Automotive Lightweight Design: Simulation Modeling of Mass-Related Consumption for Electric Vehicles

: A thorough assessment of Life-Cycle e ﬀ ects involved by vehicle lightweighting needs a rigorous evaluation of mass-induced consumption, on which energy and sustainability beneﬁts during use stage directly depend. The paper proposes an analytical calculation procedure to estimate the weight-related energy consumption of pure Electric Vehicles (EVs), since existing literature leaves considerable room for improvement regarding this research area. The correlation between consumption and mass is expressed through the Energy Reduction Value (ERV) coe ﬃ cient, which quantiﬁes the speciﬁc consumption saving achievable through 100 kg mass reduction. The ERV is estimated for a number of heterogeneous case studies derived from real 2019 European market EV models and according to three drive cycles, to consider di ﬀ erent driving behaviors. For the case studies under consideration, ERV ranges from 0.47 to 1.17 kWh / (100 km × 100 kg), with the variability mainly depending on vehicle size and driving cycle. Given the high uncertainty of mass-related consumption on car size, an analytical method is reﬁned to estimate accurately the ERV for any real-world EV model, starting from vehicle technical features. Along with energy assessment, the research also evaluates the environmental implications of lightweight design by means of the Impact Reduction Value (IRV), which is estimated for three distinct electricity grid mixes. Finally, the ERV / IRV modeling approach is applied to a series of comparative lightweight case studies taken from the literature. Such an application demonstrates the e ﬀ ective utility of the work to reduce the uncertainty for all cases where no physical tests or computer-aided simulations are available.


Introduction
Energy-resources depletion and global climate change represent one of the major concerns for modern societies worldwide [1,2]. The desire for improved energy security and reduced global climate change has led to many industry and research developments to reduce fossil fuel consumption due to human activities [3,4]. The road transportation sector accounts for a relevant quota of total energy demand and air emissions on a global scale [5]. Since operation is the most energy-consuming phase within car's Life Cycle, strong efforts have been put to improve the fuel economy of light-duty vehicles [6]. The literature provides a series of works that investigate a wide range of possible solutions to achieve this ambitious target, such as the use of alternative fuels, the development of more efficient propulsion technologies, vehicle downsizing, an increase in powertrain efficiency and reduction in vehicle size, aerodynamic drag, or rolling resistance [7][8][9]. Another highly promising way to provide more sustainable mobility is lightweight design. Lightweighting presents a very high available and that a model-specific assessment is required to properly evaluate real-life case studies. The review article of Luk et al. [45] confirms that electric cars offer the lowest energy-saving potential from lightweight design, but it stresses also that lower consumption allows downsizing the battery based on the same driving range, thus providing additional valuable mass reduction that further increases energy saving.
The state-of-the-art shows that while a notable research activity has been carried out on the analysis of mass-consumption correlation for ICEVs, large margins of investigation still remain for advanced powertrain cars. First of all, fuel-mass correlations proposed by several studies do not represent a thorough metric for FRV estimation, since they involve conflating assumptions with respect to non-mass-related loads when comparing different vehicles. Moreover, most of simulation modeling activities are based on theoretical cars, with no indications on car model names and model years. In particular, for BEVs, the literature provides only one study which performs a thorough simulation modeling of the FRV coefficient based on data of specific car models currently in use. However, the paper does not provide guidance on estimating mass-consumption correlation for real-world vehicles, and the large variability of results due to car model makes unreliable the assessment of lightweighting through generic FRVs. Additionally, the calculations are based on the standardized driving cycle effective in the geographical area of the study, with no general relevance on a global scale, and the sustainability implications of mass reduction are not taken into account.
This study presents an analytical calculation procedure for mass-induced energy consumption of pure Electric Vehicles. The target of the work is providing support in the assessment of energy and sustainability implications of lightweighting within the BEV field. The estimation of mass-consumption correlations is based on car model-specific data, in order to minimize the uncertainties of results with respect to the use of hypothetical vehicles data. The simulation modeling is carried out for a number of specific case studies belonging to a wide range of car size and class, thus taking into account a broad range of vehicle technical features. Moreover, the mass-induced consumption is evaluated based on a set of driving cycles, both developed by international standardization and research activities, to capture the effects of different driving patterns. Finally, the research includes the sustainability assessment through the calculation of environmental-impact-reduction values, which are also applied to a series of the literature case studies.

Materials and Methods
The analysis of the correlation between vehicle mass and use-stage consumption/environmental impact is carried out in two main calculation sections. The first one estimates the energy absorption for various mass-configurations of a certain number of BEV case studies by a simulation modeling of car system dynamics. The second section evaluates the effects of weight reduction on both use-phase consumption and environmental impact through the correlation between mass and energy absorbed in the different configurations.

