1
Analysis of Optimal Charging Points Location and
Storage Capacity for Hybrid and Electric Buses
An
´
alisis de ubicaci
´
on
´
optima de puntos de carga y
almacenamiento de energ
´
ıa para autobuses h
´
ıbridos y el
´
ectricos
Abstract— Aiming to be more attractive in a very
competitive market, hybrid and electric buses need to
reduce their acquisition and operation cost (TCO - Total
Cost of Ownership) compared to conventional buses. In this
regard, the sizing of the onboard energy storage system and
the charging infrastructure becomes a key design stage.
Optimal sizing of these factors is necessary to provide
adequate autonomy and service, despite the impact on high
investment costs for the manufacturer and fleet operator.
Furthermore, the complex interrelationship between these
parameters makes the best-performed system design a
challenging process. To face this issue, this paper proposes
an optimization methodology for the onboard storage
capacity of a power system and location as well as charging
stations power to reduce TCO (total cost of ownership)
in hybrid and fully electric bus routes. For this purpose,
several routes have been selected as a case study in
Donostia city (Spain) where the proposed methodology has
been assessed techno-economically regarding cost factors
such as storage systems, charging infrastructure, fuel, and
the electricity grid.
Keywords— Electric bus, hybrid bus, TCO optimiza-
tion, charging infrastructure, energy storage system.
Resumen— Con el objetivo de ser m
´
as atractivos
en un mercado muy competitivo, los autobuses h
´
ıbridos
y el
´
ectricos necesitan reducir sus costos de adquisici
´
on
y operaci
´
on (TCO - Total Cost of Ownership) con res-
pecto a los autobuses convencionales. En este contexto,
el dimensionamiento del sistema de almacenamiento de
energ
´
ıa a bordo y la infraestructura de carga es una etapa
clave del dise
˜
no. Un
´
optimo dimensionamiento de dichos
factores es necesario para ofrecer una adecuada autonom
´
ıa
y servicio, a pesar de repercutir en altos costos de inversi
´
on
para el fabricante y operador de la flota. Adem
´
as, la
compleja interrelaci
´
on entre estos par
´
ametros hace que el
dise
˜
no
´
optimo del sistema sea un proceso desafiante. Como
contribuci
´
on en esta tem
´
atica, este trabajo propone una
metodolog
´
ıa de optimizaci
´
on de la capacidad del sistema
de energ
´
ıa y ubicaci
´
on y potencia de los puntos de carga
para reducir el TCO en rutas de autobuses h
´
ıbridos y
el
´
ectricos. Para tal efecto, se ha seleccionado como caso de
estudio varias rutas en la ciudad de Donostia (Espa
˜
na)
en las cuales se ha evaluado tecno-econ
´
omicamente la
metodolog
´
ıa propuesta atendiendo a factores de costos
tales como: sistema de almacenamiento, infraestructura de
carga, combustible y energ
´
ıa desde la red el
´
ectrica.
Palabras Clave— Autob
´
us el
´
ectrico, autob
´
us h
´
ıbrido,
optimizaci
´
on de TCO, infraestructura de carga, sistema de
almacenamiento de energ
´
ıa.
I. INTRODUCTION
The transportation sector accounted for 24% of the
fuel combustion related CO2 emissions in 2017 and is
the only sector showing an upward trend [1]. Therefore,
essential objectives in transportation involve the reduc-
tion of pollutant emissions while managing the continu-
ous growth of the sector. Recent studies [2] emphasize
the leadership role of electromobility to achieve these
objectives.
One potential candidate for the massive adoption of
electric powertrains is the field of urban public transport,
due to its specific characteristics – predefined and recur-
rent routes, or several start-stop phases with low average
speeds. The Full Electric Bus (FEB) has emerged as a
promising solution in this field. Similarly, the Hybrid
Electric Bus (HEB) is understood as an intermediate step
between conventional buses and the mentioned FEBs.
