Modeling¶

This document describes the carculator model, assumptions and inventories as exhaustively as possible.

carculator is an open-source Python library. Its code is publicly available via its Github repository. You can also download an examples notebook, that guides new users into performing life cycle analyses. Finally, there is also an online graphical user interface available at https://carculator.psi.ch.

Overview of carculator modules¶

The main module model.py builds the vehicles and delegates the calculation of motive and auxiliary energy, noise, abrasion and exhaust emissions to satellite modules. Once the vehicles are fully characterized, the set of calculated parameters are passed to inventory.py which derives life cycle inventories and calculates life cycle impact indicators. Eventually, these inventories can be passed to export.py to be exported to various LCA software.

Vehicle modelling¶

The modelling of vehicles along powertrain types, time and size classes is described in this section. It is also referred to as foreground modelling.

Size classes¶

Originally, carculator defines nine size classes, namely: Micro, Mini, Small, Lower medium, Medium, Large, Medium SUV, Large SUV and Van, according to the following criteria, adapted from the work of [Christian and others, 2014] and shown in Table 1.

Example of Micro car (Microlino), Mini car (Smart) and Small/Compact car (VW Polo)

Example of Lower medium car (VW Golf), Medium car (Peugeot 408) and Large car (Tesla Model 3)

Example of Medium SUV car (Peugeot 2008), Large SUV car (Audi Q7) and Van (Fiat Ducato)

Manufacture year and emission standard¶

Several emission standards are considered. For simplicity, it is assumed that the vehicle manufacture year corresponds to the registration year, as shown in Table 2.

Size and mass-related parameters and modeling¶

The vehicle glider and its components (powertrain, energy storage, etc.) are sized according to engine power, which itself is conditioned by the curb mass of the vehicle. The curb mass of the vehicle is the sum of the vehicle components (excluding the driver and possible cargo) as represented in Figure 1.

This is an iterative process that stops when the curb mass of the vehicle converges, as illustrated in Figure 2.

Curb mass of the vehicle¶

This function calculates and sets the vehicle’s mass properties:

Curb mass: The mass of the vehicle and fuel, without people or cargo. Total cargo mass: The mass of the cargo and passengers. Driving mass: The sum of the curb mass and total cargo mass.

Function steps: 1. Set the curb mass as the product of the glider base mass and (1 - lightweighting). 2. Create a list of mass components to be included in the curb mass calculation. 3. Add the sum of these mass components to the curb mass. 4. If a target mass is provided, override the vehicle mass with the target mass. 5. Calculate the total cargo mass by summing the product of average passengers and average passenger mass, and the cargo mass. 6. Calculate the driving mass by adding the curb mass and total cargo mass.

With:

• \(m_{curb}\) being the vehicle curb mass, in kg

• \(m_{fuel}\) being the fuel mass, in kg

• \(m_{charger}\) being the electric onboard charge mass, in kg

• \(m_{conv}\) being the current converter, in kg

• \(m_{inv}\) being the current AC/DC inverter, in kg

• \(m_{distr}\) being the power distribution unit, in kg

• \(m_{comb}\) being the combustion engine mass, in kg

• \(m_{elec}\) being the electric motor mass, in kg

• \(m_{pwt}\) being the powertrain mass, in kg

• \(m_{fcstack}\) being the fuel cell stack mass, in kg

• \(m_{fcauxbop}\) being the fuel cell auxiliary components mass, in kg

• \(m_{battcell}\) being the battery cell mass, in kg

• \(m_{battbop}\) being the battery auxiliary components mass, in kg

• \(m_{fcessbop}\) being the fuel cell essential components mass, in kg

• \(m_{fueltank}\) being the fuel tank mass, in kg

For each iteration, the tank-to-wheel energy consumption (i.e., the motive energy minus any recuperated braking energy, together with the needed auxiliary energy to power onboard electronics) of the vehicle is calculated (i.e., to size the energy storage components, calculate the fuel consumption, etc.), as described later in this section.

Cargo and driving mass of the vehicle¶

The cargo mass of the vehicle is the sum of the cargo mass and the passenger mass.

Where:

• \(m_{cargo}\) is the cargo mass, in kg,

• and \(m_{passenger}\) is the passenger mass.

The driving mass of the vehicle is the sum of the curb mass and the cargo mass.

Where:

• \(m_{curb}\) is the curb mass, in kg,

• \(m_{cargo}\) is the cargo mass, in kg,

• and \(m_{driving}\) is the driving mass, in kg.

Light-weight rates¶

Because the LCI dataset used to represent the glider of the vehicle is not representative of today’s’ use of light-weighting materials, such as aluminium (i.e., the dataset “glider for passenger cars” only contains 0.5% of its mass in aluminium) and advanced high strength steel (AHSS), an amount of such light-weighting materials is introduced to substitute conventional steel and thereby reduce the mass of the glider.

As further explained under the Curb mass calibration section, the mass of the glider is reduced by replacing steel with a mix of aluminium and AHSS. Hence, the amounts of light weighting materials introduced depend on the rate of glider light weighting in 2020 relative to 2000 (approximately 11% for combustion engine vehicles). The amount of aluminium introduced is further cross-checked with the amounts indicated in [Frontier, 2019] and listed in Table 3, and comes in addition to the aluminium already contained in the LCI datasets for the engine and transmission.

