Commission Implementing Decision of 10 March 2014 on the approval of the light emitting diodes low beam module ‘E-Light’ as an innovative technology for reducing CO2 emissions from passenger cars pursuant to Regulation (EC) No 443/2009 of the European Parliament and of the Council (Text with EEA relevance) (2014/128/EU)

4. Formulae

The following steps are to be taken to determine the CO₂ savings and to determine whether the threshold value of 1 g CO₂/km is met:

Step 1

:

Calculate the power savings;

Step 2

:

Calculate the CO₂ savings;

Step 3

:

Calculate the error in the CO₂ savings;

Step 4

:

Verify the threshold value.

4.1. Calculate the power savings

For each of the 10 measurements the power which is used is to be calculated by multiplying the installed voltage with the measured current. This is to result in 10 values. Each value is to be expressed in four decimals. Then the mean value of the used power is to be calculated, which is the sum of the 10 values for the power divided by 10.

The resulting power savings are to be calculated with the following formula:

Formula (1)

Where:

ΔP

:

Power savings in W;

P_baseline

:

Power of the baseline, which is 137 W;

P_{eco-innovation}

:

Mean value of the used power of the eco-innovation in W.

4.2. Calculate the CO₂ savings

The formulae to calculate the CO₂ savings of the eco-innovation are:

• For a petrol-fuelled vehicle:

  Formula (2)

• For a diesel-fuelled vehicle:

  Formula (3)

Where in these formulae CO₂ is the CO₂ savings in g CO₂/km.

The input data for the formulae (2) and (3) are:

ΔP

:

Saved electrical power in W, which is the result of step 1

UF

:

Usage factor which is 0,33 for a low beam lamp

v

:

mean driving speed of the NEDC, which is 33,58 km/h

V_Pe-P

:

consumption of effective power for petrol-fuelled vehicles, which is 0,264 1/kWh

V_Pe-D

:

consumption of effective power for diesel-fuelled vehicles, which is 0,22 1/kWh

ηΑ

:

efficiency of the alternator, which is 0,67

CF_P

:

conversion factor for petrol fuel, which is 2 330 g CO₂/l

CF_D

:

conversion factor for diesel fuel, which is 2 640 g CO₂/l

4.3. Calculate the statistical error in the CO₂ savings

The statistical error in the CO₂ savings is to be determined in two steps. In the first step the error value of the power is to be determined as a standard deviation being equivalent to a confidence interval of 68 %.

This is to be done by formula (4).

Formula (4)

Where:

:

standard deviation of arithmetic mean [W];

x_i

:

measurement value [W];

:

arithmetic mean [W];

n

:

number of measurements, which is 10.

Then the error in the CO₂ savings is to be determined using the propagation law, which is expressed in formula (5).

Formula (5)

Where:

ΔC_CO2 :

mean total error of the CO₂ saving (gCO₂/km)

∂ C_CO2 /∂P

sensitivity of calculated CO₂ saving related to input value x_i

eP_i:

error of input value (W)

Substituting formula (2) in formula (5) leads for petrol fueled vehicles to:

Formula (6)

Where:

ΔC_CO2

:

the error in the CO₂ savings (g CO₂/km);

eP

:

the error in the power consumption (W).

Substituting formula (2) in formula (5) leads for diesel fueled vehicles to:

Formula (7)

Where:

ΔC_CO2

:

the error in the CO₂ savings (g CO₂/km);

eP

:

error in the power consumption (W).

4.4. Verify the threshold value

By means of formula (8) the threshold value is verified. The minimum threshold value is 1,0 g CO₂/km.

Formula (8):

Where:

MT

:

minimum threshold (g CO₂/km)

C_CO2

:

total CO₂ saving (g CO₂/km), which must be expressed in 4 decimals,

:

mean total error of the CO₂ saving (g CO₂/km), which must be expressed in 4 decimals.