Dual Motor Electric Powertrain

Dual Motor Superblock

The Dual Motor superblock constits of two Permanent Magnet Synchronous Motors, two Voltage-Current controllers, two Inverter/Converters, and a Battery Pack.

Permanent Magnet Synchronous Motor

A comprehensive model of the Permanent Magnet Synchronous Motor (PMSM) is established based on its speed-torque characteristics and efficiency data. This information is derived from an external efficiency map file (.efmp), which contains the torque-speed and torque-speed-efficiency characteristic curves of the motor. The data is explicitly obtained through Look-up Tables in the form of .mat files containing the relevant variables. This approach allows for the incorporation of user-defined electric motor data in vehicle simulations and ensures accurate calculation of power consumption.

The Torque-Speed characteristic curve is particularly significant as it delineates the torque boundaries for both the motor's tractive (positive) and regenerative braking (negative) regions, as shown in the figure below. These boundaries illustrate the maximum positive and negative torque that the motor can generate. The PMSM motor's characteristics encompass two distinct regions: a constant torque region and a constant power region. The motor can deliver its maximum torque up to its rated speed, and beyond that point, it can supply its maximum power.

The Torque-Speed-Efficiency curve, also known as efficiency map, is responsible for providing the efficiency values for each motor depending on its operating region. It also contains information for the motor’s traction and regenerative braking region as shown in the figure below.

Voltage-Current Motor Controllers

The Voltage-Current controller block is used to control the AC supplied to the motor. The control voltage depends on the vehicle speed, motor speed, accelerator pedal input and battery state of charge. To determine the appropriate voltage to apply to the motor, the controller employs Pulse Width Modulation (PWM) and references Torque lookup tables. Additionally, the voltage is subject to constraints imposed by the battery's state of charge (SOC). Notably, when the battery SOC exceeds 80%, the controller prohibits regenerative braking to safeguard the integrity of the battery cells, as such braking can potentially inflict damage. Conversely, if the battery SOC falls below 20%, the battery ceases to supply current, again as a protective measure for the battery cells.

A PWM Look Up table is used to calculate the PWM value using vehicle speed and accelerator pedal input. The PWM value ranges from 0 to 250. The value 50 is used for coasting i.e. at this value the motor will output 0 torque. If the PWM value is less than 50 the motor acts as a generator and is in regenerative mode. A PWM value greater than 50 means the motor is providing positive torque for traction.

Inverter/Converter Block

The inverter/converter blocks are responsible for modeling the power losses resulting from the frequency conversion process executed by the motor control. It stands in between the motor and the battery pack and provides the final power demand of each motor.

Battery Block

The Battery model receives as input the combined power demand from both motors as input. It contains the required information to determine the capacity of the battery pack. It specifies the charging/discharging losses from the vehicle operation, to estimate the battery’s state of charge.

Vehicle Control Unit Superblock

The Vehicle Control Unit block consists of the Torque Demand Estimation, the Torque Distribution Algorithm, and the Torque Ratio Calculation.

Torque Demand Estimator Block

The torque demand estimator defines the coasting region and regenerative braking using One-Pedal Driving ¹ to estimate the combined motor torque demand. The coasting region consists of two distinct boundaries, as illustrated in the accompanying image.

In the figure above, the region above pcu, is the tractive region and the region below the lower boundary (pcl) is the regenerative region. The coasting band between these boundaries increases with vehicle speed. This expansion is a deliberate design choice aimed at reducing the sensitivity of the accelerator pedal at higher vehicle speeds. The regenerative torque in the powertrain can be used to brake the vehicle in normal traffic conditions. The motor provides enough negative torque to operate the vehicle with only one pedal in case of city drives ¹. At higher vehicle velocities, the regenerative torque alone is not sufficient to stop the vehicle and hence the friction braking should be used. The regenerative torque percentage in this model changes with vehicle velocity as shown in the figure below.

To achieve standstill condition in case of fully released accelerator pedal, the regenerative torque is set to 0 at 0 vehicle speed. This is done by setting the value of the first cell in PWM lookup table to 50 which means coasting.