Nevertheless, the high upfront costs currently slow
down the large-scale adoption of these alternative bus
Josu Olmos
1,♠
, Jon Ander López-Ibarra
1
, Haizea Gaztañaga
1
, Victor Isaac Herrera
2,♣
1
IKERLAN Technology Research Centre Energy Storage and Management Area Gipuzkoa, Spain
2
Escuela Superior Politécnica de Chimborazo, Facultad de Informática y Electrónica, Riobamba, Ecuador
Email:
♠
jolmos@ikerlan.es,
♣
isaac.herrera@espoch.edu.ec
Fecha de Recepción: 16 – May – 2019 Fecha de Aceptación: 18 – Jun – 2019
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topologies. To face this issue and be cost competitive in
a very demanding market, HEBs and FEBs need to offer
better Total Cost of Ownership (TCO) values compared
to conventional buses. The Energy Storage System (ESS)
sizing and charging infrastructure definition emerge as
crucial design steps influencing the TCO, as several
studies have already highlighted [3], [4].
Sufficient ESS capacity is required for appropriate
vehicle autonomy, especially in the FEB topology. How-
ever, a huge sizing increases the initial cost, as it usually
represents around a quarter of the bus total price [2].
Besides, ESS elements suffer from capacity fade over
their life, which makes them show shorter lifespans
than the associated power electronics [5]. A low ESS
degradation must be secured if a favorable TCO is aimed.
The charging infrastructure further increases the ini-
tial costs. Different strategies can be deployed, which are
divided in charging overnight and opportunity charging
(i.e., charging through the route) [6]. Charging overnight
requires a huge ESS, and is limited depending on the
daily use of the bus. Besides, opportunity charging allows
a smaller ESS, but increases the infrastructure costs.
Different locations for the Opportunity Charging Points
(OCPs) are possible considering the bus stations.
The ESS and the charging points need to be ap-
propriately sized and located to reduce the TCO while
providing the required energy demand. In this approach,
the characteristics of the bus route need to be considered
for the best-performed design, since the TCO is highly
susceptible to the specific context of each project [3].
In this regard, the paper presents an optimization
approach employing ESS sizing, OCPs sizing, and OCPs
location, to improve the TCO of HEB and FEB lines.
The proposal includes the bus route modeling with real
GPS data and simulations of the vehicle performance. A
use case is selected, and techno-economically evaluated
regarding factors such as ESS cost, OCPs cost, fuel cost,
electricity cost, and several buses driving in the line.
II. S
CENARIO OVERVIEW
The optimized scenario corresponds to Line 28 of the
local bus service of Donostia/San Sebastian (Spain). The
general characteristics of the bus line are shown in Table
I. Fig. 1 depicts the altitude profile of the bus route. As
seen, for the HEB, a fully electric driving zone has been
considered in the city center.
Based on the information of the proposed scenario,
a speed profile has been created considering variables
such as average time to cover the line, maximum speed,
normal traffic, turns, and possible traffic lights. Stop
time of the 20s has been considered for the intermediate
stations and 5 minutes for the terminal station. The
obtained speed profile is also depicted in Fig. 1. When a
charging activity is considered in an intermediate station,
the stop time is increased to 2.5 minutes, keeping the
remainder.
The vehicle models consist of a series HEB and a
FEB, both containing an ESS composed of Batteries
(BTs). The general schemes of the models are depicted
in Fig. 2. Besides, the general characteristics of the con-
sidered vehicles are introduced in Table II. The models
and the technical characteristics are based on the HEB
with hybrid ESS proposed in [5]. In the case of the HEB,
the combustion engine has been downsized to enhance
the electric performance.
