How much energy does a car need on the road?

Applied Energy 256 (2019) 113948

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

How much energy does a car need on the road? a,b

Lukas Küng a b c

b,c

a,b

, Thomas Bütler , Gil Georges

, Konstantinos Boulouchos

a,b

T

Aerothermochemistry and Combustion Systems Laboratory, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland Swiss Competence Center for Energy Research on Efficient Technologies and Systems for Mobility, Zurich, Switzerland Swiss Federal Laboratories for Materials Science and Technology, Empa, Überlandstrasse 129, 8600 Dübendorf, Switzerland

HIGHLIGHTS

energy demand model for alternative and conventional cars. • Real-world applicable, as input data on car trip are average velocity and mean slope. • Widely of different driving styles and usage of auxiliary devices incorporated. • Impact • Correlations based on dynamometer measurements and field test. ARTICLE INFO

ABSTRACT

Keywords: Passenger cars Real-world energy demand Non-propulsive load Fuel consumption Chassis dynamometer Field monitoring

A car often requires more energy when driven in daily operation than indicated by the manufacturer. This paper presents a model to derive this real-world energy demand for a passenger car, based on a few widely available input data on vehicle operation. The approach works for conventional and alternative propulsion technologies. The underlying data stem from an extensive Swiss chassis dynamometer and on-road measurement campaign, which lasted for more than a year. The test fleet consisted of a compressed natural gas, gasoline hybrid, gasoline plug-in hybrid, fuel cell electric, and a battery-electric vehicle. The derived model adjusts the propulsive power demand within the legislative WLTP cycle for class 3b vehicles to a road mission by incorporating effects of traffic, driving styles, and topography. It additionally accounts for load from auxiliary devices. The approach works with input data from a household travel survey or traffic flow simulation and can serve as a tool to everyone who needs to estimate the average on-road energy demand of any passenger car or a fleet of them, rather than their type-approval values. Tested on a compact-sized vehicle, the approach estimates a mean discrepancy in real-world energy demand to WLTP type-approval values for Switzerland of about 22% for conventional cars. Furthermore, we can show similar gaps for hybrid technologies of around 30% and for batteryelectric cars of 25% .

1. Introduction 1.1. Relevance of vehicle energy demand estimation Energy demand is directly linked to CO2 emissions for vehicles operating on hydrocarbon fuels. Transportation is responsible for more than 20% of the globally emitted fossil CO2 [1] and has, therefore, a prominent role in achieving climate targets. It is not only the energy demand of conventional vehicles that is important to assess. With alternative propulsion technologies and direct

use of electricity as an energy carrier, two sectors become coupled, which are currently operating independently. If we want to evaluate CO2 mitigation potentials of alternative propulsion technologies, we need to consider the amount of additional electricity demand. For strategic planning or scenario analysis of grid extensions or charging stations, it is essential to determine the expected additional load. Research focusing on the replacement of conventional with battery electric vehicles need to assess their feasibility. To assure the same vehicle usage, i.e. technical feasibility to provide mobility demand, we need to either measure available range directly or approximate it by

Abbreviations: AC, Air Conditioner; BAFU, Swiss Federal Office for the Environment; CADC, Common Artemis Driving Cycle; ECU, Electronic Control Unit; EMPA, Swiss federal laboratories for Material, Sciences and Technology; EPA, Environmental Policy Agency; FTP, Federal Test Procedure; GPS, Global Positioning System; HTS, Household Travel Survey; ICCT, International Council on Clean Transportation; NEDC, New European Driving Cycle; PEMS, Portable Emissions Measurement System; PTC, Positive Temperature Coefficient; WLTC, World harmonized Light vehicle Test Cycle; WLTP, World harmonized Light vehicle Test Procedure. E-mail address: [email protected] (L. Küng). https://doi.org/10.1016/j.apenergy.2019.113948 Received 9 April 2019; Received in revised form 3 September 2019; Accepted 23 September 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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vehicle energy demand computations. Feasibility studies can either be on single-vehicle levels and daily usage by a person or fleet options focusing on car-sharing and pooling. In both applications, range and available time to recharge are important parameters, which require energy demand estimations.

computations with PEMS measurements. A similar investigation is [23], which presents a simulation-based approach using an extended Willansline with PyCSIS to model time-resolved on-road emissions of seven conventional vehicles. There exist alternative approaches to determine on-road energy demand. We can group them according to their focus in explaining the difference to legislative test values, which are either based on vehicle operation and usage (here referred to as mission) or on vehicle parameters. Examples for studies focusing on mission are the ones developing alternative driving cycles. Their premise is, that a generalized test cycle is not representative for their local study area and that on-road difference from legislative testing in energy demand or pollutant emissions can be reduced by developing a new velocity profile. Their application is limited to the study area, often a city. Examples are [24] for Mashhad (Iran), [25] for Singapore, and [26] for Celje (Slovenia). These new driving cycles do not serve as a general tool to estimate onroad energy demand. The vehicle oriented studies usually monitor on-road energy demand and correlated them to normative test values with a lumped regression. Such a parameterization depends on type approved fuel consumption, vehicle attributes or additional mission attributes, like average speed [27]. A very prominent example of conventional cars is [28]. The study presents fuel consumption regressions for diesel and gasoline cars, using the type approved value, vehicle mass and displacement volume as determiners. The parameterizations show good agreement with the measured cars and can serve as input to emission models. They were further elaborated in [29,30]. Other examples of regressions are; Ref. [5] that incorporates additional information on transmission, vehicle type and brand, as well as a dieselgate factor, Ref. [31] in which the authors are using Chinese on-road data and correlating fuel consumption with a (mathematical) power function to average vehicle speed, Ref. [32] includes driving behavioral aspects such as total annual mileage or waiting time at red lights, but also the car manufacturing country, and [33] which uses a vehicle-specific power model and additionally analyses test data of hybrid cars. Although these parameterizations cover a large share of on-road fuel consumption variance, they do not resolve any causality of these differences and are limited to conventional technologies. There exist similar parametrization studies and model approaches for real-world energy demand estimation of battery electric vehicles. In [34] the authors present a linear regression model of a Shanghai case study based on initial battery state of charge, ambient temperature, trip distance and mean speed. The study [35] contributes a data regression, which relates variations in energy demand to vehicle attributes, weather data, road characteristics, and household information. A Japanese field study presented in [36] uses a polynomial regression accounting for road grades, auxiliary load and temperature dependence of the electric motor. The paper [37] uses data of Beijing and introduces non-linear models based on battery state of charge, speed, and temperature. In [38] the authors introduce an energy demand model based on the integral on estimated propulsion power, with a focus on regenerative braking. And [39] presents an approach ranging from initial powertrain component analysis to a linear regression on observed data, including road grade, cold start, and air conditioning. The driver for such models is not pollutant emissions but mainly range availability or ecological impact analysis of battery-electric cars. They analogously relate observed energy demands to vehicle and mission attributes, with various degrees of describing the powertrain and its components. To our knowledge, there exists no parametrization approach which is applicable for all propulsion technologies and accounts for effects of different vehicle usage, i.e driving styles and operation of auxiliary devices.

1.2. Why not rely on type approval values? The International Council on Clean Transportation (ICCT) addresses the discrepancy in type approval to real-world CO2 emissions, respectively energy demand, in their series of studies From Laboratory to Road. The 2013 issue reported a discrepancy of below 10% in 2001 and a value of 25% by 2011 for Europe [2]. This value increased to 39% for 2017 [3]. The gap is not unique to Europe but exists for the United States, China, and Japan to various extents [4]. Moreover, not only conventional but also hybrid vehicles show a discrepancy [5]. The role of type approval testing is to establish a legal basis for policies and taxation, by providing boundary conditions for vehicle manufacturers to design new vehicles. A key focus lies on pollutant emissions, i.e. addresses air quality, not essentially vehicle energy demand. Having more realistic test conditions might (1) drive innovation to useful on-road applications, and (2) provide more reliable information for customers [6], especially regarding electrically-propelled vehicles where ranges are defined on type-approval tests. With the introduction of the World harmonized Light vehicles Test Procedure (WLTP), not only the legislative velocity profile, but also the test procedure is revised [7]. The difference to on-road emissions is estimated to reduce, but not fully disappear [8,9]. Various factors affecting on-road vehicle energy demand are not included in the type approval testing. We, therefore, rely on additional approximations respectively models, which account for these factors, when estimating real-world energy demands. 1.3. Existing approaches to estimate on-road energy demand Emission models are common tools for energy demand estimations. They were originally developed for air pollution assessments of conventional cars, where fuel consumption is directly linked to the exhaust emissions. These models are either inventory types to estimate emissions of national or international fleets or instantaneous models to assess single-vehicle emissions [10]. Emission inventories describe vehicle powertrains lumped in one emission factor for different vehicle classes. According to [11], the five frequently used models are MOBILE [12], COPERT [13], HBEFA [14], EMFAC [15] and ARTEMIS [16]. Other examples are VERSIT+ [17] and MOVES [18], which superseded MOBILE. All inventory models provide emission factors defined respective to distance. The total emissions are derived by multiplication with observed or estimated vehicle activity data. Some models describe the emission factors dependent on average velocity or account for traffic situations. Emission models are great for large scale conventional fleets, but do not resolve the spread in emissions and therefore energy demand, e.g. through different driving styles. Instantaneous models, on the other hand, are detail-rich vehicle simulators to compute temporally resolved emission factors. These tools increase the level of detail on the powertrain description and model it component-based. Examples are PHEM [19], AVL Cruise [20] and ADVISOR [21]. These simulators rely on defined velocity and altitude signals, as well as the design and operation strategy of the vehicle powertrain. This requirement on detailed input data limits their application scope for larger fleets. Nevertheless, if the input data is available, they are suitable to quantify single-vehicle emissions on a local road network and can resolve the effects of real-world factors relative to legislative conditions. An example study is [22], where the authors use an instantaneous vehicle model to investigate the influences of real-world conditions on emissions and validate the

