Electrification of personal vehicle travels in cities - Quantifying the public charging demand

Abstract

Charging electric vehicles is regarded as trivial with chargers installed on private property, which could accommodate the demand of 78% of the Danish cars. Hence, the owners would rarely need to charge outside the household. Car owners in the cities often do not have this option and must rely on the public charging infrastructure. In this work we quantify the need, in terms of energy demand, for public chargers on a national level and in the largest Danish cities as a function of car ownership, driving distance and household parking condition. We assess the potential of destination charging at existing shared parking facilities next to the household and the workplace to reduce the public charging demand to be up to 87%. EVs with 300 km range are able to complete the daily driving distance without range extending charging in 98.4% of the days. The analysis relies on driving and ownership data based on the Danish national transport survey. Further, we identify suitable/optimal locations for the necessary public chargers based on the total amount of parking time spent by a car at different destinations and the duration of a stay. We generalise the relationship between publicly available information such as population density and city size and the parameters that determine the public charging demand. The systematic approach enables others to estimate the demand in time and space for other cities or countries.

Full text

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Electrification of Personal Vehicle Travels in Cities
- Quantifying the Public Charging Demand
Andreas Thingvad, Peter Bach Andersen, Tim Unterluggauer, Chresten Træholt, Mattia Marinelli
Abstract—Charging electric vehicles is regarded as trivial with
chargers installed on private property, which could accommodate
the demand of 78% of the Danish cars. Hence, the owners would
rarely need to charge outside the household. Car owners in the
cities often do not have this option and must rely on the public
charging infrastructure. In this work we quantify the need, in
terms of energy demand, for public chargers on a national level
and in the largest Danish cities as a function of car ownership,
driving distance and household parking condition. We assess
the potential of destination charging at existing shared parking
facilities next to the household and the workplace to reduce the
public charging demand to be up to 87%. EVs with 300 km range
are able to complete the daily driving distance without range
extending charging in 98.4% of the days. The analysis relies
on driving and ownership data based on the Danish national
transport survey. Further, we identify suitable/optimal locations
for the necessary public chargers based on the total amount
of parking time spent by a car at different destinations and
the duration of a stay. We generalise the relationship between
publicly available information such as population density and
city size and the parameters that determine the public charging
demand. The systematic approach enables others to estimate the
demand in time and space for other cities or countries.
I. INTRODUCTION
The transportation sector accounts for 24% of the global
energy-related CO2emissions. Private passenger vehicles
account for 45% of this [1]. Electrifying private transportation
enables the use of renewable resources in the mobility
area. Combining electric vehicles (EVs) with integration of
renewable energy sources may reduce the cost of electricity
and CO2abatement [2, 3]. Due to national CO2emission
targets, an increasing number of governments are setting
targets for reaching a certain penetration of EVs in the
transport sector and/or define deadlines for closing sales
of internal combustion engine (ICE) vehicles [4]. Studies
have pointed to an effective and sufficient public charging
infrastructure as being the main perquisite for achieving
large-scale electrification [5–8]. In Europe, the Alternative
Fuel Infrastructure (AFI) directive requires each national
member state to define targets for ”appropriate” public
charging infrastructure measured in terms of the ratio between
vehicles and public charging points (PCP). The European
average is today seven EVs/PCP and the member states
highest ratio is close to ten EVs/PCP [5]. A charging point
is considered publicly accessible if it can be used by an
unspecified group of EVs. In [7] it is recommended that the
The work in this paper has been supported by the research projects FUSE
(EUDP grant nr. 64020-1092) and ACDC (EUDP grant nr. 64019-0541).
Websites: www.fuse-project.dk;www.acdc-bornholm.eu
The authors are from Center for Electric Power and Energy, Department
of Electrical Engineering. DTU - Technical University of Denmark, Roskilde,
Denmark. Email: {athing,pba,timun,ctr,matm}@elektro.dtu.dk
Corresponding author, Andreas Thingvad, email: athing@elekro.dtu.dk,
Phone: +4520818675
future charging infrastructure should not be based on a fixed
EVs/PCP ratio as countries differ regarding their framework
conditions and availability of home charging.
A. Order of Preferred Charging Options
In the following, the authors divide the PCPs into two
categories; destination charging and charging destinations.
Destination charging allows the EV owner to plug in at
locations where the vehicle would naturally be parked for an
extended duration as part of the owner’s behavioural pattern
e.g. shopping, entertainment or sport. Destination charging
generally consist of slow AC chargers, defined as mode 3by
the standard IEC 61851, which allows supply up to 43.5kW.
On the EV side the capacity is limited by the on-board charger
to a range 3.7-22 kW [6]. Conversely, charging destinations are
locations that would require a dedicated trip with the primary
purpose of recharging the vehicle. Such a trip would involve
additional energy and time consumption. In cities charging
destinations can either be curbside AC chargers or range
extending fast DC chargers. The latter, defined as mode 4by
IEC 61851, bypasses the on-board charger and can therefore
charge with higher power, available today with 50-350 kW
[6].
In Fig. 1 different charging locations are categorised
from left to right according to convenience. In this context
convenience is a function of the average time the cars
spend at each location. Destination charging is considered
most convenient since one would potentially avoid detours
as charging time spent at this location coincide with other
businesses, and thus largely eliminate the need for charging
elsewhere. For EV owners that park on their own property,
charging can be conducted with the installation of a private
charger. Car owners in the cities often do not have this
option and must rely on the public charging infrastructure.
For people living in a housing unit that occupies only part of
a building, like a housing tenure or apartment, there is often
a parking space next to the building. If the shared parking
facility has good parking conditions it would be possible to
charge if chargers were installed but it is not an individual
decision as it would be installed in a semi-public space
which requires a collective agreement. If it is not possible to
charge at the household, the most convenient location is the
workplace as the cars spend most of their time there outside the
household [9]. Available chargers at the workplace enables the
regularly visiting EV owners to meet almost all of their driving
consumption. The remaining EVs can use destination charging
if there are available chargers at the other locations they visit.
These other locations are the places of interest in the city
where the cars spend the most time outside the household and

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Destination Charging Charging Destinations
Charging
Locations
Work Other Curbside Stations
11 kW 11-22 kW 11-50 kW 11-22 kW 50-350 kW
Convenience
Price
Home Private Home Shared
11 kW
Fig. 1: Types of charging locations, with increasing price and consumer inconvenience from left to right.
workplace. The last alternative is to use charging destinations
in form of slow curbside chargers or fast charging stations.
