This document summarizes the process to generate full efficiency and power loss maps for the Chevrolet Bolt 150kW Electric Motor (MOTO) described in Momen, F., Rahman, K., Son, Y., and Savagian, P., "Electric Motor Design of General Motors’ Chevrolet Bolt Electric Vehicle," SAE Int. J. Alt. Power. 5(2):2016, doi:10.4271/2016-01-1228. The efficiency map shown in Figure 15 of the paper was utilized in the creation of this ALPHA map. The EPA generated version of the paper’s measured efficiency map represents the operating boundaries and electrical power consumption of the electric motor only (inverter and gearing losses are not considered in this efficiency map). This map is subsequently used as an input during ALPHA vehicle simulations.
SUGGESTED CITATION:
Chevrolet Bolt BEV 150kW MOTO from 2016 SAE Paper - ALPHA Map Package. Version 2024-05. Ann Arbor MI: US EPA National Vehicle and Fuel Emissions Laboratory, Advanced Technology Assessment Branch, 2024.
Motor Physical Characteristics
Set physical characteristics based on published information: Momen, F., Rahman, K., Son, Y., and Savagian, P., "Electric Motor Design of General Motors’ Chevrolet Bolt Electric Vehicle," SAE Int. J. Alt. Power. 5(2):2016, doi:10.4271/2016-01-1228 and Liu, J., Anwar, M., Chiang, P., Hawkins, S. et al., "Design of the Chevrolet Bolt EV Propulsion System," SAE Int. J. Alt. Power. 5(1):2016, doi:10.4271/2016-01-1153. The items in the table follow ALPHA’s code syntax for “emachines,” which is: emach.characteristic name_engineering units = value; % comments. The motor’s inertia value given was calculated using solid models based on the dimensions of the motor components.
emach = class_REVS_emachine_geared;
emach.name = 'Chevrolet Bolt BEV 150kW MOTO from 2016 SAE Paper';
emach.type = enum_emachine_type.Motor;
emach.gear.ratio = 7.05;
emach.inertia_kgm2 = 0.0380519;
emach.max_speed_radps = 8810 * unit_convert.rpm2radps;
emach.max_torque_Nm = 360;
emach.max_motor_power_W = 150000;
emach.max_generator_power_W = emach.max_motor_power_W;
nominalVoltage_V = 350;
Test Data
Import the specific efficiency map image data provided in Figure 15 of the reference SAE paper. The map was digitized by loading the image into MATLAB and manually tracing the efficiency contours.
table = load('extracteddata_V8.mat'); data(1).name = 'Efficiency Map Image Data'; data(1).speed_rpm = table.data(:,1)*8810; data(1).torque_Nm = table.data(:,2)*360; data(1).efficiency_norm = table.data(:,3)/100;
Motor Torque Limits
Create the maximum torque curve using the max power and torque points shown in Figure 15 of the reference paper by loading the image into MATLAB and manually tracing the maximum torque curve. The maximum torque line is set by defining maximum torque (axis 2) at discrete speeds (axis 1) of the operating map.
tbl_limit = load('max_torque.mat'); emach.positive_torque_limit_Nm.axis_1.signal = 'emach_spd_radps'; emach.positive_torque_limit_Nm.axis_1.breakpoints = tbl_limit.Max_torque(:,1) * 8810 * unit_convert.rpm2radps; emach.positive_torque_limit_Nm.axis_2.signal = 'voltage_V'; emach.positive_torque_limit_Nm.axis_2.breakpoints = nominalVoltage_V; emach.positive_torque_limit_Nm.table = tbl_limit.Max_torque(:,2) * 360;
Build the emachine Object in Matlab
The script below creates an “emach” object which is converted into power loss space (rather than efficiency space) for both the “drive” quadrant, extrapolated to the edges of the operating space, and scaled for maximum power.
emach = emach.load_data(data,'no_expand','extrapolate_speed');
Motor Efficiency Map
The following code generates the Efficiency Map shown below. The efficiency data points used to generate the efficiency map are superimposed on this image. A clean version of the efficiency map (without data points) is included in 4a- Chevrolet Bolt BEV 150kW MOTO from 2016 SAE Paper – Efficiency.pdf. The 6- Chevrolet Bolt BEV 150kW MOTO from 2016 SAE Paper - Electrical Power Consumption Data.xlsx file contains a sample data set extracted from this efficiency map.