1.4. Content of present work This paper presents an approach to estimate on-road vehicle energy demand for all commercially available powertrain technologies. A data2

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driven and computationally lean tool is developed, which can account for variations in vehicle driving, but works with input variables available from household travel surveys or traffic flow simulations to be applicable on a national scope. It is not the goal to predict time-resolved emissions, nor single vehicles. We separate effects from the vehicle technology and the vehicle operation, e.g driving style. Thereby we aim to resolve, not only correlate effects of different real-world factors. We rely on tracked on-road data of five vehicles operated in Switzerland and a dynamometer test campaign. The approach relates detailed information of the measured field trips to widely available parameters, as a set of empirical regressions. The approach is based on energy flows and accounts for load dependencies of powertrain technologies and the usage of auxiliary devices.

are the velocity profiles and the GPS signal over time. GPS positions were snapped on a map of the Swiss road network from which the altitude information is extracted [41]. From velocity and altitude arrays we can derive acceleration and road slope. The quality and frequency of GPS signals heavily vary between vehicles. To assure a reasonable resolution, we introduced a threshold in mean distance between two GPS points of a maximum of 30 m. Only trips that fulfilled this threshold served for the investigation of topography impact, whereas the effect of driving style is analyzed based on all monitored trips. The data stem from the period of October 2016 to January 2018. Table 2 list for each vehicle the number of monitored trips, number of trips which fulfill the GPS threshold and the driven distance. The monitored missions cover most parts of Switzerland as well as individual trips to the neighboring countries. Only missions in Switzerland are considered for topography analysis. When a vehicle crossed the border to a neighboring country, the mission was split at the border and only the one part accomplished in Switzerland was considered. The reason for this is the data availability of the road network to get altitude values.

2. Data 2.1. Vehicles The available data for this paper stem from the ESMOBIL-RED project and the Empa1 test facility data repository. Within the ESMOBIL-RED project, five vehicles with alternative powertrain technologies were monitored and measured for two years. Empa operated the vehicles on a sharing platform and at the same time performed numerous chassis dynamometer tests under laboratory conditions. Table 1 summarizes the main vehicle specifications. Besides the five ESMOBILRED vehicles, we use dynamometer measurement data of conventional gasoline and diesel cars as well as of additional battery-electric cars, coming from an emission inventory project on behalf of the Swiss Federal Office for the Environment (BAFU). Natural gas hybrid and diesel hybrid vehicles were not measured, but follow the powertrain scaling approach of [40].

3. Model concept In [42] the authors investigated various factors that cause differences between legislative and real-world emissions and quantified their potential impact. The highest deviations can result from congestion, aggressive driving, trailer towing and roof boxes. But also ambient temperature and auxiliary systems have an impact. This paper presents a real-world energy demand model, which accounts for these variations. The working principle of the energy demand model is illustrated in Fig. 1. Its conceptual logic follows the two main purposes of a vehicle, namely moving a person in space and providing them comfort. This relates to modeling propulsive and non-propulsive loads. The energy demand model is completed by a powertrain model, describing conversion efficiencies for different technologies. The propulsive load of a vehicle driving on a road follows from Eq. (1). It depends on vehicle mass m, respectively equivalent mass meq to account for rotating parts and the vehicle shape, which is approximated through road load coefficients, also referred to as f-coefficients ( f2 , f1 , f0 ). They express the resistive forces a car opposes on a flat road during a coast-down test, due to aerodynamic drag and rolling resistance as a function of velocity v (t ) [43]. The effective f-coefficients of a vehicle and the ones used to set up the dynamometer for legislative testing do not necessarily have to be equal. The f-coefficients are defined within a test procedure and provided by the manufacturer. In the case of the New European Driving Cycle (NEDC) testing, these values could come from a vehicle within the same family. With the introduction of the WLTP, this discrepancy is expected to be reduced [44,45]. Another parameter affecting the propulsive load is the road slope (t ) , which is not considered in type approval tests. Studies show different impacts of road gradient on fuel consumption. On average, road slope is estimated to increase the fuel consumption about 10% for passenger cars [46–48].

2.2. Chassis dynamometer campaign Multiple laboratory chassis dynamometer tests were carried out in a controlled environment. The used driving cycles were WLTC for class 3b vehicles, the Common Artemis Driving Cycle (CADC), the FTP-75 cycle of the EPA federal test procedure in a shortened form and the former Swiss legislative cycle RA. The test bench settings were in accordance with the manufacturer’s recommendation for each vehicle type, adjusted for the effective masses of the investigated vehicles. The environmental conditions were kept constant during the tests. The majority of tests were carried out at 23 °C and 50% relative humidity. Individual cycles were also repeated at 14 °C and 0 °C to determine the influence of the outside temperature. To eliminate the effects of the cold start behavior on the efficiency determination, the majority of the measurements were carried out with the driveline at operating temperature. The drivetrain efficiency was determined without auxiliary consumers. The fuel consumption of vehicles with internal combustion engines was determined using the carbon balance method, the corresponding energy demand was calculated using the fuel properties. For the electric drives, the vehicle’s current and voltage sensors were used, which were validated in separate measurements. In the case of the fuel cell vehicle, hydrogen consumption was calculated based on the tank pressure signal. The consumption values obtained were validated in the field test by the refueled amounts at the hydrogen filling station at Empa.

Ppropulsive (v (t ),

= f2 · v (t )3 + f1 · v (t )2 + f0 · cos ( (t ))·v (t ) + meq · · g ·sin ( (t ))·v (t )

dv (t )·v (t ) + m dt (1)

The test cycles of the WLTP are designed to approximate the propulsive load on average, but different driving styles, traffic conditions, and route topographies can have severe impacts. We use the monitored velocity and slope signals from the field test to compare the propulsive power from road operation to the normative value, resulting from the WLTC velocity profile. For the comparison, we reduce the high-dimensional power signal to two scalars, expressing the mean positive and negative power. The averaging operators are expressed in Eq. (2).

2.3. On-road monitoring All vehicles were equipped with a logger that accessed the vehicle’s electronic control unit (ECU) data in a 1 Hz resolution, respectively 10 Hz for the Audi cars. The main data used from the logged missions 1

(t ))

Swiss federal laboratories for Material Sciences and Technology. 3

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Table 1 Type approval specifications and road load coefficients of monitored vehicles within the ESMOBIL-RED project, adjusted for the effective vehicle mass. model

vehicle propulsion

Prated [kW]

m [kg]

Prated /m [W/kg]

meq* [kg]

f2 [kg/m]

f1 [kg/s]

f0* [N]

Audi A3 Sportback e-tron Audi A3 Sportback g-tron Volkswagen Jetta Volkswagen eGolf Hyundai ix35 FCEV

plug-in gasoline hybrid compressed natural gas gasoline hybrid battery electric fuel cell (hybrid)

110 81 110 85 100

1710 1360 1525 1590 2041

64.3 59.6 72.1 53.5 52.1

1735 1408 1530 1700 1946

0.4136 0.3769 0.3643 0.2307 0.4829

1.085 0.526 0.301 6.916 3.932

160.054 118.860 124.564 180.474 130.283

* Corrected road load coefficient for effective vehicle mass and for rotating masses lumped in equivalent mass meq .

negative ones are accordingly. Both rI and rII are described by regressions, depending on average velocity and road slope as well as normalized factors to account for driving dynamics and road layouts.

