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Analyzing the impact of battery capacity and charging
protocols when dispatching electric vehicles for aircraft towing
Simon van Oosterom∗and Mihaela Mitici †
July 10, 2022
Abstract
The aviation industry aims for net-zero emissions by 2050. In this line, achieving climate-
neutral ground operations is one of the first objectives. Electric vehicles that tow aircraft during
taxiing are a promising technology to achieve climate-neutral ground operations. In this paper,
we consider the dispatching of electric towing vehicles at an airport. We study the impact of
the maximum battery capacity of these vehicles and the battery recharging protocols, on the
total number of electric towing vehicles required at an airport. We propose a mixed-integer
linear program to determine the size of the fleet of electric towing vehicles under various battery
capacities and various battery recharging protocols. We illustrate our model for one day of
operations at Amsterdam Airport Schiphol. The results show that 41, 29, and 24 ETVs are
required to tow all aircraft when batteries capacities of 100 kWh, 320 kWh, and 500 kWh are
considered, respectively. Compared with the best performing approach existing in literature, our
model reduces the required size of the fleet of electric towing vehicles by 27% when considering
a nominal battery size of 320 kWh.
1 Introduction
Striving to meet climate-neutral targets set by the Paris Accords [4], the aviation industry aims for
net-zero emissions by 2050 [6, 7]. For some actors, like the Schiphol Group airport operator [11],
the first step to achieve this is by creating climate neutral ground operations by 2030.
Aircraft taxiing has been shown to be a large contributor to airport ground emissions, and will
have to be addressed in order to achieve zero ground emissions. In fact, it has been shown that
around 56% of the NOxemissions at London Heathrow result from taxiing aircraft [3]. Additionally,
taxiing from and to the runway has been estimated to produce between 4% and 9% of the total
flight emissions [8].
One of the promising means to reduce emissions in the near future is to tow aircraft using
Electric Towing Vehicles (ETVs). The management of a fleet of ETVs is, however, a complex
logistical problem. It concerns the assignment of to-be-towed aircraft to ETVs, while ensuring that
enough time remains for the vehicles to recharge their batteries, which can take up to several hours.
An efficient management of the ETV fleet is key for a successful implementation.
ETV fleet management optimization has been addressed scarcely, and only with simple battery
recharging protocols. For instance, in Soltani et al. [12] the authors consider an ETV fleet where
∗PhD student, Air Transport Operations research group, S.J.M.vanOosterom@tudelft.nl
†Assistant Professor, Air Transport Operations research group, M.A.Mitici@tudelft.nl
1
each vehicle has to be assigned to a subset of flights from a given flight schedule such that the
environmental impact of the ETV fleet is maximized. The authors consider a charging protocol
where ETVs can only recharge during the night. As such, the energy available for each ETV is
limited, and hence it can tow only a limited number of aircraft. The same problem has been
addressed by Van Baaren and Roling [1], while allowing for multiple battery charges during the day.
This study assumes a charging protocol where ETVs can recharge their battery throughout the day,
and where their batteries are charged up to full capacity at each visit. The authors also assume
that ETVs charge for a fixed amount of time, irrespective of the remaining state of charge of the
batteries. This, however, results in an overestimation of the charging time. As a consequence, the
required vehicle fleet size is overestimated and the ETV available for towing are used inefficiently.
To address these limitations, we consider the management of a fleet of ETVs with a preemptive
charging protocol. In this protocol, the charging time of ETVs depends on the residual battery
charge, and allows for multiple partial recharging opportunities during the day of the operations.
Also, the ETVs do not necessarily recharge to their maximum capacity at each visit to a charging
station. All flights that are eligible to be towed are towed by ETVs. As such, the objective of our
optimization problem is to minimize the required number of ETVs to tow all aircraft. The output of
the model is an assignment of ETVs to aircraft throughout the day, as well as a battery recharging
schedule for each ETV. We formulate our model as a Mixed Integer Linear Programming problem.
We illustrate our approach for a day of operations at Amsterdam Airport Schiphol, where we
analyze the impact of the ETV battery size and used charging protocol. We compare our preemptive
charging protocol with the ones used in Soltani et al. [12] and in Van Baaren and Roling [1]. The
flight schedule from the 14th of December of 2019 is used, where 750 flights are considered eligible
to be towed. We consider a range of ETV battery capacities between 100 kWh and 500 kWh, where
500 kWh is sufficiently large to tow aircraft continuously. Special attention is given to the nominal
case where the battery capacity is 320 kWh. In this case, ETVs are able to tow about 10 aircraft
on a single charge.
