This document summarizes the process to generate full efficiency and power loss maps for an Electric Drive Unit (EDU) for a Generic 150 kW Integrated Powertrain Module (IPM). The EDU includes the inverter, emotor and the gearing and the gear ratio for this EDU is 9.5:1. The data used to construct these maps were numerically derived based on a function with coefficients identified using averaged power consumption data from several confidential benchmarking test data files. The test data were obtained from several state-of-the-art internal permanent magnet synchronous reluctance (IPMSRM) e-motors used in current production battery electric vehicles. Transformation functions, whose coefficients represent the averaged power consumption data, were utilized to blend and transform the confidential test data into one final map. The final map was then scaled to 150kW to represent a generic EDU suitable for use in a BEV. The generated efficiency map is used as an input for ALPHA and represents the combined operating boundaries and electrical power consumption of the electric motor, inverter, and gearing, categorized together as an EDU.
SUGGESTED CITATION:
Generic IPM 150kW EDU - ALPHA Map Package. Version 2023-04. Ann Arbor MI: US EPA National Vehicle and Fuel Emissions Laboratory, National Center for Advanced Technology, 2023.
EDU Physical Characteristics
The following table sets the key physical characteristics for a Generic IPM 150kW EDU and are based on characteristics of the original e-motors tested. 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 = 'Generic IPM 150kW EDU';
emach.type = enum_emachine_type.EDU;
emach.gear.ratio = 9.5;
emach.gear.efficiency_norm = 1;
emach.inertia_kgm2 = 8.86 * (1/2*0.117*1/2)^2;
emach.max_speed_radps = 15000 * unit_convert.rpm2radps;
emach.max_torque_Nm = 312;
emach.max_motor_power_W = 150000;
emach.max_generator_power_W = emach.max_motor_power_W;
nominalVoltage_V = 350;
Import EDU Data
The following code imports power loss data numerically derived based on averaged power consumption data from several confidential source data files. The results of the numerical derivation are provided in 3b- Generic IPM 150kW EDU – Derived Input Data File.xlsx. 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.
tbl_mot = readmatrix('3b- Generic IPM 150kW EDU - Derived Input Data File.xlsx','Sheet','Input Data','Range','A8:R26'); data(1).speed_rpm = tbl_mot(1,3:end); data(1).torque_Nm = tbl_mot(2:end,1); data(1).elec_powerloss_W = tbl_mot(2:end,3:end)*1000; data(1).name = 'Data';
EDU Torque Limits
The following table sets the torque limits of the EDU input map based on the derived input data. The maximum torque line is set by defining maximum torque (axis 2) at discrete speeds (axis 1) of the operating map.
emach.positive_torque_limit_Nm.axis_1.signal = 'emach_spd_radps'; emach.positive_torque_limit_Nm.axis_1.breakpoints = [data(1).speed_rpm] * 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 = [311.88 311.88 311.9 311.9 311.9 279.97 227.88 190.68 162.77 141.07 123.71 109.50 97.66 87.65 79.06 71.62]; emach.negative_torque_limit_Nm.axis_1.signal = 'emach_spd_radps'; emach.negative_torque_limit_Nm.axis_1.breakpoints = [data(1).speed_rpm] * unit_convert.rpm2radps; emach.negative_torque_limit_Nm.axis_2.signal = 'voltage_V'; emach.negative_torque_limit_Nm.axis_2.breakpoints = nominalVoltage_V; emach.negative_torque_limit_Nm.table = -emach.positive_torque_limit_Nm.table;
Build the emachine Object in Matlab
The script below creates an “emach” object which is converted into power loss space for the “drive” quadrant, extrapolated to the edges of the operating space (rather than efficiency 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 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);
EDU Efficiency Map
The following code generates the Efficiency Map shown below for this EDU which includes the combined efficiency data of the electric motor, inverter, and gearing. 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- Generic IPM 150kW EDU – Efficiency.pdf. The 6- Generic IPM 150kW EDU - 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','gear_ratio',emach.gear.ratio);
Power Loss Difference (%) Table
In addition, the table below shows the relative power loss difference by comparing the power loss data derived from the power loss data found in 3b- Generic IPM 150kW EDU – Derived Input Data File.xlsx file and the ALPHA map power data. The relative power loss difference for these data points is calculated using the following formula and represented as a percentage in the table.