Table I. ROUTE CHARACTERISTICS
Line 28: ”Amara-Ospitaleak”
Round Trip 12.3 km
Time to cover the line 48’
Bus Stops 29
Buses driving simultaneously 10
Daily driving time 16 hours
Table II. VEHICLE CHARACTERISTICS
HEB FEB
Dimensions (L/W/H) [m] 12/2.55/3.4 12/2.55/3.4
Passenger Capacity (typical/max.) [-] 50/95 50/95
Electric Motor Power [kW] 196.5 196.5
Combustion Engine Power [kW] 85 -
BT Branch Capacity [kWh] 12 12
III. OPTIMIZATION METHODOLOGY
The proposed optimization approach aims to define
the optimal OCPs distribution (
Loc
OCP
), OCPs power
(
P
OCP
), and BT capacity (Cap
BT
) from the TCO point
of view. For that purpose, a methodology based on multi-
objective optimization has been developed. The multi-
objective approach aims to perform a techno-economic
analysis for evaluating the influence of each factor af-
fecting the TCO.
The TCO is an economic performance indicator,
which includes manufactured price and the costs for
maintenance, operation, energy distribution, infrastruc-
ture, emission, insurance, and end-of-life [7]. From this
approach, the following aspects have been identified as
key factors for improving the TCO: ESS cost, OCPs cost,
fuel cost, and electricity cost. Therefore, the proposed
optimization is focused on these terms.
The general overview of the proposed methodology is
depicted in Fig. 3. The approach is an iterative sequence
in which several steps (stages 2-5) are repeated. At each
iteration
i a set of feasible solutions is evaluated. The
stages are defined as in the following subsections:
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0
10
20
30
40
50
Speed (km/h)
Time (s)
0
Speed Profile
Full Electric Zone
Bus Station
500 1000 1500 2000 2500 3000
0 2 4 6 8 10
0
40
12
Distance (km)
Altitude (m)
Altitude Profile
Full Electric Zone
Bus Station
80
120
Figure 1. Speed and altitude profile of the use case.
EM
Model
DC
AC
BT
Model
DC
AC
Aux. load Crowbar
EG
Model
Genset
DC
DC
ICE
Model
EM
Model
DC
AC
BT
Model
Aux. load Crowbar
DC
DC
Charger
Charger
(a)
(b)
Figure 2. Vehicle Models: a) HEB. b) FEB.
Stage 1: Definition of Route Characteristics
Before initializing the optimization iterations, the
data presented in Fig. 1 is defined. The geographical
information of the route (i.e., the route path, location
of bus stations, and location of possible disruptions or
traffic lights) is obtained from .gpx files and processed
in Matlab. That information allows for creating a realistic
speed profile, as outlined in Section II.
Besides, some of the bus stops are defined as poten-
tial OCPs. For that purpose, the approach for
Loc
OCP
depicted in Fig. 4 is deployed. A maximum number of
potential OCPs (
n
OCP max
) is defined by means of the
expression in (1), which calculates the required charging
activities that fulfill the route demand (
T
Cons
) when the
bus works in full electric mode with the minimum BT
capacity (
min Cap
BT
(i)):
Simulation of
bus performance
Final Results
Next
set
All
set of variables
analyzed?
- BT sizing
- OCPs location
- OCPs rating power
Definition of
Route Characteristics
- Initial investment
- BT life forecast
- Grid consumption
- Fuel consumption
Economic Evaluation
N
N
Y
Y
Definiton of Current
Set of Variables (i)
Stage 1
Stage 2
Stage 3
Stage 4
Technical
Evaluation
fulfilled?
Stage 5
- Route Path
- Bus Stations
- Possible Disruptions
- Demand fulfilllment
- Charging fulfillment
- Evaluation at max.
bus capacity
Figure 3. Optimization Approach Diagram.
n
OCP max
=
T
cons
min Cap
BT
(i)
(1)
The route is therefore divided in
n
OCP max
zones, and
the bus stops located closer to the end of each zone are
defined as potential OCPs.
Stage 2: Definition of Current Set of Variables
At each optimization iteration
i the following vari-
ables are defined and introduced in the simulation model:
OCPs location (
Loc
OCP
(i)), OCPs power (P
OCP
(i)),
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and BT capacity (Cap
BT
(i)). Expressions (2-4) define
the variable bounds, and Fig. 4 shows how they are
introduced in the simulation model.