The results show that the partial charging protocol provides a significant reduction in ETV fleet
size over the formulations used in Van Baaren and Roling and in Soltiani et al.. In the nominal
case (320 kWh batteries), the ETV scheduling model with a preemptive charging protocol requires a
fleet of 29 ETVs, whereas the methods from Van Baaren and Roling and from Soltani et al. require
40 ETVs and 66 ETVs, respectively. Second, we observe a significant trade-off between the ETV
battery size and the required fleet size. Decreasing the battery size from 320 kWh to 100 kWh
results in requiring 12 additional ETVs, whereas an increase to 500 kWh or more is required in
order to remove battery life as a constraining factor.
The remainder of this paper is organized as follows. In Section 2 the ETV scheduling problem
is introduced, and in Section 3 we describe the energy consumption model of the ETVs. A Mixed
Integer Linear Programming formulation of the ETV scheduling problem is presented in Section 4,
and this model is applied in a case study in Section 5. Finally, the conclusions of this study are
presented in Section 6.
2 Problem description - Electric Towing Vehicles scheduling
We consider the dispatchment of a fleet of ETVs for towing aircraft to and from gates and runways.
During the day, the ETVs may need to recharge their batteries. While recharging, the ETVs are
not available for towing. We study the impact of the maximum battery capacity of the and the
protocols for battery charging on the size of the fleet of ETVs.
2
2.1 Airport taxiway and service road network
We consider an airport with two road networks: the taxiway network, used by aircraft towed by
ETVs, and the service road network, used for ETVs not attached by an aircraft. The taxiway
network is given by a graph GX= (NX, EX) consisting of nodes NXand directed edges EX.
Distances on the taxiway network are given by dX:EX→R. The service road network, used by
ETVs to traverse the airport when not towing aircraft, is given by the graph GS= (NS, ES) with
nodes NSand edges ES. Distances on the service road network are given by dS:ES→R.
Let NRand NGdenote the set of runway entrance and exit nodes and gate nodes, respectively.
These are the locations where an aircraft can be picked-up or dropped-off by an ETV. These nodes
are in both the taxiway and serviceroad network (NR∪NG⊂NX∩NS). Finally, there are a number
of ETV recharging stations within the service road network: NCS ⊂NS. Figure 1 gives an example
of the airport road networks.
Runway
Terminal
R1
X1 G1
G2
S1
X2
CS
node on taxiway
node on serviceroads
node on taxiway/serviceroads
Taxiway road
Service road
Figure 1: Example of an airport taxiway network and a ser-
vice road network. Here NX={R1, X1, X2, G1, G2},EX=
{(R1, X2),(X2, X1),(X1, R1),(X1, G1),(G1, X1),(G2, X 2),(X2, G2)},NS=
{R1, S1, C S, G1, G2}and ES={{R1, S1},{S1, G2},{S1, CS},{C S, G1}}. The runway en-
trance and exit is located at node R1, and the gates are located at nodes G1 and G2. The charging
station is located at node C S.
We are interested in determining the minimum size of a fleet of ETVs such that all aircraft
operating a set of flights Aare towed. For this fleet of ETVs we will propose an assignment of ETVs
to tow specific flights from A, and a battery recharging schedule conform a charging protocol.
2.2 ETV specifications
We consider a single type of ETV to tow all eligible flights. These ETVs are equipped with a battery
of capacity Q, which has a gravimetric energy density of mq. The basic mass of an ETV, excluding
the battery, is given by m0. The total mass of an ETV is given by m=m0+mq×Q. The power
required by ETVs to traverse the airport is given by P, which is a function of the velocity and towed
mass. Finally, ETVs recharge their batteries with power Pc.
We assume that ETVs traverse the road networks with constant velocity and using the shortest
path. A velocity of vxand vsis maintained on the taxiway and service roads respectively. For any
two nodes m, n ∈NX, denote the shortest distance from mto non GX(using dXas a distance
metric) as dSP
X(m, n). Similarly, for two nodes m, n ∈NS, denote the shortest distance from mto n
in GS(using dSas a distance metric) as dSP
S(m, n). Both dS P
Xand dSP
Scan be computed with, e.g.,
Dijkstra’s shortest path algorithm.