These light-weighting rates have been fine adjusted to match the curb mass of a given size class, while preserving the battery capacity. For example, in the case of the Large SUV, its curb mass should approximately be 2’200 kg, with an 80 kWh battery weighting 660 kg (e.g., Jaguar i-Pace). This is possible with a 30% light weighting rate, introducing approximately 460 kg of aluminium in the chassis (which matches roughly with the value given for an Audi e-Tron in Table 3) and 1’008 kg of AHSS, in lieu of 2’034 kg of regular steel.

Curb mass calibration¶

The final curb mass obtained for each vehicle is calibrated against the European Commission’s database for CO₂ emission tests for passenger cars (hereafter called EC-CO2-PC) using the NEDC/WLTP driving cycles [Commission, 2021]. Each vehicle registered in the European Union is tested and several of the vehicle attributes are registered (e.g., dimension, curb mass, driving mass, CO₂ emissions, etc.). This has represented about 15+ million vehicles per year for the past five years.

The figure below shows such calibration for the years 2010, 2013, 2016, 2018, 2019 and 2020 – to be representative of EURO-4, -5, 6 a/b, 6-c and 6-d-temp vehicles. No measurements are available for 2003 (EURO-3) or 2021 (EURO-6-d). After cleaning the data from the EC-CO2-PC database, it represents 27 million points to calibrate the curb mass of the vehicles with. Green vertical bars represent the span of 50% of the curb mass distribution, and the red dots are the curb mass values modeled by carculator.

Table 4 shows the mass distribution for gasoline and battery electric passenger cars resulting from the calibration. Mass information on other vehicles is available in the vehicles’ specifications spreadsheet. These numbers may change if the default input values (i.e., engine power, fuel tank size, etc.) are changed.

Energy consumption¶

The energy consumption model of carculator calculates the energy required at the wheels by considering different types of resistance. Some of these resistances are related to the vehicle size class. For example, the frontal area of the vehicle influences the aerodynamic drag. Also, the kinetic energy to overcome the vehicle’s inertia is influenced by the mass of the vehicle (which partially correlates to with the size class or body type), but also by the acceleration required by the driving cycle. Other resistances, such as the climbing effort, are instead determined by the driving cycle (but the vehicle mass also plays a role here).

Here is how the different types of resistance are calculated:

1. Rolling resistance:

   F_rolling (N) = driving_mass (kg) * rr_coef (dimensionless) * g (m/s^2) * (velocity (m/s) > 0)

2. Air resistance:

   F_air (N) = 0.5 * rho_air (kg/m^3) * drag_coef (dimensionless) * frontal_area (m^2) * velocity^2 (m^2/s^2)

3. Gradient resistance:

   F_gradient (N) = driving_mass (kg) * g (m/s^2) * sin(gradient (radians)) * (velocity (m/s) > 0)

4. Inertia:

   F_inertia (N) = driving_mass (kg) * acceleration (m/s^2)

5. Total resistance:

   F_total (N) = F_rolling (N) + F_air (N) + F_gradient (N) + F_inertia (N)

6. Motive energy at wheels:

   E_wheels (J) = max(F_total (N), 0)

7. Motive energy:

   E_motive (Wh) = E_wheels (J) / engine_efficiency (dimensionless) / transmission_efficiency (dimensionless) / fuel_cell_system_efficiency (dimensionless) * 2.778e-4 (Wh/J)

8. Recuperated energy:

   F_rolling (N) = driving_mass (kg) * rr_coef (dimensionless) * g (m/s^2) * (velocity (m/s) > 0)

9. Auxiliary energy:

   E_aux = aux_energy (Wh/km) = aux_power (W) + (p_cooling (W) / heat_pump_cop_cooling (dimensionless) * cooling_consumption (Wh/km)) + (p_heating (W) / heat_pump_cop_heating (dimensionless) * heating_consumption (Wh/km)) + p_battery_cooling (W) + p_battery_heating (W)

In this representation, E_motive represents the motive energy per kilometer driven, E_recuperated represents the energy recuperated per kilometer driven, and E_aux represents the auxiliary energy consumption per kilometer driven. The results are returned in kilojoules/km (kJ/km).

Once the energy required at the wheels is known, the model goes on to calculate the energy required at the tank level by considering additional losses along the drive train (i.e., axles, gearbox, and engine losses – see Engine and transmission efficiency). The different types of resistance considered are depicted in Figure 4, and the module calculation workflow is presented in Figure 5.

Powertrains that are partially or fully electrified have the possibility to recuperate a part of the energy spent for propulsion during deceleration or braking. The round-trip battery energy loss (which is the sum of the charge and discharge battery loss, described in Figure 4) is subtracted from the recuperated energy. For hybrid vehicles (i.e., HEV-p, HEV-d), this allows to downsize the combustion engine and improve the overall tank-to-wheel efficiency, as explained in [Brian and others, 2020].

Finally, for each second of the driving cycle, the auxiliary power load is considered. It comprises an auxiliary base power load (i.e., to operate onboard electronics), as well as the power load from heating and cooling. While electric vehicles provide energy from the battery to supply heating and cooling (i.e., thereby decreasing the available energy available for traction), combustion vehicles recover enough waste engine heat to supply adequate heating. The values considered for the auxiliary base power load and for the power load for heating and cooling are presented in Table 5. These values are averaged over the whole year, based on maximum demand and share of operation.

Where:

• \(P_{base}\) is the auxiliary base power load [W],

• \(P_{heating}\) is the power load for heating [W],

• \(P_{cooling}\) is the power load for cooling [W],

• \(D_{heating}\) is the demand for heating [0-1] (=0 for non-electric vehicles),

• and \(D_{cooling}\) is the demand for cooling [0-1].