Loc
OCP
(i) ∈{[0 0 ... 0], [0 0 ... 1], ... [1 1 ... 1]} (2)
P
OCP
(i) ∈{P
OCP 1
,P
OCP 2
, ... P
OCP j
} (3)
Cap
BT
(i) ∈ Cap
br
·{1, 2, ... k} (4)
where
j defines the number of the considered charg-
ing powers,
Cap
br
the capacity of a single BT branch,
and
k the number of maximum possible BT branches
connected in parallel.
-
Loc
OCP
(i) is a binary vector and defines which
of the potential OCPs (defined in Stage 1) are equipped
with a charger in the current iteration. The length of
the vector is defined as the number of potential OCPs,
and the number of evaluated OCPs in the current loop
(
n
OCP
(i)) as the aggregation of the binary vector terms:
|Loc
OCP
(i)| = n
OCP max
(5)
n
OCP
(i)=sum [Loc
OCP
(i)] (6)
-
P
OCP
(i) defines the power rating of the OCPs.
-
Cap
BT
(i) is a multiple of the capacity of one BT
branch (
Cap
br
). Each BT branch is constructed by series
connected BT cells in order to reach the voltage of the
electric powertrain DC bus.
Charging Power
Definition
Zone 1
Zone 2
Zones
Division
0
LocOCP(i) Vector
Zone 3
OCPs
Definition
1 0 1
100 kW
200 kW
500 kW
Number of
Branches
Definition
BT CellBT CellBT Cell
BT CellBT CellBT Cell
BT CellBT CellBT Cell
1 BT Branch
2 BT Branches
k BT Branches
BT CellBT CellBT Cell
3 BT Branches
Loc
OCP(i)
POCP(i)
CapBT(i)
Zone
nOCPmax
Normal Bus Stops
Potential OCPs
OCPs in individual i
Figure 4. Definition of Variables.
Stage 3: Simulation of Bus Performance
The HEB and FEB models (Fig. 2) have been imple-
mented in Matlab/Simulink as proposed in [5]. At each
iteration
i, the performance of the HEB or FEB with the
current variables is simulated, and the necessary data for
the technical and economic evaluations is obtained. The
model simulates the performance of the vehicle during
a round trip (Fig. 1), and the results are extrapolated to
the whole vehicle life.
Stage 4: Technical Evaluation
The simulation results are technically evaluated, con-
sidering the following aspects:
Energy and power requirements: the demand profile
of the vehicle must be fulfilled step-by-step.
Energy balance: the considered charging activities
must allow the ESS to start the next cycle (one round
trip) in similar conditions.
Besides, a new simulation is performed to check if
the previous two constraints are fulfilled when increasing
the vehicle demand (i.e., when the passengers capacity
is in the maximum). If all constraints are fulfilled, the
algorithm continues to Stage 5.
Stage 5: Economic Evaluation
The economic evaluation consists of the TCO calcu-
lation, which is, in turn, the fitness function of the multi-
objective approach. For this evaluation, the results of the
first simulation of Stage 4 are used. The fitness function
is defined as follows:
min T CO(i)=[C
BT
(i),C
ch
(i),C
f
(i),C
el
(i)] (7)
where
C
BT
(i)[e/day] refers to the BT adquisition
and replacement cost,
C
ch
(i)[e/day] to the charging
infrastructure cost,
C
f
(i)[e/day] to the fuel cost, and
C
el
(i)[e/day] to the electric charging cost. These terms,
previously identified as key factors affecting the TCO,
correspond to the objective functions of the multi-
objective approach.
• BT Cost:
C
BT
=
C
BT Ca
+ C
BT Re
t
OP
[e/day] (8)
being
C
BT Ca
[e/year] the annualized capital cost
related to the initial investment of the BT pack,
C
BT Re
[e/year] the annualized replacement cost of the
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BT pack, and t
OP
[days] the bus operation days per year.
The expression for
C
BT
Ca
stands as follows:
C
BT
Ca
= C
BT kW h
· Cap
BT
(i) · CRF [e/year ] (9)
where
C
BT kW h
[e /kW h] is the referential cost of
the BT technology and
CRF [year
−1
] the capital recov-
ery factor, which is defined as follows:
CRF =
I · (1 + I)
T
(1 + I)
T
− 1
[year
−1
] (10)
where
I [%] and T [years] refer to the interest rate
and the lifetime of the whole system, respectively.
