This document summarizes the process to generate full efficiency and power loss maps for an estimated (EST) 2010 Toyota Prius 60kW 650V MG1 electric motor and inverter (EMOT). PowerSplit hybrid vehicles use two electric motors in their drive system. One serves primarily as the drive electric motor and is called MG2 by Toyota. The other primarily serves as the generator electric motor and is called MG1 by Toyota. While the inverter voltage supplied to MG1 varies from 200 – 650 Vdc when operating in the 2010 Toyota Prius, this estimated efficiency map only focuses on MG1’s operation at 650 Vdc.
The estimated efficiency data for the MG1 map were derived using MG2 test data collected by Oak Ridge National Lab (ORNL) along with the power and voltage specifications for the MG2 motor which are detailed in NCAT’s 2010 Toyota Prius 60kW 650V MG2 EMOT - ALPHA Map Package listed in the “Related NCAT Packages.docx” file. The MG2 test data were used to inform the sizing of MG1 to provide representative operation in ALPHA’s PowerSplit model. Though similar to MG2, MG1 has a lower inertia and a constant maximum power decay profile. The generated MG1 map defines the operating boundaries and electrical power consumption of the electric motor and inverter combination which are needed for ALPHA modeling.
SUGGESTED CITATION:
EST 2010 Toyota Prius 60kW 650V MG1 EMOT - ALPHA Map Package. Version 2023-09. Ann Arbor MI: US EPA National Vehicle and Fuel Emissions Laboratory, National Center for Advanced Technology, 2023.
EMOT Physical Characteristics
The following table sets the key physical characteristics for the EST 2010 Toyota Prius 60kW 650V MG1 electric motor and inverter (EMOT) used in the ALPHA model based on published information provided in 3b- Benchmarking of Competitive Technologies Presentation by ORNL May 2011.pdf and 3c- FY2011 DOE Annual Progress Report Advanced Power Electronics and Electric Motors Program.pdf. The items in the table follow ALPHA’s code syntax for “emachines,” which is: emach.characteristic name_engineering units = value; % comments.
emach = class_REVS_emachine_geared; emach.name = 'EST 2010 Toyota Prius 60kW 650V MG1 EMOT'; emach.type = enum_emachine_type.Motor; emach.gear.ratio = 1; % MG1 ratio is set to 1 for this input file; the ratios for MG1 to engine and MG1 to drive axle are set elsewhere in the PS model emach.gear.efficiency_norm = 1; % This device is an emotor and inverter (EMOT) with no gearing, so the gear efficiency was set to 1 (100% efficiency) emach.inertia_kgm2 = 3.93 * (1/2*0.1513*1/2)^2; % Inertia = rotor mass *1/2 rotor diameter, rotor mass = 3.93kg, rotor diameter = 0.1513m. (0.0056 kg-m2) for the MG1 emach.max_speed_radps = 13500 * unit_convert.rpm2radps; emach.max_torque_Nm = 207; emach.max_motor_power_W = 60000; % Using MG2 max power emach.max_generator_power_W = emach.max_motor_power_W; nominalVoltage_V = 650; % Using MG2 voltage
Import EMOT Data
The following code imports EMOT efficiency data provided by ORNL found in 3c- 2010 Toyota Prius 60kW 650V MG2 EMOT - ORNL Test Data File.xlsx detailed in NCAT’s 2010 Toyota Prius 60kW 650V MG2 EMOT - ALPHA Map Package. ORNL provided separate motor and inverter efficiency data files which were multiplied together to provide the combined efficiency data used to create the MG2 EMOT map.
EPA reviews the quality of the test data we import to ensure consistency with expected data trends and emotor system physics. Any data points considered significant outliers are removed from the dataset before generating the final efficiency map. In addition, since many of the datasets are missing low-speed and torque datapoints, occasionally a few “grounding” datapoints are added to help the curve fitting algorithm extrapolate the gradients near the map’s boundaries.
