18(2,1) In the Proceedings of the 2023 IEEE 26th International Conference on
Intelligent Transportation Systems (ITSC)

# A Data-Driven Integrated Framework for Fast-Charging Facility Planning using
Multi-Period Bi-Objective Optimization

Mingjia He1, Panchamy Krishnakumari2, Ding Luo 3 and Jiaqi Chen 4 1Mingjia He
is with the Faculty of Civil Engineering and Geosciences, Delft University of
Technology, 2628 CN, Delft, The Netherlands<EMAIL_ADDRESS>Panchamy Krishnakumari is with the Faculty of Civil Engineering and
Geosciences, Delft University of Technology, 2628 CN Delft, The Netherlands
<EMAIL_ADDRESS>Ding Luo is with Shell plc, 1031 HW Amsterdam,
The Netherlands<EMAIL_ADDRESS>Jiaqi Chen is with Shell plc, 1031 HW
Amsterdam, The Netherlands<EMAIL_ADDRESS>
###### Abstract

With the electrification in freight transportation, the availability of fast-
charging facilities becomes essential to facilitate en-route charging for
freight electric vehicles. Most studies focus on planning charging facilities
based on mathematical modeling and hypothetical scenarios. This study aims to
develop a data-driven integrated framework for fast-charging facility
planning. By leveraging the highway traffic data, we extracted, analyzed, and
compared spatial and temporal flow patterns of general traffic and freight
traffic. Furthermore, graph theory-based network evaluation methods are
employed to identify traffic nodes within the highway network that play a
significant role in accommodating charging infrastructure. A candidate
selection method is proposed to obtain potential deployment locations for
charging stations and to-go chargers. Based on this, we present a multi-period
bi-objective optimization model to provide optimal solutions for the placement
of charging facilities, with the objectives of minimizing investment cost and
maximizing demand coverage. The case study on the Amsterdam highway network
shows how existing traffic data can be used to generate more realistic
charging demand scenarios and how it can be integrated and evaluated within
the optimization framework for facility planning. The study also shows that
the proposed model can leverage the potential of early investment in improving
the charging demand coverage.

##  I INTRODUCTION

Transportation has become one of the major contributing sectors to emissions,
accounting for approximately one-quarter of all greenhouse gas emissions in
Europe [1]. The Netherlands is ambitious to achieve zero-emission road traffic
by 2050. With incentivizing policies and tax-related measures, the Netherlands
has become one of the leading electric transport players in the world. In
freight transport, Netherlands’ government plans to raise the market share of
clean heavy-duty vehicles to reach 30% by 2030 [2]. Considering the ambition
of zero-emission policy and the current developing trend, the market for
electric freight vehicles will grow continuously and thus requires the
construction of new charging infrastructure.
There are two main types of charging solutions: alternating current (AC) slow
charging and direct current (DC) fast charging. AC charging is mainly served
for destination charging at workplaces or residences, as it requires more time
to load. An AC slow charger may take 6–8 hours to recharge the vehicle battery
to full state, while a DC fast charger can recharge up to 80% within about 30
minutes [3]. The high efficiency of DC fast chargers is attributed to the
higher voltage and direct flow of DC current into the battery without
conversion. This characteristic makes DC charging a promising solution for
long-distance travel [3]. It allows en-route charging to ease driving anxiety
and driving range restrictions. The current charging infrastructure is
insufficient to support the future growth of EVs. In particular, the existing
charging infrastructure lacks enough fast chargers [4]. In 2019, there are
more than 200 fast-charging stations in the Netherlands. Researchers expect
significant growth in the number of fast-charge points for electric cars over
the coming years, to a maximum of 8,000 by 2025 [5]. Amsterdam, The Hague,
Rotterdam, Utrecht, and Brabantstad have been designated as the focus areas to
develop charging infrastructure since 2009 [6].
To promote electrification in freight transport, the goal of this study is to
propose fast-charging infrastructure planning strategies for the en-route
charging of commercial freight vehicles along the highway. This study builds a
planning framework consisting of data fusion, network evaluation, candidate
location selection, and an optimization model for planning. A multi-period bi-
objective optimization model is constructed to find the optimal locations and
scales of fast charging facilities considering the investment and charging-
demand coverage. The case study is conducted based on the Amsterdam highway
network. The study provides evidence for long-term charging facility
investment and supports the electrification of intercity logistics.