Installation costs, cost of charging as well as customer
inconvenience increase towards the right in Fig. 1. The cost of
installation and the cost of a curbside charger are three times
the cost of a home charger with the same power due to the
demand for increased durability of the former. For a curbside
charger this leads to a price tag of C4,000 per PCP with a
power of 11-22 kW [10]. Work charging could be cheaper than
home charging if it is subsidised by the workplace, but then
it would be a form of taxable income for the employee. DC
chargers are significantly more expensive than AC chargers
due to the increased demand of power electronics and grid
connection costs. In Denmark a 50 kW DC charger cost
C70,000, which is 17 times more expensive than the AC
PCP for only twice the amount of power [10]. In Europe, a
network of 350 kW DC chargers are priced at C200,000 each
[11]. Fast charging stations will due to limitations in the EV
battery characteristics not reach a time consumption similar to
refuelling at a gas station and will in the foreseeable future
require more than 15 minutes for a charge 10-80% SOC [12].
B. Utilisation of Public Charging Points
Beyond charging, public curbside chargers are also used
as a normal parking space, which results in a low utilisation
of the charger. Here utilisation expresses the share of time
that the PCP experiences an active power flow. The utilisation
describes the maximum energy supplied per PCP with a certain
power capacity. For example, an 11 kW PCP with a utilisation
of 15% can provide up to 39.5kWh per day. Two studies
from cities in the Netherlands found that when EVs were
connected, only 12 -18% of the time was used for charging,
leading to a utilisation of only 4-5% [13, 14]. Results
from a similar study in the United States (US) found that for
only 14% of the PCP connection time the connected EV was
actually charging, which resulted in a utilisation of 7% [15].
In China the utilisation of PCPs was estimated to be less than
15% [16]. Economically viable operation of public charging
infrastructure is highly dependent on the utilisation [17]. More
idle time is a growing trend in the Netherlands, which directly
impacts on the sizing of the infrastructure, hence its cost and
availability [18]. The chargers in Amsterdam would need to
deliver twice as much energy per day to be profitable [14].
In Germany, utilisation for 11 kW charging points needed
to exceed 60% for profitable operation [19]. The work in
[20] revealed that the profitability of charging infrastructure
was highly uncertain but that utilisation higher than 33% was
needed under unfavourable conditions to meet an amortisation
of the costs. Therefore, accurately quantifying the need for
public charging is crucial in order to develop a charging
infrastructure that is convenient, sufficient and economically
efficient.
C. Current Charging Behaviour
Several studies based on real EV data showed the
importance of home charging. In the early ramp up of the EV
market in California 50-80% of charging events were at home,
15-25% at work and less than 10% at public chargers [21]. In
a survey of 4,000 EVs in 12 states in the US it was found that
57% of users charged only at home, 40% used a combination
of home, workplace and public charging where charging away
from the household usually happened at work [22]. Similar
results were seen in a survey in California, where 53% of
the EV owners solely relied on home charging, 8% and 3%
relied on work or public charging respectively [23]. The same
results were found by a national survey in the US of 8,300 EV
owners in 22 states [24]. Regarding range extension charging,
it was found in [25] that fast chargers provided 4-6% of the
total electricity consumption for driving in Norway in 2019.
Telematics data of driving and charging behaviour collected
from 7,163 Nissan LEAF EVs in the US during a whole year
showed that EVs on average drives similar yearly distances as
ICE vehicles [26].
D. Driving Behaviour of Cars in General
The charging pattern might be different in the future when
transitioning from the market of early adopters to an EV
mass market penetration. Home charging availability depends
on socio-demographic and geographical characteristics and
differs from country to country. Building an EV charging
infrastructure based on an analysis of the general driving
behaviour presents an alternative to building it based on
historic charging data for EVs. Based on empirical data
retrieved from the German National Household Travel Survey
(NHTS), [19] estimated the average probability of private
home charging at 67% for metropolitan areas, 78% for urban,
and 82% for rural areas. Using data from the US NHTS, [27]

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estimated that less than 60% of American homes in urban
areas can park on their own property, while this number
increased to around 80% in rural areas. Lack of access
to home charging determines the need for public charging
infrastructure. By using data from the US NHTS, [28] found
that charging outside the household was most likely to happen
at the workplace, followed by shopping and social destinations.
Assuming 100% EV penetration in Austria, [9] estimated that
88% of charging events would be carried out at home (the
share of the energy was not reported), 8.8% at the workplace
and only 1.7% of charging events take place at public slow
chargers and 1.5% at fast chargers [9]. However, articles
[9, 28] did not distinguish between parking on private property
at the household and on a parking lot/street near the household.
Quantifying the need for public charging infrastructure in the
metropolitan areas in the US and United Kingdom (UK),
[29, 30] similarly estimated that over 90% of the chargers and
more than 60% (UK) and 70% (US) of the required energy
could be provided by home charging.
The distribution of daily driving distances in the US was
analysed in [31], based on the US NHTS, where it was found
that a 55 kWh EV on an average day could match the range
of 98% of the cars and 80% of the driving distance. The
average driving distance was found to be significantly lower
in the cities than the rural areas, with small variations between
the cities, but the share of the long trips were the same. The
general charging demand was not investigated. The authors of
[8] analysed the distribution of long trips for 334 vehicles that
were tracked for a year in the Seattle metropolitan area. They
found that 12% of the cars could be electrified if they relied
on home charging only whereas adding workplace charging
would enable another 2% to be electrified. The study showed
that most drivers required access to range extension for a few
days per year to meet all of their driving demand, but the
energy demand from fast charging compared to home and
workplace charging was not analysed.
E. Objectives
This section has reviewed that the demand from range
extension is well documented as 1-2% of charge events/cars
in a day and 3-4% of the energy [9, 25, 31]. The main focus
of this study is on the bulk charging and not on the long
distance trips. From the above literature review we conclude
that while home charging remains the most prevalent mode
of charging - as EV penetration increases and as we seek
to electrify vehicles in urban environments - there is an
increased need for alternative charging solutions in order to
meet the demand from a full electrification of personal vehicle
travel. Concurrently some of the infrastructure established in
cities, especially curbside charging, are shown to exhibit low
utilisation, giving a low value/PCP, but also a high investment
cost, giving a high cost/PCP - exacerbating the challenge of
meeting the urban demand.
