# Understanding charging dynamics of fully-electrified taxi services using
large-scale trajectory data

Tian Lei<EMAIL_ADDRESS>Shuocheng Guo<EMAIL_ADDRESS>Xinwu Qian
<EMAIL_ADDRESS>Lei Gong<EMAIL_ADDRESS>College of Urban
Transportation and Logistics, Shenzhen Technology University, Shenzhen, China,
518118  Department of Civil, Construction and Environmental Engineering, The
University of Alabama, Tuscaloosa, AL, United States, 35487

###### Abstract

An accurate understanding of “when, where and why” of charging activities is
crucial for the optimal planning and operation of E-shared mobility services.
In this study, we leverage a unique trajectory of a city-wide fully
electrified taxi fleet in Shenzhen, China, and we present one of the first
studies to investigate charging behavioral dynamics of a fully electrified
shared mobility system from both system-level and individual driver
perspectives. The electric taxi (ET) trajectory data contain detailed travel
information of over 20,000 ETs over one month period. By combing the
trajectory and charging infrastructure data, we reveal remarkable regularities
in infrastructure utilization, temporal and spatial charging dynamics as well
as individual driver level charging preferences. Specifically, we report that
both temporal and spatial distributions of system-level charging activities
present strong within-day and daily regularities, and most charging activities
are induced from drivers’ shift schedules. Further, with 425 charging
stations, we observe that the drivers show strong preferences over a small
subset of charging stations, and the power-law distribution can well
characterize the charging frequency at each charging station. Finally, we show
that drivers’ shift schedules also dominate the individual charging behavior,
and there are strikingly stable charging patterns at the individual level. The
results and findings of our study represent lessons and insights that may be
carried over to the planning and operation of E-shared mobility in other
cities and deliver important justifications for future studies on the modeling
of E-shared mobility services.

###### keywords:

Electrified shared mobility; charging behavior; system dynamics; driver
preferences

##  1 Introduction

The growth of electric vehicles (EV) in replacing traditional gasoline
vehicles has brought significant changes to urban mobility’s composition and
behavioral characteristics. As an essential part of the urban transportation
system, shared mobility such as taxis and for-hire vehicles in multiple
metropolitan areas have shifted to utilizing EVs with policy incentives
initiated by local governments [1]. Several big cities, such as New York,
Shenzhen, and Beijing, have launched initiatives to promote the use of EVs in
the taxi industry [2], leading to a rapid growth in the adoption of EVs in
urban shared mobility systems. For instance, from 2016 to the end of 2020,
Shenzhen’s buses and taxis have all been fully electrified [3]. The increasing
penetration of EVs will further influence the behavior of shared mobility
considering its difference of charging needs when compared to the refueling of
traditional gasoline vehicles [4]. The coordination among charging demand,
charging facility distribution, and charging time and duration [5, 6] are
becoming essential factors in the operation of electrified mobility services.
As a result, there is a pressing need for an accurate understanding of the
charging dynamics for electrified shared mobility services in order to assist
the optimal operation and the planning of urban transportation facilities.

While problems such as electric taxi (ET) dispatching[7, 8] and charging
scheduling [9, 10, 11, 2, 12] are of significant interest for the electrified
shared mobility (E-shared mobility), real-world evidence from large-scale
E-shared mobility systems is still very limited. Some recent studies attempted
to address this issue by analyzing the charging and operating behavior of a
small-scale ET fleet. However, compared to the giant scale of urban shared
mobility services, those case studies can only cover a very small subset of
vehicle fleet [13, 14, 15]. In addition, due to the lack of real-world
evidence, early studies on EV modeling attempted to make various assumptions
on the charging behavior, such as competition among EV users [16, 17, 18],
drivers’ preferences over charging stations [19, 8] and drivers’ rational
behavior in trading off among charging price, future income, and the time of
charging [20]. We note that none of the studies justified their assumptions
with practical evidence, which act as decisive factors that affect outcomes
and conclusions. As a consequence, the validity of the reported findings and
insights remain questionable and would require further justification. This
motivates us to deliver systematic and statistically meaningful insights on
the charging and operating behavior under a fully E-shared mobility system.

In light of the existing gaps in the literature, this study presents one of
the first empirical evaluations on the charging dynamics of a large-scale
fully electrified shared mobility service: the ET system in Shenzhen, China.
It should be noted that Shenzhen is one of the leading cities globally in
charging infrastructure development, where over 440,000 EVs (12.4% of all
vehicles) are running on the road as of September 2020 [21]. Therefore, the
large-scale ET data makes our case study unique and representative in the era
of transportation electrification. More specifically, this study concerns the
system and individual charging dynamics of over 20,000 ETs and 38,000 drivers,
which translates to nearly 30,000 daily charging activities across 425
charging stations. In this study, we first model the temporal and spatial
charging dynamics at the system level by mining the charging activities from
GPS trajectory data of the large-scale ET fleet. Station-level charging
dynamics are further discussed to identify factors that affect drivers’
preferences over charging stations. Finally, we leverage a spatiotemporal
topic modeling approach to investigate charging preferences at individual
driver level. The combination of the three-level analyses provides a
comprehensive understanding on when, where and why the charging activities
take place. The results of our study therefore provide significant insights
and invaluable evidence in assisting the planning and operation of ET service
and E-shared mobility services. In particular, the major contributions of this
article include:

  * 1.

To the best of our knowledge, this is the first study to investigate the
interaction of a fully electrified shared mobility system and the large-scale
charging infrastructures, which enables in-depth understanding about the
charging dynamics of a fully electrified shared mobility system in urban
societies and the charging behavior of ET drivers.

  * 2.

This study examines the validity of the hypotheses applied in previous studies
about EV charging behavior and the appropriateness of equilibrium assumption
in the EV facility planning problem. The findings will pave the way for future
charging behavior modelling of E-shared mobility systems. Through identifying
underlying factors that influence ET drivers’ charging choices with realistic
demonstration, further charging behavior model can be built to quantify the
relationship between certain aspects and ET drivers’ charging decisions.

  * 3.

Finally, the present work draws import implications for practice regarding
charging infrastructure planning as well as ET charging management.
Conclusions about charging dynamics, charging facility usage and drivers’
charging choices obtained from station-level analysis as well as individual-
level charging behavior model can provide valuable reference for further
deployment of charging infrastructures and optimized resource allocation.

We summarize the organization of our study as follows. Section 2 reviews the
literature on related studies. Section 3 introduces the trajectory data,
charging station data, and driver shift data used in this study. Section 4
introduces the methods and metrics for modeling and evaluating the ET charging
dynamics. Section 5 presents the results regarding the spatial-temporal
charging dynamics, station-level charging dynamics, and individual-level
charging behavior. Furthermore, in Section 6, we will discuss the charging
behavior of the ET drivers and note the potential implications. Finally,
conclusions and future directions will be included in Section 7.

##  2 Literature Review

###  2.1 EV charging behavior modeling

The rapid development of EVs has resulted in a sprout of studies in charging
demand prediction [22, 23], charging behavior modeling [24] and the planning
of the charging infrastructure [25, 26]. A large body of studies have been
conducted on system modeling of E-shared mobility service. Particularly for
ETs, the topics include charging facility planning for ETs [27, 28], ET
service/charging strategy [7, 9, 10, 11], ET fleet dispatching [8] and
scheduling strategy [12]. To enable the modeling framework, several key
assumptions on charging behavior are made and can be grouped into three
categories that are related to system-level charging behavior coupled with
charging station usage, drivers’ preference for charging stations, and
drivers’ preference for charging time, respectively. A summary of these
studies can be found in Table LABEL:tab:assumption.

Table 1: Assumptions about charging behavior in existing studies Charging behavior |  Major assumption |  Source |  Problem
---|---|---|---
Competing behavior among EV users |  Route choice and charging time equilibrium |  [16], [29], [18], [30], [31], [32], [17], [33], [34], [35], [36] |  Charging facility planning
Drivers’ preference for charging station location |  Always go to the nearest charging station |  [37], [38], [19], [8], [39] |  ET charging schedule and dispatching strategy; EV feasibility
Drivers tend to charge at preferred charging station |  [40], [41] |  ET charging schedule
Drivers’ choice for time of charging |  Drivers prefer overnight charging |  [42] [20], [43], [35], [44], [45], [46], [47] |  EV charging coordination and EV battery range optimization; Scheduling and management of electric bus fleet; ET fleet feasibility

The first category concerns drivers’ competing behavior in selecting charging
station over the network. This assumption applies to the general EV modeling
problem (both private and shared mobility) and is commonly found in charging
infrastructure planning problems, where user equilibrium is often assumed on
the assignment rule for charging route choice [29, 33, 18]. Specifically, the
equilibrium flow assignment is established over the network to model EV users’
charging behavior in response to the planned charging facilities [48, 34, 49].
Other studies also extend the notion of equilibrium to account for waiting
time at charging locations in response to the capacity constraint[33, 17].
Under the similar setting, a more recent study [36] also models users’
equilibrium responses to statisc and dynamic charging stations. In these
studies, users are assumed to be selfish and perfectly rational, seeking to
maximize their individual utilities. Components in utility functions include
travel time, energy consumption [30], waiting time for charging [17] and
electricity cost [48]. While user equilibrium presumes perfect information
about these factors in a network, such a precondition is neither justified nor
realistic in real-world cases. As a such, the resulting charging facility
plans under the proposed framework are unlikely to be optimal in real-world
setting. This undoubtedly prohibits the applicability for charging facility
planning in large urban E-shared mobility systems.

Under a non-competing setting (e.g., rule-based), the second category
assumption is associated with drivers’ preference on the location of charging
stations. In these studies, spatial proximity is usually the major influencing
factor and a typical assumption is that drivers always visit nearest charging
stations [19, 8, 38]. In this regard, ET scheduling and fleet dispatching
strategies highly depend on spatial distribution of travel demand and charging
infrastructure. Other studies also incorporate additional factors such as
charging pile types, scale and supporting facilities at the charging stations
[50, 51]. Similar assumption is also observed when exploring EV feasibility
problems [39] and also see its application in the charging facility planning
problems [37, 38]. There are other studies assuming that ET drivers tend to
charge at their own stations (home location) [40, 41], which further
diversifies the possible outcomes regarding the driver location preference and
charging decision-making.

