Article
A Comprehensive TCO Evaluation Method for
Electric Bus Systems Based on Discrete-Event
Simulation Including Bus Scheduling and Charging
Infrastructure Optimisation
Dominic Jefferies * and Dietmar Göhlich
Department of Methods for Product Development and Mechatronics, Technische Universität Berlin,
*Correspondence: dominic.jef[email protected]
Received: 28 July 2020; Accepted: 15 August 2020; Published: 19 August 2020
Abstract:
Bus operators around the world are facing the transformation of their fleets from
fossil-fuelled to electric buses. Two technologies prevail: Depot charging and opportunity charging
at terminal stops. Total cost of ownership (TCO) is an important metric for the decision between
the two technologies; however, most TCO studies for electric bus systems rely on generalised route
data and simplifying assumptions that may not reflect local conditions. In particular, the need
to reschedule vehicle operations to satisfy electric buses’ range and charging time constraints is
commonly disregarded. We present a simulation tool based on discrete-event simulation to determine
the vehicle, charging infrastructure, energy and staff demand required to electrify real-world bus
networks. These results are then passed to a TCO model. A greedy scheduling algorithm is developed
to plan vehicle schedules suitable for electric buses. Scheduling and simulation are coupled with a
genetic algorithm to determine cost-optimised charging locations for opportunity charging. A case
study is carried out in which we analyse the electrification of a metropolitan bus network consisting
of 39 lines with 4748 passenger trips per day. The results generally favour opportunity charging
over depot charging in terms of TCO; however, under some circumstances, the technologies are on
par. This emphasises the need for a detailed analysis of the local bus network in order to make an
informed procurement decision.
Keywords:
electric bus; bus network; simulation; scheduling; charging infrastructure; depot charging;
opportunity charging; optimisation; genetic algorithm; TCO
1. Introduction
Municipal governments and public transport operators around the world have committed to
transforming their fossil-fuelled bus fleets to zero-emission fleets, using either battery electric or fuel
cell electric buses. The choice of technology has profound implications on the operational characteristics
of the vehicles and the infrastructure required.
In recent years, significantly more battery electric buses were deployed than fuel cell buses, and the
majority of bus operators in Europe appears to strategically favour this technology [
1
]. We therefore
focus on battery electric buses in this work. However, even within the realm of battery electric
buses, several charging strategies exist with vastly different operational characteristics (Figure 1).
We differentiate between depot charging (DC), opportunity charging at stationary charging points
(OC) and in-motion charging (IMC). Opportunity charging can take place at terminal stops (OC-T),
intermediate stops (OC-I) and at central charging stations (OC-C).
World Electric Vehicle Journal 2020,11, 56; doi:10.3390/wevj11030056 www.mdpi.com/journal/wevj
World Electric Vehicle Journal 2020,11, 56 2 of 43
Opportunity Charging (OC)
Depot Charging
(DC) terminal
stops (OC-T)
intermediate
stops (OC-I)
central charging
stations (OC-C)
In-motion
charging (IMC)
Figure 1. Electric bus charging strategies.
Opportunity charging at intermediate stops (OC-I) and at central charging stations (OC-C) is
rarely encountered. In Germany, for example, only two electric bus projects (out of approximately 40 in
total) used OC-I, one of which has been declared obsolete [
2
,
3
]. Our interviews with bus operators
also suggest that OC-I is not desired due to the complex nature of planning infrastructure on public
roads. OC-C has also seen only a few applications [
1
]. In-motion charging (IMC) is limited to cities that
already have a trolleybus network, one exception being Berlin where building new trolley bus lines
with in-motion charging is currently being discussed [
4
]. The majority of bus electrification projects
focuses on depot charging (DC) and opportunity charging at terminal stops (OC-T). Also, battery
swapping exists, but it is nearly exclusively applied in China. Since our focus is on the European
market, battery swapping will not be further regarded in this study.
For operators facing a decision between the two technologies, the total cost of ownership (TCO)
is an important metric [
5
]. However, despite a wealth of publications dealing with the TCO analysis
of electric bus systems, several aspects have received insufficient attention in the literature, as we
will show in our literature review in Section 3(after introducing a suitable structure for literature
comparison in Section 2). In particular, many works circumvent the problem of rescheduling bus
operations to satisfy the range and charging time constraints imposed by electric buses. This can lead
to unrealistic results for the electric bus fleet size. The issue of increased staff demand is also commonly
neglected. Most methods do not use real timetable and route data as an input, but generalised
data. Delay data is not considered in any of the studies we evaluated, yet, as we will show, it has
significant influence. We conclude from our literature evaluation that the existing methodologies are
of limited applicability for bus operators planning the electrification of their fleet and seeking the most
cost-effective option.
In Section 4of this paper, we provide details on a simulation, planning and TCO assessment
method first introduced in [6]. The method has since been further developed and currently includes
•
An object-oriented, discrete-event simulation framework, enabling the energetic simulation
of large bus fleets—including charging events en-route and in the depot—based on exact,
non-idealised scheduling data,
•
A scheduling algorithm to construct electric bus schedules adapted to range and/or charging
time constraints and service delays,
• A genetic algorithm to enable cost-optimised placement of opportunity charging stations and
• A TCO calculation module based on dynamic costing.
World Electric Vehicle Journal 2020,11, 56 3 of 43
In Section 5, we conduct a case study for a set of 39 real-world bus lines for which exact timetable,
scheduling and delay data were available. By analysis of the existing (diesel bus) schedules, we will
illustrate that a 1:1 exchange of diesel to electric vehicles often assumed in the literature is infeasible.
We then apply the charging infrastructure optimisation and scheduling algorithms to construct fully
electrified operational scenarios using depot and opportunity charging. The resulting vehicle schedules
serve as input for a fleet and depot simulation that yields fleet size, fleet energy consumption,
driver hours, etc. These values are then fed into the TCO module to obtain total system cost for
each scenario. We close our paper with a discussion of our methodology and results (Section 6) and a
final conclusion and outlook (Section 7). Detailed model equations are given in the Appendix.
2. General Workflow in Electric Bus System Planning and TCO Analysis
During recent years, an abundance of publications has emerged in the field of electric bus
systems with very different scopes. Many publications focus on individual aspects of system design
(for example, methods to obtain a feasible vehicle configuration or charging infrastructure layout for
a given bus network) or system simulation (for example, vehicle energy consumption simulation).
On the other hand, several publications deal with complete electric bus systems, mostly in order to
compare different system configurations in terms of TCO. The latter studies vary considerably in the
level of detail with which certain aspects are treated.
To facilitate a well-structured comparison of existing works, we propose a generalised
representation of the electric bus system analysis workflow, illustrated in Figure 2. Based on
comprehensive literature evaluation as well as our own developments, we identified four main steps:
1. Problem formulation and input data definition
2. System design methods
3. System simulation methods
4. TCO calculation methods.
It should be pointed out that definitions in the literature may differ. For example, in our previous
work [
7
], the entire process consisting of steps 1 to 4 is regarded as system design. Generally, steps
2 to 4 are not semantically separated in the literature. They are also often not carried out sequentially,
but simultaneously.
This is especially the case in works utilising optimisation routines where some or
all of the tasks are integrated into an objective function. For example, electric bus scheduling methods
must incorporate some sort of vehicle model to determine energy consumption and vehicle range.
In our generalised workflow, the scheduling algorithm is part of the system design methods and the
vehicle model contained therein is part of the system simulation methods. This separation of design and
simulation aspects enables us to systematically compare existing methodological contributions, even if
scope and context of the respective publications differ.
World Electric Vehicle Journal 2020,11, 56 4 of 43
Step 1
Vehicle parameters (available battery capacities, charging interfaces etc.)
Vehicle duty data (bus network data, timetables, driving profiles etc.)
Charging strategies to be modeled (DC, OC-T, OC-I, IMC etc.)
Charging infrastructure data (possible charging locations, available power etc.)
Others (ambient conditions, ridership data etc.)
Possible input data:
●
●
●
●
●
Problem formulation and input data definition
Vehicle configuration
Charging infrastructure layout
Vehicle schedules
Charging schedules
Etc.
Methods to determine:
●
●
●
●
●
Step 2
Battery capacity
Location and capacity of charging
stations
Number of depot chargers
Vehicle schedules
Etc.
●
●
●
●
●
Design variables
Fleet mileage and energy demand
Fleet size
Driver hours
Vehicle states
Charging station states
Etc.
●
●
●
●
●
●
Simulation results
Fleet size and fleet mix
Fleet mileage and energy demand
Battery charging cycles
Driver hours
Number of charging stations
Etc.
●
●
●
●
●
●
Full system specification
TCO results
Vehicle investment cost
Infrastructure investment cost
Maintenance cost
Driver wages
Interest rates
Cost escalation
Etc.
