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Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
Electric vehicle based smart e-mobility system – Definition and comparison
to the existing concept
Ivan Pavić
⁎
, Hrvoje Pandžić, Tomislav Capuder
University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb HR-10000, Croatia
HIGHLIGHTS
•Control authority in smart e-mobility is usually on the side of charging stations.
•Electric vehicle based concept is an alternative where vehicles control charging.
•In a proposed concept charging stations are merely an enabling infrastructure.
•Electric vehicle based system yields higher revenues for the vehicle owners.
ARTICLE INFO
Keywords:
Electric vehicles
Charging stations
Aggregator
Electric vehicle aggregator
Electricity market
ABSTRACT
The existing models designed to reap the benefits of electric vehicles’ flexibility in the literature almost ex-
clusively identify charging stations as active players exploiting this flexibility. Such stations are seen as static
loads able to provide flexibility only when electric vehicles are connected to them. This standpoint, however,
suffers from two major issues. First, the charging stations need to anticipate important parameters of the in-
coming vehicles, e.g. time of arrival/departure, state-of-energy at arrival/departure. Second, it interacts with
vehicles only when connected to a specific charging station, thus overlooking the arbitrage opportunities when
they are connected to other stations. This conventional way of addressing the electric vehicles is referred to as
charging station-based e-mobility system. A new viewpoint is presented in this paper, where electric vehicles are
observed as dynamic movable storage that can provide flexibility at any charging station. The paper defines both
the existing system, where the flexibility is viewed from the standpoint of charging stations, and the proposed
one, where the flexibility is viewed from the vehicles’ standpoint. The both concepts are mathematically for-
mulated as linear optimization programs and run over a simple case study to numerically evaluate the differ-
ences. Each of the four issues identified are individually examined and omission of corresponding constraints is
analysed and quantified. The main result is that the proposed system yields better results for the vehicle owners.
1. Introduction
Much focus has been given lately to the decarbonization of the
electricity production, however a greater challenge might be doing the
same with the heating and transportation sector. The transition from
conventional vehicles to low carbon emission ones is moving slower
than anticipated, despite that its importance is highlighted in all re-
levant policy documents [1]. The solutions for changing transportation
habits and preferences of end-users [2] require an integrated approach,
especially in designing models for end-users and encouraging them to
make a quicker transition to electrified transport, as designed by the
relevant regulatory goals [3]. This means being aware of technical,
economic and social constraints when creating models to make
electrification of the transport an alternative new flexibility source. If
electric vehicles (EVs) are charged uncontrollably [4], i.e. charging at
maximum power until fully charged, power system’s hunger for flex-
ibility increases, calling for additional investments in peaking units and
grid infrastructure upgrades. On the other hand, if EVs are charged in a
controllable manner [5], they resemble features of both demand re-
sponse and energy storage. Shifting their charging times represents the
aspect of demand response. This is often referred to as Grid-to-Vehicle
(G2V) mode, which requires unidirectional controllable chargers [6]. A
possibility to discharge a part of the surplus energy when not needed for
motion, often referred to as Vehicle-to-Grid (V2G) mode, corresponds to
the energy storage aspect of EVs and requires bidirectional controllable
chargers [7,8]. Detailed overviews of EV charging modes are available
https://doi.org/10.1016/j.apenergy.2020.115153
Received 10 February 2020; Received in revised form 1 May 2020; Accepted 5 May 2020
⁎
Corresponding author.
E-mail addresses: ivan.pavic@fer.hr (I. Pavić), hrvoje.pandzic@fer.hr (H. Pandžić), tomislav.capuder@fer.hr (T. Capuder).
Applied Energy 272 (2020) 115153
0306-2619/ © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/BY-NC-ND/4.0/).
T
in [9,10].
This paper proposes a new concept of using the EV flexibility more
efficiently in a world with a multitude of new data streams relying on
information-communication technologies in vehicles and without any
loss of comfort for EV drivers. We argue that the state-of-the-art lit-
erature, research projects and e-mobility sector currently conceive the
smart e-mobility in a way which leads to an underutilization of the EV
flexibility and to insufficient financial returns. The usual understanding
of smart e-mobility is that Charging Stations (CSs) use EVs to provide
flexibility to the power system (we define this as the CS-based concept),
whereas this paper challenges this approach and reverses the roles by
identifying EVs themselves as smart players that provide flexibility and
the CSs as merely an enabling infrastructure (we refer to this as the EV-
based concept).
The smart e-mobility term used in this paper refers to an advanced
multisector system where the main actors are: EVs, CSs, Electric Vehicle
Aggregators (EVAs), power grid and electricity market operators.
Merchant actors within this ecosystem have at their disposal smart EV
charging and discharging options to provide flexibility to the power
system and in return receive monetary reward. This paper analyzes a
basic illustrative example with three EVs and three CSs. The purpose of
the example is to highlight certain issues in the state-of-the-art, after
which we define a new mathematical model and demonstrate how the
issues of the current state-of-the-art are eliminated using our model
through a detailed case study.
This paper contributes to the body of knowledge in the field of EV
aggregation by providing the following:
1. a design and a formulation of a novel EVA model tracking the EVs
during their trips, thus capturing all relevant trip and battery in-
formation,
2. a systematic and rigorous comparative assessment of the CS-based
and EV-based models,
3. a demonstration that aggregate EV models without relevant fea-
tures, such as power levels and grid tariffs, result in incorrect con-
clusions regarding the cost of EV charging.
2. Illustrative example
2.1. Assumptions and description
An illustrative example presented in Figs. 1–3 compares the current
smart e-mobility CS-based model with the proposed EV-based concept.
Several simplifications and assumptions are made to keep this example
concise. We observe three EVs and three CSs (Fig. 1) and their behavior
through a 24-h period with 1-h time resolution. Each EV can be charged
at different CSs and each driving period, i.e. period when EV is not
connected to any CS, lasts one hour. Each EV has one Battery (EVB) and
one On-Board Charger (OBC), while each CS encompasses three Char-
ging Points (CPs), meaning it can serve all three EVs at a time. All three
CPs within a CS are AC and have chargers of same power capacity.
Let us assume that both EVs and CSs can individually participate in
the wholesale electricity market,
1
namely the day-ahead market, and
that their objective is to minimize the purchasing costs of electricity for
mobility purposes and/or to maximize revenue through energy arbit-
rage.
A smart e-mobility system can therefore be conceived as an EV-
based or a CS-based, as illustrated in Fig. 2. In the former model, the
EVs are the smart entities negotiating market strategy while the CSs are
merely an infrastructure with their technical constraints (CP power
capacity) and economic parameters (CS utilization fee). The latter
model observes the same entities, but from an opposite standpoint. The
CSs are the smart entities negotiating market strategy, while the EVs
only impose technical constraints (OBC power capacity) and economic
charges (battery utilization fee). The CSs must pay a fee to use the EVs’
physical equipment (battery) and the energy stored within the EVBs
when performing arbitrage (V2G mode). On the other hand, they re-
ceive payments by the EVs for the energy they charge for driving pur-
poses. Currently, the roads are populated with both hybrid and full EVs.
Hybrid EVs can be seen as a part of the bridging process toward the full
transportation electrification. Our focus is on future scenarios where
electrification is already in its final steps and where full EVs are a
dominant technology. Therefore, we do not explicitly model the hybrid
EVs in this paper.
2.2. EV-based vs. CS-based smart e-mobility model
We use the graphs in Fig. 3 to describe the differences between the
EV-based and the CS-based smart e-mobility models. The graphs to the
left show charging profiles of the three EVs, while the ones to the right
show charging profiles of the three CSs. All graphs are created from the
same data, but observed from different viewpoints: graphs to the left
are relevant for the EV-based, while the ones to the right are relevant
for the CS-based smart e-mobility model.
EVs in Fig. 3 are shown in different colors: EV1 – turquoise, EV2 –
orange, and EV3 – purple. Their respective OBC maximum powers
(OBC_LIM) are marked with straight lines: EV1 – low-power OBC
(4 kW), EV2 – medium-power OBC (8 kW), and EV3 – high-power OBC
(12 kW). The EVs can charge at three CS types: CS1 is a home charger
(4 kW) – green, CS2 is charger at work (8 kW) – blue, and CS3 is charger
at a shopping mall (12 kW) – red. EVs have different driving profiles.
EV1 has a home-work-home profile: it is connected to CS1 from midnight
to 07:00, drives to CS2 where it stays from 08:00 to 16:00, and drives
back to CS1, where it is connected from 17:00 to midnight. Charging
profile of EV2 is home-mall-home, while EV3’s profile is home-work-mall-
home. Each charging period is colored according to the corresponding
CS.