REVS_plot_emachine(emach,'efficiency'); REVS_plot_emachine_data_overlay(data, 'efficiency');
Power Loss Map
A clean version of the Power Loss map is shown below and in 5a- Chevrolet Bolt BEV 150kW MOTO from 2016 SAE Paper - Power Loss.pdf. The additional plots show system losses, converted to effective torque loss, as a function of motor output torque and speed. Effective torque loss represents the total power loss in the system as a loss of mechanical power. The associated speed is kept constant, and thus the total loss is expressed as a loss of torque. Torque losses are presented on a log scale.
REVS_plot_emachine(emach,'power loss'); REVS_plot_emachine(emach,'torque loss curves');
Generate ALPHA .m file for ALPHA Model Simulations
This code generates and writes the created ALPHA emachine definition into an “.m file” for use in later ALPHA vehicle model simulations. The .m file is the actual input file used in ALPHA that defines power consumption over the speed and torque operating limits of the Chevrolet Bolt BEV 150kW MOTO.
emach.write_mscript('emachine_Chevrolet_Bolt_BEV_150kW_MOTO_paper_image.m');
Motor Build: emachine_Chevrolet_Bolt_BEV_150kW_MOTO_paper_image.m
% ALPHA ELECTRIC MOTOR DEFINITION % Generated 29-May-2024 13:54:37 % Constructor mg = class_REVS_emachine_geared(); mg.name = 'Chevrolet Bolt BEV 150kW MOTO from 2016 SAE Paper'; mg.source_filename = mfilename; % Physical Description mg.electrical_source = 'propulsion'; mg.inertia_kgm2 = 0.0380519; mg.type = enum_emachine_type.Motor; mg.gear.ratio = 7.05; mg.gear.efficiency_norm = 1; % Capacity Limits mg.max_speed_radps = 922.58104260420259; mg.max_torque_Nm = 360; mg.max_motor_power_W = 150000; mg.max_generator_power_W = 150000; mg.positive_torque_limit_Nm = class_REVS_dynamic_lookup; mg.positive_torque_limit_Nm.axis_1.signal = 'emach_spd_radps'; mg.positive_torque_limit_Nm.axis_1.breakpoints = [ 2.1533041534382091 ; 17.941433535523927 ; 43.058702420423337 ; 77.506033389179052 ; 118.41235423720678 ; 156.44760288065027 ; 210.98967153836810 ; 251.17822433524975 ; 277.73102932244132 ; 299.97814858379911 ; 317.20181406817693 ; 373.89626429829036 ; 429.87294647725776 ; 484.41501513497559 ; 530.34478975998331 ; 571.96795607811441 ; 622.20433900999853 ; 655.93390192760808 ; 704.73382617615732 ; 754.96928652699887 ; 804.48790140773679 ; 868.35818698722585 ; 922.58104260420259 ]; mg.positive_torque_limit_Nm.axis_2.signal = 'voltage_V'; mg.positive_torque_limit_Nm.axis_2.breakpoints = 350; mg.positive_torque_limit_Nm.table = [ 336.98268000000002 ; 346.57848000000001 ; 359.56079999999997 ; 360.68976000000004 ; 360.68976000000004 ; 359.56079999999997 ; 357.86772000000002 ; 358.43220000000002 ; 357.30324000000002 ; 357.86772000000002 ; 357.86772000000002 ; 341.49815999999998 ; 327.38688000000002 ; 291.26123999999999 ; 272.63412000000000 ; 254.57147999999998 ; 233.68643999999998 ; 220.70375999999999 ; 202.64111999999997 ; 183.44952000000001 ; 171.03131999999999 ; 154.09764000000001 ; 144.00000000000000 ]; % Losses & Efficiency mg.electric_power_W = class_REVS_dynamic_lookup; mg.electric_power_W.axis_1.signal = 'emach_spd_radps'; mg.electric_power_W.axis_1.breakpoints = [ 0.0000000000000000 53.931521822116942 100.14857574108666 139.61331515314833 180.85834767086033 204.97411364735919 240.76314780548046 279.12892411819519 322.41769035865900 377.25954886545469 411.22797392897559 449.81920288783374 502.68679034506692 548.40080786099861 586.23533362227283 628.82062895703439 668.16204733879613 692.34267094564166 716.50509536005961 730.11910485393332 748.48927497968475 771.99039421802274 807.86429175115632 843.15388795730735 870.54009115298470 922.58104260420259 ]; mg.electric_power_W.axis_2.signal = 'emach_trq_Nm'; mg.electric_power_W.axis_2.breakpoints = [ 0.0000000000000000 24.348253333333332 42.740177837837834 64.786018695652160 78.210089999999994 91.453366153846162 107.44681500000000 114.84836400000000 124.23930923076924 132.05566800000000 145.77556390243899 159.12906750000002 166.63636800000000 178.04960000000000 190.78436842105259 207.79741125000001 220.02249599999999 234.44286545454545 