●
●
●
●
●
●
●
Cost parameters
System design methods
Vehicle model (traction, auxiliaries)
Fleet model
Depot model
Charging infrastructure model
Etc.
●
●
●
●
●
System simulation methods
Various costing models
TCO calculation methods
Step 3
Step 4
Figure 2.
Generalised workflow of electric bus system planning and TCO evaluation, including
examples of methods and data commonly used in the literature.
World Electric Vehicle Journal 2020,11, 56 5 of 43
3. Literature Review
In the following subsections, existing works corresponding to each of the four steps introduced in
Section 2will be evaluated.
3.1. Problem Formulation and Input Data Definition
Many different problem formulations related to electric buses have been addressed in the literature
(some examples were provided above). The selection of input data is highly dependent on the problem
formulation. For instance, vehicle configuration—in particular, battery capacity—may be fixed and
thus provided as an input parameter [
6
,
8
], or it may be part of the design problem [
5
,
7
,
9
]. The same
applies to the location of charging infrastructure. An aspect of high practical relevance is the form of
vehicle operation profile that is used as an input. Various types of operation profiles are observed:
•
Driving profiles, i.e., a time series of velocity and elevation. These may be measured in real-world
operation [
10
], taken from standard dynamometer driving cycles [
7
,
11
] or generated from
microscopic traffic simulation [12].
•
Simplified bus line and timetable data. Real-world timetables are reduced to headway and trip
duration (sometimes variable over the course of the day), neglecting absolute departure and
arrival times; bus lines are commonly reduced to a single route variant [
5
,
8
,
9
,
13
–
15
]. (It is common
for bus lines to have full-length services operating “from end to end” as well as services operating
on a shorter route inbetween, or to have several different branches. We term each of these a route
variant.) A slightly more detailed timetable representation is found in Ke et al.
[16]
where absolute
departure times and variable trip durations are considered, but resampled to 5-minute intervals.
Timetable data is often complemented with driving profiles to determine trip energy
consumption [5,9,14,15].
•
Exact bus line and timetable data. No simplifications are made to timetable data; any sequence of
trips on any line and any route variant can be considered. This approach is common to all works
specifically dealing with bus scheduling (see Section 3.2), but seldom encountered in electric bus
TCO studies, exceptions being Rogge et al. [17], Lindgren [18] and Jefferies and Göhlich [6].
•
Transportation demand data. Some publications do not assume fixed timetables, but regard the
timetable as part of the design problem. They use demand data (e.g., passengers per hour) as an
input [19,20].
3.2. System Design Methods
Depending on the problem description, considerably different methodologies are employed in
this step. A common design task carried out in electric bus publications is to determine a feasible set of
vehicle parameters, such as the battery capacity required for a given bus line [
7
,
9
,
21
] or a TCO-optimised
battery capacity and/or charging power [22,23].
Also, various methods to determine charging infrastructure locations have been developed.
They commonly use mixed-integer linear programming (MILP) and place charging infrastructure
such that total system cost is minimised, for example, [
24
,
25
]. Some approaches also simultaneously
determine cost-optimised battery capacities [
22
,
23
]. Lindgren
[18]
uses an optimisation heuristic
to determine charging infrastructure locations and then sets the vehicles’ battery capacities such
that a certain lifetime is achieved. However, all aforementioned methodologies assume unchanged
vehicle schedules. Their applicability is therefore limited to situations where charging at intermediate
stops (OC-I), or, in the case of Lindgren
[18]
and Liu and Song
[23]
, in-motion charging (IMC) is
allowed. If charging is only desired at terminal stops (OC-T), a feasible solution may not be found
depending on the dwell times available. Kovalyov et al.
[20]
formulate an optimisation problem to
determine cost-optimised fleet mix, departure frequencies and charging infrastructure layout; however,
no implementation is provided and it is thus unknown if real-world problem instances can be solved.
World Electric Vehicle Journal 2020,11, 56 6 of 43
If it is not possible to operate existing vehicle schedules with electric buses—due to range or
charging time limitations—the issue of vehicle scheduling arises. We consider scheduling to be a central
part of electric bus system design and a prerequisite for TCO analysis [
6
]. However, like the literature
on charging infrastructure optimisation, publications dealing with electric bus TCO analysis often do
not address the scheduling problem.
In TCO studies dealing with depot charging (DC), the scheduling problem is commonly
circumvented by assuming that the daily distance covered by each vehicle does not exceed the
electric buses’ range [
11
,
26
] or by setting a sufficiently high battery capacity, even beyond what is
available on the market [
13
]. When treating opportunity charging (OC), the need for rescheduling
is eliminated in several works by assuming charging at intermediate stops (OC-I) and deploying a
sufficient amount of charging stations such that dwell times at the terminal stops can remain unchanged
[
5
,
9
,
13
,
18
]. (The work by Lindgren
[18]
does make use of a scheduling algorithm; however, it is used
to generate diesel bus schedules because original scheduling data was not available, and no details of
the algorithm are given.) These assumptions result in unchanged vehicle demand compared to the
existing, conventional bus fleet. However, we have previously shown this not to reflect the reality of a
metropolitan bus network [6] and will further elaborate on this in Section 5.2.
The aforementioned works do not provide a solution for depot charging if schedule lengths
exceed vehicle range; neither do they allow opportunity charging exclusively at terminal stops (OC-T).
The work by Pihlatie et al.
[26]
does deal with OC-T, but assumes sufficient dwell times are available
to recharge at the termini. We have also shown this assumption not to hold true in real-world bus
operation, especially if service delays are taken into account [6].
We are currently aware of only two contributions (other than our own) that determine electric bus
system TCO utilising electric vehicle scheduling. Rogge et al.
[17]
developed a genetic algorithm to
determine feasible, TCO-optimised schedules for depot charging, including a charging sequence at the
depot minimising vehicle and charging infrastructure demand. This method yields a set of vehicle schedules
that satisfies exact, real-world timetables and therefore enables a realistic determination of the resulting fleet
size. However, it is applicable to depot charging (DC) only. In the TCO study by Ke et al.
[16]
, a scheduling
algorithm for opportunity charging at central charging stations (OC-C) and depot charging (DC) is
developed. Timetable data resampled to 5-minute intervals is used as an input. However, the algorithm
does not consider the duration of deadhead trips—as a result, vehicles may be assigned trip sequences
they cannot actually serve—and is subject to arbitrary restrictions, the rationale of which remains
unexplained: Opportunity charging can take place only once an hour, and depot charging commences
only after all vehicles have completed all trips.
Due to the lack of universally applicable scheduling methods found in electric bus TCO studies,
we conducted a survey of publications focusing exclusively on electric bus scheduling. Table 1gives
an overview of these works as well as those already discussed above. They are compared with respect
to the following criteria:
•
Whether or not an optimal solution to the vehicle scheduling problem (VSP) is sought
(column ”optimisation”).
• The ability to handle multiple depots.
•
The ability to specify vehicle type restrictions for each trip. This is highly relevant to practical
operation as different trips are often served by different vehicle types (e.g., small or large vehicles).
• The charging strategies considered (see Section 1for their respective definitions).
•
Whether route restrictions are imposed in terms of energy (i.e., battery capacity), time or distance.
•
Whether charging duration is evaluated based on the actual vehicle state of charge (SOC) or
assumed constant.
• Whether partial charging is allowed or a full charge is assumed at each charging event.
•
Whether charging stations and/or depots have a limited number of charging points
(capacity constraints).
World Electric Vehicle Journal 2020,11, 56 7 of 43
•
Whether a variable fleet mix is determined, for example, an optimal combination of short-range
and long-range electric buses or an optimal combination of diesel and electric buses.
•
Whether or not the approach determines the optimal location of OC charging stations (OC charging
location optimisation).
Table 1.
Comparison of electric bus scheduling methods. Legend:
•
yes;
◦
no; – not applicable;
? unclear.
