Longitudinal EV Model in Simulink with IDC, MIDC and WLTP Drive Cycles

The problem

Range and energy use are the first questions asked about any EV design, and they depend strongly on the drive cycle. Indian urban driving (IDC, MIDC) is slow and stop-start, while WLTP includes high-speed phases. A transparent road-load model lets a student see exactly where energy goes, and is the foundation for almost every later EV simulation project.

Objectives

• Derive and implement the road-load equation for rolling resistance, aerodynamic drag, grade and inertia.
• Build a forward-facing model with a driver controller that tracks a reference speed trace.
• Model motor torque limits, a constant drivetrain efficiency and a simple battery energy balance including regeneration.
• Compare Wh/km, peak power and regenerated energy across IDC, MIDC and WLTP.
• Run parameter sweeps on mass, drag area and rolling resistance with sim() and report sensitivities.

What you need

Key concepts

Road-load equation

Tractive force F = m·g·Crr·cosθ + ½·ρ·Cd·A·v² + m·g·sinθ + m·a. Each term can be logged separately to show where the energy goes.

Forward-facing model

A driver controller compares reference and actual speed and commands torque, and the vehicle speed comes from integrating force over mass. It respects actuator limits, unlike a backward-facing model.

Regenerative braking energy

When the motor torque is negative, power flows back to the battery, reduced by drivetrain and motor efficiency and limited by the motor and battery.

Wh/km

Net battery energy over the cycle divided by distance travelled. It is the standard figure for comparing EV consumption across cycles.

Step-by-step guide

1. 1

   Fix requirements and example parameters

   Write a parameter script for an example compact car: test mass 1500 kg, Cd 0.30, frontal area 2.2 m², Crr 0.010, wheel radius 0.30 m, gear ratio 9:1, motor peak 200 N·m and 80 kW, drivetrain efficiency 0.92, motor efficiency 0.90 and a 40 kWh battery. Label these clearly as example values. Define outputs: Wh/km at the battery, peak tractive power, regenerated energy and speed-tracking error for each cycle.

   Checkpoint: A parameter script that runs without error and a one-page requirements table listing outputs and acceptance criteria.

2. 2

   Prepare drive-cycle data

   Import the IDC, MIDC and WLTP speed–time traces from CSV with readmatrix, convert km/h to m/s and resample to a uniform 0.1 s grid with interp1. Compute distance by cumtrapz and the maximum and mean speed of each cycle. Store each cycle as a timeseries object for a From Workspace block, or use the Powertrain Blockset Drive Cycle Source block for WLTP if you have it.

   Checkpoint: Computed distance, duration and maximum speed for each cycle match the published values within about 1 per cent.

3. 3

   Model the vehicle body

   In Simulink, build a subsystem that takes tractive force at the wheel and outputs speed. Compute rolling, aerodynamic and grade forces with Gain and Product blocks, sum them with the tractive force and divide by an equivalent mass that includes a rotating-inertia allowance of about 3–5 per cent. Integrate acceleration with an Integrator block whose lower limit is zero so the car cannot roll backwards on flat ground.

   Checkpoint: With a constant 500 N tractive force, the car accelerates and settles at the speed where drag plus rolling resistance equal 500 N, which you can check by hand.

4. 4

   Add motor and drivetrain

   Convert wheel speed to motor speed through the gear ratio. Limit commanded torque with a 1-D Lookup Table of maximum torque against speed (constant torque up to base speed, then constant power). Multiply torque by gear ratio and efficiency to get wheel force when motoring, and divide by efficiency when regenerating. Log motor torque, speed and mechanical power with signal logging.

   Checkpoint: A full-throttle run from standstill reaches the expected top speed and the torque trace follows the torque–speed envelope.

5. 5

   Add the driver controller

   Use a PID Controller block (PI form) acting on speed error to command a normalised torque between −1 and +1, with anti-windup by clamping. Add a feed-forward term from the road-load equation at the reference speed to reduce lag. Tune Kp and Ki on WLTP until the speed error stays small through the high-speed phase without oscillating at stops. Record the final gains in the parameter script so every later run uses the same driver.

   Checkpoint: Speed tracking error stays within ±2 km/h for most of each cycle, shown on a Simulation Data Inspector overlay of reference and actual speed.

6. 6

   Model battery energy

   Compute battery power as motor electrical power plus a constant auxiliary load (for example 300 W). Integrate power to energy and compute SOC from usable capacity. Limit regenerative power to a set value and add mechanical braking for the remainder. Use a fixed-step solver (ode4, 0.01 s) or a variable-step solver with a maximum step of 0.1 s; check that both give the same energy within 0.5 per cent.

   Checkpoint: Energy drawn on WLTP gives a consumption in a sensible range for the example car, roughly 130–180 Wh/km at the battery.

7. 7

   Verify the energy balance

   Log the energy dissipated by each road-load term, by drivetrain and motor losses, by mechanical braking and the kinetic energy at the end of the cycle. Sum them and compare with the net battery energy. Any mismatch above 1 per cent points to a sign error or a missing loss path. Repeat this check on all three cycles before drawing any conclusions.

   Checkpoint: An energy-balance table for each cycle that closes within 1 per cent.

8. 8

   Compare the three cycles

   Write a script that loops over cycles, sets the From Workspace variable, runs sim() and collects Wh/km, peak power, regen fraction and share of energy spent on each road-load term. Plot stacked bars of energy by term for IDC, MIDC and WLTP. Explain why aerodynamic drag dominates WLTP while inertia and rolling resistance dominate IDC. Keep the script generic so that a new cycle, such as a logged city route, can be added by dropping its CSV file into the cycles folder.

   Checkpoint: Stacked-bar plot and table for three cycles, with regen recovering a larger share of traction energy on the urban cycles than on WLTP.

9. 9

   Run sensitivity sweeps

   Use a Simulink.SimulationInput array to sweep mass (±20 per cent), CdA (±20 per cent) and Crr (±30 per cent), one factor at a time, and run them with sim() (or parsim if Parallel Computing Toolbox is available). Plot the percentage change in Wh/km against the percentage change in each parameter for each cycle. Compute an approximate sensitivity coefficient from the slope.

   Checkpoint: Sensitivity plots showing, for example, that drag area matters more on WLTP and mass matters more on IDC.

10. 10

    Report the results

    Write up the model equations, block diagrams, parameter table with sources, verification checks, cycle comparison and sensitivity results. Estimate range for the example 40 kWh pack using 90 per cent usable energy on each cycle and discuss why a single published range figure can mislead. State the limits: constant efficiencies, no thermal effects and a flat road unless grade is added.

    Checkpoint: A report with reproducible scripts, closed energy balances and range estimates for all three cycles.

Testing & validation

• Cycle distance and duration match the published cycle definitions.
• Constant-force and full-throttle tests agree with hand calculations.
• Energy balance closes within 1 per cent on every cycle.
• Results are insensitive to solver step size (less than 0.5 per cent change).
• Speed-tracking error stays within a stated band.

Expected results

A reusable Simulink longitudinal EV model with closed energy balances, a cycle-by-cycle comparison of consumption and regeneration on IDC, MIDC and WLTP, and sensitivity coefficients for mass, drag and rolling resistance.

Take it further

• Replace constant efficiencies with a motor efficiency map.
• Add a road-grade profile from a real route.
• Add an equivalent-circuit battery to see voltage sag and its effect on power limits.
• Compare the forward-facing result with a backward-facing QSS model of the same car.

Viva and review questions

Learn it at DIYguru

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