GM VOLT PERFORMANCE SIMULATION
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1 GM Volt - Vehicle, Motor, Road, and Enironmental Parameters: Enable Generator Only Mode Gear Ratio, Inefficiencies: GR 8 η Max Motor Power: Power max 111 kw.9 axle.9 Battery Energy: Energy P Generator 53 kw Power max P Generator.9 bat 16 kw hr 7. Max Motor Torque: Tm 73 ft lbf Tm = N m Tire Radius*: r tire in 195/55R1 Tm Max Force, Fm Fm GR η Fm = lbf RPM n axle Power max = hp r tire ω max 1 RPM Power max ω CP n Constant Power ω CP RPM RPM CP CP = Motor Torque, ω: Tm π Power max Constant Power k 1 3 CP CP = mph Tm = N m ehicle elocity, Fm CP : Aerage Wind Velocity: Shape Correction Factor: Drag Coeff: Cross Wind Drag Coff: Air Density: Road Rolling Resist: Rotational Inertia Coeff: k m 1.8 Passenger Weight: Gross Weight: M M gross gross M curb + Passengers = lb Motor Breaking Force in g: MotorBrake g GR Tm ( k m M gross r tire g M curb WeightToHP Vehicle Dynacs Equations: Power max Road Resistance, Ft: Aerodynac Loss, Fa: Opposing Force, Fo: Tractie Force: Third Law of Motion: (a is acceleration End 3 GM VOLT PERFORMANCE SIMULATION Vw mph Power max = 99.9 kw SCF.85 Cd.8 Cd cw.14 gm ρ gm liter liter RR road. Ft( M gross g d t ( t F( ( t Fo( ( t Gien = d k m M gross acc g ( t a( elocity( t sec P m ω Rolling Resistance Per Tire: RR tire.7 Tire Hysteresis, Th: Th sec θ (radians: (Aerage % road grade θ atan( Curb Weight: M curb Th sin( θ + ( RR tire + RR road cos( θ + sin( θ ( x Fa(.5 ρ Af ( + Vw Cd + Cd cw.5 + V cw Fo( Fa( + Ft( Power max F( if CP, Fm, η axle T F( Fo( ω ω a( ( T ω ( ω k Effectie Cross Wind V: Frontal Area*: Frontal Area Corrected: ( = ( T ω k π ω RPM kw 314 lb Passengers M batt 3lb MotorBrake g =.539 WeightToHP = elocity 17 lb lb hp T( F( r tire GR π r tire GR RPM k m M gross P( F( Applying maximum motor torque, find the elocity starting from initial elocity = mph. V cw Afg.16 m Af Fo( 6 mph = lbf mph Afg SCF Af = m P( 6 mph = hp Odesole( t, End elocity( 3 = 11.8 x mph s m Time sec time( root( elocity( Time, Time Time to Accelerate from 4 to 6 mph: time( 6 mph = s time( 6 mph time( 4 mph = s
2 Dyno Motor Torque, Power (kw G M V O L T 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 Force T ω ( ω lbf ft P m ( ω NS o ( 5 mph NumStarts, P o, S Dyno Torque and Power s. RPM Cures F( mph 1 lbf 8 4 Time ssr 3n Power dissloss (, P o NSo and NS are iteratie conerging estimates of NumStarts ( floor ( Cruise_Range, P o, S Constant Power ω Dyno Motor Speed (RPM * 1 Dyno Force Cure Dyno elocity (mph Find the Single Charge (@SOC = 5% Cruise Range for a gien Velocity Driing Pattern/Profile: Gien we cruise at constant speed and Time for start, stop, and regen breaking, Time ssr = eery 15 nutes. Drie Train Power Efficiency - Battery Loss to Force Commanded Vehicle Velocity: State of Charge for generator is SOC gen. SOC gen is 5% for recharge. 