Torque Distribution Algorithm Block

Four different torque distribution strategies are available focused on battery consumption reduction:

1. Evenly Distributed (ED): a fixed 50-50% torque distribution is considered up to the point it cannot provide sufficient torque. When this limit is reached and additional torque is required, the system utilizes the remaining torque capacity of the motor with higher torque capabilities. Relies solely on motors’ maximum torque information (torque curve).
2. Single Axle (SA): or overflow method – The torque is requested from a single motor while that motor can provide the entire torque. If a single motor cannot provide the torque, the residual is provided by the second motor – the torque request overflows to the second motor. Uses only motors’ maximum torque information (torque curve).
3. Switch Threshold (ST): Calculates power losses online, based on provided motors’ efficiency maps and switches between ‘SA’ and ‘ED’ to reduce power consumption ², ³.

   $P_{los{s}_{SA}}=T_{dem}\cdot \omega \cdot \left(\frac{1}{{\eta }_{SA}+e_r}-1\right)$

   $P_{los{s}_{ED}}=\frac{1}{2} T_{dem}\cdot \omega \cdot \left( \frac{1}{{\eta }_{E{D}_f}+ e_r}-1 \right)+ \frac{1}{2} T_{dem}\cdot \omega \cdot \left(\frac{1}{{\eta }_{E{D}_r}+ e_r}-1 \right)\left( \frac{1}{{\eta }_{E{D}_r}+ e_r}-1 \right)$

   Where,

   • $\omega$ : motor speed
   • $T_{dem}$ : torque demand
   • $P_{los{s}_{SA}}$ : power losses originating from single (rear) motor operation
   • $P_{los{s}_{ED}}$ : power losses originating from dual motor 50-50 torque distribution operation
   • ${\eta }_{SA}$ : rear motor efficiency ${\eta }_{SA}$ = ${\eta }_{SA}\left(w, T_{dem}\right)$ , determined by motor's characteristic efficiency map
   • ${\eta }_{E{D}_f}$ : front motor's efficiency ${\eta }_{E{D}_f}$ = ${\eta }_{E{D}_f}\left(w, 0.5T_{dem}\right)$ , determined by motor's characteristic efficiency map
   • ${\eta }_{E{D}_r}$ : rear motor's efficiency ${\eta }_{E{D}_r}$ = ${\eta }_{E{D}_r}\left(w, 0.5T_{dem}\right)$ , determined by motor's characteristic efficiency map
   • $e_r$ : small number to avoid division by zero

   Algorithm

   At every time step:

   1. Calculate both $P_{los{s}_{SA}}$ , $P_{los{s}_{ED}}$
   2. If $P_{los{s}_{SA}}$ < $P_{los{s}_{ED}}$ set torque bias = 1

      Else: set torque bias = 0.5

4. Optimal Torque Ratio (OTR): Offline exhaustive search method to determine optimal torque distribution for all torque-speed scenarios within motors’ capabilities ⁴. An optimal torque map is formed in advance, automatically utilizing the motors’ torque limits and efficiency data. Total electric power consumption is minimized by targeting each motor’s most efficient operating point. It is then used as a Look-up Table to select the most efficient torque split ratio in the range 0-100%.

   The method considers all possible combinations of motor angular speeds and torques within the range of each motors’ capabilities, which are defined by the .efmp files. Then, calculates the overall system efficiency using the following equation, for every possible torque split ratio. Outside of motors’ torque- speed range, the map provides the torque ratio that leads to maximum combined torque. Finally, the torque split ratio that results in optimum efficiency is selected, thus forming the optimal torque ratio map.

   ${\eta }_{sys} = \frac{\left(1-r\right) T_{dem} {\omega }_f + r T_{dem} {\omega }_r }{\frac{\left(1-r\right) T_{dem} {\omega }_f}{{\eta }_f\left(\omega , \left(1-r\right) T_{dem}\right) + e_r}+\frac{r T_{dem} {\omega }_r}{{\eta }_r\left(\omega , r T_{dem}\right)+ e_r}+e_r}$

   Where,

   • $r$ : torque split ratio
   • $T_{dem}$ : combined torque demand on both motors
   • ${\omega }_{f,r}$ : front/ rear axle’s angular velocity, assumed equal
   • ${\eta }_{f,r}$ : front/ rear motor’s efficiency as a function of $\omega$ , $r$ , $T_{dem}$

     Calculated in python, by interpolating motor’s efficiency map

   • $e_r$ : small number used to handle arithmetical errors, such as division by zero
   The figure below shows the 3D map that contains the optimal torque ratios for the default motor configuration. It is generated automatically before every simulation based on the motors’ provided data by the .efmp files.