##  II LITERATURE REVIEW

With the increasing market share of electric vehicles in road transportation,
extensive research has investigated the charging infrastructure-planning
problem. Based on the way to represent charging demand, research approaches
can be categorized into the node-based model, flow-based model, and
trajectory-based model [7, 8]. In the node-based model, it is assumed that the
charging demand is generated at the nodes in the network [9, 10]. The flow-
based model uses a set of origin–destination trips and allows charging demand
to be served during journeys [11]. The trajectory-based model considers the
travel pattern of electric vehicles [12, 13] and might incorporate the
individual charging decision and route scheduling [14]. Optimization models
would be established after obtaining charging demand. Many researchers
considered multiple objectives for various benefits of different stakeholders.
Yang et al. [3] established bi-objective programming models for charging
demand assignment, fast charging station operation, and power line expansion,
with objectives to maximize charging service profit and minimize total
charging time. Bian et al. [15] proposed the charging station configuration
model from the perspective of users considering traffic congestion and signal-
lights waiting time. To find the Pareto optimal solution set, the simulated
annealing particle swarm optimization algorithm was used with objectives of
minimum investment cost, maximum profitability, and minimum time-consuming
cost. Liu et at. [16] established the bi-level planning model for electric
vehicle charging stations and used the firefly algorithm to find solutions.
The upper model optimized the location and capacity of charging stations with
the objective of maximizing the annual profit. The lower model optimized
individual electric vehicle charging plans to achieve minimum charging cost.
Wang et al. [17] proposed an optimization model for the planning of slow-
charging piles and fast-charging piles, incorporating the impact of road
traffic conditions on the user’s charging additional cost. To efficiently find
the Pareto solution sets, the NSGA-II algorithm was improved by modifying the
initial population generation and crossover operator. The algorithm was proved
to have better performance in terms of searchability and global convergence.
The development of charging infrastructure is likely to take several years in
practice. Considering the dynamic charging demand and limited investment, it
is difficult to deploy all the charging stations within one-step planning[18].
Some researchers have suggested that sing-stage optimization could lack the
capacity to deal with long-term charging demand dynamics [19]. Charging
infrastructure planning can be formulated as a sequential decision-making
process, enabling the construction strategies to be changed according to
charging demand [20, 21]. Meng el at. [22] selected candidate charging station
sites based on social limitations and proposed a sequential expansion-
downsizing strategy for station construction. The proposed method provided
flexible construction plans to balance the increase and decrease of charging
demand. The objective was to minimize the total social cost by incorporating
drivers’ cost and construction investment. Kadri et al. [18] used a multi-
stage stochastic integer programming approach to address uncertainties in both
EV-trip numbers within the road network and EV flows within trips. Scenario
trees were used to approximate the evolution of the stochastic process over
time, and the benders decomposition approach was extended to find optimality.
Compared to the deterministic model, the proposed stochastic one provided a
significantly greater coverage of charging demand. Previous studies have
provided in-depth insights into the charging station location problem. A
majority of charging facility deployment strategies are based solely on
mathematical modeling and implemented in hypothetical scenarios. As real-world
data becomes more accessible and informative, more research is needed to
develop data-driven planning methods capturing valuable information from a
variety of sources (traffic flow, point-of-interest (POI) information, network
configuration). In addition, the charging infrastructure layout should fit
into the structure of the road network, reflecting the characteristic of the
network. Yet, research into potential charging station locations has rarely
considered network evaluation. Furthermore, many studies have applied multi-
period planning and multi-objective planning in recent years, but few have
combined these two aspects into a model that takes into account both demand
dynamics and benefit trade-offs. To this end, the contribution of this study
has three folds: 1) to leverage the information of freight traffic data and
POI data into the charging facility planning process; 2) to propose a
comprehensive selection process of candidate locations for charging facilities
incorporating charging demand, network structure, interests of service
providers, and construction flexibility; 3) to develop a multi-period bi-
objective optimization model considering the charging demand dynamics over
years and the trade-offs between total cost and demand coverage.