Source
Optimisation
Multiple Depots
Vehicle Type Restrictions Per Trip
Charging
Strategies
Route Restriction
Charging Duration Dependent on Vehicle SOC
Partial Charging Allowed
Charging Station Capacity Constraint
Depot Capacity Constraint
Variable Fleet Mix
OC Charging Location Optimisation
DC OC-T OC-C
Rogge et al. [17]• ◦ ◦ • ◦ ◦ energy • ◦ –◦ • –
Ke et al. [16]◦ ◦ ◦ • ◦ • energy • ◦ ◦ ◦ ◦ ◦
Jefferies and Göhlich [6]◦ ◦ • • • ◦ energy • ◦ ◦ ◦ ◦ ◦
Paul and Yamada [27]◦–◦ ◦ • ◦ none • • ◦ –• ◦
Wang and Shen [28]• • ◦ • ◦ ◦ time ◦– – • ◦ –
Li [29]• ◦ ◦ • • • distance ◦–• • ◦ ◦
Adler and Mirchandani [30]• • ◦ • • • energy ◦–◦ • ◦ ◦
Wen et al. [31]• • ◦ • • • energy • • ◦ ◦ ◦ ◦
Li et al. [19]• • • a• • • energy ◦–• ◦ b• •
Reuer et al. [32]•?◦ • • • energy ◦–◦?•c◦
van Kooten Niekerk et al. [33]• ◦ ◦ • • • energy • • ◦ ◦ ◦ ◦
a
This work differs from the others in that timetable creation is part of the problem formulation, so timetables are
not given explicitly. In constructing the timetable, however, different vehicle capacities are considered based on
passenger demand. bOverall fleet size constraint. cMix of diesel and electric buses.
Most works focus on finding an optimal solution to the VSP, which, when considering battery
capacity limitations, is NP-hard [
29
]. The central task in solving such problems is to develop feasible
solution heuristics. Discussing these solution procedures is beyond the scope of this paper; it should be
noted, however, that application is not always proven for large problem instances of several thousand trips.
For example, the time-space-energy network approach by Li et al.
[19]
—the approach in Table 1with the
most general problem formulation—was not able to solve an instance consisting of a comparatively small
route network with four terminal stops, despite time being discretised to 30-minute intervals. The methods
by Wen et al.
[31]
and van Kooten Niekerk et al.
[33]
were successfully applied to instances with around
500 trips, the method by Li
[29]
to around 900 trips. Adler and Mirchandani
[30]
demonstrated successful
application for over 4000 trips and Reuer et al. [32] for over 10,000 trips.
The approaches by Ke et al.
[16]
, Paul and Yamada
[27]
as well as our own [
6
] employ greedy
algorithms and therefore do not yield optimal solutions, but are considerably less cumbersome
to implement than optimisation methods and provide fast results even for very large problem
instances. They are, however, applicable only to single-depot problems and are limited to DC and
OC-T charging strategies.
As mentioned above, the ability to consider different vehicle types in the timetable is of great
significance for real-world applications. Most works, however, do not enable this and would therefore
World Electric Vehicle Journal 2020,11, 56 8 of 43
require generating a separate problem instance for each vehicle type. This would provide feasible
results only if capacity constraints and charging location optimisation are not part of the problem.
3.3. System Simulation Methods
In this section, existing methods for vehicle, fleet and depot simulation are compared.
3.3.1. Vehicle Modelling
Traction energy consumption is commonly determined by one of three approaches. Some
works employ a longitudinal dynamics model comprising a detailed representation of the vehicle
drivetrain [9,10,14,15,17,34,35].
A driving profile (see Section 3.1) is required as an input to the model.
Others use empirical correlations describing traction consumption as a function of, for example, average
velocity, eliminating the need for driving profiles [
5
,
8
]. The most simple approach to traction
modelling is to assume constant specific consumption (e.g., in kWh/km) irrespective of the actual
driving profile [6,13,16].
The heating, ventilation and air-conditioning (HVAC) system is the most energy-consuming auxiliary
device in an electric bus, its consumption potentially exceeding that of the drivetrain depending on
weather conditions [
7
]. Despite this, most works related to electric bus system analysis and design
do not model the HVAC system explicitly. Sebastiani et al.
[15]
do not consider the HVAC system at
all.
Hegazy et al. [35]
perform vehicle simulations for various auxiliary powers, but they are not linked
to a specific choice of an HVAC system or specific weather conditions. Several authors use average
overall vehicle consumption values, but do not state whether they include auxiliary consumption [
8
,
13
,
16
].
Lajunen
[9]
employs HVAC consumption data from Lajunen and Kalttonen
[36]
, but it is unclear how
the values were determined. Rogge et al.
[17]
employ a vehicle model from Sinhuber et al.
[34]
which
uses measured values for auxiliary consumption (including the HVAC system). A detailed standalone
HVAC system model was developed by the authors of this work [
37
,
38
]; however, its complexity
impedes application within a fleet model. Kunith
[5]
uses this model to compute HVAC consumption
for selected ambient temperatures prior to fleet simulation.
Explicit modelling of other auxiliaries in electric buses, such as air compressor, steering pump and
battery heating/cooling, is—to the best of our knowledge—not encountered in the literature within
the context of electric bus system analysis and design.
3.3.2. Fleet Modelling
We distinguish between two approaches to fleet simulation. Object-oriented or agent-based
models using a discrete-event framework were popularised in autonomous taxi fleet and general
logistics simulation [
39
–
42
], but are also applied to bus fleets [
14
,
15
,
43
,
44
]. All objects in the
simulation—vehicles, charging stations, depots, etc.—are simulated simultaneously in a shared
environment with a central simulation clock, each object having its own individual state. Events change
the system state at discrete time steps and allow for communication between objects. The second
approach is sequential models in which vehicles do not share an environment and each vehicle’s state
is evaluated separately [
10
,
16
,
17
]. Some models assume that all vehicles have a uniform operation
profile [
5
,
8
,
9
,
13
], hence only one vehicle is evaluated and its energy consumption is multiplied by the
fleet size.
3.3.3. Depot Modelling
Especially in the case of depot charging, the charging process at the bus depot can be a
bottleneck with major influence on the e-bus fleet size (and therefore on TCO), as we will show in
Section 5.4. Several TCO studies, however, do not consider depot operations at all [
8
,
9
,
13
]. Some works
approximate the additional vehicle demand arising from exchanging buses with depleted battery
capacity and recharging them at the depot [
5
,
45
], but this specific approach is only applicable when
using simplified timetable and route data (assuming constant travel duration and headway all day).
World Electric Vehicle Journal 2020,11, 56 9 of 43
Rogge et al.
[17]
already consider the depot charging process at the scheduling stage
(see Section 3.2); hence, its influence on fleet size is accounted for. However, as mentioned above,
the methodology cannot handle opportunity charging.
A comprehensive electric bus depot model applicable to real-world bus schedules and any
charging strategy is presented by Lauth et al.
[46]
. It is based on discrete-event simulation and
considers all relevant processes at the depot, including cleaning, maintenance, parking, charging
and dispatch.
3.4. TCO Calculation Methods
TCO calculation may be carried out on the basis of a static [
8
,
16
,
17
] or dynamic [
5
,
9
,
13
] costing
model. Static models assume a constant value of money over time, while dynamic models operate
in terms of net present value (NPV). Usually, dynamic models also feature cost projections for
future expenditures.
Aside from the type of costing model, the existing TCO studies also vary in the selection of cost
components. While all studies include vehicle and infrastructure investment cost and energy cost,
the following cost components are not always accounted for: financing, driver wages, grid connection,
vehicle and infrastructure maintenance, carbon emissions, salvage values.
3.5. Comparison of Electric Bus TCO Studies
Following our survey of individual methodological contributions to electric bus system design,
simulation and TCO calculation, we will now analyse existing TCO studies that compare electric bus
systems in their entirety. Table 2lists some features of electric bus TCO studies:
• The charging strategies considered,
• Whether exact timetable data is used as input,
• Whether delays are considered during system design,
• Whether bus scheduling is performed for fleet size calculation and in what manner,
• Whether charging at the depot is considered for fleet size calculation,
• How the location and/or number of required charging points is determined,
• Whether staff (i.e., driver) demand is part of the calculation.
The majority of the works uses simplified scheduling or no scheduling at all. As a consequence,
application of these methods is limited to theoretical cases where the existing schedules do not have
to be changed for electrification (see Section 3.2). Also, most works cannot operate on real-world
timetable data, do not consider operational delays, and do not consider the charging process at the
depot for fleet size calculation. The only work to feature an exact approach to scheduling and depot
operations (Rogge et al. [17]) can treat depot charging only.
For a bus operator facing a procurement decision between various electric bus system alternatives,
it is desirable to determine the TCO of each electric bus system for the local operating conditions,
i.e., the exact local routes and timetables, rather than for generalised or simplified cases that may not
adequately reflect local conditions. We must conclude, however, that none of the methods discussed in
this section can deliver this.
World Electric Vehicle Journal 2020,11, 56 10 of 43
Table 2.
Comparison of electric bus system TCO studies. Legend:
•
yes;
◦
no; – not applicable;
? unclear.
Source
Charging
Strategies
Exact Timetables
Delays
Fleet Size
Calculation
Charging
Infrastructure
Demand Calculation
Staff Demand Calc.