The CS charging curves are composed of the charging curves of the
EVs connected to it. For example, the graph for CS1 (upper-right in
EV 3
EV 2
EV 1
CS 3
CS 2
CS 1
...
...
EVB
EVB
EVB
CP
CP
CP
EV 3
EV 2
EV 1
CS 3
CS 2
CS 1
...
...
EVB
EVB
EVB
CP
CP
CP
Fig. 1. Illustrative example composed of three EVs and three CSs - general
overview.
Physical connecon
Market parcipaon – smart EV
Energy bids
Schedules
Market parcipaon – smart CS
Energy bids
Schedules
EVB EV CP CS Grid
Energy flow
Fig. 2. Physical connection and market participation of EV-based and CS-based
smart e-mobility models.
1
Currently this is done through aggregators due to energy bid thresholds in
most markets.
I. Pavić, et al. Applied Energy 272 (2020) 115153
2
Fig. 3) shows that all three EVs are connected to it from 00:00 to 07:00.
The power required at CS1 during that time is the sum of the OBC
powers of the EVs using it. EV2 (orange) is staying longer at CS1 (until
11:00), while EV1 (turquoise) comes back home earlier than others (at
17:00). Since EV1 and EV3 are at work during the morning and midday
hours, CS2 has two connected EVs from 08:00 to 16:00 (turquoise EV1
and purple EV3), and no connected EVs in other hours. EV2 goes to a
shopping mall, where it charges at CS3 from 12:00 to 21:00, while EV3
goes to the mall after work form 17:00 to 21:00 (third graph on the
right-hand side). The areas in the graphs to the right correspond to
stacked OBC powers, while the maximum CP power limits are indicated
with fixed straight lines. In instances where CP_LIM is lower than OB-
C_LIM, the CP is the limiting factor for charging power.
The lower graphs in Fig. 3 are aggregate curves based on the EVs’
behavior (on the left) and the CSs’ behavior (on the right). The colors
display which EV (on the left) or CS (on the right) contributes to the
aggregated behavior at a specific period of time. The outline curve is
the same in the left and the right graphs, meaning that if there is only
one central aggregation entity that oversees all EVs and CSs, it does not
matter whether it is defined as an EV- or a CS-based. However, it does
matter when multiple aggregators enter the market. Interesting re-
search concerning EV and CS measurements data sets can be found in
[11] where they observe similar issue of EV and CS viewpoints.
The areas with the yellow background in the graphs in Fig. 3 show
the EV state of energy (SOE) throughout the day. In graphs to the left,
each SOE curve corresponds to the corresponding EV, while in graphs to
the right only the SOE curve of EV3 is displayed for simplicity.
Both concepts base their predictions for available power and energy
on the accurate SOE estimations. Those estimations itself could be
highly uncertain due to differences in chemical structure of the cells
and due to different algorithms used for the estimations [12,13].
From the ecological perspective, EV batteries effect greenhouse
emission at both the production and the utilization stages. The
production stage contributes to around 150–200 kg CO
2
-eq/kWh ac-
cording to [14], where most of production-stage emissions are the re-
sult of battery manufacturing and material processing. Manufacturing
and processing are mostly nonflexible, meaning that the energy mix of
the power system defines the exact level of emissions. A solution to
lower the emission at the production stage is therefore decarbonization
of the power system. The concepts of smart EV charging does not di-
rectly lower the production emissions, but they do foster the power
system decarbonization. In other words, the EV-based e-mobility system
could significantly increase the share of renewable power in power
systems.
Research carried out in [15] concludes that the emissions related to
EVs during the utilization phase are by far the lowest in high-renewable
energy case studies. European Energy Agency confirmed that decrease
of emissions from transport electrification is significantly higher than
the increase in emissions due to higher electricity production to support
transportation electrification [16]. In this paper we assume that elec-
tricity price follows the renewable generation, i.e. low price indicates
abundance of renewable generation and vice versa. Therefore, the EV
scheduling by price minimization also tends to maximize renewable
generation utilization. However this is not always the case. Thus, if an
EV user wants to schedule its EV directly to maximize renewable gen-
eration, the objective function should be reformulated to consider the
amount of renewable generation in the system. In general, the proposed
EVBA concept allows decarbonization due to its better adaptability to
changes in the power system, resulting in reduced system operator’s
flexibility needs.
2.3. Data transfer
Different data forms must be exchanged between the EVs and the
CSs, which is essential for proper smart e-mobility operation in both the
EV- and CS-based system. In the EV-based system the CS data must be
Fig. 3. Illustrative example - daily curves for three EVs and three CSs; left figures - EV view on charging profiles, right figures - CS view on charging profiles.
I. Pavić, et al. Applied Energy 272 (2020) 115153
3
sent to EVs, while in the CS-based system the EV data must be sent to
CSs.
Required EV data are:
1. technical data – parameters such as OBC power levels, battery ca-
pacity, etc.,
2. infrastructure cost – expenses arising from EV usage apart from
mobility reasons, such as V2G battery degradation,
3. preferences – EV users’ desires related to charging, such as minimum
SOE under which an EV does not offer flexibility, targeted SOE at
some point in time, etc.,
4. behaviour – historic driving/parking data which serve as a base for
future EV behaviour forecasts.
Required CS data are:
1. technical data – parameters such as CP connector type and CP power
levels,
2. infrastructure cost – expenses arising from the CS usage for any kind
of charging and discharging, e.g. CS operation and maintenance
cost, CS investment return, and grid fees.
3. Issues and proposed solution
In the CS-based smart e-mobility system the CSs submit their in-
dividual bids in the market. Each of them runs their own optimization
algorithm based on their own predictions. However, this results in the
issues individually elaborated below, each followed by a proposed so-
lution using the EV-based concept.
3.1. Issue 1 – insufficient information on EVs’ behavior at other CSs
3.1.1. CS-based issue
The first issue is that a CS only tracks the EVs’ SOE in the periods
when they are connected to it. From the mathematical standpoint,
power to be charged/discharged and the SOE while the EVs are either
parked at other premises or driving are unknown and included in the
model as stochastic parameters. Only when EVs are connected to this CS
those values become controllable variables. If observing the SOE curve
of EV3 in Fig. 3, it is broken down into several segments (at points S1-
S3), where each CS can see only one part of it but not the entire daily
curve. This is a major drawback since the values of the (dis) charging
variables should come directly from forecasting the four main attributes
of each EV:
1. arrival time of vehicle v(
tv
ARR
),
2. SOE at arrival (
SOEv
ARR
),
3. departure time (
tv
DEP
),
4. required SOE at departure (
SOEv
DEP
).
For the CSs in the presented example, the following stands for EV3:
•CS1 forecasts
tDEP
and
SOEv cp, 1
DEP
at S1 and
tARR
and at S3’,
•CS2 forecasts
tARR
and
SOEv cp, 2
ARR
at S1’ and
tDEP
and
SOEv cp, 2
DEP
at S2,
•CS3 forecasts
tARR
and
SOEv cp, 3
ARR
at S2’ and
tDEP
and
SOEv cp, 3
DEP
at S3.
The CSs must do the same for all EVs coming to charge.
Mathematically, this is represented as follows:
= +
t
soe soe e e
if
· / ;
_ _ _
v cp
T
v t v t v t v t
,
,
EV , 1
EV ,
SCH SCH ,
DCH DCH
parked at observed CS
(1)
=
=
t t
soe SOE
else-if
;
v cp
v t v cp
,
ARR
,
EV
,
ARR
(2)
=t t
soe SOE
else-if
;
v cp
v t v cp
,
DEP
,
EV
,
DEP
(3)
t
soe v t
else
unconstrained , .
_ _ _ _ _
v cp
T
v t
,
,
EV
driving or parked at other CS
(4)
The first equation tracks an EVB while the EV is parked at the ob-
served CS (
v cp,
is a set of EVs vat charging point cp at time t), with
variables
soe e,
v t v t,
EV
,
SCH
and
ev t,
DCH
denoting the EV’s SOE, energy charged
and discharged, respectively, and
SCH
and
DCH
the corresponding ef-
ficiencies. Eqs. (2) and (3) set the
soev t,
EV
at arrival/departure based on
the SOE forecasts or requirements. The periods when an EV is driving or
parked at other CSs are not explicitly modeled and its behavior during
these periods can only be considered through the forecasted values of
unknown parameters, eq. (4).
