Applied Energy 269 (2020) 115095
Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
A scalable energy modeling framework for electric vehicles in regional
transportation networks
Xiaodan Xua,
T
⁎,1
, H.M. Abdul Azizb,2, Haobing Liuc, Michael O. Rodgersc, Randall Guenslerc
a
Texas A&M Transportation Institute, 1111 RELLIS Pkwy, Bryan, TX 77807, United States
Department of Civil Engineering, Kansas State University, Manhattan, KS 66506, United States
c
School of Civil and Environmental Engineering, Georgia Institute of Technology, 790 Atlantic Drive, Atlanta, GA 30332, United States
b
HIGHLIGHTS
model predicts electric vehicle energy usage in large-scale networks.
• Activity-based
Network method is used to estimate energy rates by operating conditions.
• ATheBayesian
model closely reproduces full vehicle simulation but is 100× faster.
• The inference
approach was demonstrated in an Atlanta case study.
• The modeling
• modeling approach is scalable and transferable to other regions.
ARTICLE INFO
ABSTRACT
Keywords:
Electric vehicle
Transportation network
Vehicle drivetrain simulation
Bayesian Network
Regional-scale energy prediction
Vehicle electrification plays a central role in reducing global energy use and greenhouse gas emissions.
Predicting electric vehicle (EV) energy use for future transportation networks is critical for the planning, design,
and operations of sustainable transportation systems. However, there is currently a lack of EV energy modeling
approaches that are fully-scalable to large transportation network applications and consider actual on-road
vehicle operating conditions. Such an approach is required for the accurate assessment of EV energy impact
under various transportation scenarios. Here we present a simulation-based quasi-statistical approach to estimate EV energy consumption under various on-road vehicle operating conditions. In this approach, a Bayesian
Network method is used to integrate outputs from full-system vehicle simulation tools for specific makes and
models of EVs under a wide-variety of on-road operating conditions. These outputs are used to develop inference
models that greatly improve computational efficiency, while maintaining most of the prediction accuracy of the
complete system models. This approach is both highly scalable and transferable for analyzing the energy impact
of EV fleet deployment in different regions, can facilitate the estimation of network-level EV energy consumption, and can be incorporated into a wide-variety of transportation planning models. In our case study of Atlanta,
GA, the results indicate that if 6.2% of urban travel distances and 4.9% of rural travel distances were to be driven
by EVs, regional fuel savings would be around 4.0% for a typical travel day in 2024.
1. Motivation and background
Transportation systems accounted for 27% of worldwide energy use
and are major contributors to global greenhouse gas (GHG) emissions in
2010 [1]. Electric vehicles (EVs), including battery electric vehicles
(BEVs), hybrid-electric vehicles (HEVs), plug-in hybrid-electric vehicles
(PHEVs), and fuel cell electric vehicles (FCEVs), have great potential to
reduce transportation energy use and greenhouse gas (GHG) emissions
[1–3]. Electric motors are very efficient at converting energy to tractive
force, electric utilities are more energy efficient than engines, as a result, EVs can greatly reduce energy consumption during vehicle operation compared to their conventional gasoline vehicle counterpart
[4]. EVs can also operate partly or entirely on electricity generated from
local, renewable, and less-carbon-intensive energy sources than
Corresponding author.
E-mail addresses: X-Xu@tti.tamu.edu (X. Xu), azizhusain@ksu.edu (H.M.A. Aziz), haobing.liu@gatech.edu (H. Liu),
michael.rodgers@ce.gatech.edu (M.O. Rodgers), randall.guensler@ce.gatech.edu (R. Guensler).
1
ORCID ID: orcid.org/0000-0002-9650-9156.
2
ORCID ID: orcid.org/0000-0002-8135-4577.
⁎
https://doi.org/10.1016/j.apenergy.2020.115095
Received 27 September 2019; Received in revised form 12 April 2020; Accepted 25 April 2020
Available online 18 May 2020
0306-2619/ © 2020 Elsevier Ltd. All rights reserved.
Applied Energy 269 (2020) 115095
X. Xu, et al.
gasoline [5], which makes wide adoption of EVs a promising approach
to reduce dependence on petroleum fuels and reduce GHG emissions.
Hence, EVs are likely to have a significant impact on the overall lifecycle efficiency of future transportation systems.
In 2017, global sales of new EVs exceeded one million units, and
global EV stock surpassed three million vehicles [6]. The US Energy
Information Administration expects that a 9% EV market share in annual sales can be achieved by 2025 in the U.S. with current technology,
economic, and demographic trends [7]. However, the actual energy
impacts EV market penetration in large-scale transportation networks
remains uncertain. While current energy and emission models, such as
MOtor Vehicle Emissions Simulator (MOVES) from the U.S. Environmental Protection Agency [8], can reliably predict the relationship
between activity and energy consumption of conventional vehicles,
those are not able to directly predict energy use and emissions from
EVs, including HEVs. Although metrics like average fuel economy are
often used in regional energy analyses, they are not always representative, because actual on-road energy efficiency may be significantly lower than the laboratory test results [9]. As a result, better
modeling tools are needed so policy makers and auto manufacturers can
assess how variation in fleet composition and operation conditions will
change on-road energy use and emissions. The work presented in this
paper develops a scalable modeling approach that can predict EV energy use for the wide-variety of on-road operating conditions under
which EVs will be driven. The proposed approach provided a direction
for modeling EV fleet from corridor-level activity to network-level (i.e.,
functions in MOVES), allowing the framework to be used in assessing
the impacts of regional transportation infrastructure development scenarios.
1.2. Research goals
A scalable EV energy model should be able to predict regional energy use patterns for all common EV technologies, under a wide-range
of operating conditions, and should be able to assess the impacts of
future system-level changes, such as operational improvements introduced by shared and autonomous vehicles. To address current model
shortcomings, the proposed methodology needs to:
(1) Support energy use modeling accommodating all existing EV technologies including BEVs, HEVs, PHEVs and FCEVs;
(2) Accept inputs that are directly measurable from transportation
systems, treating factors such as powertrain specifications as hidden
variables that are linked to measurable factors;
(3) Predict energy use under a wide range of operating conditions, such
as vehicle speed, vehicle acceleration, and road types.
(4) Assess EV energy impacts under different transportation operation
scenarios, different fleet composition and in different regions.
In this paper, we developed a Bayesian Network based modeling
approach that can predict the energy use of all types of EVs for the
wide-variety of on-road operating conditions. The modeling approach is
compatible with MOVES and is transferable to different regional
transportation networks. Furthermore, with greatly improved computational efficiency, our model is highly scalable and can be used in
assessing the impacts of large-scale regional transportation infrastructure development scenarios. Finally, the potential of the proposed
model framework is demonstrated in an Atlanta, GA case study to assess
energy savings caused by EV adoption.
2. Methodology
1.1. Literature review
To model EV energy consumption, it is necessary to estimate the
total energy required across a comprehensive set of operating conditions, and then to quantify how that energy demand is split across
different power sources in hybrid electric vehicles (i.e., the internal
combustion engine and electric motor) [29]. Given the low EV market
share and limited funding available for comprehensive data collection,
it is not practical to collect sufficient energy data for all makes and
models of EVs under all potential real-world operating conditions. In
this case, vehicle simulation tools provide a viable alternative to the
collection of in-field energy use data, until such comprehensive data
sets become widely available.