E-Scheduling Depot
Fusco et al. [8] OC-I, OC-T ◦ • aapprox. ◦heuristic ◦
Bi et al. [13] DC, OC-I ◦ ◦ none ◦?◦
Jefferies and Göhlich [6] DC, OC-T • • exact •heuristic •
Kunith [5] DC, OC-I ◦ ◦ approx. bapprox. coptimisation dpartly e
Rogge et al. [17] DC • ◦ exact f•optimisation g•
Ke et al. [16] DC, OC-T •h◦approx. i•?◦
Lajunen [9] DC, OC-I, OC-T ◦ ◦ ?◦heuristic ◦
Lindgren [18] OC-I, IMC • ◦ none ◦optimisation ◦
Vilppo and Markkula [21] OC-T ◦ ◦ none ◦heuristic ◦
Pihlatie et al. [26] DC, OC-T ◦ ◦ none ◦heuristic ◦
a
Delays are considered implicitly by measurement of real trip durations.
b
For depot charging (DC) only.
c
For DC
only.
d
Optimisation using mixed-integer linear programming (MILP) model.
e
Only additional staff demand for
DC. fFull scheduling with genetic optimisation. gOptimisation using MILP model. hTimetables are resampled to
5-minute intervals, but it may be assumed that the model can also operate with higher resolution data.
i
Simplified
scheduling without deadheading.
4. Electric Bus System Simulation and Planning Tool
To be able to perform a TCO comparison of electric bus systems for a real-world, metropolitan bus
network, we developed eFLIPS (Electric Fleet and Infrastructure Planning/Simulation), a simulation
and planning tool first presented in [
6
]. It alleviates most of the limitations of existing methods
discussed in the previous section: It operates on the basis of exact timetable and delay data; vehicle
operations are rescheduled to account for range and charging time limitations; individual vehicle
states are traced; it includes operations at the depot when determining fleet size; it enables the use of
detailed vehicle consumption models. Development took place in multiple projects, not only in the
context of electric buses, but also battery-electric trains and electric sanitation vehicles.
eFLIPS was implemented in Python [
47
] using strict object orientation. A discrete-event simulation
framework was built using SimPy [
48
], a package providing a simulation clock, an event and process
system, and capacity-constrained resources. Figure 3gives an overview of the tool’s main features,
the workflow involved in performing a TCO study as well as the inputs and outputs of each step.
Each of the features will be explained in the following.
4.1. Bus Scheduling Algorithm
Our scheduling algorithm can plan schedules for depot charging (DC) and opportunity charging
at terminal stops (OC-T). It follows a greedy approach similar to Paul and Yamada [27], but provides
more flexibility: It can handle multiple vehicle types; it is possible to plan schedules for depot charging
or refuelling; in the case of opportunity charging, charging is not assumed at every terminus, but only
at those stops defined as charging points. Like the algorithm by Paul and Yamada
[27]
, it is limited to
a single depot.
The main input to the algorithm is a timetable, i.e., a list of passenger trips sorted by departure time.
A trip has the following attributes: trip type (passenger or deadhead trip); vehicle type (e.g., standard
or articulated bus); departure time; trip duration; delay; dwell time succeeding the trip (at this stage,
the dwell time is unknown and thus set to zero). Also, a list of charging locations and a set of vehicle
parameters must be provided. The output is a list of schedules, which, essentially, are also lists of trips,
except they include deadhead trips and must only consist of trips of identical vehicle type.
World Electric Vehicle Journal 2020,11, 56 11 of 43
Bus scheduling
algorithm Schedules
Timetables
Grid
Delay data
Charging point locations
Depot location
Vehicle parameters
Scheduling parameters
Bus scheduling
TCO model
Fleet size
Number of charging
facilities and slots
Annual energy demand
Annual driver hours
Annual fleet mileage
Simulation results
Unit cost data
Component service life
General discount rate
Interest rate
Cost escalation/degression
per component
Cost parameters
Overall TCO (€/km)
CAPEX (vehicles,
batteries, infrastructure)
OPEX (driver, energy,
maintenance
TCO results
TCO calculation
Schedule simulation
Line 1
Line 2
Depot
Simulation
Schedules
Grid
Delay data
Charging facility locations
and parameters
Depot locations and
parameters
Vehicle parameters
Ambient parameters
Global simulation
parameters
Schedule simulation
parameters
Annual temperature and
insolation data
+
Fleet size
Time series of vehicle
states (SoC, power,
delay, ...)
Time series of charging
facility states
(occupation, power)
Time series of depot
states
Fleet mileage
Energy demand
Driver hours
Schedule simulation
results
Annual energy demand
Annual driver hours
Annual fleet mileage
+
Figure 3.
Overview of eFLIPS (Electric Fleet and Infrastructure Planning/Simulation) main features
and workflow.
The algorithm operates in two stages: First, schedules are built from successive trips without
deadheading (other than the depot trips at the start and end of the schedule), i.e., the next trip must
always begin at the destination of the previous. If the destination is a charging point, sufficient
dwell time is provided to fully recharge the energy storage before the next trip commences. A global
minimum dwell time can be specified. Optionally, delays can be added to the dwell time to ensure
sufficient charging time and punctuality. After the addition of each trip, the vehicle SOC is evaluated.
A schedule is terminated if one of the following is true: There are no more serviceable trips from
the current destination (either no trips with a matching vehicle type are left at all, or those that are
left exceed the maximum permitted dwell time); or, a critical state of charge is reached. In the latter
case, trips are subsequently removed from the end of the schedule until the state of charge is valid.
Figure A1 in Appendix Ashows a flowchart of this stage of the algorithm.
World Electric Vehicle Journal 2020,11, 56 12 of 43
In the second stage, depicted as a flowchart in Figure A2 (Appendix A), it is attempted to
concatenate the schedules created in stage I in order to maximise schedule length and to avoid
unnecessary trips to the depot. The algorithm tries to join each schedule with the earliest reachable
follow-up schedule through a deadhead trip until no more reachable schedules exist or a critical SOC
is encountered. Similarly to stage I, the duration of the deadhead trip and the subsequent dwell time
are capped to avoid excessive dwelling.
The distance of deadhead trips, i.e., depot trips and trips connecting different schedules,
is determined through the openrouteservice car routing API [
49
]. A constant average speed is assumed
to determine the duration of deadhead trips. For each of the two scheduling stages, it is possible to
allow or disallow line changes.
4.2. Schedule Simulation
The schedule simulation forms the main component of eFLIPS. It enables simulation of any kind
of predefined schedules using one of the four charging regimes introduced in Section 1.
As pointed out above, the implementation follows an object-oriented approach. Thus, a schedule
simulation replicates the physical objects encountered in the real world as depicted in Figure 4:
•
A list of schedules to be served is provided, as well as the geographical grid comprising grid points
and connecting arcs. Typically, the schedules cover a single operational day, but any time window
up to a week is possible.
• The ambient (omitted in Figure 4) provides ambient temperature and insolation.
•
The charging network consists of charging points for stationary charging and charging arcs where
vehicles can charge while in motion. Points and arcs each correspond to a point or arc in the
grid, respectively. Charging facilities have a specific charging interface through which they can
transfer energy to a vehicle. They are implemented as a SimPy resource with a defined capacity
(i.e., the number of charging slots available). If a vehicle issues a charging request and all slots are
occupied, it must queue for a free slot in order to charge.
• One or more depots exist where vehicles start and end their respective schedules.
•
A central dispatcher reads the list of schedules and, when a schedule is about to commence,
requests a vehicle of the required type from the depot specified in the schedule. It also assigns a
driver to the vehicle.
•
Each vehicle provides various actions: Switching the ignition and air-conditioning on and off,
driving along a specified leg of a schedule, driving along a specified velocity profile, modifying
the payload (through boarding and alighting of passengers), etc. It has several sub-components,
mainly the traction device, auxiliary devices and energy storage, as well as one or more charging
interfaces. The vehicle model is explained in detail in Section 4.2.2 and Appendix C.
•
The driver executes vehicle actions according to the schedule. It also keeps track of the time spent
driving and idling.
A formal listing of all inputs to the schedule simulation is given in Appendix B.
World Electric Vehicle Journal 2020,11, 56 13 of 43
Vehicle
Depot
Dispatcher
Schedules
Driver
Grid point Grid arc
Charging point
drives along grid,
computes energy
consumption
requests
charging
facilities
drives vehicle
according to
schedule
assigns
schedule
and driver
to vehicle reads
schedules
provides
vehicle
requests
vehicle
Figure 4. Simplified overview of the relationships between objects in the schedule simulation.