3
2.3 Aircraft arrival/departure flight schedule
Let the interval Tdenote a day of operations at the airport, with a length of 24 hours. Let Adenote
the set of flights which arrives at or departs from the airport during Tand are eligible/certified to
be towed by an ETV. Each arriving aircraft is to be towed from its pick-up runway node in NR
to its drop-off gate node in NG; the reverse holds for departing aircraft. For an aircraft a∈A, let
np
a∈NG∪NRdenote its pick-up location and let nd
a∈NG∪NRdenote its drop-off location. The
time at which ais to be picked-up at np
ais given by tp
a∈T. As such, the drop-off time of aat nd
ais
given by td
a=tp
a+dSP
X(np
a, nd
a)/vX.
2.4 ETV battery charging protocol
By towing aircraft and driving across the service roads, ETVs deplete their battery. ETVs recharge
their batteries at one of the charging station in NCS . Charging is done with power Pc. At the end
of the day of operations, all vehicles return to a depot ndep ∈NCS to fully recharge their battery
before the start of the next day of operations.
In this paper we consider three different charging protocols:
1. ETV battery night-charging (NC): This battery charging protocol assumes that the ETVs
are recharged only after performing their last tow of the day. In other words, we assume that
the battery of the ETVs is large enough to support several towing tasks during a day of
operations. Recharging is required only during the night, when no more towing tasks need to
be performed. This protocol has been used in Soltani et al. [12].
2. The constant-time ETV battery charging (CTC): This battery charging protocol allows
for ETVs to charge throughout the day of operations. Under this protocol, every time ETVs
re-charge their batteries they are charged to full capacity. Battery recharging takes a constant
time Q/P c, irrespective of the residual charge of the battery. This protocol has been used in
Van Baaren and Roling [1].
3. The partial ETV battery charging (PC): This battery charging protocol allows for ETV
battery charging throughout the day, but permits preemptive charging. As such, ETVs may
leave the charging station without a full battery. The charge loaded in the battery depends
on the time spent at the charging station.
Fig. 2 shows a simple example of charging protocols NC, CTC and PC. For simplicity, in this
example we assume that towing an aircraft always requires 30% of the battery capacity of an ETV.
The NC protocol postpones charging for the night period, while CTC and PC protocols allow for
battery charging during the day.
3 ETV energy consumption
The energy consumed by an ETV per unit of time, P, depends on the velocity vand mass that it
is towing mtow:
P(v, mtow ) = µg(v)×(m+mtow )×g×v, (1)
µg(v) = µ0×1 + v/v0,(2)
4
PC protocol
CTC protocol
NC protocol
start of day end of day
time
100% 70% 40% 10% 70% 40% 10% 100%
100% 70% 40% 100% 70% 40% 100%
100% 70% 40% 10% 100%
Figure 2: Example of ETV battery re-charging schedules under charging protocols NC, CTC, and
PC. In this example, towing an aircraft always requires 30% of the ETV battery capacity (blue
blocks). ETV battery recharging is indicated by green boxes.
where µgis the coefficient of rolling resistance, which depends on the velocity and on the constants
µ0and v0. The gravitational acceleration is denoted by g. As such, the energy consumed by an
ETV while towing aircraft a∈Ais denoted by qX(a) and is given by:
qX(a) = dSP
X(np
a, nd
a)/vx×P(vx, ma) (3)
The energy required by an ETV to traverse the service roads (where mtow = 0) from nto m∈NS
is given by:
qS(n, m) = dSP
S(n, m)/vs×P(vs,0) (4)
For simplicity, we use the following notation for aircraft a, b ∈A:
qS
f(a) := qS(ndep, np(a)), qS
l(a) := qS(nd(a), ndep), qS
d(a, b) := qS(nd(a), np(b)),(5)
where qS
f(a) denotes the energy to drive from the depot to the pick-up point of a,qS
l(a) the
energy to drive from the drop-off point of aback to the depot. Finally, qS
d(a, b) denotes the required
energy to drive directly from the drop-off point of ato the pick-up point of b.