   
   
   

Torque Ratio Calculation Block

Determines the final motor’s torque ratio considering parameters such as motors’ capabilities and vehicle’s state (tractive or regenerative braking). The motor’s torque ratio, as opposed to torque split ratio, is the percentage of motor’s torque utilization that is determined by the VCU and is indited by the following equation:

$t_{r_m}=\frac{T_m}{{{\rm T}}_{m_{max}}\left(\omega \right)}$

Where,

• $T_m$ : motor's torque
• ${{\rm T}}_{m_{max}}\left(\omega \right)$ : motor’s maximum torque as a function of speed

The torque ratio can receive values in the range of [-100, 100], where positive values depict motor operation in tractive mode and negative values regenerative braking mode.

Note: The complete Twin Activate diagram of the powertrain model can be accessed from: <install_dir>\ hwdesktop\hw\mdl\mdllib\Common\FMU_Library\Motor\FMU_source\Activate_Models.

Datasets

Motor Properties

The torque distribution algorithms found on the VCU, rely on real motor torque-speed-efficiency data provided by external efficiency map files (.efmp). These files are a representation of the motors’ Torque-Speed and Torque-Speed-Efficiency characteristic curves. The paths pointing to these files are received as inputs in the Motor Properties Dataset.

Template

Evaluate Motor Properties

It is responsible for the initialization of an internal script (MotorProperties.py) before every simulation, used to:

• Read the Teimorbit format .efmp file.
• Extract motor properties.
• Generate .mat files specific to the .xml file and store them in the run folder.
• Assign the correct .mat file paths/variables in the FMU parameters section.
• And finally, execute – if selected - the OTR torque distribution strategy to generate the optimal torque ratio map.

Solver Variables

Entities	Type	Description	Comments
Driver Throttle Output	Attachment solver variable	Throttle signal from driver	0-1
Driver Clutch Output	Attachment solver variable	Clutch signal from driver	Not used in the model but required by the driver’s attachment
Driver Gear Output	Attachment solver variable	Gear signal from driver	Not used in the model but required by the driver’s attachment
FMU Torque - rear/front	Solver Variable	Rear/ Front motor output torques	N-mm
FMU Omega rear/front	Solver Variable	Rear/ Front motor output wheel velocities	rad/s
Torque Ratio - rear/front	Solver Variable	Rear/Front motor speed torque utilization	0-100
Vehicle Longitudinal Velocity m/s	Solver Variable	Vehicle’s longitudinal velocity	m/s
Battery SOC	Solver Variable	Battery’s State-Of-Charge	0 - 1
Combined battery power demand	Solver Variable	The combined battery power demand from both motors	Watt
Combined motor torque demand	Solver Variable	The combined torque demand from both motors	N-m
Predicted combined torque demand	Solver Variable	The combined motor torque demand predicted by the VCU	N-m
Torque split - rear	Solver Variable	Rear-front torque distribution, where 100% represents rear-wheel drive and 0% signifies front-wheel drive.	0 - 100

FMU Entity

Represents the FMU of the Dual Motor Electric Powertrain with inputs, outputs, parameters, and solver settings. The inputs of the FMU powertrain can be customized and you are free to change the system, however some inputs and outputs need to be present to correctly simulate a driver event. The schematic below shows the necessary inputs and outputs of the FMU powertrain block. The powertrain receives throttle, transmission input shaft speed front and rear, vehicle speed and outputs torque.

FMU Inputs

Connections	Description	Units	Comments
Motor speed rear	Rear Gearbox input shaft speed	rad/s
Motor speed front	Front Gearbox input shaft speed	rad/s
Throttle from driver	The accelerator pedal’s input from driver	0 - 100	Unit conversion required from MV’s 0-1 to FMU’s 0-100
Vehicle speed	Vehicle’s longitudinal velocity	m/s	Unit conversion required from MV’s mm/s to FMU’s m/s

