise Range as a Function of Traction Battery Idle Power, Po =.5 Cruise_Range( 15 mph,,.3 = Cruise_Range( 55 mph,,.5 = km hr Cruise_Range( 55 mph,,.25 Cruise_Range( 55 mph,,.5 Cruise_Range( 55 mph,,.5 = hr =.482 Single Charge Cruise Mileage Range Cruise_Range( v mph,,.3 Cruise Range (les Cruise_Range( v mph,,.4 Cruise_Range( v mph,,.5 Cruise_Range( v mph,,.3 Cruise_Range( v mph,,.4 Cruise_Range( v mph,, v velocity (mph

9 Find the Power to Maintain Constant Velocity Note: The generator's output is 54 kw. This allows it produce a net charge up to mph cruise. Power cruise v, P o Power dissloss ( v, P o Power cruise ( mph, = kw n n n n.. τ n w vv n n 2 Power cruise vv mph, n P cruisen k watt Cruising Power (kwatts Power cruise vv n mph, k watt Power cruise vv n mph, k watt Power cruise vv n mph, k watt Cruise Power Curve FTPF UDDSF HWYF FP HY US6F 9 vv n velocity (mph READPRN (" READPRN (" READPRN (" READPRN (" READPRN (" READPRN (" AER Given Three Different Driving Schedules Read US6 and FTP Driving Profile Files The US6 cycle represents an 8.1 le (12.8 km route with an average speed of 48.4 les/h (77.9 km/h, maximum speed.3 les/h (129.2 km/h, and a duration of 596 seconds. The Federal Test Procedure(FTP is composed of the UDDS followed by the first 5 seconds of the UDDS. It is often called the EPA75. FP is a Hz Sampling. HY is the Hz Highway schedule. FTP FTPF 1 tx FTPF rows( FTP = UDDS UDDSF 1 rows( UDDS = HWY HWYF 1 R hwy rows( HWY FTPV submatrix( FP,, rows( FP 1, 1, cols( FP 1 HWYV submatrix( HY,, rows( HY 1, 1, cols( HY 1 US6 US6F 1 time US6F n

10 All Electric Range, AER, for Driving Profile Velocity/Time File, P Sampling Rate, Hz, and SOC = Regen Efficiency Curve vs Decel (g: REff ( g e g 28.8 Gg mph sec g AER( P, Hz Ebat E diss v old n 1 N rows( P 1 Energy bat while E diss < kw hr n n + 1 t v P t mod( n, N.5 v avg v + v old mph Hz k m M gross ( v v old v avg mph sec P accel if v > v old TInvE GPE mph Hz P accel k m M gross ( v v old v avg mph REff v old v sec sec Power dissloss ( v mph, + P accel E diss E diss + kw hr Hz v old v Ebat E n diss Hz Gg otherwise n R m = R ( P + P mod( m, N mod( m+ 1, N mph sec 2 Hz AER( US6, 1 = r1.. rows( HY 1 AER( FTP, 1 = HWY HWYV r1 ceil r1+ 1 AER( HWY, 1 = , mod( r1, AER( HWY, = 1 MPG city AER( FTP, 1 MPG epa EPA 85 Cycle MPG Fuel Economy Least Squares Fit Regression for AER to SOC =.55 MPG city +.45 MPG hwy MPG city = MPG epa = MPG hwy AER( HWY, 1 X 1 r r.. rows( FTP 1 Distance r max( Distance = r = FTP r rr rr.. rows( US6 1 Distance.rr max( Distance. =.8 rr = US6 rr

11 SAVE PROFILES X X X WRITEPRN ("EFTP.PRN" AER( FTP, 1 E FTP READPRN ("EFTP.PRN" max E FTP = WRITEPRN ("EUS6.PRN" AER( US6, 1 E US6 READPRN ("EUS6.PRN" max E US6 = WRITEPRN ("EHWY.PRN" AER( HWY, 1 E HWY READPRN ("EHWY.PRN" max E HWY = 26.8 Speed (mph, Dist (Mile/, E (kw* US6 Distance. E US6 9 US6 Drive Cycle: Distance, E(Bat Drain time Time (seconds Speed (mph, Dist (Mile/, E (kw* FTP Drive Cycle: Distance, E(Bat Drain 1 9 FTP UDDS Distance E FTP tx Time (seconds