To convert it into an energy consumption \(F_{aux}\) [kj/km], the auxiliary power load is multiplied by the time of the driving cycle and divided by the distance driven:

Where: \(T\) is the driving cycle time [seconds] and D is the distance [m].

A driving cycle is used to calculate the tank-to-wheel energy required by the vehicle to drive over one kilometer. For example, the WLTC driving cycle comprises a mix of urban, sub-urban and highway driving. It is assumed representative of average Swiss and European driving profile - although this would likely differ in the case of intensive mountain driving.

Figure 6 exemplifies such calculation for a medium battery electric passenger car manufactured in 2020, using the WLTC driving cycle.

So, the tank-to-wheel energy consumption \(F_{ttw}\) is the sum of the motive energy and the energy required to power auxiliary equipment. It is calculated as:

Where:

• \(F_{motive}\) is the motive energy,

• and \(F_{aux}\) is the auxiliary energy.

There are no fuel consumption measurements available for fuel cell vehicles. Values found in the literature and from manufacturers data are used to approximate the engine and transmission efficiency and to calibrate the final energy consumption.

Engine and transmission efficiency¶

Engine and transmission efficiencies for the conventional gasoline, diesel and electric powertrains (including fuel cell electric powertrains) are defined as a function of the utilized engine power for each second of the driving cycle (i.e., the power load over the rated power output of the engine). Such relation is shown in Hjelkrem et al. 2020 [Hjelkrem et al., 2020]. Unfortunately, such relation is not given for compressed gas powertrains, which we assume to be 17.5% less efficient than diesle powertrains [JEC Well-to-Wheels report v5: Well-to-Wheels analysis of future automotive fuels and powertrains in the European context, 2020]. The specific values for engine and transmission efficiency in relation to utilized power can be consulted here . Hjelkrem et al. 2020 [Hjelkrem et al., 2020] only give the overall tank-to-wheel efficiency, which we decompose, assuming a static transmission efficiency and a varying engine efficiency (the product of which gives the tank-to-wheel efficiency).

For diesel and gasoline hybrid vehicles, the approach to estimating the engine and transmission efficiencies is similar, but a small electric motor allows for energy recuperation and reducing the engine size, which leads to higher efficiency levels. The amount of energy recuperated is determined by the driving cycle as well as the round-trip efficiency between the wheels and the engine and cannot be superior to the power output of the engine. Further on, the share of recuperated energy over the total negative motive energy (i.e., the braking or deceleration energy) is used as a discounting factor for brake wear particle emissions.

Electric energy storage¶

Battery electric vehicles can use different battery chemistry (Li-ion NMC, Li-ion LFP, Li-ion NCA and Li-LTO) depending on the manufacturer’s preference or the location of the battery supplier. Unless specified otherwise, all battery types are produced in China, as several sources, among which BloombergNEF [Henze, 2020], seem to indicate that more than 75% of the world’s cell capacity is manufactured there.

Accordingly, the electricity mix used for battery cells manufacture and drying, as well as the provision of heat are assumed to be representative of the country (i.e., the corresponding providers are selected from the LCI background database).

The battery-related parameters considered in carculator for 2020 are shown in Table 6. For LFP batteries, “blade battery” or “cell-to-pack” battery configurations are considered, as introduced by CATL [Xinhua, 2019] and BYD [Mark, 2020], two major LFP battery suppliers in Asia. This greatly increases the cell-to-pack ratio and the gravimetric energy density at the pack level.

Overall, the gravimetric energy density values at the cell and system levels presented in Table 6 are considered conservative: some manufacturers perform significantly better than the average, and these values tend to change rapidly over time, as it is being the focus of much R&D. Hence, by 2050, the gravimetric energy density of NMC and NCA cells are expected to reach 0.5 kWh/kg, while that of LFP cells plateaus at 0.15 kWh/kg (but benefits from a high cell-to-pack ratio)..

On account that:

• the battery cycle life values were obtained in the context of an experiment [Yuliya and others, 2020],

• with loss of 20% of the initial capacity, the battery may still provide enough energy to complete the intended route, cycle life values for NMC and NCA battery chemistry are corrected by +50%.

Table 7 gives an overview of the number of battery replacements assumed for the different battery electric vehicles in carculator.

Users are encouraged to test the sensitivity of end-results on the number of battery replacements.

The number of battery replacement is calculated as follows:

Where:

• \(L_{veh}\) is the lifetime of the vehicle [km],

• and \(L_{batt}\) is the lifetime of the battery [km].

Liquid and gaseous energy storage¶

The energy stored in the fuel (oxidation energy stored), the mass of the fuel tank for diesel, gasoline and compressed gas vehicles are calculated. Here are the formulas and units used:

Calculate oxidation energy stored:

Oxidation energy stored (MWh) = fuel mass (kg) * LHV fuel (MJ/kg) / 3.6

Calculate fuel tank mass for liquid fuels:

Fuel tank mass (kg) = oxidation energy stored (MWh) * fuel tank mass per energy (kg/MWh)

Calculate fuel tank mass for compressed natural gas:

Fuel tank mass (kg) = oxidation energy stored (MWh) * CNG tank mass slope + CNG tank mass intercept

The set_energy_stored_properties function calculates the oxidation energy stored in the fuel, based on the fuel mass and the lower heating value (LHV) of the fuel. The fuel mass (in kilograms) is multiplied by the LHV fuel (in megajoules per kilogram), and the result is divided by 3.6 to convert the energy to megawatt-hours (MWh).

Next, the function calculates the mass of the fuel tank by multiplying the oxidation energy stored (in MWh) by the fuel tank mass per energy (in kilograms per MWh).