Simulation Modeling of Vehicle Consumption
The calculation of car consumption is carried out through a simulation model developed by the software MATLAB-Simulink [46]. The refined model simulates vehicle longitudinal dynamics, and it falls in the category of "forward models", according to the literature examples [35,36,47]. The modeling provides the calculation of motor torque required to follow a certain driving cycle by reproducing the operation of all drivetrain components [48]. The model is composed of four main sections ( Figure 1): driver, powertrain, driveline, and energy management. The driver section is based on a speed-follower Proportional-Integral-Derivative (PID) controller. The model includes a look-forward secondary PID for driving cycle acceleration and deceleration anticipation (anticipation factor being 1 s) with derivative part set to zero. The PID controller is functional to appropriately "smooth" simulated driving when adopting rigid cycles that provide suddenly varying acceleration sequences (e.g., the New European Driving Cycle (NEDC), for which acceleration is supposed to pass immediately from zero to constant value). The brake blending controller (Drv control in Figure 1) regulates the brake request from the user, to provide separate torque request from powertrain (regenerative braking torque) and mechanical braking.
The powertrain section includes the battery and motor sub-models. The battery sub-model (Thevenin-based) is built on the characteristics of Mitsubishi i-MiEV cells (used in a 16 kWh battery pack [49]), and it is adapted to the specific vehicle case study by scaling on the basis of the effective battery capacity. The motor sub-model is based on look-up-tables ( Figure 2) functional to define traction torque, regenerative braking torque, and efficiency (combined value considering motor and inverter). Data are coming from automotive Permanent Magnet Synchronous Motor (PMSM) testing [50], and they are rescaled and adapted to vehicle case studies (a typical approach for archetype comparison), on the basis of car model specifications (nominal torque, motor speed, and efficiency). The driver section is based on a speed-follower Proportional-Integral-Derivative (PID) controller. The model includes a look-forward secondary PID for driving cycle acceleration and deceleration anticipation (anticipation factor being 1 s) with derivative part set to zero. The PID controller is functional to appropriately "smooth" simulated driving when adopting rigid cycles that provide suddenly varying acceleration sequences (e.g., the New European Driving Cycle (NEDC), for which acceleration is supposed to pass immediately from zero to constant value). The brake blending controller (Drv control in Figure 1) regulates the brake request from the user, to provide separate torque request from powertrain (regenerative braking torque) and mechanical braking.
The powertrain section includes the battery and motor sub-models. The battery sub-model (Thevenin-based) is built on the characteristics of Mitsubishi i-MiEV cells (used in a 16 kWh battery pack [49]), and it is adapted to the specific vehicle case study by scaling on the basis of the effective battery capacity. The motor sub-model is based on look-up-tables ( Figure 2) functional to define traction torque, regenerative braking torque, and efficiency (combined value considering motor and inverter). Data are coming from automotive Permanent Magnet Synchronous Motor (PMSM) testing [50], and they are rescaled and adapted to vehicle case studies (a typical approach for archetype comparison), on the basis of car model specifications (nominal torque, motor speed, and efficiency). The driveline section models inertia (evaluated as vehicle mass in running order corrected by a factor representing equivalent inertia of main rotating elements in driveline) and friction characteristics (calculated on the basis of car aerodynamics and tire rolling friction). The section is composed of the following sub-models: braking (providing braking torque to the wheels), wheels (providing longitudinal force from braking and traction force, modified according to rolling friction), car body (modeling longitudinal dynamics including equivalent rotating masses), and auxiliaries (modeling lighting and basic electric and electronics components, average consumption being about 180 W).
The energy management section estimates the electricity consumption, taking into account the regenerative braking. The model is based on a simplified blending criteria between electric and mechanical braking (Figure 3), which is aimed at limiting the regenerative braking torque within the driveline admissible limits (exceeding braking torque, when needed, is provided by the mechanical braking system). The selected approach provides over various driving cycles results comparable to expectations (e.g., regenerated energy over known driving cycles being in the range from 15 to 25%, depending on cycle characteristics [48]). The section is composed of the following sub-models: battery, super-capacitor, and range extender. Super-capacitor and range-extender sub-models are not used for this application, since the energy management provides that power is simply redirected to the battery. The calculation of energy consumption is performed for 10 BEV case studies belonging to A/B, C, and D/E classes. The choice of a wide spectrum of car size allows us to model the correlation between mass and electricity absorption, taking into account the strong variation of vehicle technical The driveline section models inertia (evaluated as vehicle mass in running order corrected by a factor representing equivalent inertia of main rotating elements in driveline) and friction characteristics (calculated on the basis of car aerodynamics and tire rolling friction). The section is composed of the following sub-models: braking (providing braking torque to the wheels), wheels (providing longitudinal force from braking and traction force, modified according to rolling friction), car body (modeling longitudinal dynamics including equivalent rotating masses), and auxiliaries (modeling lighting and basic electric and electronics components, average consumption being about 180 W).