255.28002749999996 279.12442499999997 306.55268999999993 319.20510000000002 332.64623999999998 357.27551999999997 ]; mg.electric_power_W.table = [ -1.9661395029904905 21.843149048458660 32.945353328727947 100.27889892368162 169.11820976361764 245.37234889732272 341.42654470508950 379.02007278929869 423.07965467607306 471.45164575736146 651.85333034544715 1011.7999389203237 1231.3361142819999 1563.4807987718846 1887.3705337899632 2164.7348966191371 2238.6976794482425 2238.2360152123356 2273.4741648428503 2929.7365919767067 4059.2994204819115 4628.0828261385514 5243.1461578842654 6437.5105344731091 ; 28.647906321298098 1408.8237858147349 2514.5365042107587 3900.5884719882192 4757.6159380854551 5629.4767771709385 6669.6246280344312 7151.9751641800067 7737.2087554132349 8218.9294660244668 9117.7858713733422 10100.046866532597 10670.970943452365 11543.909676436240 12540.133604448720 13893.234092961025 14786.045668282863 15736.980720907046 17036.796229917458 19025.093214861459 21675.334899095025 22913.812270528240 24253.597348378236 26653.521774731293 ; 66.687368955096815 2581.0263838477267 4533.8002628559925 6931.1234611400705 8428.2443814757698 9887.9820152442499 11702.264664815197 12555.643390626334 13637.702780639236 14540.164818249183 16152.265026414940 17723.474108012197 18612.841582417244 19971.641822661793 21533.189607524313 23707.569486049448 25282.734791391627 27122.482691427449 29529.971443817794 32680.243916789947 36764.224611725505 38596.857170387535 40641.327609971559 44019.895969098870 ; 95.980570835818213 3586.7661130137126 6271.9146646893905 9550.2711973522892 11563.760115204623 13562.113219327926 16009.544454366056 17151.307871276938 18608.820904113138 19826.993882449438 21991.303108968168 24115.889779073390 25306.860613720019 27120.074463822126 29193.248736141675 32015.854490851390 34055.256849586447 36450.979781296315 39956.230758312653 44155.218642752981 49538.967717958527 52046.185702976982 54686.521188725979 59333.697652884075 ; 112.39725480799736 4644.3096356497872 8099.4932465807706 12267.848990530643 14826.728028261577 17383.582946706181 20496.487476969483 21947.610452895762 23799.254258219247 25346.232084130650 28081.527478597811 30762.901772632813 32283.835875796027 34614.712443834935 37234.831497892861 40738.558666361248 43283.417463722872 46293.254851032587 50765.703667602451 55962.385756953336 62340.833360090161 65486.548483158018 68882.719841279060 75073.791583998202 ; 122.46362034668626 5264.6167568526998 9168.3731707869683 13855.925329645966 16732.874503594674 19620.731907241516 23127.944489970505 24754.805147344152 26826.219187828530 28564.322180394298 31638.564718073532 34647.088762549065 36349.002154179791 38957.478480402177 41901.517548819182 45851.894652605137 48698.886602390696 52085.884061349527 57055.923540784293 62831.145461025881 69740.038871173732 73147.095632178301 76822.081177451793 83746.165714322138 ; 140.14227561804623 6173.5262349463474 10744.579810909336 16237.719709941050 19609.239917983992 22975.003623220524 27064.535784845430 28955.478550862561 31358.742696153968 33368.825382432093 36930.883691295152 40423.880889851847 42394.786716423885 45400.902973388707 48781.405299781509 53359.711966971503 56672.245709614333 60611.775159318990 66341.578411803057 72967.735032343742 80767.922763267634 84452.460337808428 88404.337030727256 95975.753320272372 ; 164.35000733827349 7139.3595940573286 12440.530652240810 18798.727721737654 22689.501533767481 26570.805381337948 31277.338602345120 33458.544682451473 36228.717576937037 38542.057035835431 42624.742616757510 46632.230756091201 48895.840732579090 52348.138419364397 56210.187993097330 61417.105114059312 65196.257330079861 69703.144609900235 76265.827280595026 83839.000943916835 92705.140074238705 96846.048798060147 101247.37434626640 109558.76692668605 ; 195.67080058082666 8250.4861482978376 14351.789044748981 21661.807070176270 26133.176051248429 30588.517490782691 35992.117743938368 38500.325235996446 41687.435556253055 44345.315560795440 49032.213344407952 53633.563923114860 56230.407854788238 60187.004328036965 64604.527827983824 70578.145440253575 