##  III METHODOLOGY

This study will model the charging facility planning problem and provide
insight into how charging facility providers can make construction plans for
the future of freight transportation electrification. The proposed
methodological framework shown in Figure 1 consists of four parts: data
preparation, network evaluation, candidate location selection, and charging
location optimization. Data preparation and network evaluation leverage the
valuable information of data and knowledge of graph theory into the planning
process. Using indicators of centrality, the rankings of nodes within the
highway network can be determined. We will identify the nodes that play a more
significant role in the network by evaluating the connections among nodes.
Moreover, a clear procedure for selecting candidate locations is established.
For integrated planning, the mathematical model considered multi-period
optimization with two objectives minimizing total cost and maximizing demand
coverage.

Figure 1: Methodological framework

###  III-A Data Preparation

The proposed framework will be implemented on the real highway network in the
Netherlands. The datasets required in this study include freight traffic flow
data, highway network data, and POI data. Traffic data on highways can be
obtained from the data website, NDW [23]. We extracted one-week traffic data
from the date 2022-06-27 to 2022-07-03. The information includes the date,
time period, route ID, flow, speed, and vehicle class. Freight traffic flow
data can be used to determine freight charging demand. As a percentage of the
total traffic flow, the market penetration rate is used to determine the
amount of traffic to be charged. The datasets of the highway road network and
POI data can be obtained from Open Street Map [24]. POI data would provide
information on the category of locations and geographical coordinates.

###  III-B Network Evaluation

The highway network can be defined as an undirected graph $G=(N,A)$, where $N$
represents the set of nodes (highway junctions) and $A=\\{(i,j),i,j\in N,i\neq
j\\}$ represents the set of arcs (roads). Network evaluation would answer the
question of how important a node is in the highway network. To evaluate the
role of nodes, centrality indicators are calculated including degree
centrality, closeness centrality, and betweenness centrality. Degree
centrality ($DC_{i}$) measures the number of connected nodes (Equation (1)).
Nodes with a high degree score have higher connectiveness. Closeness
centrality ($CC_{i}$) measures the average inverse distance to all other
nodes, reflecting a node’s closeness to others (Equation (2)). Nodes with a
high closeness score have a shorter total distance to all other nodes.
Betweenness centrality ($BC_{i}$) represents the degree to which nodes stand
between each other. It involves calculating the shortest paths between all
pairs of nodes in the network (Equation (3)).

$DC_{i}=\dfrac{D}{N-1}$ (1) $CC_{i}=\dfrac{1}{\sum_{i,j\in G,i\neq j}d_{i,j}}$
(2) $BC_{i}=\sum_{i,j,v\in G,i\neq j\neq
v}{\dfrac{\sigma_{j,v}(i)}{\sigma_{j,v}}}$ (3)

Where $N$ is the total number of nodes; $d_{i,j}$ represents the shortest path
length between node $i$ and node $j$; $G$ is the vertices set in the network;
$\sigma_{j,v}$ is the total number of shortest paths from node $j$ and node
$v$; $\sigma_{j,v}(i)$ is the number of those paths passing through node $i$.

###  III-C Candidate Location Selection

The charging facility planning model considers deploying charging facilities
in the candidate locations rather than all possible locations. There are four
types of candidate locations for the deployment of charging facilities: 1)
those with existing facilities; 2) those recommended by network evaluation
results; 3) those selected by service providers; and 4) those for to-go
charging.
Existing facilities are included first on the list as the existing charging
stations can be expanded. In the second type of candidate locations, the graph
theory will determine the highway nodes of importance, and candidate locations
will be selected around these nodes. Furthermore, this study includes
locations chosen by service providers based on business considerations. In
addition to building charging stations, the last type of candidate location
considers that fast chargers can be deployed at supermarkets (instead of
charging stations) to provide high-efficiency charging. For the selection
process, those POIs with the labels ‘fuel station’, ‘truck stop’, and ‘parking
area’ are considered for existing facilities, while those labeled
‘supermarket’ are for to-go charging. It should be noted that only POIs that
are less than 500 meters from the highway are considered to serve enroute
charging demand.

###  III-D Multi-period Bi-objective 0ptimization Model

A multi-stage optimization model is proposed with the objectives of minimizing
the total cost and maximizing the coverage number of freight vehicles.
Considering the development of transport electrification, it is assumed that
the proportion of electric freight vehicles increases over the years. The
notation for the optimization model is presented in Table I.