FMU Outputs

Connections	Description	Units	Comments
Torque from rear motor	The output torque from the rear motor	N-m	Unit conversion required from FMU’s N-m to MV’s N-mm
Motor speed rear output	rear motor shaft speed	rad/s
Traction Coast Regen State rear	Integer value that shows the operating mode of the rear motor: -1 indicates that powertrain is in regenerative braking mode, 0 means it is operating in coasting band and a value of 1 indicates that the motor is operating in tractive region	-1, 0, 1
PWM rear value	It corresponds to the pulse width modulation value which can be converted to voltage applied to the rear motor	0-250
Power demand rear motor	Power demand from rear motor to the battery	Watt
Torque from front motor	The output torque from front motor	N-m	Unit conversion required from FMU’s N-m to MV’s N-mm
Motor speed front output	Front motor shaft speed	rad/s
Traction Coast Regen State rear	Integer value that shows the operating mode of front motor: -1 indicates that powertrain is in regenerative braking mode, 0 means it is operating in coasting band and a value of 1 indicates that the motor is operating in tractive region	-1, 0, 1
PWM front value	It corresponds to the pulse width modulation value which can be converted to voltage applied to the front motor	0 - 250
Power demand front motor	Power demand from front motor to the battery	Watt
Battery SOC	The state of charge of the battery	0 - 1
Combined battery power demand	The combined battery demand from both motors	Watt
Combined Motor Torque Demand	The combined torque demand from both motors	N-m	Unit conversion required from FMU’s N-m to MV’s N-mm
Rear motor efficiency	Rear motor’s efficiency	0 - 1
Front motor efficiency	Front motor’s efficiency	0 - 1
Rear torque spit	Torque distribution, using rear motor as a reference point	0 - 100
Predicted combined torque demand	The combined motor torque demand predicted by the VCU	N-m	Unit conversion required from FMU’s N-m to MV’s N-mm
Torque ratio rear	Rear motor’s torque ratio	0 - 100
Torque ratio front	Front motor’s torque ratio	0 - 100

FMU Parameters

Parameters	Description	Units
converter_efficiency	Converter’s efficiency value
inverter_efficiency	Inverter’s efficiency value
num_modules_pack_parallel	Number of module packs in parallel
num_cells_per_module_parallel	Number of cells per module in parallel
capacity_cell	Cell’s capacity	Amp-hours
battery_charging_losses	Coefficient to determine battery charging losses while at recuperation region
nominal_voltage_cell	Cell’s nominal voltage	V
num_cells_per_module_series	Number of cell rows per module
num_modules_pack_series	Number of module packs rows
SOC_initial	Initial State-Of-Charge level (%)
battery_discharging_losses	Coefficient to determine battery discharging losses while at tractive region
emotor_efficiency_scale	Parameter to enable efficiency scaling
max_pwm	Maximum PWM value
pwm_zero_torque	PWM value corresponding to 0 torque output
SOC_limit_high	Upper limit for SOC
SOC_limit_low	Lower limit for SOC
max_vehicle_speed	Vehicle’s maximum velocity	m/s
coast_m	Polynomial degree to determine coasting region
coast_phi	At what pedal value coasting is desired
coast_ch	Range of coasting to define pcl and pcu values
max_pedal	Maximum throttle value	0 - 100
traction_gamma	Polynomial degree to define the correlation between throttle and torque ratio for the traction region
regen_psi	Order of polynomial to define the correlation between throttle and torque ratio for the regenerative region
traction_max	Percentage of maximum available torque	N-m
pedal_0_regen_percent 1-4	These parameters define the percentage of regenerative braking contribution to total braking as a function of velocity. Specifically, you can specify the regenerative braking percentage to determine the three sections of Figure 8.
pedal_0_vx 1-4	These parameters specify the corresponding velocities at specific regenerative braking percentages. Specifically, they are used to define the velocity values that designate the three sections of Figure 8.
Path char Warning: This parameter is automatically updated, it should not be manually modified.	Mat file path that contains both motor characteristics, such as rated and maximum speed, rated torque
Vcu_type	Set VCU torque distribution strategy: 1: ED 2: SA 3: ST 4: OTR
matfilename - Rear Motor data mat file path Warning: This parameter is automatically updated, it should not be manually modified.	Path pointing to rear motor’s mat file. Appearing multiple times in the FMU.
matfilename - Front Motor data mat file path Warning: This parameter is automatically updated, it should not be manually modified.	Path pointing to front motor’s mat file. Appearing multiple times in the FMU.
matfilename - Optimal Torque ratio map mat file path Warning: This parameter is automatically updated, it should not be manually modified.	Path pointing to optimal torque ratio .mat file path.
matvarname Warning: This parameter is fixed, it should not be altered.	Refers to the rear, front motor or optimal torque ratio map .mat files’ variable names, used for data extraction. It appears multiple times in the FMU.

Motor Front/Rear Systems

Includes the integrated motor-inverter unit.

Bodies

Motor/Engine - Represents the lumped mass and inertia of each motor in a non-operating condition. The motor’s output shaft is assumed to be hard coupled with gearbox input shaft and hence their speed is going to be the same. The motor’s shaft and its rotation are not modeled. Since the inertia of the rotating shaft is not modeled, this inertia can be added in other rotating elements in the driveline.