3V HV battery idle power is Po. 1V battery gies Accessory Power. The Traction Inerter x motor Efficiency - TInE, HV Power Electronics at Idle Efficiency - IPEE, and Gear Power Efficiency - GPE are 9%, 95%, and 97%, respectiely. Brake Regen efficiency of kinetic energy is deacceleration =.315g. Then the number of starts per hour as a function of elocity, NS, NumStarts(, Po, is TInE.9 Fo( + ( NS, P o, S IPEE.95 P o watt IPEE Vehicle elocity (mph Dyno Motor Power (hp Energy bat ( 1 S NS o ( ( Energy bat ( 1 S NS, P o, S elocity( t mph acc g ( t 1 g P( mph hp ( Energy bat ( 1 S NumStarts, P o, S Energy accel ( ( Time ssr Power dissloss, P o GPE.95 Regen.69 SOC gen.5 USABC Round Trip Battery Energy Efficiency RTEff.9 Energy accel ( Power max time( Energy accel ( ( Power dissloss, P o \Velocity & Acceleration (gx1 Cure Energy accel ( ( Time ssr Power dissloss, P o t time (sec Dyno Motor Power Cure Dyno elocity (mph Regen M gross Regen M gross Regen M gross
3 Velocity Range,.. 8 Cruise Range (les ( Cruise_Range mph, 5, SOC gen ( Cruise_Range mph, 1, SOC gen Single Charge Highway Cruise Range Estimate ( = Cruise_Range 55 mph, 5, SOC gen Single Charge Cruise Mileage Range elocity (mph Specsmanship: Twice as much range at 3 mph than 7 mph. Conclusion: I need a bigger or a better battery! Cruise Range as a Function of Traction Battery Idle Power, Po Cruise_Range( 15 mph, 5,.3 = Cruise_Range( 55 mph, 5,.5 = Single Charge Cruise Mileage Range Cruise Range (les Cruise_Range( mph, 5,.3 Cruise_Range( mph, 5,.4 Cruise_Range( mph, 5,.5 Cruise_Range( mph, 1,.3 Cruise_Range( mph, 1,.4 Cruise_Range( mph, 1, elocity (mph
4 Note: The Volt generator's output is 54 kw. This allows it produce a net charge up to 8 mph cruise. i.. 5 Ft g, θ θ i. i Phill, θ Find the Power to Maintain Constant Velocity at Road Grades Power cruise, P o ( Power dissloss (, P o ( k watt n P n cruisen Power cruise mph, 1 n ( ( M gross g Th sin( atan( θ + ( RR tire + RR road cos( atan( θ + sin( atan( θ Ft ( ( g (, θ + Fa( P hilln i ( Phill mph, θ, n i Power (hp@ Grade,, 4, 6, 8, 1 (% Cruise Power Loss s. Road Grade, Speed elocity (mph Cruising Power (kwatts Cruise Power@ 1W Acc, Cd.5 s elocity (mph AER Gien Three Different Driing Schedules FP1 HY1 US6F READPRN (" READPRN (" READPRN (" The US6 cycle represents an 8.1 le (1.8 km route with an aerage speed of 48.4 les/h (77.9 km/h, maximum speed 8.3 les/h (19. km/h, and a duration of 596 seconds. The Federal Test Procedure(FTP is composed of the UDDS followed by the first 55 seconds of the UDDS. It is often called the EPA75. FP1 is a 1 Hz Sampling. HY1 is the 1 Hz Highway schedule. t ft FTPF FTP FTPF 1 rows( FTP = UDDS UDDSF 1 rows( UDDS = time US6F US6 US6F 1 n HWY HWYF 1 R hwy rows( HWY mean( FTP = 1. Read US6 and FTP Driing Profile Files FTPF READPRN (" UDDSF HWYF READPRN (" READPRN (" FTP1V submatrix( FP1,, rows( FP1, 1, cols( FP1 HWY1V submatrix( HY1,, rows( HY1, 1, cols( HY1