Using data from the Danish National Travel Survey
(NTS) this study adds to previous work by proposing a
quantitative methodology that provides as results; estimates
of the charging demand that public infrastructure will need to
meet; quantifying how much charging demand shared parking
facilities and workplace parking facilities can potentially
cover; and finally how much of the residual demand may
potentially be served using public destination charging at
points of interest in the cities. All calculations/estimates
are based on neutral regulatory conditions, i.e., based on
the technical aspects. Regulatory frameworks and incentives
potentially impact and could ultimately shift around charging
preferences. The following three points constitute the main
novelties that addresses the gaps identified in the literature:
1) Generalising the relationship between publicly available
information such as population density, city sizes and
the resulting energy demand that needs to be served by
public chargers enable us to take a systematic approach
to accurately determining the demand in time and space
for a specific city or country.
2) The analysis is centred around the household and
workplace parking conditions. By identifying the
parking conditions, we can clearly classify home
charging into subgroups such as: charging on private
property and charging on a shared parking facility. In
the former, the installation of a charging station is
solely dependent on the property owner, while the latter
requires a collective agreement. This aspect was not
addressed in previous work.
3) Finally, we characterise the residual public charging
demand that can be met with destination charging at
points of interest in the city; shopping, entertainment
and sport.
The remainder of the paper is organised as follows. Section
II describes the method and assumptions on which the study
is based; Section III quantifies the public charging demand
for both long distance and daily driving. Section IV estimates
to what extent charging at shared parking facilities at the
household and workplace can meet this demand. Section
V analyses the potential for covering the residual charging
demand with public destination charging at points of interest.
Finally, Section VI summarises the findings and highlights
relevant future work.
II. ME TH OD
The section below describes the method for calculating car
ownership, driving distance and household parking conditions,
which determine the demand for public chargers.
A. Calculation of Demand for Public Chargers
When calculating the demand for public chargers, several
assumptions have to be made, namely:
1) A 100% EV penetration scenario is assumed to avoid
selection bias due to early adopters, geographical
differences etc.
2) It is assumed that the overall transportation behaviour
will remain the same as for the ICE based driving, i.e.
as before the electrification of the vehicles.
3) An EV has an average energy consumption of 200 Wh
per km including losses during charging.

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4) Drivers that park on private property at the household
will install a charger and become almost self-sufficient
with electricity with regards to their driving needs.
5) The aggregated driving distance corresponding to people
with good parking conditions at shared parking facilities
at the household and at the workplace could be
electrified through the right incentives and regulatory
framework.
6) There is a need for range extension from fast chargers
for cars that drive more than 300 km in one day,
corresponding to a battery capacity of 60 kWh.
B. Driving Distance per Car
The Danish NTS is a person based (not household based)
interview survey which documents the travel patterns of the
Danish population [32]. It provides a consistent, statistical
picture of transport in Denmark for Danish residents age
10-84. Each interview, referred to as a session, in the survey
data describes the travelling of a single person during a single
day which may consist of multiple trips. The total travelled
distance by all the cars owned by the Danish households λ
is achieved by accumulating the distance of all the trips that
comply with the following conditions: the interviewed is the
driver (not the passenger) of a passenger car/van which is
owned by the household. This excludes all distances driven in
borrowed cars, employers cars, car sharing and rented cars, to
be consistent when dividing with the number of cars owned
by all the households.
All the sessions in one year are scaled with the session
weight ρaccording to social, economic and geographical
characteristics, to give a snapshot of the population for that
year. When analysing the data for multiple years (2014-2019),
the distance is normalised by the duration (number of years
Ny= 6). Hence the total driven distance over N sessions, with
Mktrips per session is found with (1).
λ=1
Ny
N
X
k=1
Mk
X
g=1
λk,g ·ρk(1)
It then follows that the total number of cars owned by the
households κis found as in (2). The car ownership of each
household θkis scaled with the session weight divided with
the number of people in the household ξk.
κ=1
Ny
N
X
k=1
θk·ρk/ξk(2)
Considering a uniform distribution of energy consumption,
with a mean value η= 200 Wh/km, the mean daily energy
consumption can be estimated by (3). The mean energy
consumption quoted above accounts for the overall energy
use per driven kilometre and includes the efficiency of the
drive train, the charger conversion losses and the electricity
consumption for the EV auxiliary systems like heating [33].
The energy consumption is the average over the year which
means that it would be higher in the winter and lower in the
summer. The energy demand is normalised per car in (4).
=λ·η(3)
φ=λ/κ ·η(4)
C. Parking Conditions
The parking conditions at the household determine the
potential for home charging. Since it is not the whole
population that lives in a household with a car, the parking
conditions are found for people who live in a household with
a car ownership of minimum one. Those that can park on their
own private property as a fraction of the whole population is
referred to as µpriv =Npriv/Ntot where Npriv is the population
in the group that can park on their own property and Ntot is
the total population living in a household with a car. Similarly
the ratio of the population with good parking conditions on a
shared facility at the household is called µsh. The good parking
conditions are described as; always or normally available
space, free and time unlimited. If it is technically possible
to install chargers at these parking lots it would be possible
for the residents to cover their every day driving needs at the
household.
The NTS also describes the parking conditions at the place
of occupation for employees, the self-employed and those
seeking education. The workplace is the prevalent location
regarding transportation by car compared to educational
locations. 25% of the total driving distance by car involves
commuting to a workplace and only 2% is for educational
purposes. It is therefore referred to as the workplace. The
fraction of the population that has good parking conditions at
the workplace is referred to as µwork. The parking conditions
at the workplace is only relevant for people with a workplace
different from the place of residence, but µwork is calculated
as the fraction of the whole population.
D. Distribution of Energy Demand per Parking Condition
The distribution of the charging demand is described in four
scenarios. The base case (scenario 1) is that everyone that can
not park on their own property must rely on public charging
infrastructure. Some of this public demand could be reduced
by instead either charging at the shared parking facilities at
the household (scenario 2) or at the relevant parking lots at
the workplace (scenario 3) or a combination of both (scenario
4).