Where
In cases where the original 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 data 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
----------------------------------
EDU Torque ( Nm ) \ EDU Speed ( RPM)
0 RPM 105 RPM 211 RPM 316 RPM 421 RPM 526 RPM 632 RPM 737 RPM 842 RPM 947 RPM 1053 RPM 1158 RPM 1263 RPM 1368 RPM 1474 RPM 1579 RPM
__________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________
2962.9 Nm -0.21 -0.04 -0.32 -0.09 -0.29 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2821.8 Nm 0.26 0.39 0.15 0.3 0.53 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2469.1 Nm -0.45 -0.26 -0.44 -0.37 -0.28 0.07 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2116.3 Nm 0.57 0.65 0.34 0.27 0.45 0.49 -0.68 NaN NaN NaN NaN NaN NaN NaN NaN NaN
1763.6 Nm -0.3 -0.16 -0.25 -0.36 -0.02 -0.01 0.74 -0.34 NaN NaN NaN NaN NaN NaN NaN NaN
1410.9 Nm -0.03 0 -0.01 -0.2 0.18 -0.11 -0.01 0.52 0.15 -0.55 NaN NaN NaN NaN NaN NaN
1058.2 Nm -0.03 -0.09 0.03 -0.15 0.07 -0.01 -0.27 -0.2 0.51 0.22 0.01 -0.08 -0.63 NaN NaN NaN
634.2 Nm -0.14 -0.23 -0.03 -0.02 -0.21 0.09 -0.12 -0.15 -0.06 -0.07 -0.08 -0.05 -0.07 NaN NaN NaN
493.8 Nm 0.61 -0.04 0.07 0.01 -0.57 0.5 0.36 0.17 0.33 0.93 1.4 1.62 1.71 -0.64 -1.4 NaN
423.3 Nm -0.96 -1.12 -0.88 -0.87 -1.05 -0.68 -0.86 -0.97 -1.02 -0.88 -0.78 -0.7 -0.62 -0.41 -0.45 -1.98
352.7 Nm -2.07 -2.1 -1.78 -1.73 -1.79 -1.47 -1.74 -1.89 -1.95 -1.79 -1.75 -1.69 -1.64 -0.34 -0.21 -0.94
282.2 Nm -5.36 -4.51 -4 -3.72 -3.47 -3.12 -3.47 -3.58 -3.55 -3.62 -3.63 -3.59 -3.55 -2.3 -1.98 -1.72
211.6 Nm 2.02 1.45 1.33 1.16 1.17 0.7 0.83 0.88 0.68 0.8 0.6 0.53 0.48 1.74 1.96 2.16
141.1 Nm 11.06 8.57 7.25 6.55 6.28 4.56 5.51 5.97 5.48 5.38 4.91 4.7 4.57 4.05 4.13 4.22
105.8 Nm 16.46 12.73 10.47 9.45 9.03 6.48 8.02 8.81 8.15 7.71 7.07 6.77 6.6 4.35 4.34 4.36
70.5 Nm 4.05 2.86 4.34 4.02 3.87 3.07 3.58 3.78 3.56 3.32 3.11 3.01 3.04 2.3 2.3 2.36
35.3 Nm -5.81 -3.27 -2.89 -2.31 -2.05 -0.88 -1.5 -1.9 -1.61 -1.67 -1.39 -1.28 -1.08 -0.46 -0.43 -0.35
0.0 Nm -20.04 -13.94 -12.23 -10.61 -9.69 -6.51 -8.25 -9.13 -8.15 -7.89 -7 -6.58 -6.19 -5.41 -5.26 -5.06
Power Loss Map
A clean version of the Power Loss map is shown below and in 5a- Generic IPM 150kW EDU - 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 Generic IPM 150kW EDU.