In this research, we classify potential modeling tools for vehicle
energy estimation into three categories: (1) powertrain and full-system
vehicle simulations, (2) simulation-based inference derived from simulation outputs, and (3) purely data-driven models. Full simulation
models, such as Autonomie [14] and FASTSim [15] predict the power
flow within a vehicle, using embedded engine maps and power transmission rules [30]. While full-system simulation models provide highfidelity results, they require detailed engine specifications as input and
are often challenging to apply within large transportation networks,
due to computational cost and resource limitations [31,32]. Powertrain
simulators are also not well-suited for answering reverse engineering
problems, such as how to optimize vehicle operation at the networklevel to reduce energy consumption [32]. Data-driven models, such as
the MOVES, have been widely used for modeling mobile source emissions [33]. In the MOVES model, classification and regression tree
(CART) analysis of laboratory testing data and on-board monitoring
data is used to bin energy use and emission rates by on-road operating
condition and the model is scalable to large transportation networks
[31,34–36]. Data-driven models with higher dimensionalities, such as
neural networks, have also been applied to define EV energy use by onroad operating conditions from existing data [12]. The quality of datadriven models highly depends on the quality of training data, which
remain sparse. Data-driven models also tend to over-simplify the
Numerous studies have investigated the system-level factors that
significantly impact EV energy use. These research findings were typically derived from real-world vehicle measurements or full-system vehicle simulators. Studies that have used real-world energy measurements, such as those derived from on-board diagnostic (OBD) system
data, have identified multiple factors that affect EV energy use and
available range, including vehicle powertrain design and control strategies [9,10], on-road operating conditions [9–12], physical roadway
characteristics [11,12], battery state-of-charge (SOC) [9], and ambient
environmental conditions [13].
The conclusions of studies that have used full-system vehicle simulation tools, such as Autonomie [14], developed by Argonne National Laboratory (ANL), and FASTSim [15], developed by National
Renewable Energy Laboratory (NREL), generally align with field results
[16–19]. Many of the studies in the literature focused on identifying or
assessing powertrain control strategies designed to minimize vehicle
energy use [19–21], rather than assessing regional impacts. Case studies and scenarios have typically focused on one or two EV types and
only covered a subset of operating conditions within what are normally
highly-dynamic transportation networks [11,12,18]. Hence, research
results from different studies are not directly comparable to each other,
nor are they generally transferable, as they lack the scalability required
to assess energy consumption in regional-level transportation networks
[22,23]. Most of the existing regional studies have therefore used fuel
economy and driving range as surrogates for quantifying EV energy use
at the regional scale [24–26]. However, these results are not sensitive to
key factors that significantly affect energy use, such as speed/acceleration, road grade, accessory use, and charging frequency. Furthermore, EV powertrain control technologies continue to evolve, requiring
ongoing data collection and assessment efforts. But the low EV adoption
rate [27], lack of open data from manufacturers, and limited research
funding for in-use data collection have hampered EV model development [10,18,28].
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Applied Energy 269 (2020) 115095
X. Xu, et al.
scalability is tested in a regional-level case study. The details of each
step are elaborated in the following sections.
complex functions and interactions within powertrain operations and
struggle to explain complex non-linear and discontinuous operations.
Thus, full-simulation and data-driven aggregate models have significant
limitations in estimating EV energy use, especially hybridized EVs.
In this study, a parameterized simulation-based inference approach
balances the benefits of full-system simulation modeling with the efficiency of data-driven modeling. The modeling framework combines
vehicle performance knowledge derived from simulations with a datadriven structure, which greatly improves scalability. The vehicle powertrain is represented by a Bayesian Network statistical model, which
adopts the domain knowledge as a priori, and can be trained using data
driven approach [37,38]. The structure of a Bayesian Network is
composed of nodes and arrows, where the nodes represent the probability distribution of variables that are either observable or hidden,
and the arrows represent the dependence or even causal relationship
between variables. Unlike full-system simulation models, in which
outputs are generated from complex physical formula in deterministic
form, the Bayesian Network uses simple parametric form [37,38]. The
developed model in this form can be easily applied to vehicle operation
data using estimated parameters. Unlike the data-driven approaches,
this method adopts the Bayesian Theorem and uses domain knowledge
to reduce uncertainty in predictions. Hence, the knowledge of vehicle
design and control is used to build the architecture of arrows and nodes
in the model, which helps reduce uncertainty in predictions and improves model interpretability. Finally, the model uses observable values
within the transportation network, such as on-road vehicle operating
conditions and roadway characteristics were used as independent
variables, helping to ensure that the model is sensitive to factors of
interest and directly connected to the transportation system. In sum, the
Bayesian Network model makes the system scalable, from meso-scale
corridor-level activity to macro-scale transportation networks.
In the analyses that follow, the Autonomie full-system vehicle simulation tool is used to generate energy use data for training under a
wide-variety of on-road driving conditions, for a representative set of
EVs. Four analytical steps are undertaken to convert the full-system
simulation outputs to scalable EV energy models for application in
large-scale transportation networks. Fig. 1 below illustrates overall
modeling approach. These steps include input generation, vehicle simulation, statistical analysis, and network applications. A set of BEV,
HEV, PHEV, and FCEV models were configured for analysis in Autonomie, and energy use data for each vehicle option were generated for a
wide range of on-road operating conditions. The energy consumption
models were then developed for the various EV types using Autonomie
outputs, combining the physical knowledge about vehicle operation
with data-driven inferences. The energy model is verified using a separate trip data set to obtain the goodness-of-fit metrics and the
2.1. Data preparation
As discussed above, vehicle powertrain design, on-road vehicle
operations, roadway characteristics, and ambient environment have
significant impact on energy use of electric vehicles. It is critical to
account for the impact of those factors using model variables that can
be observed/measured in the real world. The following sections introduce the key considerations in preparing data for the modeling
processes.
2.1.1. Vehicle powertrain design
Vehicle powertrain specifications, include the power source and
power converter information, cannot be discerned directly by observing
the vehicle fleet. Hence, vehicle type information is typically used as a
surrogate for powertrain specification, assigning powertrain information reported by manufacturers to selected vehicle types in the modeling process. In this study, we selected seven typical EV models to
represent the current EV fleet. The Toyota Prius and Prius Prime (39%
of market share), Ford Fusion hybrid and similar models (15% of
market share), Tesla series models (9% of market share), Chevrolet Volt
and similar models (4% of market share), and Nissan Leaf (2% of
market share), which taken together account for nearly 70% of the EV
market (BEV + PHEV + HEV) in 2017 [39,40]. The Toyota Mirai was
selected as the base model for FCEVs, as it is one of the few early
commercialized FCEV models [41]. The powertrain specifications of
these seven EV types are summarized in Table 1 below.