4 Model formulation
In this section, we propose a Mixed Integer Linear Programming (MILP) to optimally schedule a
fleet of ETVs for aircraft towing and battery re-charging. We consider multiple battery charging
protocols (see Section 2.4).
4.1 Notation
Depending on the assumed charging protocol, ETVs may have the opportunity to recharge their
battery between aircraft towing tasks. ETVs always use the charging station closest to the pick-up
point of their next task b, which is denoted by nC(b)∈NCS . We use the following abbreviations
for energy consumption:
qS
C1(a) := qS(nC(a), np(a)),(6)
qS
C2(a, b) := qS(nd(a), nC(b)) + qS(nC(b), np(b)),(7)
5
where qS
C1(a) denotes the required energy to drive to the pick-up point of aircraft a∈Afrom
nC(a), and qS
C2(a, b) denotes the required energy to drive from the drop-off point of bto the pick-up
point of avia nC(b).
Next, we define the sets of aircraft which can be towed by the same ETV consecutively. Let Ain
a
and Aout
adenote the sets of aircraft which can be towed before and after towing a, respectively. For
a∈A, let b∈Aout
aif td(a) + dSP
S(nd(a), np(b))/vs≤tp(b). For two tasks a∈A, b ∈Aout
a, let tC(a, b)
denote the available charging time between towing aand b. Let tC
l(a) denote the available charging
time after towing auntil the end of the day.
Under the CTC protocol, it is possible to charge between towing aand bif tC(a, b) is longer then
Q/P c, the time required to fully recharge a depleted battery. We denote this set by ACT C
a⊂Aout
a.
Under the PC protocol, it is possible to charge between towing aand bif tC(a, b) is positive and if,
after charging, the state of charge of the ETV at the start of towing bcan be larger than it would
have been if it did not charge. We denote this set by APC
a⊂Aout
a.
4.2 Decision variables
We consider the following decision variables in order to determine the order in which the aircraft
are towed:
xab =
1 if a, b ∈Aare
towed consecutively
0 else
xf
a=
1 if a∈Ais the
first an ETV tows
0 else
xl
a=
1 if a∈Ais the
last an ETV tows
0 else
(8)
Additionally, the qvariables follow the battery state throughout the day of operations:
qa∈[qX(a), Q] ETV battery state-of-charge at the start of towing a∈A(9)
4.3 Objective function
We aim to minimize the required size of the ETV fleet such that all flights from Acan be towed;
denote this number by nET V . We claim that nET V = minx,q {Pa∈Axf
a}. In order to see this, note
that all flights can only be towed by one ETV and hence that for a∈A,xf
a= 1 implies that a
unique ETV has to leave the depot and start its day by towing a. Conversely, if for a specific ETV
there is no flight that it serves first on the day, it is not towing any flights at all that day and hence
is not required.
4.4 Constraints
We consider the following constraints. These hold for all three charging protocols:
6
xf
a+X
b∈Ain
a
xba = 1 ∀a∈A, (10)
xl
a+X
b∈Aout
a
xab = 1 ∀a∈A, (11)
qa≤Q−xf
aqS
f(a)∀a∈A, (12)
0≤qa−xl
a(qX(a) + qS
l(a)) ∀a∈A, (13)
Q≤qa−qX(a)−qS
l(a)+Pc×tC
l(a)+Q×(1 −xl
b)∀a∈A. (14)
Constraint (10) ensures that each aircraft ais either the first towed aircraft of the day by an ETV or
is preceded by another aircraft that is towed. Constraint (11) ensures that each aircraft is either the
last towed aircraft of the day by an ETV or an ETV subsequently tows another aircraft. Constraint
(12) limits the battery charge at the start of the day, and Constraint (13) ensures that at the end of
the day the ETV has sufficient energy to reach the depot. Last, Constraint (14) ensures that there
is enough time to recharge the battery of an ETV at the end of the day.
NC protocol specific constraints
Under the NC protocol, charging is only performed after the last towing task (at the end of the day
of operations). Constraints (14) ensure that there is enough time for recharging before the start of
a new day of operations. Throughout the day, the battery charge depends only on what task has
been executed previously:
qb≤qa−xab(qX(a) + qS(a, b)) + (1 −xab )×Q∀a∈A, b ∈Aout
a(15)
This constraint limits the battery state-of-charge between two consecutively aircraft towing tasks.