Besides drivers’ choice for charging station location, assumptions on drivers’
choice for time of charging are also made in related studies in charging
coordination strategy. It assumes that drivers’ preferred charging time
depends on the coordination among charging demand, charging price and future
income. In particular, the overnight charging is assumed as the preferred
charging time for lower charging and service fee [42, 20, 43], which is also
adopted in the scheduling and management of electric bus fleet [44, 45]. As
for ET systems, the hypothesis that overnight charging will grant ETs
sufficient range for one day of operation was often made when discussing ET
feasibility [46, 47]. Since overnight charging enables ET drivers to replenish
their vehicles off the shift, the daytime charging and fast charging option
for ET systems are barely discussed. Nevertheless, the underlying assumption
that all ETs will have access to overnight charging options is itself highly
questionable and requires further justification.

To summarize, the above three categories of assumptions are expected to play a
decisive role in the E-shared mobility modeling process, and their validity
will largely determine the effectiveness of decision-making in a real-world
system. Given the limited practical evidence in the large-scale ET
application, these assumptions have not been well justified and sufficiently
debated. Therefore, there is a dire need of real-world evidence about E-shared
mobility systems’ charging behavior, which will establish the foundation for
further planning and operation of E-mobility systems.

###  2.2 Studies on charging behavior with trip data

We also note that there were several preliminary work on justifying the
charging dynamics of E-shared mobility systems. With limited data sources,
some studies attempted to explore the charging behavior of ET fleet through
agent-based simulation [52, 53, 54]. For instance, Bischoff et al. [55]
explored the performance of ET fleet and its feasibility through agent-based
simulation. Yu et al. [54] analyzed the spatial-temporal charging pattern
electric taxi based on trajectory data of conventional internal combustion
taxis through using a simulation framework. Nevertheless, charging decisions
in these studies were modeled based on the trajectory data of gasoline taxis,
which is unlikely to represent he practical performance of E-mobility systems
in the real world.

With the adoption of E-shared mobility in some big cities, few more recent
studies attempted to investigate the charging behavior of ET fleet using the
GPS trajectory data [15, 13, 14]. However, we report that the contributions of
these studies are restrictive due to limited ET fleet size and the coverage of
service areas, which can only provide limited insights of charging and
operating behavior of the E-shared mobility system. Specifically, Fraile-
Ardanuy et al. [14] evaluated the spatiotemporal energy usage pattern by
summarizing the dynamics of 466 ETs in San Francisco. Tian et al. [15]
explored the operating characteristics of 600 ETs in Shenzhen, China. Wang et
al. [56] investigated the evolution of charging dynamics using ET trajectory
data from 2013 to 2018, where the ET grew from 2.7% to 65.2% of the fleet,
during which time the number of charging stations increased from fewer than 30
to 117. This study focused on the changes of mobility and charging patterns
with increasing adoption of EVs. It provided important insights for staged
planning, but of limited values for guiding the fully electrification of
urban-scale fleet and long-term facility planning. Other researchers explored
the driver behavior and charging characteristics of ETs or EVs based on
realistic operational data including the State of Charge (SoC) [57, 58, 59].
However, those papers concentrated more on the evaluation of energy
consumption and efficiency, which is beyond our research scope. While the
charging needs of ET systems highly relies on public charging infrastructures,
a comprehensive understanding about the charging dynamics of fully electrified
ET systems is critical for charging facility planning and ET operation
management. Large-scale data set is therefore necessary to indicate the
overall spatiotemporal distribution of charging activities. With the
inevitable trend of fully electrification of urban shared mobility systems, a
comprehensive understanding of fully electrified ET system is yet to be
established.

So far, we have identified major gaps in the existing studies with respect to
the charging behavior of E-shared mobility systems. Due to various
restrictions, most studies failed to account for full complexity and subtlety
of real charging behavior under a large-scale ET fleet. As such, efforts are
made in this study to close existing gaps by exploring the spatiotemporal
charging behavior under a large fleet of fully-electrified taxis from the
system and individual levels.

##  3 Data

###  3.1 Electric taxi trajectory data

The trajectory data used in this study cover the entire taxi fleet in
Shenzhen, China, with a total of 21,371 vehicles. The ETs can be easily
distinguished from the gasoline taxis based on the plate ID, and there are
20,130 ETs in total. This implies that Shenzhen has the largest ET fleet in
the world, covering nearly 95% of the entire fleet as in September 2019, which
helps to gain insights into the charging dynamics of a fully electrified
large-scale shared mobility service. There is only one model adopted by
Shenzhen’s ET fleet, BYD E6 [60], with a battery capacity of 57 kWh and a
mileage range of up to 300 km [61]. The GPS trajectory data was obtained
through the collaboration with Shenzhen Transportation Planning Center. The
data include the ET plate ID, longitude-latitude coordinates, the timestamps,
and ET status (occupied or not). An example of sampled ET trajectory data is
shown in Table 2. It should be noted that although one month data might be
relatively short to indicate long-term evolution of charging patterns, it is
sufficient to provide valid observations in terms of daily patterns on system-
level charging dynamics, the usage of charging infrastructure, and the
differences in charging behavior at the individual level, which are
concentration of the present work.

Table 2: Example data samples Taxi GPS | plateID |  timestamp |  longitude |  latitude |  speed |  occupied
---|---|---|---|---|---|---
BDXXXX |  9/18/2019 15:01:53 |  113.9745 |  22.55643 |  42 |  1
Charging Station | stationID |  acessibility |  longitude |  latitude |  fast-charging piles |  slow-charging piles
3892 |  public |  114.342759 |  22.67359 |  15 |  5
Taxi schedule | plateID |  driver ID |  shift |  primary shift days |  secondary shift days |  Total operation days
BDXXXX |  XX491 |  Primary |  30 |  - |  30
BDXXXX |  XX191 |  Secondary |  - |  30 |  30

###  3.2 Charging station information

In addition to the trajectory data, we also collect the information of all
charging stations in Shenzhen [62]. Detailed information of these charging
stations include station name, address, the number of slow-/fast-charging
piles, charging service operator, accessibility (public or dedicated), open
hours, electricity price, service fee, and parking fee. A sample of the
collected charging station information is presented in Table 2. We next match
the addresses with the longitude-latitude coordinates via the python package
‘Geocoder’ [63]. To better describe different types of zone, we categorize the
City of Shenzhen into three classes: city center, suburb, and periphery, based
on the traffic analysis zone. This classification criteria is analogous to
Nie’s work [64], where a detailed layout of Shenzhen is included therein.

After removing private charging stations and charging stations without
charging piles, we end up with 425 charging stations in total. Following the
standards adopted in the China EV market, we use the terms ”slow charging” and
”fast charging” to represent Level 2 charging and DC Fast charging,
respectively [65]. The slow charging indicates the pile with power less than
10 kW (industrial commons are either 3.5 kW or 7 kW). And the fast charging
pile can at least charge 80% of a 50kWh ET within one hour under the charging
rate of up to 60 kW [66]. Among the 425 charging stations, 160 of them are
installed with fast charging piles. The spatial distribution of these charging
stations, along with the number of charging piles, are shown in Figure 1. It
can be observed that the charging stations are more densely located in the
city centers of Shenzhen (including Nanshan, Futian, and Luohu district), most
of which are small-sized stations (e.g., fewer than 100 piles) with primarily
slow charging piles. On the other hand, there are a few large-scale charging
stations with more than 300 charging piles and they mainly located on the edge
of the core business districts or in more distant peripheral areas.

Figure 1: Distribution of slow and fast charging stations with the radius of
the circle representing the number of corresponding charging piles.

###  3.3 Taxi driver shift schedule

We also obtain the taxi drivers’ shift schedule in September 2019, which
include information about the ET company, plate ID, the drivers on primary and
secondary shift, and the total operation days per driver. A preprocessing of
the data suggested that there were 19,943 active ETs in this month, accouting
for over 99% of all ETs in Shenzhen (20,130 in total). We next divide the ETs
into two sets based on their operation mode: single-shift and double-shift
ETs, which accounts for 33.2% (6,622 total ETs) and 66.6% (13,321 total ETs)
respectively. As for the ET drivers, there are 35,549 individual drivers:
4,630 of whom served in single-shift mode and the other 30,919 drivers served
in double-shift mode. As a consequence, double-shift is the dominant mode for
daily ET operations. In the following sections, we will further explore the
charging behavior of urban ETs considering the difference between the two
shift modes.

##  4 Method

###  4.1 Charging event identification

To explore the charging behavior of ETs, we first identify charging events
from the trajectory data based on the proximity to the charging stations and
the dwelling duration. We consider that a valid charging event would require a
minimum stop duration. This can be translated into first finding stopping
events: a sequence of trajectory points with a minimal change in the GPS
location and the corresponding time duration exceeds a user specified
threshold. Besides, the taxi should be unoccupied following the loading status
of each ET in the data. Moreover, it should be noted that the identified
stopping events should be adjacent to a charging station. Based on these
conditions, charging events are then identified using the following rules and
an example is shown in Figure 2.

First, we define a stopping event to be valid if (1) the total spatial
displacement does not exceed 1,000 meters for at least 10 minutes ($\Delta
d\leq 1000$ and $\Delta t\geq 10$), and (2) the nearest charging station is
located within 200 meters ($\Delta d_{CS}\leq 200$). In addition, the ET
drivers may turn off their GPS device for multiple times during the operation
horizon (e.g., taking a break, having lunch, etc.). As such, we also consider
the potential charging event while the GPS device is turned off. Let $n_{off}$
and $n_{on}$ be the last location that the GPS device is off and the first
location that the GPS device is on. Specifically, if the GPS is off for more
than 10 minutes, we only require that (1) the displacement is under 1,000
meters and (2) either $n_{off}$ or $n_{on}$ is within 200 meters to the
nearest charging station ($\Delta d^{cs}_{n_{off}}\leq 200$ or $\Delta
d^{cs}_{n_{on}}\leq 200$).

After processing, each piece of identified charging event is represented as a
data tuple, consisting of (1) the start and end time of charging, (2) location
coordinate of charging, (3) the ID of the nearest charging station, (4) the
travel time and distance to the charging station since the last passenger
being dropped off, and (5) the travel time and distance from the charging
station to the next passenger being picked up.

Figure 2: Illustration of charging event identification

Ground truth To further examine the feasibility of charging event
identification method, we take two different approaches to verify the validity
of the identified charging events.