2.1.2. On-road vehicle operation and roadway characteristics
The most common method to explicitly define on-road vehicle operating conditions and roadway characteristics, is to collect second-bysecond speed, acceleration, and location information collected using a
GPS system and spatially-match the data to roadway location to obtain
road parameters and grade [42,43]. Even for vehicle simulators that use
average speeds and road types as indicators of operating conditions, the
underlining distributions are often derived from real-world driving
traces [44,45]. It is especially important to perform the spatial data
link, given that on-road speed and acceleration rates are not independent of road grade [46]. In this case, the second-by-second speed
and road grade profiles selected as model inputs come from GPS traces
collected during the Atlanta Household and Activity Travel Survey in a
20-County Region of Metro Atlanta [46–48]. The GPS traces contain
speeds, as well as the paired road grade generated from the U.S. Geological Survey (USGS) USGS digital elevation model (DEM) [46]. The
Fig. 1. Workflow of the energy model framework development and application.
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X. Xu, et al.
Table 1
Electric vehicle powertrain specifications.
Vehicle Type
100-mile BEV
300-mile BEV
Fuel Cell EV
Parallel HEV
Power-split HEV
Power-split PHEV
Series PHEV
EV Type
Base Model
BEV
2016 Nissan
Leaf
1659
0.32
2.76
80
–
30.41
0.99
0.14
–
–
BEV
2016 Tesla Model
S
2270
0.30
2.83
285
–
101.18
0.99
0.04
–
–
FCEV
2016 Toyota
Mirai
1760
0.30
2.79
113
–
1.82
0.70
0.40
114
–
HEV
2015 Ford Fusion
HEV
2015 Toyota
Prius
1669
0.31
2.37
68
57
1.26
0.90
0.10
–
90
PHEV
2017 Toyota Prius
Prime
1712
0.31
2.37
68
57
8.11
0.90
0.10
–
98
PHEV
2016 Chevrolet Volt
Vehicle Weight (kg)
Drag Coefficient
Frontal Area (m2)
Maximum Motor Power (kW)
Maximum Motor2 Power (kW)
Battery Size (kWh)
Maximum SOC
Minimum SOC
Maximum Fuel Cell Power (kW)
Max engine power (kW)
1639.7
0.30
2.25
79
–
1.46
0.90
0.10
–
105
(a) Training set, speed and acceleration
1893
0.30
2.57
87
48
14.89
0.90
0.10
–
75
(b) Testing set, speed and acceleration
(n = 87,443 vehicle-seconds)
(n= 99,549 vehicle-seconds)
(d) Testing set road grade
(n = 99,549 vehicle-seconds)
(c) Training set road grade
(n = 87,443 vehicle-seconds)
Fig. 2. Vehicle operation input for the training set and testing set.
sample trips that covered a wide range of possible operating conditions
were selected from the GPS traces, and were split into two sets for
model development: a training set (refers to training and validation set
in machine learning) with 152 trips and a testing set with 146 trips. The
vehicle speed-acceleration distribution and road grade distribution by
different sets are illustrated in Fig. 2 below.
demand and current battery state-of-charge (SOC). However, battery
SOC information has been particularly difficult to obtain in previous
transportation energy analyses. Most previous studies assume vehicles
operate in their all-electric range (AER) [18], assume equal initial and
final SOC levels [49], or use additional parking and charging information [17]. In this study, the initial SOC is randomly generated
using uniform distributions within the allowed SOC ranges for each
vehicle, and each trip accounts for a wide range of operating conditions
that begin with the assigned initial SOC. The randomized scheme helps
2.1.3. Battery state-of-charge (SOC)
The EV powertrain operating mode depends upon current power
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X. Xu, et al.
delineate the variation of energy use under various SOC levels. As initial SOC data become more widely available from EV monitoring studies, users will be able to match energy use under distinct SOC level
from this study with SOC levels from the real-world to account for local
charging conditions.
M - vehicle mass (Kg)
g - acceleration due to gravity (9.8 m/s2)
- density of the air (Kg/m3)
v - vehicle speed (m/s)
A - vehicle frontal area (m2)
Cd - drag coefficient
cr - rolling resistance coefficient
2.1.4. Ambient environment conditions
During hot/cold weather conditions, the use of cabin climate control can contribute a significant amount of auxiliary load to the vehicle
[13,16,50]. In this case, an additional heating, ventilation, and air
conditioning (HVAC) load is assigned into the model process based on
the severity of ambient temperature and humidity. The HVAC load is
assumed constant during the trip to limit final model complexity, and
the energy use under various HVAC loads was modeled separately using
a smaller trip sample to reduce overall computational time. However, it
will be relatively easy to re-run the models, once detailed HVAC load
profiles during operation become available.
The drag coefficients and frontal area for the seven EVs modeled in
this study can be found in Table 1. In this model, the coefficient of
rolling resistance is assumed to be a function of speed with
cr = 0.008 + 0.00012v (where v is the speed). In some models [55,56],
emissions are derived as a function of vehicle specific power (VSP),
which is the vehicle tractive power divided (standardized) by a standardized vehicle weight (metric tons). This analysis also uses VSP as an
indicator of vehicle power demand to support comparisons across vehicles. VSP connects the vehicle energy demand with operating characteristics including speed, acceleration, and road grade. However,
because the vehicle control strategies introduced in the following sections still use on-road operating conditions to develop control rules,
vehicle speed, acceleration, and road grade were all retained for
breakpoint detection in the modeling process.
The HVAC load also contributes to the power demand. In this study,
we assume the meteorology is constant during a trip, which adds a
constant HVAC demand to the powertrain. Modeling such constant load
within the regression model can raise singularity issues; hence, the
HVAC energy use is handled separately by post-processing the energy
output. This simplification may lead to potential inconsistent prediction
errors associated with HVAC load in model application, but remains the
best solution until such time as HVAC load interactions with engine
load become available in monitored drivetrain performance data
streams for use in updating these models.
2.2. Vehicle representation and simulation
A vehicle is a complex system consisting of thousands of components that are controlled by both the driver and on-board powertrain
control software. Full-system simulation tools provide great advantages
because they explicitly model the complex relationships between the
various drivetrain components [15,51]. However, drivetrain simulators
often generate hundreds of attributes, with high multi-collinearity
among the generated data attributes. A parameterized model retains
only those key attributes that predominantly affect vehicle energy use.
The model features (independent variables) were selected based upon
fundamentals of vehicle design and operations, as introduced below.
2.2.1. Vehicle power demand
All vehicles are designed to convert on-board energy storage into
kinetic energy that provide work to overcome friction resistance, uphill
and downhill load due to road grade, aerodynamic wind resistance,
rotational load, accessory load, etc. [52–54]. Tractive power demand is
often used as a vehicle load parameter in energy modeling. In one form,
vehicle tractive power PT can be simplified to [54]:
PT = (Ma + Fw + Tr + Fu ) v
1 3
= Mav +
v ACd + cr Mgvcos ( ) + Mgvsin ( )
2
2.2.2. Vehicle power supply
Given the input vehicle tractive power demand, the vehicle control
system determines the total energy required and the split among different power sources under any specific driving condition [29]. The
delivery of energy to the wheels is governed by characteristics of the
entire powertrain system, from power source, through transmission and
differential torque-multiplication, to the diameter of the wheels [53].