Lastly, if the powertrain is an ICEV-g, the function adjusts the fuel tank mass based on the oxidation energy stored and the coefficients for the CNG tank mass slope and intercept.

Fuel cell stack¶

All fuel cell electric vehicles use a proton exchange membrane (PEM)-based fuel cell system.

Table 8 lists the specifications of the fuel cell stack and system used in carculator in 2020. The durability of the fuel cell stack, expressed in hours, is used to determine the number of replacements needed - the expected kilometric lifetime of the vehicle as well as the average speed specified by the driving cycle gives the number of hours of operation. The environmental burden associated with the manufacture of spare fuel cell systems is entirely allocated to vehicle use as no reuse channels seem to be implemented for fuel cell stacks at the moment.

The fuel cell system efficiency \(r_{fcsys}\) is calculated as:

Where:

• \(r_{fcstack}\) is the fuel cell stack efficiency [%],

• and \(r_{fcown}\) is the rate of auto consumption [%].

For reference, the rate of auto-consumption in 2020 for a fuel cell system is 15% (i.e., 15% of the power produced by the fuel cell system is consumed by it).

The fuel cell system power \(P_{fcsys}\) is calculated as:

Where:

• \(P_{veh}\) is the vehicle engine power

• and \(r_{fcshare}\) is the fuel cell system power relative to the vehicle engine power [%].

Finally, the fuel cell stack mass is calculated as:

Where:

• \(P_{fcsys}\) is the fuel cell system power [kW],

• \(A_{fc}\) is the fuel cell fuel cell power area density [kW/cm2],

• and \(m_{fcstack}\) is the fuel cell stack mass [kg].

The battery power is calculated as:

Where:

• \(P_{fcsys}\) is the fuel cell system power [kW],

• and \(r_{fcshare}\) is the fuel cell system power share [%].

The number of fuel cell replacements is based on the average distance driven with a set of fuel cells given their lifetime expressed in hours of use. The number is replacement is rounded up as we assume no allocation of burden with a second life. It is hence is calculated as:

Where:

• \(L_{veh}\) is the lifetime of the vehicle [km],

• \(V_{avg}\) is the average speed of the driving cycle selected [km/h],

• and \(L_{fc}\) is the fuel cell lifetime in hours [h].

Light-weighting¶

The automotive industry has been increasingly using light weighting materials to replace steel in engine blocks, chassis, wheels rims and powertrain components [Frontier, 2019]. However, vehicles light weighting has not led to an overall curb mass reduction for passenger cars and trucks, as additional safety equipment compensate for it. According to [Mock, 2017], passenger cars in the EU in 2016 were on average 10% heavier than in 2000.

The dataset used to represent the chassis of passenger cars (i.e., “glider, for passenger car”) does not reflect today’s use of light weighting materials, such as aluminium and advanced high strength steel (AHSS).

A report from the Steel Recycling Institute [Sebastian and Thimons, 2017] indicates that every kilogram of steel in a car glider can be substituted by 0.75 kilogram of AHSS or 0.68 kilogram of aluminium. Looking at the material composition of different car models three years apart, [Troy and others, 2017] show that steel is in fact increasingly replaced by a combination of both aluminium and AHSS. However, they also show that the use of AHSS is generally preferred to aluminium as its mass reduction-to-cost ratio is preferable.

Hence, it is considered that, for a given mass reduction to reach, two-third of the mass reduction comes from using AHSS, and one third comes from using aluminium. This means that one kilogram of mass reduction is achieved by replacing 3.57 kilogram of steel by:

• 1.76 kilogram of AHSS

• 0.8 kilogram of aluminium

Additionally, additional efforts is made to ensure that the final aluminium content in the chassis corresponds to what is actually found in current passenger car models, according to [Frontier, 2019].

While ecoinvent v.3.8 has a LCI dataset for the supply of aluminium, it is not the case for AHSS. However, an LCA report from the World Steel Institute [Association, 2015] indicates that AHSS has a similar carbon footprint than conventional primary low-alloyed steel from a basic oxygen furnace route (i.e., 2.3 kg CO₂-eq./kg). We therefore use conventional steel to represent the use of AHSS.

The amount of light-weighting obtained from the use of light-weighting materials is:

\(\Delta m_{glider} = m_{glider} \times r_{lightweighting}\)

Where:

• \(\Delta m_{steel}\) is the mass reduction of the glider [kg],

• and \(r_{lightweighting}\) is the light-weighting ratio [%].

Sizing of onboard energy storage¶

Sizing of battery¶

The sizing of batteries for battery electric vehicles is conditioned by the battery mass, which is defined as an input parameter for each size class. The battery masses given for the different size classes are presented in Figure 9 using the battery chemistry NMC, and is based on representative battery storage capacities available today on the market - which are represented in relation to the curb mass. The data is collected from the vehicle’s registry of Touring Club Switzerland.

Seventy percent of the overall battery mass is assumed to be represented by the battery cells in the case of NMC and NCA batteries. Given the energy density of the battery cell considered, this yields the storage capacity of the battery. A typical depth of discharge of 80% is used to calculate the available storage capacity.

Hence, the battery cell mass is calculated as:

Where:

• \(m_{pack}\) is the mass of the pack,

• and \(s_{cell}\) is the cell-to-pack ratio.

And the electricity stored in the battery is calculated as:

Where:

• \(E_{battery}\) being battery capacity [kWh],

• \(C_{cell}\) is the cell energy density [kg/kWh],

• and \(m_{cell}\) is the cell mass [kg].