Specifically for this dataset, the efficiency datapoints associated with 0.0 torque were removed since the values associated with those datapoints did not make sense physically.
tbl_inv = readmatrix('3c- 2010 Toyota Prius 60kW 650V MG2 EMOT - ORNL Test Data File.xlsx','Sheet','650V INV Only', 'Range','B6:P27'); tbl_mot = readmatrix('3c- 2010 Toyota Prius 60kW 650V MG2 EMOT - ORNL Test Data File.xlsx','Sheet','650V Motor Only', 'Range','B6:P27'); data(1).speed_rpm = tbl_mot(1,2:end); data(1).torque_Nm = tbl_mot(3:end,1); data(1).efficiency_norm = tbl_mot(3:end,2:end)/100 .* tbl_inv(3:end,2:end)/100; data(1).name = 'Data';
EMOT Torque Limits
The torque limits for the EST 2010 Toyota Prius 60kW 650V MG1 EMOT were set to follow a constant decay profile which is automatically applied in the ALPHA build process. The secondary axis information is provided below to keep the build process consistent across other emachines.
emach.positive_torque_limit_Nm.axis_2.signal = 'emach_voltage_V';
emach.positive_torque_limit_Nm.axis_2.breakpoints = nominalVoltage_V;
Build the emachine Object in Matlab
The script below creates an “emach” object which is converted into power loss (rather than efficiency) for the “drive” quadrant, extrapolated to the edges of the operating space, and scaled for maximum power.
These power losses were then “mirrored” to the regen quadrant considering the average of the empirical internal mechanical and electrical losses differences typically seen between operating in the “drive” and “regen” quadrants. Since the ORNL dataset did not have any regen data, we mirrored the drive quadrant power loss data onto the regen quadrant compensated by a factor of 1.05 (or 105 %) which represents an empirical average encountered in confidential data available to this program.
emach = emach.load_data(data,'mirror_factor',1.05,'use_cluster_breakpoints');
EMOT 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- EST 2010 Toyota Prius 60kW 650V MG1 EMOT – Efficiency.pdf. The 6- EST 2010 Toyota Prius 60kW 650V MG1 EMOT - Electrical Power Consumption Data.xlsx file contains a sample data set extracted from this efficiency map.
This data set also includes data in the negative speed quadrants (not shown in the figure). These data are created by rotating the positive speed quadrants, such that losses in the third quadrant (negative speed and negative torque) match losses in the first quadrant (positive speed and positive torque), and losses in the fourth quadrant (negative speed and positive torque) match losses in the second quadrant (positive speed and negative torque).
REVS_plot_emachine(emach,'efficiency'); REVS_plot_emachine_data_overlay(data, 'efficiency');
For comparison, the Combined Inverter-Motor Efficiency Map shown below was published by ORNL in a technical presentation provided in 3b- Benchmarking of Competitive Technologies Presentation by ORNL May 2011.pdf and 3c- FY2011 DOE Annual Progress Report Advanced Power Electronics and Electric Motors Program.pdf.
Power Loss Difference Table
In addition, the diagram below shows the power loss difference by comparing the power loss data derived from the ORNL efficiency data found in 3c- 2010 Toyota Prius 60kW 650V MG2 EMOT - ORNL Test Data File.xlsx and the ALPHA map power data. The power loss percentage difference for these data points is calculated using the following formula.
Where
In cases where the original ORNL data contain abrupt changes in curvature, the ALPHA curve-fitting function produces a smooth surface through the points, resulting in a noticeable difference between the values of the original ORNL points and the curve fit surface. Additionally, larger percentage values for power loss difference are typical where the magnitude of the power loss is small (for example, at low torques and speeds).