The conceptual structure of different hybrid powertrains is represented
in Fig. 3 below [52]. Powertrain 1 has the unidirectional power supply
to both final drive and Powertrain 2, while Powertrain 2 has bidirectional power flow, which supplies final load and recovers energy from
vehicle braking for Powertrain 1. The internal combustion engine vehicles (ICEVs) only have Powertrain 1. The BEVs only have Powertrain
2, and the energy recovery is enabled by regenerative braking. The
PHEVs, HEVs, and FCEVs have both powertrains on-board and a
(1)
where
Fw - aerodynamic drag
Tr - tire rolling resistance (front tires, Trf , and rear tires, Trr )
Fu = Mgsin ( ) - uphill gravity force component
- road grade (rad)
Fig. 3. Conceptual structure of hybrid electric vehicles [52].
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Table 2
Energy model performance summary.
Vehicle Type ID
100-mile BEV
300-mile BEV
Fuel cell EV
Parallel HEV
Power-split HEV
Power-split PHEV
Series PHEV
EV Type
Original sample size
Final sample size
Percentage of Non-relevant Data
Electricity Rate RMSE (Watt)
Electricity Rate R2
Fuel Rate RMSE (Watt)
Fuel Rate R2
Total Energy Rate RMSE (Watt)
Total Energy Rate R2
BEV
987,092
874,436
11%
1947
0.99
–
–
1947
0.99
BEV
987,092
866,845
12%
3536
0.97
–
–
3536
0.97
FCEV
987,092
894,938
9%
2002
0.85
7102
0.96
7412
0.95
HEV
987,092
910,143
8%
3118
0.77
10,485
0.92
8496
0.95
HEV
987,092
924,320
6%
3491
0.58
7,808
0.96
7181
0.97
PHEV
987,092
873,137
12%
8210
0.69
22,014
0.80
12,143
0.91
PHEV
987,092
860,727
13%
7303
0.60
16,036
0.83
14,489
0.90
coupler to join the power from both powertrains. A PHEV can be
treated as a HEV with larger battery storage. A FCEV can be treated as a
HEV, where the gasoline engine is replaced by a fuel cell and electric
motor. Hybridized FCEVs enable energy recovery from braking and
smooth operation under severe weather conditions [52]. The model
therefore accounts for three different types of hybrid configurations
(parallel, series, and power-split), which employ different power coupling systems. For vehicles equipped with two powertrains, it is important to optimize fuel economy while maintaining the state-of-charge
(SOC) of the battery at a desired level to ensure efficient operations
over a wide range of driving conditions [29].
Vehicle operating modes are classified based on the control mode of
Powertrain 1 and Powertrain 2. In general, Powertrain 1 (internal
combustion engine or hydrogen fuel cell) can be either on or off, and
Powertrain 2 (battery and tractive motor) can be either charging or
discharging, also known as operating in charging sustaining (CS) and
charging depleting (CD) modes. As the battery is often used to supply
vehicle controllers and auxiliary devices during operation [57], it is
very rare to have Powertrain 2 totally off in real-world cases. So,
Powertrain 2 in the off mode is combined with the discharging mode.
The combination of Powertrain 1 status and Powertrain 2 status defines
the four modes introduced below:
were captured in this study using different techniques:
• The vehicle powertrain is represented by vehicle type, and separate
models are developed for each vehicle type.
• VSP is selected as an independent variable to represent the combi•
•
nation effect of operation and roadway characteristics, with speed,
acceleration and road grade occasionally added as independent
variables to split activity into distinct operating conditions.
Simulated SOC curves serve as independent variables for determining vehicle control and corresponding energy use.
The HVAC load was applied during post-processing, as a scaling
factor to account for the energy surcharge under high/low temperature conditions.
All of the selected attributes described above were exported from
Autonomie simulation results. However, simulated energy rates and
VSP distributions can occasionally be unreasonably high or low under
extreme input conditions that fall outside of a vehicle’s physical performance constraints. The data that are out of the Tukey fence [58]
were identified as non-relevant data points and removed from the
analytical dataset. Any output that did not follow the input cycles were
also removed. The fraction of removed data ranges from 6% to 13%
(presented in Table 2 in the following section).
• EV only mode: the engine/fuel cell is off, the battery-motor powertrain provides all of the propulsion power to the final drive.
• Regenerative braking mode: the battery receives power generated
from energy recovery during braking.
• Hybrid mode: both powertrains supply propulsion power to the
final drive.
• Power-split mode: Powertrain 1 supplies power to the final drive as
2.3. Energy model development
In this study, the Bayesian Network allows integration of the powertrain structure illustrated in Fig. 3, and the probability distribution of
each variable can be inferenced using a statistical learning approach.
The Bayesian Network is applied for fuel and electricity consumption,
respectively. This is important because fuel may be used to provide
tractive power or to recharge batteries, and electricity may be used at
higher rates to provide acceleration under certain conditions.
The conceptual framework of a full hybrid vehicle powertrain given
in Fig. 3 is represented by the directional graph in Fig. 4 (BEV model is
a special case of this framework). In this problem, the list of nodes is
defined as N = [C1, C2', C2 ", E11, E10, E01, E00]. The definition of each
well as to the generator to recharge batteries.
Powertrain control systems are designed to assign the proper operating mode to on-road operation conditions to ensure the optimal fuel
economy and driving performance [52]. Hence, it is critical to define
the control modes in the modeling process under each driving condition.
2.2.3. Vehicle simulation and post-processing
In Autonomie, the Vehicle Propulsion Controller (VPC) allocates
power demand among components at the vehicle level, using the given
vehicle model and driving cycle [51]. Based on the discussion above,
the fuel consumption rate and electricity consumption rate (denoted by
Efuel and Eelec ) were selected as dependent variables. The hidden vehicle
control variables, including engine/fuel cell mode and battery charging/discharging mode (denoted by C1 and C2 ), were also selected to
represent control modes and split energy use by modes. As discussed
earlier, vehicle powertrain design, on-road operating conditions,
roadway characteristics, battery state-of-charge (SOC), and ambient
environmental conditions all have significant impact on EV energy
consumption and should be included in the modeling approach. They
Fig. 4. Conceptual structure of Bayesian Network.
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X. Xu, et al.
node is listed below:
1
0
1
C2 =
0
C1 =
(powertrain
(powertrain
(powertrain
(powertrain
1
1
2
2
Some early EV models may use more simplistic rule-based power
management strategies [29,59], which assigns distinct control modes
under certain ranges of driving conditions. For example, the parallel
HEV modeled in this study uses such a control algorithm and is not
predicted very well by logistic regression. A simple alternative in those
cases is to use a non-parametric decision tree method, which is easy to
interpret and capable of predicting nonlinear relationships [60]. The
probability of different control mode can be predicted using following
equation:
on)
is the mode of Powertrain 1.
off )
discharging )
is the mode of Powertrain 2.
charging )
C2' = (C2 |C1 = 1) is the mode of Powertrain 2 given Powertrain 1 is
on.
C2 " = (C2 |C1 = 0) is the mode of Powertrain 2 given Powertrain 1 is
off.
E is the energy consumption rate (kJ/sec).