TABLE I: Notation Variable |  Description
---|---
Parameters
$K$ |  Set of planning horizons.
$I$ |  Set of candidate locations for charging stations.
$J$ |  Set of candidate locations for to-go charging piles.
$C_{k}$ |  The total cost of the planning horizon $k$.
$D_{k}$ |  The demand coverage of the planning horizon $k$.
$\gamma$ |  The weight in the objective of demand coverage.
$c^{x^{k-1}_{i},x^{k}_{i}}_{s}$ |  The cost of station i from the state $x^{k-1}_{i}$ to $x^{k}_{i}$.
$c_{t}$ |  The cost of installing one fast charging pile near the supermarket.
$d^{k}_{i}$ |  The demand coverage of charging station i in horizon $k$.
$d^{k}_{j}$ |  The demand coverage of to-go charging facilities $j$ in horizon $k$.
$q^{k}_{i}$ |  The freight flow can be covered by facility $i$ in horizon $k$.
$p^{k}$ |  Market penetration rate of electric freight vehicles in horizon $k$.
$b^{k}$ |  The maximum investment in horizon $k$.
$cap_{l}$ |  The capacity of a charging station with the scale $l$.
$cap_{t}$ |  The capacity of a to-go charging pile.
$Nmin^{k}$ |  The minimum number of charging stations in horizon $k$.
$Nmax^{k}$ |  The maximum number of charging stations in horizon $k$.
$Mmin^{k}$ |  The minimum number of locations for to-go chargers in horizon $k$.
$Mmax^{k}$ |  The maximum number of locations for to-go chargers in horizon $k$.
$dist_{i,j}$ |  The distance between station $i$ and station $j$.
$dist_{min}$ |  The minimum distance between two charging stations.
$s$ |  The maximum construction scale of charging stations.
$n$ |  The maximum number of fast-charging plies near the supermarket.
Decision variables
$\eta^{k}_{i}$ |  Binary variable: whether a charging station is deployed at the location $i$ in horizon $k$.
$\eta^{k}_{j}$ |  Binary variable: whether to-go chargers are deployed at the location $j$ in horizon $k$.
$x^{k}_{i}$ |  The construction scale of station $i$ in horizon $k$.
$y^{k}_{j}$ |  The number of installed fast-charging piles near supermarket $j$ in horizon $k$.

####  III-D1 Planning horizons

This model considers five planning horizons, representing different stages of
development, with EFV penetration rates of 20%, 40%, 60%, 80%, and 100%. The
initial planning period uses the current charging facility layout. Starting
from the second planning period, each subsequent period builds upon the layout
of the previous periods. This means that the results of one horizon serve as
the input for the optimization model of the next horizon.

####  III-D2 Model formulation

The first objective is to minimize the total cost in Equation (4), considering
that the service provider would control the project investment and reduce it
as much as possible. As indicated by the previous research on charging
facility planning, the total cost could be an influential factor in the scale
of the planning project (e.g. the number and size of charging stations). The
construction cost in each horizon consists of the cost of charging stations
and the cost of to-go charging at supermarkets (in Equation (5)).

$min\quad Z_{1}(k)=C_{k}$ $None$
$C_{k}=\sum_{i=1}^{I}c^{x^{k-1}_{i},x^{k}_{i}}_{s}+\sum_{j=1}^{J}(y^{k}_{i}-y^{k-1}_{i})c_{t},\quad
k\in K$ $None$

The second objective in Equation (6) is maximizing the coverage of charging
demand. The parameter $\gamma_{k}$ determines whether the next-horizon
planning is included in the current planning objectives. In Equations (7) and
(8), the demand coverage is determined by electric freight flow coverage and
facility capacity. The electric freight flow coverage can be calculated by
penetration rate $p^{k}$ multiplying the average freight flow at the nearest
starting point of highway segments. The facility capacity is determined by the
construction scale of charging stations and to-go charging facilities.