On the other hand, the expression for
C
BT
Re
from
(8) is defined as follows:
C
BT Re
=
r
BT
i=1
C
BT kW h
· Cap
BT
(i) · CRF
(1 + I)
i·Life
BT
[e /year]
(11)
being
r
BT
[-] the number of BT replacements, and
Life
BT
[yars] the BT life estimation.
The W
¨
ohler Curve method [5] obtains the lifespan
estimation. It defines the amount of charge and discharge
cycles that the BT can withstand at each Depth of Dis-
charge (DOD) before reaching the End-Of-Life (EOL).
To count the cycles, the Rainflow Algorithm is used
[5]. The algorithm analyzes the SOC profile obtained at
the simulation, counting the cycles and grouping them
in ranges of DODs. The lifespan expression stands as
follows:
Life
BT
=
n
DOD
j=1
n
BT
dj
· t
OP
CF
uj
−1
[years] (12)
where
n
DOD
[-] denotes the number of different DOD
ranges (100 in the current approach),
n
BT dj
[-] the cycles
counted at each DOD range
j, and CF
uj
[-] the maximum
cycles allowed at each range.
• Charging Infrastructure Cost (OCPs Cost):
C
ch
=
C
ch Ma
+ C
ch Ca
t
OP
·
n
OCP
(i)
n
share
[e /day] (13)
being
C
ch Ma
[e /year] the value related to the main-
tenance cost of a single OCP,
C
ch Ca
[e /year] the an-
nualized capital cost related to the initial investment of a
single OCP, and
n
share
[-] the number of buses that share
the OCPs. The last term allows normalizing the cost of
the infrastructure to a single bus.
C
ch
Ca
is defined as
follows:
C
ch Ca
=(C
OCP
f ix
+C
OCP
kW
·P
OCP
(i))·CRF [e/year]
(14)
where
C
OCP
f ix
[e ] represents the fixed costs of a
single OCP (e.g. structure and connection point), and
C
OCP
kW
[e /kW ] the costs related to the sizing of a
single OCP (e.g. power electronic devices).
• Fuel Cost:
C
f
= Cons
f
(i) · C
f
L
[e /day] (15)
being
Cons
f
(i)[liter/day] the daily fuel consumption,
and
C
f L
[e /liter] the referential cost of the fuel.
• Electric Charging Cost:
C
el
= C
el
fix
+ C
el var
[e /day] (16)
being
C
el fix
[e /day] the cost related to the connec-
tion of the OCPs to the grid, and
C
el var
[e /day] the
cost related to its consumption. Each term is defined as
follows:
C
el fix
=
C
el kW
· P
OCP
(i)
t
OP
·
n
OCP
n
share
[e /day] (17)
C
el
var
= Cons
el
(i) · C
el kW h
[e /day] (18)
where
C
el kW
[e /kW/year] represents the referen-
tial annual cost of the power connection to the grid,
Cons
el
(i)[kW h/day] the daily electricity consumption,
and
C
el kW h
[e /kW h] the electricity referential cost.
I V. R
ESULTS AND DISCUSSION
For the validation of the optimization approach, a base
case has been evaluated. From the conclusions obtained
in the base case, a set of improved cases have been
proposed and also evaluated.
Table III shows the economic values considered in
the approaches of the current section, selected from
actual market prices and similar approaches [3], [5], [8],
[9]. Besides, Table IV shows the variable constraints
considered for each bus topology.
