An Agent-Based Model of Heterogeneous Driver Behaviour and Its Impact on Energy Consumption and Costs in Urban Space

Abstract

By 2020, over 100 countries had expanded electric and plug-in hybrid electric vehicle (EV/PHEV) technologies, with global sales surpassing 7 million units. Governments are adopting cleaner vehicle technologies due to the proven environmental and health implications of internal combustion engine vehicles (ICEVs), as evidenced by the recent COP26 meeting. This article proposes an agent-based model of vehicle activity as a tool for quantifying energy consumption by simulating a fleet of EV/PHEVs within an urban street network at various spatio-temporal resolutions. Driver behaviour plays a significant role in energy consumption; thus, simulating various levels of individual behaviour and enhancing heterogeneity should provide more accurate results of potential energy demand in cities. The study found that (1) energy consumption is lowest when speed limit adherence increases (low variance in behaviour) and is highest when acceleration/deceleration patterns vary (high variance in behaviour); (2) vehicles that travel for shorter distances while abiding by speed limit rules are more energy efficient compared to those that speed and travel for longer; and (3) on average, for tested vehicles, EV/PHEVs were £233.13 cheaper to run than ICEVs across all experiment conditions. The difference in the average fuel costs (electricity and petrol) shrinks at the vehicle level as driver behaviour is less varied (more homogeneous). This research should allow policymakers to quantify the demand for energy and subsequent fuel costs in cities.

Full text

Citation: Olmez, S.; Thompson, J.;
Marfleet, E.; Suchak, K.; Heppenstall,
A.; Manley, E.; Whipp, A.;
Vidanaarachchi, R. An Agent-Based
Model of Heterogeneous Driver
Behaviour and Its Impact on Energy
Consumption and Costs in Urban
Space. Energies 2022,15, 4031.
https://doi.org/10.3390/en15114031
Academic Editor: Abu-Siada
Ahmed
Received: 25 April 2022
Accepted: 26 May 2022
Published: 30 May 2022
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4.0/).
energies
Article
An Agent-Based Model of Heterogeneous Driver Behaviour and
Its Impact on Energy Consumption and Costs in Urban Space
Sedar Olmez 1,2,* , Jason Thompson 3, Ellie Marfleet 1, Keiran Suchak 1, Alison Heppenstall 2,4 ,
Ed Manley 1,2 , Annabel Whipp 1and Rajith Vidanaarachchi 3
1School of Geography, University of Leeds, Seminary St, Woodhouse, Leeds LS2 9JT, UK;
ll16e7m@leeds.ac.uk (E.M.); k.suchak@leeds.ac.uk (K.S.); e.j.manley@leeds.ac.uk (E.M.);
gy14aw@leeds.ac.uk (A.W.)
2The Alan Turing Institute, 2QR, John Dodson House, 96 Euston Rd, London NW1 2DB, UK;
alison.heppenstall@glasgow.ac.uk
3Transport, Health and Urban Design Research Laboratory, The University of Melbourne, Grattan Street,
Parkville, VIC 3010, Australia; jason.thompson@unimelb.edu.au (J.T.);
rajith.vidanaarachchi@unimelb.edu.au (R.V.)
4School of Social & Political Sciences, University of Glasgow, Adam Smith Building, Bute Gardens,
Glasgow G12 8RT, UK
*Correspondence: solmez@turing.ac.uk
Abstract:
By 2020, over 100 countries had expanded electric and plug-in hybrid electric vehicle
(EV/PHEV) technologies, with global sales surpassing 7 million units. Governments are adopting
cleaner vehicle technologies due to the proven environmental and health implications of internal
combustion engine vehicles (ICEVs), as evidenced by the recent COP26 meeting. This article proposes
an agent-based model of vehicle activity as a tool for quantifying energy consumption by simulating
a fleet of EV/PHEVs within an urban street network at various spatio-temporal resolutions. Driver
behaviour plays a significant role in energy consumption; thus, simulating various levels of individual
behaviour and enhancing heterogeneity should provide more accurate results of potential energy
demand in cities. The study found that (1) energy consumption is lowest when speed limit adherence
increases (low variance in behaviour) and is highest when acceleration/deceleration patterns vary
(high variance in behaviour); (2) vehicles that travel for shorter distances while abiding by speed
limit rules are more energy efficient compared to those that speed and travel for longer; and (3) on
average, for tested vehicles, EV/PHEVs were £233.13 cheaper to run than ICEVs across all experiment
conditions. The difference in the average fuel costs (electricity and petrol) shrinks at the vehicle level
as driver behaviour is less varied (more homogeneous). This research should allow policymakers to
quantify the demand for energy and subsequent fuel costs in cities.
Keywords:
agent-based model; electric vehicles; traffic simulation; energy intake; urban environment;
fuel costs; public policy
1. Introduction
According to [
1
], by 2050, 70% of the world’s population will live in urban areas,
accounting for roughly 6.3 billion people. Battery-powered electric vehicle sales increased
from 5.3 million sales in 2019 and are projected to reach over 39.9 million units by 2030 [
2
].
Given that the majority of people live in urban areas and infrastructure development
is targeted at these areas [
3
], it could be assumed that the majority of electric vehicles
(EVs) will be driven in these areas. An environmental benefit that EVs present is the
ability to consume energy from renewable energy sources (e.g., wind turbines and solar).
Furthermore, the total energy use among EVs is 3.4 times lower than ICEVs that rely on
petroleum, diesel or gas, which emit CO
2
that is harmful for the environment. During a
well-to-wheel (WTW) analysis of ICEV and EV efficiency, Ref. [
4
] found that EVs, when
Energies 2022,15, 4031. https://doi.org/10.3390/en15114031 https://www.mdpi.com/journal/energies