First, we conducted a field investigation to reach out to taxi drivers in
Shenzhen (by street & App hailing) and obtained their help in distributing an
online survey to the drivers’ community. The survey was designed using a tool
called Wenjuanxing (Chinese version of Qualtrics) and mainly inquired charging
related behavior. To increase the return rate, we intended to send out a short
survey with only 6 questions, and the details of the survey can be found in
the Appendix. Survey questions are about ET drivers’ charging frequency,
minimum and maximum stay time, and the preferred charging behavior. After one
week period, 172 valid responses were collected from 55 single-shift (32%)
drivers and 117 double-shift drivers (68%). The population is biased towards
single-shift drivers as 14% of all drivers are single-shift per the official
record. We then visualize below the charging frequencies of both types of
drivers, and the results suggested that single-shift drivers on average charge
1.6 times a day while double-shift drivers will charge more than 1.7 times a
day. The weighted average daily charging frequency across all ETs is 1.7
times.

Figure 3: Survey statistics about ET drivers’ charging frequency

Besides the charging frequency, the minimum and maximum stay time at a
charging station are especially helpful in determining the hyperparameters for
charging events identification. We show below the distribution of minimum and
maximum stay duration for both types of drivers. It is observed most of the
drivers (95%) stay a minimum of 15 minutes at the charging stations and the
charging duration is usually less than 3 hours. Single-shift drivers, on the
other hand, may stay longer to fully charge their battery (11%). Our survey
results are different from previous studies where a 30-minute time threshold
was used for charging events identification from ET GPS trajectory data [15,
56].The reason for such a difference is likely due to the advances in fast
charging facilities in recent years.

(a) Minimum stay time at charging stations by shift

(b) Maximum stay time at charging stations by shift

Figure 4: Survey statistics about time spent at charging stations

Second, based on the survey results, we further conducted a cross-validation
experiment to verify how the number of charging events is affected by the
distance threshold and time threshold. The results are presented in Figure 5.
In detail, 16 temporal thresholds and ten distance limits are considered,
resulting in a grid search of 160 scenarios. The temporal thresholds to
identify a sufficient charging duration are from 5min to 20min, incremented by
1min. And the spatial thresholds for the distance limit to the nearest
charging station are from 50 to 500, incremented by 50. The results indicate
that a combination of from 200 meters and 10 minutes to 300 meters and 15
minutes may all be appropriate for charging events identification, with the
average number of identified charging events ranging from 1.7 to 1.9 per ET.
By combining the findings from both the survey and the cross-validation
experiment, we decide to choose a minimum time threshold of 10 minutes which
is capable of capturing almost all charging events. And the distance threshold
is then set to 200 so that the average number of charging events is 1.7. This
combination best agrees with our survey results with the weighted average
number of charging frequency being 1.7, and is also aligned with the findings
in previous studies [56, 57].

Figure 5: Average charging times per ET under different justification rules

###  4.2 Spatiotemporal charging behavior

With the identified charging events, we next perform spatial-temporal analyses
to understand the consistency of charging behavior at the system level.

First, to investigate the temporal dynamics of daily charging behavior, we use
the data from the first four weeks of September and group the city-level
charging events into one-hour time intervals. The autocorrelation analysis is
then conducted using the constructed time series data to examine the
distribution of autocorrelation values over different lag values. The
autocorrelation value lies in the range of -1 to 1, with 1 indicating a strong
positive correlation and -1 for strong negative correlation at the
corresponding time lag $k$. Denoting the number of charging events at time $t$
as $Y_{t}$, the number of charging events at time $t+k$ as $Y_{t+k}$ and the
average number of charging events as $\bar{Y}$, the autocorrelation at lag $k$
can be computed as:

$\gamma_{k}=\frac{\sum_{t=0}^{T-k}(Y_{t}-\bar{Y})(Y_{t+k}-\bar{Y})}{\sum_{t=0}^{T}{(Y_{t}-\bar{Y})^{2}}}$
(1)

To understand the spatial dynamics of everyday charging events, we further
group the charging events at each individual charging stations for every one-
hour time interval as the representation of spatial distribution for charging
events. This creates a vector $C_{t}$ of length $1\times 425$ for every time
interval $t$. We then calculate the Pearson correlation between $C_{t}$ and
$C_{t+k}$ to evaluate if there are significant differences between the spatial
distributions of two time intervals. In particular, the Pearson correlation
coefficient can be measured as:

$\gamma(t,t+k)=\frac{\sum_{i}(C_{t}^{i}-\bar{C}_{t})(C_{t+k}^{i}-\bar{C}_{t+k})}{\sqrt{\sum_{i}(C_{t}^{i}-\bar{C}_{t})^{2}\sum_{i}(C_{t+k}^{i}-\bar{C}_{t+k})^{2}}}$
(2)

where $C_{t}^{i}$ denotes the $i$th element of $C_{t}$ and $\bar{C}_{t}$
represents the average of all elements in $C_{t}$. One benefit of Pearson
correlation is that the results are scale invariate. In this regard, even
though the total number of charging events may not be strictly the same
between two time intervals, a Pearson correlation value close to 1 will still
imply a highly consistent distribution of charging activities at different
charging stations.

###  4.3 Modeling individual charging behavior

We model individual charging behavior using a two-dimensional Latent Dirichlet
Allocation (LDA) model, which was first introduced by Blei et al. [67] and
extended by Sun et al. [68] to capture the spatiotemporal charging patterns of
individual ET drivers. The LDA method is an unsupervised method that helps to
identify latent topics in the large corpus of documents, which can be
analogous to obtain classes of charging patterns from the sequence of charging
events. In our study, we consider each charging event as a spatiotemporal
point. Let $\mathcal{S}$ be the set of charging stations for the spatial
dimension and $\mathcal{T}$ represent the set of hourly intervals of one day.
In this regard, the charging events of an ET can be expressed as follows:

$E_{v}=\\{\left(e_{vi}^{s},e_{vi}^{t}\right):i\in\\{1,...,N_{v}\\},s\in\mathcal{S},t\in\mathcal{T}\\}$
(3)

where $E_{v}$ is the collection of charging events for all ETs
$v\in\mathcal{V}$. $N_{v}$ is the total number of charging events for ET $v$
in our data. The tuple $(e_{vi}^{s},e_{vi}^{t})$ demonstrates the charging
events on spatial and temporal dimensions. Note that the spatial points
$e_{vi}^{s}$ are labeled by the charging station IDs regardless of their exact
coordinates, since we focus more on finding the representative spatial
patterns than the neighborhood clusters based on physical distance. To better
understand our framework, we compare the notions used in this study with the
typical elements in the LDA model: topics, documents, and words (or set of
vocabulary). In detail, we consider charging patterns ($z\in\mathcal{Z}$) as
topics, ETs $v\in\mathcal{V}$ as documents, and charging events
$(e_{vi}^{s},e_{vi}^{t})$ as words. The major purpose of utilizing the two-
dimension model is to simultaneously capture the spatial and temporal activity
patterns on the individual level while considering their dependencies [68].
Compared with user-level analyses based on the high spatial-temporal dimension
by enumerating $\mathcal{S}\times\mathcal{T}$ [69], the two-dimension model
exhibits the merits under the significantly varying size of the spatial and
temporal dimensions ($|\mathcal{S}|=425$,$|\mathcal{T}|=24$ in our case).

Figure 6: Graphical model of the two-dimensional LDA adapted from [68]

We present the graphical model of our LDA in Figure 6. The parameters in the
grey circles can be either pre-determined (i.e., $\alpha,\beta,\gamma$) or
observed in data (i.e., $e_{vi}^{s},e_{vi}^{t}$). Let $J$ and $K$ denote the
number of patterns on spatial and temporal dimensions. In this case,
$\phi_{j}$ is the $j$-th spatial pattern-event distribution and $\psi_{k}$ is
the $k$-th temporal pattern-event distribution. Further, the charging pattern
distribution $\theta_{v}$ can be expressed a two-dimensional simplex, denoted
by $J\times K$, with respect to the probability distributions on spatial and
temporal dimensions. We specifically express such two-dimensional simplex as
$\theta_{vjk}$ such that $0\leq\theta_{vjk}\leq 1$ and
$\sum_{j=1}^{J}\sum_{k=1}^{K}\theta_{vjk}=1$. Formally, the generative process
in the LDA model [70] can be expressed as follows.

  1. Step 1

: For each ET $v\in\mathcal{V}$, select a pattern distribution $\theta_{v}\sim
Dirichlet_{|\mathcal{S}|\times|\mathcal{T}|}\left(\alpha\right)$

  2. Step 2

: For each spatial pattern select spatial distribution $\phi_{j}\sim
Dirichlet_{|\mathcal{S}|}\left(\beta\right)$

  3. Step 3

: For each temporal pattern select time distribution $\psi_{k}\sim
Dirichlet_{|\mathcal{T}|}\left(\gamma\right)$

  4. Step 4

: For each ET $v\in\mathcal{V}$, for each charging event
$\left(e_{vi}^{s},e_{vi}^{t}\right)$:

    1. (a)

Select one pattern $z$ from the charging events following
$z=\left(z^{s},z^{t}\right)\sim M(\theta_{v})$

    2. (b)

Select one charging event on spatial dimension $e^{s}$ given the pattern
$z^{s}$ following $e^{s}\sim M(\phi_{z^{s}})$

    3. (c)

Select one charging event on temporal dimension $e^{t}$ given the pattern
$z^{t}$ following $e^{t}\sim M(\psi_{z^{t}})$

In the generative process, $\alpha$, $\beta$, and $\gamma$ are the Dirichlet
priors. And $M$ is the Multinomial distribution. It is worthy to note that the
Dirichlet distributions are selected as the prior since they are conjugate to
the Multinomial distribution. By integrating $\theta_{v}$, $\phi_{j}$, and
$\psi_{k}$, we can compute the joint distribution $P(e_{vi}^{s},e_{vi}^{t})$,
which can be expressed as:

$P(e_{vi}^{s},e_{vi}^{t},z^{s},z^{t})=P(e_{vi}^{s}|z^{s})P(e_{vi}^{t}|z^{t})P(z^{s},z^{t})$
(4)

where the terms $P(e_{vi}^{s}|z^{s})$, $P(e_{vi}^{t}|z^{t})$, and
$P(z^{s},z^{t})$ can be obtained following similar forms as in Griffiths and
Steyvers [71]. However, there is no closed-form solution to directly obtain
the posterior distribution for each ET $v$, following
$P(z^{s},z^{t}|e_{vi}^{s},e_{vi}^{t})=\frac{P(e_{vi}^{s},e_{vi}^{t},z^{s},z^{t})}{\sum_{s=j}^{J}\sum_{t=k}^{K}P(e_{vi}^{s},e_{vi}^{t},z^{s},z^{t})}$.
Instead, the parameters can be estimated under Markov Chain Monte Carlo
procedure using Gibbs sampling approach [72]. Readers are referred to
Griffiths and Steyvers [71] for a detailed description on the parameter
estimation using Gibbs sampling, and Sun et al. [68] for the modeling on
spatiotemporal activity patterns.