The fraction of the population with certain parking
conditions at the household and at the workplace (µpriv,µsh
and µwork) is compared with the fraction of the distance driven
by the specific cars with those parking conditions. The cars
that can park on private property at the household drives a part
of the total driving distance, νpriv =λpriv/λ where λpriv is the
distance driven by the population in the group that can park on
their own property. Similarly the cars that can park on a shared
parking facility at the household drives a part νsh of the total
driving distance. The cars that have good parking conditions

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at the workplace and can not park on private property at the
household (scenario 3), drives a portion νwork1of the total
driving distance. The cars that have good parking conditions
at the workplace and has generally poor parking conditions
at the household (scenario 4), drives a part νwork2of the total
driving distance.
On an average day, the majority of the population is not
the driver of a car. Thus more data is available to describe
the fraction of the population with certain parking conditions
(µpriv,µsh and µwork), than is available to describe the ratio of
the distance driven by the specific cars with certain parking
conditions (νpriv,νsh ,νwork1and νwork2). When insufficient
data is available the fraction of the distance can be estimated
based on the fraction of the population and νwork1can be
estimated as (1 −µpriv)·µwork and νwork2can be estimated
as (1 −µpriv −µsh)·µwork.
The energy consumption associated with each segment
under consideration can be estimated by considering the
product between the total energy consumption with the
fraction of total driven distance by the given segment, namely:
priv =·νpriv (5)
sh =·νsh (6)
work1=·νwork1(7)
work2=·νwork2(8)
The residual public charging demand in scenario 1to 4is
found with (9)-(12)
pub1=−priv (9)
pub2=−private −sh (10)
pub3=−priv −work1(11)
pub4=−priv −sh −work2(12)
E. Destination Layover Time
The total time cars spend at different locations outside the
household and workplace τis calculated with (13), where
τk,g is the time the respondent spent during each visit a
specific type of location. Layover time is only counted if the
respondent travelled to the destination by a car/van owned by
the household where the respondent was the driver (not the
passenger). There can be up to Mkvisits at each location, so
the time spent is the sum of the duration of the individual visits
by the same respondent multiplied with the session weight.
The number of cars that visits the specific location by car
in a day is called κloc. The average time spent per visiting car
is called πand is calculated with (14). The average time a
car spends per week at the specific location is called ψand is
calculated with (15) by dividing with the total number of cars
and multiplying with the number of days in a week Nw= 7.
The average number of days between a car visits one of the
locations σis found with (16).
τ=1
Ny
N
X
k=1
Mk
X
g=1
τk,g ·ρk(13)
π=τ/κloc (14)
ψ=τ·Nw/κ (15)
σ=κ/κloc (16)
III. PUBLIC CHARGING DEM AN D ON NATI ONAL AN D
CITY LEV EL
The analysis is based on the TU0619v2 [32] version of
the NTS. The most recent six years, before the impact of
COVID-19, (2014-2019) of data where the NTS included
questions about parking conditions at the household and
workplace, was analysed. In the period there was on average
9388 sessions per year and the total number of sessions for the
six-year period is N=56328. The NTS estimates the population
size with a margin of 0.1-0.4% for the individual years,
compared to the National Government Statistics Denmark
(DST). The remaining paper does not differentiate between
individual years and analyses all of the 56328 sessions together
as an average year. There is a similar growth in car ownership
and driving distance in the period, which does not affect the
results.
The home address of the respondent is identified by a city
code and a municipality code, which are used to group the
sessions. DST uses a combination of municipality codes and
city codes, where large cities comprising several municipalities
are divided at the municipality border. Information about the
population density of the individual cities is taken from DST
so the NTS data has been grouped in the same way. This
means that the urban area of Greater Copenhagen which covers
several municipalities is divided into several cities according
to the municipality border. All statistical calculations are made
with a minimum of 1000 sessions, which limits the calculation
of (µpriv,µshared and µwork) in individual cities to the 27 largest
cities in Denmark (C27), and limits the calculation of (νpriv,
νshared,νwork1 and νwork2 ) to the national level and the capitol
Copenhagen. To be able to analyse the situation in the more
rural parts of the country where there are fewer sessions
per town, every city/town has been grouped according to the
population rounded to the nearest step of either 1000 or 5000
people. The groups are chosen so that each group includes a
minimum of 1000 sessions.
A. Demand for Average Driving Days
The six year average figures for the Danish population
indicate a total population of 5.73 million people, living in
2.56 million households, owning 2.74 million vehicles. This
yields a car ownership of 0.47 cars per person and 1.07
cars per household. The cars are however not evenly spread
between the households as 23% of the households do not own
a car, 51% own one car and 22% own two cars. Ref. [34] has
shown a similar distribution of car ownership in Scotland. Car

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ownership for C27 is depicted in Fig. 2a, where the area of
the circles is proportional to the population size of the city,
which for the seven largest cities is also given in the colour
coded legend. The red line shows the national average. The
car ownership is closely related to the population density and
it is close to twice as high in the least dense cities compared
to Copenhagen but in all cases significantly below the national
average. The car ownership also depends on the income
level as can be seen for Frederiksberg. The municipality of
Frederiksberg is located in the centre of the municipality of
Copenhagen but the average disposable income is 21% higher
than in the municipality of Copenhagen, which results in a
higher car ownership despite a significantly higher population
density [35]. All cities considered are significantly below the
national average for car ownership.
On a weighted average day the cars are driving 123.29
million km corresponding to 45 km per car. The cars are not
all driven daily and on an average day only 84% of the Danish
cars are driven, equal to 2.1million cars, driving 55 km each.
The cars on average are driving 47 minutes per day, which
means they are parked 96.6% of the time. Not only are there
fewer cars in the more densely populated cities but they also
drive shorter distances, as shown in Fig. 2b for C27. The red
line shows the national average. On an average day the cars
in Frederiksberg and Copenhagen drive 26% and 20% shorter
than the national average. The less dense cities are spread
around the national average and the lowest numbers are seen
for cities close to Copenhagen.
(a) Car ownership vs. population density.
(b) Driving distance vs. population density.
Fig. 2: (a) Car ownership and (b) Driving distance vs. population density for
the 27 largest cities in Denmark. The area of the circle is proportional to the
population.
The NTS sessions are spread throughout the year so the
different behaviour of the different days are taken into account.
This study is based on a weighted average day, which means
that some days will have a lower or higher driving distance.