The questions that inspired this research were: How would each of
the CSs forecast the four uncertain values (arrival time, SOE at arrival,
departure time and required SOE at departure) for all the EVs with
sufficient accuracy? How would they anticipate the EVs’ behavior while
driving and especially while at other CSs? One option is that each EV
sends its data to all the CSs where it could potentially park and charge.
Another option is that each CS sends its own forecasts for each EV to all
CSs in surroundings, i.e. all the CSs should optimize their portfolio in a
joint optimization or using separate optimizations with coupling SOE
constraints. On top of the issue of global optimality of such approach,
the amount of data to be transmitted becomes critical and data security
issues could easily render such model inapplicable.
3.1.2. EV-based solution
In the EV-based smart e-mobility system, the three EVs in Fig. 3
submit their individual bids to the market operator. Each of them runs
its own independent optimization algorithm based on own predictions.
Contrary to the CS-based system, each EV knows its behavior (SOE
curve) throughout the day wherever it is. From the mathematical
standpoint, power to be (dis) charged and the SOE is always known to
the EV. If the SOE curve of EV3 in Fig. 3 is observed, EV3 sees it as a
continuous line without interruptions at points S1-S3, while the CSs see
only their portion of this curve. The EV-based model can thus be
mathematically represented as follows:
= + +
soe
soe e e E e
v t
· / / ·
, ;
v t
v t v t v t v t v t
,
EV
, 1
EV
,
SCH SCH ,
DCH DCH ,
RUN RUN ,
FCH FCH
(5)
It sets the EVs’ SOE considering the SOE from the previous time step,
charging at a slow CS (SCH), energy discharged in V2G mode (DCH),
discharged for driving purposes (RUN), and energy charged at fast
charging stations (FCH). Compared to Eqs. (1)–(4) in the CS-based
system, this model observes and controls all variables at all time per-
iods. The forecasting effort is drastically reduced and simplified since
the EV predicts its own behavior, while in the CS-based system each CS
must predict behavior of a multitude of EVs. There is no need for the
EV-to-CS communication nor for additional CS-to-CS communication.
Each EV keeps its driving/parking information and its technical data to
itself and does not send any data to other entities. The complexity of
data flow is reduced, while its security is increased as compared to the
CS-based model.
3.2. Issue 2 – inability to transfer flexibility between CSs
3.2.1. CS-based issue
The second issue in the CS-based system relates to daily human
activities and the way the CSs are usually organized. In our example,
CS1 is a home charger and has access to the EVs mostly during the
night. On the other hand, CS2 has EVs connected to it only during
I. Pavić, et al. Applied Energy 272 (2020) 115153
4
daytime, while the EVs are at CS3 mostly during the evening periods.
When performing energy arbitrage, the energy should be shifted from
peak to low-price periods. Usually, the prices are lower during the night
(when the consumption is low) and midday (when PV generation is
high and load is at its local minimum), while the peak prices occur in
the morning and evening (when PV generation is low and consumption
high). The CSs aiming to perform energy arbitrage with EVs should thus
roughly follow the sequence: night
charging, morning discharging,
midday charging, evening discharging. CS1 has only one EV con-
nected to it in the morning and the evening so it cannot discharge all
the EVs at peak periods. At midday it does not have any EVs connected
to it and thus cannot recharge them. CS2 cannot transfer energy from
night to evening periods because it does not have any EVs connected to
it in the evening, but can discharge the EVs in the morning and recharge
them at midday. However, to have enough energy to discharge EVs in
the morning it must communicate with CS1 and request additional
charging (more than necessary for mobility). CS3 can discharge EVs in
the evening, but it needs to communicate the additional energy with
CS2.
3.2.2. EV-based solution
The EV-based concept follows the EVs throughout the day. EV3 in
Fig. 3 can provide optimal charge–discharge sequence following the
typical daily price curve elaborated above. It can charge during the
night at CS1 and discharge in the morning at CS2, where it can also
recharge around midday. Then, it can discharge in the evening at CS3
and start charging at CS1 late in the evening. In the EV-based system,
the EV flexibility can thus be fully exploited without the need for CS-to-
CS communication. To summarize, the proposed EV-based concept re-
sults in higher savings, no privacy issues and lower communication
burden.
3.3. Issue 3 – insufficient power constraints
3.3.1. CS-based issue
Throughout the day, EVs with their own OBC power capacities park
at CSs with various power capacities. This issue is illustrated in the
graphs to the right in Fig. 3, where each CP installed power capacity is
shown with a fixed value, CP_LIM, while the EVs’ OBC power con-
straints are shown as stacked colored areas. If the OBC power con-
straints are omitted, the CSs could end up scheduling higher power than
technically possible to deliver, e.g. EV1 at CS2. On the other hand, if the
OBC power constraint is higher than the CP power constraint, the CP
constraint is binding and does not affect the EV scheduling, e.g. EV2 at
CS1.
Such events can cause differences between the scheduled and de-
livered energy and lead to additional balancing costs. The OBC installed
power is an additional parameter that all EVs must communicate to the
CSs or CSs must anticipate, which can lead to errors. Furthermore, this
EV-to-CS communication is highly inconvenient due to large amount of
dynamic data as well as security issues.
3.3.2. EV-based solution
EVs change their location during the day. In our example EV1 and
EV2 park at two, while EV3 parks at three different locations. Since CSs
have different installed charging powers, the EVs must anticipate the
installed power of the CSs where they park. This is illustrated in Fig. 3
on graphs to the left, where each EV’s OBC installed power (OBC_LIM)
is shown as a fixed value, while the CSs’ capacities vary through the day
(visualized as stacked colored areas). If the CS power constraint is
omitted, the EVs whose OBC is of higher power than the CS’s maximum
power could schedule more charging power than possible in reality, e.g.
EV2 during night/morning parked at CS1.
As in the CS-based concept, both the OBC and CS maximum char-
ging power constraints need to be included in the optimization model.
However, most CSs publicly publish their chargers’ technical
parameters, such as connector type and installed power, and EVs can
easily download the required data. The EV-to-CS communication is
again avoided making the EV-based system easier to implement than
the CS-based system.
3.4. Issue 4 – incomplete costs
3.4.1. CS-based issue
Each EV must pay energy cost for its basic mobility charging in the
electricity market (through its CS supplier). Apart from energy ex-
penditures, each load must pay a grid fee (upper part of Fig. 2). CSs are
connected to the low voltage distribution grid and the grid fees account
for a significant share in their total costs transferred to the EVs. To
properly address the cost of EV charging, grid fees must be taken into
account.
2
Apart from energy cost and grid fees, there is a cost associated with
remuneration between the EVs and the CSs. When it comes to basic
mobility charging, EVs pay fees to the CSs to recover the operation and
maintenance costs, as well as the investment. However, when CSs use
EVBs for energy arbitrage or other actions beside basic mobility char-
ging, they should pay a fee to the EVs for using their battery since in-
creased battery cycling causes faster degradation. In the CS-based
system, a CS must obtain data from EVs on their infrastructure (battery)
costs. Again, the EVs must send their private data to all relevant CSs.
3.4.2. EV-based solution
In the EV-based system, EVs obtain data on CS infrastructure costs
and grid fees. Unlike the EVs, the CSs are public and already publish
their prices online to attract EVs. In the proposed EV-based system, EVs
must pay a fee to CSs whenever they use them for energy arbitrage and/
or basic mobility charging. The EV-to-CS communication is not neces-
sary as the relevant CS data are available online.
4. Current state-of-the-art, industry practices and proposed
concept
4.1. Literature review
State-of-the-art literature on smart e-mobility scheduling can be
divided into several research approaches. Table 1 summarizes the lit-
erature considering three topics (smart home/microgrids, EV ag-
gregators, smart parking lots/charging stations) and the way they
tackle the four issues detected in Section 3. Under Issue 1 we add an
intermediate step between the CS-based and EV-based concepts for
papers using equations similar to (5), but not specifying chargers or
considering only residential chargers.
4.1.1. Smart homes/microgrids
Smart home algorithms often include EVs as one of the demand
response appliances that help minimize the total home electricity bill
[17–21,24,27,28]. Papers [17,27] seek to optimize a smart home
comprising of demand response devices, PVs, energy storage and EVs to
cut down the peak power and electricity cost. Paper [18] consists of two
parts: EV charging scheduling algorithm for smart homes/buildings and
implementation of a prototype application for home/building EMS. In
[19] a detailed structure of a household user capable of energy trans-
actions between consumers and load-serving entities is presented. Au-
thors in [20] propose a heuristic method that suggests most suitable
charging/discharging instances for an EV battery in a time-of-day re-
gime. Paper [21] investigates the optimal sizing of PV, wind turbine,
and storage in a smart home with EV. In [24] the authors presented a
model for participation of sub-aggregators in the aggregation of EVs in
2
Generation facilities mostly do not pay the grid fees. In case of V2G dis-
charging, such fees could have a major effect on its financial profitability.