####  4.3.1 Model selection

In the LDA model, the number of spatial and temporal charging patterns $J$ and
$K$ are pre-determined. We adopt the perplexity to find the optimal
combination of $J$ and $K$, where the lower perplexity score indicates better
performance on the model generalization. The procedure of calculating the
perplexity score are as follows. Given the trained model, we select a set of
ETs as the validation set. And the perplexity of ET $v$ can be expressed as
below:

$perp(\mathbf{e}_{v}^{s},\mathbf{e}_{v}^{t}|\mathbf{e}_{train})=\exp{\left(-\frac{\log
P(\mathbf{e}_{v}^{s},\mathbf{e}_{v}^{t}|\mathbf{e}_{train})}{N_{v}}\right)}$
(5)

where $P(\mathbf{e}_{v}^{s},\mathbf{e}_{v}^{t}|\mathbf{e}_{train})$ can be
approximated by Monte Carlo method [68], which can be expressed as an average
over the samples in validation set $\mathcal{U}$:

$P(\mathbf{e}_{v}^{s},\mathbf{e}_{v}^{t}|\mathbf{e}_{train})=\frac{1}{|\mathcal{U}|}\sum_{u\in\mathcal{U}}\prod_{i=1}^{N_{v}}\left(\sum_{j=1}^{J}\sum_{k=1}^{K}\theta_{vjk}\phi_{e_{vi}^{s}\leavevmode\nobreak\
j}^{u}\psi_{e_{vi}^{t}\leavevmode\nobreak\ k}^{u}\right)$ (6)

Given the perplexity score, we will conduct a grid search procedure to
determine the best combination of $J$ and $K$ with the lowest perplexity
score.

###  4.4 Individual driver regularity

After introducing the topic model in identifying charging patterns, we then
investigate the potential regularity of individual charging activities.
Specifically, the temporal regularity for ET $v\in\mathcal{V}$ for all weeks
$w\in\mathcal{W}$ can be quantified by the cosine similarity. The cosine
similarity is scale-invariant and bounded between 0 and 1, which makes it an
ideal choice for comparing regularity among ET drivers. We first denote by
$\cos(w,w^{\prime}|v)$ the cosine similarity for ET $v$ between week $w$ and
$w^{\prime}$, which follows the form:

$\cos\left(w,w^{\prime}|v\right)=\frac{\mathbf{p}(z^{s},z^{t}|e_{vi}^{s,w},e_{vi}^{t,w})\cdot\mathbf{p}(z^{s},z^{t}|e_{vi}^{s,w^{\prime}},e_{vi}^{t,w^{\prime}})}{||\mathbf{p}(z^{s},z^{t}|e_{vi}^{s,w},e_{vi}^{t,w})||\leavevmode\nobreak\
||\mathbf{p}(z^{s},z^{t}|e_{vi}^{s,w^{\prime}},e_{vi}^{t,w^{\prime}})||}$ (7)

where $\theta_{vjk}^{w}$ can be obtained following the similar procedures as
described, by treating $\mathbf{e}_{v}^{w,s},\mathbf{e}_{v}^{w,t}$ as a
dedicated set of charging events for ET $v$ in week $w$. We next compute the
expectation of the ET $v$’s cosine similarity between all weeks
$w\in\mathcal{W}$, which can be expressed as follows:

$\overline{\cos\left(v\right)}=\frac{1}{|\mathcal{W}\times\mathcal{W}|}\sum_{w\in\mathcal{W}}\sum_{w^{\prime}\in\mathcal{W}}\left(\cos(w,w^{\prime}|v)\right)$
(8)

##  5 Results

###  5.1 System-level charging dynamics

With the identified charging events, we first report the distribution of the
number of charging events, the number of unique ETs (the ETs with the same
plate ID) and accumulated number of unique ETs over the first four weeks
(9/1/2019 - 9/28/2019) as shown in Figure 7. Note the sample size on 9/13
(Friday) is comparably smaller due to the Mid-Autumn Festival with a one-day
break. As seen in Figure 7a, the daily-average number of charging events is
17,015 and the average number of unique ETs covered by the charging events is
9,725, or nearly 48.6% of all ETs. As a result, the identified daily number of
charging events cover fewer number of ETs than the actual fleet size and the
reasons are multi-fold. First, not all ETs may operate on a daily basis and
require a daily charging, especially those on a single shift. Second, some of
the ETs may turn on and off their GPS devices outside the vicinity of a
charging station and are therefore not captured by our identification
algorithm. Finally, GPS device errors could be another reason. Nevertheless,
the identified charging events still capture a stable overall trends over the
entire week for majority of the ETs, with Sunday having slightly fewer number
of charging activities as compared to other days of the week.

(a) Daily charging events and number of unique ETs

(b) ET captured by number of days

Figure 7: Number of identified charging events and number of ETs covered in a
selected week

On the other hand, we also find that there are 19,880 ETs that appears at
least two days over the four-week period (see Figure 7b, accounting for over
97.5% of total operated ETs in this month. The number of ETs that are captured
for at least 6 and 10 days of the week are 17,336 and 13,370, respectively.
This implies that the data contain sufficient details so that longitudinal
behavior at the individual level can be tracked for over 66.5% of all ETs in
the city. Finally, even in the case when more than 18 days are required, the
identified events can still cover 29.9% unique ETs, which is significantly
greater than any reported cases in the literature. Based on these
observations, we argue that the charging events identified are reliable, and
the number of charging activities and unique ETs covered are sufficient to
derive statistically representative conclusions for the entire ET population.

After verifying the quality of the identified charging events, we next
concentrate on the weekly-average observations and investigate the within-day
dynamics of ET charging and examine system-level differences between single-
shift and double-shift ETs. Figure 8 shows the temporal distribution of
charging events for both single-shift and double-shift ETs on the weekly
average. Besides, the average charging duration for charging events that took
place in the corresponding hour is also visualized. One immediate observation
is that the daily charging dynamics at the system level show repetitive
patterns over the week, which will be further investigated in the following
discussions. In addition, we found that the total number of charging events
for double-shift ETs is significantly higher than that of single-shift ETs.
While the total number of double-shift ETs doubles that of single-shift ETs,
the number of charging events for double-shift vehicles is more than three
times higher than that of single-shift ETs at most time of the day. This
clearly articulates the difference in within-day charging dynamics between the
two types of ETs and implies that their behavior should be treated differently
when modeling the ET services. Despite the differences in charging frequency,
both classes of ETs follow a similar pattern of three daily charging peaks,
taking place at late night period (from 2 AM to 5 AM), noontime period (from
11 AM to 1 PM ), and late afternoon to the evening time period (from 4 PM to 7
PM), respectively. These three charging peaks correspond to four distinct
types of charging behavior. The noontime charging is aligned with the lunch
break so that ET drivers can save dedicated charging trips, and such type of
charging behavior is observed for both single and double-shift ETs. Moreover,
the charging duration is found to be significantly shorter (around 30 minutes
shorter on average) than most of the other time periods. The only exception is
around 8 PM, which may correspond to the time of the dinner break. The
afternoon period is aligned with the afternoon shift schedule of double-shift
drivers, and this type of behavior is more evident among double-shift drivers.
Finally, the late-night charging activities are found to be different between
single and double-shift ETs. In particular, the peak for single shift ETs
occurs 1-2 hours earlier than double shift ETs while having a longer charging
duration. For double shift ETs, this corresponds to the morning shift
schedule, where the drivers again need to be responsible for the electricity
consumption of their night shift before turning the ET to the next driver. As
for single-shift ETs, the observations mainly capture the behavior of those
drivers who do not have access to charging infrastructure at home, and they
may need to visit the charging station before ending or starting their shift.

Figure 8: Temporal distribution of charging dynamics based on drivers number
of shifts.

While observing a trend of repeating dynamics in Figure 8, we next
quantitatively evaluate the temporal consistency of dynamics. The
autocorrelation is computed with the time series of charging counts at the
hourly level. And the autocorrelation plot for both single-shift and double-
shift ETs is shown in Figure 9. The 90% and 95% confidence levels are also
visualized as solid and dash lines, respectively. Based on the results, a
significant temporal correlation that exceeds the lines of 95% confidence
interval can be observed at different time lags. Notable time lags of interest
are located around lags 6, 18, 24, 30, 42, and 48. Most importantly, the
autocorrelation takes the highest value at the time lag of 24, followed by the
time lag at 48. With each lag being a one-hour time interval, the results
present statistically significant evidence that the system level charging
dynamics are stable and highly consistent on a daily basis. And this
observation holds for both single and double shift ETs despite their different
within-day dynamics. On the other hand, strong temporal cross-correlations are
also observed every 6 and 18 hours. These two values are reflective of the
shift schedules for double shift ETs, where each driver is responsible for a
shift of 12 hours, and the results again echo the findings in Figure 8.

Figure 9: Temporal autocorrelation of charging events at system level

Besides the temporal autocorrelation, a more striking finding on system-level
charging dynamics can be found through the Pearson correlation between the
spatial charging activity distributions of two time intervals. Figure 10
presents a $168\times 168$ matrix summarizing the pairwise Pearson correlation
coefficients over the entire week. While daily regularity was reported at the
aggregate level, such a regularity still holds even considering the charging
counts at individual charging stations. That is, a Pearson correlation
coefficient close to 1 is still captured every 24 hours. And further details
can also be understood by tracing local blocks of high Pearson correlation
coefficients. Specifically, local blocks of high correlation can be found near
12 PM, between 0-6 AM, between 4-7 PM, as well as from 8 PM to 11 PM. As a
consequence, besides regularity on a daily basis, the charging dynamics can be
categorized into at least four clusters based on the local affinity of
charging activity distributions at individual charging stations, where the
charging dynamics are self-similar within these time intervals. Finally, we
find two time windows, one between 9-11 AM and the other shortly before
midnight, where the charging activity distributions are most dissimilar to all
other time intervals (where the value of Pearson correlation is close to zero
and is shown as the white space) over the day. Moreover, it is observed from
Figure 8 that these two time windows also correspond to the lowest number of
charging activities across the day, which further implies that the charging
behavior is least structured and more ad-hoc during the off-peak time.