The days are categorised as different day types shown in
Table I. The largest driving distances are seen on Fridays and
weekdays before a public holiday, where the distance is 14%
higher compared to the weighted average. This means that the
busy driving days will only cause an increase of electricity
consumption of up to 14%.
Description Days Distance
Normal weekday ”Mon-Thur” 191 49 km (110%)
Friday and weekday before public holiday 50 51 km (114%)
Special weekdays (most workplaces are closed) 8 44 km (97%)
Saturday 53 36 km (79%)
Sunday and last public holiday before weekday 53 36 km (79%)
Holiday/Sunday - next day is Sat/Sun/holiday 10 31 km (68%)
TABLE I: Day types and average driving distance in km and in percent of
the weighted average.
Several studies have shown that EV owners rarely charge
their EV every day, unless it is necessary [26, 36]. By looking
at the distribution of daily driving distances, shown in Fig. 3a,
it can be seen that few cars need to be charged daily. On an
average day, 66% of the cars that drive will drive less than 50
km and 86% will drive less than 100 km.
(a) Distribution of cars (left) and cumulated share (right) vs. the driving distance.
(b) Share of driven vehicles in Denmark and the 7largest cities with insufficient range
on a log–linear scale vs. the Vehicle Driving Range.
Fig. 3: Distribution of the driving distances of privately owned cars during a
single day.
Considering a hypothetical mean range of 300 km, only
14% would need to charge more than every third day.
Therefore it can be assumed that the difference in driving
distance of individual days does not result in the same
difference in electricity consumption as the charging behaviour
has a smoothing effect.

7
B. Demand for Long-Haul Driving Days
The share of the cars not having enough range for a full day
of driving depends on the total range of the car. Fig. 3b shows
the share of the cars that that during a single day would need
to stop to charge vs. the driving range of the vehicle. This
share is shown for all of Denmark and for the residents of
the seven largest cities. Even though the cars in the cities on
average drive less, the share of the long trips is the same,
resulting in the same need for fast chargers.
On an average day, 1.4% of the cars will drive longer
than 300 km, which means that they would need to charge
during the day to complete the trip. As shown in Fig. 3a, it
is important to electrify this group as they drive 13% of the
total distance of all cars. Those findings are consistent with
results of [9, 31]. The charging demand can be met with a
network of fast chargers that can deliver the missing range
beyond 300 km to reach the destination. The 1.4% of long-haul
cars on average drive 404.8km (81.6kWh), resulting in an
average need of extra supply of 104.8km range (21.6kWh) to
reach their destination. Differences in the driving consumption
caused by higher driving speed for the long distance trips is not
taken into account. On the national level the range extension
would account for 0.86 GWh per day or 3.36% of the total
consumption. For the residents in Copenhagen, it would be
3.62% of the driving consumption. This is close to the situation
today in Norway [25].
C. Parking on Private Property at the Household
The share of people, living in a household with a car
ownership of minimum one, that can park on their own
property is shown in Fig. 4a for C27 vs. the population
density. The red line indicates the national average of µpriv =
77.5%. The least densely populated cities have a share
above 80% and are in general above 50%. Only Copenhagen
and Frederiksberg significantly stand out at 23% and 17%
respectively.
In Fig. 4b the smaller and less densely populated areas of
Denmark have been investigated by grouping the sessions with
a similar city size. In towns with a population around 500
people, 98% are able to park on their own property. The share
gradually decreases for cities with a larger population. The
population size and density are related and can both be used
to describe the share of population that can park on their own
property. For the case of Frederiksberg, which can be seen in
both Fig. 4a and 4b, it does not follow the trend for the city
size due to the high population density.
D. Charging Demand Outside the Household
The national average daily energy consumption is φ= 9
kWh per car. The fraction of the population parking on private
property is µpriv = 77.5%. The cars that can park on private
property drives a larger share of νpriv = 80.9% of the total
driving distance, because of the differences between urban and
rural areas where the areas with the best parking conditions
have the highest car ownership and drive longer distances per
car and thus have a larger weight. For Copenhagen the share
(a) µpriv vs. population density for the 27 largest cities in Denmark. The area of the
circle is proportional to the population.
(b) µpriv vs. city size for all of Denmark.
Fig. 4: The fraction of the population that park on their own property vs. (a)
population density in C27 and (b) city size.
of the population µpriv = 22% is higher than their share of the
distance νpriv = 19%.
In Fig. 5 is shown the public charging demand normalised
per car φpub1calculated as φ·(1 −µpriv)for each city in C27
and the national average of 2kWh per car. The public charging
demand is increasing with the population density, despite the
average driving distance showing the opposite trend.
Fig. 5: φpub1calculated as φ·(1 −µpriv)vs. population density for the
27 largest cities in Denmark. The area of the circle is proportional to the
population.
Table II depicts the daily energy consumption for personal
transportation in all of Denmark and for the largest city
Copenhagen. Copenhagen has 153,000 cars that on average
drive 35 km/day with a consumption of 7kWh/day per
car. Only 22% of the cars can park on private property at
the household, so situation is reversed compared to all of
Denmark. It can be seen that the overall demand per car in
Copenhagen (7kWh), is lower than the national average of 9

8
kWh per car per day. However, the parking conditions cause a
significantly higher public charging need. With 5.7kWh, the
public charging demand in Copenhagen is 331% higher than
the national average of 1.7kWh per car. , is all the energy
demand, including the share of the long trips with a distance
above 300 km, which should be delivered by range extension
chargers.
Denmark Copenhagen
(φ)24.66 GWh (9.0kWh) 1.07 GWh (7.0kWh)
priv (φpriv)19.95 GWh (7.3kWh) 0.20 GWh (1.3kWh)
pub1(φpub1)4.70 GWh (1.7kWh) 0.87 GWh (5.7kWh)
TABLE II: Daily energy consumption, in total and per car φin Denmark and
Copenhagen, in overall and divided in the cars that park on private property
and those that does not.
IV. ROLE OF SHARED PARKING FACI LI TI ES AT TH E
HOU SE HO LD A ND T HE WORK PLACE
We here determine how much the residual public charging
demand can be reduced by fully utilising charging options at
the workplace and shared facilities at the household.