I. Pavić, et al. Applied Energy 272 (2020) 115153
5
a residential complex. In [28] authors propose an EV charge/discharge
management framework for the effective utilization of PV output
through coordination of home and grid energy management systems.
All these algorithms observe only a single EV at a single location, which
directly makes them susceptible to Issues 1 &2.
EVs and smart homes can also be grouped under a microgrid where
EVs act as flexibility providers [22,23]. In future interconnected smart
grid, EVs will be able to interact both with the smart communities (local
microgrids) and the central grid to offer their services [29]. The smart
building could also be considered a microgrid (including vehicle-to-
building control strategy to dispatch the EVs as a flexible resource)
where the objective function is minimization of microgrids/buildings
electricity costs [25]. Optimization of a microgrid could also be made in
a multi-objective manner where microgrid (containing EVs) is opti-
mized regarding cost-economy, operation-efficiency and system-se-
curity [26].Table 1 shows that papers related to home/microgrids are
mostly CS-based and focused on home-chargers with fixed power levels
(Issue 3) and consider only energy prices (Issue 4). Exception to the
standard CS-based models are papers [27,28], which model the EV
behavior throughout the day in a parking-driving sequence, but neglect
the possibility of charging at other CSs. In addition to home charging,
only paper [29] considers parking lots and charging stations, but as
independent entities capable of utilizing the EVs’ flexibility.
4.1.2. EV aggregators
Apart from observing a single CP or locational aggregation through
microgrids, EVs can be seen as a decentralized source scheduled by an
aggregator and without considering their location. Such models can
have various goals, such as minimizing the EVs’ total charging costs
[30,31,33,35,38,39,43], minimizing frequency deviations [32,36]
maximizing conditional value-at-risk [34], optimizing reserve provision
[37] or maximizing revenue [42,40,41]. Paper [30] investigates a joint
optimization of EVs and home energy scheduling, while [31] proposes a
two-stage charging scheme for an EV aggregator to minimize the
charging costs while taking uncertain renewable generation and ag-
gregator’s capacity into account. In [33,35] the authors describe a new
optimization algorithm for optimizing manual reserve bids of EV ag-
gregator. Paper [38] determines the optimal bidding strategy of an EV
aggregator participating in the day-ahead energy and regulation mar-
kets using stochastic optimization. Authors of [39] develop a smart
charging framework to identify the benefits of non-residential EV
charging to the demand aggregators and the distribution grid. Paper
[43] proposes necessary market adaptations to include EV aggregation
in electricity markets. Paper [40] proposes a multi-stage stochastic
model of a PEV aggregation agent to participate in day-ahead and
intraday electricity markets. On the hand paper [41] aims to determine
the potential value that EVs could generate by providing reserve and
identify EV user impacts on the provision of reserves.
Table 1 shows that papers related to EV aggregators mostly focus on
home chargers within the CS-based concept (in [39] only non-re-
sidential chargers are observed) (Issues 1 and 2) and consider fixed
power levels and only energy prices (Issues 3 and 4). For example, paper
[36] presents a CS-based framework where aggregators group CSs while
EVs migrate among them. On the other hand, authors of [42,43] do
indeed model EVs’ behaviour throughout the day, but only as avail-
ability periods at unspecified types of chargers, i.e. they do not address
the fact that EVs charge and discharge at other CSs as well.
Although papers [30–36,38,42,43,41] model EVs connected to the
distribution grid, they take into account only energy and/or balancing
prices without network fees or infrastructure costs (Issue 4). Paper [39]
apart energy tariffs take into account the peak demand chargers as well.
4.1.3. Parking lots/charging stations
In addition to residential parking, EVs can also be charged at
workplace/commercial/leisure parking lots or fast charging stations.
EVs generally park at parking lots for longer times and power capacity
of AC CPs is usually low to medium. On the other hand, EVs do not park
at fast (DC) charging stations but only stop to charge, resembling the
existing gas stations. Both the smart parking lot and charging station
algorithms aim either at maximizing the benefits [44,45,47–51,57], or
minimizing electricity costs [46,51–54] while preserving customers
expectations. Parking lots could be seen equal to conventional tech-
nologies in power system operation process where they provide both
energy and reserve [55]. Since many parking lots have integrated
photovoltaics, it could be beneficial to optimize the charging at char-
ging station and PV generation [56].Table 1 shows that papers related
to parking lots/charging stations are CS-based and specific locations are
observed without proper multiple power levels (Issue 3) or costs (Issue
4). In [54] authors proposed optimal bi-directional charging control
strategies to integrate electric vehicle in commercial and public parking
facilities into the power grid as distributed energy resources for demand
response programs by two-stage distributed optimization and water-
filling algorithm. Paper [44] studies the optimal EV charging sche-
duling in a workplace parking lot, powered by both the PVs and the
power grid. Research done in [45] solves the parking-lot EV charging
scheduling problem through a noncooperative game approach. In [47]
an optimization model for determining optimal mix of solar-based DG
and storage units, as well as the optimal charging prices for EVs has
been presented. Authors of [48] propose a centralized EV recharging
scheduling system for parking lots using a realistic vehicular mobility/
Table 1
Categorization of research papers related to Issues 1–4 (comm. – commercial; ch. – charging; inf. – infrastructure; deg. – degradation).
Issue 1 – insufficient information on EVs’ behavior at other CSs Issue 2 – inability to transfer flexibility between CSs
Literature type CS-based EV-based with only 1
CS
EV-based Households Work/comm. ch. station Multiple
hline Smart homes/
microgrids
[17–26] [27–29] –[17–23,27,28,24–26] –[29]
EV aggregators [30–41] [42,43] –[30–34,36,38,42,43],[39] [35,37,40,41]
Parking lots/ ch. stations [44–58] – – [50] [44–49,51–58] –
Proposed concept – – ✓ – – ✓
Issue 3 – insufficient power constraints Issue 4 – incomplete costs
Literature type Fixed CP or OBC only Both CP and
OBC
No grid/inf./deg. cost With grid fee/ inf. cost With deg. cost
Smart homes/ microgrids [17–22,27–29,24–26] [23] –[17,18,20–23,28,29,24–26] [19] [27]
EV aggregators [30,32–34,36–43] [31,35] –[30–35,37,38,43] [39] [36,40,42,41]
Parking lots/ ch. stations [44–46,48–52,54–56], – [47] [44–46,48–56],[47] [53,57,51]
Proposed concept – – ✓ - ✓/✓ ✓
I. Pavić, et al. Applied Energy 272 (2020) 115153
6
parking pattern. In [49] an online intelligent demand coordination of
EVs in distribution systems has been proposed. Paper [50] formulates
an optimization model with central scheduler aiming to maximize the
profit of smart household users. Authors in [51] propose an online
charging strategy for EV charging stations in distribution systems while
obeying power flow and bus voltage constraints. Paper [52] model a
game that aims to minimize the total electricity cost at the utility
company meanwhile maximizing the payoff of each charging station. In
[53] the authors propose a novel cooperative charging strategy for a
smart charging station in the dynamic electricity pricing environment,
which helps EVs to economically accomplish the charging task by the
given deadlines.
Papers [44–49] model workplace/commercial parking lots, while
[50,57] observes residential private and public parking lots. Similarly,
all the papers modeling CS operation tackle a specific CS connected to a
single point in the grid and managed by a centralized controller
[51–53], inflicting Issues 1 &2.
With respect to Issue 3, i.e. insufficient power constraints, papers
[44–46,49,50,57,51,55] use fixed CP power constraints at a parking lot
or a CS without considering the OBC maximum power. In [48] the
authors use one fixed value for OBC (the one of Nissan Leaf). Only
paper [47] defines both the EV and the CP power limits, but it only
considers CPs at their own parking lot. All the papers investigating CSs
use only chargers’ power limits without mentioning the OBC power
levels [51–53].
Unlike the majority of papers which do not consider any grid fees
(Issue 4), the cost of charging in [47] includes both the electricity price
and the grid fees, while [53,57] takes into account battery degradation
costs.