Energies 2022,15, 4031 2 of 24
using renewable energy, can reach an efficiency level of 40 to 70% depending on the location
and environmental factors. In contrast, gasoline- and diesel-powered ICEVs had an WTW
energy efficiency of 11–27% and 25–37%, respectively. Almost all vehicle manufacturing
companies have started building and testing EV/PHEVs for the commercial market [
5
,
6
].
Governments are facilitating benefits to persuade people to replace ICEVs with EVs through
economic incentives or legislation. However, not all countries have renewable technology
to power these vehicles; some countries, such as China, still depend on coal to power
the majority of their electric grid infrastructure [
7
,
8
]. In Australia, only 24% of electricity
is generated from renewable sources [
9
]. In their review of EVs and their impact on the
climate, Ref. [
10
] found that vehicles using electricity from sources with lower global
warming potentials (GWP) [
11
] are better than ICEVs. In contrast, Ref. [
12
] found it was
counterproductive to promote EV uptake in countries where electricity is produced from
fossil fuels. The statistics mentioned above reaffirm the need to explore the impact these
technologies have on future cities.
This study demonstrates how agent-based modelling (ABM) can be harnessed to
quantify energy demand in cities from electric-powered vehicles at various spatio-temporal
resolutions. To test the model, two variables are configured across multiple test scenarios to
demonstrate the subtle differences in outcomes. These variables are the speeding behaviour
(known as adherence to speed limits) and the number of vehicles on the street network
(density of vehicles). Through experimentation, we show that individual vehicle behaviours
and the number of vehicles on the street network impact the total energy usage (the amount
of energy required by the vehicles to complete their drive cycle in kWh). Drive cycle is
defined as a series of data points representing the speed of a vehicle versus time.
This article contributes an energy calculation extension (Figure 1) which can be used in
conjunction with the agent-based model [
13
] to quantify EV energy usage. While the focus
is centred around electric-powered vehicles, to demonstrate the effectiveness of the model,
we illustrate how ICEV vehicles can also be incorporated by converting energy to petrol
(L/km), allowing a direct comparison between individual-level behaviours/patterns using
two types of vehicles and their relative impact on costs and efficiency. The novelty of this
article is three-fold. Firstly, an agent-based method for quantifying energy demand from
vehicle behaviour at the individual level is presented. Secondly, heterogeneity among driver
behaviour and road characteristics is included, directly impacting the energy required,
which is the case in the real world. Finally, the proposed model enables practitioners to
quantify the potential energy costs these vehicles incur and compare scenarios such as high
traffic to low traffic densities. For clarity, driver behaviour is defined as the interactions
of the human driver and the impact those interactions have on the vehicle being driven.
This includes, for example, the driver’s foot dynamics and its impact on acceleration [
14
].
This is represented as the speed limit adherence and non-speed limit adherence behaviours,
enhancing heterogeneity.

Energies 2022,15, 4031 3 of 24
Figure 1.
Workflow diagram depicting processes the UTS undergoes during run-time including the
Energy Calculation Extension.
2. Background
A traffic system is characterised by multiple individual actors (e.g., drivers) and a
street network made up of individual rules characterised by (for example) traffic lights and
posted speed limits. Given this system’s individual-level components, it is amenable to
being studied using individual-based modelling methods. According to [
15
], individual-
based modelling refers to simulation models that treat individual entities as unique and
discrete elements with at least one property (e.g., age, height, speed), and these properties
change during the life cycle of the entities. Therefore, in this study, vehicles can be thought
of as individual heterogeneous entities with their properties and rules, while the urban
street network is the environment within which these vehicle entities are observed.
Agent-based modelling (ABM) is an individual-based modelling method. It pro-
vides the means to plan, design and experiment with micro-heterogeneous agents in an
artificial, computational environment. ABMs have been utilised in various domains to
explain complex phenomena such as those that occur in crime [
16
,
17
], ecology [
18
–
20
],
economics [
21
,
22
], sociology [
23
,
24
], geography [
25
,
26
] and transportation [
27
,
28
]. One
advantage of using ABMs is that they are able to represent a richer and more detailed set of
individual actors leading to potential policy alternatives and outcomes compared to the
alternative, statistical models [29].
Several agent-based models have focused on electric vehicle research. Ref. [
30
] de-
veloped an agent-based model that measured consumer needs and decision strategies
by policymakers to shift from ICEVs to EVs. They found that effective policy requires a
long-lasting implementation of a combination of monetary, structural and informational
measures. Similarly, Ref. [
31
] developed a spatially explicit agent-based vehicle con-
sumer choice model to identify the various influences that can affect the uptake of PHEVs.
The study found that providing consumers with ready estimates of expected lifetime fuel
costs associated with other vehicle types, including the rise of petrol costs, can generate
preferences for purchasing EV/PHEVs over ICEVs.
Several studies have also explored the total cost of ownership between EVs and ICEVs
from a consumer perspective to quantify the economic differences in ownership between
vehicle types. Findings differ geographically due to international differences in the price
of petrol, diesel, and electricity. In a study focused on New Zealand, Ref. [
32
] estimated

Energies 2022,15, 4031 4 of 24
that the per-kilometre cost of ownership (PCO) for a used EV was twelve percent lower
than that of a used petrol-powered car over twelve years (25.5 NZ cents and 31.5 NZ
cents for petrol vehicles). Although this study primarily focused on the differences in fuel
costs, others have included additional factors such as insurance, vehicle depreciation and
maintenance. Ref. [
33
] analysed these factors between 1995 and 2015 and found that in the
UK, USA and Japan, owners of both mid-size battery EVs (BEVs) and hybrid EVs (HEVs)
incurred lower costs than owners of ICEVs during the same period.
Fuel and electricity prices need to be estimated beyond the current year to provide
insight into the future costs in ownership between EVs and ICEVs. This is difficult given
the inherent fluctuation in oil and electricity markets. However, when investigating the
relationship between oil and electricity prices, Ref. [
34
] found that the Engle–Granger co-
integration method identified a short-term relationship between these fuel types. Ref. [
32
],
on the other hand, assumed that changes in fuel prices would follow the past decade
trends, which exhibit a 1.4% per year increase for petrol and a 1.1% increase for electricity.
Their findings for New Zealand, therefore, cannot be easily transferred to an international
context because user-end electricity costs differ drastically between countries, with higher
household electricity costs in Germany, Denmark and Italy and lower costs in Mexico,
Korea, and Turkey [
35
]. Such discrepancies in findings are reflected in international stud-
ies [
36
], which found that without subsidies, limited models of BEVs and HEVs incurred
lower running costs than ICEVs at the time. Given the complexities mentioned above of
integrating fluctuating costs of petrol and electricity into our analyses, we will use the most
recent cost of electricity kWh per km and petrol per L/km in the UK.
As the discussion above indicates, EV modelling is a relatively new area of research.
Prior studies also focused on a narrow set of issues such as market penetration and charging
infrastructure, which may ultimately be driven by price considerations made by individual
prospective owners. We, therefore, contend that planning and developing forecasts of elec-
tric energy consumption alongside pricing in urban street networks is of critical importance
because electricity demand and pricing will influence uptake.
3. Model Description
This section describes the agent-based model adopted for this study. The overview
design and details (ODD) protocol will be utilised to explain all aspects of the model [37].
3.1. Purpose
The agent-based model used in this research is the 3D Urban Traffic Simulator (UTS)
in Unity [
13
]. The model was developed to allow researchers to simulate hypothetical
vehicle drive cycle scenarios in a 3D urban environment. The model delivers heterogeneous
autonomous vehicle agents with granular features such as mass, velocity and traction
control. Similarly, the road network is designed around a built-up environment that
contains all the characteristics of a dense urban street network with varying speed limits
and intersection rules adopted from the UK Speed Limits [
38
]. Lastly, the model was used
by researchers looking at how driver behaviour impacts collision rates [28].
3.2. Variables
The model requires input parameters to run an experiment and produces output
results for later analysis. The parameters that can be tuned are listed in Table 1.
The model has two entities: the vehicle agents and the model environment in which
these agents are based. The vehicle parameters are:
•
The vehicle mass parameter, drawn from a random uniform distribution between 1000
and 3000 kg (inclusive), allows the model to simulate a wider variety of vehicle types,
from sedans to SUVs and hatchback. The rationale behind this distribution was to try
intersect the EV and ICEV vehicle types, which larger vehicles such as vans or trucks
are not part of; the model distributes vehicles arbitrarily across the environment with
varying weights (source [39]).