By deduction, the balance of plant mass is:

Where:

• \(m_{battery}\) is the mass of the battery [kg],

• and \(m_{cell}\) is the cell mass [kg].

Finally, the range autonomy is calculated as:

Where:

• \(C_{battery}\) is the battery capacity [kWh],

• \(r_{discharge}\) is the discharge depth [%],

• and \(F_{ttw}\) is the tank-to-wheel energy consumption [kWh/km].

Similarly, plug-in hybrid vehicles are dimensioned to obtain an energy storage capacity of the battery that corresponds with the capacity of models available today. The sizing of the battery is similar to what is described above for battery electric vehicles. The energy storage capacity of the battery is particularly important for plugin hybrid vehicles, as it conditions the electric utility factor (the share of kilometers driven in battery-depleting mode) which calculation is described in the next section.

Electric utility factor¶

Diesel and gasoline plugin hybrid vehicles are modeled as a composition of an ICE vehicle and a battery electric vehicle to the extent determined by the share of km driven in battery-depleting mode (also called “electric utility factor”). This electric utility factor is calculated based on a report from the ICCT [Patrick and others, 2020], which provides measured electricity utility factors for 6’000 PHEV private owners in Germany in relation to the vehicle range in battery-depleting mode.

A first step consists in determining the energy consumption of the PHEV in electric mode as well as its battery size, in order to know its range autonomy. When the range autonomy is known, the electric utility factor is interpolated based on the data presented in Table 11.

Once the electric utility factor \(U\) is known, it is used as a partitioning ratio to compose the vehicle between the PHEV in combustion mode, and the PHEV in electric mode, where:

Where:

• \(F_{ttw_phev_e}\) is the tank-to-wheel energy consumption [kWh/km] of the electric PHEV,

• \(F_{ttw_phev_c}\) is the tank-to-wheel energy consumption [kk/km] of the combustion PHEV,

• \(m_{curb_phev_e}\) is the curb weight [kg] of the electric PHEV,

• and \(m_{curb_phev_c}\) is the curb weight [kg] of the combustion PHEV.

Inventory modelling¶

Once the vehicles are modeled, the calculated parameters of each of them is passed to the inventory.py calculation module to derive inventories. When the inventories for the vehicle and the transport are calculated, they can be normalized by the kilometric lifetime (i.e., vehicle-kilometer) or by the kilometric multiplied by the passenger occupancy (i.e., passenger-kilometer).

Road demand¶

The demand for construction and maintenance of roads and road-related infrastructure is calculated on the following basis:

• Road construction: 5.37e-7 meter-year per kg of vehicle mass per km.

• Road maintenance: 1.29e-3 meter-year per km, regardless of vehicle mass.

The driving mass of the vehicle consists of the mass of the vehicle in running condition (including fuel) in addition to the mass of passengers and cargo, if any. Unless changed, the passenger mass is 75 kilograms, and the average occupancy is 1.6 persons per vehicle.

The demand rates used to calculate the amounts required for road construction and maintenance (based on vehicle mass per km and per km, respectively) are taken from [Spielmann and Scholz, 2005].

Because roads are maintained by removing surface layers older than those that are actually discarded, road infrastructure disposal is modeled in ecoinvent as a renewal rate over the year in the road construction dataset.

Vehicle maintenance¶

The modelling of the maintenance life.cycle phase is simple. It is based on the ecoinvent’s dataset for the maintenance of a 1,250 kg gasoline-run VW Golf IV. carculator simply normalize the input requirements per kg of vehicle to maintain, and multiply them by the vehicle mass.

Fuel properties¶

For all vehicles with an internal combustion engine, carbon dioxide (CO₂) and sulfur dioxide (SO₂) emissions are calculated based on the fuel consumption of the vehicle and the carbon and sulfur concentration of the fuel observed in Switzerland and Europe. Sulfur concentration values are sourced from HBEFA 4.1 [Benedikt and others, 2019]. Lower heating values and CO₂ emission factors for fuels are sourced from p.86 and p.103 of [for the Environment, 2021]. The fuel properties shown in Table 12 are used for fuels purchased in Switzerland.

Because large variations are observed in terms of sulfur concentration in biofuels, similar values than that of conventional fuels are used.

Exhaust emissions¶

Emissions of regulated and non-regulated substances during driving are approximated using emission factors from HBEFA 4.1 [Benedikt and others, 2019]. Emission factors are typically given in gram per km. Emission factors representing free flowing driving conditions and urban and rural traffic situations are used. Additionally, cold start emissions as well as running, evaporation and diurnal losses are accounted for, also sourced from HBEFA 4.1 [Benedikt and others, 2019].

For vehicles with an internal combustion engine, the sulfur concentration values in the fuel can slightly differ across regions - although this remains rather limited within Europe. The values provided by HBEFA 4.1 are used for Switzerland, France, Germany, Austria and Sweden. For other countries, values from [Miller and Jin, 2019] are used.

The amount of sulfur dioxide released by the vehicle over one km [kg/km] is calculated as:

Where:

• \(r_{S}\) is the sulfur content per kg of fuel [kg SO2/kg fuel],

• \(F_{fuel}\) is the fuel consumption of the vehicle [kg/km],

• and \(64/32\) is the ratio between the molar mass of SO2 and the molar mass of O2.

Country-specific fuel blends are sourced from the IEA’s Extended World Energy Balances database [(IEA), 2021]. By default, the biofuel used is assumed to be produced from biomass residues (i.e., second-generation fuel): fermentation of crop residues for bioethanol, esterification of used vegetable oil for biodiesel and anaerobic digestion of sewage sludge for bio-methane.