A. Parking on a Shared Facility at the Household
The fraction of the population with good parking conditions
on a shared parking facility at the household is shown in
Fig. 6a for C27. The fraction is around 20% across the 27
cities and is independent of the population density, because
it excludes people with poor parking conditions. The poor
parking conditions on a shared facility at the household are
described as either rarely/never space, time-limited or against
payment. More people parks on shared facilities in the more
densely populated cities but the larger share mostly consist of
facilities with poor parking conditions. On the national level
14.7% of the population parks on a shared facility next to
their household and 12.9% (88% of them) have good parking
conditions.
The fraction of people parking on a shared facility at the
household in all of Denmark, grouped by city size, can be
seen in Fig. 6b. There is a clear trend of less people parking
on a shared facility in smaller towns. Assuming that the µsh =
12.9% of people parking on a shared facility at the household
also drives 12.9% of the distance, it shows that up to µsh/(1−
µpriv) = 57% of the public charging need can potentially be
covered by installing chargers at shared parking facilities.
B. Parking at the Workplace
The share of the population in Denmark that has good
parking conditions at the workplace is µwork = 55.5%. The
remaining 44.5% either have poor parking conditions or do
not have a relevant workplace. In Fig. 7a, it is shown how the
share of the population with good parking conditions at the
workplace is lower in cities with higher population density, but
there is a relatively low difference between the highest 62%
in Esbjerg and the lowest 40% at Frederiksberg. The parking
conditions at the workplace are similar in the rural and mid
size cities but decrease in the largest cities as shown in Fig. 7b.
(a) µsh vs. population density for the 27 largest cities in Denmark. The area of the circle
is proportional to the population.
(b) µsh vs. city size for all of Denmark.
Fig. 6: The fraction of the population that has good parking conditions on a
shared facility next to their household vs. (a) population density in C27 and
(b) city size.
Charging at the workplace has a large potential throughout the
country with most places being close to the national average
of 55.5% and is expected to have the potential of reducing the
public demand with a similar share.
C. Distribution of Charging Demand
The cars with the best parking conditions are driven more
than the cars with poor parking conditions which causes the
share of the population to deviate from the share of the
distance. The average driving distance per car in each group is
shown for each scenario in Table III. The scenarios are defined
in subsection II-D.
Scenario 1234
Private 46.67 46.67 46.67 46.67
Shared 40.14 40.14
Work 50.84 50.41
Public 39.17 37.89 26.26 24.11
TABLE III: Average daily driving distance (km/day) of cars with different
parking conditions in scenario 1-4.
Fig. 8 illustrates the share of the total driving distance that
potentially could be covered at different locations according
to scenario 1and 4as found with (6)-(12) for (left) all of
Denmark and (right) the city of Copenhagen. The demand
for range extension has been taken into account. The main
pie chart depicts the distribution in the base case, scenario 1,
where the charging demand only is divided in priv,pub1and
range extension. The subset of the pie chart shows how much
pub1could be reduced by meeting as much of the demand as

9
(a) µwork vs. population density for the 27 largest cities in Denmark. The area of the
circle is proportional to the population.
(b) µwork vs. city size for all of Denmark.
Fig. 7: The fraction of the population that has good parking conditions at the
workplace vs. (a) population density in C27 and (b) city size.
possible with sh and work2. Thus resulting in the minimum
demand for public charging pub4.
Range Extension
3.36%
Private
78.18%
Shared
10.73%
Work
5.39%
Public4
2.34%
Public1
18.46%
Denmark
Range Extension
3.62%
Private
17.94%
Shared
23.15%
Work
33.76%
Public4
21.53%
Public1
78.44%
Copenhagen
Fig. 8: Share of driving distance in Denmark (left) and in Copenhagen (right)
that can be supplied at different locations in scenario 1(main pie chart) and
4(subset pie chart).
1) Denmark: The starting point is scenario 1where 81%
of the daily distance is driven by cars that can park on
their own property, when subtracting the demand for range
extension 78% will be charged at home on private property.
The remaining 18% of the driving demand has to be delivered
outside the household. The cars that park on a shared facility at
the household with good parking conditions drive νsh = 11%
of the total distance, close to the share of the population
µsh = 13%. Parking lots with good parking conditions can
potentially reduce the public charging need by 58%. The cars
that can not park on private property but have good parking
conditions at the workplace (scenario 3) drive νwork1= 13%
of the total daily driving distances. Therefore, work charging
could potentially contribute to reducing public charging need
by up to 68%, which is more than that of the shared facilities
at the households. The cars in scenario 4that have poor
parking conditions at the household but good conditions at
the workplace drive νwork2= 5% of the total driving distances.
Going from scenario 2to 4, adding the workplace charging
on top of the charging at the shared parking facilities at the
household have the potential of reducing the public charging
need with 60.2%. The combined use of both the shared
facilities at the household and at the workplace could supply
16% of the total driving distances. In scenario 4the public
charging need is reduced by 87% compared to scenario 1to
the minimum level of 2% or φpub4= 0.22 kWh per EV per
day. The reduction potential from workplace charging of 68%
and 60% is higher than the 55.5% that was calculated based
on the national value of µwork. The cars with good parking
conditions at the workplace are driven twice as far per day
than the cars that do not have good parking conditions and
therefore have a higher weight.
2) Copenhagen: As shown in the right part of Fig. 8,
Copenhagen initially (scenario 1) has the opposite distribution
than the national as only νpriv = 18% of the distance is driven
by cars that are able to charge on private property and 78%
of the energy has to be delivered outside the household. The
fraction of people is µpriv = 22%. The potential for providing
the residual energy by the shared facilities (scenario 2) is
twice as large as the national level and νsh = 22% of the
distance is driven by those cars. The fraction of people is also
µsh = 22%. The potential of instead providing the residual
energy with workplace charging (scenario 3) is also more
than double compared to the national level as the workplace
charging has a potential to cover νwork1= 51% of the distance,
corresponding to a reduction of the public charging demand
of 63%. When adding workplace charging on top of charging
at the shared parking facilities at the household (scenario 4),
work charging could meet νwork2= 34% of the demand and
reduce the public demand with 61% compared to scenario
2. In scenario 4the combined use of shared facilities and
workplace charging can cover up 57% of the total demand
and reduce the public charging need to 22%. This is a 73%
reduction compared to scenario 1. The reduction potential of
workplace charging is significantly higher than the share of the
people µwork = 46.35%. In scenario 4,40% of the national
public charging need is in Copenhagen, despite the cars in
Copenhagen only drive 4% of the overall distance.