Energies 2022,15, 4031 5 of 24
•
The top speed measure is between 30 and 45 mph (48, 72 km/h) and is only applied
to vehicles that do not adhere to speed limits. This measure is applied only if Speed
Adherence is ≥1 (source [40]).
•
The gap acceptance parameter can be between 1 to 10 for each vehicle. The variable
assigns a distance between two vehicles in meters. This ensures a wider variety of
visual impairment is captured as some people with healthier eyes keep a fair distance
from vehicles in front usually adhering to the 2-s rule compared to people with worse
vision. Furthermore, the distance had to be relative to the average road distance in
the model.
The environment-specific parameters are:
•
The number of vehicles generated in the model,
N
. This can be between 1 and 500.
However, this can be adjusted depending on the compute power accessible. The hard-
ware accessible at the time of writing this article could only efficiently simulate up to
500 vehicles in 3D space while yielding valid results (refer to the Conclusions section
for more on this limitation).
•
The speed adherence variable can be between 0
≤x≤N
. This quantifies the
proportion of vehicles that will not adhere to the speed limits applied to the road they
are driving on.
•
The urban road network consists of 1295 roads which vehicles drive on and 354 inter-
sections which consist of traffic rules (Algorithm 1, Ref. [
28
]). The road network has
been designed to depict a small urban town.
The parameters above are used to produce output variables that observe various data
points at every step of the simulation run, collecting individual-level data from each vehicle.
Table 2describes the output variables that the model produces.
Table 1. Model entities and parameter values (source: [28]).
Entity Parameter Values
Vehicle Mass [1000, 3000] (kg)
Top speed [30, 45] (mph), [48, 72] (km/h)
Gap acceptance [1, 10] (m)
Environment N. of vehicles [1, 500]
Speed adherence [0, N]
Roads 1295
Intersections 354
The ABM outputs thirteen variables that can be used for analysis (refer to Table 2).
As the agent ID variable is present, a micro-level analysis of the agent behaviours during
model execution (e.g., observing individual drive cycles) can be explored. The collisions
variable tracks the number of times a vehicle has collided with another. Top speed is
the speed limit associated with the road that the vehicle is driving on, which the vehicle
tries to match. However, in scenarios where some vehicles do not adhere to speed limits,
this would be a value between 30 and 45 mph (48, 72 km/h). The current speed value
is the vehicle’s speed at the current time step of the model. The distance of travel tracks
the vehicle’s distance from the starting position on the road network at each time step in
metres. The gap acceptance length is the distance the vehicle keeps from vehicles ahead.
The velocity magnitude is a scalar value indicating the rate of motion at that specific time
step. The vehicle mass variable assigns a weight to the vehicle between 1000 to 3000 in
kilograms. The physics engine requires that every object have a mass assigned to it to
ensure gravity is applied. The downforce coefficient is set to 0.1; for this research, it is left
at 0.1 to have no impact on the vehicles. Lastly, date-time stamps are included in each
row of data recorded such that time-series analysis can be applied. These output data are
then used as input to the energy calculation extension, which calculates energy intake and
outputs energy-specific data, as seen in Table A1.

Energies 2022,15, 4031 6 of 24
Table 2. Model output variables.
Variable Output Type
AgentID Integer
xAxisPos Float
zAxisPos Float
collisions Integer
topSpeed (mph) Float
currentSpeed (mph) Float
distanceOfTravel (meters) Float
gapAcceptance (raycastLength) Integer
tractionControl Bool
velocityMagnitude Float
vehicleMass Integer
downforce Float
date-time DateTime
3.3. Model Overview
The agent-based model was developed using the Unity development stack. Unity is a
3D game engine consisting of a rendering and physics system and a graphical user interface.
The primary programming language is C#. Unity has received widespread adoption in
several industries, including gaming, automotive, and film [41].
The following workflow diagram (Figure 1) describes the processes that the model [
13
]
undergoes during run-time. In addition, the energy consumption calculation extension is
also depicted.
The UTS [
13
] workflow (Figure 1) starts by taking input values for the five variables
described in Table 1. The software then resets all settings to launch the simulation scene to
render the agents and environment. Once the reset process is complete, the model processes
all agents, their starting locations and environment parameters. Next, the model can run
each frame, and every change that occurs is captured and stored with a time-stamp in a
CSV file. Fixed Update is used to compute physics elements such as vehicle wheels, mass,
velocity. Update, on the other hand, computes variables for each frame. The model uses
Fixed Update due to the sheer number of physics components involved; these variables
are tracked multiple times each frame. Once the user stops the model, the sixteen output
variables are saved in a directory, and the model is destroyed (stopped). The output dataset
is then used as input to an energy calculation notebook (Figure 1), which uses the outputs
to calculate
F
from Equation (A3), with vehicle parameters from Tables 3 and 5. The output
from this calculation is then used to calculate Equations (A6) and (A7) (Section 4.1).
3.4. Agent
The vehicles in the model are classed as autonomous agents; the vehicle population
is heterogeneous, meaning every vehicle will have varying features. These agents inherit
similar characteristics as real-world vehicles; they have four wheels, a steering angle,
traction, mass and drag. Each agent applies a set of rules outlined in the article [28].
The rules described in [
28
] allow autonomous vehicle agents to navigate the envi-
ronment and act as data collectors. Each vehicle follows the same condition-action rules.
However, the parameters vary and depend on the input values from Table 1. These vehicle
agents are a simplification of real-world vehicles. Therefore, they are not expected to mimic
the actions and behaviours of real-world vehicles perfectly, but they do include the essential
behaviours that all vehicles demonstrate, such as stop/start and give-way behaviour.
If a vehicle is not adhering to the speed limits, it can increase its speed between 30 and
45 mph (48, 72 km/h). If vehicle A is ahead of B, B should decrease speed to match vehicle
A’s speed. When a vehicle arrives at an intersection, if it has the right of way (i.e., on a
horizontal lane and no vehicles are on the intersection), it drives through the intersection at
10 mph (16 km/h). If the vehicle is at the intersection and does not have the right of way, it
should wait until the intersection is cleared. If the vehicle is at an intersection and does not