CTC protocol specific constraints
Under the CTC protocol, charging is performed between two towing tasks if and only if the available
charging time in-between is large enough to fully recharge the battery. As such, the following two
constraints determine the state of charge of the ETV throughout the day:
qb≤qa−xab(qX(a) + qS(a, b)) + (1 −xab )×Q∀a∈A, b ∈Aout
a\ACT C
a,(16)
qb≤Q−xabqS
C(b)∀a∈A, b ∈ACT C
a.(17)
Constraint (16) is identical to constraint (15) of the NC-protocol, but only applies to the couples
of aircraft between towing which the ETVs battery cannot be fully charged. When this can be done,
it is replaced with Constraint (17), which resets the ETV battery to full capacity.
PC protocol specific constraints
Under the PC protocol, batteries may be partially charged throughout the day of operations. In
order to accommodate this, an additional constraint is added:
7
qb≤qa−xab(qX(a) + qS(a, b)) + (1 −xab )×Q∀a∈A, b ∈Aout
a\AP C
a,(18)
qb≤Q−xabqS
C(b)∀a∈A, b ∈AP C
a,(19)
qb≤qa−xab(qX(a) + qC(a, b)−Pc×tC(a, b)) + Q(1 −xab )∀a∈A, b ∈AP C
a.(20)
Constraints (18) and (19) are the same as Constraints (16) and (17) before. Constraint (20)
limits the ETV battery charge if a charging station is visited between towing two aircraft. This is
done by adding the charged energy PC×tC(a, b) to the ETV battery.
5 Case study
In this section, we apply the ETV scheduling models in a case study at Amsterdam Airport Schiphol
(AAS), using the flight schedule of December 14, 2019. First, we shall study the ETV schedules
for the different charging protocols assuming a single battery size in Subsection 5.1. After this, we
shall compare the optimal fleet size for different combinations of ETV battery sizes and charging
protocols in Subsection 5.2.
Figure 3 shows the map of AAS which we use for our case study, based one the Schiphol aerodrome
charts [10]. The runway and gate nodes are indicated by vertically hatched circles and the charging
stations (C1 up to C5) are indicated by horizontally hatched circles. The ETV depot is assumed to
be located at charging station C5. The service roads and taxiway network are indicated by dashed
and solid lines, respectively.
We consider the flight schedule of an entire day of operations at AAS, using flight data from
December 14, 2019. We assume that the narrow-body aircraft, 750 in total, are eligible to be
towed by an ETV. Figure 4 shows the distribution of arriving and departing narrow-body aircraft
throughout the day. Flights arrive/depart between 6AM (on December 14) and 3AM (on December
15). The masses of the towed aircraft are given by either the MTOW, for departing flights, or the
EOW, for arriving flights.
Finally, the ETV specifications can be found in Table 1. The ETVs use Li-Ion batteries with a
specific energy density of 6.25 kg/kWh [13].
5.1 Results: Nominal battery size
First, we consider a base case in which we assume that the ETVs will be equipped with batteries
with a capacity Q= 320 kWh. In this case, the NC, CTC, and PC protocols require a fleet size
of 66, 40 and 29, respectively. Figures 5a, 5b and 5c show Gannt-charts for the ETV schedules for
the NC, CTC and PC protocol, respectively. When an ETV is towing an aircraft, a solid blue bar
is displayed, and when it is recharging its battery, a hatched green bar is displayed. Specifications
of the schedules are detailed in Table 2, which gives the average number of towed aircraft, charging
cycles and utilization time per ETV. A charging cycle is given as a switch from discharging a battery
to charging. The utilization time is defined as the total time during which an ETV is either towing
an aircraft, driving across the service roads or charging, i.e. the total time it is not idle. Last, the
corresponding state-of-charge of the ETV of these schedules can be found in Figure 6.
As can be seen in the schedule, and in the schedule specifications in Table 2, using the NC
protocol has a drastic impact on the ETV utilization. Because of the choice to only recharge the
8
36C
18C
09
22
18L
27
06
C1
C2
C3
C4
C5
36L
22
27
04
24
B
C
D
E
F
G
H/M
Figure 3: Runways NRand gate nodes NG, together with taxiways (solid lines), service roads
(dashed lines) and charging stations (C1, ..., C5) at AAS. The map is based on the Schiphol aero-
drome charts [10].