4.2. Industry practices and research projects
Current e-mobility related companies can be seen through three
business schemes: Charging Point Operators (CPOs), E-Mobility
Providers (EMPs), and energy-related companies (electricity suppliers,
grid operators). CPOs are the companies operating and maintaining a
pool of CPs, while EMPs provide charging services to EV users by en-
abling them access to CPs (authentication) and offering payment op-
tions. EVs have contracts only with EMPs who forward their customers’
payments to the CPOs. EMPs have contracts with many CPOs, while the
CPOs have contracts with energy suppliers as well as grid operators. If
energy arbitrage or flexibility provision through an aggregator is the
target, EVs and EMPs cannot directly provide it, only the CPOs can. This
is in line with the CS-based smart e-mobility, as illustrated in Fig. 4. On
the other hand, in the EV-based e-mobility approach the aggregator
must be connected to EVs or EMPs. Grid fees are still assigned to CPOs
because the physical connection does not change (see Fig. 2).
The Internet-of-Things (IoT), energy and e-mobility companies al-
ready took the CS-based path of the smart e-mobility [59–62]. The
smart charging in the current industry practices usually means sche-
duling charging for household users at low electricity tariffs or cutting
the peak load of larger CSs. Research projects such as [63–65] tackle
mostly the issue of V2G testing on bidirectional chargers without in-
tegrating an aggregator into a real-world e-mobility system.
It is clear that the e-mobility industry does not yet operate within
the EV-based smart e-mobility concept, which would change the role of
the main beneficiaries in the smart environment from CPOs to EMPs.
4.3. Proposed concept
The CS-based concept arises from a conventional way of addressing
the EVs – they are an electric load stationary connected at a specific
location to a specific CS. This CS does not have information about the
EV’s battery SOE prior and after the connection and must forecast those
values. In this sense, an EVA aggregates specific CSs physically located
at households, parking lots or dedicated charging stations and their
proper name should be EV Charger Aggregator or EVCA.
We argue that EVs should not be observed as conventional loads but
as mobile batteries. EVA should not aggregate specific CSs but the EVs
with their batteries. The new concept of EVA is therefore named EV
Battery Aggregator or EVBA. EVBA continuously monitors and records
EV information (SOE, planed trips) as a part of the future IoT concept.
CPOs should allow all EVs to connect without restrictions but for a
charging fee. CPOs should be understood as infrastructure operators
similar to transmission/distribution system operators and charging a
fee in a way that transmission and distribution fees (tariffs) are charged.
Additional benefits of the EVBA concept are the payment possibi-
lities. Slow chargers are usually part of other consumer facilities and
they are controlled within their smart environment (smart households,
buildings, parking lots, etc.). It is not quite clear how an EVCA can
aggregate CPs at someone else’s property. That is why each EV should
have its own independent metering device so energy to/from an EV can
be exactly measured as in the EVBA case.
Although EVBA is contrary to scientific research and current in-
dustry practises, as discussed in Sections 4.1 and 4.2, it is in line with
the ISO 15118 standard, which foresees two controllers essential for
deployment of a smart e-mobility system: an EV communication con-
troller and a CP communication controller. In such advanced commu-
nication architecture, the EVBA can easily communicate the schedules
to its EVs and the EVs can send all required data back to the EVBA. The
data transfer between EVs and CSs can be easily achieved through EV
and CP controllers.
5. Models
To demonstrate the arguments, models of both the EV-based (EVBA)
and the CS-based aggregator (EVCA) are formulated in the following
subsections and evaluated in the case study presented in Section 6.
5.1. Nomenclature
5.1.1. Abbreviations
BMS Battery management system.
CC-CV Constant-current-constant-voltage.
CP Charging point.
CS Charging station.
DOD Depth-of-discharge.
EV Electric vehicle.
EVBA Electric vehicle battery aggregator.
EVCA Electric vehicle charge aggregator.
Fig. 4. Position of an aggregator and grid operator in the CS-based and EV-
based concepts.
I. Pavić, et al. Applied Energy 272 (2020) 115153
7
LIB Lithium-ion battery.
OBC On-board charger.
OF Objective function.
SOE State-of-energy.
V2G Vehicle-to-grid.
5.1.2. Sets and indices
Set of charging points, indexed by cp.
Set of time steps, indexed by t.
Set of vehicles, indexed by v.
5.1.3. Input parameters
Cv
BAT
Capital battery cost of vehicle v(€).
C_
v t cp, ,
CP FCH
Charging point fee for fast chargers at charging point
cp (€/kWh).
C_
v t cp, ,
CP SCH
Charging point fee for slow chargers at charging point
cp (€/kWh).
Ct
EP
Electricity price during period t(€/kWh).
C_
v t cp, ,
G FCH
Grid tariff for fast chargers at charging point cp
(€/kWh).
C_
v t cp, ,
G SCH
Grid tariff for slow chargers at charging point cp
(€/kWh).
CAPv
BAT
Battery capacity of vehicle v(kWh).
D1
BAT
Fixed battery degradation coefficient for higher values
of depth-of-discharge.
D2
BAT
Variable battery degradation coefficient (based on
discharged energy) for higher values of depth-of-dis-
charge.
D3
BAT
Variable battery degradation coefficient (based on
depth-of-discharge) for higher values of depth-of-dis-
charge.
D
4
BAT
Variable battery degradation coefficient (based on
discharged energy) for lower values of depth-of-dis-
charge.
E_
cp
CP MAX
Maximum energy limit of charging point cp during one
time step (kWh).
E_
FCH MAX
Maximum energy limit of fast charging point during
one time step (kWh).
E_
v
OBC MAX
Maximum energy limit of OBC of vehicle vduring one
time step (kWh).
Ev t,
RUN
Energy consumed for mobility purposes of vehicle v
during time step t.
SOEv cp,
ARR
Anticipated SOE at time of arrival at cp of vehicle vin
a CS-based system.
SOEv
CV
SOE curve breaking point between CC and CV char-
ging phases of vehicle v(%).
SOEv cp,
DEP
Anticipated SOE at time of departure from cp of ve-
hicle vin a CS-based system.
SOEv
MIN
Minimum allowed SOE of vehicle v(%).
SOEv
MAX
Maximum allowed SOE of vehicle v(%).
SOEv
0
Initial SOE of vehicle v(%).
Tv cp,
ARR
Time step when vehicle varrives at charging point cp
in a CS-based system.
Tv cp,
DEP
Time step when vehicle vdeparts from charging point
cp in a CS-based system.
Tv cp,
OFF
Set of time steps when vehicle vwhen vehicle vis
disconnected from charging point cp in a CS-based
system.
Tv cp,
ON
Set of time steps when vehicle vis connected to
charging point cp in a CS-based system.
DCH
EV V2G discharging efficiency.
FCH
EV fast charging efficiency.
RUN
EV mobility discharging efficiency.
SCH
EV slow charging efficiency.
v t cp, ,
Matrix indicating whether vehicle vis connected to
charging point cp at time step t.
5.1.4. Variables
cv t,
DEG
Degradation cost of vehicle vat time t(€).
cEV
Overall cost of charging all EVs (€).
ev t,
DCH
Energy discharged from vehicle vat time t(kWh).
ev t,
FCH
Energy fast charged to vehicle vat time t(kWh).
ev t,
SCH
Energy slow charged to vehicle vat time t(kWh).
soev t,
EV
State-of-energy of vehicle vat time t(kWh).
5.2. Mathematical formulation of an EV-based aggregator
Objective function minimizes the total EV charging costs:
= + + +
+ + +
c
e C C C e C c
e C C C
min
( ·( _ _ ) ·
·( _ _ )) .
v t
v t t v t cp v t cp v t t v t
v t t
EV
,
SCH EP , ,
G SCH , ,
CP SCH ,
DCH EP ,
DEG
,
FCH EP G FCH CP FCH
OF
(6)
The first row in Eq. (6) corresponds to payments due to EV charging
at slow chargers, where
ev t,
SCH
is charged energy,
Ct
EP
is energy price,
C_
v t cp, ,
G SCH
is the grid fee for slow chargers
3
and
C_
v t cp, ,
CP SCH
is the CS fee. The
second row represents EV discharging income and cost of degradation,
where
ev t,
DCH
is the amount of discharged energy,
Ct
EP
is V2G revenue and
cv t,
DEG
battery degradation cost. The third row captures payments due to
EV charging at fast chargers,
4
where
ev t,
FCH
is the amount of charged
energy,
C_
G FCH
is the grid fee for fast chargers, and
C_
CP FCH
is the fast
CS fee. EV slow charger charging fees depend on the type of charger,
e.g. this fee is zero for home chargers. On the other hand, EV fast
charging is modeled using only one fast charging type and cost.In order
to add additional services to grid operators, the objective function
should be reformulated with new revenue streams/costs. For example,
provision of reserves would require addition of the reservation and
activation fees. Grid congestion management could be added by re-
formulating the grid fees and making them more expensive during the
peak periods etc.