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Table III. ECONOMIC PARAMETERS
Parameter Value
General
t
op
[days/year] 300
I [%] 2.5
Battery Cost C
BT kW h
[e/kWh] 1500
OCP Cost
C
OCP
f ix
[e] 240,000
C
OCP
kW
[e/kW] 60
C
ch
Ma
[e/year] 7,000
Fuel Cost C
f L
[e/L] 1.1
Grid Cost
C
el kW
[e/kW/year] 25.9
C
el kW h
[e/kW] 0.088
Table IV. OPTIMIZATION CONSTRAINTS
HEB Study Case FEB Study Case
n
OCP
(i) ∈{0, 1...3}{0, 1...3}
P
OCP
(i) ∈{100, 200...500}{100, 200...500}
Cap
BT
(i) ∈{12, 24...60}{12, 24...300}
A. Base Case Optimization
Considering that urban bus lines can be driven si-
multaneously by more than one bus, the base case has
been set assuming a single HEB or FEB driving in the
line (
n
share
=1). Due to the multi-objective nature of
the optimization approach, the results returned by the
algorithm are a set of alternative optimal solutions with
different techno-economical characteristics. For a better
display, the solutions have been ranked in ascending
order regarding the TCO. Figure 5 depicts the first six
solutions of the base case optimization for each bus
topology. The figure also indicates the best solutions
regarding each objective.
The results of the HEB (Fig. 5a) show that there is
a set of solutions close in terms of TCO, as it differs
less than the 6% between Solutions 1-6. The results
suggest that the bus line needs a single OCP located at
the terminal station (Solutions 1-6). The best result with
2 OCPs (Solution 15, out of the Figure) involves a TCO
gain of the 63% comparing with the best overall result.
Regarding the OCP power, the best results are around
100-200 kW, what infers that the HEB does not need
fast charging (
>300 kW). Solution 5, which proposes
exactly 300kW, allows the lowest fuel consumption.
However, Solutions 1, 2, and 6 obtain similar con-
sumptions keeping the charging power at 200kW. It is
also worth to highlight the diversity on the ESS config-
urations of the depicted solutions, which vary from 24
kWh to 60 kWh. The results show a correlation between
the BT capacity and the number of replacements, as
the latter are increased in the proposals with the lowest
BT capacity. This increase, however, affects the initial
investment.
The multi-objective nature of the optimization allows
the comparison of the different factors affecting the TCO.
Considering that the TCO variation between Solutions 1-
6 can be neglected (
<6%), other factors can be used to
select the most suitable solution. For instance, as already
mentioned, if fuel use reduction is aimed, Solution 5 is
the most suitable option. On the contrary, if lower electric
use is preferred, Solution 4 is the most appropriate. This
solution is also the best option if a small investment in
BT systems is aimed.
On the other hand, the results of the FEB (Fig.
5b) show that the TCO variation between the depicted
solutions is higher than in the HEB case. Only Solutions
1-3 are in the window of 6%. All the depicted solutions
propose a single OCP in the terminal station, as in
the HEB. The deployment of a second OCP involves
a TCO increase of the 54% in the best case (Solution
44, out of the Figure). Regarding the OCP power, all
the solutions propose 400 kW, except for Solution 5
(500kW, with no noticeable advantage). Therefore, the
main difference between Solutions 1-6 lies on the ESS.
The BT configurations differ from 48 to 96 kWh. It is
hence proved that the storage capacity and charging rate
is increased when turning into a fully electric powertrain.
The comparison of the different factors affecting the
TCO is only effective to obtain a comparison of the
BT costs since the OCP and electricity costs are very
similar. The main cause is the reduction of the operation
possibilities in the FEB topology, as all the consumption
Figure 5. Results of Base Case Optimization: a) HEB b) FEB.
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is electric. Consequently, the best solution regarding BT
cost coincides with the best overall.
To analyze the cost-effectiveness of the base case,
a comparison between the best base results (Solutions
1-2 from each topology) and a conventional diesel bus
driving in the same line has been set. Fig. 6 summarizes
the obtained results. To make a more comprehensive
comparison, the effect of the fuel price variation has also
been included (with low, base, and high fuel price sce-
narios). The numeric values represent the TCO variation
concerning the base fuel price.