The energy management section estimates the electricity consumption, taking into account the regenerative braking. The model is based on a simplified blending criteria between electric and mechanical braking (Figure 3), which is aimed at limiting the regenerative braking torque within the driveline admissible limits (exceeding braking torque, when needed, is provided by the mechanical braking system). The selected approach provides over various driving cycles results comparable to expectations (e.g., regenerated energy over known driving cycles being in the range from 15 to 25%, depending on cycle characteristics [48]). The section is composed of the following sub-models: battery, super-capacitor, and range extender. Super-capacitor and range-extender sub-models are not used for this application, since the energy management provides that power is simply redirected to the battery. The driveline section models inertia (evaluated as vehicle mass in running order corrected by a factor representing equivalent inertia of main rotating elements in driveline) and friction characteristics (calculated on the basis of car aerodynamics and tire rolling friction). The section is composed of the following sub-models: braking (providing braking torque to the wheels), wheels (providing longitudinal force from braking and traction force, modified according to rolling friction), car body (modeling longitudinal dynamics including equivalent rotating masses), and auxiliaries (modeling lighting and basic electric and electronics components, average consumption being about 180 W).
The energy management section estimates the electricity consumption, taking into account the regenerative braking. The model is based on a simplified blending criteria between electric and mechanical braking (Figure 3), which is aimed at limiting the regenerative braking torque within the driveline admissible limits (exceeding braking torque, when needed, is provided by the mechanical braking system). The selected approach provides over various driving cycles results comparable to expectations (e.g., regenerated energy over known driving cycles being in the range from 15 to 25%, depending on cycle characteristics [48]). The section is composed of the following sub-models: battery, super-capacitor, and range extender. Super-capacitor and range-extender sub-models are not used for this application, since the energy management provides that power is simply redirected to the battery. The calculation of energy consumption is performed for 10 BEV case studies belonging to A/B, C, and D/E classes. The choice of a wide spectrum of car size allows us to model the correlation between mass and electricity absorption, taking into account the strong variation of vehicle technical  The calculation of energy consumption is performed for 10 BEV case studies belonging to A/B, C, and D/E classes. The choice of a wide spectrum of car size allows us to model the correlation between mass and electricity absorption, taking into account the strong variation of vehicle technical features (mainly mass, motor power, and power-to-weight ratio) that occurs passing from one segment to another. To obtain realistic values of energy consumption, technical features of case studies refer to specific vehicle models from the 2019 EV European market. The choice to use real-life cars is performed in order that the considered case studies are as much as possible representative of the vast majority of BEVs sold in Europe, thus covering all possible intended uses, from entry level to high-performance/luxury segments. Table A1 in Appendix A reports the technical features of vehicle models taken into account in the simulation modeling.
As regards the driving pattern for the estimation of energy consumption, calculations are performed on the basis of three different driving cycles: New European Driving Cycle (NEDC) [51], World Light Test Procedure (WLTP) [52], and All-Long Driving Cycle (ALDC) developed within the European research project "Ageing and efficiency Simulation & TEsting under Real world conditions for Innovative electric vehicle Components and Systems" (ASTERICS) [53]. NEDC is the driving cycle that had been adopted for the type-test approval in Europe up to 2017, while the WLTP is the current European type-test-approval cycle. Despite that the NEDC is no longer in force, it is included to allow comparison of energy/fuel reduction values with past studies (perhaps dealing with different powertrain technologies such as ICEV). On the other hand, the choice to adopt the standardized driving cycle at European level (WLTP) is due to the need for consistency, transparency, and comparability with present and future works. Finally, the ALDC was selected since it has been specifically developed to reproduce the real usage conditions of current Electric Vehicles within urban and suburban areas [54]. Table A2 in Appendix A reports the main descriptive parameters of the three drive cycles, while Appendix Figure A1 reports the speed profile of the ALDC.

Estimation of Reduction Values for Energy Consumption and Environmental Impact
The evaluation of mass-related energy absorption is carried out on the basis of consumption values obtained in the simulation modeling step. The calculation procedure provides that, for each vehicle case study, the energy absorption is estimated for the reference mass configuration and for four lightweight mass configurations, with respectively 5%, 10%, 15%, and 20% weight reduction with respect to the reference one. Then the mass-induced consumption is determined as the slope of the regression line of electricity absorption in function of mass ( Figure A2 in Appendix A), and it is determined by means of the Energy Reduction Value (ERV) coefficient, according to the following equation: where ERV = Energy Reduction Value (kWh/(100 km × 100 kg)); ∆EC = reduction in energy consumption achieved through vehicle mass reduction (kWh/100 km); and ∆M = 100 kg vehicle mass reduction.