Table 2 Total mileages and numbers of considered trips from the monitored field missions for every test car. model

# trips [–]

Audi e-tron Audi g-tron VW Jetta VW eGolf Hyundai ix35

446 576 706 556 914

# trips(w/

[–]

total distance [km]

399 522 5 75 13

17,266 23,983 26,265 7673 24,310

GPS)

+ P model = rII+·rI+· P (vWLTC ,

= 0) +

P model = rII · rI ·P (vWLTC ,

= 0)

rI+ =

P (vmission, P (vWLTC ,

= 0) + = 0) +

rII+ =

P (vmission, P (vmission,

+ mission ) +

(4) (5) (6)

= 0)

The non-propulsive load is solely dependent on driver preferences. For passenger cars, the two required energy forms are heat for the cabin and electricity for any other device. The load can largely vary by propulsion technology and season, respectively temperature, and especially impact battery electric vehicles [49,50]. Average annual values are reported to range between 310 and 640 W [51]. The estimation of the non-propulsive load is data-driven and results directly from the conducted field study. It depends on ambient temperature and user settings. The vehicle powertrain can be understood as a black-box converting the stored on-board energy carrier to useful energy. It is modeled as transformation function , relating mean positive and negative output power to the required input according to Eq. (7).

Pin =

We use Willans-lines [52] derived from the dynamometer test campaign to describe powertrain technologies. The observed inputoutput behavior is assumed valid for the tested range, regardless if the vehicle is on a chassis dynamometer test bench or the road. The required fuel, respectively electric power for a mission result from the demanded propulsive and non-propulsive loads according to Eq. (8). For battery electric vehicles the stored on-board energy carrier is directly accessible for all devices and does not need to be converted.

Fig. 1. Concept of the energy demand model: For a defined vehicle, the mean propulsive power within the WLTC cycle is corrected for on-road driving through two multiplication factors rI and rII . These are dependent on average mission parameters. The powertrain output load is determined by the corrected propulsive and additional non-propulsive load. The conversion efficiency is modeled by technology-specific Willans-lines.

x+=

(x (t ))·x (t ) dt

x

( x (t ))·x (t ) dt

=

Pfuel =

0 1

if k 0 if k > 0

propulsive ,

P propulsive )

+ + (P propulsive , P propulsive) + P non

propulsive

(8)

4. Methodology 4.1. Powertrain model

(2)

The transformation functions of Eq. (7) for conventional and alternative powertrain technologies are expressed as Willans-lines [52]. These are linear correlations relating input and output power. They are apparent for time-resolved and averaged consideration, and exist for conventional and alternative technologies [53,40]. This paper extends the approach of [54] and models the powertrain performances normalized according to the rated power of the main energy converter. Feasibility of vehicle-specific power correlations for conventional cars was shown in [55,56]. For the powertrain model, we take the measured dynamometer fuel

where

(k ) =

+ + (P propulsive + P non

Pelectricity =

dt dt

(7)

+ (P out , P out )

(3)

The divergence in propulsive load is addressed by two multiplication factors rI and rII according to Eq. (4). The first one accounts for the representativity of the WLTC velocity signal for the on-road operation and the second includes the effect of topography. The definition of these correction factors are given in Eqs. (5) and (6) for positive powers, the 4

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and wheel power signals over a driving cycle, respectively cycle phases (e.g. urban part of WLTC) and compute mean positive wheel power and mean positive power out of the prime on-board energy storage. The observed input-output behavior can be approximated by a linear fit with slope A+ and interception B+. All powertrains show a very good linear tendency, with R2 -values above 0.98. Fig. D.19 in the appendix illustrates the measurement data and the fitted lines for different technologies. We need to distinguish between vehicle operation on fuel out of a tank and pure battery-electric operation. In the former, the conversion unit between prime on-board energy storage and wheel operates unidirectional (internal combustion engine, fuel cell stack), while the later works bidirectional (electric motor). The amount of recoverable breaking energy depends on the mean negative output power. The recuperation for battery-electric operation is modeled as the inverse direction to forward propulsion with identical losses limiting the efficiency. Therefore, A is the inverse of A+ and B is set identical to B+. Hybrids can also recuperate, but the prime energy storage component is the fuel tank and not the high voltage battery. Thus, hybrids are modeled as unidirectional powertrains. The effect of recuperation is incorporated by the lower fuel demand at times of battery mode operation. For the Willans line approximation, the measurement was corrected for the state-of-charge of the high voltage battery. Plug-in hybrid cars operating in charge depleting mode without the prime converter can be understood as battery electric vehicles. Eq. (9) concludes the uniform powertrain transformation function of Eq. (7). For all powertrains with unidirectional converters A and B are equal to zero. The detailed slope and interception values are listed in Table 3.

P in+

=

+ (A+ ·P out

+

B+· Prated )

Fig. 2. Scatter of observed rI+ from the monitored missions expressed over ratio in mean trip velocity. Each point represents the ratio with which to adjust the positive propulsion power in the WLTC to match the real-world vehicle usage. The colors indicate measured driving dynamics.

++ racc

dv dt mission ++ dv dt WLTC

(12)

between the test vehicles reA chi-square homogeneity test in vealed different vehicle driving styles for similar types of missions. Either the observed data set is biased in drivers or not extensive enough to show homogeneity or the powertrain has an impact on the driving dynamics of vehicle operators. To include this potential feedback from ++ the car, we extend racc by the vehicle power-to-mass ratio as explaining parameter for driving dynamics. Eq. (13) displays the new parameter rdynamic .

In this section, we present the derivation of rI+ and rI regressions from all monitored trips of the field measurement campaign. The two values as shown by Eq. (5) are the ratios in propulsion power between the velocity profile of the WLTP cycle for class 3b vehicles and the logged velocity signal. They correct the propulsive load for real-world vehicle driving relative to legislative testing when neglecting topography. For the description of rI+ and rI , we introduce two variables to incorporate type of vehicle usage, e.g for urban or rural trips, and different driving dynamics. We set the average velocity as an indicator for the type of on-road mission and represent it normalized to the legislative driving cycle as of Eq. (10). For the inclusion of driving dynamics we compute the average of the positive acceleration instances of the monitored trip according to Eq. (11) (different denominator than Eq. ++ (2)) and represent it relative to the value of the legislative cycle as racc (Eq. (12)).

vmission vWLTC

( ) = ( )

++ racc

4.2. Adjustment of propulsive power for real-world driving

rvelocity =

(11)

(x (t )) dt ++

(9)

+ (A ·P out + B ·Prated)

(x (t ))·x (t ) dt

x ++ =

++ rdynamic = racc ·

Prated m

(13)

4.2.1. Positive power correction: rI+ Fig. 2 illustrates the rI+ values of every field trip as a function of the normalized velocity rvelocity . There exists a clear trend, which we approximate with a quadratic polynomial function through the origin according to Eq. (14). The scatter around the mean fit in Fig. 2 results from different driving styles, since the logged velocity signal is the only varying input to the power computation. For a given mean velocity the upper limit represents dynamic and the lower eco-friendly driving. The color depicts the introduced driving factor rdynamic . We observe two main trends; at first, trips with lower mean velocity have higher average acceleration values than faster missions. This result is intuitive, as the stop-and-go behavior in urban areas results in more acceleration and deceleration intervals than driving on rural streets or even highways. The second trend is that regardless of the mean velocity ratios, we see a

(10)

Table 3 Resulting Willans-line coefficients from the dynamometer measurement campaign for every propulsion technology. powertrain

A+

B+

A

B

R2

# vehicles

# cycle phases

EURO EURO EURO EURO EURO EURO FCEV BEV

3.0930 2.5979 2.8132 3.3014 2.7730 3.0028 2.3047 1.1229

0.0597405 0.0546462 0.0834192 −0.0213241 −0.0195058 −0.0297762 −0.0021162 0.0052462

0 0 0 0 0 0 0 0.8906

0 0 0 0 0 0 0 0.0052462

0.9877 0.9942 0.9990 0.9950 – – 0.9947 0.9974

7 10 1 2 – – 1 4

53 60 33 66 – – 9 99

6 6 6 6 6 6

gasoline diesel natural gas hybrid gasoline hybrid diesel hybrid natural gas

5

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similar stratification around the mean line. To include these observations in the model, we express the coefficients bI+ and cI+ dependent on rdynamic . Eq. (15) presents the resulting approximation.

rI+ = bI+·rvelocity + cI+·(rvelocity ) 2

bI+ =

(14)

0.24715 + 0.01303·rdynamic

cI+ = 0.38028 + 0.00245· rdynamic

(15)

At this point, we derived a model to adjust the positive propulsion power of a vehicle in the WLTC to an on-road mission using only the mass-specific vehicle power and the mission mean velocity and mean positive acceleration. We test the rI+ -correction by comparison of PI + through Eq. (16) with the mean positive power based on the monitored + velocity signals P (vmission, = 0) for every trip. The relative differences follow from Eq. (17), with the approximated value x approx from the model and the reference value x ref based on the monitored velocity signal, without topography.