E11 = (E|C2' = 1) – energy rate under hybrid mode
E10 = (E|C2' = 0) – energy rate under power-split mode
E01 = (E|C2 " = 1) – energy rate under EV only mode
E00 = (E|C2 " = 0) – energy rate under regenerative braking mode
'
1 ( 2)
Eij P (C2=j|C1 = i ) P (C1 = i )
Efuel (Eelec ) =
E11 1 2'
+ E10
+ E00 (1
'
2)
1 (1
1)(1
2")
+ E01 (1
=
1
1 + exp( u)
u = h (X ) +
(6)
X
X {Speed,
–
independent
variables,
Acceleration, VSP , SOC , grade}
Rm - the mth region (leaf node),
M - the total number of regions,
th
m - the probability for the predicted control mode in m region.
The conditional fuel and electricity rates under each control mode
were estimated using linear regression (equation (7)):
(7)
E11 (E10, E01, E00) = h (X ) +
where
X
X {Speed,
–
independent
variables,
Acceleration, VSP , SOC , grade}
h (X ) potential linear basis expansions of the variable (e.g., polynomial, piecewise or binning)
– model coefficients
– error term
The parameters were estimated using 80% of the samples and finetuned using the remaining 20% of samples to reduce mean square error.
The complete list of parameters is provided in Appendix A. The model
goodness-of-fit metrics, including R2 and root-mean-square error
(RMSE) for the verification set are listed in Table 2 below. Overall, the
predicted fuel rates have R2 greater than 0.8 and the predicted electricity rates have R2 greater than 0.6. The combined energy rates
(fuel + electricity) of all EVs have R2 close to, or higher than, 0.9. The
goodness-of-fit metrics for electricity were generally lower than fuel,
which is potentially caused by eliminating factors related to electric
machine operation, such as variation of internal impedance and battery
state-of-health. Finally, the model prediction errors from current
models compared to real-world fleet are subject to the errors associated
with underlying Autonomie simulation. The full-system simulation
model developed in Autonomie has been previously calibrated using
vehicle testing data by Argonne National Lab and has the prediction
errors within 5% under most test cases [61], which suggests the impact
of simulation error should be small for the vehicles employed in the
modeling work.
1) 2"
(3)
The next step is to estimate the probabilities of each control mode
and conditional energy consumption rates using common parametric
statistical models. For motor control under Powertrain 1 off C2 ", the
vehicle operates as a BEV and it is almost sure that the Powertrain 2 is
discharging while VSP > = 0 and is discharging while VSP < 0 (regenerative braking) [52]. For control mode C1 and C2' , the probability of
control mode selection can be predicted by logistic regression in most
cases using Eqs. (4) and (5). Depending on the potential discontinuity of
energy use in response to some input variables (i.e., energy use patterns
differ with SOC above or below target SOC), the linear basis expansions
are adopted to incorporate piecewise variables.
'
1 ( 2)
Rm}
where
(2)
i = 0,1 j = 0,1
m I {X
m =1
In this network, the mode of Powertrain 1 (on and off) is predicted
first, based on the vehicle power demand, then the mode of Powertrain
2 (CS and CD) is predicted based on the mode of Powertrain 1. The
energy use as a function of vehicle control mode is estimated last. In a
modern hybrid powertrain design, the engines and fuel cells are often
designed for steady power output, while the battery power often serves
as the power damper to assist the engine or fuel cell [52]. In this case, it
is intuitive to first predict control mode for Powertrain 1, then predict
Powertrain 2.
The model assumes that variables C1, C2' , C2 " follow a Bernoulli
distribution with probabilities 1, 2', 2 " [0, 1] respectively. For BEVs,
1 = 0 (only an electric drivetrain is in operation). For FCEVs, we assume 1 = 1. For other vehicle types, the operations probabilities range
between 0 and 1. The model assumes that variables E11, E10 , E01, E00
follow normal distributions N (µi , i2)(i = 1, 2, 3, 4) . The instantaneous
energy use by fuel and electricity can be represented as the summation
of conditional energy use by control mode, multiplied by the probability of the given control mode:
Efuel (Eelec ) =
M
=
(4)
2.4. Energy model post-processing
(5)
Finally, the conditional energy rates under vehicle heating and
cooling are adjusted with a supplemental linear factor ( ). The adjustment factor is developed by running Autonomie simulation from
0.5 kW (base) to 6 kW (high) of auxiliary load under EPA standardized
cycles for all EV types. The adjustment factors under distinct VSP level
and control mode were defined using following equation:
where
X
X {Speed,
–
independent
variables,
Acceleration, VSP , SOC , grade}
h (X ) potential linear basis expansions of the variable (e.g., polynomial, piecewise, or binning)
– model coefficients
– error term
|vsp, control
where
7
mode
=
(EHVAC
load high
HVAC
EHVAC
load
load base )
|vsp, control
mode
(8)
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X. Xu, et al.
Fig. 5. Energy prediction results under EPA combination cycles and 5 kW auxiliary load.
EHVAC load high - the energy rate under high HVAC load
EHHVAC load base - the energy rate under base HVAC load
HVAC load - difference between high and base HVAC loads
The adjustment of HVAC load proposed in this study does not incorporate potential factors that may affect the auxiliary energy use,
such as vehicle design and thermal management factors [13,50].
However, the simple adjustment will not add significant additional
variance to the final results and will still maintain the robustness of the
final trained model. Further research efforts can be conducted to improve the accuracy of the model with respect to HVAC impacts by incorporating more detailed factors.
For BEVs and PHEVs, the electricity loss during transmission and
charging is considered in calculating the final energy supply from the
power plant. In this study, regional transmission efficiency is set to
In this case, the updated energy rates under given HVAC load can be
calculated as follows:
EHVAC
load pred |vsp, control mode
= [EHVAC
|vsp, control
load base
mode
+
(HVAC load pred
HVAC load base )]
(9)
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Fig. 6. Verification of trip-level energy results.
95.1% and charging efficiency is set to 85% for Georgia, taken from the
Greenhouse gases, Regulated Emissions, and Energy use in
Transportation (GREET®) model [62,63], which leads to a combined
80.8% of energy efficiency from power plants to on-board electricity.
methodology from previous studies [65] with the assumption that the
on-road fleet is composed of 100% conventional vehicles. The energy
consumption rates for ICEVs come from the MOVES-Matrix multi-dimensional array of MOVES2014a energy and emission rates [66].
2.5. Energy model results and verification
3.1. Network preparation and energy calculation
The simulation inference energy model was verified using a separate
set of 146 trips with speed, acceleration and road grade distributions
given in Fig. 2 above. The second-by-second speed, acceleration, road
grade, a constant auxiliary load, and randomized initial battery level
SOC served as model inputs, with fuel rate, electricity rate and SOC
level predicted using proposed method introduced in Section 2.3. In this
study, the SOC is updated each minute of vehicle operation, since updating the SOC level every second tends to greatly increase the computational time. The SOC level is updated using following equation,
using a constant battery capacity C provided in Table 1, available
electricity E0 at trip beginning defined by initial SOC and electricity
consumption Et by time t:
Energy consumption is estimated using link-level traffic attributes
(average speed, road type, link length, and volume) and a randomized
distribution of initial SOC. On each link, a portion of the on-road fleet
on each link is assumed to have been converted to EVs, based upon EV
sales rates from 2011 to 2024, as projected by U.S. Energy Information
Administration (USEIA) for the South Atlantic Region and illustrated in
Fig. 7 below [7,67,68]. The projected EV penetration rates from USEIA
were developed under reasonable economic growth, policy content and
technology development trends, and represent one likely scenario of EV
adoption in the near future. The EV penetration rates prior to 2011 are
assumed to be negligible. Currently, vehicle type and technology information are not available from our transportation demand model, so
we assume that EVs penetrate into the fleet by model year based on the
flat rate specified in Fig. 7. The adopted EV penetration was applied to
different age distributions for rural and urban road types, as currently
defined by the Atlanta Regional Commission in the activity-based travel
demand model in Fig. 7, to obtain the final travel distances split of
ICEVs and EVs in light-duty vehicle (LDV) fleet. For the urban roads,
6.2% of total travel distances were contributed by EVs, and for the
exurban and rural roads, the fraction is 4.9%.