$min\quad Z_{2}(k)=-(D_{k}+\gamma_{k}D_{k+1})$ $None$
$D_{k}=\sum_{i=1}^{I}min(q^{k}_{i}p^{k},cap_{l}x^{k}_{i})+\sum_{j=1}^{J}min(q^{k}_{j}p^{k},cap_{t}y^{k}_{j}),$
$\quad i\in I,j\in J,k\in K$ $None$
$\gamma_{k}=\begin{cases}1\quad\text{k=1,2,3,4}\\\
0\quad\text{k=5}\end{cases}$ $None$

Subject to constraints:

$\sum_{i=1}^{I}c^{x^{k-1}_{i},x^{k}_{i}}_{s}+\sum_{j=1}^{J}(y^{k}_{j}-y^{k-1}_{j})c_{t}<b^{k},\quad
k\in K$ $None$ $\eta^{k}_{i}\eta^{k}_{j}dist_{i,j}<dist\\_min,\quad i,j\in
I,k\in K$ $None$ $x^{k}_{i}\leq x^{k+1}_{i},\quad i\in I,k\in K$ $None$
$y^{k}_{j}\leq y^{k+1}_{j},\quad j\in J,k\in K$ $None$
$Nmin^{k}<\sum_{i=1}^{I}\eta^{k}_{i}<Nmax^{k},\quad k\in K$ $None$
$Mmin^{k}<\sum_{j=1}^{J}\eta^{k}_{j}<Mmax^{k},\quad k\in K$ $None$
$\eta^{k}_{i}\in(0,1),\quad i\in I,k\in K$ $None$ $0\leq x^{k}_{i}\leq s,\quad
i\in I,k\in K$ $None$ $0\leq y^{k}_{j}\leq n,\quad j\in J,k\in K$ $None$

The limitations for investment are set for each planning horizon. Constraints
(9) ensure that the cost in each horizon can not exceed the pre-set value.
Constraints (10) indicate that the distance between two stations should be
larger than the minimum distance threshold. Constraints (11) and (12) ensure
that the scale of charging stations and the number of to-go chargers can not
decrease with development, as it is considered that the charging facilities
constructed in the previous horizons will remain in the subsequent horizons.
For the first horizon ($k=1$), the planning is based on the initial (existing)
facility layout ($k=0$). Constraints (13) and (14) set restrictions on the
number of facilities. Constraints (15) represents the binary decision
variables on whether to build facilities in candidate locations. Constraints
(16) and (17) define two sets of integer variables for the scale of charging
facilities, namely, scales of charging stations $x^{k}_{i}$ and scales of to-
go charging facilities $y^{k}_{i}$.

####  III-D3 Solution Algorithm

we apply the non-dominated sorting genetic algorithm II (NSGA-II) to solve the
bi-objective optimization problem with multiple horizons. Figure 2 shows how
NSGA-II solves the proposed multi-period bi-objective charging facility
planning model. In each horizon, NSGA-II will produce Pareto optimal
solutions. These solutions will be compared to select one for the
implementation and to be used to update the facility layout preparing for the
next-period optimization.

Figure 2: The procedure of optimization

##  IV CASE STUDY

###  IV-A Travel Pattern Analysis

Figure 3 (a)-(d) depict traffic flow during morning and evening peak hours on
both workdays and weekends. Comparing Figure 3 (a)(b) to Figure 3 (c)(d), it
is evident that overall traffic demand was higher on workdays than weekends,
in both morning and evening peak periods. During workday mornings, the
northern part of the study area, including A4, A9, and A2, exhibited increased
traffic demand. In the evenings, demand decreased, particularly in the north,
while heavy traffic persisted on A9 and A1. On weekends (Figure 3 (c)), the
road network experienced low traffic demand, with an average volume below 1400
vehicles per hour in the morning. However, during evening peak hours, there
was an increase in traffic volume on A9, A4, and A1. The temporal and spatial
distributions of truck demand (in Figure 4 (a)-(d)) were relatively different
from the overall traffic on the highway. Temporal patterns of truck volume
were similar on workdays and weekends, morning and evening. Spatially, certain
road segments (e.g., A9, A1/A10 intersection, southwest A10) consistently
experienced high truck travel demand on both workdays and weekends. Suburban
areas along A4 and A1 also had notable traffic demand.