PI

+

= rI+ rvelocity,

xapprox , x ref =

Prated ++ , racc ·P (vWLTC , m x approx

= 0) +

(16)

x ref

x ref

(17)

Table 4 lists the mean of the relative differences and its standard deviation for PI + and also the uncorrected cycle value P (vWLTC , = 0) + . The presented approach matches not only well for all missions, but also the single vehicles. The mean relative difference is an order of magnitude lower for the model results than when using the WLTC directly. Significant is the reduction in standard deviation. By applying the derived regression to the same train data set, we expect the mean positive power to match on average. In A we have a closer look at the dependency of the train data set and apply bootstrapping to address over-fitting. In Fig. 3a, we have a closer look at the model performance and illustrates the distribution in relative differences of PI + . We observe a symmetrical histogram shape around zero. With minimal additional information about the mission, we can estimate more than half of the trips below a relative error of 6.2% . The added benefit of the presented approach becomes even more prominent when we consider the relative differences to the WLTC directly. In Fig. 3b we observe a strongly skewed distribution with a heavy tail up to 400% . For all trips on the left of zero the mean positive propulsion power is underestimated by the driving cycle, while for the ones on the right side of zero the WLTC provides too high power values. The existing shape results from the large quantity of monitored urban trips, or simply ones which are generally slower than the WLTC. The standardized test cycle has a fixed share of urban, rural, high and extra-high driving sections and can, therefore, be very off in estimating individual non-average road missions. The WLTC is not wrong but represents an average vehicle driving, from which our set of logged trips differ. The histogram in Fig. 3b would look different for another field test. Interested readers are

Fig. 3. Comparison in mean positive wheel power estimation approaches respective to the result using the fully observed velocity time series. The top figure displays the outcome of the presented model and the bottom one the comparison to WLTP Class 3 driving cycle. The figures correspond to the overall line in Table 4.

referred to B for further explanations regarding the effects of the observed mission data set. 4.2.2. Negative power correction: rI For battery electric vehicles we additionally need to adjust the mean negative propulsion power. Fig. 4 represents the equivalent of Fig. 2 for mean negative power ratio rI . We observe a negative quadratic shape. This implies that for both slow urban and fast highway trips the mean breaking power is lower than in the WLTC. For small velocities, this is due to reduced power requirements which are directly dependent on velocity. Faster missions tend to show lower fluctuations in cruising speed, i.e fewer acceleration and deceleration events than as the WLTC. We approximate the power ratio rI with a quadratic polynomial function in rvelocity according to Eq. (18) and describe the coefficients bI and cI dependent on the rdynamic of Eq. (13). We deliberately use the identical explaining variable for driving dynamic to keep the number of input parameters minimal.

Table 4 + Relative differences of the mean positive cycle power P (vWLTC , = 0) and the modeled power PI + to the reference value from the detailed velocity signal + P (vmission, = 0) (neglected topography). WLTC vehicle overall Audi e-tron Audi g-tron VW Jetta VW eGolf Hyundai ix35

rI+ -adjusted

mean [%]

std [%]

mean [%]

std [%]

73.2 164.3 52.9 29.5 72.3 169.6

301.7 714.2 156.4 112.2 131.4 34.0

0.4 −1.8 −4.2 8.3 −0.9 −0.8

17.2 9.7 8.1 27.7 16.6 11.3

rI = max (0, bI · rvelocity + cI ·(rvelocity ) 2) bI =

0.91651 + 0.03926· rdynamic

cI =

0.88818 + 0.03172· rdynamic

3.79·10 4 ·(rdynamic ) 2

(18)

(19)

In analogy to Eq. (16), we can adjust the mean negative power of the WLTC to an on-road mission value PI . The relative differences of 6

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Table 5 Relative differences of the mean negative cycle power P (vWLTC , = 0) and the modeled power PI to the reference value from the detailed velocity signal P (vmission, = 0) (neglected topography). WLTC vehicle

mean [%]

std [%]

mean [%]

std [%]

54.1 59.0 5.1 68.2 48.7 75.0

380.5 322.1 58.4 573.5 522.3 179.9

−3.4 7.6 −5.6 −1.9 −2.8 −8.9

35.3 19.8 16.7 47.2 26.3 41.8

overall Audi e-tron Audi g-tron VW Jetta VW eGolf Hyundai ix35

4.3. Adjustment of propulsive power for road topography

Fig. 4. Observed rI values to adjust negative propulsion power in the WLTC for different real-world vehicle usage, expressed over ratio in mean velocity. The colors indicate measured driving dynamics.

We account the topography impact with rII+ and rII as shown by Eq. (6). These two represent the ratio in propulsion mean power with road slope to the power on a flat road. We compute rII+ and rII for all monitored missions with sufficient frequency in GPS signals for the two Audi vehicles and the VW eGolf (see Table 2). All power estimations follow Eq. (1) and use the monitored velocity signal of the respective missions, therefore the only difference in propulsion power is caused by the road slope. For the description of rII+ and rII we introduce two variables. The main indicator is the average slope defined in Eq. (22) as the ratio of altitude difference z between origin and destination and the trip distance. As a second parameter, we define the variable + according to Eq. (23). It represents the slope of an on-road trip when only uphill driving is considered. It, therefore, relates to instances when additional power from the powertrain is demanded. + serves as a measure for the directness of the road linking origin an destination. For trips with a positive altitude difference the minimum + is equal to , and zero for all other trips. Any deviation from the minimum value indicates the road altitude is not monotonically increasing, respectively decreasing. These deviations can be interpreted as unnecessary uphill and downhill driving segments of the route to cover the altitude difference between origin and destination. We refer to it as vertical detour.

the modeled negative wheel powers to the ones computed with the monitored velocity signals are summarized in Table 5. The model performance is not as good as for positive powers but still reduces the error compared to the WLTC. The standard deviation is significantly lower for the adjusted powers compared to the cycle values. ++ 4.2.3. Normalize driving dynamics: racc The introduced mean power adjustment only depends on three parameters, but while mean trip velocity, respectively trip distance and duration, as well as vehicle power and mass are easily available para++ meters, the estimation of average positive acceleration racc is not straight forward. It results from a velocity signal, which is often not known. This paragraph provides an approach on how to estimate the average positive acceleration without having detailed insights about the mission, respectively the driving style of the driver. In Fig. 2 we already noted the symmetrical tendency of rdynamic around the mean line. The same trend is also apparent for the average ++ . The mean value is dependent on velocity, but positive acceleration racc the shape of the distribution is invariant. We can therefore normalize it ++ with Eqs. 20 and 21, which express racc as a function of the mean value ++ racc and a spread sprdacc around it. The factor fdynamic represents the normalized driving dynamics factor and ranges between 0 and 1, with 0.5 representing the mean line. ++ ++ racc = racc + (2· fdynamic ++ racc = 1.5646

fdynamic sprdacc =

sin ( ) =

1)·sprdacc ·1.0417

sin (

0.5334· rvelocity + 0.0643·(rvelocity )2

rI -adjusted

(20)

+)

=

z (t ) dt v (t ) dt

=

z distance

(z (t ))· z (t ) dt (z (t ))·v (t ) dt

=

(22)

z+ distance+

(23)

0.5:

++ racc

0.9596 + 0.3142·rvelocity fdynamic > 0.5: 2.606

rvelocity + 0.1279·(rvelocity )2

++ racc

(21)

With the factor fdynamic we created a parameter describing the driving style in a normalized manner. Eqs. (20) and (21) translate this factor to a physical property, here speed-dependent average positive acceleration. We can reverse the process and derive the fdynamic factors for all our monitored trips to get a feeling of how dynamic our test drivers were operating the cars. Fig. 5 illustrates the resulting distribution. The proposed normalization results in a quite symmetrical shape with the mean value of around 0.5. The black line indicates a fitted normal distribution with a mean value of 0.5 and a standard deviation of 0.2175. This approximation of driving styles is unique to not only our set of drivers but also traffic situation, speed limits and generally road design. To what extent this distribution is applicable to other areas of the world is uncertain.

Fig. 5. Distribution in normalized driving dynamic factor fdynamic from the monitored missions and fitted with a normal distribution (mean of 0.5 and standard deviation of 0.2175 ). 7

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further elaborates on the distribution and relevance of mean alpha.