Since powertrain resizing has a negligible impact on the energy saving of BEVs [55], the modeling is performed while assuming primary mass reduction only; that is, all vehicle parameters in the lightweight configurations remain unchanged with respect to the reference one with the sole exception of mass. The calculation section closes with the assessment of the environmental implications provided by mass reduction. Such an assessment is based on the modeling of energy reduction coefficients, and it provides that the ERVs are converted into Impact Reduction Value (IRV) coefficients by multiplying the mass-induced electricity consumption by a specific impact factor. The impact factor is defined as the Global Warming Potential (GWP) involved by the production of 1 kWh electricity through a specific grid mix, according to the following equation: where IRV = Impact Reduction Value (kg CO 2 eq/(100 km × 100 kg)); ERV = Energy Reduction Value (kWh/(100 km × 100 kg)); and GWP kWh = Global Warming Potential impact due to the production of 1 kWh electricity (kg CO 2 eq/kWh).
The IRV is calculated by taking into account three distinct electricity grid mixes: Norwegian (NO), average European (EU28), and Polish (PL). The choice to consider Norwegian and Polish scenarios is made to have a comprehensive overview on the sustainability effects of the electricity supply chain. Indeed, these mixes are characterized by diametrically opposed energy and environmental profiles: Electricity produced through the Norwegian mix is almost completely from renewable resources, while the Polish grid mix is mainly based on fossil resources. Table 1 reports the ERV and IRV coefficients for all vehicle case studies and driving cycles, while Table 2 characterizes ERV/IRV in terms of minimum and maximum value, range max-min, arithmetic mean, and standard deviation (for both single classes and totality of car models). Table A3 in Appendix A provides the electricity consumption of vehicle case studies for each mass configuration.    Table 1 stresses that the ERV varies widely based on vehicle case study and driving cycle, with an overall variability range of 0.47-1.17 kWh/(100 km × 100 kg). Figure 4 shows the arithmetic mean of ERV over vehicle models per car class and driving cycle; the black bars in the section refer to all case studies that identify the maximum range of variation. The ALDC provides the highest mass-induced consumption (ERV ALDC ) for both single segments and the totality of vehicles: The arithmetic mean over all models is 0.97 kWh/(100 km × 100 kg), with an increase respectively of about 60% with respect to WLTP and NEDC. Figure 4 also stresses that ERV ALDC has the greatest dispersion around the arithmetic mean (range min-max of 0.77-1.17 kWh/(100 km × 100 kg)) and standard deviation of 0.12 kWh/(100 km × 100 kg), with notably lower variability provided by WLTP and NEDC (Table 1). Despite the correlation mass-consumption is strongly influenced by technical features of the specific car model, the generally higher ERVs in the ALDC can be explained by two main reasons. The first and most important one is that the specific energy consumption (electricity per kilometer) involved by mass-dependent resistance factors (rolling and acceleration resistance) is greater in the ALDC than in NEDC and WLTP, due to the more dynamic run of this drive cycle. ALDC, in fact, does not present a prolonged "high speed" section, in which aerodynamic friction become predominant in comparison with other mass-related phenomena. The second explanation is the lower average efficiency over the entire cycle with which the electric motor operates in the ALDC than in NEDC and WLTP. This is because the car works under partial load conditions for a relevant share of total ALDC duration, due to the frequent speed fluctuations and the high accelerations that characterize the cycle. In this regard, simulations data show that the motor base efficiency is lower in the lightweight mass-configurations than in the reference one and that the efficiency decreases at mass reduction growing: The reason for this may be found in the lower motor load required by lightweight configurations to follow the given velocity profile. Therefore, it can be said that the energy-saving potential achievable through lightweighting is higher in the ALDC than in the other drive cycles.  Table 1 stresses that the ERV varies widely based on vehicle case study and driving cycle, with an overall variability range of 0.47-1.17 kWh/(100 km × 100 kg). Figure 4 shows the arithmetic mean of ERV over vehicle models per car class and driving cycle; the black bars in the section refer to all case studies that identify the maximum range of variation. The ALDC provides the highest massinduced consumption (ERVALDC) for both single segments and the totality of vehicles: The arithmetic mean over all models is 0.97 kWh/(100 km × 100 kg), with an increase respectively of about 60% with respect to WLTP and NEDC. Figure 4 also stresses that ERVALDC has the greatest dispersion around the arithmetic mean (range min-max of 0.77-1.17 kWh/(100 km × 100 kg)) and standard deviation of 0.12 kWh/(100 km × 100 kg), with notably lower variability provided by WLTP and NEDC (Table 1). Despite the correlation mass-consumption is strongly influenced by technical features of the specific car model, the generally higher ERVs in the ALDC can be explained by two main reasons. The first and most important one is that the specific energy consumption (electricity per kilometer) involved by mass-dependent resistance factors (rolling and acceleration