Figure 3: The distribution of overall traffic flow Figure 4: The distribution
of truck traffic flow

###  IV-B Candidate Location Selection

To select the candidate locations, POI information is filtered according to
the built-environment category. POIs with the label ‘fuel station’, ‘parking
area’, ‘truck stop’, and ‘supermarket’ remained. It is noted that only the
locations that lie in the 500-meter buffering of the highway would be used as
candidates. Next, nodes in the highway network are evaluated. Table II shows
the information of the top 10 ranked candidates. The indicators, degree
centrality (DC), closeness centrality (CC), and betweenness centrality (BC)
are calculated and normalized. The score is the average of indicators. Node 17
is ranked the top with the highest values for all indicators, followed by Node
11, 5, and 3.

TABLE II: The numerical results of network evaluation Rank | Score | DC | CC | BC | ID
---|---|---|---|---|---
1 | 1.673 | 1.000 | 0.310 | 0.363 | 17
2 | 1.609 | 1.000 | 0.267 | 0.342 | 11
3 | 1.489 | 1.000 | 0.287 | 0.202 | 5
4 | 1.446 | 1.000 | 0.265 | 0.181 | 3
5 | 1.250 | 0.667 | 0.277 | 0.306 | 20
6 | 1.209 | 0.667 | 0.292 | 0.249 | 18
7 | 1.188 | 0.667 | 0.295 | 0.226 | 4
8 | 1.164 | 0.667 | 0.248 | 0.249 | 25
9 | 1.136 | 0.667 | 0.267 | 0.202 | 24
10 | 1.130 | 0.667 | 0.225 | 0.239 | 12

Figure 5 shows the distribution of nodes in the highway network. The nodes in
red color represented the nodes with the top 10 rankings, which play a more
important role in this highway network. These nodes were the highway junctions
that were more connected with other junctions and were more likely to
influence other junctions in the network. As shown in Figure 6, 119 candidate
locations are selected in total, with 84 candidates for charging station
deployment and 35 candidates for to-go charging points installment. The
candidates selected by POI data accounted for the largest proportion 63.4%.
According to the network evaluation, 15 candidate locations were added near
the top 10 nodes in the network, as indicated by the orange points.

Figure 5: The distribution of evaluated nodes Figure 6: The distribution of
evaluated nodes and candidate locations

###  IV-C Integrated Charging Facility Planning

The optimization model will find the (near) optimal solutions for locations
and construction scales of charging facilities. For charging stations, we
define five construction scales for charging stations, extremely-small scale
stations, small-scale stations, medium-scale stations, large-scale stations,
and extremely-large-scale stations, represented by $x^{k}_{i}=(1,2,3,4,5)$.
$x^{k}_{i}=0$ means there is no station constructed at the location $i$. For
to-go chargers at supermarkets, we optimize the number of charging piles to
install ($y^{k}_{i}$). The optimization model has parameters in terms of
investment, capacity, construction scale, distance, etc. The settings of
parameters are presented in Table IV in Appendix A. In setting these
parameters, we have taken into account the parameter settings in previous
research [25, 26] and have tuned the parameters based on our case study. For
NSGA-II algorithm, we set the population size to be 500, the iterations number
to be 300, the crossover probability to be 0.9, and the mutation probability
to be 0.1.

###  IV-D Multi-period Facility Planning

During multistage planning, the initial results of the infrastructure planning
can certainly affect subsequent planning stages. As bi-objective optimization
can have more than one optimal solution in each horizon, called Pareto optimal
solutions, one solution should be selected from the Pareto set for the next-
horizon planning. To evaluate these impacts of solution selection, two
scenarios are defined following different solution selection rules in each
horizon planning. In Scenario 1, the solution with maximum demand coverage is
selected for next-horizon planning. In Scenario 2, the solution with (the
nearest) median demand coverage is selected. To evaluate the performance of
looking ahead policy of our model, we define Scenario 3 in which the planning
of each horizon only considers the demand in the current horizon, instead of
the potential changing in the nearest future. In Scenario 3, the objective on
the demand coverage only considers the effects on the current horizon, and the
solution with maximum demand coverage was selected for next-horizon planning.
By comparing Scenario 1 and Scenario 2, we can observe the impact of solution
selection on the final deployment layout. And Scenario 2 and Scenario 3 can
show whether planning one step ahead can benefit long-term planning. As shown
in Table III, Scenario 1 has a total cost of 6.250 million euros (MER), and
the demand coverage can reach 369 freight vehicles per hour in the last
planning horizon. Scenario 2 saves 61% of total cost compared to Scenario 1,
the covered demand decreases by 29%. Therefore, selecting maximum demand
coverage in every horizon could obtain solutions with higher demand coverage,
while it is noted that the cost-efficiency of investment could be smaller.
When looking into the planning horizons, it can be found that Scenario 1 tends
to construct new facilities as many as possible reaching the upper limit of
the maximum number of facilities. The investigation of to-go chargers at the
early stage indicates the advantage of flexible chargers at supermarkets for
capturing charging demand with a relatively lower initial investment. The
number of facilities in Scenario 2 is above the half level of that in Scenario
1.
Compared to Scenario 1, Scenario 3 neglects the growth of charging demand and
tends to invest less in the first four horizons. Although in each horizon,
Scenario 3 selects the solution with the largest demand coverage, it covers
94% charging demand compared to that in Scenario 1. In the final horizon,
Scenario 1 constructs more charging stations than Scenario 3 and has the same
number of to-go chargers.