4.2.1. Discrete-Event Simulation Framework
The discrete-event system allows for communication between objects. For example, if a vehicle’s
traction power changes, the traction device triggers a state change event. The vehicle’s charge controller
listens for state change events and, upon receiving such an event, updates the energy flow to or from
the energy storage. Similarly, charging facilities keep track of the total energy flow and the number of
vehicles present. State change events also control when an object’s state is logged by the data logging
system: The state of any object is only evaluated when it changes, saving computing time and memory.
4.2.2. Vehicle Model
A vehicle comprises a primary and, optionally, a secondary energy subsystem, each consisting of
an energy storage, any number of connected devices (loads)—including traction, HVAC and other
auxiliary devices—and any number of charging or refuelling interfaces. A charge controller routes the
energy flow between loads, storage and interfaces. Upon each state change event, the energy storage
integrates the net energy flow to determine the amount of energy charged or discharged. The structure
of the vehicle and energy subsystem models is shown in Figure 5. The primary subsystem always
includes the traction motor; a secondary subsystem may be present, for example, if the heating system
uses a different fuel than the traction motor, as is the case in electric buses with diesel-fueled heating.
Charge
controller
Energy
storage
m
1
Charging
interfacesLoads
Energy subsystemVehicle
Sub-components
●
●
●
●
primary energy subsystem
secondary energy subsystem (optional)
charging logic
driver
Parameters
●
●
●
●
●
vehicle ID
vehicle type
traction system
parameters
HVAC system
parameters
charging interfaces
States
●
●
●
●
●
●
●
location
velocity
no. of passengers
cabin temperature
delay
heating/cooling load
total power primary/
secondary
●
●
●
●
SoC primary/
secondary
ignition on/off
HVAC on/off
odometer, operation
time, cumulated energy
consumption, ...
n
1
... ...
e.g.: Traction,
HVAC, other
auxiliaries
e.g.: plug,
pantograph
Energy flow port
●
●
●
●
●
●
energy storage
parameters
kerb weight
aux power
(excluding HVAC)
UA value
insolation area
cabin temperature
Figure 5. Vehicle and energy subsystem model.
World Electric Vehicle Journal 2020,11, 56 14 of 43
Two traction models are available for simulation (cf. Section 3.3.1): A constant specific
consumption model that determines energy consumption on a per-arc basis, and a longitudinal
dynamics model requiring a driving profile. The latter currently cannot be used for schedule simulation,
however it is used to determine typical mean consumption values for standard driving cycles that can
later be used in a schedule simulation.
Several HVAC component models were implemented using parameters from manufacturers’
data: Electric heat pump, electric air conditioning, electric resistance heater and diesel heater can
be combined to several HVAC system configurations. Auxiliaries other than the HVAC system are
modelled as one device with constant power.
A charging logic checks for the availability of suitable charging facilities at the current location
during every time interval and controls the vehicle’s behaviour accordingly. The actions invoked by
the charging logic are depicted in Figure 6. Queueing and manoeuvring are generally only applicable
to stationary charging points. Various queueing strategies can be defined: Vehicles can queue for a
free charging slot or skip charging if all slots are occupied; also, vehicles can release the charging
slot once they are fully charged, or remain at the charging point until departure. These features
were implemented to be able to evaluate the impact of different driver break regulations on charging
infrastructure demand. It is also possible to force vehicles to always wait until fully charged (even if
this causes a delay), or to depart as punctually as possible (even if this leaves no time to charge).
Furthermore, several energy storage (battery, diesel tank) and charging interface models
(stationary pantograph, trolleybus pantograph, CCS plug, diesel nozzle, train pantograph) were
implemented. When connected to a charging interface, a constant charging power is assumed.
A full documentation of the model equations is given in Appendix C.
queue for
charging slot
manoeuvre
to charging
position
dock interface
charge
undock interface
wait for
departure
P
manoeuvre
to parking
position
P
Figure 6. Actions controlled by charging logic.
4.2.3. Depot Model
Vehicles start and end their schedules at a depot. Any number of depots can be defined in the
simulation. Each depot keeps track of the number of vehicles currently in service and the number
of vehicles present at the depot for charging and parking. All depots are empty at the start of the
simulation. If a vehicle is requested for line service from a depot by the dispatcher, the first available
vehicle currently parked at the depot is chosen; if no vehicle is available, a new vehicle is generated
and added to the depot. Thus, the required fleet size can be determined by counting the number of
vehicles generated in total by the end of the simulation, as illustrated schematically in Figure 7.
When a vehicle arrives at the depot and a charging slot is available, charging commences
immediately after a defined dead time for manoeuvring has passed. Vehicles are charged at full
power. After charging, vehicles are again blocked for a certain dead time before being able to return
to service.
World Electric Vehicle Journal 2020,11, 56 15 of 43
Vehicles
in service
Vehicles
in depot
Vehicle demand:
4 vehicles
time
►New vehicle object generated
►Vehicle 1: Schedule 1
►Vehicle 4: Schedule 4
►Vehicle 3: Schedule 3
►Vehicle 2: Schedule 2
Vehicle 1: Schedule 5
Vehicle 2: Schedule 6
Vehicle 1
Vehicle 2
Vehicle 3
Vehicle 4
Vehicle 1
Vehicle 2
State of charge (SOC)
Figure 7. Vehicle demand calculation.
4.3. Year Simulation and TCO Calculation
To determine the fleet’s annual energy demand required for TCO calculation, it is important to
consider the seasonal variation of HVAC system consumption. Thus, a batch simulation module was
developed allowing simulation of any number of parameter sets. We use the batch simulation module
to determine annual simulation results on the basis of a year’s temperature and insolation function.
Both functions are discretised into
n
intervals such that a list
T
of temperature and insolation values
and the respective number of days (i.e., the width of the interval) is produced:
T=(Ndays,1,T1,˙
qsol,1), . . . , (Ndays,n,Tn,˙
qsol,n). (1)
For each quantity
Q
obtained from a schedule simulation for one single day, the annual quantity
Qais obtained through
Qa=
n
∑
i=1
Ndays,iQ(Ti,˙
qsol,i), (2)
where Qmay be the fleet energy consumption Efleet, fleet mileage Mfleet or driver hours ∆tdriver.
Vehicle and infrastructure demand are not determined from the year simulation, but from a
separate schedule simulation using a critical consumption case (usually a very cold winter day).
Once the vehicle demand, infrastructure demand, annual fleet mileage, annual energy demand
and annual driver hours have been determined, they are passed to a dynamic TCO model. We assume
loan capital is acquired for capital expenditures and repayed in the form of an annuity over the lifetime
of the respective component (vehicles, batteries, charging infrastructure). The unit cost of all capital
and operational expenses is determined for all relevant years using cost escalation factors that may
be individually defined for each year. It is assumed payments take place at the beginning of the year.
Salvage values are not considered. Once the annual cash flows for all types of expenses have been
calculated, they are discounted to a base year to compensate for general inflation. Figure 8gives an
overview of the calculation method.
The overall system TCO is obtained by summing up all discounted cash flows. A full description
of the calculation can be found in Appendix D.
World Electric Vehicle Journal 2020,11, 56 16 of 43
t
tstart tend
(a) Investments
CAPEX
CCAPEX,c(t)
tbase
∆tdp,c ∆tdp,c
t
tstart tend
CFCAPEX,c(t)
tbase
(b) Cash flows (annualised)
t
tstart tend
CFCAPEX,NPV,c(t)
tbase
(c) Cash flows discounted
to base year
OPEX
t
tstart tend
CFOPEX,c(t)
tbase
(d) Cash flows (e) Cash flows discounted
to base year
t
tstart tend
CFOPEX,NPV,c(t)
tbase
∆tproject
Figure 8. TCO calculation method.
4.4. Genetic Algorithm for Charging Infrastructure Optimisation
The functions of eFLIPS presented thus far—electric bus scheduling, schedule simulation,
year simulation and TCO calculation—require the specification of charging infrastructure locations
as an input parameter. In the case of depot charging, this is trivial. When dealing with opportunity
charging, however, deciding upon the location of charging points can become a complex task: As any
combination of charging points poses a separate scheduling problem, the effect of charging point
positions on overall system cost is difficult if not impossible to predict by intuition. Also, real-world
bus networks produce solution spaces of considerable magnitude, as our case study presented in
Section 5will illustrate. It therefore seems purposeful to develop an optimisation method to determine
a cost-optimised set of charging locations for opportunity charging.
To enable this, the entire process shown in Figure 3was wrapped into a single function that
returns the TCO of an electric bus system, using timetable data and charging point locations as the main
inputs. A binary genetic algorithm (GA) was implemented that uses this aggregated TCO function as
a fitness function.
A list of possible locations for OC charging infrastructure
L= (l1
,
. . .
,
li
,
. . .
,
lNloc )
defines the
length
Nloc
of each chromosome
c= (b1
,
. . .