resistance) is greater in the ALDC than in NEDC and WLTP, due to the more dynamic run of this drive cycle. ALDC, in fact, does not present a prolonged "high speed" section, in which aerodynamic friction become predominant in comparison with other mass-related phenomena. The second explanation is the lower average efficiency over the entire cycle with which the electric motor operates in the ALDC than in NEDC and WLTP. This is because the car works under partial load conditions for a relevant share of total ALDC duration, due to the frequent speed fluctuations and the high accelerations that characterize the cycle. In this regard, simulations data show that the motor base efficiency is lower in the lightweight mass-configurations than in the reference one and that the efficiency decreases at mass reduction growing: The reason for this may be found in the lower motor load required by lightweight configurations to follow the given velocity profile. Therefore, it can be said that the energy-saving potential achievable through lightweighting is higher in the ALDC than in the other drive cycles. Concerning the dependence of ERV on vehicle size, Figure 4 highlights that the mass-induced consumption grows at car segment level increasing, with a percentage variation comprised within 17% and 24% (depending on drive cycle), passing from A/B to D/E class. This outcome is substantially confirmed by Figure 5, which reports the reduction values in function of electricity consumption. The ERV increases at energy-demand-growing and higher-class vehicles have greater consumption than lower segments: A/B-class provides the lowest electricity absorption (within 9.6-15.7 kWh/km, depending on vehicle model and driving cycle) and the lowest ERV (0.47-0.96 kWh/(100 km × 100 kg)), while D/E-class cars have the highest electricity absorption (14.2-23.3 kWh/km) and the highest ERVs (0.58-1.17 kWh/(100 km × 100 kg)). The growth of ERV with specific consumption generally occurs for all the drive cycles, and it is more pronounced for the ALDC than WLTP and NEDC. Concerning the dependence of ERV on vehicle size, Figure 4 highlights that the mass-induced consumption grows at car segment level increasing, with a percentage variation comprised within 17% and 24% (depending on drive cycle), passing from A/B to D/E class. This outcome is substantially confirmed by Figure 5, which reports the reduction values in function of electricity consumption. The ERV increases at energy-demand-growing and higher-class vehicles have greater consumption than lower segments: A/B-class provides the lowest electricity absorption (within 9.6-15.7 kWh/km, depending on vehicle model and driving cycle) and the lowest ERV (0.47-0.96 kWh/(100 km × 100 kg)), while D/E-class cars have the highest electricity absorption (14.2-23.3 kWh/km) and the highest ERVs (0.58-1.17 kWh/(100 km × 100 kg)). The growth of ERV with specific consumption generally occurs for all the drive cycles, and it is more pronounced for the ALDC than WLTP and NEDC. As regards the characterization of impact reduction, Figure 6 provides the arithmetic mean of IRV over car models per vehicle class and driving cycle. The first point is that, due to the analytical definition of IRV, the reduction values are directly dependent on the electricity grid mix. The choice to adopt Norwegian and Polish mixes allows us to evaluate diametrically opposite sustainability scenarios, among which all other possible alternatives are comprised. As a confirmation, the average IRV over all case studies is between the following:
Meanwhile, intermediate values are obtained for the average European grid mix. Results highlight that the variability of IRV based on electricity production is definitely high, especially if compared with the dependence on vehicle class and driving cycle. From the above, it is clear that the choice of the specific grid mix represents a decisive point for the effective convenience of a lightweight design solution. As regards the characterization of impact reduction, Figure 6 provides the arithmetic mean of IRV over car models per vehicle class and driving cycle. The first point is that, due to the analytical definition of IRV, the reduction values are directly dependent on the electricity grid mix. The choice to adopt Norwegian and Polish mixes allows us to evaluate diametrically opposite sustainability scenarios, among which all other possible alternatives are comprised. As a confirmation, the average IRV over all case studies is between the following: • 0.02 kg CO 2 eq/(100 km × 100 kg) (IRV NEDC ) and 0.03 kg CO 2 eq/(100 km × 100 kg) (IRV ALDC ) when considering the Norwegian grid mix; • 0.55 kg CO 2 eq/(100 km × 100 kg) (IRV NEDC ) and 0.96 kg CO 2 eq/(100 km × 100 kg) (IRV ALDC ) when considering the Polish grid mix.

Modeling Approach for ERV and IRV Estimation
This paragraph is aimed at refining a modeling method able to provide affordable values of ERV/IRV for real-world cars, taking into account the variability on the main vehicles' technical features. Such an approach was developed by starting from mass reduction values resulting from simulations performed for the different case studies. Meanwhile, intermediate values are obtained for the average European grid mix. Results highlight that the variability of IRV based on electricity production is definitely high, especially if compared with the dependence on vehicle class and driving cycle. From the above, it is clear that the choice of the specific grid mix represents a decisive point for the effective convenience of a lightweight design solution.