Energies 2022,15, 4031 7 of 24
have the right of way, and there are no other vehicles at the intersection, the vehicle is free
to reduce speed to 10 mph (16 km/h) and drive through the intersection. Lastly, all vehicles
that adhere to the speed limit increase or decrease speed to match the road’s speed limit.
3.5. Environment
The agents described in the last sub-section require an environment to function within.
The UTS [
13
] deploys an urban street network that is described as a T-type network pattern
in [
42
] which contains similar characteristics as downtown Philadelphia, PA [
43
] and San
Francisco [
44
]. T-network patterns are like grid-shaped networks but include t-junctions.
Several added features such as the eight-lane intersections described in [
45
] also exist.
The street network contains 1295 roads and 354 intersections, arbitrarily generated to cover
a small town. The individual roads, speed limits and intersection rules are described in the
following Figure 2.
Figure 2. Urban Street Network roads and intersections (source: [28]).
The environment consists of three road types with varying speed limits and intersec-
tions with right-of-way rules. The model environment is a simplification of the real world.
Therefore, it does not capture all intersection types. However, it does contain the basic char-
acteristics of an urban street network which have also been observed in several cities across
the United States [
43
,
44
,
46
]. The vehicles also adhere to stop-go rules (conceptualisation of
traffic lights) enforced at junctions. These rules are present in the vehicle’s decision-making
algorithm [28]. The following list describes each road and intersection in Figure 2:
• (A) A two-way local road with a speed limit of 20 mph (32 km/h);
• (B) A two-way corner road with a speed limit of 10 mph (16 km/h);
• (C) A two-way fixed road with a speed limit of 30 mph (48 km/h);
•
(D) An eight-way intersection. Right-of-way is for traffic on horizontal lanes, and the
speed limit is 10 mph (16 km/h);
•
(E) A two-way t-junction. Right-of-way is for horizontal lanes, and the speed limit is
10 mph (16 km/h).
The speed limits for the three types of roads (Figure 2A–C) were derived from UK
government sources such as [
40
], where urban street networks consist of local 20 mph
(32 km/h) and fixed 30 mph (48 km/h) zones; however, corner roads sometimes require
lower speeds such as 10 mph (16 km/h) as vehicles require more room to turn. The ‘setting
local speed limits’ report by the UK Government’s Department for Transport outlines that
most urban streets (roads in built-up areas) have a fixed speed limit of 30 mph (48 km/h).
However, for dense areas—usually city centres—this may be designated 20 mph (32 km/h)
by local councils to keep pedestrians safe from collisions [28,47].

Energies 2022,15, 4031 8 of 24
4. Results
This section will analyse the experiments designed to quantify electric energy con-
sumption across multiple vehicle densities and adherence levels. Once this is achieved,
the model will quantify fuel consumption by simulating an ICEV drive cycle as a direct
comparator between PHEV/EV and ICEV fuel consumption. The aforementioned compara-
tor experiment will present novel insight by comparing drive cycle, fuel consumption and
costs of ICEV and compare these patterns to the alternative PHEV/EV outputs. The output
data from the energy calculation extension notebook can be found in Table A1.
Before running the experiments and analysing outputs, the model must be tested
against either (1) empirical data, which entails vehicle drive cycle and energy consumption
in kWh over km travelled, or (2) model outputs from a different model utilised in research
by the research community. Without a baseline comparator, there is no way in knowing if the
model utilised in this research, namely [
13
], outputs energy consumption accurately. Almost
all agent-based models are validated using the former or latter processes [17,28,48–52].
The data used to compare model outputs were adopted in the following study [
53
].
This study utilised German automotive statistics from empirical sources to generate drive
cycles of EV journeys using a mathematical model. The variables of interest are kilowatt-
hour over distance travelled in kilometres. The specific dataset used contains the drive
cycle of 200 vehicles, where input parameters are derived from the statistics mentioned
above and the physical properties of vehicles used in Germany [
54
]. The main drawbacks
of this model are:
•
That it produces outputs at a time resolution of 15 min; our model, on the other hand,
has a time resolution of 1 s. This way, we can capture finer detail such as the impact of
traffic lights on acceleration/deceleration and momentary traffic congestion;
•
That it only captures trips that are split into commuters and non-commuters. Thus,
the modelled scenarios revolve around two profiles of drivers. Our model manipulates
the entire system from the street network to traffic rules and vehicles; thus, no single
driver profile is modelled, but a heterogeneous set of behaviours are captured.
These factors play an essential role in the electric energy consumption post-simulation
run. The main strength of [
53
] is that variables such as heat transfer, weather, road condition
and slope are all introduced as parameters to produce more robust energy consumption
results. In our study, we make some basic assumptions, such as: our road surfaces are
flat, and no weather parameters are introduced; these variables add complexity to the
agent-based model and can hamper computation which, in turn, can affect outputs. We
have, however, introduced rolling resistance (Equation (A1)) and braking energy recovery
(Figure A1) which both impact electric intake. Adding additional levels of complexity is an
area for future development.
4.1. Electric Energy Consumption Calculation
As the vehicle agents are not configured to mimic a specific vehicle, the goal is to adopt
parameters from empirical statistics to ensure our findings are consistent with those within
the UK given the environmental parameters adopted, such as local and fixed speed limits
(Figure 2). Currently, the most popular EV/PHEV in the UK is the Mitsubishi Outlander
(source [
55
]), with over 46,400 units sold as of June 2020. Therefore, this is the chosen
vehicle in our analyses. However, the model can be readily adapted to other vehicles and
can replicate a heterogeneous fleet.
Equations (A3), (A6) and (A7) were applied to the model outputs to calculate electric-
ity intake:
•
For Equation (A3),
F
is calculated by using the following parameter variables:
θ=
0 as
the surface area is flat,
CD=
0.33,
A=
3.078
m
(where height = 1.71 m,
width = 1.80 m)
,
m= 1925 kg (Table 3),
a=∆v
∆t
, where
∆v
is the velocity change over time period
∆t
,
and lastly, v= velocityMagnitude (Table 2).