,
bi
,
. . .
,
bNloc )
. The position
i
of each allele maps to location
li
and the value of the allele indicates whether a charging station is present at this location (
bi=
1)
or not (
bi=
0). A population size
Npop
is defined and an initial population is generated randomly.
For each new generation, the best
Nkeep =xselect Npop
chromosomes are kept,
xselect
being the selection
share, and the rest is discarded. Chromosome pairs (parents) are randomly selected to produce
offspring through single-point crossover until the original population size is reached. The offspring is
then mutated using the mutation rate
µ
. We define
µ
as the share of alleles that is randomly modified,
i.e.,
Nmut =d(Nchrom −1)Nloc µe
alleles at random positions are switched,
Nchrom
being the number
of chromosomes in the population subset that mutation is applied to.
The number of charging slots is set to an arbitrary, high value for all stations in the schedule
simulation so that, effectively, no capacity constraints exist. This is because the scheduling algorithm
currently does not support charging station capacity constraints.
To reduce computation time, a simplified TCO calculation method was adopted for the GA fitness
function: Instead of performing a year simulation using a temperature distribution, annual energy
consumption is obtained by simply multiplying energy consumption for the critical consumption case
by 365. Also, a static costing model is used.
World Electric Vehicle Journal 2020,11, 56 17 of 43
Further reduction in computation time is obtained by skipping the fitness evaluation of infeasible
solutions: Solutions not including at least one charging location per bus line are penalised by being
assigned a very low fitness (i.e., high cost) value. Their actual TCO is not evaluated. Also, the algorithm
caches all chromosomes and their respective fitness values such that no chromosome is evaluated
twice. Parallel processing support was realised using Python’s multiprocessing package.
5. Case Study: Electrification Scenarios for an Urban Bus Network
To illustrate the application of our methodology, we conducted a case study for a real-world
bus network consisting of 39 lines, of which 28 operate at daytime, 2 provide 24-hour service and 9
are night lines. For these lines, the current diesel bus schedules—from which the timetables can be
generated by discarding the empty trips—and delay data were made available by the bus operator.
5.1. Vehicle Specifications and Energy Consumption
For the schedule simulation and TCO calculation, it is paramount to obtain representative vehicle
parameters and consumption values. Our approach outlined in the following is to define a set of
vehicle parameters based on market data, and to determine specific consumption for standard driving
cycles by longitudinal dynamics simulation. The specific consumption obtained in this manner is later
used for the constant consumption model in the schedule simulation.
5.1.1. Parameterising the Longitudinal Dynamics Model
Detailed standard on-road test (SORT) [
50
] test data was available from a bus manufacturer for
an 18 m articulated electric bus. The test yields specific vehicle consumption in kWh/km for a SORT 1,
2 and 3 cycle using a fixed payload. These experimentally determined consumption values were used
to parameterise and validate the vehicle model presented in Appendix C.
The parameters
fr
,
cw
,
Afront
and
λ
used in Equations
(A25)
and
(A26)
were obtained from the
literature (Table 3). The HVAC system power
PHVAC
is zero because the HVAC system was switched
off during the SORT test. This leaves the total drivetrain efficiency
ηtotal
in Equation
(A23)
and the
power of the remaining auxiliaries
Paux,other
in Equation
(A2)
unknown. They were determined by
least-squares approximation such that
3
∑
i=1eSORT,i,sim −eSORT,i,exp2→min, (3)
where
i=
1
. . .
3 corresponds to the respective SORT profile,
eSORT,i,sim
is the specific consumption
obtained from longitudinal dynamics simulation and
eSORT,i,exp
is the experimentally determined
specific consumption. The least-squares approximation yielded
ηtotal =
0.86 and
Paux,other =
5.40
kW
,
both of which are plausible (e.g., by comparison with Sinhuber et al.
[34]
). Using these parameters, the
SORT cycle energy consumption obtained through simulation was within 2% of the experimentally
determined consumption, as Table 4indicates. The parameters will thus be used henceforth.
Table 3. Parameters used for longitudinal dynamics simulations.
Quantity Symbol Value Source
Rolling resistance coefficient fr0.0075 [51]
Drag coefficient cw0.66 [34]
Frontal projection area Afront 8.8 m2[34]
Rotational mass factor λ1.1 [5]
World Electric Vehicle Journal 2020,11, 56 18 of 43
Table 4.
Comparison of simulated and experimentally determined energy consumption for standard
on-road test (SORT) cycles.
Profile Spec. Consumption (kWh/km) Relative Deviation
Simulation Experiment
SORT 1 1.62 1.63 −0.5 %
SORT 2 1.43 1.40 +1.7 %
SORT 3 1.36 1.37 −1.1 %
5.1.2. Defining Vehicle Types for the Simulation
We defined five base types of electric buses: Three depot charging types with low (120 km),
medium (200 km) and high (300 km) range, and two opportunity charging types with a range of 60 km
and different charging powers (300 kW and 450 kW). For each base type, parameters for a standard
12 m bus and an articulated 18 m bus were defined, yielding 10 electric bus configurations in total.
For each vehicle configuration, the battery capacity was set such that the desired range can be
fulfilled on a SORT 2 cycle with 50% occupation on a very cold winter day (
−
10
°C
) with the HVAC
system enabled. Cabin temperature was set to 17
°C
in accordance with the VDV guidelines on
passenger cabin air-conditioning [
52
]. To ascertain that the range requirement can be satisfied even at
the end of the battery lifetime, a battery state of health (SOH) of 80% was assumed. A root finder was
used to obtain the matching battery capacity because the discrete-event simulation model does not
permit solving for the battery capacity explicitly. The resulting battery weight was determined using
energy density values taken from current manufacturer datasheets; for the high-range depot chargers,
a 20% increase in energy density was assumed. Lithium-ion NMC batteries were assumed for the
depot chargers and LTO batteries for the opportunity chargers. Vehicle base weights (without battery)
were obtained as mean values from the literature. The full set of vehicle parameters used henceforth is
listed in Table 5.
World Electric Vehicle Journal 2020,11, 56 19 of 43
Table 5. Vehicle parameters used for schedule simulation. Values of the form X/Y denote standard and articulated buses, respectively.
Depot Charging Opportunity Charging Sources and Comments
Short Range Medium Range Long Range Low Power High Power
Desired range (km) 120 200 300 60
Base weight (kg) 11175/16097 [53–55]
Kerb weight (kg) 12646/18164 13696/19638 14383/20604 13764/19734 Vehicle + battery
Maximum passenger occupation 70/99 [56]
UA value (kW/K) 0.562/0.843 Calculated from [57]
Insolation area (m2) 11.4/17.1
Aux power excl. HVAC (kW) 4.0/5.4 Simulation
Number of HVAC units 1/2
Battery parameters
- Energy density (Wh/kg) 171 171 205 53 [58,59]
- Capacity (kWh) 252/353 431/606 658/925 137/193 Simulation
- SOC (min-max) 0.05–0.95 0.10–0.95
- Maximum C rate 0.62 4.35 [58,59]
- SOH 0.80
Fast charging parameters
- Charging power (kW) 300 450
- Efficiency 0.95
- Dead time before-after (s) 15–15
Depot charging parameters
- Charging power (kW) 60–150
- Efficiency 0.95
- Dead time before-after (s) 60–60
Traction consumption (kWh/km) a0.73/0.99 0.77/1.05 0.80/1.09 0.77/1.06 Simulation
Total consumption (kWh/km) a1.51/2.12 1.55/2.18 1.58/2.22 1.55/2.18 Simulation
aSORT 2, −10/17 °C, 50% occupation.
World Electric Vehicle Journal 2020,11, 56 20 of 43
5.2. Simulation of Existing Schedules With Electric Buses
To assess the operability of the existing diesel bus schedules with electric buses, we performed
simulations of the 317 unchanged schedules that cover the 39 lines on a weekday. Five scenarios,
each corresponding to one of the vehicle types in Table 5, were simulated. Critical consumption
parameters (SORT 2, 50% occupation,
−
10
°C
outside, 17
°C
inside) were assumed as outlined in the
previous section.
For the opportunity charging scenarios, the location of charging stations has to be defined.
(The word charging station is used synonymously with charging point; a station has several charging
slots.) The charging optimisation algorithm introduced in Section 4.4 cannot be applied in this case
because it enforces rescheduling of the vehicles. To avoid subjective decisions, a simple heuristic
was chosen: A charging point was assumed at every terminus, even at termini that are only seldom
visited. This yielded a total of 128 OC charging stations (more than three stations per line). It must
be noted that this approach does not in any way reflect operational practice; it simply constitutes the
upper boundary in terms of available energy supply and thus can be considered a theoretical best-case
scenario for OC.