After quantifying the travel distances to be replaced by EVs on each
link by area type, the next step is to estimate the energy use for EV
travel distances. The fleet composition, on-road operating conditions,
and other inputs for EV energy calculation were generated using following methodology:
SOCt =
E0
Et
C
(10)
A sample trip prediction with EPA standardized driving cycle, 5 kW
auxiliary load, and 90% initial SOC level as input is provided in Fig. 5
below. While there are significant differences on a second-by-second
basis for some on-road operating conditions, the predicted fuel use,
electricity use, and decrease in SOC follow the general trends predicted
by Autonomie. The SOC predictions are close to Autonomie-generated
SOC curve, and the total energy prediction errors are low.
For 146 tested trips with random initial SOC and 0.5 kW auxiliary
load, the trip-level energy prediction results are illustrated in Fig. 6
below. The predicted energy use by fuel and electricity by the Bayesian
Network model generally match with the energy consumption originally generated by Autonomie. The proposed model provides representative energy use profiles under a wide range of driving conditions and is suitable for network-level applications for the vehicles that
have been modeled.
• Fleet Composition: EV travel distances were assigned to BEVs,
3. Application and results
In this section, the energy model is applied to 20-county
Metropolitan Atlanta regional-network to analyze the potential energy
impacts of EV adoption. The loaded network from a typical travel day in
2024 forecast year was generated by the regional activity-based travel
demand model developed by the Atlanta Regional Commission [64,65].
The modeled transportation network contained 74,505 roadway links
and predicted 17.7 million personal vehicle trips per day in the region
for 2024. Regional energy consumption was generated using
•
9
HEVs, PHEVs and FCEVs based on the 2024 fleet composition derived from Fig. 7. For BEVs and PHEVs, the vehicle types by different electric ranges and different powertrains were randomly assigned. The battery capacity for all EVs are provided in Table 1.
However, users can customize the EV battery size under the same
engine and motor size settings and the SOC curves will be adjusted
accordingly.
On-road Operating Conditions: The corresponding driving cycles
were randomly selected from real-world driving data collected in
the Atlanta travel survey [48] for all the EVs on the same link based
on link length, road type, and link average speed. As the SOC distributions are unknown for the region, the initial SOC for each vehicle on that link is drawn from an assumed uniform distribution
between maximum and minimum SOC values, as given in Table 1.
Applied Energy 269 (2020) 115095
X. Xu, et al.
Fig. 7. EV fraction input [7,67,68] and network input split by urban (red) and rural (blue) road types.
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Fig. 8. Energy processor for individual vehicles on each link.
• Environmental Inputs: The temperature was assumed to be 20 °C
baseline scenario (no EVs) in Fig. 9 below. Higher fuel and electricity
use generally occurred in locations with higher traffic volumes, such as
Interstate highways and major arterials. The fuel saving benefits are
higher in the more urbanized areas than in rural areas, given that the
urban light-duty fleet is newer (average vehicle age is 8.5 years) than
the rural fleet (average vehicle age is 10.7 years), which provided
greater urban area EV market penetration, and more regenerative
braking occurs in urban areas.
Energy use variation by time of day is provided in Fig. 10 below.
The energy efficiency benefits provided by EVs yielded an hourly fuel
savings of 4.1–4.3% compared to the 100% ICEV fleet. In addition,
electricity use remains small compared to fuel use for these EV market
penetration rates. The total daily electricity consumption from EVs is
only 1863 MWh compared to a total 370,886 MWh of fuel used by all
vehicles. The energy savings result from the inherent efficiency of
HEVs, and only 0.5% of the total on-road energy is supplied by the
electrical grid given these penetration rates.
The network total fuel consumption, aggregated by facility type and
average speed bin, are provided in Fig. 11. The fuel consumption EVs
was compared to the energy results under the no EV scenario. For facility type, fuel consumption was aggregated by unrestricted road (local
streets) and unrestricted roads (highways), and for rural and urban
classes, respectively. For link average speeds, fuel consumption was
aggregated from 0 km/h to 120 km/h in 10-km/h increments. The
largest fuel consumption and largest energy savings both occurs on
urban restricted roads around medium average speeds (25–65 km/h).
The energy saving benefits are much lower on rural roads and on urban
(70 °F). In this case, a 0.5 kW auxiliary load was added to all the EVs
for HVAC and accessory operations.
After preparing the input, the energy use for each EV on each link
was estimated using the procedure illustrated in Fig. 8 below. First,
link-level travel distances and battery capacity by EV type, random
initial SOC, driving cycle, road grade, and environmental conditions on
each link were prepared from ABM outputs. Next, the second-by-second
inputs were post-processed for different EVs to obtain instantaneous
VSP, available on-board electricity, and HVAC load. Then, the proposed
energy framework is applied to each type of EV with HVAC load, VSP,
SOC, speed and acceleration as model inputs. Finally, the second-bysecond control strategies, energy consumption, SOC drop, and remaining range were generated for the selected driving cycles and projected over the link to estimate the link-level energy inventory. The
energy consumption of ICEVs was also adjusted to reflect the reduction
in their fleet composition and travel distances. The total link-level energy use is generated by adding the energy use from ICEVs and EVs for
each hour of operation.
3.2. Network-level energy results
Fuel use, electricity use, and total energy consumption for each link
and the entire network are generated for each hour. The spatial distributions of traffic volume, fuel use, electricity use, and percent of fuel
(gasoline) savings for a morning peak hour are compared to the
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freeways. The higher energy saving benefits on urban streets comes
from higher urban travel distances, energy recovery from stop-and-go
activity on urban roads, and the younger urban area fleet (more EV
market penetration).
4. Discussion
With proper customization, the methodology employed in this study
is transferable to any on-road fleet and future scenario. Local fleet
compositions differ significantly across regions, and different market
penetration rates for EV technologies are likely to apply in other geographic regions. The analyses presented in this paper used simulations
of the predominant EV technologies currently sold in the U.S. market.
For electric vehicles of significantly different design, such as those sold
in other countries where different standards apply, the models presented in this paper will need to be updated to properly parameterize
the full simulation models for these vehicles. Similarly, as new EV
technologies that are currently under development begin to enter the
fleet, additional modeling work will be needed. On-road operating
conditions on each transportation link need to reflect the driving profiles that result from regional travel demand, local traffic management
systems, and local driving styles in other regions or countries. Hence,
analysts should ensure that the driving cycles reflect local conditions.