V. POT EN TI AL O F PUBLIC DES TI NATI ON CHARGING
This residual public driving demand can to some extent be
supplied with destination charging at other locations where the
cars spend most time. The locations are grouped according to
the purpose of the visit.
A. Distribution of Visit Duration
The three most common purposes of a visit to a location,
excluding the household and the workplace, are in descending
order: shopping; entertainment (cinema, cafe, restaurant, sport
spectator, church, etc.) and participation in sports. The average
time spent πwhen visiting the location indicates the amount
of energy that can be charged per plug-in session. The visit
must be of certain duration before it is beneficial, in terms
of received energy, for the EV owner to make the effort of
plugging in. How much time cars generally spend per week at
the location ψalso depends on the number of days between

10
a visit σ. Given a certain charging power, ψrepresents the
amount of energy that can be charged from the location type
per week if there are available chargers. Table IV shows π,ψ
and σfor the three different locations.
Purpose N π ψ σ
Shopping 29872 39 minutes 94 minutes 2.9days
Entertainment 5270 161 minutes 72 minutes 15.7days
Sport 5086 130 minutes 55 minutes 16.5days
TABLE IV: Number of sessions (N), average time spent during a visiting
day (π), the average time spend during a week (ψ) and the number of days
between a visit (σ) at the most common purpose of a visit to a location,
excluding the household and the workplace.
A car in Denmark on average spends 94 minutes per week at
locations with a shopping purpose. On the days the car is used
for shopping it stays on average 39 minutes at the location,
which means that it is used for shopping once every 2.9days.
When the cars are used to visit a location with the purpose
of entertainment or sport, the visits are generally longer but
since they have a lower occurrence of only one visit per 15.7
or 16.5days, overall less time is spend there. Fig. 9a shows
the cumulative share of the visits with different duration and
the cumulative share of the total time spent. 86% of visits
with the purpose of shopping last less than one hour, while
84% and 78% of visits at entertainment and sport facilities
last more than one hour. A share of the visits are very short
and would not be suitable for charging. The threshold below
which it does not make sense to plug in is chosen as visits
of less than 15 minutes duration, which accounts for 25% of
shopping visits but only 6% of the time spent at a shopping
location. The short visits accounts for only 0.2% and 0.1% of
the time spent at entertainment and sport.
B. Coverage of Driving Demand
Unlike the household and the workplace, the time the cars
spends at the three investigated locations is not abundant. It
is therefore necessary to assume a specific charging power
that determines the needed charging time to cover the driving
demand. An example is given for an 11 kW AC charger. It
can be seen in Table III (scenario 4) that the cars that neither
are able to charge at the household nor at the workplace on
average drive 24.11 km per day. Thus resulting in a driving
consumption of 4.8kWh/day or 33.8kWh/week. Using an
11 kW charger, the consumption could be covered with 185
minutes of charging per week. Assuming available chargers
at all three types of locations, the average EV owner could
charge 16.2kWh (excluding visits of <15 minutes duration)
at shopping, 13.2kWh at entertainment and 10.1kWh at sport
per week. The sum of the potential destination charging is 39.5
kWh per week, which is 117% of the energy need.
Destination charging is in this case limited in time by
the natural duration of the visit. Thus the utilisation and the
energy that can be delivered per charge point per day at these
locations is determined by the distributions of the visits. If
all the cars visit at the same time there can only be a single
charging session per day, while if the visits are spread equally
throughout the day, there can be multiple consecutive charging
sessions with low charger idle time. Fig. 9b shows the share
of active visits during the day. The behaviour at specific
times during the day differ between weekdays and weekend
so Fig. 9b is only based on weekdays (Monday-Friday). The
maximum share of active visits in a day ζfor shopping is
ζ= 8.8%. For entertainment it is ζ= 34.9% and for sport it
is ζ= 27.4%.
(a) Cumulative distribution of daily visits and time spent at different types of location.
(b) Share of active visits at the same time of all visits throughout the day.
Fig. 9: (a) Cumulative distribution of daily visits and time spent and (b) share
of active visits at locations with the purpose of shopping, entertainment and
to participate in sport.
The necessary amount of chargers to install at the different
locations depends on the maximum share of all the cars that
are at the location at the same time α. The maximum share
of the visiting cars that are at the locations at the same time ζ
is multiplied with the share of all the cars that visit a location
during a day 1/σ in (17).
α=ζ/σ (17)
The peak share of all cars visiting shopping locations is
calculated as α= 8.8%/2.9 = 3.0%, which means that the
charging demand can be covered by one charger for every 33
cars in Denmark. The EVs/PCP ratio is found with (18).
EVs/PCP = 100%/α (18)
The peak visits at Entertainment locations are 2.2% of all
the cars which requires one charger per 44 cars. The peak
visits at sport locations are 1.7% of all the cars which requires
one charger per 60 cars to meet the demand. The ratios are
significantly higher than the current situation in Europe where
the ratio is 7-10 EVs/PCP, which indicates that the profitability
of each PCP could be improved significantly by optimally
choosing the location. If the chargers only were used by the

11
residual cars in scenario 4, they would supply the charging
need for 123,783 cars. To meet this demand at shopping
locations would require 123,783/33 = 3713 charge points,
supplying 77.2kWh/day each. The entertainment locations
would need 2752 charge points, delivering 84.8kWh/day each
and sport locations would need 2056 charge points, supplying
86.9kWh/day each. Assuming a constant power of 11 kW,
supplying 77.2-86.9kWh/day would require a utilisation of
29-33%.
The visits at shopping locations are spread out evenly
between 10:00 in the morning and 17:00 in the evening, where
5−8.8% of the cars are shopping at the same time. The
spread of visits during the day together with the duration of
the visits from Fig. 9a could enable a very high utilisation.
The low number of days between shopping might enable the
owner in having a cheaper EV with less range as there is a
potential for charging regularly. The long time between visits
at entertainment and sport locations could indicate that they
contain separate sub-distributions of some cars that weekly
are driving with the specific purpose and others that never
do. Thus the ratio would be reduced to half the calculated
value. If there is a homogeneous distribution of visits to
entertainment and sport, the long time between visits could
also be problematic as an EV with 60 kWh capacity - if driving
more than the average distance during a week - would run out
of charge. Finally the very long visits might be more than
the needed charging time and together with the higher peak
correlating visits could result in a significantly lower utilisation
compared to shopping.