Motor Mounts

Motors are attached to chassis by four bushings. The mount locations must be provided on the attachment body by specifying the coordinates of the mounts and the orientation of the bushings specified using the vectors corresponding to each mount.

Solver Variables

Entities	Type	Description	Comments
FMU Torque	Solver Variable	Motor output torque from FMU	N-mm
FMU Omega	Solver Variable	Motor output wheel velocity from FMU	rad/s
Throttle input to motor 100	Solver Variable	Throttle input from driver	0-100
FMU Power demand motor	Solver Variable	Motor power output	W
Traction/Coast/Regen state	Solver Variable	Integer value that shows the operating mode of motor: -1 indicates that powertrain is in regenerative braking mode, 0 means it is operating in coasting band and a value of 1 indicates that the motor is operating in tractive region	-1, 0, 1
PWM value	Solver Variable	It corresponds to the pulse width modulation value which can be converted to voltage applied to the rear motor	0-250
Motor Efficiency	Solver Variable	Motor’s efficiency	0-1

Gearbox Front/Rear Systems

Bodies

Gearbox – Contains the mass and inertia properties of gearbox body in a non-operating condition. Gearbox is also assumed to be directly attached to the motor body, with the usage of a fixed joint. The motor’s output shaft is assumed to be hard coupled with gearbox input shaft and hence their speed is going to be the same.

Datasets

Gearbox Data

Label	Description
Final Drive Ratio	Differential’s final stage of gear reduction ratio, used to calculate the final drive torque.
Gearbox Efficiency	Gearbox’s overall efficiency, used to calculate the final drive torque.

Solver Variables

Entities	Type	Description	Comments
Torque from Gear Box	Solver Variable	Mathematical expression used to calculate gearbox’s final output torque.	N-mm
Gear Box Input Shaft Speed	Solver Variable	Mathematical expression used to calculate gearbox’s input shaft speed.	rad/s

Forces

Gearbox Output Torque - Represents the powertrain’s output torque on the differential’s carrier body. The torque is calculated by the ‘Torque from Gear Box’ Solver Variable expression.

Battery Pack

If the battery pack module has been selected from the Assembly Wizard, it can be found as a separate system, out of the primary Dual Motor Powertrain system. It includes:

Bodies

Battery Pack - Represents body's mass and inertia properties.

Battery Mounts

Battery is attached to chassis by four bushings. The mount locations must be provided on the attachment body by specifying the coordinates of the mounts and the orientation of the bushings specified using the vectors corresponding to each mount.

1. The Vehicle Tools extension must be loaded.
   1. From the menu bar, select File > Extensions.
   2. Load the Vehicle Tools extension by sliding the Load button to the right.
      The Vehicle Tools ribbon is add in MotionView.

      
      
      

2. In the Vehicle Tools ribbon, click the Assembly tool to open the Assembly Wizard.
3. Select the Full Vehicle with Driver model and click Next.

   
   
   

4. Choose the Four wheel drive driveline configuration and then select the Dual Motor Electric Powertrain (FMU), which is listed in the Powertrain drop-down menu.

   
   
   

5. After selecting the vehicle’s powertrain type, you can also opt for a Battery Pack body.

   
   
   

$---------------------------------------------------------------------ALTAIR_HEADER
[ALTAIR_HEADER]
FILE_TYPE     =  'efmp'
FILE_VERSION  =  1.0
FILE_FORMAT   =  'ASCII'
$--------------------------------------------------------------------------UNITS
[UNITS]
(BASE)
{length  force      angle       mass    time}
'm'   'newton'   'degrees'   'kg'    'sec'
(USER)
{unit_type    length  force  angle  mass  time  conversion}
'rpm'          0       0      1      0     -1     6.0
'torque'       1       1      0      0      0     1.0
$-------------------------------------------------------------------------Motor Details
[EFFICIENCY_MAP]
(X_DATA)
{speed}
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$-------------------------------------------------------------------------Efficiency
(YZ_DATA)
{a b c d e f g h i j k l m n o p}
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$-------------------------------------------------------------------------ENGINE
[TORQUE_CURVE]
(DATA)
{speed torque}
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+1.345479E+04	+5.056248E+01
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+1.500000E+04	+0.000000E+00

• The rotational inertia of the motor’s shaft should be added in the rotating bodies in the driveline.
• The default motor configuration assumes that the motor regenerative region is the same as tractive, in terms of efficiency mapping.