Charging/discharging energy constraints are:
e e e v t, , 0 , ;
v t v t v t,
SCH
,
DCH
,
FCH
(7)
e E v t·_, ;
v t
cp
v t cp cp,
SCH
, ,
CP MAX
(8)
e E v t·_, ;
v t
cp
v t cp cp,
DCH
, ,
CP MAX
(9)
e E v t
_, ;
v t v,
SCH OBC MAX
(10)
e E v t
_, ;
v t v,
DCH OBC MAX
(11)
e E
v t
_·
, ;
v t v
soe
SOE CAP
,
SCH OBC MAX 1
1 ·
v t
v v
,
EV
CV BAT
(12)
e E v t·_, .
v t
cp
v t cp
,
FCH
, , FCH MAX
(13)
Constraint (7) imposes nonnegativity on all energy variables. Con-
straints (8) and (9) limit the energy charged/discharged at slow CSs
based on the mapping parameter
v t cp, ,
that determines which EV is
connected to which CP at each time step. As the EVs move between
3
Slow chargers refer to AC chargers, i.e. the ones that require OBC to convert
alternating to direct current.
4
Fast chargers refer to DC chargers, i.e. the ones that convert alternating to
direct current and circumvent the OBC. Therefore, the OBC capacity is not
relevant when using fast chargers.
I. Pavić, et al. Applied Energy 272 (2020) 115153
8
different CPs, maximum charging power depends on index cp. OBC
limits on EV slow charging and discharging are imposed by constraints
(10) and (11), respectively. The OBC power capacity
E_
v
OBC MAX
depends
only on the EV type. Constraint (12) additionally constrains the OBC
charging power at high state-of-energy (SOE) due to inherent nature of
the li-ion battery (LIB) charging process consisting of the constant-
current (CC) and the constant-voltage (CV) part. Parameter
SOECV
is
empirically obtained and indicates SOE value (in percentage) at which
the constant voltage phase starts. More information on this formulation
can be found in [32,66]. Finally, the fast charging power limit
E_
FCH MAX
is imposed by constraint (13).
LIB degradation is calculated as follows:
+
+
c C D D
D v t
·( · ·100
· ·100) , ;
v t v
e
CAP
soe
CAP
,
DEG BAT 1
BAT 2
BAT
3
BAT 1
v t
v
v t
v
,
DCH
BAT
,
EV
BAT
(14)
c C D
v t
·( · ·100)
, .
v t v
e
CAP
,
DEG BAT 4
BAT v t
v
,
DCH
BAT
(15)
LIB degradation depends on four main variables: charging/dis-
charging current, voltage, temperature and cell balance. In most LIB
applications the last two variables are kept at optimal operating point
by a dedicated battery management system (BMS) and they can be left
out of the degradation model. During slow AC charging the currents are
rather low (up to 0.2C
5
) and their impact on degradation is negligible.
Thus, the only variable that must be taken into account is voltage,
which is closely related to SOE, thus constraints (17) and (18) keep the
voltage within the allowed range. In order to consider degradation, a
penalization cost is introduced as in [67], but in a linearized form in
order to avoid binary variables [68]. Geometric surface of the linear-
ized degradation cost is modeled by constraint (14), which includes two
variables: discharged energy and depth-of-discharge (DOD = 1 – SOE).
Constraint (15) is an additional geometric surface binding at higher
values of SOE when surface from eq. (14) goes to zero or becomes
negative. Constraint (15) depends only on discharged energy. Para-
meters
D1 4
are obtained using the best-fit option applied to LIB de-
gradation data (life-cycle loss vs. DOD) from [69].
Energy balance constraints are:
= +
+
soe soe e e
E e v t
· /
/ · , ;
v t v t v t v t
v t v t
,
EV
, 1
EV
,
SCH SCH ,
DCH DCH
,
RUN RUN ,
FCH FCH
(16)
soe SOE CAP v t· , ;
v t v v,
EV MIN BAT
(17)
soe SOE CAP v t· , ;
v t v v,
EV MAX BAT
(18)
=soe SOE CAP v t· , 24;
v t v v,
EV 0 BAT
(19)
Eq. (16) is the main energy balance equation calculated for each
vehicle vand time step t. Energy accumulated during the current time
step must be equal to the energy accumulated in the previous time step
plus the energy withdrawn from the grid via slow or fast charging
points and minus the energy discharged for motion or back into the
grid. In the first time step the term
soev t, 1
EV
is substituted with
SOEv
0
,
which corresponds to energy stored in vehicle vbefore the first time
step. Constraints (17) and (18) limit the battery capacity of each EV,
while constraint (19) sets the minimum SOE in the last time step (i.e.
the SOE in the last timestep must be greater or equal the initial SOE).
5.3. Mathematical formulation of a CS-based aggregator
Mathematical model of the CS-based aggregator is:
min (1)
subject to
= +
+
soe soe e e
e v t T
(2) (10), (12) (14)
· /
· , ;
v t v t v t v t
v t v cp
,
EV , 1
EV ,
SCH SCH ,
DCH DCH
,
FCH FCH ,
ON
(20)
= =soe SOE v t T cp, , , ;
v t v cp v cp,
EV
,
ARR
,
ARR
(21)
=soe SOE v t T cp, , , .
v t v cp v cp,
EV
,
DEP
,
DEP
(22)
It contains all constraints as the EV-based aggregator model except
for (16), which is replaced with constraints (20)–(22). Energy balance
constraint (20) does not include energy discharge for driving as it only
tracks the EVs when they are connected to a CP. Hence the time domain
in eq. (20) is
Tv cp,
ON
. Eqs. (21) and (22) are used to set the anticipated SOE
at arrival and required SOE at departure from each CP.
6. Results and discussion
The models elaborated in Section 5are validated on the small test-
case which is elaborated in details in Section 2. The small test case
considers the most frequent trip combinations and therefore provides
adequate representation of the EV fleet while preserving simplicity and
readability of the paper. Issues 1 &2(insufficient information on EV
behavior at other CSs and inability to transfer flexibility between CSs)
are observed together as they both depend on the EVs’ daily SOE curve.
Issues 3 &4(insufficient power constraints and incomplete costs) are
addressed individually and only for the EVBA case, as their repercus-
sions are the same for both models.
6.1. Input data
The proposed model resembles a price taker scheme where an ag-
gregator forecasts prices in order to efficiently submit its energy bids in
the market. Although both the prices, driving activity and times of ar-
rival and departure from CPs are stochastic parameters, we consider all
parameters deterministic for better demonstration of optimality of both
formulations, as well as quantification of the resulting schedules.
We use historic energy prices data for year 2018 from EPEX power
exchange in France. Three sets are used resembling high, medium and
low volatility of electricity prices, as shown in Fig. 5. The high-volatility
prices date from Nov. 21, medium from March 11, and low from June
30. Each charger type has different grid and charger tariff fee, as listed
in Table 2. All grid fees are modeled using a two-tariff system: night and
day, and the fees are aligned with the ones in [70]. Grid fees represent
both transmission and distribution fees, while charger fees are used to
retrieve investment and cover for operation and maintenance costs of
the charging infrastructure. Generally, higher charger power results in
lower grid fees, but higher charger fees. Charger fees are obtained from
real fast charging fees in [71,72] reduced by average energy price and
grid tariff fees and scaled based on investment cost to match the cor-
responding charger type. The investment costs of chargers are from
[73].
Efficiencies used in this paper are as follows: slow charging
=0.95
SCH
, discharging for driving
=0.90
RUN
, discharging to drive
=0.85
DCH
, and fast charging
=0.80
FCH
. SOE parameters used for all
EVs are following:
= = =SOE SOE SOE1.00, 0.20, 0.80
MAX MIN CV
, and
=SOE 0.60
0
. Battery capacities are 20 kWh for EV1, 40 kWh for EV2
and 60 kWh for EV3. Battery degradation parameters are:
= = =D D D0.342900, 0.034030, 0.004287
1
BAT
2
BAT
3
BAT
, and
=D
4
BAT
0.008317
.