VI. CONCLUSION
The role of DC fast charging amounts to 3% of the total
driving demand which corresponds to supplying the range
extension for daily driving distance above 300 km. The fast
charging infrastructure is not seen as a direct competitor to
destination charging due to the significantly higher cost and
the increased inconvenience for the EV owner to go out of
their way to charge and due to the duration of a 10-80% charge
being above 15 minutes.
For Denmark it is found that 78% of the energy for
driving can be covered by charging on private property at the
household, while the residual must be supplied outside the
household. 11% of the energy consumption can be covered
by charging on shared parking facility at the household.
Providing chargers at these locations can reduce the need for
public charging points (PCP) with up to 58%. For commuters
without a home charging option, workplace charging plays
an important role which could reduce the need for PCPs
with 68%. With the right regulatory framework and incentives
which both enable the charging at the shared parking facilities
at the household and at the workplace there is a potential
to reduce the need for public charging with 87%, ultimately
leaving only 2.4% of all driving distance to be served by
PCPs. In this case 40% of the residual national public charging
need is in the city of Copenhagen, despite the residents in
Copenhagen only drives 4% of the overall distances. Public
slow charging infrastructure will mainly play an important role
in urban areas and to a lesser degree in rural areas. In this study
it is demonstrated how the residual public charging demand for
a specific city can be calculated based on the average driving
distance, car ownership and the average parking condition
at the household and the workplace. It is then shown how
these key figures can be related to the population density
and the city size, thus demonstrating a way to generalise the
applied method to other cities with similar or less available
information. The residual demand for charging that is neither
covered by charging at the household nor the workplace
can to a large extend be provided with destination charging
where cars spend the most time. Those locations are shopping,
entertainment and sports facilities. Based on the average time
a car spends at these locations during a week it is possible
to cover charging corresponding to more than the full driving
demand.
Future work involves taking socio-economic aspects into
account, since high income households are expected to be
more likely to buy a long range EV. Future work should also
involve assessing the efficacy of specific regulatory framework
and incentives to accommodate the charging infrastructure
development.
VII. APPENDIX
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12
Population NµPeople/km2Cars/Person µpriv µsh µwork NνDistance/Car νpriv νsh νwork1
νwork2
Denmark 5728940 56328 126 0.48 77.5% 12.9% 55.5% 23840 44.97 km 80.9% 11.1% 13.0% 5.6%
Copenhagen 632340 15610 8231 0.22 22.0% 21.7% 46.3% 1224 36.0km 19% 24% 52% 35%
Aarhus 280534 7063 2854 0.29 59.2% 21.9% 51.1% 696 45.2km 61% 19% 28% 15%
Odense 180302 4900 2276 0.36 68.6% 15.2% 56.3% 551 39.5km 67% 17% 30% 15%
Aalborg 117351 3547 2330 0.34 58.6% 25.5% 56.6% 377 48.5km 51% 34% 37% 14%
Frederiksberg 104305 3142 11979 0.29 15.6% 26.1% 40.2% 286 32.7km 30% 15% 37% 28%
Gentofte 74830 2045 3129 0.41 65.5% 11.0% 49.6% 261 37.6km 75% 7% 17% 12%
Esbjerg 72037 2068 1654 0.42 72.3% 19.0% 60.7% 286 38.0km 79% 15% 16% 3%
Gladsaxe 69112 2451 3198 0.36 59.0% 24.8% 55.5% 491 34.9km 50% 26% 35% 16%
Randers 62482 1712 1936 0.41 70.5% 19.4% 51.7% 236 49.5km 75% 17% 20% 7%
Kolding 61121 1730 1608 0.42 75.9% 13.4% 60.6% 249 52.3km 78% 13% 18% 9%
Horsens 59449 1499 2082 0.40 77.5% 13.4% 59.1% 211 48.6km 82% 9% 13% 7%
Vejle 57655 1526 1744 0.40 72.2% 18.3% 58.9% 215 50.4km 79% 14% 15% 7%
Lyngby-Taarbæk 55903 1595 3056 0.39 63.8% 21.7% 54.5% 189 37.8km 54% 34% 29% 9%
Hvidovre 53505 1375 2857 0.34 61.3% 28.6% 48.9% 159 34.9km 50% 30% 33% 18%
Roskilde 51262 1829 2417 0.37 58.9% 30.5% 56.7% 360 39.0km 56% 32% 32% 11%
Herning 50332 1385 1551 0.40 80.5% 14.2% 57.9% 187 48.8km 78% 11% 15% 8%
Helsingør 47360 1262 2646 0.40 68.5% 18.7% 54.7% 139 37.8km 55% 21% 32% 20%
Silkeborg 46923 1394 1652 0.41 83.4% 11.5% 60.5% 181 46.6km 83% 12% 14% 5%
Næstved 43803 1244 2036 0.40 73.0% 20.3% 56.6% 148 44.4km 59% 31% 19% 10%
Greve Strand 43309 1168 1977 0.43 78.2% 19.7% 51.9% 153 43.8km 80% 16% 14% 4%
T˚
arnby 42539 1084 3119 0.38 71.6% 18.7% 54.7% 134 38.2km 76% 15% 23% 11%
Fredericia 40981 1217 1512 0.43 70.9% 17.8% 49.8% 152 42.8km 78% 12% 16% 8%
Viborg 40778 1150 1620 0.41 75.4% 20.2% 58.0% 163 43.8km 76% 21% 20% 1%
Rødovre 40551 1010 3612 0.34 54.7% 32.5% 54.5% 122 33.3km 59% 32% 20% 5%
Ballerup 39528 1125 2518 0.39 63.9% 29.8% 58.6% 126 30.8km 68% 24% 24% 5%
Køge 37754 1040 2032 0.37 71.7% 21.8% 57.7% 148 45.0km 75% 16% 20% 9%
Holstebro 36643 1095 1577 0.42 81.0% 12.3% 59.1% 141 48.5km 76% 16% 13% 5%
TABLE V: Key figures for Denmark and the 27 largest cities. Nµand Nνare the number of interview sessions/samples each estimate is based on.
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