Figure 10: Pearson correlation of charging station usage at different hours of
day

###  5.2 Dynamics at charging stations

With strong spatial and temporal regularity at the system level, we next
discuss how charging events are distributed at individual charging stations.

Figure 11 shows the daily-average charging frequency of all 425 stations. One
important observation here is that the complementary cumulative distribution
function (CCDF) of charging frequency across the stations can be well
approximated by the power-law distribution $P(X\geq x)\propto x^{-\alpha}$,
with $\alpha$ calibrated as 1.18. As such, the station-level usage shows a
strong trend of preferential attachment, indicating that a small fraction of
the charging stations serves majority of the charging demand (24 stations or
less than 6% of all stations account for more than 50% of total charging
demand). In particular, based on the statistics at each station, we report
that 45 charging stations are found to have never been visited, 136 stations
are visited 1 to 10 times daily, and 149 stations are visited 10 to 100 times.
Only 29 charging stations (12%) are more frequently visited with more than 100
daily charging activities, where 3 of them are much more heavily preferred by
the drivers with over 600 daily visits. These observations lead to significant
implications in understanding the charging preference of ET drivers. On the
one hand, the charging station choice is unlikely to be ad-hoc. Instead, the
charging behavior is highly structured and is likely to be planned ahead for
most of the drivers, where they prefer to visit stations that they are
familiar with or stations that are frequently used by other drivers. On the
other hand, the power-law distribution also alerts the resilience issue for
satisfying the charging needs of large-scale ETs. The power failure at top
visited charging stations may result in significant disturbances to the ET
mobility services as they are searching alternate charging stations. This
asserts the need for considering resilience and back-up plans when planning
charging facilities.

Figure 11: CCDF of charging visits at all charging stations in log-log scale.

To further understand the choice of charging stations, we visualize the
spatial distribution charging frequencies of all 425 charging stations in
Figure 12a. In particular, we select three typical charging stations with
distinct daily usage patterns, e.g., Minle P+R station, Zhuzilin station, and
Shoping Park station. And their within-day charging dynamics in half-hourly
time intervals is shown in Figures 12b–12d. From the spatial distribution, we
report that stations close to the city centers (places closer to higher
passenger demand) are in general more favored over more distant areas.
Nevertheless, we also observe that distinct attributes pertaining to each
charging station appear to have greater influence on the charging dynamics
than merely the spatial proximity to high demand areas. As an example, Minle
P+R station is observed to serve nearly 3.7% of total daily charging demand.
The leading reason for the popularity of Minle station is likely due to its
cheaper cost. In particular, Minle station adopted a dynamic pricing structure
where the electricity price during off-peak hours is reported to be 30% lower
than peak hours [73]. In addition, a discounted service fee is offered to
E-shared mobility vehicles. As a consequence, we find that the time periods
where Minle station is most visited (Figure 12b) are almost perfectly aligned
with the published time for off-peak charging price. Besides its cheaper cost,
Minle P+R station is also the largest fast charging station for EVs with 637
fast charging piles. The station is located near the transportation hub and is
adjacent to urban expressways, and the station offers rest area with lounge
facilities to accommodate the needs of drivers. Moreover, the stations is
within walking distance to the Minle metro station. As a consequence, the
service reliability, accessibility as well as the level of convenience are
likely other factors that make it the top charging station for drivers to take
the shift.

(a) Spatial distribution of charging station usage

(b) Minle P+R station

(c) Zhuzilin station

(d) Shopping Park station

Figure 12: Charging dynamics at the charging station level

Next, we show the usage pattern at the Zhuzilin station (see Figure 12c),
which accounts for 3.0% of total daily charging demand. Similar to Minle P+R
station, Zhuzilin also serves as a dedicated charging station for ETs and the
station is adjacent to a number of restaurants with affordable price. Compared
with Minle, similar usage patterns during noontime peak can be found for its
convenience and accessibility. However, one notable difference at Zhuzilin
station is during the late-afternoon/early-evening periods (5 PM for Minle and
8 PM for Zhuzilin). We report that one potential reason for the lay-back
charging peak is to get prepared for the upcoming demand peak during the
early-night period (7-9 PM). In this case, the ETs may charge for longer
duration (over 50 minutes during 4-5 PM) or get a quick implement right before
the evening demand peak (less than 35 minutes after 7 PM). Further, this
location lies in the residential and business area of Futian District with a
high demand level. As a consequence, this charging station is more favored
during the short lunch break and for an increase opportunity to pick up the
next passenger.

Finally, we present the usage pattern at the Shopping Park station (shown in
Figure 12d). To avoid misleading due to outliers, we only present the average
duration in the 30-minute interval with more than one charging count per day.
The Shopping Park station is equipped with more than 140 reported charging
piles and serves nearly 1.8% of total charging demand. This station is located
in the urban core of Futian District and next to Ping An Finance Center, which
is surrounded by bars and restaurants, movie theaters, shopping malls, as well
as workplaces. Different from two other dedicated stations, the charging
counts during the mid-late night is much higher than other times of the day,
which is potentially due to the high demand during the nighttime back to the
residential locations. Also, we report the charging peak hours are well
aligned with the period of valley electricity price (37.7% lower than the
price in the normal period). Therefore, the high capacity of the charging
station, lower electricity price, and increased opportunity for potential high
demand at the urban core are three contributing factors that attract the
charging demand.

The charging dynamics at the three selected charging stations highlight the
importance of location specific characteristics in attracting charging demand.
On the other hand, as a commonly seen and seemingly rational assumption, the
distance to the nearest charging station is believed to be another determining
factor that drivers the choice of charging locations. We next quantitatively
assess how charging distance may be related to the charging behavior, and the
results are presented in Figure 13. Here we define additional travel distance
as the gap between travel distance from the last dropoff location to the
actual charging station and the distance from last dropoff location to the
nearest charging station. And we simultaneously visualize the cumulative
distribution of 7 days in a week. The important takeaway, as indicated from
the figure, is that few ETs visited the nearest charging station. Around 40%
of the drivers will travel up to 1.5 additional kilometers, and 80% of them
may cruise up to 5 extra kilometers for charging. And this observation is
consistent across the week. Moreover, there are a small portion of drivers who
will travel over 15 kilometers to visit their preferred charging stations. We
believe this is most likely due to their last dropoff location is far from the
scheduled shift location. These observations are well aligned with the power-
law distribution of charging frequency at station level, which indicates that
there are some frequently used charging stations which are more preferred by
ET drivers. That is, ET drivers may drive for longer distance to charge at
preferred charging stations. As a result, we conclude that ET drivers are less
sensitive to the distance to charging station, especially if the distance is
below a certain threshold such as 5 kilometers.

Figure 13: Cumulative distribution of additional travel distance to the
charging location as compared to visiting the nearest charging station.

###  5.3 Charging pattern analyses

We use the LDA model [67] to capture the ET driver’s charging pattern and
temporal regularity. We first manually divide the charging events into single-
shift events and double-shift events based on the historical taxi schedule.
Furthermore, we select 2,200 single-shift ETs and 7,000 double-shift ETs that
appear more than 10 days of the 19 selected weekdays ( a Friday, 9/13/2019, is
neglected due to Mid-Autumn Festival). To determine the optimal LDA model, we
next partition the ETs into training and validation sets (1,800 vs. 400 for
single-shift ETs and 6,300 vs. 700 for double-shift ETs). Finally, we conduct
a grid search procedure with the spatial dimension set,
$J=\\{10,20,30,40,50\\}$ and the temporal dimension set
$K=\\{6,8,10,12,14,16\\}$. Based on the perplexity scores, the combination of
$(J=30,K=10)$ and $(J=30,K=12)$ are determined as the optimal grid for the
single-shift and double-shift ETs, respectively. Other hyperparameters
($\alpha=\beta=\gamma=0.01$) in the LDA model are consistent with Sun et al.
[68].

####  5.3.1 Individual-level charging activity pattern

With the optimal pattern numbers $J$ and $K$, we present the spatial and
temporal charging patterns that are summarized from the charging events per ET
over four weeks. Here we present 10 most dominant spatial patterns both the
single- and double-shift ETs in Figure 14, where the corresponding percentages
are attached in the brackets. The overview of all spatial patterns is
presented in A. In the figures, the size of each circle represents the
probability of a charging event at the specific charging stations. Based on
the results, we summarize three major spatial charging patterns as follows:

  * 1.

Planned charging in suburbs and peripheries (e.g., Patterns 1-22, 1-30, 1-2,
and 2-15): this feature shows the charging activities at several dedicated
charging stations (e.g., Minle P+R station) located in the suburbs and
peripheries, which may indicate less waiting time but with sufficient supplies
of charging piles.

  * 2.

Planned charging in city centers (e.g., Patterns 1-4, 1-20, 1-14, 2-27, 2-25,
2-17, and 2-10): these patterns denote the common choices when single-/double-
shift ETs need to charge. In the planning stage, more charging piles are
required so as to accommodate the extensive charging demand in the city
centers.

  * 3.

Unplanned charging in city centers (e.g., Patterns 1-16, 1-11, 1-8, 1-3, 2-11,
2-18, 2-1, 2-22): in this feature, the corresponding charging stations may
encounter the local congestion in some time periods such that the ETs will
detour to find the available charging piles nearby.

By considering all spatial patterns (see Figures 18 and 19), we report that
the proportion of spatial patterns in city centers, suburbs, and peripheries
are 61.84%, 16.82%, and 21.30% for single-shift ETs and, 69.81%, 23.26%, and
6.89% for double-shift ETs. In this regard, compared with double-shift ETs,
more single-shift ETs tend to charge in the peripheries. This may be because
the single-shift ETs have a more flexible time schedule such that the ET
drivers have sufficient time to rest at those peripheral charging stations
equipped with accessible lounges or restaurants. On the other hand, we also
observe a significantly larger proportion of double-shift ETs that charges
around the city centers ($69.81\%$ versus $61.84\%$). This indicates that the
double-shift ET drivers tend to make efficient usage of their on-service time,
which in turn translates to limited time for the charging-related activities
(waiting, charging, and traveling to and from charging stations), resulting in
more charging activities in city centers.