PII

aII+ = 0.97202 +

aII = 1.00503 + bII = 24.54730 cII = 158.86528

+·4.29226

(25)

+

At this point, we can estimate the topography impact using the derived approximation based on mean road slope and + according to Eq. (26). The performance of the model relative to the power estimation with a time-dependent slope signal is summarized in Table 6. Overall the model matches the effective mean amplification factor but also performs well for the individual vehicles. Moreover, the relative differences to the detailed power estimation are negligible and its standard deviation in relatively close borders. We can already conclude that based on Figs. 2 and 6 the correction for average speed is much more important than the topography correction for relative differences. For the vast majority of trips, the rII+ values range closely around one. C

(26)

(27)

2

+·8.09337

(28)

= 0.01649 + (2·froad

sprdslp =

1)· sprdslp

(29)

0.01649 froad 0.5 0.03458 froad > 0.5:

(30)

We can compute froad for all our trips with logged GPS traces. Fig. 7 displays its distribution. We see a very large peak at around 0.5 and an almost symmetrical shape. The black line is a t-distribution approximating the histogram with a mean location of 0.5, = 2.696 , and a scaling factor of 0.1091. The presented result is a characteristic of the Swiss road network and its applicability is therefore limited to Switzerland or areas with similar road networks.

Table 6 Effect of topography on mean positive wheel power: comparison of rII+ between the detailed simulation using measured velocity and altitude signals and the presented model approach. Model

+

4.3.3. Normalize road layouts: + In analogy to the correction in driving style, we have derived an approach to incorporate the effects of topography. The only additional input requirements are mean slope and mean positive slope +. The latter is again not an easy variable to estimate when no detailed data about the mission, or more precisely the route, exist. We thus introduce a normalized parameter froad between 0 and 1, with 0.5 representing the mean value of + . Eq. (29) links the physical positive road slope to the bounded normalized froad factor. The positive and negative deviations from the mean are expressed as a spread variable sprdslp in Eq. (30).

bII+ = 18.35444

Data

= 0)

The results of the negative power estimation are collected in Table 7. The overall impact of topography is larger on the mean negative power. The model shows a slightly smaller mean ratio than observed from the monitored data, overall and consistently for all vehicles individually. When looking at the mean relative differences, we observe a very good agreement in mean values and an acceptable standard deviation.

(24)

cII+ = 127.64154

+)· P (v mission,

rII = aII + bII · + cII ·

4.3.1. Positive power correction: rII+ Fig. 6 illustrates the rII+ values depending on the introduced mean slope . Similar to other studies, we see a positive correlation with an interception larger than one. The positive correlation is intuitive; driving uphill increases the power demand while going downhill has the opposite effect. The positive intercept results from traffic and speed limitations. Although, in reality, the potential energy is conservative for a zero mean slope, the vehicles cannot fully recover this energy when going downhill due to breaking events caused by traffic signalization, interactions with other cars or the duty to obey speed limits. We approximate the correlation in positive power ratio by a secondorder polynomial function with Eq. (24). The color in Fig. 6 represents + . We identify a relatively symmetrical distribution of + around the mean line and describe the interception a II + dependent on this vertical detour factor while keeping the other shape parameters of the fit constant. Eq. (25) presents the fitted coefficients. 2

= rII+ ( ,

4.3.2. Negative power correction: rII For the bidirectionally operating battery electric vehicles, we also need to estimate negative propulsion power. Identically to the positive mean power we derive the correction ratio in mean negative power. The resulting ratios are approximated by Eq. (27), which depicts a second-order polynomial function in mean road slope. Its coefficients are shown in Eq. (28). The shape factors are again modeled constant and the intercept is dependent on + . We rely on the same describing parameter for the scatter around a mean line to keep the number of input variables to estimate propulsion power minimal.

Fig. 6. Observed rII+ values to adjust positive propulsion power due to topography over the mean mission slope. The colors indicate mean positive road slope.

rII+ = aII+ + bII+· + cII+·

+

Table 7 Effect of topography on mean negative wheel power: comparison of rII between the detailed simulation using measured velocity and altitude signals and the presented model approach.

relative difference

rII+

rII+

vehicle

mean [–]

mean [–]

mean [%]

std [%]

vehicle

overall Audi e-tron Audi g-tron VW eGolf

1.069 1.075 1.060 1.100

1.067 1.068 1.063 1.095

0.1 −0.6 0.5 0.5

7.6 4.8 8.8 10.3

overall Audi e-tron Audi g-tron VW eGolf

8

Data rII

Model rII

mean [–]

mean [–]

mean [%]

std [%]

1.186 1.196 1.178 1.190

1.163 1.171 1.158 1.157

0.0 −0.1 −0.1 0.6

16.1 19.7 13.3 12.2

relative difference

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Table 9 Propulsion power model performance: modeled total amplification factor of negative wheel powers and relative differences of P model to mean power values P (vmission, mission) from detailed measured velocity and altitude signals. Model

rII ·rI vehicle overall Audi e-tron Audi g-tron VW eGolf

relative difference

mean [–]

mean [%]

std [%]

1.19 1.22 1.20 0.97

−0.1 7.9 −5.4 −5.6

20.0 16.7 10.6 23.6

Fig. 7. Distribution in normalized vertical detour factor froad of a route from the monitored missions and fitted with a t-distribution (mean of 0.5, = 2.696 and scaling factor of 0.1091).

4.4. Combined adjustment of propulsive power The two correction steps in the previous sections can be combined according to Eq. (4) to estimate mean positive, respectively negative propulsion power. Tables 8 and 9 compare the mean and standard deviation of the model output relative to power values based on detailed time-series signals. The results largely resemble the correction of WLTC for average mission velocity. This is explained by the difference in ranges of the power ratios rI+ and rII+ . Fig. 2 illustrates a range between 0 and 4, while the respective values for topography impact mainly ranges between 0.9 and 1.2 . The relative difference is thus mainly determined by rI+ . In general, we observe a slight underestimation with the introduced approach within a relatively narrow standard deviation.

Fig. 8. Observed usage of the heater and the AC for different temperature ranges.

conditioner becomes more important and is in operation for the majority of trips above 20 °C . Between 15 and 25 °C roughly a third of the on-road trips did not use any auxiliary device to condition the cabin. We can see a large variation in usage depending on temperature, which has a direct impact on vehicle energy demand. For powertrains operating on fuels, the sole additional load is the AC unit, whereas battery electric vehicles need to supply electricity from the high voltage battery to heat the cabin. The monitored vehicle data covers one calendar year and therefore all seasons. The mean ambient temperature was 12.7 °C , with a slightly skewed trend towards warmer temperatures.

4.5. Non-propulsive power demand estimation To understand the impact of non-propulsive load, we rely on monitored real-world usage of heating, air conditioning and other auxiliary devices from the field study. In essence, the non-propulsive load is defined by a 12 V electrical system and the two additional auxiliaries heater and air conditioner (AC). These three independent loads are investigated separately as a function of ambient temperature. For chemical converters, the heat is assumed to be abundantly available while an AC always generates additional load.

4.5.2. 12 V vehicle electrical system For the official fuel consumption test, no auxiliaries are switched on, except the daytime running lights (if the vehicle is equipped with such a system). Further, it is allowed to fully charge the 12 V battery before performing the fuel consumption test. Therefore, the 12 V electrical system does not need to be charged during the test cycle. When assessing the on-road energy demand, we need to account for the 12 V electrical system output load. Three of the five monitored vehicles logged the voltage and current of the 12 V electrical system. For every monitored trip, we compute the mean positive power out of the battery. Fig. 9 illustrates these values by vehicle as a function of ambient temperature. It is apparent, that the battery electric vehicle has much lower power demands from the 12 V system. The two hybrid vehicles show almost identical values. There seems to be a slight dependency on temperature, which we neglect in the approximation due to its low variance in absolute power. We, therefore, introduce two constant power demand according to Eq. (31) depending on the powertrain technology.

4.5.1. Usage of auxiliaries The heater and air conditioner allow for four operation modes, which strongly depend on the ambient temperature. Fig. 8 illustrates their respective usage shares based on all available field data. For temperatures below 10 °C the heater is almost always turned on, in most trips as the sole auxiliary device. With increasing temperatures the air Table 8 Propulsion power model performance: modeled total amplification factor of + to mean power values positive wheel powers and relative differences of P model + P (vmission, mission) from detailed measured velocity and altitude signals. Model

rII+·rI+ vehicle overall Audi e-tron Audi g-tron VW eGolf

relative difference

mean [–]

mean [%]

std [%]

1.09 1.06 1.18 0.57

−2.7 −1.6 −3.6 −2.7

11.2 10.6 10.6 16.7

P12V =

240 for BEV 480 for others

(31)

4.5.3. Positive temperature coefficient (PTC) heater The electric heater is the most relevant auxiliary device in terms of additional load for battery electric vehicles [49]. Its operation can 9

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Fig. 9. Mean 12 V electrical system power for every logged mission for the different vehicles as a function of temperature and the introduced mean approximations.