To highlight Issues 1 &2in the EVCA model, two different values of
SOEv cp,
DEP
are used. The first one corresponds to a conservative driver who
sets the SOE before every trip to at least 95% (nearly full), and we name
this model high-SOE. The second one corresponds to a risk-prone driver
5
C-rate is the ratio of the charging (or discharging) power and battery energy
capacity.
I. Pavić, et al. Applied Energy 272 (2020) 115153
9
willing to earn more for providing flexibility at an expense of its EV
range. This person sets the SOE before every trip to at least 60%. We
name this model low-SOE. Note that most models in literature assume a
conservative driver who always desires (nearly) full battery at de-
parture.
6.2. Issues 1 & 2
The results related to Issues 1 &2are displayed in Figs. 6–10. Results
in Fig. 6a indicate that in total, i.e. combined for all three EVs, the
EVBA model results in the lowest charging costs for all price volatility
scenarios, followed by the EVCA low-SOE, while the worst results are
achieved for the EVCA high-SOE model. Detailed individual EV costs
are shown in Fig. 7, where the EVBA model provides the cheapest so-
lution for all three EVs over all price volatility scenarios, while the two
EVCA cases alternate in terms of the quality of the solution. For EV1,
the high-SOE case is always a better option, while for EV2 the low-SOE
case is a better option for all price scenarios. For EV3 however, in low-
volatility price scenario the high-SOE case yields better results, while in
medium- and high-volatility scenarios the low-SOE case performs
better. The reason for EVBA superiority over the EVCA models are
twofold: (i) in the EVCA models the EVs are often charged at high prices
and (ii) their energy arbitrage opportunities are reduced due to strict
SOE requirements. Generally, all three models discharge most energy in
the high-volatility price scenario as such scenario favors arbitrage, as
can be seen in Fig. 6b. In the low-volatility scenario the EVBA model is
the least aggressive in V2G mode, but in the high-volatility scenario it
discharges the most energy. In all price-volatility scenarios the EVBA
model observes price differences during the whole day and adjusts its
discharging schedule accordingly. On the other hand, in EVCA models
the CSs are blind to prices outside of the timeframe when an EV is
connected to them and they need to adjust their discharging quantities
to keep the departing SOE at the minimum allowed level. This happens
even if this discharge incurs higher recharging costs at subsequent CSs.
In general, higher price volatility yields lower costs in all three
cases. However, the EVBA model is able to better monetize flexibility
over the day and the charging costs reduce drastically as the price vo-
latility increases (EV2 generates profit already in medium-volatility
price scenario). This is highly related to Issue 2 (transfer of flexibility
between CSs). Since the EVBA model observes EVs throughout the day,
it can schedule optimal amount of discharging when prices are high
allowing the EVs to drive to another CSs with sufficient SOE.
Issue 1 (problems with SOE prediction at EV arrival) are analyzed in
details in Figs. 8–10 for the highly volatile price scenario. In all three
figures the periods when EVs are parked at CSs, are shaded in the re-
spective CS color. In case of EV1 and highly volatile prices, the first
driving period precedes the periods of high prices. In the EVBA model,
EV1 charges before the first trip and discharges after, as shown in
Fig. 8b. It recharges before the second trip (during the low-price hours
13–16) and again discharges at the next CS. It charges for the last time
at the end of the day at low prices. A similar schedule is obtained with
the EVCA high-SOE model. However, CS1 is oblivious to the low prices
in the afternoon and slightly discharges EV1 in hour 7, as opposed to
the EVBA model that charges EV1 in hour 7 (compare Figs. 8b and 8c).
To make up for this lack of energy, the high-SOE EVCA model needs to
charge more energy in hour 14 than the EVBA model. This is sub-
optimal since the price in hour 14 is much higher than in hour 7. The
charging quantities in all the other hours are the same. Graph in Fig. 8d
indicates that the EVCA low-SOE model behaves quite differently than
the other two. Since the CS before the first trip only satisfies the EV’s
desired SOE of 60% at the departure and at the same time minimizes
costs of EV charging only at this CS, it significantly discharges EV1
before the first trip. When prices are highest, after the first trip, EV1
discharges much less energy than in the other two cases due to lower
SOE after the trip. Before the second trip, EV1 is again charged only to
satisfy the desired SOE at the next departure time, and therefore has
less energy to be discharged after the second trip (compare hours 19
and 20). Considering the SOE graphs and charging schedules from
Fig. 8, the conclusion is that the EVCA high-SOE model performs much
closer to the optimal EVBA model than the ECVA-low model.
In the case of EV2 and highly volatile prices (Fig. 9) the first driving
period takes place after the periods of high prices. In the EVBA model,
whose charging schedule is shown in Fig. 9b, EV2 charges early in the
Fig. 5. Three electricity price scenarios from EPEX taken for days with the
highest/average/lowest price volatility in 2018.
Table 2
Charger point (CP) data used for the simulations (kW and €/kW).
CP Type Description Power Grid Low Grid High CP Tariff
(kW) (€/kW) (€/kW) (€/kW)
1 Home 4 0.022840 0.047040 0.004000
2 Work 8 0.016120 0.033600 0.018300
3 Leisure 12 0.016120 0.033600 0.030000
4 DC Fast 100 0.010750 0.022840 0.200000
Fig. 6. Results related to Issues 1 &2, showing total charging costs and energy injection/extraction for all three EVs.
I. Pavić, et al. Applied Energy 272 (2020) 115153
10
morning and discharges before the first trip taking advantage of
peaking prices in hours 8–11. It fully recharges after the first trip (hours
15–17) to be able to fully discharge during hours 18–20. Energy for the
second trip is charged just before the trip, in hour 21, at very low cost.
The required SOE is achieved by charging EV2 after the final trip at low
cost (hours 23 and 24). Comparison of the EVBA charging schedule and
the low-SOE EVCA schedule in Fig. 9d, as well as the corresponding
daily SOE curves in Fig. 9a, indicates that the low-SOE EVCA model
behaves quite similar to the optimal EVBA model. The only differences
are as follows:
•The EVCA low-SOE model discharges less energy in hour 11 as it
requires at least 60% of SOE at departure.
•Due to higher SOE, the EVCA low-SOE model requires less charging
in hour 17. Since the electricity price in hour 11 is much higher than
in hour 17, this model overlooked an arbitrage opportunity between
those hours.
•Again, due to 60% required SOE, the EVCA low-SOE model dis-
charges less energy in hour 18.
•Due to higher SOE, the EVCA low-SOE model requires less charging
in hour 24. Again, it did not exercise arbitrage between hours 18
and 24 due to a required SOE level at departure.
The results of the high-SOE EVCA are shown in Fig. 9c. This model
does not take advantage of discharging at higher prices due to a more
constrained SOE requirement at departure and thus results in much
worse solution. For instance, instead of discharging in hours 8–11 as the
EVBA and EVCA low-SOE models, the EVCA high-SOE model is, due to
the departing SOE restriction, only able to perform partial discharge in
hour 9. This repeats again in the evening hours when the EVCA high-
SOE model is only able to perform discharge in hour 19, instead of
hours 18–20. As a consequence, the EVCA high-SOE model is left with a
lot of energy stored in the late evening hours. This energy is partially
discharged in the last two hours of the day, but at a relatively low
profit.
The EV3 case for the highly volatile prices is shown in Fig. 10. In the
EVBA model (Fig. 10b), EV3 charges before the first trip and discharges
after it to take advantage of peak hours 9 and 10. It recharges before the
Fig. 7. Results related to Issues 1 &2, showing total charging costs for each EV individually.
Fig. 8. Results related to Issues 1 &2, EV1 schedules for the highly volatile price scenario.
I. Pavić, et al. Applied Energy 272 (2020) 115153
11
second trip to be able to discharge again after the trip, thus performing
arbitrage. It again recharges before and after the third trip to meet the
required end-of-day SOE. Graphs in Fig. 10a indicate that optimal EVBA
case is similar to the high-SOE EVCA case during the morning and the
daytime, but during the evening it resembles the low-SOE case. The
morning charging period at CS1 (green area) ends at hour 7, when the
high-SOE EVCA model charges EV3 to 95%. This is quite similar to the
optimal EVBA model, which charges EV3 only to a slightly higher SOE.
At CS2 (blue area), the high-SOE model charges the EV again to 95%,
while the EVBA model charges it slightly below that value. The major
difference occurs in the evening hours at CS3 (red area), where the
high-SOE EVCA model again charges EV3 to 95% of its SOE, while the
Fig. 9. Results related to Issues 1 &2, EV2 schedules for the highly volatile price scenario.