REVS_table_data_comparision_emachine(data,emach, 'loss_diff_pct');
Data Power Loss Percent Difference
----------------------------------
Motor Torque ( Nm ) \ Motor Speed ( RPM)
500 RPM 1000 RPM 2000 RPM 3000 RPM 4000 RPM 5000 RPM 6000 RPM 7000 RPM 8000 RPM 9000 RPM 10000 RPM 11000 RPM 12000 RPM 13000 RPM
__________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________
200.0 Nm -3.71 1.62 1.36 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
190.0 Nm 8.01 -3.19 -3.11 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
180.0 Nm -3.17 2.37 1.72 0.95 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
170.0 Nm -0.33 -1.36 -0.64 -1.43 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
160.0 Nm 4.46 0.99 0.38 0.82 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
150.0 Nm -5.2 -0.48 0.32 0.23 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
140.0 Nm -0.65 1.91 0.42 -0.6 0.08 NaN NaN NaN NaN NaN NaN NaN NaN NaN
130.0 Nm 5.08 -2.26 -1.13 1.31 -0.74 NaN NaN NaN NaN NaN NaN NaN NaN NaN
120.0 Nm -4.04 1.44 1.45 -1.45 0.84 NaN NaN NaN NaN NaN NaN NaN NaN NaN
110.0 Nm -0.27 0.41 -1.46 0.41 0.36 NaN NaN NaN NaN NaN NaN NaN NaN NaN
100.0 Nm 1.04 -0.22 0.36 -0.19 0.68 -1.2 NaN NaN NaN NaN NaN NaN NaN NaN
90.0 Nm 0.66 -0.16 1.89 0.07 -0.54 1.85 NaN NaN NaN NaN NaN NaN NaN NaN
80.0 Nm 0.28 -0.22 -3.71 0.5 -0.58 0.7 -2.74 NaN NaN NaN NaN NaN NaN NaN
70.0 Nm -0.07 0.23 2.21 -0.44 0.38 0.43 3.18 NaN NaN NaN NaN NaN NaN NaN
60.0 Nm -0.12 -0.06 0.51 0 -0.49 -0.92 0.58 -0.7 NaN NaN NaN NaN NaN NaN
50.0 Nm -0.42 0.32 -0.36 0.47 -0.28 1.06 -1 1.87 -1.08 NaN NaN NaN NaN NaN
40.0 Nm -0.56 0.22 -0.12 -0.56 0.25 1.8 -0.62 -0.09 1.73 -0.38 -2.19 NaN NaN NaN
30.0 Nm -0.66 -0.18 -0.83 -0.22 -0.3 -2.74 1.32 -0.34 -0.8 0.47 2.88 -3.06 -0.78 NaN
20.0 Nm -1.37 -1.19 -1.24 -1.62 -2.77 -1.64 -1 -0.73 0.8 -0.65 1.21 4.92 1.04 -2.51
10.0 Nm 3.63 1.4 2.64 2.61 3.23 3.3 -0.25 1.33 -0.21 1.09 -0.36 -0.3 0.91 2.9
Power Loss Map
The Power Loss map is shown below and in 5a- EST 2010 Toyota Prius 60kW 650V MG1 EMOT - Power Loss.pdf. Following this are two graphs expressing losses in the EMOT as “effective torque loss” as functions of motor output torque and speed. 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 EST 2010 Toyota Prius 60kW 650V MG1 EMOT.