TABLE III: The optimization results of Scenarios | Horizon 1 | Horizon 2 | Horizon 3
---|---|---|---
Scenario 1 |  |  |
Construction cost (MEUR) | 1.450 | 1.500 | 1.000
Demand coverage (veh/h) | 98 | 204 | 256
Number of stations | 9 | 12 | 12
Number of to-go chargers | 25 | 25 | 25
Scenario 2 |  |  |
Construction cost (MEUR) | 0.03 | 0.508 | 0.508
Demand coverage (veh/h) | 37 | 95 | 157
Number of stations | 7 | 8 | 9
Number of to-go chargers | 15 | 19 | 23
Scenario 3 |  |  |
Construction cost (MEUR) | 1.142 | 1.458 | 0.700
Demand coverage (veh/h) | 98 | 196 | 256
Number of stations | 9 | 11 | 12
Number of to-go chargers | 21 | 25 | 25
| Horizon 4 | Horizon 5 | Total
Scenario 1 |  |  |
Construction cost (MEUR) | 1.300 | 1.000 | 6.250(100%)
Demand coverage (veh/h) | 316 | 369 | 369(100%)
Number of stations | 13 | 15 | 15
Number of to-go chargers | 25 | 25 | 25
Scenario 2 |  |  |
Construction cost (MEUR) | 0.502 | 0.9 | 2.448(39%)
Demand coverage (veh/h) | 203 | 262 | 262(71%)
Number of stations | 10 | 11 | 11
Number of to-go chargers | 24 | 24 | 24
Scenario 3 |  |  |
Construction cost (MEUR) | 0.950 | 1.100 | 5.350(86%)
Demand coverage (veh/h) | 304 | 346 | 346(94%)
Number of stations | 12 | 12 | 12
Number of to-go chargers | 25 | 25 | 25

Figure 7 shows the distribution of charging facility deployment plans of
Scenario 1 and Scenario 2 respectively. In order to display the locations of
newly constructed stations, existing stations are not shown. The yellow points
represent the constructed charging stations only in Scenario 1. The red points
represent the charging stations constructed both in Scenario 1 and Scenario 2.
It should be noted that the locations for charging stations in Scenario 2 are
also selected in Scenario 1. The overlap of scenarios may help facility
planners to identify the locations that are more cost-efficient in the
configuration of optimal deployment strategies. The spatial distribution of
these stations is in line with the highway segments with high freight traffic
flow in Figure 4.

