This section displays what are the powertrain architectures for which this simulator is applicable. For the current version, the simulator applies only to:

• single motor, single speed transmission, with front-wheel drive (FWD)
• single motor, single speed transmission, with front-wheel drive (RWD)

Future versions of the application will take into account also dual-motor architectures, with one motor on each axle.

This section contains the user input data for the simulation. There are 3 main categories:

• Performance data

  • Vehicle range [km] : this the expected range of the vehicle; function of this parameter the battery energy content is calculated
  • Top speed on flat road [km] : this is the required maximum speed of the vehicle, usually advertised by the manufacturer; it is used for the calculation of the wheel power; the actual power of the vehicle could be bigger than this value, mainly function of the continuous power of the electric motor
  • Top speed on road with slope [km] : this parameter is used to calculate the wheel power on a motorway driving cycle; it's used together with the Road slope for high speed [%] parameter; for more information on how to calculate the slope resistance at wheel, read the article How to calculate road slope (gradient) force
  • Top speed on hill climb [km] : this parameter is used when calculating the wheel power and torque for hill climb
  • Road slope for simulation [%] : this parameter is used for drive cycle simulation and also performance simulation; only use it if you want to see the acceleration performance of the vehicle on a road with slope
  • Road slope for high speed [%] : this is used together with the Top speed on road with slope [km] parameter to calculate the wheel torque and power requirement
  • Hill climb slope [%] : this parameter defines the maximum slope of the road ; it's used to calculate the wheel torque and power requirements
  • Acceleration time 0-100 kph [s] : this parameter is not used in any calculation, it's only used as a reference for the Simulation results
  • Curb height [m] : this parameter defines the height of the curb which needs to be climbed by both wheels of the drive axle. For more information on how the calculation is done read this article How to calculate wheel curb climbing torque

• Vehicle data

  • Aerodynamic drag coefficient [-] : this parameter is used to calculate the aerodynamic drag force; for more information on the aerodynamic drag of a vehicle, read the article How to calculate aerodynamic drag force
  • Maximum frontal area [m²] : this parameter is used to calculate the aerodynamic drag force; for more information on the aerodynamic drag of a vehicle, read the article How to calculate aerodynamic drag force
  • Vehicle mass [kg] : this is the curb mass of the vehicle, which is usually the empty mass of the vehicle and driver; this parameter is used for drive cycle and performance simulations
  • Maximum payload [kg] : this parameter plus the curb mass of the vehicle define the gross mass of the vehicle, which is the maximum allowed mass of the vehicle; this parameter is only used for hill and curb climb calculation
  • Rolling resistance coefficient [-] : this parameter is used to calculate the rolling resistance force; for more information on the rolling resistance force of a vehicle, read the article How to calculate rolling resistance
  • Tire rolling radius [m] : this parameter is used to convert from rotational wheel speed into linear wheel speed and vice-versa; also it's used to calculate the wheel force knowing the wheel torque; this parameter can be calculated from the tire symbol, for more information read the article How to calculate wheel radius
  • Driveline efficiency [%] : this parameter is used to calculate the motor power or torque knowing the wheel power or torque; for more information on the driveline efficiency read the article Drivetrain losses (efficiency)
  • Transmission gear ratio [-] : this is the total gear ratio of the transmission; if the transmission has two pairs of gears, this parameter is the product between the gear ratio of each gear set; for more information on how a gear ratio is calculated, read the article How to calculate a gear ratio
  • Tire friction coefficient [-] : this parameter is used to calculate the maximum traction force at the wheel; the maximum traction force at the wheel is limited by the friction force at the wheel; for more information regarding the calculation of friction force, read the article How to calculate friction force
  • Axle load ratio during acceleration [%] : this parameter determines how much of the vehicle weight is transferred on the motor axle during acceleration; if the vehicle is RWD the ratio should be more than 50%; if the vehicle is FWD the ratio should be less than 50%