Fig. 11. Mean AC power for every monitored mission where the air conditioner was used. On top a sigmoid approximation of the mean values for each temperature bin.

impact the autonomy range of a battery-electric car, which is why we need to account for the extra load. The Volkswagen eGolf and the Audi A3 Sportback e-tron are equipped with the same heater, labeled PTC Z115. For both vehicles, the heater power is monitored. The Audi is a plug-in hybrid, but for the analysis of the electric heater load, we only consider the missions that are driven entirely in battery-electric mode. For each trip that used the heater device at least once, we compute the mean heater power and plot the respective values over the ambient temperature in Fig. 10. The crosses represent mean values over a range of two degrees (to assure enough observations). We derive the crosses for all data points between the 2.5 and 97.5% -percentiles and approximate them with a sigmoid function as defined by Eq. 32. The only input variable is the ambient temperature Tamb in degrees Celcius.

PHT + =

1763.3 (1 + e0.3548·(Tamb

11.14) )

PAC + =

680.3 (1 + e

0.3147·(Tamb 23.92) )

(33)

The absolute load for an AC is much lower than for a heater. Contrary to the heater, the air conditioner is basically operating over the entire temperature range. Between 0 and 20 °C , we assume the AC to assist the cabin ventilation by condensing the water from ambient air. 4.6. Limitations on model applicability Propulsive and non-propulsive load estimations follow correlations based on fitting of field measurement. This data is unique to the set of drivers, route choices, traffic situations and road topography of the geographic recording area. We cannot prove (or disprove) the validity of the model for different regions of the world. The two-stage propulsive load adjustment technically introduces an error by considering driving dynamics and topography decoupled. We neglect that the additional load from road slopes changes the time instances at which the propulsive load is positive, respectively negative. This affects the filter function of Eq. (3) resulting in a non-commutative behavior. In order to keep the model approach simple, we neglect this effect. As the results show, this assumption does not cause the relative errors to largely diverge from the ones without topography consideration. We, therefore, conclude it acceptable. When we compute the energy demand of a single vehicle, we estimate adjusted numbers to the respective mission, which still represent averages. By limiting the number of input variables, the corrections become widely applicable, but also generic. Individual, mission-specific attributes are not incorporated in the energy demand estimation. We can therefore never predict single-vehicle missions, but rather average performance for the given vehicle and mission combination, or the average performance for a large enough set of trips.

(32)

4.5.4. Air conditioner (AC) The air conditioner shows an inverse behavior to the heater, but nonetheless dependent on temperature. Fig. 11 illustrates the mean AC power demand for every trip where the air conditioner was turned on, plotted over ambient temperature. The crosses represent again the average value for a two degree Celsius range. We approximate the mean AC power by the sigmoid function defined in Eq. (33).

5. Results of model applications This Section (1) validates the quality of the introduced method to the monitored energy demand of the VW eGolf and the Audi g-tron, (2) demonstrates how to apply the identified correlations on an example trip to result with a distance specific energy demand and (3) estimates the gap between legislative and on-road energy demand for different technologies. Fig. 10. Mean heater power for every monitored mission where the heater was used. On top a sigmoid approximation of the mean values for each temperature bin.

5.1. Validation: apply approach on VW eGolf trips In order to validate the functionality of the presented energy 10

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Fig. 12. Comparison of logged and modeled energy demand for the Volkswagen eGolf; total and separated by components.

Fig. 13. Fuel energy demand for all Audi g-tron trips performed on natural gas, illustrated over mean trip velocity. The blue points are monitored field signals and the orange points the modeled values. The lines indicate the average values.

demand estimation, we recompute every monitored VW eGolf mission and compare the results to the observed signals. The reason why we choose the VW eGolf is the excellent measurement data availability, where the electric motor, heater, and AC are monitored individually. We consider all 556 road trips and set froad to 0.5, where no information regarding the route is available. This analysis primarily allows the validation of the propulsive energy demand approximation through mean mission velocity adjustment and Willans-lines, but also the modeling of auxiliary load. Fig. 12 compares the measured and modeled energy demands per distance. The left side displays the values for the entire vehicle and the right side separate for components. The propulsive load is the most important factor and accounts for 76% of the energy demand. The second-largest share with 18% is caused by the heater. Air conditioning load is on average around 1% . The figure shows the results for propulsive energy demand estimation of two different models; one uses the Willans-line as displayed in Table 3 from all tested battery electric vehicles, while the other uses a Willans-line only based on the VW eGolf data. The former approach represents the energy demand of an average battery-electric car, while the latter is specific to the VW eGolf. With this differentiation, we can separate the effects of vehicle description and functionality of the energy demand model. With the model based on VW eGolf Willans-line, we see a slight underestimation in total energy demand of 2.3% . This can be due to various phenomena not considered in the modeling, e.g. side winds, air density variations with ambient temperature [22], road condition or real vehicle mass due to payload and passengers [42]. In general, the agreement to the measured data is very good on average and also in distribution around it. The mean power approximations of auxiliary loads seem to work very well for the monitored VW eGolf. The largest deviations in energy demand per distance are actually caused by the heater and not the propulsion. Furthermore, the scatter results from the representation over distance, as apparent from the 12 V vehicle electrical system values, which are modeled as constant load. This might suggest, that energy demand per kilometer is not the best-suited unit to model vehicle energy demand.

natural gas. With this filter, 343 trips remain for validation purposes. The total auxiliary load results from the AC and the 12 V vehicle electrical system, as heat is assumed abundant from the internal combustion engine. The energy demand is computed for operation with and without AC and weighted according to the usage displayed in Fig. 8. We link the illustrated usage share to the mean bin temperature and linearly interpolate between them for all other average trip temperatures. Thereby, the monitored ambient temperature serves as the sole determiner for the auxiliary load. Fig. 13 illustrates the monitored fuel signals and computed energy demand for every trip, displayed over the average trip velocity. Apparent is the strong increase towards slower trips. Although the introduced model only depends on average trip values, it is capable of capturing these effects of different vehicle usage. The two solid lines represent the average speed-dependent fuel consumption. The model matches in shape and magnitude. It slightly underestimates the real load but performs well in general. The r-square value for the large set of trips is close to one. Furthermore, Fig. 13 displays why the WLTP underestimates the real-world energy demand. It is a single-point test, suited to approximate energy demands for trips with a similar mean velocity than the WLTC. Occurrences of slower trips with higher fuel consumption lead to the reported discrepancy. 5.3. How to apply the approach: example trip We apply the identified correlations to a diesel, gasoline hybrid and battery electric vehicle in the size range of a Volkswagen Golf to result with energy demand per distance values. The example mission goes via the highway from Zurich to Bern. We are interested in the energy demand of each vehicle for that specific mission. The procedure is the following: 1. Compute mean propulsion powers in WLTC: As a matter of simplification we assume no weight differences between the vehicles. All cars are defined by f2 = 0.363 kg/m, f1 = 0.986 kg/s, f0 = 98 N , meq = 1360 kg and a power to mass ratio of 68 W/kg . With these specifications the resulting propulsion powers are P + = 5579 W and P = 1644 W . 2. Adjust for mean mission velocity and driving dynamics: The trip distance is 124 km and it takes 87 min to reach the destination. This results in a velocity ratio of rvelocity = 1.84 . We assume an average driving style ( fdynamic = 0.5) and therefore end up with rdynamic = 54.5 W/kg . With this value we can compute the coefficients for the power ratios and with the velocity ratio we end up with rI+ = 2.19 and rI = 1.28. Since the trip to Bern is mainly highway driving, the velocity and therefore power ratios are larger than one. 3. Adjust for road inclination:

5.2. Validation: apply approach on Audi g-tron trips As a second validation, this section recomputes the energy demand of the natural gas vehicle. The Audi g-tron, contrary to the VW eGolf, operates on an internal combustion engine and does not provided any load information of auxiliary devices, nor how the test drivers operated them during the field trips. Therefore, the present validation does not only test the functionality of the Willans-approximation for conventional powertrains but additionally the model approach for the auxiliary load. For the validation, we consider only the trips that were carried out on natural gas operation, without the usage of gasoline. The threshold is set to 98% of the fuel energy content that has to be provided by the 11