Figure 7: The distribution of charging stations in Scenario 1 and Scenario 2

###  IV-E Sensitivity Analysis on Investment Limitation

In the optimization model, the cost in each horizon can not exceed an
investment limit ($b=1.5$ million euro). To investigate the impact of the
investment limitation, we defined an investment rate $\theta$. By setting the
maximum investment to be $b*\theta$, the optimization results for $\theta=$
0.4, 0.6, 0.8, 1.0, 1.2, 1.4, and 1.6 in each horizon were derived and the
demand coverages were presented in Figure 8. The demand coverage grows with
facilities building/upgrading from Horizon 1 to 5. Higher values of investment
limits result in larger demand coverage in each horizon. The investment
limitation has a significant impact on increasing demand coverage when
$\theta$ increases from 0.4 to 1.0. It is possible that $\theta=$1.4 may
leverage the full potential of investment, as the small difference between
$\theta=$1.4 and $\theta=$1.6 may result from limitations on facility size and
number. In addition, the market penetration rate of freight vehicles has been
set to be increased evenly across horizons, the covered demand does not change
in the same manner. With the larger value of $\theta$, the slopes of lines in
Figure 8 become closer to the growth rate of market penetration.
Taking $\theta$ = 1.0 as the reference, Figure 9 shows the percentages of
total construction cost and demand coverage with varying $\theta$. It is noted
that $\theta$ less 1.0 could produce solutions that are more cost-efficient,
as the percentage of total construction cost is lower than the percentage of
demand coverage. Therefore, higher investment limitation tends to increase
charging demand coverage, but this effect weakens as it increases. When
$\theta$ is larger than 1.0, even with higher investment, the demand coverage
can not be improved significantly.

Figure 8: The demand coverage in each planning horizon Figure 9: The total
demand coverage of planning horizons

##  V CONCLUSION

In this study, we develop a data-driven integrated framework for fast-charging
facility planning to address the growing enroute freight charging demand. By
analyzing highway traffic data, we extract the spatial and temporal patterns
of the freight flow. The charging demand is determined based on freight
traffic data and used to identify the significant traffic nodes along highways
based on graph theory. We propose a candidate selection method to locate
potential sites for charging stations and to-go chargers. We build a multi-
period bi-objective optimization model to find optimal charging facility
locations, considering minimum investment cost and maximum demand coverage. We
applied the proposed framework to the Amsterdam highway network and utilized
NSGA-II to solve the model. Scenario comparison reveals that the scenario
(Scenario 1) considering next-horizon planning and selecting the solution with
the highest demand coverage covers more charging demands when compared to
other scenarios (Scenario 2 and 3). Sensitivity analysis demonstrates that
higher investment can significantly increase demand coverage in each horizon
($\theta<1$), although the impact diminishes as the investment further
increases.

There are several directions for future research. We can extend the
methodological framework to include logistics-related POI information, such as
distribution centers and warehouses, and use the origin-destination data of
electric freight vehicles. In addition, we apply Euclidean distance to select
the potential locations in this study, which can be less realistic as roads in
the real-world network are connected. Future research may consider obtaining
the route between potential stations and freight vehicles on highways and
calculating the charging demand coverage based on the real network. Finally,
this study takes the highway near Amsterdam as a case study, more
investigations can be done to extend the modeling problem to large highway
networks.

## APPENDIX

The parameters are listed in Table IV. In setting these parameters, we refer
to the parameter settings in previous research [25, 26] and have tuned the
parameters based on our case study.

TABLE IV: Parameter settings Variable | Setting
---|---
$dist_{min}$ | 3 (km)
$s$ | 5
$n$ | 5
$c_{t}$ | 2000 (euro)
$cap_{l},l\in L$ | [0, 30, 35, 40, 45, 50] (vehicles/hour)
$cap_{t}$ | 2 (vehicles/hour)
$p^{k},k\in K$ | [0.2, 0.4, 0.6, 0.8, 1]
$b^{k},k\in K$ | [1.5, 1.5, 1.5, 1.5, 1.5, 1.5] (million euro)
$Nmin^{k},k\in K$ | [0, 0, 0, 0, 0]
$Nmax^{k},k\in K$ | [5, 5, 5, 5, 5]
$Mmin^{k},k\in K$ | [0, 0, 0, 0, 0]
$Mmax^{k},k\in K$ | [15, 15, 15, 15, 15]
$c^{0,l}_{s},l\in L$ | [[0, 0.5, 0.6, 0.7, 0.8, 0.9] (million euro)
$c^{1,l}_{s},l\in L$ | [0, 0, 0.2, 0.3, 0.4, 0.5] (million euro)
$c^{2,l}_{s},l\in L$ | [0, 0, 0, 0.25, 0.35, 0.45] (million euro)
$c^{3,l}_{s},l\in L$ | [0, 0, 0, 0, 0.3,0.4] (million euro)
$c^{4,l}_{s},l\in L$ | [0, 0, 0, 0, 0, 0.45] (million euro)

## ACKNOWLEDGMENT

This study is supported by Shell through a research collaboration initiative
with the Delft University of Technology in the space of transportation
electrification.

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