• Battery pack

  • Battery pack nominal voltage [V] : this parameter defines the battery pack voltage around 50% state of charge (SoC)
  • Battery cell nominal voltage [V] : this parameter is used to calculate the number of battery cells in a string; by dividing the battery pack nominal voltage to the cell voltage we get the number of cells in a string
  • Battery cell rated capacity [Ah] : this parameter is used to calculate the energy content of a battery cell, by multiplying it with the voltage of the battery cell
  • Battery cell C-rate [h^-1] : this parameter is used to calculate the maximum current in a string by multiplying it with the battery cell capacity
  • Battery cell mass [kg] : this parameter is used to calculate the total mass of the battery pack only taking into account the total number of battery cells; the actual total mass of the battery pack is much bigger since it contains also wiring, casing, coolant, electronic boards, etc.
  • Auxiliary systems power [W] : this parameter represents the energy consumption of the auxiliary systems on board of a vehicle (e.g. DCDC converter, lightning systems, heating and cooling systems, etc.); by default is set to a very low value meaning that there are no other consumers active except for the DCDC system
  • Additional battery strings [-] : this parameter is used to add more battery strings to the ones calculated automatically; the purpose of this parameter is to increase the current and battery capacity of the battery after a performance simulation, if the current and power limits are passed
  • Minimum battery SoC [%] : this parameter represent the discharge limit of the battery pack; the battery is not allowed to be discharged below this limit
  • Maximum battery SoC [%] : this parameter represents the upper limit of the battery charge; it is used as initial value during the drive cycle and performance simulations

For more information regarding the calculation of a battery pack, read the article EV design – battery calculation

This section calculates the required wheel power, torque and speed for several scenarios:

• top speed with and without road slope
• hill climb and curb climb
• top vehicle speed

The wheel force is calculated as:

\[ F_{wheel} = m \cdot g \cdot \left [ \sin(\theta) + C_{r}(v) \cdot \cos(\theta) \right ] + \frac{1}{2} \cdot \rho \cdot C_{d} \cdot A \cdot v^{2} \tag{1} \]

where:

• m [kg] : mass acting on wheel
• g = 9.81 m/s² : gravitational acceleration
• θ [rad] : road slope
• C_r [-] : rolling resistance coefficient
• ρ = 1.202 kg/m³ : air density
• C_d [-] : air drag coefficient
• A [m²] : frontal area of the vehicle
• v [m/s] : vehicle speed

The wheel power is calculated as:

\[ P_{wheel} = F_{wheel} \cdot v \tag{2} \]

The wheel torque is calculated as:

\[ T_{wheel} = F_{wheel} \cdot r_{w} \tag{3} \]

where r_w [m] is the radius of the wheel.

The wheel speed is calculated as:

\[ \omega_{wheel} = \frac{v}{r_{w}} \tag{4} \]

For more information regarding wheel road load simulation read the article Vehicle acceleration and maximum speed modeling and simulation.

Based on the calculated wheel power, torque and speed, the motor power, torque and speed are calculated, taking into account the driveline efficiency and transmission gear ratio. These values are minimum requirements to satisfy the driving scenarios and hill and curb climb.

The motor torque is calculated as:

\[ T_{motor} = \frac{T_{wheel}}{\eta_{drv} \cdot i_{x}} \tag{5} \]

where:

• η_drv [-] : driveline efficiency
• i_x [-] : gear ratio of the transmission

The motor speed is calculated as:

\[ \omega_{motor} = \omega_{wheel} \cdot i_{x} \tag{6} \]

The motor power is calculated as:

\[ P_{motor} = \omega_{motor} \cdot T_{motor} \tag{7} \]

The motor power, torque and speed calculated above represent the minimum required performance for top speed and hill and curb climb. Further, the user will define the motor torque (peak and continuous) which needs to be above minimum required performance.

The motor used for this application is a permanent magnet asynchronous type motor. The output torque and power curves are generated based on the input data:

• Maximum peak torque [Nm] : this is the maximum torque which can be output be the motor for a short duration of time, defined by the peak torque maximum time parameter.
• Maximum continuous torque [Nm] : this is the maximum torque of the motor which can be generated without interruption
• Peak torque maximum torque [s] : this is the maximum operating time at peak torque of the motor; in the performance simulation, after this time has passed, the motor torque is limited by the maximum continuous torque
• Base motor speed [rpm] : this is the motor speed up to which the motor torque is constant; for motor speeds above base speed, the motor power will be constant, until the motor speed reaches maximum value
• Maximum motor speed [rpm] : this is the maximum rotational speed of the motor; this value is not limiting the motor speed in the simulation, it's just defined as reference for comparison
• Motor and inverter efficiency [%] : this parameter is used to calculate the battery power, using motor power; in reality the motor efficiency depends on the speed and torque of the motor, but, for simplification, we'll use a constant value

For more information regarding motor efficiency and design read the article EV design - electric motor.