(a) Single-shift ETs

(b) Double-shift ETs

Figure 14: Selected spatial patterns of charging activities

Aside from the spatial pattern, we also explore the temporal patterns for the
single- and double-shift ETs. Three peaks of charging activities can be
observed regarding the late night/early morning (1-6 AM), around noon (11 AM -
2 PM), and afternoon/early evening (4 - 6 PM). For the single-shift ETs, three
particular patterns (Patterns 1,2,10) indicate the charging events at late-
night periods (12 AM - 4 AM), which may capture the times when ET drivers rest
and conduct charging activities near home locations. In addition, two-mode
temporal patterns can be found in single-shift ETs (e.g., see Figure 15a
Pattern 2, 3, and 5), which can be interpreted as the charging before-and-
after the daily operation. As for the double-shift ETs, the ET drivers prefer
to charge before the morning and evening peaks (about 6 AM and 5 PM), so as to
provide mobility service with less disturbance for charging and gain more
revenue from the extensive demand. Similarly, the two-mode temporal patterns
(e.g., Patterns 8, 9, 10, 11, and 12) are also found in the double-shift ETs,
which suggests the potential shift time between two ET drivers. For such
patterns, we report that the shift time does not strictly follow the morning-
evening shifts, but the time may slightly deviate, e.g., 5 AM - 5 PM, 6 AM - 6
PM, and 7 AM - 8 PM as shown in Pattern 8, 9, and 10 in Figure 15b,
respectively. Finally, we note that the around-noon activities are observed in
both ET patterns (at around 11 AM - 2 PM), implying that the ET drivers may
have lunch or take a break while charging.

(a) Single-shift ETs

(b) Double-shift ETs

Figure 15: Temporal patterns of charging activities

By considering both spatial and temporal dimensions, we present the
spatiotemporal charging pattern with the corresponding probability
distributions on each axis. From the aspect of temporal dimension (the
vertical bars), the patterns with high probabilities mainly capture the late-
night/early-morning charging during 12 AM - 3 AM for single-shift ETs (see
Pattern 1 and 10 in Figure 15a) and during 1-4 AM double-shift ETs (see
Pattern 5 and 6 in Figure 15b). As for the single-shift ETs on the spatial
dimension, two significant patterns are observed with high probabilities
(Patterns 1-16 and 1-22 with $6.4\%$ and $6.01\%$), indicating the planned
charging patterns in the periphery, which evidences the relatively sufficient
time for the single-shift ET drivers. On the other hand, the frequent patterns
of double-shift ETs are more likely to be charging with preference in the city
centers (Patterns 2-11 and 2-18 with $5.6\%$ and $5.48\%$). In this case, the
ET drivers can ensure high service efficiency with minor disturbance due to
charging.

Furthermore, we summarize several spatiotemporal patterns with high
probability, as seen in the dark-colored cells in Figure 16a. We report that
one major pattern is the cell $(2,22)$, which denotes the double-mode charging
in the peripheral area. With a further look in the pattern “1-22”, the
dominant charging station is within a urban village in Longhua District, which
is surrounded by several populated residential areas and one transportation
hub. As such, it is of great potential to attract the ET drivers who live
nearby to charge before and after the daily operation. Also, given the spatial
pattern of “1-11”, two temporal patterns suggest the planned charging in city
centers during the late-night period (the cell $(1,11)$ and $(10,11)$). The
charging stations in city centers are potentially near the bars and
restaurants, and also provides the time-of-use electricity price, which is
particularly attractive during the late-night period. One example is the
charging activities in the Shopping Park station. Similar physical
interpretation can also be captured in the double-shift ETs regarding the
three significant spatiotemporal cells: $(5,18),(6,18),(7,18)$, denoting the
planned charging in city centers during the late-night/early-morning period.
It implies that the double-shift ET drivers have to follow the shift schedule
spanning about 12 hours and prefer to charge near the high-demand locations.
As such, we conclude that those common features can well reveal the latent
spatiotemporal patterns that underline in both single- and double-shift ETs.

(a) Single-shift ETs

(b) Double-shift ETs

Figure 16: Spatiotemporal patterns of charging activities

####  5.3.2 Regularity of individual charging activities

After presenting the charging patterns in spatial and temporal dimensions, we
finally investigate the underlying spatiotemporal regularity of the individual
charging behavior by computing the average cosine similarity over one ET’s
weekly charging event. Specifically, we only select the 19 weekdays of the
first four weeks in September 2019, where the Mid-Autumn Day (a Friday) is
omitted. Next, for each ET, we generate sequences of charging events in a
rolling time window fashion with a length of 5. In this regard, we treat the
charging events covered by one rolling window for each ET as a document. And
the output is a collection of vectors, where each vector represents the
probabilities of one sequence of charging events being assigned to each
spatiotemporal pattern. Finally, the spatiotemporal regularity of each ET is
quantified by the average cosine similarity score, measured by the cosine
distance between all pairwised vectors associated with the particular ET.
Intuitively, a high similarity score indicates a high level of regularity such
that future charging patterns can be accurately predicted based on historical
records. Note that we use the same set of ETs in training set for the charging
pattern analyses in the previous section (1,800 for single-shift ETs and 6,300
for double-shift ETs).

As seen in Figures 17a and 17b, we report a slightly left-skewed distribution,
indicating that most of the ETs conduct charging activity following similar
charging patterns on the spatiotemporal dimensions. Specifically, the average
similarity scores of double-shift ETs are higher than the single-shift ETs
(0.84 vs. 0.73). The higher level of similarity may result from the more
generalized shift time along the day as observed in the temporal patterns for
double-shift ETs. In addition, a few observations with a score under $0.6$ are
also found in single-shift ETs. It suggests the anomaly level over each week,
implying more flexibility for the single-shift ET drivers. Finally, we
highlight that these similarities in the spatiotemporal charging pattern will
shed light on charging stations’ coordinated management to satisfy the
charging demand at similar time periods and specific spots. More detailed
discussion and implications are presented in the next section.

(a) Single-shift (weekly)  (b) Double-shift (weekly)

Figure 17: Dynamics of individual temporal regularity.

##  6 Discussion

Based on the results at the system level, charging station level and
individual driver level, we summarize the following five major findings and
discuss their implications for charging planning and management of ETs, and
potentially for E-shared mobility systems in general.

Finding 1: The system-level charging dynamics show spatiotemporally unbalanced
intraday charging station usage, which is observed to be stationary across
days.

From the aspects of the ET operation and management, the spatiotemporally
unbalanced distribution of charging activities leads to the prolonged waiting
time at the charging stations during peak hours, and subsequently, a shortage
of supply for mobility services. While the charging behavior of ETs is closely
related to their shift schedules, policies and guidelines may be necessary to
motivate a staggered shift schedule for ETs with two shifts. This finding also
has significant implications for the modeling and planning of charging
facilities. The stationary dynamics support the appropriateness of the
assumption on equilibrium behavior for system models. However, caution should
be exercised in terms of the assumed utility function that drives the
equilibrium solutions.

Finding 2: Preferential attachment behavior for usage at the charging station
level.

A considerable number of charging facilities are expected to be developed to
cope with the booming of EVs worldwide. However, given a budget of investment,
it is important to consider the realization of a skewed facility usage pattern
at each charging station. It is especially so with the construction of
charging hubs, which brings in the scale of the economy (more charging piles
with reduced charging cost and easy access to other facilities), which can
offer better personal utility for ET drivers. In this regard, simply
increasing spatial coverage of the charging station may not be necessary and
will likely result in a waste of resources. Moreover, special attention should
be paid to the coupling between the mobility service system and the
reliability of the power system. The power-law charging visits distribution
implies a charging infrastructure system that is efficient yet vulnerable. The
concentration of charging needs may result in the local failure of the power
grid due to demand surge, which will backpropagate and cause cascading failure
in the mobility service systems. Therefore, cautious is much needed to develop
a failure-resilience charging infrastructure plan and backup operation
strategy at major charging hubs in case of a facility failure.

Finding 3: Stationary dynamics at system-level is the result of strong
charging activity regularity at the individual driver level.

While system-level stationarity may be achieved via frequent but symmetric
changing behavior from individual drivers, we report that the individual-level
behavior shows very strong regularity over time for the majority of the
drivers. However, this strong regularity is a mixture of unplanned charging in
the city center and planned to charge activities in other regions. This shapes
a sharp contrast to the refueling behavior of gasoline vehicles. The finding
also suggests the possibility for accurately predicting exact charging
activities at many of the charging stations. As such, modeling approaches
based on individual charging activity sequences can be established and will
contribute to much more efficient operational management of the rate of charge
that may best serve EVs for mobility services.

Finding 4: Factors other than the distance to the charging station have a
greater influence on drivers’ preference for the location of charging
stations.

This finding echos our discussion on the choice of utility function for
driving equilibrium behavior. It is noted that many existing studies
considered spatial proximity as the most influential factor, which we report
may barely hold for the modeling of E-shared mobility services. Instead of
visiting the nearest charging station, most drivers cruise extra kilometers to
a charging station that best aligns with their other interests, including but
not limited to the capacity of a charging station, the charging cost, the
convenience for making a shift, the availability of supporting facilities such
as the rest area and restaurants, and even their acquaintance of a charging
station. As this outcome contradicts the assumption of many existing studies,
it highlights the pressing need to quantitatively assess the determining
factors that best characterize the utility of a charging activity for
heterogeneous drivers of E-shared mobility services.

Finding 5: Overnight charging is not viable for most of the drivers,
especially for double-shift ET drivers.

Another common assumption, if not a misperception, is that E-shared mobility
drivers may charge overnight (e.g., at home), and charging activities during
the daytime are less important. Through our analyses, we argue that overnight
charging is not viable for the majority of the drivers for E-shared mobility
services. On the one hand, overnight charging implies owning a private parking
spot equipped with charging piles. This is, however, unlikely for E-shared
mobility drivers given the excessively high cost. On the other hand, even at
charging facilities, we report that only 35.8% of all charging activities
occur between 12 AM and 7 AM. Out of these activities, 0.86% of the charging
activities have a duration longer than 4 hours. This implies that drivers are
also unlikely to charge overnight at the charging stations. It should be noted
that although the present work only identifies charging activities at public
charging stations, it has been examined by the ground truth survey that most
of the ET drivers (over 95%) use public charging stations other than private
ones, which could further support our observations regarding overnight
charging. One primary reason is to avoid the overtime cost (e.g., parking cost
at charging stations). Consequently, the coordination of daytime charging for
E-shared mobility services becomes an important research topic that requires
extra attention. Moreover, it may be worthwhile considering the introduction
of dedicated park-and-charge facilities, which may best prevent the overflow
of charging demand to the power grid during the daytime. Doing so may lead to
a win-win situation that reduces the E-mobility system’s charging cost and
improves the power system’s reliability.