Energies 2022,15, 4031 9 of 24
•
For Equation (A6),
Eout
is calculated by multiplying the output from Equation (A3)
with total_distance (d) travelled in meters per second for each agent; see Table 2.
•
Lastly, Equation (A7) is calculated by multiplying the output from Equation (A3) (
F
)
with the distance travelled
d
divided by the engine efficiency
k=
0.65.
Ein
is then
divided by 3.6 ×10−6to convert from joules to kilowatt-hours (kWh).
Table 3. Vehicle parameters (PHEV).
Parameter Value
Height (m) 1.71
Width (m) 1.80
k65% (source [56]) 1
m(kg) 1925
CD0.33
1
The official engine efficiency statistic is not provided by the vehicle manufacturer; therefore, an average engine
efficiency for PHEVs was acquired from the cited academic source.
To compare both emobpy [
54
] with UTS [
13
], we ran UTS for one hour, where fifteen
vehicles were present. To add complexity, we set five of these vehicles to break speed limits;
this allows us to capture the subtle differences between rule followers and rule breakers and
their relative energy efficiency and energy consumption over a drive cycle. In comparison,
fifteen vehicles were taken from emobpy and plotted against our model outputs.
We aggregated the fifteen vehicles from [
13
] to five gradient colours to simplify the
legend in Figure 3.
Figure 3.
Model output comparison: electric energy consumption (kWh) against distance travelled
(km), with 15 vehicles over a 1 h drive cycle (5 vehicles break speed limits).
Figure 3distinguishes between the rule followers and rule breakers. We can see the
clustered lines at the bottom of the graph; these are vehicles that fully adhere to speed
limits. On average, these vehicles consumed roughly 0.15–0.25 kWh/km. The five vehicles
that broke speed limit rules travelled further as they were speeding and, on average,
consumed more energy and were less energy-efficient, as expected. Furthermore, the urban
environment has impacted the distances these vehicles could cover (differences in distance
travelled). The furthest a vehicle has travelled is 28 km. We also found that the least energy
efficient vehicle was consuming roughly 0.50 kWh/km. It is evident that the model outputs
from emobpy and UTS are in agreement, where the longer and faster a vehicle drives the

Energies 2022,15, 4031 10 of 24
less efficient it becomes. These characteristics of energy efficiency and consumption are
evident in empirical literature [57,58].
This small sample shows that the confidence intervals for emobpy are small. This
means that vehicles are likely to follow similar drive cycle patterns and configurations,
leading to similar energy consumption outputs. However, due to heterogeneity, our model
captures a more diverse range of outputs from the same environment, which is a strength
of the ABM approach over standard mathematical models.
The energy consumption (kWh/km) patterns are similar for both emobpy and UTS;
see Figure 4. These preliminary results are promising as they show that UTS is capable
of producing behaviours of realistic drive cycles of electric vehicle energy consumption
that have also been observed in a completely different model [
53
]. Now that we have
shown that UTS produces valid estimates of electric energy consumption, we can devise
experiments to quantify the effects of speed limit adherence and vehicle density on electric
energy (kWh/km) and petrol consumption (L/km).
Figure 4.
Model Output comparison: electric energy consumption (kWh) for both UTS (model) [
13
]
and emobpy [54].
4.2. Experiments
Due to the computational processes required to render 3D vehicles through space and
time [
13
] and the hardware capacity at hand, nine computationally cheaper experiments
were designed. The independent variables were density and adherence to speed limits.
These experiments are formally described in Table 4.
Table 4. Experiment conditions.
Variable Low Adherence Medium Adherence High Adherence
Low Density Condition 1, 10 vehicles,
10 non-adherence
Condition 2, 10 vehicles,
5 non-adherence
Condition 3, 10 vehicles,
0 non-adherence
Mid Density Condition 4, 50 vehicles,
50 non-adherence
Condition 5, 50 vehicles,
25 non-adherence
Condition 6, 50 vehicles,
0 non-adherence
High Density Condition 7, 100 vehicles,
100 non-adherence
Condition 8, 100 vehicles,
50 non-adherence
Condition 9, 100 vehicles,
0 non-adherence

Energies 2022,15, 4031 11 of 24
These experiments should, in theory, allow us to explore energy consumption in dif-
ferent environmental and behavioural scenarios. The experimental conditions should yield
an array of patterns that quantify energy consumption under these conditions. To explore
these data, we produce several visualisations and later interpret outcomes.
As more vehicles adhere to speed limits, we see that the cumulative energy consump-
tion is at its lowest 0.1–2 kWh (Figure 5c,f,i). On the contrary, as more vehicles break speed
limits, we see cumulative energy consumption at its highest (Figure 5a,d,g). As density
increases, the cumulative energy consumed also increases (Figure 5g,h,i) regardless of
speed limit adherence.
As adherence to the speed limit increases, it was observed that the overall distance
travelled by vehicles was smaller; thus, energy consumption decreased Figure 6.
According to official Mitsubishi statistics [
59
], the range of the Outlander (kWh/km)
is 0.169. To compare, the outputs in Figure 6show that as adherence increases (Experi-
ment Conditions 3, 6, 9), the cumulative energy consumed is closer to the manufacturer’s
statistics. The similarity in high adherence cases and energy consumption compared to
official statistics can be explained because these statistics were based on fixed/local speed
limits in urban environments and do not account for speeding behaviour or consumption
levels resulting from motorway speeds. Furthermore, energy efficiency increases as driver
behaviour becomes more homogeneous (high adherence), which is what we would expect
to see. These data show that the Energy Calculation Extension notebook seen in Figure 1
enables the UTS [
13
] to quantify the electric energy consumption, so long as the parameters
outlined in Table 3are provided.
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 5.
Distribution of the cumulative energy consumption (kWh) for each experiment condi-
tion: (
a
) 10 vehicles, 10 non-adherence; (
b
) 10 vehicles, 5 non-adherence; (
c
) 10 vehicles, 0 non-
adherence; (
d
) 50 vehicles, 50 non-adherence; (
e
) 50 vehicles, 25 non-adherence; (
f
) 50 vehicles, 0 non-
adherence; (
g
) 100 vehicles, 100 non-adherence; (
h
) 100 vehicles, 50 non-adherence;
(i) 100 vehicles
,
0 non-adherence.
To recap, the previous Section 4.1 developed experiments comparing outputs from
the UTS [
13
] to a mathematical model of energy fuel intake, emobpy [
53
], for validation.