emach.write_mscript('emachine_est_2010_Toyota_Prius_60kW_650V_MG1_EMOT.m');
Motor Build: emachine_est_2010_Toyota_Prius_60kW_650V_MG1_EMOT.m
% ALPHA ELECTRIC MOTOR DEFINITION % Generated 11-Sep-2023 15:07:09 % Constructor mg = class_REVS_emachine_geared(); mg.name = 'EST 2010 Toyota Prius 60kW 650V MG1 EMOT'; mg.source_filename = mfilename; % Physical Description mg.electrical_source = 'propulsion'; mg.inertia_kgm2 = 0.0056227713562499995; mg.type = enum_emachine_type.Motor; mg.gear.ratio = 1; mg.gear.efficiency_norm = 1; % Capacity Limits mg.max_speed_radps = 1413.7166941154069; mg.max_torque_Nm = 207; mg.max_motor_power_W = 60000; mg.max_generator_power_W = 60000; 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 = [ -1427.8538610565611 -1413.7166941154069 -1327.0473197136373 -1071.4487114419444 -898.40887060548050 -773.48965966454955 -679.06860379921011 -605.19190953973566 -545.81232674049500 -497.04389682415115 -456.27559045663583 -421.68808398251099 -391.97483108979321 -366.17329633055812 -343.55872593958787 -323.57499276213832 -305.78824968415296 -289.85507246376812 0.0000000000000000 289.85507246376812 305.78824968415296 323.57499276213832 343.55872593958787 366.17329633055812 391.97483108979321 421.68808398251099 456.27559045663583 497.04389682415115 545.81232674049500 605.19190953973566 679.06860379921011 773.48965966454955 898.40887060548050 1071.4487114419444 1327.0473197136373 1413.7166941154069 1427.8538610565611 ]; mg.positive_torque_limit_Nm.axis_2.signal = 'emach_voltage_V'; mg.positive_torque_limit_Nm.axis_2.breakpoints = 650; mg.positive_torque_limit_Nm.table = [ 0.0000000000000000 42.441318157838758 45.213157894736838 55.998947368421057 66.784736842105247 77.570526315789493 88.356315789473683 99.142105263157887 109.92789473684211 120.71368421052631 131.49947368421053 142.28526315789475 153.07105263157894 163.85684210526315 174.64263157894737 185.42842105263156 196.21421052631578 207.00000000000000 207.00000000000000 207.00000000000000 196.21421052631578 185.42842105263156 174.64263157894737 163.85684210526315 153.07105263157894 142.28526315789475 131.49947368421053 120.71368421052631 109.92789473684211 99.142105263157887 88.356315789473683 77.570526315789493 66.784736842105247 55.998947368421057 45.213157894736838 42.441318157838758 0.0000000000000000 ]; % 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 = [ -1361.3568165555769 -1256.6370614359173 -1151.9173063162575 -1047.1975511965977 -942.47779607693792 -837.75804095727813 -733.03828583761833 -628.31853071795865 -523.59877559829886 -418.87902047863895 -314.15926535897938 -209.43951023931945 -104.71975511965972 0.0000000000000000 104.71975511965972 209.43951023931945 314.15926535897938 418.87902047863895 523.59877559829886 628.31853071795865 733.03828583761833 837.75804095727813 942.47779607693792 1047.1975511965977 1151.9173063162575 1256.6370614359173 1361.3568165555769 ]; mg.electric_power_W.axis_2.signal = 'emach_trq_Nm'; mg.electric_power_W.axis_2.breakpoints = [ -200.00000000000000 -190.00000000000000 -180.00000000000000 -170.00000000000000 -160.00000000000000 -150.00000000000000 -140.00000000000000 -130.00000000000000 -120.00000000000000 -110.00000000000000 -100.00000000000000 -90.000000000000000 -80.000000000000000 -70.000000000000000 -60.000000000000000 -50.000000000000000 -40.000000000000000 -30.000000000000000 -15.000000000000000 0.0000000000000000 10.000000000000000 20.000000000000000 30.000000000000000 40.000000000000000 50.000000000000000 60.000000000000000 70.000000000000000 80.000000000000000 90.000000000000000 100.00000000000000 110.00000000000000 120.00000000000000 130.00000000000000 140.00000000000000 150.00000000000000 160.00000000000000 170.00000000000000 180.00000000000000 200.00000000000000 ]; mg.electric_power_W.table = [ 289089.20593803411 260287.68783703394 245886.31198532184 