06 08 10 12 14 16 18 20 22 00 02 04 06
Time [hh]
20
10
0
10
20
Number of flights
Arrivals
Departures
Figure 4: Distribution of tp(a) for all narrow-
body aircraft arriving and departing from AAS
on December 14, 2019.
Parameter Explanation Value
Q[kWh] Battery capacity 100 - 500
m0[kg] ETV base mass 12000 [1]
mq[kg/kWh] ETV battery en-
ergy density
6.25 [13]
Pc[kW] Charging power 100 [1]
µ0[-] Rolling resistance
coefficient
0.1 [2]
v0[km/h] Rolling resistance
base velocity
41.16 [2]
vs[km/h] Service road veloc-
ity
30 [5]
vx[km/h] Towing velocity 42.5 [9]
Table 1: Electric towing vehicle specifications.
battery once every day of operations, the number of aircraft which an ETV can tow is relatively
limited to just over 11 on average. Towing these aircraft and recharging the battery takes an ETV
roughly no more then half of the day of operations (e.g. from 7AM to 1PM for ETV 2), and thus
leaves the ETV out of service for the other half of the day. Hence, for this combination of Qand P,
night charging does not seem to provide an efficient solution.
When using the CTC protocol, the ETVs tow 18.75 aircraft on average (+65% compared to the
NC protocol) at the cost of requiring 1.85 charging cycles on average. In Figure 5b one can see that
9
the tows are distributed much more evenly throughout the day per ETV and that the utilization is
larger than when using the NC protocol. On the other hand, there are still relatively large gaps in
the schedule (e.g. between 4PM and 8PM for ETV 1) as a result of charging only if the time gap is
large enough.
Finally, when using the PC protocol the highest ETV fleet utilization is used, the ETVs tow 25.86
aircraft on average (+ 128% compared to the NC protocol) at the cost or requiring 4.17 charging
cycles. In Figure 5c, one can see that similar to the CTC protocol the ETVs tow aircraft evenly
distributed throughout the day, but that there are much less long gaps in which they are idle. This
is also reflected by the average utilization time of 12:26 hours.
10
06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00 02:00 04:00 06:00
Time [hh:mm]
2
6
10
14
18
22
26
30
34
38
42
46
50
54
58
62
66
Towing Vehicle
ETV schedule: night charging
Towing
charging
(a) ETV schedule for the night-charging (NC) protocol.
06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00 02:00 04:00 06:00
Time [hh:mm]
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
Towing Vehicle
ETV schedule: Constant-time charging
Towing
charging
(b) ETV schedule for the constant-time-charging (CTC) protocol.
06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00 02:00 04:00 06:00
Time [hh:mm]
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Towing Vehicle
ETV schedule: Partial charging
Towing
charging
(c) ETV schedule for the preemptive charging (PC) protocol
Figure 5: ETV schedules for the nominal use case with a battery capacity of 320 kWh for charging
protocols NC, CTC and PC. Blue bars indicate an ETV is towing an aircraft. Green hatched bars
indicate that an ETV is recharging its battery. 11
Charging Average
protocol Towed aircraft Charging cycles Utilization [hh:mm]
NC 11.36 1.00 05:29
CTC 18.75 1.85 08:55
PC 25.86 4.17 12:26
Table 2: Specifications of the ETV schedules from Figure 5 for the three corresponding charging
protocols. Towed aircraft, Charging cycles, and Utilization give the average number of towed aircraft,
charging cycles, and non-idle time per ETV.
06 08 10 12 14 16 18 20 22 00 02 04 06
Time [hh]
0
25
50
75
100
Battery SoC [%]
(a) SoC of the ETVs for the night-
charging (NC) protocol.
06 08 10 12 14 16 18 20 22 00 02 04 06
Time [hh]
0
25
50
75
100
Battery SoC [%]
(b) SoC of the ETVs for the
constant-time-charging (CTC) pro-
tocol.