Energies 2022,15, 4031 12 of 24
We found the UTS and Energy Calculation Extension notebook Figure 1produced results
consistent with the mathematical model of driver behaviour [
53
]; see Figures 3and 4.
The subsequent section, across nine experimental conditions, compared the effect that
adherence to speed limits and vehicle density had on electric energy consumption by
modelling a specific vehicle type (Table 3) and subsequent results (Figures 5and 6).
Figure 6.
Box plots of energy consumption per kilometer (kWh/km) across all experiment conditions.
4.2.1. Fuel Consumption of Internal Combustion Engine Vehicle Fleet
Following the aims set out in Section 1, to produce estimates of petrol consumption
(L/km), an ICEV must be modelled. This process is straightforward, as the UTS is not
vehicle-specific; other fuel types such as petrol and diesel can be modelled using the
formulae from Appendix A.1.
As previously discussed in Section 4.1, a specific type of vehicle must be identified
to model energy consumption. From January 2020 to December 2020, the Ford Fiesta ST
was purchased (registered) 49,174 times in the UK, making it the most-purchased ICEV
according to [
60
]; therefore, it was the chosen ICEV. The vehicle parameters can be observed
in Table 5.
Table 5. Vehicle parameters (source [61]) (ICEV).
Parameter Value
Height (m) 1.469
Width (m) 1.941
k0.33% ([62]) 1
m(kg) 1635
CD0.341
1
The official engine efficiency statistic is not provided by the vehicle manufacturer; therefore, an average engine
efficiency for ICEVs was acquired from the cited source.
Equations (A3), (A6) and (A7) were applied to the model outputs to calculate petrol intake:
•
For Equation (A3),
F
is calculated by using the following parameter variables:
θ=0
as the surface area is flat,
CD=
0.341,
A=
2.851
m
(where height = 1.469 m,
width = 1.941 m)
,m= 1635
kg
(Table 5),
a=∆v
∆t
where
∆v
is the velocity change
over time period ∆t, and lastly, v= velocityMagnitude (Table 2).
•
For Equation (A6),
Eout
is calculated by multiplying the output from Equation (A3)
with total_distance (d) travelled in meters per second for each agent; see Table 2.
•
Lastly, Equation (A7) is calculated by multiplying the output from Equation (A3) (
F
)
with the distance travelled
d
divided by the engine efficiency
k=
0.47.
Ein
is then
multiplied by 2.923 to convert joule to gasoline/petrol (L).
To ensure comparability, the experiment conditions in Table 4will be re-run using the
vehicle-specific parameters from Table 5.

Energies 2022,15, 4031 13 of 24
As engine efficiency for ICEVs is relatively low compared to EV/PHEVs, the amount
of petrol converted to power that moves the vehicle is also low. Roughly 70% of energy is
lost during this process [
62
]. Given the aforementioned, it is likely that the fuel consumption
outputs seen in Figure 7deviate from the true value by some margin.
As expected, the energy calculation extension notebook used in conjunction with
UTS [
13
] produced outputs for the nine experimental conditions in Table 4with a different
fuel type (Table 5). The drive cycle patterns for the ICEV scenario (Figure 7) are similar
to those of the PHEV scenario (Figure 6). At an individual level, the outliers for both
conditions (Figures 6and 7) could be due to traffic congestion, vehicle weight and routes
travelled. According to the vehicle’s technical specification, [
61
], in extra-urban environ-
ments, the vehicle is claimed to do 5.1 L/100 km. Therefore, on average, the expected fuel
consumption would be roughly 0.05 litres per kilometer (19.608 km/L), as described in
the PHEV case, as adherence increases and driver behaviour is more compliant with rules.
The energy consumption patterns are closer to the manufacturers’ specification in Figure 7
for Experiment Conditions 3, 6 and 9. However, as adherence decreases, distance travelled
increases, and the fuel consumption levels deviate from the vehicle manufacturer’s tech-
nical specifications. This would be an expected behaviour as every vehicle is driving at
various speeds (heterogenous driver behaviour), which is an unrealistic observation of
driver behaviour. The vehicle manufacturer may not have considered this when estimating
fuel consumption. It could be that the tests carried out to measure the fuel economy are
conducted using specific drive cycles such as high adherence.
Two examples of simulated fuel types have been quantified with a reasonable degree
of accuracy. This has resulted in enough data to quantify the costs of running these vehicles
in the hypothetical urban street network.
Figure 7. Box plots of energy consumption per kilometer (L/km) across all experiment conditions.
4.2.2. Monetary Costs of Fuel and Electric Consumption
The domestic cost of fuel per litre (L) and electricity per kilowatt-hour (kWh) fluctuates
over time. The price for each varies, depending on vehicle fuel efficiency, distance travelled,
weight and the fuel price [
63
]. Therefore, to quantify the cost in Great British Pounds (GBP),
the current cost of petrol and electricity is adopted. These are GBP 1.43 (per L/km) [
64
]
and GBP 0.17 (per kWh/km) [65], respectively.
To calculate the cost of petrol, the amount of petrol intake calculated for each vehicle
was multiplied by 1.428, while the amount of electric energy intake was multiplied by 0.17.
This produced a rough estimate of the fuel costs per car for each experiment condition for
the UK.
The total cost of electric and petrol across all experiment conditions were £248.76 and
£481.89, respectively (These costs are merely estimates produced from the vehicle-specific
parameters seen in Tables 3and 5and drive cycle scenarios from Table 4in an urban street
network. These costs will not be the same in different types of street networks such as

Energies 2022,15, 4031 14 of 24
highways, motorways and rural roads). Overall, it is £233.13 cheaper to run PHEVs over
ICEVs. As engine efficiency is greater for EV technologies [
66
], it is likely that these vehicles
would be more fuel-efficient and thus cost less than both PHEVs and ICEVs. In Figure 8,
a pattern emerges, where as driver adherence decreases (speeding increases) the cost of
electricity and petrol increases (experiment conditions 1, 4 and 7) relative to vehicle density.
Furthermore, as adherence increases, the difference in price between the fuel types shrinks
(experiment conditions 3, 6 and 9) as vehicles have travelled roughly the same distances
Figures 6and 7
. Similarly, these trends are broken down in the average cost per km in
Table A2. Overall, we observe that PHEVs on average are cheaper per kilometer travelled
than ICEVs. Furthermore, when the total cost of each model condition results are compared,
we see a clear distinction between costs, and overall, PHEVs are cheaper (Figure 8).
Figure 8.
The total sum of petrol/electric costs (GBP) for each experiment condition across all vehicles.
A core strength of ABMs over mathematical models, as specified earlier, is the spatio-
temporal resolution variability of data. For instance, individual-level (vehicle-level) data
are attained and should provide a more enhanced snapshot of the impact behaviour had
on fuel costs.
An individual-level break-down of the fuel expenditure costs across all vehicles and
types are discerned in Figures 9and 10 and in Appendix C.1, Figures A2–A5. These results
re-enforce our earlier made suppositions. For instance, as more vehicles regulate speed,
the difference in average costs decreases, as seen in Figures 9C and 10C. Despite these
trends, it could be argued that as variability amongst acceleration/deceleration increases
(heterogeneity), PHEV owners will save more money compared to ICEV owners. The net
benefits may not be substantial sums of money, but the environmental benefits (which have
not been modelled) could be a bonus for consumers. Furthermore, as empirical evidence
indicates, autonomous electric vehicles (AEVs) are more efficient than PHEVs/ICEVs [
67
].
Consequently, we could expect a greater extent of financial savings and environmental
benefits for owners of AEVs.
To conclude, when vehicle fleet is heterogeneous (more variability among speeds), this
leads to greater savings in adopting PHEVs over ICEVs as the engine efficiency is greater.
Consequently, more energy is converted to power than ICEVs (Experiment Conditions 4,
7). In contrast, as speeds become more regulated and similar, the average monetary costs
between the two vehicle types reduce, as seen in Figures 9C and 10C. Furthermore, these
findings are consistent for all fleet sizes, as seen in Figures A2F, A4F, A3I and A5I.