12 Read Charge Depletion Mode Data Read Charge Sustaining Mode Data (Disabled Volt READPRN ("Volt_tVelwMAgTPmFP.prn" Volt READPRN ("VoltSus_tVelwMAgTPmFP.prn" cols( Volt = Volt READPRN ("VoltGenOnly_tVelwMAgTPmFP.prn" PT( v q q Pv v Volt 8 P cruisev Volt 9 q ( ( n ω xn Ttot T n tot ω xn Tm2 T n m2 ω xn Tice T n icem2 ω xn Vx velocity tz n n ( F tot ( Vx mph Fo( Vx mph F tot Vx mph P n tot Vx mph n Ax( Vx ax Ax Vx k m M gross g n ( n Ft Pt n N n hp PreWtTotM2ICVA augment ω x, tz, Ttot, Tm2, Tice, Vx, ax, Ft, Pt WRITEPRN ("Pre3PB.txt" PreWtTotM2ICVA Prius (Black vs. Sustaining Mode Volt (Red Acceleration Performance Volt Power reduced from 111 kw to Generator Power x 9% = 47.7 kw in Sustaining Mode. Volt to mph time increases from 8.5 to 15 seconds. Volt mph to mph Sustaining passing time increased from 3.3 seconds to 8.5 seconds. P tot ( v mph n.. P tot ( v F tot ( v mph v mph hp 1 time v Volt v v Volt 1 ω v Volt 2 k mphv Volt 3 g v Volt 4 n tz n 1 q ( N m T v Volt 5 P v Volt 6 F v Volt 7 hp 9 Torque (Total,MG2,ICE,Volt vs RPMs Vehicle Velocity & g Acceleration (x Dyno Motor Torque (Nm Vehicle velocity (mph and g's x Motor Rotor Speed, (RPM time (sec Dyno Motor Force (N Dyno Road Force (N vs. Velocity (mph Dyno velocity (mph Dyno Power (hp Dyno Power (hp vs. Velocity (mph Dyno velocity (mph

13 Read Comparison Files Either for GenIV No Battery Power or Full Power Gen III Prius ω z Pre Fz Pre 7 Pre READPRN ("Pre3PB.txt" time z Pre 1 Ttotz Pre 2 Pre Tm2z Pre 3 READPRN ("PreGenIII.txt" Ticez Pre 4 Pz Pre 8 Comparison Prius Gen III (Sold vs. Prius Gen IV (Dotted Comparison Prius No Battery (Solid vs. Battery (Dotted Vz Pre 5 PreWtTotM2ICVA az Pre 6 Agx( t accel( t g 9 Torque (Total,MG2,ICE vs. Speed Velocity & g Acceleration (x Curve Motor Torque (Nm Motor Speed (RPM velocity (mph and g's x time (sec Motor Force (N Road Force (N vs. Velocity (mph 9 velocity (mph DYNO Power (hp DYNO Power (hp vs. Velocity (mph 9 9 DYNO velocity (mph Fuel_Use READPRN (" T Cruising Power (kwatts Cruise Power Demand Curve velocity (mph

14 Switch Solid and Dotted Curves Comparison Prius No Battery (Dotted vs. Battery (Solid Comparison Prius Gen III (Dotted vs. Prius Gen IV (Solid 9 Torque (Total,MG2,ICE vs. Speed Velocity & g Acceleration (x Curve Motor Torque (Nm Motor Speed (RPM velocity (mph and g's x time (sec Motor Force (N Road Force (N vs. Velocity (mph 9 velocity (mph DYNO Power (hp DYNO Power (hp vs. Velocity (mph 9 9 DYNO velocity (mph