A number of fuel-related emissions other than CO₂ and SO₂ are considered, using the HBEFA 4.1 database [Benedikt and others, 2019].

Six sources of emissions are considered:

• Exhaust emissions: emissions from the combustion of fuel during operation. Their concentration relates to the fuel consumption and the emission standard of the vehicle.

• Cold start emissions: emissions when starting the engine. The factor is given in grams per engine start. 2.3 engine starts per day are considered [for the Environment, 2021] and an annual mileage of 12’000 km.

• Diurnal emissions: evaporation of the fuel due to a temperature increase of the vehicle. The factor is given in grams per day. Emissions are distributed evenly along the driving cycle, based on an annual mileage of 12’000 km per year.

• Hot soak emissions: evaporative emissions occurring after the vehicle has been used. The factor is given in grams per trip. The emission is added at the end of the driving cycle.

• In addition, running loss emissions: emissions related to the evaporation of fuel (i.e., not combusted) during operation. The factor is given in grams per km. Emissions are distributed evenly along the driving cycle.

• Other non-exhaust emissions: brake, tire road wear and re-suspended road dust emissions, as well as emissions of refrigerant.

For exhaust emissions, factors based on the fuel consumption are derived by comparing emission data points for different traffic situations (i.e., grams emitted per vehicle-km) for in a free flowing driving situation, with the fuel consumption corresponding to each data point (i.e., MJ of fuel consumed per km), as illustrated in Figure 11 for a diesel-powered engine. The aim is to obtain emission factors expressed in grams of substance emitted per MJ of fuel consumed, to be able to model emissions of passenger cars of different sizes and fuel efficiency and for different driving cycles.

Hence, the emission of substance i at second s of the driving cycle is calculated as follows:

Where:

• \(E(i,s)\) is the emission of substance i at second s of the driving cycle,

• \(F_ttw(s)\) is the fuel consumption of the vehicle at second s,

• and \(X(i, e)\) is the emission factor of substance i in the given driving conditions.

To that, we add the following terms:

• Cold start emissions on the first second of the driving cycle

• Evaporation emissions: on the last second of the driving cycle

• Diurnal and running losses: distributed evenly over the driving cycle

However, as Figure 11 shows, the relation between amounts emitted and fuel consumption is not always obvious and using a linear relation between amounts emitted and fuel consumption can potentially be incorrect. In addition, emissions of ammonia (NH₃) and Nitrous oxides (N₂O) seem to be related to the emission standard (e.g., use of urea solution) and engine temperature rather than the fuel consumption.

To confirm that such approach does not yield kilometric emissions too different from the emission factors per vehicle-kilometer proposed by HBEFA 4.1, Figure 12 compares the emissions obtained by carculator using the WLTC driving cycle over 1 vehicle-km (red dots) with the distribution of the emission factors for different traffic situations (green box-and-whiskers) as well as the traffic situation-weighted average emission factor (yellow dots) given by HBEFA 4.1 for different emission standards for a medium diesel-powered passenger car.

There is some variation across traffic situations, but the emissions obtained remain, for most substances, within the 50% of the distributed HBEFA values across traffic situations. Also, the distance between the modeled emission and the traffic-situation-weighted average is reasonable.

NMHC speciation¶

After NMHC emissions are quantified, EEA/EMEP’s 2019 Air Pollutant Emission Inventory Guidebook provides factors to further specify some of them into the substances listed in Table 16.

Non-exhaust emissions¶

A number of emission sources besides exhaust emissions are considered. They are described in the following sub-sections.

Engine wear emissions¶

Metals and other substances are emitted during the combustion of fuel because of engine wear. These emissions are scaled based on the fuel consumption, using the emission factors listed in Table 17, sourced from [Agency, 2019].

Abrasion emissions¶

We distinguish four types of abrasion emissions, besides engine wear emissions:

• brake wear emissions: from the wearing out of brake drums, discs and pads

• tires wear emissions: from the wearing out of rubber tires on the asphalt

• road wear emissions: from the wearing out of the road pavement

and re-suspended road dust: dust on the road surface that is re-suspended as a result of passing traffic, “due either to shear forces at the tire/road surface interface, or air turbulence in the wake of a moving vehicle” [Beddows and Harrison, 2021].

[Beddows and Harrison, 2021] provides an approach for estimating the mass and extent of these abrasion emissions. They propose to disaggregate the abrasion emission factors presented in the EMEP’s 2019 Emission inventory guidebook [Agency, 2019] for two-wheelers, passenger cars, buses and heavy good vehicles, to re-quantify them as a function of vehicle mass, but also traffic situations (urban, rural and motorway). Additionally, they present an approach to calculate re-suspended road dust according to the method presented in [EPA, 2011] - such factors are not present in the EMEP’s 2019 Emission inventory guidebook - using representative values for dust load on European roads.

The equation to calculate brake, tire, road and re-suspended road dust emissions is the following:

With:

• \(EF\) being the emission factor, in mg per vehicle-kilometer

• \(W\) being the vehicle mass, in tons

• \(b\) and \(c\) being regression coefficients, whose values are presented in Table 18.

The respective amounts of brake and tire wear emissions in urban, rural and motorway driving conditions are weighted, to represent the driving cycle used. The weight coefficients sum to 1 and the coefficients considered are presented in Table 19. They have been calculated by analyzing the speed profile of each driving cycle, with the exception of two-wheelers, for which no driving cycle is used (i.e., the energy consumption is from reported values) and where simple assumptions are made in that regard instead.