Modeling Approach for ERV and IRV Estimation
This paragraph is aimed at refining a modeling method able to provide affordable values of ERV/IRV for real-world cars, taking into account the variability on the main vehicles' technical features. Such an approach was developed by starting from mass reduction values resulting from simulations performed for the different case studies.
The first section of the paragraph investigates the variability of mass-induced energy consumption with respect to car technical features mass (M), maximum power (P max ), and power-to-mass ratio (P/M). The effectiveness of the correlation is analyzed through regression lines of ERV in function of the three parameters. Figure 7 reports ERV as a function of M, P max , and P/M, with regression lines and related coefficients of determination for the driving cycles NEDC, WLTP, and ALDC.
First of all, it can be noted that the ERVs increase with the considered parameters and that the slope of the regression lines in the ALDC is significantly higher than in NEDC and WLTP. These results appear to be in accordance with average data presented in previous paragraph, as explained by the following: • Higher class-level case studies generally have higher M, P max , and P/M; • The greater mass-dependent resistance forces in the ALDC make that the ERV increases more rapidly at car size increasing with respect to the other driving cycles.
Concerning the correlation analysis, the values of R 2 stress that the weaker dependence is detected for parameter P/M, whose coefficients of determination are around 0.55 for all the drive cycles. Higher R 2 refers to P max (about 0.75), while the strongest correlation occurs for M, with R 2 abundantly over 0.8 (0.83 for both NEDC and WLTP and 0.87 for ALDC). Based on previous considerations, the chosen approach for the modeling of mass-induced energy consumption of real-world vehicles is the use of regression lines of ERV in function of mass. Such a criterion allows us to estimate in a simple way the ERV for any generic case study only from the knowledge of vehicle weight. However, the model is composed by three equations (one for each driving cycle), without any indication on the choice of them. In this regard, the following has to be taken into account:

•
The NEDC had been the standardized driving cycle for European type approval tests until 2017, when it was replaced by the WLTP. However, the cycle is widely criticized to not represent the driving behavior of current real-world drivers and cars, since numerous studies show that actual on-road fuel consumption and emissions might be substantially higher than values determined through the NEDC [56][57][58][59].

•
The WLTP is a global, harmonized standard for determining the levels of fuel consumption/pollutants of both conventional and hybrid cars, as well as the range of fully Electric Vehicles. In the light of the above, the recommendation when evaluating the energy and environmental implications of lightweighting for a real-world case study is to assume three separate use-phase scenarios: One referred to ALDC, and the other ones referred to NEDC and WLTP. The first scenario should be used as the reference for the study, as it provides the actual and most affordable assessment. On the other hand, results obtained through the NEDC and WLTP should be considered as means of comparison with past and current studies that deal with alternative/competing solutions for the same applications. The equations of regression lines of ERV in function of mass are reported in Table 2 for the three driving cycles (ERV ALDC , ERV NEDC , and ERV WLTP ).
As regards the environmental assessment section, Figure 8 shows IRVs in function of M with related regression lines and R 2 for the considered driving cycles. The figure reports only data in function of mass because the impact reduction coefficient has the same correlation of ERV with the considered parameters. The equations of regression lines are reported in Table 3 for the three driving cycles and the three electricity grid mixes. Another remarkable thing provided by the analysis of impact reduction coefficients is that the variability on electricity grid mix is notably higher with respect to the dependence on driving cycle. For example, assuming as reference the regression line of IRV in the average European grid mix and NEDC (IRV EU28_NEDC ), the increase is higher when passing to the Poland mix while maintaining the driving cycle (IRV PL_NEDC ) than when passing to ALDC while maintaining the grid mix (IRV EU28_ALDC ).

Implementation of Modeling Approach on Real-Word Case Studies
This paragraph provides a practical example of the functionality of ERV/IRV modeling approach in the assessment of lightweighting within the electro-mobility field. Such an approach is applied to a series of sustainability case studies provided by Reference [60]: • These are comparative Life-Cycle Assessments (LCAs) of reference and innovative design solutions for different modules installed on a C-class EV; • The lightweight components are based on composites and hybrid materials and they have been

Implementation of Modeling Approach on Real-Word Case Studies
This paragraph provides a practical example of the functionality of ERV/IRV modeling approach in the assessment of lightweighting within the electro-mobility field. Such an approach is applied to a series of sustainability case studies provided by Reference [60]: • These are comparative Life-Cycle Assessments (LCAs) of reference and innovative design solutions for different modules installed on a C-class EV; • The lightweight components are based on composites and hybrid materials and they have been specifically developed for fully electric cars; • The environmental analysis is carried out considering the entire Life Cycle (LC) of the modules and it is based on several impact categories, including the Global Warming Potential (GWP).