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The altitude difference between Zurich and Bern is assumed 132 m , which with the provided distance equates to a mean slope of 1.06·10 3 rad . We assume an average road profile ( froad = 0.5) and compute the power ratios of rII+ = 1.06 and rII = 1.11. Combined with the two previous steps we estimate the mean propulsive powers for the given mission and vehicles to be P + = 12, 996 W and P = 2342 W . These values differ largely from the initial estimate of the driving cycle. 4. Account for auxiliary devices: The non-propulsive load is modeled only temperature dependent. We assume an ambient temperature of 12 °C and both heater and air conditioner to be in use. The respective mean loads are PAC = 16 W and PHT = 748 W . The 12 V electric system load is 240 W for the battery electric car and 480 W for the others. 5. Include powertrain conversion: According to Eq. (8), for the diesel and gasoline hybrid car, the powertrain output power is the sum of propulsive and non-propulsive load, with the heater power set to zero. For the battery electric vehicle, the propulsion power and auxiliary load are considered separately. Using Eq. 9, we result with mean fuel respectively electricity powers of Pdiesel = 40.1 kW, PHEV , gasoline = 42.6 kW and PBEV = 14.5 kW . Therefore, the respective energy demands are ediesel = 469 Wh/km, eHEV , gasoline = 498 Wh/km eBEV = and 169 Wh/km . It is interesting, that the diesel is modeled advantageous to the gasoline hybrid. Due to the large highway share the mean power is high, at which diesel combustion is performing superior to the gasoline hybrid configuration. 5.4. Gap in on-road energy demand by powertrain technology The presented approach allows quantifying the gap in energy demand between legislative testing and on-road driving for all powertrain technologies. To compute the real-world factors for Switzerland, we consider a representative, compact-sized vehicle defined by f2 = 0.363 kg/m, f1 = 0.986 kg/s, f0 = 98 N, meq = 1360 kg and a power to mass ratio of 68 W/kg . We choose all monitored trips with a complete altitude profile for the computation. For this set of missions, we use the distance, duration, altitude difference, ambient temperature as well as normalized fdynmc and froad values as input. We repeat the process for all powertrain technologies. Vehicle mass differences due to different propulsion technologies are neglected for simplification. Therefore, we can use the same f-coefficients for all technologies. Fig. 14a illustrates the resulting distance specific energy demand of the used energy carrier. The boxplots represent on-road energy demands, while the crosses show the respective computed WLTC values (driving cycle as mission, no auxiliary loads). The three conventional vehicles show the highest energy demands, with the diesel engine being the most efficient one. Hybridization results in a nominal reduction in energy demand, but still shows a gap in on-road operation. The fuel cell electric vehicle can be grouped with the other hybrid powertrains. Its energy demand and on-road gap are comparable. The battery-electric car has the lowest energy demand, due to the most efficient propulsion technology. Additional heating load impacts the gap to on-road energy demand. The real-world energy factors do not directly follow from Fig. 14a due to two limitations; (1) the boxplots illustrate the results of the individual missions, treating every mission equally important (average over missions). But in terms of real-world factor, the total trip energy and not distance specific value is of relevance. The trip distances weight the importance of the computed mission-specific energy demands. And (2), the ensemble of considered missions follow from the field study and does not have to coincide with a representative vehicle usage for Switzerland. To incorporate national representativity, we choose the mean mission velocity as characteristic mission determiner. Fig. 14b illustrates the computed energy demands as a function of mean velocity for every powertrain. The lines represent mean values, identical to the

Fig. 14. Computed energy demands for an average Swiss vehicle for different powertrains, based on the monitored vehicle operation of the field study.

results shown for the Audi g-tron validation in Fig. 13. All technologies show a velocity dependency. The conventional cars have a severe fuel increase for slow, city-like trips due to part-load behavior. Hybridization manages to largely reduce this effect and additionally improve fuel consumption, resulting in lower, almost straight lines. Battery-electric cars also show an increase in slower trips. This is due to the increased relevance of non-propulsive load (mainly heating) as the propulsion demand reduces. Based on the mean mission velocity, we assign a weighting factor to each trip. These weights come from introducing velocity bins and comparing their relevance to the national household travel survey (HTS) called Mikrozensus Mobilität und Verkehr (MZMV) [57]. Fig. 15 shows the velocity distributions for our field measurement in red (ESMOBIL-RED project) and the HTS data in gray. The project over-represents faster missions, related to long-distance highway trips. We assume this behavior an artifact of the car-sharing platform, where people deliberately rented a car for weekend trips (which are generally longer than work commutes). We correct this bias through the introduction of a weighting factor for each bin. Table 10 summarizes the real-world factors for all propulsion technologies. Mission Averages are built on the bases of individual trips, averaging their real-world factors and thereby considering each mission equally important. The effective difference in energy demand for a set of missions is apparent when building the Energy Ratio over all observed trip. We summarize the absolute energy demand of every mission and compare it to the total normative energy demand, resulting from multiplication of the type-approval value with the observed mileage. 12

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Table 10 displays three entries for battery-electric vehicles. They differ in the consideration of battery charging, which is included based on the model derived within the ESMOBIL-RED project and published in [54]. Depending on the application of real-world factors, different definitions are relevant. As a starting point, a hypothetical user can compute the energy demand of any battery-electric car (existing or not) in a WLTC or use the measured WLTP value. The latter include charging losses. For range anxiety studies the operational energy demand is important, whereas energy analyses rely on factors with charging included, i.e. the electricity demand for the grid. With a real-world energy factor of 1.25, the electric car shows a similar divergence than the other technologies. Charging losses largely increase the energy demand and should be included in every study which assesses the grid load of battery-electric cars. The energy demand values of plug-in vehicles can be estimated from the battery-electric and respective hybrid values, using a utility factor as the weighting of the two. It implies the share of distance which can be covered all-electrically to the total driven distance. Legislative test procedure estimates a consolidated European utility factor based on monitored vehicle usage analysis (WLTP and FIAT ECODRIVE database) and uses the electric range as input [58]. With a current plug-in hybrid battery capacities the nominal all-electric ranges are in the order of 40–50 km, which results in a utility factor around 70% . This means only 30% of the driven distance is considered to require the chemical energy converter (internal combustion engine or fuel cell stack). Since legislation considers electric operation emission-free, the CO2 emission value of a plug-in hybrid in our example would be set as 30% of the emission during hybrid operation. In reality, a vehicle can be operated differently, adding customer behavior to the list of uncertainty factors affecting the real-world energy demand value.

Fig. 15. Distribution in trip velocity of the field measurement campaign in red (ESMOBIL-RED project) and the data of the national household travel survey in grey (Mikrozensus Mobilität und Verkehr 2015 (MZMV)), used for the representativity correction for national scale. Table 10 Modeled real-world energy demand factors for different propulsion technologies of a compact-sized car. Mission Average results from averaging the real-world factors of all monitored road-trips, treating every mission identically. Energy Ratio accounts for the higher relevance of longer trips and represents the observable real-world factor at a fuel pump or charging station. Project refers to the uncorrected field campaign data of the ESMOBIL-RED project, whereas HTS are the mean velocity corrected values for Switzerland. powertrain

Missions Average

Energy Ratio

Project

HTS

Project

HTS

EURO 6 gasoline EURO 6 diesel EURO 6 CNG

1.38 1.38 1.39

1.58 1.59 1.63

1.17 1.16 1.13

1.22 1.22 1.20

EURO 6 hybrid gasoline EURO 6 hybrid diesel EURO 6 hybrid CNG FCEV

1.36 1.35 1.35 1.36

1.37 1.36 1.32 1.43

1.35 1.36 1.39 1.30

1.30 1.31 1.32 1.28

BEV (w/o charging)a BEV (incl. real-world charging)b BEV (w/ charging)c

1.38 1.75 1.38

1.37 1.77 1.40

1.31 1.60 1.27

1.28 1.59 1.25

6. Conclusions The developed approach is a tool to estimate on-road vehicle energy demand as an alternative to corrected legislative cycle values by emission factors. It is a fast empirical model, suitable to describe average fleet emissions. Its modular setup separates mission and vehicle effects and makes it universally applicable to all powertrain technologies. Vehicle power specific Willans-lines exist for every propulsion system and were derived through a dynamometer measurement campaign. Furthermore, the approach accounts for different driving styles, the largest influencing factor on real-world fuel consumption [42]. We describe it with one normalized factor and can translate its effect to any mission, defined by mean velocity. Our data analysis showed, that the type of mission, i.e. city, rural or highway has a much higher impact on energy demand than topography. It is therefore much more essential to adjust for mean mission velocity than to resolve road slopes. This finding confirms why locally developed city driving cycles outperform WLTC in energy demand estimation for a specific area. In addition to the propulsive load, we quantified the influence of heaters and air conditioners dependent on ambient temperature and their usage based on driver preferences. The PTC heater not only operates on higher loads, but it is much more often used than the air conditioner in the case of Switzerland. For battery electric operation, the heater is by far the most relevant auxiliary device. We could limit the number of required input data to widely available parameters from e.g. a household travel survey and use these parameters to describe the variation in on-road energy demand. The accuracy is limited to average vehicle results. The approach cannot be used to predict single, or time-resolved vehicle emissions. Local relevant factors like winds, different road resistances, effective vehicle masses, and shapes are lumped in the description of the vehicle (fcoefficients) and not resolved in the model approach. Furthermore, cold start effects or vehicle preconditioning by a garage are not considered in the present study.

a No charging considered, only operational energy demand; real-world operation w.r.t. operation in WLTC. b Include charging for all road missions; real-world operation and charging (grid energy demand) w.r.t. operation in WLTC (no charging). c Effective real-world factor for WLTP; real-world operation and charging w.r.t. operation in WLTC and charging (WLTP value).