emach.write_mscript('emachine_Generic_IPM_150kW_EDU.m');
Motor Build: emachine_Generic_IPM_150kW_EDU.m
% ALPHA ELECTRIC MOTOR DEFINITION % Generated 06-Apr-2023 16:27:35 % Constructor mg = class_REVS_emachine_geared(); mg.name = 'Generic IPM 150kW EDU'; mg.source_filename = mfilename; % Physical Description mg.electrical_source = 'propulsion'; mg.inertia_kgm2 = 0.0075802837500000006; mg.type = enum_emachine_type.EDU; mg.gear.ratio = 9.5; mg.gear.efficiency_norm = 1; % Capacity Limits mg.max_speed_radps = 1570.7963267948965; mg.max_torque_Nm = 312; 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 = [ 0.0000000000000000 104.71975511965977 209.43951023931953 314.15926535897933 418.87902047863906 523.59877559829886 628.31853071795865 733.03828583761833 837.75804095727813 942.47779607693792 1047.1975511965977 1151.9173063162575 1256.6370614359173 1361.3568165555769 1466.0765716752367 1570.7963267948965 ]; 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 = [ 311.88000000000000 311.88000000000000 311.89999999999998 311.89999999999998 311.89999999999998 279.97000000000003 227.88000000000000 190.68000000000001 162.77000000000001 141.06999999999999 123.70999999999999 109.50000000000000 97.659999999999997 87.650000000000006 79.060000000000002 71.620000000000005 ]; mg.negative_torque_limit_Nm = class_REVS_dynamic_lookup; mg.negative_torque_limit_Nm.axis_1.signal = 'emach_spd_radps'; mg.negative_torque_limit_Nm.axis_1.breakpoints = [ 0.0000000000000000 104.71975511965977 209.43951023931953 314.15926535897933 418.87902047863906 523.59877559829886 628.31853071795865 733.03828583761833 837.75804095727813 942.47779607693792 1047.1975511965977 1151.9173063162575 1256.6370614359173 1361.3568165555769 1466.0765716752367 1570.7963267948965 ]; mg.negative_torque_limit_Nm.axis_2.signal = 'voltage_V'; mg.negative_torque_limit_Nm.axis_2.breakpoints = 350; mg.negative_torque_limit_Nm.table = [ -311.88000000000000 -311.88000000000000 -311.89999999999998 -311.89999999999998 -311.89999999999998 -279.97000000000003 -227.88000000000000 -190.68000000000001 -162.77000000000001 -141.06999999999999 -123.70999999999999 -109.50000000000000 -97.659999999999997 -87.650000000000006 -79.060000000000002 -71.620000000000005 ]; % 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 104.71975511965972 209.43951023931945 314.15926535897938 418.87902047863889 523.59877559829886 628.31853071795877 733.03828583761810 837.75804095727801 942.47779607693815 1047.1975511965977 1151.9173063162575 1256.6370614359175 1361.3568165555769 1466.0765716752364 1570.7963267948967 ]; mg.electric_power_W.axis_2.signal = 'emach_trq_Nm'; mg.electric_power_W.axis_2.breakpoints = [ -311.88118811881191 -259.90099009900990 -222.77227722772278 -185.64356435643560 -148.51485148514851 -111.38613861386139 -66.757425742574256 -46.351006068348774 -29.702970297029701 0.0000000000000000 29.702970297029712 46.351006068348767 66.757425742574256 111.38613861386139 148.51485148514851 185.64356435643560 222.77227722772278 259.90099009900990 311.88118811881191 ]; mg.electric_power_W.table = [ 10011.292391662248 7295.3977212824284 4991.8914938964199 3626.1058633956582 2521.9897047176073 1616.2883812044786 792.10058544321760 516.72654722041807 325.71137250736064 134.24061525644436 308.27126770141228 491.50637763044813 754.57278789106465 1539.3523429958125 2401.8945502117003 3453.4336872709619 4754.1823536903439 6947.9978360553678 9534.5641803261005 ; 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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 ];