The proposed EV energy modeling approach can also be expanded
and integrated with a variety of transportation and energy studies. For
example, in this paper, we have examined the impacts of specific EV
market penetration rates on electric power demand. This power demand can then be fed into electric grid simulation models to assess how
EVs affect the grid performance within the region. In addition, life-cycle
energy and cost-effectiveness analysis can also be performed by combining predicted on-road energy use with upstream energy and emissions factors for electricity and fuel prediction from models such as
GREET®. The energy model can employ any driving cycle as input and
can be used to optimize driving cycles to minimize energy consumption.
Hence, eco-driving and eco-routing benefits can also be analyzed when
second-by-second vehicle traces are collected or simulated.
Several future developments can be done to improve this EV modeling approach. For example, EV degradation functions by vehicle age
can be introduced for life-cycle vehicle ownership analysis, and the
accuracy of SOC distribution can be improved using real-world vehicle
measurement data. To make better prediction of EV energy consumption, it is also useful to consider the EV market penetration across demographic groups and sub-regions, and factor in differences in driving
behaviors by vehicle technology types.
5. Conclusions
In this study, a scalable modeling approach for EVs is developed to
quantify the energy savings of adopting EVs in large-scale transportation networks. The model design combines data-driven energy inferences derived from full system simulation model outputs to develop
energy use rates that can be readily combined with on-road vehicle
operations to predict energy consumption. This methodology is suitable
for most existing EV technologies for which full powertrain simulation
models are available and is scalable to all network-level applications.
The proposed energy modeling approach enables the integration of EVs
into standard energy and emission rate models (such as MOVES in the
U.S.), allowing analysts to estimate the energy and cost impacts of
adopting different kinds of EVs under various transportation planning,
design, and operation scenarios, and helping to optimize EV implementation strategies.
The proposed modeling approach has been applied to Atlanta regional network under forecast year 2024, with a fraction of EVs replacing ICEVs derived from a reasonable market penetration forecasts.
The link-level energy consumption for the assumed EV fleet penetration
is compared to baseline consumption (no-EV scenario) to assess the
Fig. 9. Traffic volume, fuel use, electricity use and percentage of fuel saving
from 20-County Atlanta network (8:00 a.m. – 9:00 a.m.).
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X. Xu, et al.
Fig. 10. Travel distances, energy use and percentage of fuel saving by time of day.
energy benefits. The results demonstrated that if 6.2% of urban travel
distances and 4.9% of rural travel distances were driven by EVs, the
network-level fuel savings would be around 4.0% for a normal travel
day in 2024. In addition, the urban unrestricted roads (local streets)
would provide the 4.3% fuel saving benefits at the network-level given
a larger EV adoption rate and potential energy recovery benefits gained
from regenerative braking, which is greater than other roadway
facilities. Finally, the energy saving benefits at other regions and under
future scenarios can also be evaluated by adjusting the methodology
employed in this study to other local conditions, including local fleet
composition and on-road operating conditions. The proposed EV energy
modeling approach can also be applied to assess the impact of EVs on
other aspects, such as air quality and power grid operation across different regions in the United States.
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Fig. 11. Energy use by facility type and average speeds.
CRediT authorship contribution statement
Transportation, a National University Transportation Center sponsored
by the U.S. Department of Transportation (DOT 69A3551747114). The
contents of this paper reflect the view of the authors, who are responsible for the facts and accuracy of the data presented herein. The
contents do not necessarily reflect the official view or policies of the
Department of Transportation. This paper does not constitute a standard, specification, or regulation. The research team would like to acknowledge the Atlanta Regional Commission for providing the regional
models and data for this project, as well as Argonne National
Laboratory the use of Autonomie. The research team also acknowledges
Oak Ridge National Laboratory and US Department of Energy for their
support.
Xiaodan Xu: Conceptualization, Methodology, Formal analysis,
Writing - original draft, Writing - review & editing, Visualization,
Funding acquisition. H.M. Abdul Aziz: Conceptualization, Writing original draft, Writing - review & editing, Supervision. Haobing Liu:
Resources, Supervision, Writing - review & editing, Funding acquisition. Michael O. Rodgers: Conceptualization, Supervision, Writing original draft, Writing - review & editing, Visualization, Funding acquisition.
Randall
Guensler:
Conceptualization,
Resources,
Supervision, Writing - original draft, Writing - review & editing,
Visualization, Funding acquisition.
Declaration of Competing Interest
Code Availability
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence the work reported in this paper.
The software that produces this work can be freely accessed at
https://github.com/arielgatech/EV_energy_model, under the GPL-3.0
license.
Acknowledgement
This work was supported by the National Center for Sustainable
14
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Appendix A. Developed energy models
1. 100-mile BEV
C1 = 0, C2={
Eelec =
1(vsp 0)
0(vsp < 0)
1.95
1.32
vsp + 929.03(vsp 0)
vsp + 764.41(vsp < 0)
2. 300-mile BEV
1(vsp 0)
0(vsp < 0)
C1 = 0, C2 =
Eelec =
2.65
1.78
vsp + 688.61(vsp 0)
vsp + 624.28(vsp < 0)
3. FCEV
1(vsp 0)
0(vsp < 0)
C1 = 1, C2 =
Efuel =
Eelec =
1.29 105 SOC + 4.03
3892.00(vsp < 0)
1.07
10 4
SOC + 1.48
3.81
103
SOC + 0.797
vsp + 97, 903.30(vsp
vsp
0.376
vsp
Efuel
0.302
0)
4848.27(vsp
Efuel
0)
3029.3(vsp < 0)
4. Parallel HEV
p (C1 = 1) =
1
1 + exp ( u)
u=
(SOC
2.67
0.5) + 1.55
(0.45
SOC < 0.5) + 1.82
0.699 (SOC < 0.45) (Speed
0.371 (SOC < 0.45) (Speed
0.097 (SOC < 0.45) (Speed
0.018 (SOC < 0.45) (Speed
p (C2' = 1) =
0.925 (SOC 0.45) (Speed <
0.038 (SOC 0.45) (Speed
0.668 (SOC 0.45) (vsp
0.992 (SOC < 0.45)
C2 " =
< 3.7)
< 3.7)
3.7)
3.7)
3.7)
3.7)
100)
(vsp
(SOC < 0.45) + 9.46
(vsp < 0)
(vsp 0)
(vsp < 230)
(vsp 230)
(vsp < 100)
(vsp < 100)
(vsp < 0)
0)
1(vsp 0)
0(vsp < 0)
0(C1 = 0)
4.21
Efuel =
(
Eelec =
2.79
(2.97
105
10 4
10 4
SOC + 3.97
805.21
SOC + 4.36
vsp + 25795.59(C1 = 1, C2' = 1)
(vsp < 0)+
vsp + 140, 439.00)
(vsp
1.27 vsp + 550.86(C1 = 0, C2 " = 0)
1.96 vsp + 570.97(C1 = 0, C2 " = 1)
SOC + 0.234 vsp 12, 204.64) (SOC
0)(C1 = 1, C2' = 0)
0.45)+
(0.224 vsp + 484.24) (SOC < 0.45)(C1 = 1, C2' = 1)
(2.32 103 SOC + 1.33 vsp 385.5) (vsp < 0)+
(8.56
10 4
SOC
38, 795.65)
(vsp
0)(C1 = 1, C2' = 0)
15
10
5
vsp + 0.691
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5. Series PHEV
p (C1 = 1) =
1
1 + exp ( u)
u=
(SOC
3.06
0.3) + 8.08
10
2
Speed + 3.76
5
10
max{vspt , vspt 1, vspt 2} + 1.66
10
5
min{vspt , vspt 1, vspt 2}
2.27
5
min{vspt , vspt 1, vspt 2}
1.94
where t is the current time step in second.