For the simulation of existing schedules, the question of interest is whether vehicles can sustain
a valid state of charge during scheduled operation. Depot operations are irrelevant at this stage.
Thus, no depot simulation was carried out; a new, fully charged vehicle was generated for each
schedule. If vehicles arrived at a terminus delayed, the dwell time (and, therefore, the charging time in
the OC cases) was shortened to permit a punctual departure whenever possible.
Simulation was carried out for punctual and delayed operation. For the latter case, historical
delay data was available from the bus operator; the delay assigned to each trip was obtained as the
90th percentile of all delays observed on similar trips within the same hour of the day (similar trips are
defined as trips on the same line in the same direction).
The simulation results are shown in Figure 9. It is observed that delays exert only a minor influence
in the depot charging scenarios; in the opportunity charging scenarios, however, the results change
considerably when delays are taken into account. As expected, the higher the DC vehicles’ range and
the higher the OC vehicles’ charging power, the more schedules can be served. There is, however, no
scenario that permits electric bus operation with completely unchanged schedules. Also, it must be
emphasised that the OC results for a more realistic charging infrastructure setup would be considerably
worse. These results reinforce our point that the transition to electric buses in a metropolitan bus
network requires a rescheduling of vehicle operations [6].
5.3. Fully Electrified Scenarios: Scheduling and Charging Infrastructure Optimisation
We will now proceed to construct scenarios for fully electric bus operation. Six scenarios were
generated: Five electric bus scenarios corresponding to the vehicle types in Table 5and a diesel
reference scenario for comparison. Diesel vehicles were modelled using a specific average consumption
of 44.4 litres/100 km for standard buses and 59.4 litres/100 km for articulated buses (values from a bus
operator’s fleet consumption evaluation over an entire year). HVAC system and other auxiliaries were
not modelled for diesel buses, they were included in the average consumption.
For each of the scenarios, a new set of schedules has to be generated. In order to invoke the
scheduling algorithm presented in Section 4.1, we first have to define a timetable. This is achieved by
filtering the existing schedules for passenger trips on the specified lines. For the daytime lines, all trips
during a weekday were chosen (this typically includes all trips between 4:00 a.m. and 1:00 a.m. of
the following day). For the night lines, all trips departing on the evening of the same weekday and
during the following night were considered. For the 24-hour lines, a time window must be chosen.
We considered all trips departing between 3:00 a.m. and 2:59 a.m. on the following day, in accordance
with the bus operator’s definition of an operational day. The resulting timetable consists of 4748 trips.
All trips shall be served by a single depot.
World Electric Vehicle Journal 2020,11, 56 21 of 43
DC (120 km)
punctual
93 (29%)
7 (2%)
217 (68%)
DC (200 km)
129 (41%)
6 (2%)
182 (57%)
DC (300 km)
245 (77%)
14 (4%)
58 (18%)
OC (300 kW)
315 (99%)
2 (1%)
OC (450 kW)
315 (99%)
2 (1%)
delayed
93 (29%)
4 (1%)
220 (69%)
128 (40%)
6 (2%)
183 (58%)
244 (77%)
10 (3%)
63 (20%)
260 (82%)
57 (18%)
290 (91%)
27 (9%)
OK critical invalid
Figure 9.
Results from the simulation of existing diesel bus schedules with electric buses. The pie
charts indicate the number of schedules for which the following applies: Green—schedules can be
served within the state of charge (SOC) limits of the battery and also leave an operational safety
margin of 10 km; yellow—schedules can technically be operated, but violate the 10 km safety margin;
red—schedules are inoperable because they violate the SOC limits of the battery.
For scheduling, the minimum dwell time was set to zero as some lines currently operate with
zero dwell time at certain termini. Maximum dwell time and maximum deadheading time were set
to 45 minutes. The average velocity used to compute the duration of deadhead trips was defined as
25 km/h. Line changes were only permitted during the second stage of scheduling (cf. Section 4.1).
A reserve range of 10 km was assumed for all vehicle types and the effective battery capacity available
for scheduling was reduced accordingly.
Delays were taken into account in all scenarios during scheduling: The minimum dwell time
at every terminus was increased by the delay upon arrival such that a punctual departure for the
succeeding trip is always possible. Technically, it would also be conceivable to consider delays only in
the case of OC, since only OC requires “guaranteed” dwell times for recharging even in the presence
of delays. However, this would imply the OC systems can maintain a higher level of punctuality than
the DC and diesel systems. To ensure a consistent quality of service for the passenger in all scenarios,
it is thus appropriate to always consider delays.
A cost-optimised charging station layout was determined for each of the OC scenarios using the
genetic algorithm presented in Section 4.4. The parameters were: population size
Npop =
120, selection
share
xselect =
0.5 and mutation rate
µ=
0.2. Infeasible solutions not including at least one charging
station per bus line were assigned a TCO of 10
€
/km. All of the 93 terminal stops were provided as
charging location candidates, enabling 2
93 ≈
10
28
possible combinations. Iteration was halted after
approximately 5 days and 750 generations, having produced only incremental improvements once
the infeasible solutions with a high cost penalty were removed from the population. A 12-core Intel
Xeon E5-2640 machine with 64 GB RAM was used. Figure 10 shows the TCO of the best solution
per generation over the course of the iteration. (Note that because of the simplified TCO model
implemented within the GA, the TCO obtained by the GA does not match the TCO calculated in
Section 5.5 using the full model.)
The genetic iteration yielded a set of 42 charging locations for the 300 kW scenario and 44 charging
locations for the 450 kW scenario. These configurations were subsequently used for schedule generation
and system simulation. Further discussion of the charging network optimisation results is found in
Section 6.
World Electric Vehicle Journal 2020,11, 56 22 of 43
(a) 300 kW scenario
0 200 400 600 800
Generation
4.6
4.7
4.8
4.9
Cost ( /km)
0 20 40 60 80 100 120
Computation time (h)
(b) 450 kW scenario
0 200 400 600
Generation
4.6
4.7
4.8
4.9
Cost ( /km)
0 20 40 60 80 100 120
Computation time (h)
Figure 10. Progress of charging infrastructure optimisation.
The results of the scheduling process are listed in Table 6. The scheduling efficiency was
determined for each schedule as the ratio
ηschedule =tproductive
ttotal
, (4)
where
tproductive
is the time spent during revenue service, i.e., on passenger trips excluding pauses,
and
ttotal
is the total operation time. Computing time for schedule generation was 333 s, or
≈
56 s per
scenario, on an Intel Core i5-6200U using a single core.
Table 6. Scheduling statistics.
Case Number of Schedules Mean Distance (km) Mean Duration (h) Mean Efficiency (%)
DC (120 km) 667 96.7 5.9 88.2
DC (200 km) 441 138.6 8.6 91.5
DC (300 km) 350 171.2 10.7 92.8
OC (300 kW) 340 176.1 12.3 93.3
OC (450 kW) 327 182.3 12.4 93.4
Diesel 302 195.8 12.3 93.7
As would be expected, in the case of DC, the lower the vehicle range, the more schedules were
generated and the lower is the resulting schedule efficiency. This is because more depot trips are
required for the same number of passenger trips. The OC schedules provide higher efficiency than
the DC schedules, indicating that the unproductive time for recharging OC vehicles is lower than the
unproductive time for additional depot trips in the DC case. Diesel schedules have the highest mean
efficiency and distance.
5.4. Fully Electrified Scenarios: System Simulation
The schedules generated for each technology in the previous section serve as the main input
for the system simulation. The goal of the system simulation is to obtain the number of vehicles
and charging points required to operate the schedules under critical conditions (a cold winter day as
outlined in Section 5.2). Each individual vehicle is simulated; example SOC plots from a single-day
simulation are given in Figure 11.
Schedules were generated for five electric bus scenarios (scenarios 1–5) and a diesel reference
scenario (scenario 8) as illustrated in the previous section. Two additional electric bus scenarios
(scenarios 6 and 7) not requiring additional scheduling were simulated to observe the impact of
reducing the charging power at the depot: the medium range DC scenario and the low power OC
scenario are replicated with a depot charging power of 60 kW instead of 150 kW.
World Electric Vehicle Journal 2020,11, 56 23 of 43
(a) DC
0 2 4 6 8 10 12 14 16 18 20 22 0 2 4
Time (hours)
0.00
0.25
0.50
0.75
1.00
SoC
(b) OC
0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6
Time (hours)
0.00
0.25
0.50
0.75
1.00
SoC
Figure 11. Typical vehicle SOC time series from schedule simulation.