74920.374868598636 80032.835495787702 87517.425773089286 96215.373940860969 106358.54563355436 111140.01421392668 116189.44160135115 125503.23416947486 ; 238.38885057296204 9663.3667655925692 16779.947747072678 25319.333828547486 30532.024033874062 35699.053153196110 41979.768572658730 44898.665066686575 48609.409129462358 51704.807991836024 57148.724780179786 62474.757950335217 65483.837378294258 70083.051965415085 75222.980470443159 82146.395163889640 87240.974184646169 93219.234745407579 101729.64857065950 112072.22833155870 124227.66891801465 129733.57265977051 135614.57686800725 146627.56445445938 ; 265.17940458543063 10532.901199181682 18280.128050506613 27569.213029793049 33246.420195727624 38869.604598335762 45697.043248920403 48864.944344356969 52888.963529394729 56243.490758789405 62152.022370016683 67967.973627057785 71234.666097234163 76195.296653045210 81720.626026278376 89271.402033782739 94838.137158004392 101365.42880684003 110615.41252494417 121876.44708324426 135243.71672431749 141259.85837606929 147744.57895668081 159790.91843377386 ; 295.88016846544230 11519.395285980927 19992.018958751560 30115.808760870153 36325.120246952458 42477.062015853713 49939.021840847454 53400.039894828049 57797.009277652185 61464.164145517090 67931.439705645578 74277.396364515444 77850.684832479994 83277.840901306918 89383.165425025072 97662.552581831900 103681.75069311973 110810.43928884949 121240.42485651048 133817.28600483877 148442.50970550595 154762.74865003765 161788.89998310103 174903.92142932792 ; 343.07528389601379 12881.014818661795 22351.290039660475 33609.314954306137 40565.166406103344 47460.756405043539 55821.094446211115 59702.964514405721 64638.247423667075 68756.838696940904 76016.870218737356 83129.381311732956 87156.856335115270 93326.732718979329 100265.00804291115 109557.40403888471 116388.64950000623 124518.12239276452 136905.80028089508 151606.54253655841 167395.44492480444 174425.49356184571 181970.55028411059 196115.54150756530 ; 399.05233225643775 14052.519750438674 24378.221784953705 36705.532621142112 44324.415128483408 51852.037431162717 60983.043591695612 65233.786147047198 70644.159723126359 75161.591217965455 83115.821390444311 90932.449341563901 95376.110783395095 102156.20615446508 109749.81259450412 120083.19057294777 127762.30418520882 137086.63010532857 150912.71149646802 166605.43166771272 183803.77430356547 191588.92390150912 199841.41314293176 215031.49732024001 ; 458.07547050657053 15036.428554484632 26078.451973835934 39370.170133167972 47499.190586070297 55515.027526995938 65291.633664663277 69849.522323081721 75655.253816134180 80491.561427036213 89027.068800052672 97466.537830686168 102242.66872447832 109539.73967017431 117771.61598429490 129114.19329041916 137667.27477772941 147866.45679132285 162550.72240760544 179058.61365652460 197468.20797194389 205855.41195279820 214733.44499809580 230952.05238199129 ; 534.34574803200985 16220.256539144588 28007.600527191764 42329.473788268981 51025.537420413741 59631.726427871894 70214.572546009702 75136.801026630812 81392.167588060314 86603.926515667728 95831.751522831401 104967.84503868139 110144.65757967527 118075.82545123913 127149.27031064326 140058.71509561042 149353.23008946169 160161.24105004099 175653.97939657953 193153.91491679140 212932.29927297574 221982.18303237873 231568.68266375369 249061.86193489074 ; 600.27256002613524 17325.333820998105 29900.978599513885 45114.381385701621 54341.775646654758 63554.176714577072 74874.922648847016 80119.403137702422 86788.203490667758 92364.270358478403 102246.73166423234 112032.82468350574 117643.63077186891 126373.92255240605 136516.21307743422 150318.63430964356 160034.10233133798 171415.06595034941 187739.44838628583 206239.87416278585 227286.84367074203 236944.53055053126 247185.07073955267 265897.18126664369 ; 641.53596973057631 17986.676575266767 31079.681979382683 46797.244872520896 56400.097037358435 65998.853362385082 77737.046721764855 83186.027285481076 90124.806463584580 95931.664645148077 106222.49873122055 116460.80872151874 122407.29826819082 131699.20335803580 142296.79903420969 156463.37757394215 