06 08 10 12 14 16 18 20 22 00 02 04 06
Time [hh]
0
25
50
75
100
Battery SoC [%]
(c) SoC of the ETVs for the pre-
emptive charging (PC) protocol
Figure 6: State-of-Charge of the ETV batteries for the nominal use case with a battery capacity of
320 kWh for charging protocols NC, CTC and PC. These graphs correspond to the schedules from
Figure 5
12
5.2 Results: ETV fleet size vs ETV battery capacity
Last, Figure 7 shows the impact of the ETV battery capacity on the required towing vehicle fleet
size. We have varied the battery capacity between Q= 100 and Q= 500 kWh in steps of ∆Q= 20
kWh. For each value of Q, we have applied the models from Section 4 for each of the three charging
protocols, in order to obtain the minimum possible fleet size. The fleet sizes for each charging
protocol are graphed in Figure 7. It highlights the nominal case of Subsection 5.1, where Q= 320
kWh, with a larger gray marker. Finally, without battery life constraints, the minimum required
fleet size is 24 ETVs, and this line is also displayed in Figure 7.
100 150 200 250 300 350 400 450 500
Battery capacity [kWh]
20
30
40
50
60
70
80
90
100
Number of ETVs
Minimum possible = 24
Minimum required ETV fleet size
Protocol
NC
CTC
PC
Figure 7: Pareto front of the required number of ETVs to tow all eligible flights against the battery
capacity of an ETV, for each charging protocol (night charging (NC), constant time charging (CTC),
and partial charging (PC)). The nominal case where Q= 320 kWh is highlighted with a larger, gray,
marker. The smallest possible fleet size (when battery constraints are ignored) is 24 ETVs.
There are a number of notable features in Figure 7. First, for any value of Qthe ETV fleet size
is always smallest for the PC protocol, followed by the CTC protocol and by the NC protocol. For
the PC protocol, the fleet size varies between 41 and 24 ETVs, such that for Q= 500 kWh, the
battery capacity is no longer a limiting factor in the ETV schedule. For the CTC protocol, the fleet
size varies between 45 and 40 ETVs. Finally, the vehicle fleet for the NC protocol varies between
210 ETVs, outside the bounds of this graph, and 45 ETVs. In the best case scenario, the CTC and
the NC protocol require a 67% and 87% larger fleet then the PC protocol, respectively, but in all
cases it provides the smallest fleet size.
The second notable feature of Figure 7 is that the vehicle fleet size for the CTC protocol is almost
not sensitive to the battery capacity. Instead of decreasing with increasing battery size, the ETV
fleet size remains more-or-less constant, and even attains its smallest value at Q= 320 kWh, almost
in the middle of the domain of Q. This could be explained by the fact that when the battery size
increases, and thus the number of aircraft which can be towed on a single charge with it, the time
that an ETV has to retire to charge its battery also increases with it. Hence on average, the number
of aircraft which can be towed within a given time remains constant. This continues up until the
moment when the battery size is sufficiently large to not form a constraining factor in the schedule
anymore.
13
This is opposed by the NC protocol, which is very sensitive to the ETV battery size. This can
be explained by the fact that the number of aircraft which can be towed by an ETV on a single
charge is approximately linear in Q. As each ETV in the NC protocol only uses one battery charge,
the number of required ETVs should be proportional with 1/Q, which corresponds to the results.
6 Conclusion
This paper compares the effect of battery size and recharging protocol on the impact which elec-
tric towing vehicles (ETVs) are able to make at large airports. This is done by using a Mixed-
Integer-Linear-Optimization program to determine the smallest possible ETV fleet required to tow
all considered aircraft. We consider three versions of this model, corresponding to the three charging
protocols: night, constant time, and partial charging. The battery size considered ranges from 100
kWh to 500 kWh.
We have applied the model in a case study at Amsterdam Airport Schiphol and found that the
partial charging protocol yields a significant improvement over the other protocols. The considered
flight schedule consists of 750 narrow-body aircraft, arriving throughout the day of operations. In
the nominal case, when we consider an ETV battery of 320 kWh, the required fleet size is 66, 40
(-39%) and 29 (-56%) for the night charging, constant time charging, and partial charging protocol,
respectively. Additionally, it was found that the constant time charging protocol is almost insensitive
to the battery size.
Future research could consider creating a cost-benefit analysis of the environmental impact as
a function of the ETV fleet size. Additionally, the economic impact of using more charging cycles
could be studied.
Acknowledgment
This research has received funding from the European Union’s Horizon 2020 research and innovation
program under grant agreement No 892928 .
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