Energies 2022,15, 4031 15 of 24
Figure 9.
The total sum of electric costs (GBP) for each PHEV, model conditions 1 to 3. Where (
A
):
10 vehicles, 10 non-adherence, (
B
): 10 vehicles, 5 non-adherence and (
C
): 10 vehicles, 0 non-adherence.
Figure 10.
The total sum of petrol costs (GBP) for each ICEV, model conditions 1 to 3. Where (
A
):
10 vehicles, 10 non-adherence, (
B
): 10 vehicles, 5 non-adherence and (
C
): 10 vehicles, 0 non-adherence.
5. Discussion
This article set out to quantify the energy consumption by a fleet of vehicles in an urban
street network using agent-based modelling. Given the current global agenda on climate
change through various institutions and policies (i.e., COP 26, Paris Climate Accord 2015,
Organisation for Economic Co-operation and Development, Green Economic Recovery
(UK)), political discourse worldwide has shifted focus to green agendas, particularly
renewable technologies, to facilitate a reduction of carbon emissions. The work conducted
in this article plays a significant role in aiding national governments in modelling the
potential landscape of energy consumption by EV/PHEVs. Previous literature has focused
on mathematical models; however, this method is limited. Agent-based models are better
suited to modelling individual-level drive cycle behaviours than mathematical models.
The former typically provides an aggregated average of energy expenditure, while the
latter provides a finer spatio-temporal resolution of individual-level energy consumption,

Energies 2022,15, 4031 16 of 24
highlighting the immediate environment’s impact on a vehicle’s drive cycle, which affects
energy consumption and efficiency. The model presented has demonstrated vehicle energy
efficiency patterns that have been identified in empirical literature [
57
,
58
], namely that
the longer distances travelled at speed reduces battery/engine efficiency, and conversely,
vehicles that abide by rules in the long-term are more efficient. Another crucial finding was
that as speed adherence increased, the energy consumption per kilometer better reflected
vehicle manufacturer statistics for consumption; this was the case for both PHEV and ICEV
tests, suggesting that vehicle manufacturers might be testing their vehicles at constant,
more regulated speeds. Finally, we found that PHEVs overall are cheaper vehicles to run
compared to ICEVs. This is due to several reasons, but primarily that PHEVs are more
engine-efficient compared to ICEVs.
This work makes a novel methodological contribution to the modelling of vehicle
energy consumption using agent-based modelling. While several attempts to model vehicle
activity to quantify energy have been made, the majority of these models have hard-coded
driver behaviour, which is bounded by constant speeds [
54
,
68
]. This, we believe, is not
informative of energy consumption in urban spaces, where the stochastic environment
plays a more significant role in affecting energy intake, such as urban speed limits, stop-go
rules, and other vehicles in the street network.
Another vehicle technology that is beginning to gain traction is autonomous vehicles
(AVs). UK Government projections show a net gain of 823,000 jobs and over £82 billion
from the manufacturing and shipping of AVs [
69
]. AVs are likely to be electric, so their
ascendance may also be considered in relation to electric energy usage of vehicles of the fu-
ture. Ref. [
67
] outlines how AVs and electric vehicles may reduce energy consumption due
to their connected environment, as route choice can be optimised to avoid congestion, un-
dertake routes with fewer stops and ensure multiple passengers are catered to at once due
to dynamic ride-sharing capabilities. Additionally, AVs may be able to drive in an optimally
efficient manner due to the incorporation of traffic conditions received through communica-
tion and sensors. Ref. [
67
] estimates the energy consumption from these smoother driving
cycles would decrease current energy use by between −10% and −20%.
In more revolutionary scenarios in which proportions of fully autonomous vehicles
outweigh human-operated vehicles, vehicle-to-vehicle (V2V) communication could enable
velocity synchronisation and shorter spaces between vehicles (i.e., platooning). Refs. [
70
,
71
]
outline how this can improve string stability and increase network capacity as vehicles will
operate with decreased acceleration noise and maintain closer distances to nearby vehicles,
thus reducing aerodynamic drag. Ref. [
67
] outlines the energy and emissions reduction from
autonomous vehicle platooning to be between 7% and 35%. Although sophisticated au-
tonomous fleets (levels 4 and 5) are yet to be technologically perfected, as currently, the highest
level of autonomy achieved in vehicles on sale is level 3 [
72
], these findings provide insight
into the combined benefits of electric autonomous vehicle (EAV) fleets in the future.
6. Conclusions
A future avenue to explore would be to extend the model environment to cater for AVs.
This should be achievable as the model can currently model specific vehicles and adherence
levels. By modelling AVs, the variation of energy consumption scenarios of typical EVs and AVs
can be compared. Furthermore, this could allow policymakers to model charging infrastructure
in cities to test how these different vehicles can adapt optimally to these environmental changes.
A significant limitation of this work is computational tractability. The compute de-
mand exponentially grows as we increase the number of vehicles or induce complex
environmental settings. This can prevent users from simulating a greater capacity of vehi-
cles or more complex cities. Secondly, we assume the world to be a flat plane in the model.
However, this diverges from the real world. This assumption was due to computational
demand, and we tried to configure the most simple environmental setting to ensure compu-
tation was not hampered. However, as cloud computing technologies become mainstream,
this problem can be overcome.