The simulation of the range of the vehicle is based on predefined driving cycles. The following cycles can be used for vehicle range simulation:

• WLTC (Worldwide Harmonized Light Vehicles Test Cycle) : is a global harmonized standard for determining the levels of pollutants, CO₂ emissions and fuel consumption of traditional and hybrid cars, as well as the range of fully electric vehicles.
• FTP (Federal Test Procedure) : is composed of the UDDS (Urban Dynamometer Driving Schedule) followed by the first 505 seconds of the UDDS. FTP cycle it's often called the EPA75 cycle; the UDDS cycle is commonly called the "LA4" or "the city test" and represents city driving conditions. It is used for light duty vehicle testing.
• HWFET (Highway Fuel Economy Driving Schedule) : represents highway driving conditions under 60 mph.
• US06 : is a high acceleration aggressive driving schedule that is often identified as the "Supplemental FTP" driving schedule.
• CUSTOM : is a cycle defined by the user; to work properly, the first values of time and speed should be 0; also, the time increment MUST be 1 s; all values for both time and speed MUST be separated by commas.

Each cycle is used to calculate an average energy consumption per km. This parameter will be further used to calculate the parameters of the battery.

The battery pack parameters are calculated function of the vehicle range, average energy consumption per km and battery cell data. The battery parameters are calculated for each driving cycle. The main battery parameters (energy, capacity, maximum power and maximum current) are displayed only for the selected cycle.

At each simulation RUN, the battery parameters are recalculated. The user has the option to hold the battery parameters calculations in order to check the impact of different input data on the same battery.

The equations used to calculate the battery pack parameters are described in the article EV design – battery calculation.

The setup section allows the user to select the:

• NUMERICAL SOLVER : there are two numerical solvers integrated in the simulation: Euler 1^st order and Runge-Kutta 4^th order; The RK method is more accurate but slower, compared with Euler; both integration methods provide robust results so can be used as desired
• SIMULATION TIME STEP : this parameter defines how often the integration of the differential equation for vehicle dynamics is being executed; the lower the time step, the more accurate the results but the slower the simulation; use with care.
• SIMULATION TYPE
  • drive cycle : this mode runs the vehicle range simulation, function of the selected drive cycle
  • performance : this mode is used to simulate the performance of the vehicle: acceleration time and top speed
• PERFORMANCE DURATION : this parameter sets the duration of the performance simulation

The vehicle follows the target speed of the drive cycle with the use of a PID (speed) controller; The output of the controller is the motor torque, which is applied to the wheel through the transmission gear ratio

The speed controller is calibrated to have a medium reaction to the speed error, calculated between the drive cycle target speed and simulated vehicle speed. The user can tune the reaction of the speed controller by modifying the values of the proportional, integral and derivative gains.

This section summarizes all the simulation parameters.

The drive cycle data can be plotted for visualization, while the performance data is displayed against the targets. If the performance targets are not met, the user is advised on how to improve them, by modifying the input data.

The Alerts section highlights if any of the components limits are reached. Based on this information and the advice provided, the user can modify the input data to remain below limits.

• general
  • there is no wheel slip
  • the vehicle's weight distribution is always 50-50% between front and rear axles
  • the vehicle is running in a perfect straight line, no lateral dynamics is taken into account
  • no internal resistance of the battery pack is taken into account
  • the efficiency of the components are considered constant throughout the simulation
• drive cycle
  • one pedal driving: the vehicle braking is done only with the electric motor and all the kinetic energy is recuperated
  • the electric motor torque is allowed to increase up to peak torque
  • the speed controller is keeping the vehicle stationary
• performance
  • the electric motor is running at maximum performance
  • the peak torque is only applied at the beginning of the simulation for the duration set by the user

• every time the input data is modified, the RUN button must be pressed in order to re-run the simulation with the new data
• the data of from the previous simulation run is memorized and displayed on the plot
• the numerical data displayed has also a relative difference calculated, using the data from the previous simulation run
• the input data is stored in the local storage container of the browser; the user will be able to restart the simulations from the last data entered
• to reset the input data to the initial values, the local storage of the page must be deleted: for example, in the Chrome browser this is done by clicking More Tools > Developer Tools > Application > Local Storage