Finally, for electric and (plugin) hybrid vehicles, the amount of brake wear emissions is reduced. This reduction is calculated as the ratio between the sum of energy recuperated by the regenerative braking system and the sum of negative resistance along the driving cycle. The logic is that the amount of negative resistance that could not be met by the regenerative braking system needs to be met with mechanical brakes. This is illustrated in Figure 13, where the distance between the recuperated energy and the total negative motive energy corresponds to the amount of energy that needs to be provided by mechanical brakes. Table 20 lists such reduction actors for the different powertrains.

The sum of PM 2.5 and PM 10 emissions is used as the input for the ecoinvent v.3.x LCI datasets indicated in Table 21.

Finally, we assume that the composition of the re-suspended road dust is evenly distributed between brake, road and tire wear particles.

Figure 14 shows the calculated abrasion emissions for passenger cars in mg per vehicle-kilometer, following the approach presented above.

Re-suspended road dust emissions are assumed to be evenly composed of brake wear (33.3%), tire wear (33.3%) and road wear (33.3%) particles.

Refrigerant emissions¶

The use of refrigerant for onboard air conditioning systems is considered for passenger cars until 2021. The supply of refrigerant gas R134a is accounted for. Similarly, the leakage of the refrigerant is also considered. For this, the calculations from [P. and others, 2016] are used. Such emission is included in the transportation dataset of the corresponding vehicle. The overall supply of refrigerant amounts to the initial charge plus the amount leaked throughout the lifetime of the vehicle, both listed in Table 22 This is an important aspect, as the refrigerant gas R134a has a Global Warming potential of 2’400 kg CO₂-eq./kg released in the atmosphere.

Noise emissions¶

Noise emissions along the driving cycle of the vehicle are quantified using the method developed within the CNOSSOS project [Kephalopoulos and others, 2012], which are expressed in joules, for each of the 8 octaves. Rolling and propulsion noise emissions are quantified separately.

The sound power level of rolling noise is calculated using:

With:

• \(v_m\) being the instant speed given by the driving cycle, in km/h

• \(v_{ref}\) being the reference speed of 70 km/h

• and \(A_{P,i,m}\) and \(B_{P,i,m}\) are unit-less and given in Table 23.

The propulsion noise level is calculated using:

With:

• \(v_m\) being the instant speed given by the driving cycle, in km/h

• \(v_{ref}\) being the reference speed of 70 km/h

• and \(A_{P,i,m}\) and \(B_{P,i,m}\) are unit-less and given in Table 23.

A correction factor for battery electric and fuel cell electric vehicles is applied, and is sourced from [Pallas and others, 2016]. Also, electric vehicles are added a warning signal of 56 dB at speed levels below 20 km/h. Finally, hybrid vehicles are assumed to use an electric engine up to a speed level of 30 km/h, beyond which the combustion engine is used.

The total noise level (in A-weighted decibels) is calculated using the following equation:

The total sound power level is converted into Watts (or joules per second), using the following equation:

The total sound power, for each second of the driving cycle, is then distributed between the urban, suburban and rural inventory emission compartments.

Figure 15 illustrates a comparison of noise levels between an ICEV and BEV as calculated by the tool, over the driving cycle WLTC. In this figure, the noise levels at different frequency ranges have been summed together to obtain a total noise level (in dB), and converted to dB(A) using the A-weighting correction factor, to better represent the “loudness” or discomfort to the human ear. Typically, propulsion noise emissions dominate in urban environments (which corresponds to the Road demand section of the driving cycle), thereby justifying the use of electric vehicles in that regard. This is represented by the difference between the ICEV and BEV lines in the Road demand section of the driving cycle in Figure 15. The difference in noise level between the two powertrains diminishes at higher speed levels (see Fuel properties, Exhaust emissions and Non-exhaust emissions) as rolling noise emissions dominate above a speed level of approximately 50 km/h. This can be seen in Figure 16, which sums up the sound energy produced, in joules, over the course of the driving cycle.

The study from [Stefano and others, 2019] provides compartment-specific noise emission characterization factors against midpoint and endpoint indicators - expressed in Person-Pascal-second and Disability-Adjusted Life Year, respectively.

Electricity mix calculation¶

Electricity supply mix are calculated based on the weighting from the distribution the lifetime kilometers of the vehicles over the years of use. For example, should a BEV enter the fleet in Poland in 2020, most LCA models of passenger vehicles would use the electricity mix for Poland corresponding to that year, which corresponds to the row of the year 2020 in Table 24, based on ENTSO-E’s TYNDP 2020 projections (National Trends scenario) [ENTSO-E, 2020]. carculator calculates instead the average electricity mix obtained from distributing the annual kilometers driven along the vehicle lifetime, assuming an equal number of kilometers is driven each year. Therefore, with a lifetime of 200,000 km and an annual mileage of 12,000 kilometers, the projected electricity mixes to consider between 2020 and 2035 for Poland are shown in Table 24. Using the kilometer-distributed average of the projected mixes between 2020 and 2035 results in the electricity mix presented in the last row of Table 24. The difference in terms of technology contribution and unitary GHG-intensity between the electricity mix of 2020 and the electricity mix based on the annual kilometer distribution is significant (-23%). The merit of this approach ultimately depends on whether the projections will be realized or not.

It is also important to remember that the unitary GHG emissions of each electricity-producing technology changes over time, as the background database ecoinvent has been transformed by premise [Sacchi and others, 2022]: for example, photovoltaic panels become more efficient, as well as some of the combustion-based technologies (e.g., natural gas). For more information about the transformation performed on the background life cycle database, refer to [Sacchi and others, 2022].