Energies 2022,15, 4031 17 of 24
Another limitation of this article is that it utilises an urban road typology only. While
necessary, as most EV infrastructure is focused on cities, this does not necessarily imply
that energy consumption from urban street networks would remain identical to other road
typologies (e.g., motorways, dual-carriageways, rural roads). Therefore, in the future,
the model can be extended by analysing vehicle behaviours and their subsequent impact
on energy consumption in various road typologies.
This study highlights the importance of individual-based modelling methods such as
ABMs in investigating future transport systems in cities. As some of the most important
global policy agendas focus on the diffusion of low carbon-emitting technologies, this
research is well-timed and crucial in planning for the future city.
Author Contributions:
Conceptualization, S.O., E.M. (Ellie Marfleet) and K.S.; Formal analysis, S.O.;
Funding acquisition, A.H.; Investigation, S.O., E.M. (Ellie Marfleet), K.S. and A.W.; Methodology, S.O.
and K.S.; Project administration, S.O., J.T., A.H. and A.W.; Software, S.O. and K.S.; Supervision, J.T.
and A.H.; Validation, J.T.; Visualization, S.O.; Writing—original draft, S.O. and E.M. (Ellie Marfleet);
Writing—review & editing, S.O., J.T., E.M. (Ellie Marfleet), K.S., A.H., E.M. (Ed Manley), A.W. and
R.V. All authors have read and agreed to the published version of the manuscript.
Funding:
This project has received funding from the Economic and Social Research Council, grant
number: ES/P000401/1; the Economic and Social Research Council, The Alan Turing Institute, grant
number: ES/R007918/1, UK Prevention Research Partnership (UKPRP): MR/S037578/2, Medical
Research Council: MC_UU_00022/5 and The Scottish Government Chief Scientist Office: SPHSU20.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
Open source code and data access: (1) the datasets for both PHEV and
ICEV can be accessed at the following source [
73
]; (2) the Urban Traffic Simulator Agent-Based Model
can be accessed at the following link: https://www.comses.net/codebases/32e7be8c-b05c-46b2- 9
b5f-73c4d273ca59/releases/1.1.0/ (accessed on 20 May 2022); (3) the Energy Calculation Extension
can be found at the following link https://codeocean.com/capsule/9598578/tree (accessed on 25
May 2022).
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Appendix A.1. Energy Calculation
To calculate the electricity energy consumption required to move the vehicles, the ap-
plication of classical mechanics [74] including the drag equation from fluid dynamics [75]
were adopted for this article.
When a vehicle is moving at a constant velocity, its forces are balanced (i.e., the forces
driving it forward are equal to those resisting). However, vehicle velocity is not constant
when driver behaviour changes over the drive cycle period (e.g., halting at traffic lights,
matching the speed of vehicles ahead). Therefore, we assume velocity
v
is not constant in
this model. A vehicle travelling at a non-constant speed results from an imbalance in the
forces acting on it, i.e., the net force acting on the vehicle is non-zero. Considering the drive
force from the engine, the force of gravity, the drag force and rolling resistance opposing
motion, the net (or total) force acting on a vehicle, Ftotal , can be calculated as:
Ftotal =
drive
z}|{
F−
gravity
z }| {
mg ×sin(θ)−
drag
z }| {
1
2ρCDAv2−
rolling resistance
z }| {
Crrmg ×cos(θ), (A1)
where:
•Fis the force provided by the engine driving the vehicle forward (N);
•mis the mass of the vehicle (kg);
•gis the gravitational acceleration (m/s2);

Energies 2022,15, 4031 18 of 24
•θis the angle of the surface on which the vehicle is driving on;
•ρis the density of air (1.225 kg/m3);
•CDis the drag coefficient;
•Ais the reference area of the vehicle (m2) (width ×height);
•vis the velocity (m/s), and;
•Crr is the coefficient of rolling resistance.
For this investigation, the value of the coefficient of rolling resistance is taken to be
0.012 based on the assumption that all vehicles in the system are passenger vehicles and
the road surfaces are made of smooth asphalt [
76
]. The total force acting on the vehicle
can be expressed as the product of the vehicle’s mass and its acceleration, i.e.,
Ftotal =ma
,
and consequently, we can write Equation (A1) as:
ma =F−mg ×sin(θ)−1
2ρCDAv2−Crrmg ×cos(θ). (A2)
In this investigation, we are concerned with the force produced by the engine,
F
,
and the associated energy expended to produce this force. As a consequence, we may wish
to rearrange Equation (A2) as:
F=ma +mg ×sin(θ) + 1
2ρCDAv2−Crrmg ×cos(θ). (A3)
In the scenario where the road surface is flat, i.e., the vehicle is not travelling uphill
or downhill,
θ=
0. This results in the gravitational aspect of the forces resisting motion being
zero, i.e.,
mg sin(θ) =
0; it also results in the rolling resistance being
Crrmg ×cos(θ) = Crrmg
.
Equation (A3) therefore becomes:
F=ma +1
2ρCDAv2+Crrmg, (A4)
which returns the force output by the car’s engine to accelerate at rate
a
. In cases when the
vehicle is travelling at a constant speed, Equation (A4) simplifies to:
F=1
2ρCDAv2+Crrmg. (A5)
Once the force exerted by the engine,
F
, and the distance of travel over which it is
being exerted
d
are both known, the energy expended by the engine,
Eout
, can be calculated:
Eout =F×d. (A6)
In this case,
Eout
is the energy output by the engine. To find the energy provided to the
engine in the form of fuel, the engine efficiency,
k
, is needed. Assuming that the efficiency
of the engine is constant, i.e., that it has the same efficiency for all scenarios, the energy that
needs to be provided to the engine can be found using the following equation:
Ein =F×d
k, (A7)

Energies 2022,15, 4031 19 of 24
Appendix B
Tables
Table A1. Energy Calculation Extension notebook output data (EV/PHEV example).
Variable Output Type
VelocityChange Float
Acceleration Float
Deceleration Float
Braking Energy (kWh) 1Float
Drag_Force Float
Acceleration_Force Float
Total_Force Float
Drag_Work Float
Acceleration_Work Float
Total_Work Float
Energy_Input (kWh) Float
Energy_Input_Sum (kWh) Float
1
An amount of energy is generated every time a vehicle brakes (decelerates), also known as regenerative braking.
This is accounted for in the notebook using the braking energy formula from the following source: [77].
Table A2. Average cost (£) per km for both vehicle types.
MC PHEV ICEV
1 0.60 0.92
2 0.43 0.56
3 0.22 0.34
4 1.93 4.42
5 1.50 2.25
6 0.67 1.22
7 2.79 5.66
8 1.72 3.71
9 1.12 1.98
Appendix C
Appendix C.1. Figures
Figure A1. Box plots of braking energy recovered in kWh for each experiment condition.

Energies 2022,15, 4031 20 of 24
Figure A2.
Thetotal sum of electric costs (GBP) for each PHEV, model conditions 4 to 6. Where (
D
):
50 vehicles, 50 non-adherence, (
E
): 50 vehicles, 25 non-adherence and (
F
): 50 vehicles, 0 non-adherence.
Figure A3.
The total sum of electric costs (GBP) for each PHEV, model conditions 7 to 9. Where
(
G
): 100 vehicles, 100 non-adherence, (
H
): 100 vehicles, 50 non-adherence and (
I
): 100 vehicles,
0 non-adherence

Energies 2022,15, 4031 21 of 24
Figure A4.
The total sum of petrol costs (GBP) for each ICEV, model conditions 4 to 6. Where (
D
):
50 vehicles, 50 non-adherence, (
E
): 50 vehicles, 25 non-adherence and (
F
): 50 vehicles, 0 non-adherence.
Figure A5.
The total sum of petrol costs (GBP) for each ICEV, model conditions 7 to 9. Where
(
G
): 100 vehicles, 100 non-adherence, (
H
): 100 vehicles, 50 non-adherence and (
I
): 100 vehicles,
0 non-adherence
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