##  7 Conclusion

In this study, we investigated the spatial-temporal charging dynamics of ETs
on the system level and also explored the individual-level ET driver’s
charging behavior and regularities using ETs’ GPS trajectory data in Shenzhen
for four weeks in 2019. From the temporal distribution, we report three
charging peaks over one day during late-night/early-morning periods, noontime,
and late-afternoon/early-evening periods. On the other hand, the usage pattern
of the charging station is observed to follow the power-law distribution,
which necessitates more tailored decision-making on the planning stage so as
to make full usage of the charging resources. Furthermore, the spatial and
temporal correlation analyses suggest strong intraday regularities and
interday similarities. Besides, we capture the charging patterns on both
system and individual levels via the two-dimensional LDA model. The results
suggest that most of the charging events can be categorized based on several
key features, e.g., charging peaks and preference on charging stations for
both single- and double-shift ETs. Finally, we quantitatively analyze the
regularity of charging patterns on an individual level using the cosine
similarity. Most ETs exhibit a similarity score of over 0.8, indicating a high
level of regularity in terms of individual charging preferences, which is a
driving force to the system-level stable charging dynamics.

We note that the identified charging events serve as a subset of all charging
activities due to the data limitation on the specified charging status, the
latest layout of the charging stations, and the level of accuracy of the GPS
trajectory data. But a large number of identified charging activities are
sufficient to lay out statistically meaningful results that best capture the
charging dynamics of a city-scale E-shared mobility system. For future
studies, efforts can be made towards dedicated charging station planning based
on the key features of the ET drivers’ interests and preferences. Meanwhile, a
charging station recommendation algorithm incorporated by pricing strategies
will help to (1) balance the skewed usage pattern of the charging resources
and (2) coordinate the charging activities to minimize the waiting time at
charging stations. In addition, as the study depicted the initial dynamics on
charging behavior of ET drivers, it is important to perform a comprehensive
assessment by modeling the influencing factors and understanding how they
affect the choice of charging stations. Finally, under a collaboration with
Shenzhen Transportation Planning Center, we can only access the one-month
trajectory data. A more comprehensive study, e.g., long-term evolution of ET
charging patterns, can be conducted if the data is available to support the
investigation over a longer time horizon.

##  8 Acknowledgments

This research was partly supported by Research on Trip Chain of Public Transit
Passenger by Research on the Coordination Strategies and Methods of Transport
Supplies to Satisfy the Tempo-spatial Pattern of Public Transit Transferring
in the Context of Data Fusion from Multiply Sources (General Research Project
of Humanities and Social Sciences of the Ministry of Education under Grant
No.21YJC630029), the Guangdong Basic and Applied Basic Research Foundation
(No. 2020A1515111001), Research on Guidance Management of Travel Demand in
Metropolitan Bay Area based on Travel Pattern (Philosophy and Social Science
Planning Project of Guangdong Province under Grand No. GD20CGL30) and
Development and Application of Simulation System of Travel Behavior based on
Data Fusion in the Context of V2X (Natural Science Foundation of Top Talent of
SZTU under Grant No. 20200218).