Fig. 10. Results related to Issues 1 &2, EV3 schedules for the highly volatile price scenario.
I. Pavić, et al. Applied Energy 272 (2020) 115153
12
EVBA model charges it to only 33 kWh in hour 21. This demonstrates
the negative effect of constraint on the departure SOE in the high-SOE
EVCA model. EV3 is thus required to charge instead of discharge at very
high prices. Consequently, after the final trip it has more energy then
required by the end-of-day SOE constraint and CS1 (green area) dis-
charges it, but at a low gain, in hours 23 and 24.
The EVCA low-SOE case schedules EV3 quite differently before the
first and second trips. It does not charge as much energy since the re-
quired SOE before the trips is only 60%. This enables it to perform
arbitrage at CS1 and discharge a part of the energy in hour 7 just before
the trip (Fig. 10c). Since hours 9 and 10 are peak-price hours, it dis-
charges more energy and charges again in hours 13–16 at lower prices.
It again performs arbitrage in hours 19 and 21, but with much lower
energy volume than the EVBA model. Based on the conducted analysis,
we derive the following conclusions:
1. for EV1, the high-SOE EVCA model is close to the optimal EVBA
model;
2. for EV2, the low-SOE EVCA model is close to the optimal EVBA
model,
3. in the case of EV3, the high-SOE EVCA model is close to the optimal
EVBA solution until evening, but during the evening and night the
low-SOE EVCA case becomes more similar to the optimal EVBA
solution.
Therefore, without the EVBA optimization model there is no way to
decide what is the best required SOE at the time of departure to
maximally transfer flexibility and utilize daily energy arbitrage.
6.3. Issue 3
To analyze Issue 3 (insufficient power constraints), we examine the
results of the EVBA model with highly volatile prices using four dif-
ferent sets of power constraints. First, we use fixed power constraint of
4 kW throughout the day. Second and third sets of constraints use only
OBC and CP power constraints, respectively. The fourth set of con-
straints uses both the OBC and CP power constraints.
As shown in Fig. 11a, the minimum expected costs are obtained
when using only OBC power constraint, followed by the CP-only power
constraint, then both power constraints, while the highest cost is ob-
tained for a fixed 4 kW power constraint. This is a direct result of energy
arbitrage volumes shown in the same chart. In order to verify feasibility
of the obtained charging schedules, Fig. 11b shows the exceeded OBC
and CP limits. The green shaded areas indicate that the injected/ex-
tracted power exceeds the CP limit, while the orange shaded areas in-
dicate the surpassed CP limit. The CP power limit is exceeded in hours
3, 8–10, 23 and 24 by the OBC-only case as the OBC rated power is
higher than the CS1 rated power. On the other hand, the OBC power
capacity is exceeded in hours 15, 16, 19–21 by the CP-only case as the
OBC capacity is lower than the CP capacity during those hours. Cases
with fixed 4 kW power constraint and inclusion of both the OBC and CP
power constraints never exceed the power limits. Therefore, the cases
with only OBC and only CP power constraints provide higher revenues
only at first sight. However, their real-time operation cannot be phy-
sically carried out and they would suffer from additional balancing
costs not included in Fig. 11a. On the contrary, if EVs are too con-
strained, as in the case with fixed 4 kW power limit, the EV charging
schedule is overconstrained, which diminishes the arbitrage opportu-
nities. This brings us to conclusion that considering both the OBC and
CP power constraints results in optimal solution.
6.4. Issue 4
From mathematical perspective, Issue 4 (incomplete costs) deals
with different terms in the objective function. Fig. 12 shows that adding
the cost terms usually omitted in the existing literature significantly
reduces the attractiveness of energy arbitrage. Five objective functions
(OF) with different elements are observed:
1. OF1: base case with only the cost of electricity,
2. OF2: cost of electricity and battery degradation costs,
3. OF3: cost of electricity and grid tariff,
4. OF4: cost of electricity and CS tariff,
5. OF5: all the costs, including cost of electricity, battery degradation
costs, grid tariff and CS tariff.
The graph in Fig. 12a shows that the total cost rises from −4.0 €in
the electricity-only case to 3.6 €in the case with all relevant costs in-
cluded, which makes a huge difference in the EV charging economics.
The main factor are degradation costs (OF2 value is 2.2 €), while the
lowest impact has the CS tariff (OF4 value is −1.9 €).
The overall costs are in direct relation with the volume of arbitrage
as the spread in the price between the purchased and is the sold elec-
tricity needs to cover for additional costs of battery degradation and
tariffs. Therefore, OF5 results in the least charged energy, followed by
OF2, as shown in Fig. 12b. With respect to this, total discharged energy
reduced from 90,57 kWh in the OF1 case to a mere 4,07 kWh in the all-
costs case, as shown in Fig. 12c.
7. Conclusion
This paper has demonstrated on a small example the shortcomings
of the Charging station based concept, which is predominantly used in
the research community. The main drawback of this concept is that it
observes the electric vehicle batteries only when connected to a specific
charging station. This results in suboptimal charging schedules and
aggregator revenues. Furthermore, charging stations have to forecast
the battery parameters (arrival and departure times and SOE at arrival
Fig. 11. Results related to Issue 3; left figure - total costs for different sets of power constraints, right figure - EV2 chargins schedule for different power constraints.
I. Pavić, et al. Applied Energy 272 (2020) 115153
13
and departure), which further reduces the optimality of the charging
schedule.
As opposed to the charging station based concept, which aggregates
the charging stations, the proposed electric vehicle based concept ag-
gregates vehicles themselves. This enables optimal charging schedule
for each electric vehicle, regardless where it is charged. On top of this, it
resolves the communication issues as there is no need for electric ve-
hicles to send their private data to charging stations. Another issue with
the current literature is the lack of power constraints. This is related to
charging capacities of vehicles on-board charger and charging points, as
the lower of these two values is binding and, thus, both should be
considered in the models. The electric vehicle charger aggregator
concept requires vehicles to send the on-board charger capacity data to
charging stations in order to determine their future flexibility volume,
which is avoided with the electric vehicle battery concept. The final
issue we identified are incomplete costs of charging as majority of the
published papers do not consider grid fees or infrastructure costs. In the
charger aggregator model, this infrastructure are vehicles themselves,
which means they should send their costs to charging stations so an
charger aggregator can decide on its charging schedule. Again, the
proposed battery aggregator model requires charging stations, which
are infrastructure in this case, to send their costs to vehicles and these
costs are already public.
Charging station based system yields sub-optimal results for the
vehicle owners. The proposed electric vehicle based system where ve-
hicles take the leading role in electricity markets proved to be much
more economically attractive for the owners. This is especially the case
when volatility of electricity prices is high. In such case the electric
vehicle based model results in 3.87 times lower overall costs for the
three observed vehicles than the charging station based models.
Opposed to the electric vehicle based model, the analyzed charging
station based models cannot accurately anticipate the optimal arriving
and departing state-of-energy and cannot exchange flexibility among
stations. Also, the paper showed that insufficiently modeled constraints
and costs can steer the scheduling results in a wrong direction leading
to infeasible charging/discharging bids and higher actual operating
costs. Analysis of accurate power constraints points out the value of
higher installed power capacities both for on-board charger and ex-
ternal charging station equipment.
The proposed model and the presented results can be of significant
value for EV aggregators when developing business models and can be
applied to designing charging prices when approaching potential end-
users. The initial results suggest that integrating the proposed EVBA
approach could create substantial market advantage and result in
higher profits as compared to the traditional EVCA approach.
The validation on a small test case is a first step into the EV-based
smart e-mobility system research. It provides a proof that the EV-based
system yields better results than the traditional approach, however
further investigation is needed to fully capture and demonstrate the
significance of this improvement. Future research will focus on un-
certainty in electric vehicle based models and participation of an
electric vehicle battery aggregator in ancillary services markets and test
the electric vehicle based concept on a large fleet.
CRediT authorship contribution statement
Ivan Pavić: Conceptualization, Methodology, Software,
Investigation, Writing - original draft. Hrvoje Pandžić: Resources,
Writing - review & editing, Supervision, Funding acquisition. Tomislav
Capuder: Conceptualization, Resources, Supervision, Funding acquisi-
tion.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Acknowledgement
This work has been supported in part by the European Structural
and Investment Funds under project KK.01.2.01.0077 bigEVdata (IT
solution for analytics of large sets of data on e-mobility).
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