Fuel Consumption Model

The Fuel Consumption Model of the Parametric CO2MPAS is based on the Extended Willans Lines Model and is physically represented as follows:

, where:

Sources:

• Indicative Sources: L. Guzzela et al. Introduction to modelling and control of internal combustion engines, Second Edition, Springer
• A. Urlaub, Verbrennungsmotoren, Springer-Verlag, Berlin, Germany, 1994
• X. Wei, Modeling and control of a hybrid electric drivetrain for optimum fuel economy performance and driveability, PhD dissertation, Ohio State university, 2004
• Yuan Zou et al., Optimal Sizing and Control Strategy Design for Heavy Hybrid Electric Truck, Mathematical Problems in Engineering, Volume 2012, Article ID 404073

Inputs

Name	Units	Source / Comments	Parameter

Outputs

CO2 Emissions [g/sec] / co2_emissions

Source Code

Bellow the main raw python function is provided.

def calculate_co2_emissions(
        engine_speeds_out, engine_powers_out, mean_piston_speeds,
        brake_mean_effective_pressures, engine_coolant_temperatures, on_engine,
        engine_fuel_lower_heating_value, idle_engine_speed, engine_stroke,
        engine_capacity, engine_idle_fuel_consumption, fuel_carbon_content,
        params, sub_values=None):
    
    p = params.valuesdict()

    if sub_values is None:
        sub_values = np.ones_like(mean_piston_speeds, dtype=bool)

    # namespace shortcuts
    n_speeds = mean_piston_speeds[sub_values]
    n_powers = brake_mean_effective_pressures[sub_values]
    lhv = engine_fuel_lower_heating_value
    e_speeds = engine_speeds_out[sub_values]
    e_powers = engine_powers_out[sub_values]
    e_temp = engine_coolant_temperatures[sub_values]
    e_off = np.logical_not(on_engine[sub_values])

    fc = np.zeros_like(e_powers)

    # Idle fc correction for temperature
    b = (e_speeds < idle_engine_speed[0] + MIN_ENGINE_SPEED)

    if p['t'] == 0:
        n_temp = np.ones_like(e_powers)
        fc[b] = engine_idle_fuel_consumption
    else:
        n_temp = calculate_normalized_engine_coolant_temperatures(e_temp, p['trg'])
        fc[b] = engine_idle_fuel_consumption * np.power(n_temp[b], -p['t'])

    FMEP = partial(_calculate_fuel_mean_effective_pressure, p)

    b = np.logical_not(b)

    fc[b] = FMEP(n_speeds[b], n_powers[b], n_temp[b])[0]  # FMEP [bar]

    fc[b] *= e_speeds[b] * (engine_capacity / (lhv * 1200))  # [g/sec]

    ec_p0 = calculate_p0(
        p, engine_capacity, engine_stroke, sum(idle_engine_speed), lhv
    )
    b = (e_powers <= ec_p0) & (e_speeds > sum(idle_engine_speed))
    fc[b | (e_speeds < MIN_ENGINE_SPEED) | (fc < 0)] = 0

    co2 = fc * fuel_carbon_content

    return np.nan_to_num(co2)