## References

  * [1] Nakul Sathaye.  The optimal design and cost implications of electric vehicle taxi systems.  Transportation Research Part B: Methodological, 67:264–283, 2014\.
  * [2] TU Wei, Ke Mai, Yatao Zhang, Yang Xu, Jincai Huang, Ming Deng, Qingquan Li, et al.  Real-time route recommendations for e-taxies leveraging gps trajectories.  IEEE Transactions on Industrial Informatics, 2020.
  * [3] Shenzhen Municipal Transportation Bureau.  https://wenku.baidu.com/view/1fb570818f9951e79b89680203d8ce2f016665ec.html.  Accessed 31 July 2021.
  * [4] Jie Yang, Jing Dong, Zhenhong Lin, and Liang Hu.  Predicting market potential and environmental benefits of deploying electric taxis in nanjing, china.  Transportation Research Part D: Transport and Environment, 49:68–81, 2016.
  * [5] Jie Yang, Jing Dong, and Liang Hu.  Design government incentive schemes for promoting electric taxis in china.  Energy Policy, 115:1–11, 2018.
  * [6] Willett Kempton.  Electric vehicles: Driving range.  Nature Energy, 1(9):1–2, 2016.
  * [7] Chien-Ming Tseng, Sid Chi-Kin Chau, and Xue Liu.  Improving viability of electric taxis by taxi service strategy optimization: A big data study of new york city.  IEEE Transactions on Intelligent Transportation Systems, 20(3):817–829, 2018.
  * [8] Yiwen Song, Ningning Sun, and Huimiao Chen.  Demand adaptive multi-objective electric taxi fleet dispatching with carbon emission analysis.  In 2019 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), pages 1–5. IEEE, 2019.
  * [9] Zhiyong Tian, Taeho Jung, Yi Wang, Fan Zhang, Lai Tu, Chengzhong Xu, Chen Tian, and Xiang-Yang Li.  Real-time charging station recommendation system for electric-vehicle taxis.  IEEE Transactions on Intelligent Transportation Systems, 17(11):3098–3109, 2016.
  * [10] Zaiyue Yang, Tianci Guo, Pengcheng You, Yunhe Hou, and S Joe Qin.  Distributed approach for temporal–spatial charging coordination of plug-in electric taxi fleet.  IEEE Transactions on Industrial Informatics, 15(6):3185–3195, 2018\.
  * [11] Yang You, Zhaoxia Jing, and Yichuan Huang.  Charging guiding strategy for pet based on q learning algorithm (ispec 2020).  In 2020 IEEE Sustainable Power and Energy Conference (iSPEC), pages 2206–2212. IEEE, 2020.
  * [12] Jiaming Shen, Laili Wang, and Jialei Zhang.  Integrated scheduling strategy for private electric vehicles and electric taxis.  IEEE Transactions on Industrial Informatics, 17(3):1637–1647, 2020\.
  * [13] Rao Rao, Hua Cai, and Ming Xu.  Modeling electric taxis’ charging behavior using real-world data.  International Journal of Sustainable Transportation, 12(6):452–460, 2018.
  * [14] Jesús Fraile-Ardanuy, Sandra Castano-Solis, Roberto Álvaro-Hermana, Julia Merino, and Ángela Castillo.  Using mobility information to perform a feasibility study and the evaluation of spatio-temporal energy demanded by an electric taxi fleet.  Energy conversion and management, 157:59–70, 2018.
  * [15] Zhiyong Tian, Yi Wang, Chen Tian, Fan Zhang, Lai Tu, and Chengzhong Xu.  Understanding operational and charging patterns of electric vehicle taxis using gps records.  In 17th International IEEE Conference on Intelligent Transportation Systems (ITSC), pages 2472–2479. IEEE, 2014.
  * [16] Fang He, Di Wu, Yafeng Yin, and Yongpei Guan.  Optimal deployment of public charging stations for plug-in hybrid electric vehicles.  Transportation Research Part B: Methodological, 47:87–101, 2013\.
  * [17] Rui Chen, Xinwu Qian, Lixin Miao, and Satish V Ukkusuri.  Optimal charging facility location and capacity for electric vehicles considering route choice and charging time equilibrium.  Computers & Operations Research, 113:104776, 2020.
  * [18] Haoxiang Liu and David ZW Wang.  Locating multiple types of charging facilities for battery electric vehicles.  Transportation Research Part B: Methodological, 103:30–55, 2017\.
  * [19] Jintao Ke, Xuekai Cen, Hai Yang, Xiqun Chen, and Jieping Ye.  Modelling drivers’ working and recharging schedules in a ride-sourcing market with electric vehicles and gasoline vehicles.  Transportation Research Part E: Logistics and Transportation Review, 125:160–180, 2019.
  * [20] Mohammad AS Masoum and Seyed MH Nabavi.  Hybrid optimal online-overnight charging coordination of plug-in electric vehicles in smart grid.  Journal of Power Sources, 330:7–17, 2016.
  * [21] Shenzhen Internet Information Office.  Shenzhen new energy vehicle ownership data.  https://baijiahao.baidu.com/s?id=1707038306996722133&wfr=spider&for=pc.
  * [22] Cai Yun, Zhang wanquan, You wei, and Mao pan.  Prediction on the charging demand for electric vehicles in chengdu.  In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 2018.
  * [23] Sungwoo Bae and Alexis Kwasinski.  Spatial and temporal model of electric vehicle charging demand.  IEEE Transactions on Smart Grid, 3(1):394–403, 2011.
  * [24] Mingyu Zhao, Yinghui Wang, Zhi yuan Lu, and Weiguo Zhang.  Electric vehicle operating characteristics analysis based on structural equation model.  In Applied Mechanics and Materials, volume 278, pages 202–206. Trans Tech Publ, 2013.
  * [25] R Paul Brooker and Nan Qin.  Identification of potential locations of electric vehicle supply equipment.  Journal of Power Sources, 299:76–84, 2015.
  * [26] Alireza Khaksari, Georgios Tsaousoglou, Prodromos Makris, Konstantinos Steriotis, Nikolaos Efthymiopoulos, and Emmanouel Varvarigos.  Sizing of electric vehicle charging stations with smart charging capabilities and quality of service requirements.  Sustainable Cities and Society, 70:102872, 2021.
  * [27] Huimiao Chen, Yinghao Jia, Zechun Hu, Guanglei Wu, and Zuo-Jun Max Shen.  Data-driven planning of plug-in hybrid electric taxi charging stations in urban environments: A case in the central area of beijing.  In 2017 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe), pages 1–6. IEEE, 2017.
  * [28] Hua Wang, De Zhao, Yutong Cai, Qiang Meng, and Ghim Ping Ong.  Taxi trajectory data based fast-charging facility planning for urban electric taxi systems.  Applied Energy, 286:116515, 2021.
  * [29] Fang He, Yafeng Yin, and Siriphong Lawphongpanich.  Network equilibrium models with battery electric vehicles.  Transportation Research Part B: Methodological, 67:306–319, 2014\.
  * [30] Hong Zheng, Xiaozheng He, Yongfu Li, and Srinivas Peeta.  Traffic equilibrium and charging facility locations for electric vehicles.  Networks and Spatial Economics, 17(2):435–457, 2017.
  * [31] Min Xu, Qiang Meng, and Kai Liu.  Network user equilibrium problems for the mixed battery electric vehicles and gasoline vehicles subject to battery swapping stations and road grade constraints.  Transportation Research Part B: Methodological, 99:138–166, 2017\.
  * [32] Yantao Huang and Kara M Kockelman.  Electric vehicle charging station locations: Elastic demand, station congestion, and network equilibrium.  Transportation Research Part D: Transport and Environment, 78:102179, 2020.
  * [33] Zhibin Chen, Fang He, and Yafeng Yin.  Optimal deployment of charging lanes for electric vehicles in transportation networks.  Transportation Research Part B: Methodological, 91:344–365, 2016\.
  * [34] Zhibin Chen, Wei Liu, and Yafeng Yin.  Deployment of stationary and dynamic charging infrastructure for electric vehicles along traffic corridors.  Transportation Research Part C: Emerging Technologies, 77:185–206, 2017.
  * [35] Yue Zhou, Ruoxi Wen, Hewu Wang, and Hua Cai.  Optimal battery electric vehicles range: A study considering heterogeneous travel patterns, charging behaviors, and access to charging infrastructure.  Energy, 197:116945, 2020.
  * [36] Xiaotong Sun, Zhibin Chen, and Yafeng Yin.  Integrated planning of static and dynamic charging infrastructure for electric vehicles.  Transportation Research Part D: Transport and Environment, 83:102331, 2020.
  * [37] Long Jia, Zechun Hu, Yonghua Song, and Zhuowei Luo.  Optimal siting and sizing of electric vehicle charging stations.  In 2012 IEEE International Electric Vehicle Conference, pages 1–6. IEEE, 2012.
  * [38] Wei Tu, Qingquan Li, Zhixiang Fang, Shih-lung Shaw, Baoding Zhou, and Xiaomeng Chang.  Optimizing the locations of electric taxi charging stations: A spatial–temporal demand coverage approach.  Transportation Research Part C: Emerging Technologies, 65:172–189, 2016.
  * [39] Liang Hu, Jing Dong, Zhenhong Lin, and Jie Yang.  Analyzing battery electric vehicle feasibility from taxi travel patterns: The case study of new york city, usa.  Transportation Research Part C: Emerging Technologies, 87:91–104, 2018.
  * [40] Yongjun Ahn, Chulmin Jun, and Hwasoo Yeo.  Analysing driving patterns of electric taxi based on the location of charging station in urban area.  In 2016 IEEE International Smart Cities Conference (ISC2), pages 1–6. IEEE, 2016.
  * [41] Zheng Dong, Cong Liu, Yanhua Li, Jie Bao, Yu Gu, and Tian He.  Rec: Predictable charging scheduling for electric taxi fleets.  In 2017 IEEE Real-Time Systems Symposium (RTSS), pages 287–296. IEEE, 2017.
  * [42] Peter Richardson, Damian Flynn, and Andrew Keane.  Optimal charging of electric vehicles in low-voltage distribution systems.  IEEE Transactions on Power Systems, 27(1):268–279, 2011.
  * [43] Fabian Heymann, Vladimiro Miranda, Nilufar Neyestani, and Filipe Joel Soares.  Mapping the impact of daytime and overnight electric vehicle charging on distribution grids.  In 2017 IEEE Vehicle Power and Propulsion Conference (VPPC), pages 1–6. IEEE, 2017.
  * [44] Antti Lajunen.  Lifecycle costs and charging requirements of electric buses with different charging methods.  Journal of cleaner production, 172:56–67, 2018.
  * [45] Adnane Houbbadi, Rochdi Trigui, Serge Pelissier, Eduardo Redondo-Iglesias, and Tanguy Bouton.  Optimal scheduling to manage an electric bus fleet overnight charging.  Energies, 12(14):2727, 2019.
  * [46] Oscar Olsson, Anne Faxér, Magda Collado, Johan Wedlin, and Stefan Pettersson.  Lessons learned from electric cars in daily taxi operation in gothenburg.  In EVS30 Symposium Stuttgart, Germany, October 9-11, 2017, 2017\.
  * [47] Matthew Moniot, Clement L Rames, and Erin Burrell.  Feasibility analysis of taxi fleet electrification using 4.9 million miles of real-world driving data.  Technical report, National Renewable Energy Lab.(NREL), Golden, CO (United States), 2019.
  * [48] Fang He, Yafeng Yin, and Jing Zhou.  Deploying public charging stations for electric vehicles on urban road networks.  Transportation Research Part C: Emerging Technologies, 60:227–240, 2015.
  * [49] Zhibin Chen, Yafeng Yin, and Ziqi Song.  A cost-competitiveness analysis of charging infrastructure for electric bus operations.  Transportation Research Part C: Emerging Technologies, 93:351–366, 2018.
  * [50] Yutaka Motoaki and Matthew G Shirk.  Consumer behavioral adaption in ev fast charging through pricing.  Energy policy, 108:178–183, 2017.
  * [51] Rick Wolbertus and Robert Van den Hoed.  Electric vehicle fast charging needs in cities and along corridors.  World Electric Vehicle Journal, 10(2):45, 2019.
  * [52] Kong Deyang, Ma Dan, and Wang Minmin.  A simulation study of upgrading urban gasoline taxis to electric taxis.  Energy Procedia, 104:390–395, 2016.
  * [53] Kay W. Axhausen Sebastian Hörl, Felix Becker.  Simulation of price, customer behaviour and system impact for a cost-covering automated taxi system in zurich.  Transportation Research Part C: Emerging Technologies, 123:102974, 2021.
  * [54] Haidong Yu and Aiqiang Pan.  Spatial-temporal charging pattern analysis for electric taxi grid integration study.  In 2019 IEEE Innovative Smart Grid Technologies-Asia (ISGT Asia), pages 3229–3234. IEEE, 2019.
  * [55] Joschka Bischoff and Michal Maciejewski.  Agent-based simulation of electric taxicab fleets.  Transportation Research Procedia, 4:191–198, 2014.
  * [56] Guang Wang, Fan Zhang, Huijun Sun, Yang Wang, and Desheng Zhang.  Understanding the long-term evolution of electric taxi networks: A longitudinal measurement study on mobility and charging patterns.  ACM Transactions on Intelligent Systems and Technology (TIST), 11(4):1–27, 2020.
  * [57] Yuan Zou, Shouyang Wei, Fengchun Sun, Xiaosong Hu, and Shiao Yaojung.  Large-scale deployment of electric taxis in beijing: A real-world analysis.  Energy, 100:25–39, 2016.
  * [58] Xudong Zhang, Yuan Zou, Jie Fan, and Hongwei Guo.  Usage pattern analysis of beijing private electric vehicles based on real-world data.  Energy, 167:1074–1085, 2019.
  * [59] Yang Zhao, Zhenpo Wang, Zuo-Jun Max Shen, and Fengchun Sun.  Assessment of battery utilization and energy consumption in the large-scale development of urban electric vehicles.  Proceedings of the National Academy of Sciences, 118(17), 2021.
  * [60] EV Charge +.  Byd e6.  https://evchargeplus.com/ev-specification/e6/, 2021.  Accessed on June 2021.
  * [61] Guang Wang, Wenzhong Li, Jun Zhang, Yingqiang Ge, Zuohui Fu, Fan Zhang, Yang Wang, and Desheng Zhang.  sharedcharging: Data-driven shared charging for large-scale heterogeneous electric vehicle fleets.  Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies, 3(3):1–25, 2019.
  * [62] Electric vehicle charging station map in china.  https://admin.bjev520.com/jsp/beiqi/pcmap/do/pcMap.jsp, 2021.  Accessed on June 2021.
  * [63] Geocoder: Simple, consistent — geocoder 1.38.1 documentation.  https://geocoder.readthedocs.io/, 2021.  Accessed 28 June 2021.
  * [64] Yu Marco Nie.  How can the taxi industry survive the tide of ridesourcing? evidence from shenzhen, china.  Transportation Research Part C: Emerging Technologies, 79:242–256, 2017.
  * [65] Yanchong Zheng, Ziyun Shao, Yumeng Zhang, and Linni Jian.  A systematic methodology for mid-and-long term electric vehicle charging load forecasting: The case study of shenzhen, china.  Sustainable Cities and Society, 56:102084, 2020.
  * [66] Zheng Hu and Jiahai Yuan.  China’s nev market development and its capability of enabling premium nev: Referencing from the nev market performance of bmw and mercedes in china.  Transportation Research Part A: Policy and Practice, 118:545–555, 2018.
  * [67] David M Blei, Andrew Y Ng, and Michael I Jordan.  Latent dirichlet allocation.  the Journal of machine Learning research, 3:993–1022, 2003.
  * [68] Lijun Sun, Xinyu Chen, Zhaocheng He, and Luis F Miranda-Moreno.  Routine pattern discovery and anomaly detection in individual travel behavior.  Networks and Spatial Economics, pages 1–22, 2021.
  * [69] Samiul Hasan and Satish V Ukkusuri.  Urban activity pattern classification using topic models from online geo-location data.  Transportation Research Part C: Emerging Technologies, 44:363–381, 2014.
  * [70] Mark Steyvers and Tom Griffiths.  Probabilistic topic models.  In Handbook of latent semantic analysis, pages 439–460. Psychology Press, 2007.
  * [71] Thomas L Griffiths and Mark Steyvers.  Finding scientific topics.  Proceedings of the National academy of Sciences, 101(suppl 1):5228–5235, 2004.
  * [72] Stuart Geman and Donald Geman.  Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.  IEEE Transactions on pattern analysis and machine intelligence, pages 721–741, 1984.
  * [73] EV Resources.  Visiting the world’s largest charging station.  https://www.evpartner.com/news/202/detail-45938.html.

##  Appendix A Complete results of spatial charging patterns

Figure 18: Charging activities of single-shift ETs Figure 19: Charging
activities of double-shift ETs

##  Appendix B Questionnaire for Shenzhen ET drivers