5 Calculate All Electric Range, AER, for Driing Profile Velocity/Time File, P and Sampling Rate, Hz Regen Efficiency Cure s Decel (g: REff ( g ( e 7.19 g 8.48 Gg mph sec g AER( P, Hz Ebat E diss old n 1 N rows( P while E diss < 8 n = n n n + 1 t P t mod( n, N (.5 ag + old mph Hz k m M gross ( old ag mph sec P accel if > old mph Hz P accel k m M gross ( old ag mph REff old sec ( sec Power dissloss ( mph, 1 + P accel E diss E diss + kw hr Hz old Ebat E n diss ( Hz Gg otherwise n R m = R ( P + P mod( m, N mod( m+ 1, N mph sec Hz r1.. rows( HY1 1 Calculated AER(Miles: EPA Federal Test Procedure and Highway Driing Profiles AER( FTP, 1 = AER( HWY, 1 = AER( US6, 1 = EPA 85 Cycle MPG Fuel Economy Least Squares Fit Regression for AER 1 MPG city AER( FTP, 1 MPG city = MPG hwy AER( HWY, 1 X 1 4 MPG epa.55 MPG city +.45 MPG hwy MPG epa = 8.79 r r.. rows( FTP Distance r max( Distance = r = FTP r rr rr.. rows( US6 Distance.rr max( Distance. = 8.8 rr = US6 rr 1 6 6
6 Plot EPA Driing Profiles WRITEPRN ("EFTP.PRN" AER( FTP, 1 4 WRITEPRN ("EUS6.PRN" AER( US6, 1 4 WRITEPRN ("EHWY.PRN" AER( HWY, 1 4 E FTP E US6 E HWY READPRN ("EFTP.PRN" READPRN ("EUS6.PRN" READPRN ("EHWY.PRN" ( X ( X ( X max E FTP = 39.1 max E US6 = 5.65 max E HWY = Speed (mph, Dist (Mile/1, E (kw*4 US6 Distance. E US US6 Drie Cycle: Distance, E(Bat Drain time Time (seconds Speed (mph, Dist (Mile/1, E (kw*4 FTP Drie Cycle: Distance FTP 7 UDDS 6 Distance t ft Time (seconds r.. rows( HWY r Distance r r = HWY r time HWYF mean( HWY = 48.4 max( HWY = 59.9
7 Speed (mph, Dist (Mile/1, E (kw*4 HWY Distance E HWY HWY Drie Cycle: Distance, E(Bat Drain time Time (seconds
8 Compare Volt Sustaining (Dotted s. Generator Only (Solid Mode: Volt For Comparison to Prius See: Volt%EREV%s%Prius.pdf For Comparison to Corolla See (Page 5: Read Charge Depletion Mode Data READPRN ("VoltGenOnly_tVelwMAgTPmFP.prn" Store Variables n.. 3 time Volt Volt 5 T w ( lbf ft TW( ω T ω ( ω lbf ft Volt 1 P w Volt 6 VV( t Read Charge Sustaining Mode Data (Disabled Data Format in File: Time, Vel, Angular Speed, MPH, Accel(g, Torque(rpm, Power (rpm, Force(, P( Volt ω Volt F Volt 7 elocity( t mph READPRN ("VoltSus_tVelwMAgTPmFP.prn" mph Volt 3 P Volt 8 AG( t g Volt 4 acc g ( t 1 g P cruisev Volt 9 Plot Compare Sustaining (Dotted s. Generator Only (Solid Mode: Dyno Motor Torque, Power (kw Dyno Torque and Power s. RPM Cures 3 5 Constant Power Dyno Motor Speed (RPM * 1 Vehicle elocity (mph Vehicle Velocity & Accel(gx1 Cure time (sec Dyno Motor Force Dyno Road Force Cure Dyno elocity (mph Dyno Motor Power (hp Dyno Motor Power Cure Dyno elocity (mph
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