p (C2' = 1) =
1
1 + exp( v )
v=
10
2.41
4
vsp + 0.0458
1(vsp 0)
0(vsp < 0)
C2 " =
105
2.75
(SOC
1.18
3.91
10 4
7.80
0(C1 = 0)
9.09 105
SOC
(SOC < 0.36)+
4.75 vsp + 288, 932.84(C1 = 1, C2' = 1)
106 SOC (SOC < 0.3) 3.55 105 (SOC > 0.3)+
Efuel =
Eelec =
0.36)
(SOC
vsp + 385, 522.62(C1 = 1, C2' = 0)
1.56 vsp + 538.26(C1 = 0, C2 " = 0)
2.28 vsp + 476.19(C1 = 0, C2 " = 1)
0.36) + 2.58 105 SOC (SOC < 0.36) + 0.139
vsp
78, 908.85
C2'
2.25
105
(C1 = 1,
= 1)
(SOC < 0.3) + 6.75
SOC
1.79
10 4
(SOC > 0.3)
75, 129.88(C1 = 1, C2' = 0)
vsp
6. Power-split PHEV
p (C1 = 1) =
1
1 + exp ( u)
u=
(SOC
2.68
0.3) + 4.24
10
2
Speed + 9.16
5
10
max{vspt , vspt 1, vspt 2} + 1.65
10
where t is the current time step in second.
p (C2' = 1) =
1
1 + exp( v )
v=
Speed
0.117
C2 " =
2.81
10
4
vsp + 0.0420
1(vsp 0)
0(vsp < 0)
3.39
105
(SOC
SOC
4.15
Eelec =
1.70
105
0.36)
0(C1 = 0)
1.17 106
SOC
(SOC < 0.36)+
3.36 vsp + 363, 839.00(C1 = 1, C2' = 1)
(SOC < 0.3) 2.77 105 SOC (0.3 SOC < 0.36)
Efuel =
2.03
105
vsp + 87, 600.85(C1 = 1,
C2'
10 4
(SOC
= 0)
1.33 vsp + 346.42(C1 = 0, C2 " = 0)
2.45 vsp + 144.39(C1 = 0, C2 " = 1)
0.36) + 5.79 105 SOC (SOC < 0.36) + 0.558
(SOC
7.17
vsp
173, 651.62
(0.3
SOC < 0.36)
C2'
3.48
102
Speed
1.47
6.92
10 4
10 4
(SOC
SOC
0.36)
(C1 = 1,
= 1)
(SOC < 0.3) 3.37
0.351
10 4
SOC
vsp + 3, 199.50(C1 = 1, C2' = 0)
16
0.36)+
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7. Power-split HEV
p (C1 = 1) =
u=
1
1 + exp ( u)
1.778
(SOC
0.5)
p (C2' = 1) =
1
1 + exp( v )
v=
Speed
0.136
C2 " = {
0.031
4
3.11
10
10 4
(SOC
Speed + 4.22
10
4
vsp
0.225
vsp + 0.325
1(vsp 0)
0(vsp < 0)
4.73
0.5)
0(C1 = 0)
9.01 10 4
SOC
(SOC < 0.5)+
C2'
Efuel =
7.19
4.31 vsp + 50467.53(C1 = 1,
= 1)
SOC (SOC < 0.4) 7.64 10 4 SOC (0.4
4.38 10 4 (SOC 0.6)+
10 4
4.00
SOC < 0.6)
vsp + 48986.67(C1 = 1, C2' = 0)
10 4 (SOC 0.5) 1.851 10 4 SOC (SOC < 0.5)
+ 1.28 vsp + 11660.53(C1 = 0, C2 " = 0)
2.55 vsp + 609.69(C1 = 0, C2 " = 1)
10 4 SOC (SOC < 0.4) 2.93 10 4 SOC (0.4 SOC < 0.6)
+ 1.78 10 4 (SOC 0.6) + 1062.09 Acc 173, 651.62
1.035
3.06
Eelec =
1.05
10 2
Speed + 2.28
10 4
+ 1.56
10 4
(C1 = 1, C2' = 1)
SOC (SOC < 0.4) + 2.48
(SOC
0.6)
10 4
14753.88(C1 = 1,
SOC
C2'
(0.4
SOC < 0.6)
= 0)
Appendix B. Sensitivity analysis of EV energy use by different state-of-charge (SOC)
In this study, a sensitivity analysis is performed using scatter plots of EV energy rates under different link-level inputs for each type of EV to show
the relationship between operation conditions and energy results. For each vehicle type, 4,000 Monte Carlo samples were randomly drawn to
represent the combination of input operating conditions (assuming uniform distribution within proposed ranges for each variable). The specification
of Monte Carlo sample for each vehicle type is provided in table below.
Range specifications of Monte Carlo sample
Variable
100-mile BEV (2016
Nissan Leaf)
Road Type
Average speed
(mph)
Initial SOC
HVAC load
Road grade
Arterials vs. Freeway
5–75 mph
N/A
1–4 kW
−5 to 5%
300-mile BEV (2016 Tesla Series PHEV (2016
Model S)
Chevrolet Volt)
N/A
Power-split PHEV (2017
Prius Prime)
Power-split HEV (2015
Toyota Prius)
Parallel HEV (2015
Ford Fusion)
20–90%
Using the energy rate estimation method introduced in this paper, the energy rates were estimated for the 4000 Monte Carlo samples and for each
type of EVs in table above. For BEVs, the SOC does not show significant impact during model training (the electricity power won’t be affected by the
SOC drop). The scatter plots for PHEVs and HEVs under different SOC levels are provided below to investigate the impact different SOC input on
energy output. Based on the Fig. B1 below, the common feature shared by all types of PHEVs and HEVs is that the fuel rates and electricity rates show
opposite effects under different SOC levels. As the initial SOC level increases, the vehicle has more available electricity in power storage; hence, fuel
rates will decrease, and electricity rates increase. In this case, if the prior distribution of SOC has higher expected values, the electricity rates will
grow, and the fuel rates will drop.
17
Applied Energy 269 (2020) 115095
X. Xu, et al.
Fuel
Electricity
(a) Energy rates of series PHEV under different SOC
(b) Energy rates of power-split PHEV under different SOC
(c) Energy rates of power-split HEV under different SOC
(d) Energy rates of parallel HEV under different SOC
Fig. B1. Energy rates by EV types under different initial SOC.
18
Applied Energy 269 (2020) 115095
X. Xu, et al.
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