231484.57587825140 217082.54817290459 202680.56167363506 188279.32644923098 173880.03978661777 159484.47853237166 145095.04933546839 130714.76013857922 116347.06331261322 101995.51016254206 87663.153996351743 73351.654416933117 59060.084088232368 44783.541872393711 30511.858398142849 16228.966647891046 2352.7841194099710 -17433.266760237842 -36523.088716737955 -49298.482510351438 -62085.820574877558 -74872.905184812276 -87653.174701753887 -100424.05205419019 -113185.47773423072 -125938.76428721282 -138685.78716448147 -151428.46748799764 -164168.48122536647 -176907.12919196757 -189645.31203781351 -202383.56736759766 -215122.13888651165 -227861.05836378795 -240600.22972962281 -253339.51076458493 ; 267071.12992103695 240479.53555049002 227184.35500592654 213889.54644239575 200595.07026634066 187300.64536337255 174005.64257961366 160708.98658470347 147409.08963676987 134103.85948612355 120790.84918339782 107467.64791292706 94132.644426698243 80786.316585251174 67433.188967374997 54084.515795723171 40761.527024509916 27498.636512627516 14470.750115211407 1736.0744463647693 -16743.859404853905 -34472.073689135505 -46173.083097492199 -57841.921502006597 -69505.448682601753 -81178.224905628260 -92866.472480387369 -104571.30585508735 -116291.08559325122 -128022.98520477637 -139763.94363908953 -151511.18184635401 -163262.43353441067 -175016.00268083991 -186770.72532398478 -198525.88506447474 -210281.11115574016 -222036.27401571421 -233791.38399349677 ; 245067.42641398858 220666.04124637228 208466.16831732768 196266.81915756915 184068.03331661716 171869.64052855870 159671.18747595130 147471.89381470025 135270.65052737662 123066.06795837868 110856.56423984913 98640.451281974005 86415.919262234529 74180.739383235123 61931.406837647861 49661.361815723554 37357.925214803807 24997.794168962806 13000.962757487947 1302.4806849416564 -15648.283778590583 -31609.501602426626 -42301.167821370691 -53007.035862185410 -63720.180059329774 -74439.289430266435 -85165.022698057786 -95898.109002940982 -106638.61798811246 -117385.88954246900 -128138.75735216393 -138895.84284735634 -149655.80593768487 -160417.51092028560 -171180.10637639835 -181943.03613694379 -192706.00308690296 -203468.90515502513 -214231.75758093849 ; 223078.09915685249 200845.96417872392 189729.94139404796 178614.02146955294 167498.37286612298 156383.24363978853 145268.92014552478 134155.62338740777 123043.30394730142 111931.28418064433 100817.69057448581 89698.633279495451 78567.146077035766 67412.028294918942 56216.960077877389 44960.603857572503 33618.812739396220 22527.677995015136 11715.442187846134 1120.5782258726379 -14343.052244836517 -29118.605369709290 -38651.826369982577 -48279.874562840509 -57973.585359033903 -67707.980651765436 -77464.598237459402 -87231.333799046595 -97001.168008627705 -106770.63655450258 -116538.47964976296 -126304.62749214956 -136069.52384799221 -145833.72404537647 -155597.68929771410 -165361.70906746085 -175125.90045019763 -184890.25008284434 -194654.67698513149 ; 201084.05254929553 181020.44043219136 170986.43915251645 160950.78156690139 150912.70456131763 140871.44239752894 130826.26349266036 120776.46425887659 110721.34755548020 100660.25576074426 90592.778053136601 80519.286465279394 70441.935618061238 60366.129446819468 50302.155106334772 40266.205949805590 30279.465463232274 20412.883754535243 10680.960306662504 1144.1883231888901 -12733.418145931038 -26173.309659778737 -34996.749310969280 -43770.406326854798 -52515.612023864982 -61248.527170280526 -69979.247905748562 -78712.947149103318 -87451.621396442366 -96195.619271929492 -104944.64668856503 -113698.26746206296 -122456.05536270345 -131217.57017239393 -139982.28907379266 -148749.56899808918 -157518.66860137932 -166288.82836238126 -175059.39302718613 ; 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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 ];