Thereby, we account for the relevance of longer trips. In general, the Mission Averages are higher, as the more frequent, short trips, which are usually slow, city-like trips, have a higher impact. This mainly affects the conventional powertrains and the battery-electric car, that show a large non-linear increase in energy demand at lower velocities according to Fig. 14b. The differences between Project and HTS stem from the mean velocity weighting introduced through Fig. 15. The real-world factors to adjust national activity data (vehicle mileage) to match fuel sales statistics are thus the Energy Ratio values in the HTS column. For conventional cars, this factor is about 1.22, respective to the normative WLTP values. It agrees in magnitude with the reported increase from NEDC to WLTP of around 10–15% [8,45] and the average, European NEDC to real-world emission gap of 39% according to ICCT [3]. However, the average, conventional trip has a real-world factor of around 1.6 . Hybrid propulsion technologies show a mean real-world factor of around 1.3. As hybridization largely evades the speed-dependency on fuel consumption, these values are only mildly affected by the reweighting steps and, therefore, similar for all columns in Table 10. The results indicate that the gap for on-road emissions might further increase through the introduction of hybrid vehicles. 13

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The monitored data is specific to Switzerland and the set of drivers within the ESMOBIL-RED project. To confirm a general validity, additional validation on different data sets is required.

Acknowledgments The authors gratefully acknowledge the financial support of the Swiss Federal Office of Energy (BFE) [SI/501311–01] that supported this research project.

Appendix A. Bootstrapping: model performance depending on logged field data The presented regressions use all available field trip data as a train set. Potential bias within the monitored data impacts the approximations and might affect the general applicability of the found fits. Each mission is weighted identically, meaning they are not adjusted to express representative vehicle usage (if such a thing even exists). The field campaign setup might lead to individual trips that do not represent how vehicles are effectively used. Such outliers impact the identified regressions. Furthermore, the approximation itself is prone to over-fitting, which needs to be tested. We apply bootstrapping to estimate the bias within the monitored data. It uses the existing set of observations but creates an artificial second sample set by drawing with repetition. Through the sampling for observed missions, we account for the relevance of individual measurements to the identified regressions. Fig. A.16 shows the distribution in mean relative difference for the bootstrapped sample sets. We observe a very symmetrical shape with a narrow standard deviation. Table A.11 lists the respective numbers, also for the standard deviation. Both, positive and negative power approximations show good results with a small variation in standard deviation. We conclude, that the presented regressions are capable to adjust the respective power values regardless of the train data set. They are therefore generally applicable. The WLTC with its fixed share in cycle phases should be much more dependent on the selection of trips. The mean values in Table A.11 are more or less stable, but the standard deviation highly changes with the set of monitored trips. B further addresses the dependency between WLTC and the train data set.

+ Fig. A.16. Distribution in mean relative difference of PI , model + to PI (vmission) resulting from bootstrapping the logged missions.

Table A.11 Results of bootstrapping on mean value and standard deviation of relative difference in estimated propulsion power to value based on logged velocity signal, for the introduced model approach and the WLTC. mean [%]

std [%]

0.4 ± 0.3 −3.4 ± 0.6

17.0 ± 2.9 35.2 ± 0.7

rel. diff. in

PI PI

+

P (vWLTC ,

= 0)

P (vWLTC ,

= 0)

+

73.2 ± 5.3

292.4 ± 73.1

54.8 ± 6.7

364.9 ± 108.0

Appendix B. Controlled sampling: WLTC performance depending on monitored field data In this section, we address the dependency of our field data set on WLTC power estimation accuracy. Fig. 3b shows a large deviation in relative difference when using the WLTC to estimate the mean positive propulsion for the monitored missions. This effect has to do with the representative design of the test cycle. It consists of four cycle phases, each representing driving behavior on a different road type. The fixed combination of these individual parts accounts for average vehicle operation. In reality, no single mission follows such an average tendency. But over a large set of trips, the WLTC should approximate the mean energy demands. The total bar heights in Fig. B.17 illustrate the histogram in mean mission velocities relative to the average test cycle speed. Interestingly, the mean value of all field trips is identical to the WLTC. But we see a skewed and unsymmetrical distribution. There exist a lot of slower, urban trips, probably resulting from the VW eGolf. These missions cause the heavy tail in Fig. 3b. We test the applicability of the representative WLTC, by selecting a set of measurements that should match the cycle vehicle usage on average. We control the sampling, i.e. limit the mission selection to result in a normal distribution around one. The red bars in Fig. B.17 indicate the sampled 14

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Fig. B.17. Distribution in rvelocity . The red bars represent the normally distributed subset of trips from the controlled sampling.

Table B.12 Results of controlled mission sampling on mean value and standard deviation of relative difference in estimated propulsion power to value based on logged velocity signal, for the introduced model approach and the WLTC. mean [%]

std [%]

3.2 ± 0.4 −5.2 ± 0.6 21.2 ± 0.7

17.0 ± 3.9 29.9 ± 0.8 60.3 ± 5.2

11.5 ± 1.7

73.0 ± 11.8

rel. diff. in

PI PI

+

P (vWLTC ,

= 0)

P (vWLTC ,

= 0)

+

subset of field data. The results of multiple sampling runs are collected in Table B.12, showing the dependency of the selected data set on the mean value and standard deviation. The mean relative difference in the power estimation of the WLTC is better than for the complete data set. Significant is the reduction in standard variation, for both positive and negative power estimation. We see, that the controlled sampled data set better represents the average driving of the WLTC, and therefore leads to lower relative differences. Still, the introduced approximation which does account for the differences in average velocity to the test cycle outperforms the WLTC results. Appendix C. Distribution of mean alpha This section focuses on the possible values of the average road slope. Fig. C.18 illustrates the distribution of mean alpha for the monitored missions with a GPS signal above the set threshold. We observe a symmetrical behavior of around 0. The black line represents a fitted t-distribution with mean location of 0.00036, = 1.47608, and scaling of 0.00245. Even for a country like Switzerland, the majority of mean slopes are close to 0. Many trips are limited to a relatively small area, i.e. within a city and its surrounding suburbs, but not across the entire country. With longer trips, it becomes more likely to have a higher altitude difference, but its relevance decreases with mission length. Therefore, the mean road slopes accumulate around 0. The symmetric shape is believed to result from how vehicles are used. A car is usually operated from one location and returns there by the end of the day. Therefore, the overall height difference is 0.

Fig. C.18. Observed distribution in mean road slope.

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Appendix D. Chassis dynamometer measurements Table D.13 gives an overview of the tested vehicles, lists their rated power and number of available cycle measurements grouped by powertrain technology. The observed and normalized mean positive input and output powers are illustrated in Fig. D.19. Each graph represents one powertrain technology and contains the fitted Willans-line. Table D.13 Tested vehicles on chassis dynamometer. model

Prated [kW]

# cycle phases [#]

GASOLINE IC-Engine (Euro 6) VW Golf VII R BMW 428i Alfa-Romeo Giulietta 1.4 TB Fiat 500 Skoda Octavia C 1.8 4 × 4 Suzuki SX4-Cross Audi A3 1.4 TFSI

221 180 125 77 132 88 92

53 8 8 8 8 8 8 5

DIESEL IC-Engine (Euro 6) VW Golf VII 1.6 TDI Mazda CX-5 D LP 4WD BMW 530d Xdrive Touring F11 Mercedes-Benz GLK220 BlueTec VW Passat 2.0 Bl. TDI Renault Scenic 1.6 dCi130 Mini Cooper D Mercedes-Benz A220 CDI BMW X3 xDrive 20D Peugeot 308 SW Blue HDI

81 110 190 125 103 96 85 125 140 110

60 5 5 5 5 5 3 8 8 8 8

81

33 33

GASOLINE HYBRID (Euro 6) Audi A3 Sportback e-tron Volkswagen Jetta Hybrid

110 110

66 33 33

HYDROGEN FUEL CELL HYBRID Hyundai ix35 FCEV

100

9 9

BATTERY ELECTRIC Mitsubishi iMiev Renault Kangoo EV Ford Focus EV VW eGolf

49 44 107 85

99 53 9 25 12

NATURAL GAS IC-Engine (Euro 6) Audi A3 Sportback g-tron

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Fig. D.19. Fitted Willans-lines for different powertrain technologies based on dynamometer measurements.

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