166509.82427895238 178277.34998644202 195152.68132955764 214298.36748698750 236130.54201236507 246161.66260584441 256803.59115502529 276265.11883109220 ; 686.47367162486466 18665.728844238871 32276.241125545675 48531.736528830799 58489.882887187567 68435.652957771221 80592.681227159526 86254.162698550950 93468.728027087171 99508.257932039065 110224.10756374021 121039.72308199212 127334.91431869827 137079.95083959235 148009.05625014403 162562.49697777809 172937.75928481307 185102.85196838068 202549.66677760857 222356.57952776752 244977.90161440370 255382.36078071143 266424.89458727004 286632.50878691749 ; 714.32291157411078 19053.027388076309 32947.185933131303 49532.271225084194 59682.838275682836 69813.357361218557 82207.055494496279 87988.108755749141 95357.987265752061 101531.49469200463 112521.41993680161 123696.31088266231 130163.78988530635 140106.06201173743 151208.48126037751 165990.90003261509 176549.61036371731 188939.44788231980 206713.47335454487 226897.89722288173 249965.72099638206 260580.64803018761 271848.71020307031 292475.33646237419 ; 754.80166069223708 19580.224146410281 33847.229428261358 50890.662049849365 61298.905149828715 71679.216968801207 84393.564607383014 90335.611245250693 97913.235757216142 104270.72821315598 115663.21583616491 127316.47176932263 133996.36919999484 144172.06087322699 155509.84431165439 170610.36671076357 181415.84432077032 194108.86700063222 212328.25068030998 233026.32826541999 256698.50310738734 267597.55385782430 279169.75704003195 300360.43293895206 ; 813.32332857319795 20263.575547456698 34986.431910808766 52605.111191782402 63362.372390749340 74081.546747519620 87211.614291860984 93361.390661697456 101206.87330093475 107822.24812083408 119799.69247546110 131974.69435436593 138862.78715934628 149328.43363506670 160982.14881678356 176506.12966588265 187629.01200125666 200709.79051243258 219504.18363065374 240866.86044163167 265316.09857017297 276578.93028509698 288539.88892940525 310449.50249765284 ; 920.56794776073150 21345.774043000110 36757.556408417156 55095.885907356191 66479.401820712752 77797.339864654175 91592.800926832671 98073.119774599370 106332.33394054629 113362.55856798400 126247.81062142213 139011.56666130951 146189.11494887603 157099.48076606801 169258.73165796677 185465.13150382132 197084.33467939164 210761.11079030292 230441.66461172741 252834.55558251747 278480.16838276229 290299.20665326808 302852.88289935916 325853.70047569415 ; 1039.3975289521563 22406.713658963592 38522.366104636567 57652.915980372338 69565.522535372831 81436.348534742196 95953.063930481047 102771.54841936352 111528.34835696539 119026.86845020647 132571.00077874103 145832.30043552860 153300.25370448740 164660.42975998751 177331.93824356995 194234.34519641657 206356.44544465703 220630.29412537935 241189.17470096206 264605.47726302379 291436.97822064877 303804.20530199894 316940.62196910859 341010.18124569254 ; 1134.4910059947522 23206.794596340151 39866.055381342259 59688.952446740281 71999.063623206632 84288.527530299019 99409.519325896486 106555.33952040985 115748.94896346462 123527.82467188641 137434.74686852482 151094.43316753666 158791.02949639727 170503.24274399880 183575.22807713848 201023.73570201415 213541.18168710193 228283.49672871578 249527.03862333720 273739.49804128212 301493.79782449518 314286.83744975948 327875.51874537551 352773.38285311521 ; 1318.5213470476433 24653.892262295656 42274.335776436499 63497.264881980562 76655.608882301502 89849.679936221102 106196.15410672502 113898.82687399822 123756.53843665670 132021.70147899253 146665.23180094900 161064.43510489530 169189.60087665138 181568.40908201481 195404.21127479573 213898.68382764529 227175.38202443838 242817.18051333725 265368.44081475679 291095.53965605650 320606.53858134116 334209.40232620505 348657.74565086450 375128.52409839322 ]; mg.unpowered_torque_loss_Nm = class_REVS_dynamic_lookup; mg.unpowered_torque_loss_Nm.axis_1.signal = 'emach_spd_radps'; mg.unpowered_torque_loss_Nm.axis_1.breakpoints = [ -15000.000000000000 15000.000000000000 ]; mg.unpowered_torque_loss_Nm.table = [ 0.0000000000000000 0.0000000000000000 ];