The comparative case studies are reviewed for the only GWP impact category by quantifying the LC mileage at which the novel design results environmentally preferable with respect to the reference one [60]. Such an LC distance is defined as the Break-Even Point (BEP), and it is determined by quantifying the impact variation in all LC stages involved by lightweighting: The GWP changes in production and End-of-Life (EoL) are directly taken from Reference [60], while the use phase is estimated through the ERV/IRV approach, using regression lines reported in Table 2. The following equation provides the analytical model for the calculation of BEP: where BEP = Break-Even Point (km); ∆GWP Prod+EoL = variation in Global Warming Potential impact due to lightweight design (kg CO 2 eq); IRV = Impact Reduction Value (kg CO 2 eq/(100 km × 100 kg)); and ∆M light = variation in vehicle mass due to lightweight design (kg). Table A4 in Appendix A reports ∆GWP Prod+EoL and ∆M for all the considered sustainability case studies, including a brief description of baseline and innovative design solutions, as well as the main technical features of the reference car model for the modules. Figure 9 shows BEP for the five components taking into account all possible combinations between driving cycles and electricity grid mixes (numerical data are reported in Table A5 in Appendix A). The considered modules are Front Module (FM), Front Hood (FH), Front Door (FD), Cross Dashboard Beam (CDB), and Suspension Arm (SA). The diagram reveals that, when considering the Norwegian scenario, for all case studies, BEP is greatly higher than the reference LC mileage assumed by [60] (150,000 km), with a variability comprised between 35 million kilometers (referred to FD module in the NEDC) and 0.93 million kilometers (referred to CDB module in the ALDC). Therefore, a lightweight designs appear to be definitely not convenient from an environmental point of view, as weight reduction enables low mass-specific impact saving due to the very small GWP intensity of the Norwegian grid mix. BEPs are notably lower when considering the European scenario, even if the only component for which the novel alternative results preferable (in all driving cycles) is CDB. However, BEP for SA and FM in the ALDC are not so far from 150,000 km (respectively about 220,000 and 250,000 km). Finally, the analysis based on the Polish grid mix involves a further decrease of BEP due to the very high fossil energy intensity of the cycle. Indeed, lightweighting appears to be an effective strategy for CDB (in all drive cycles), SA (in WLTP and ALDC), and FM (in ALDC), with BEPs just above the LC threshold for the other modules and driving cycles (within the range 160,000-260,000 km); the only exception is represented by FD, which provides a BEP notably higher (around 620,000-1,080,000 km).
ALDC are not so far from 150,000 km (respectively about 220,000 and 250,000 km). Finally, the analysis based on the Polish grid mix involves a further decrease of BEP due to the very high fossil energy intensity of the cycle. Indeed, lightweighting appears to be an effective strategy for CDB (in all drive cycles), SA (in WLTP and ALDC), and FM (in ALDC), with BEPs just above the LC threshold for the other modules and driving cycles (within the range 160,000-260,000 km); the only exception is represented by FD, which provides a BEP notably higher (around 620,000-1,080,000 km). The environmental section is completed by the analysis of the influence of vehicle model on BEP. Figure 10 reports BEP in function of car mass for the sustainability case studies FM, FH, and SA, respectively, for Norwegian, average European, and Polish grid mixes and including all the considered driving cycles. As the design solutions refer to a C-class vehicle, it is chosen to investigate the mass range 1250-1650 kg, which is found to be representative of medium-size EV's segment. Table A6 in Appendix A reports BEP for the considered case studies, assuming M = 1250 kg and M = 1650 kg. The environmental section is completed by the analysis of the influence of vehicle model on BEP. Figure 10 reports BEP in function of car mass for the sustainability case studies FM, FH, and SA, respectively, for Norwegian, average European, and Polish grid mixes and including all the considered driving cycles. As the design solutions refer to a C-class vehicle, it is chosen to investigate the mass range 1250-1650 kg, which is found to be representative of medium-size EV's segment. Table A6 in Appendix A reports BEP for the considered case studies, assuming M = 1250 kg and M = 1650 kg.