The TCO of the best HEB solution is 29% higher
than the baseline of the diesel bus, while the best FEB
solution is 25% higher. Neither of them shows a better
TCO than the high fuel price scenario. Even if the
energy cost (fuel+electricity cost) is lower for the electric
options, the high charging infrastructure cost increases
the TCO overmuch. Consequently, it can be deduced that
the implementation of a single HEB or FEB in the current
route scenario has not cost competitive.
0
0.8
1
1.2
TCO (p.u.)
Diesel Bus
0.6
0.4
0.2
1.4
+27%
+25%
Full Electric Bus
+29%
+34%
Hybrid Electric Bus
1
2
1
2
High Price
Scenario
Low Price
Scenario
Electricity
OCP
ESS
Fuel
Fuel Cost Variation
Fuel Cost Baseline
Figure 6. Base Case Results Comparison.
B. Improved Scenarios Optimization
More optimizations have been conducted to under-
stand the effect of deploying several HEBs or FEBs in
the current bus line (
n
share
> 1). A maximum of 10
buses has been considered in the analysis, in accordance
with the real data of the line (Table I). The results have
been normalized to a single bus cost (TCO/bus), so the
different scenarios can be compared. Fig. 7 summarizes
the obtained results, representing the TCO of the best
overall solution of each improved scenario. In all the new
scenarios, the same optimal configurations as in the base
case (Fig. 5) have been obtained. The TCO of the diesel
bus is also included in the graph, together with the effect
of the fuel cost fluctuation. The numeric values represent
the TCO variation in relation to the base fuel price.
The results show that the increase of buses involves
a high TCO reduction, mainly since the OCP cost de-
creases. This fact makes the electrification of the line
cost competitive. The increase in the number of HEBs
shows that two vehicles are required to reduce the TCO
below the base fuel price scenario (5% lower). One more
bus makes the TCO fall beneath the low price scenario
(17% lower than the base price). In the case of the FEB,
the results show that two vehicles are also enough to turn
the line electrification cost competitive, with the TCO
reduced a 16% compared to the base price scenario. If the
low price scenario is analyzed, the FEB is very close to
the diesel bus. Therefore, the deployment of an additional
bus is recommended (30% lower than the base price).
0
0.8
1
1.2
TCO/bus (p.u.)
0.6
0.4
0.2
1.4
10123456789
-5%
-17%
-33%
Diesel
Bus
HEBs driving in the line (-)
(a)
(b)
0
0.8
1
1.2
TCO/bus (p.u.)
0.6
0.4
0.2
1.4
10123456789
+25%
-16%
-30%
-49%
Diesel
Bus
FEBs driving in the line (-)
+29%
Fuel Cost Variation
Fuel Cost Baseline
HEB/FEB
Diesel Bus
Figure 7. TCO variation of the best overall solution when increasing
the number of buses driving in the line: a) HEBs b) FEBs
V. C ONCLUSIONS
This paper has presented a multi-objective optimiza-
tion approach to defining the OCPs location, OCPs power
rate, and ESS sizing for HEBs and FEBs lines. The
different steps of the methodology have been outlined.
A real scenario has been selected and modeled by the
real data of the bus line. Finally, the usefulness of the
methodology has been validated by means of the techno-
economic analysis of the results obtained at the proposed
base case.
The techno-economic analysis has revealed that for
both bus topologies, the optimal solution consists of an
Revista Técnico - Cientíca PERSPECTIVAS
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8
OCP located at the terminal station. The deployment of
a second OCP has been found to increase the costs of
around 50-60%. The comparison of the base case with
a conventional bus has proved that the deployment of a
single FEB or HEB is not cost competitive (25% and
29% increase, respectively). Further analysis has shown
that the bus line electrification turns into cost competitive
when more buses are simultaneously driving and sharing
the OCPs since the OCP costs are shared among more
buses.
Future evaluations may consider the sharing of OCPs
among different bus lines to improve the TCO further, or
the upscale of the optimization methodology considering
the energy management strategy.
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Revista Técnico - Cientíca PERSPECTIVAS
Volumen 1, Número 2. (Julio - Dicimbre 2019)
e -ISSN: 2661-6688