Life cycle inventory modelling¶

Once the vehicles are specified, the material and energy inputs and emission outputs occuring throughout the different phases of their life-cycle are linked to life-cycle assessment datasets. Those are either sourced from the literature, or from the life-cycle assessment database ecoinvent.

The table below shows the correspondence between vehicle components and the life-cycle assessment datasets used.

Component Concerns Dataset name Source Glider All market for glider, passenger car ecoinvent Lightweighting material All

Inventories for fuel pathways¶

A number of inventories for fuel production and supply are used by carculator. They represent an update in comparison to the inventories used in the passenger vehicles model initially published by [Brian and others, 2020]. The fuel pathways presented in Table 25 are from the literature and not present as generic ecoinvent datasets.

Inventories for energy storage components¶

The source for the inventories used to model energy storage components are listed in Table 26.

Life cycle impact assessment¶

To build the inventory of every vehicle, carculator populates a three-dimensional array A (i.e., a tensor) such as:

The second and third dimensions (i.e., M and N) have the same length. They correspond to product and natural flow exchanges between supplying activities (i.e., M) and receiving activities (i.e., N). The first dimension (i.e., L) stores model iterations. Its length depends on whether the analysis is static or if an uncertainty analysis is performed (e.g., Monte Carlo).

Given a final demand vector f (e.g., 1 kilometer driven with a specific vehicle, represented by a vector filled with zeroes and the value 1 at the position corresponding to the index j of the driving activity in dimension M) of length equal to that of the second dimension of A (i.e., M), carculator calculates the scaling factor s so that:

Finally, the scaling factor s is multiplied with a characterization matrix B. This matrix contains midpoint characterization factors for a number of impact assessment methods (as rows) for every activity in A (as columns).

As described earlier, the tool chooses between several characterization matrices B, which contain pre-calculated values for activities for a given year, depending on the year of production of the vehicle as well as the REMIND climate scenario considered (i.e., “SSP2-Baseline”, “SSP2-PkBudg1150” or “SSP2-PkBudg500”). Midpoint and endpoint (i.e., human health, ecosystem impacts and resources use) indicators include those of the ReCiPe 2008 v.1.13 impact assessment method, as well as those of ILCD 2018. Additionally, it is possible to export the inventories in a format compatible with the LCA framework Brightway2 or SimaPro, thereby allowing the characterization of the results against a larger number of impact assessment methods.

Presentation of results¶

Life-cycle impacts are presented across the following categories/life-cycle phases:

• direct - exhaust

• direct - non-exhaust

• energy chain

• powertrain

• glider

• energy storage

• maintenance

• end-of-life

• road

A comprehensive presentation of life-cycle assessment (LCA) results for passenger cars should offer insights into various aspects that contribute to the overall environmental impact. Each category or life-cycle phase addresses a different set of environmental impacts, and assessing them individually helps to paint a complete picture. Below is an extended description of each category or life-cycle phase:

Direct - Exhaust¶

Description: This category evaluates the environmental impacts associated with the direct emissions from the vehicle’s exhaust system, including greenhouse gases (GHGs), particulate matter (PM), and volatile organic compounds (VOCs).

Substances measured:

• Carbon dioxide (CO2)

• Nitrogen oxides (NOx)

• Particulate matter (PM)

• Hydrocarbons

• VOCs

Note that not all substance contribute to all impact categories. For example, NOx and VOCs contribute to the formation of ozone, but not to climate change.

Direct - Non-Exhaust¶

Description: This section focuses on emissions and impacts not related to the exhaust system, such as brake and tire wear, as well as emissions from air conditioning.

Parameters measured:

• PM from brake, tire, road and engine wear, as well as re-suspended dust

• Refrigerant losses (e.g., R143a) from air conditioning

Energy Chain¶

Description: Assesses the environmental impacts associated with the production, transportation, and distribution of the energy source used in the vehicle, be it gasoline, electricity, hydrogen, or any other.

Parameters Measured:

• Energy source extraction impacts

• Transportation emissions

• Energy generation, transmission and distribution emissions

Powertrain¶

Description: This part examines the environmental burden from the manufacturing, operation, and disposal of the vehicle’s engine and transmission systems.

Parameters Measured:

• Raw material extraction

• Manufacturing emissions

• Operational efficiency

Glider¶

Description: The glider refers to the body, chassis, and interior components of the car. This phase assesses the impact of these elements over the vehicle’s lifetime.

Parameters Measured:

• Materials used (aluminum, steel, plastics)

• Manufacturing emissions

• Aerodynamics and its impact on fuel/energy consumption

Energy Storage¶

Description: This category is particularly relevant for electric and hybrid vehicles and looks at the environmental impacts associated with batteries.

Parameters Measured:

• Resource extraction for battery materials

• Battery production

Battery disposal or recycling is included in the end-of-life category.

Maintenance¶

Description: This phase focuses on the environmental impacts associated with maintaining the vehicle, including oil changes, part replacements, and repairs.

Parameters Measured:

• Mass of the vehicle

End-of-Life¶

Description: Assesses the environmental impacts when the vehicle is no longer in use. This includes dismantling, recycling, and disposal processes.

Parameters Measured:

• Mass of vehicle’s components

• Battery

• Emissions from landfilling, scrapping and recycling processes

Road¶

Description: This category considers the environmental impacts related to the infrastructure supporting the vehicle, such as road construction and maintenance. Those are scaled on the basis of the vehicle’s mass.

Parameters Measured:

• Mass of the vehicle

• Material consumption for road construction

• Emissions from maintenance machinery

• Runoff pollution