The diagrams reveal that, beyond the inherent features of the specific modules, the Norwegian mix (Figure 10a) provides the highest absolute variability of BEP with respect to car mass (BEP variability comprised within 350,000 and 750,000 km based on case study and drive cycle). The reason for this is that BEPs are very high due to the definitely low embodied GWP of electricity production. Indeed, the Break-Even is comprised between two and nine million kilometers, thus evidencing that the lightweight options are far from an effective profitability, even for cars with great mass. As regards the average European mix (Figure 10b), BEPs are significantly lower than the Norwegian one. However, the Break-Even is not reached within the 150,000 km threshold for any of the innovative design alternatives. That said, BEP for SA module in the ALDC with a 1650 kg car is about 200,000 km, which could be also reached by an EV. Lastly, Figure 10c shows that the Polish electricity grid mix involves the lowest absolute variability of BEP with the mass (BEP variability comprised within 10,000 and 25,000 km, depending on case study and drive cycle). As the Break-Even mileages have the same order (within the range of 80,000-270,000 km) than the assumed LC distance, the dependence on vehicle model becomes decisive to establish the effective environmental convenience of the lightweight solutions. As a confirmation, BEP for the SA module in the WLTP and the FH module in the ALDC results above 150,000 km when considering low-mass cars (respectively about 155,000 and 158,000 km for 1250 kg EVs), while high-mass vehicles provide a BEP which is below the LC limit (respectively around 141,000 and 139,000 km for 1650 kg cars). This means that these solutions result in being environmentally advantageous for high-size models, while they are not when applied to entry-level C-class vehicles. Concerning the other modules/driving cycles, the variability of BEP with car weight does not involve a threshold crossing. Two opposite examples for this are the FH module in the NEDC and the SA module in the ALDC. When passing from lower to upper mass limit, the BEP for the FH reduces by about 22,000 km, without, however, approaching significantly the 150,000 km (BEP varies from about 270,000 to 248,000 km). On the other hand, the change for the SA module (around 12,000 km) entails a significant increase in the convenience of the lightweight solution (BEP ranges from about 98,000 km to 86,000 km). In the light of previous considerations, it can be concluded that the variability of BEP on vehicle model represents a key factor when engaging with the following:

•
Dealing with lightweight case studies characterized by a low mass-specific GWP increase in production and EoL (∆GWP Prod+EoL /∆M light ); • Assuming fossil-intensive electricity grid mixes and driving cycles with highly dynamic run. The diagrams reveal that, beyond the inherent features of the specific modules, the Norwegian mix (Figure 10a)

Conclusions
To date, fuel-mass correlation has been widely studied for ICE light duty vehicles, while great margins of investigation still exist for advanced powertrain technologies, especially for pure electric cars. The study refines a comprehensive framework for the estimation of EVs' mass-induced consumption to provide support in the energy and sustainability assessment of lightweight design solutions when physical tests or computer-aided simulations are not available. A simplified method to estimate consumption-weight correlation is proposed based on the calculation of ERV coefficients, expressed in kWh/(100 km × 100 kg). The simulations are performed for a set of car case studies, using technical features of specific 2019 European market EV models, chosen as a representative of different segments (A/B, C, and D/E). The ERV coefficients are estimated according to three driving cycles, both internationally standardized and developed in research activities (NEDC, WLTP, and ALDC), to assess the influence of different driving styles on mass-induced consumption. The ERV is finally converted into the IRV coefficient, which expresses the GWP saving achievable through a 100 kg mass decrease and it is quantified for Norwegian, average European, and Polish grid mixes. The ERVs obtained for the different case studies show that there is a wide variability based on vehicle model and driving cycle, with values in the range of 0.47-1.17 kWh/(100 km × 100 kg). Beyond the influence of the specific car model, results stress that ERV is closely related to car consumption (economy) and it grows at car size increasing: For example, the average ERV ALDC in the A/B class is 0.89 kWh/(100 km × 100 kg), while it reaches 1.10 kWh/(100 km × 100 kg) for the D/E segment, with intermediate value for C class. As a result, a given amount of lightweighting (kilograms saved) provides the most benefit when applied to upper-level class EVs with high energy consumption. Concerning the influence of driving cycle, the ERV is notably higher for the ALDC than NEDC and WLTP, because of the great dynamics of the cycle (high acceleration/deceleration), which makes bigger the mass-induced energy consumption. The analysis of the dependence of ERV on the main vehicle technical features highlights that there is a strong correlation with car mass, based on which an analytical method is refined for providing affordable values for any real-life case study. Such a criterion allows us to thoroughly assess weight-related consumption when dealing with the comparison between reference and lightweight solutions from both energy and sustainability point of view. The ERV/IRV modeling approach is finally applied to a series of lightweight case studies from the literature, where the profitability of innovative solutions is assessed through the quantification of BEP. These case studies refer to several design solutions that strongly differ both in terms of technical features (materials and technologies used) and application field/boundary conditions (car size, driving cycle, and electricity grid mix). Results show that BEP is strongly influenced by vehicle model, especially when assuming fossil-intensive electricity grid mixes and driving cycles with highly dynamic run. This leads to the conclusion that a careful car model-specific approach is recommended, thus highlighting the utility and usability of the refined method.    Golf  1440  100  69  7  Nissan Leaf  1448  80  55  8  Mercedes B-class  1625  132  81  9  Tesla model-S  2050  285  139  10 Tesla model-X 2252 237 105