To correctly simulate depot operations, the schedules have to be repeated twice such that a period
of three consecutive days is simulated as illustrated in Figure 12: only on the second day will there
exist an equilibrium state that reflects actual weekday depot operation. This is because at the beginning
of the simulation, the depot starts empty and it takes some time until all vehicle objects have been
generated; at the end of the simulation, all schedules have ended and all vehicles are returned to the
depot. In reality, this never happens because a certain number of vehicles is always in service at any
time of day.
20 22 0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12
0
50
100
150
200
250
300 S_12m_DC_low
A_18m_DC_low
total
Recurring 24-hour interval
(equilibrium state)
Number of vehicles
Start of
simulation:
Depot empty End of
simulation:
All vehicles
return to depot
Peak depot occupation
= number of depot
charging points
Vehicles in depot (Scenario 1)
Time (hours)
Figure 12. Using repeated schedules to obtain an equilibrium state in the bus depot.
The number of required fast charging slots was obtained as the sum of the maximum occupation of
each charging station; an example is provided in Figure 13. The number of available slots per station was
set to a high value in the simulation so that, effectively, charging station capacity was unconstrained.
Vehicles were configured to occupy their charging slot until departure (see the discussion of queueing
strategies in Section 4.2.2). The required number of depot charging slots was determined from
the maximum depot occupation as illustrated in Figure 12. One depot charging slot per vehicle
was assumed.
World Electric Vehicle Journal 2020,11, 56 24 of 43
3 6 9 12 15 18 21 0 3 6 9 12 15 18 21 0 3 6 9 12 15 18 21 0 3 6 9
Time (hours)
0
2
4
6
8
Number of vehicles
Charging point occupation
peak
occupation:
8 vehicles
Figure 13. Example of opportunity charging (OC) charging point occupation.
The simulation results are presented in Table 7. We observe the following:
•
Generally, the electric bus scenarios require at least 20 more vehicles (+12%) compared to the
234 vehicles in the diesel reference scenario. The only exception is the long-range DC scenario
(scenario 3) that requires only three more vehicles (+1.3%).
•
Reducing the charging power at the depot from 150 to 60 kW incurs a significantly larger fleet in
the case of depot charging (+14 vehicles or 4%). In the case of opportunity charging, the increase
in fleet size is less pronounced (+2 vehicles or 0.8%).
•
Increasing the DC vehicles’ range from 120 to 200 km increases the required fleet size substantially
by 32 vehicles or 10%. This is because in the 200 km case, many vehicles run out of energy
during the afternoon when vehicle demand is at its peak and, thus, many new vehicles have to be
generated. In the 120 km case, however, most vehicles return to the depot for charging before the
afternoon peak and can then cover the entire afternoon shift uninterrupted. This surprising result
illustrates the limits of the greedy scheduling algorithm: the objective pursued by the algorithm
to maximise schedule length does not necessarily lead to a minimum fleet size.
Table 7. Simulation results for fully electric scenarios and diesel reference scenario.
Scenario No. Name Fleet Size aFast Charging Slots Depot Charging Slots
1 DC (120 km) 116/188/304 0 272
2 DC (200 km) 130/206/336 0 305
3 DC (300 km) 94/143/237 0 205
4 OC (300 kW) 104/158/262 127 223
5 OC (450 kW) 100/154/254 117 215
6 DC (200 km), 60 kW 133/217/350 0 319
7 OC (300 kW), 60 kW 105/159/264 127 225
8 Diesel 94/140/234 0 201
aStandard buses/articulated buses/total.
5.5. Fully Electrified Scenarios: TCO Comparison
For the final step of our analysis, the TCO comparison, a year simulation was carried out for each
of the scenarios to obtain annual energy demand and driver hours (see Section 4.3). A temperature
function for Germany [
60
] was used and discretised into monthly intervals. Vehicle and infrastructure
demand was taken from the simulation of the critical consumption case in the previous section.
The cost parameters used in the TCO calculation are presented in Table 8. To obtain the driver hours,
it was assumed that drivers are paid an additional 20 minutes per schedule for vehicle preparation and
parking. Dwell times were only deducted from the paid labour hours if they have a certain minimum
World Electric Vehicle Journal 2020,11, 56 25 of 43
duration; short dwell times were assumed to be fully paid. This reflects the labour agreement of a
bus operator, the details of which we cannot disclose. The cost for depot construction and depot grid
connection was not considered. Identical unit cost was assumed for 150 and 60 kW depot charging
points due to a lack of data. The construction and grid connection cost for fast charging stations was
assumed equal for all stations, regardless of charging power and number of slots.
Table 8.
TCO parameters. Values of the form X/Y denote standard and articulated buses, respectively.
Quantity Value Source
Base year and project start 2020 Assumption
Project duration 12 years Assumption
Discount rate (general inflation) 1.4% p.a. [61] (1999–2019)
Interest rate 4% Assumption
Electric bus base cost (without battery) 450,000 €/ 585,000 €Calculated based on [62–64]a
Diesel bus cost 250,000 €/ 325,000 €[62,63]
Vehicle lifetime 12 years Assumption
Battery cost (NMC) 500 €/kWh [64]
Battery cost (LTO) 800 €/kWh Assumption
Battery cost escalation −8% p.a. Calculated based on [64]
Battery lifetime 6 years, 12 years Assumption
300 kW fast charging station 200,000 €per slot Own market research
450 kW fast charging station 250,000 €per slot Own market research
Fast charging station construction/grid connection 225,000 €per station Own market research
Depot charging station 100,000 €per slot Own market research
Charging infrastructure lifetime 20 years Assumption
Charging station efficiency 95% Assumption
Electricity cost 0.15 €/kWh
Electricity cost escalation +3.8% p.a. [65] (2005–2019)
Diesel cost 1 €/L
Diesel cost escalation +0.7% p.a. [65] (2005–2019)
Fast charging station maintenance 1000 €/a per slot Own market research
a
Price of standard electric bus [
62
]: 600 k
€
. Assuming a 300 kWh NMC battery, this leads to 450 k
€
for the
base bus. The articulated bus base cost was calculated assuming the same cost ratio as for diesel buses [
62
,
63
]:
450 k€·(325 k€/250 k€) = 585 k€.
The eight scenarios were evaluated in two variants: One assuming a battery change after half
of the bus lifetime, and the other without battery change. The results for both variants are shown in
Figure 14. Vehicles and batteries are always treated as separate cost entities in the figures.
The key findings in the TCO comparison are:
•
In the calculation with battery renewal, the lowest-cost DC electric bus scenario has a TCO 4–6%
higher than the OC scenarios. Without battery renewal, this gap reduces to 1–2%.
•
Reducing the depot charging power from 150 to 60 kW has a more pronounced impact on the
TCO of the DC scenario (+2%) than on the TCO of the OC scenario (+0.2%), as would be expected
from the vehicle demand presented in the previous section.
• If no battery renewal is necessary, system cost is reduced by 2% to 4%.
•
The short-range and long-range DC scenarios have equal TCO if battery renewal is considered;
in this case, the reduced vehicle demand in the long-range scenario is countered by higher battery
replacement cost. The calculation without battery renewal, however, favours the long-range
scenario, albeit by a narrow margin (−2.5% compared to the short-range scenario).
•
The 450 kW OC scenario is slightly more competitive than the 300 kW scenario by a very small
margin (−1%).
•
Charging infrastructure has little influence on TCO: Its contribution ranges from 0.6% to 1.0% for
DC and from 3.0% to 3.4% for OC.
World Electric Vehicle Journal 2020,11, 56 26 of 43
•
Staff cost (driver wages) accounts for 50% to 64% of TCO depending on the scenario. The electric
bus scenarios increase the staff cost by the following, compared to the diesel scenario: DC (120 km):
8%; DC (200 km): 3%; DC (300 km): 1%; OC (300 kW): 5%; OC (450 kW): 4%.
•
The electric bus scenarios incur an overall TCO 15–31% higher than the diesel scenario if battery
renewal is considered, and 13–25% without battery renewal.
(a) With battery renewal
(1) DC (120 km)
(2) DC (200 km)
(3) DC (300 km)
(4) OC (300 kW)
(5) OC (450 kW)
(6) DC (200 km), 60 kW
(7) OC (300 kW), 60 kW
(8) Diesel
0
1
2
3
4
5
TCO ( /km)
4.53
/km
116 S
188 A
4.79
/km
130 S
206 A
4.53
/km
94 S
143 A
4.34
/km
104 S
158 A
4.29
/km
100 S
154 A
4.89
/km
133 S
217 A
4.35
/km
105 S
159 A
3.74
/km
94 S
140 A
Vehicles
Batteries
Fast charging infrastructure
Depot charging infrastructure
Energy
Vehicle maintenance
Infrastructure maintenance
Staff
(b) Without battery renewal
(1) DC (120 km)
(2) DC (200 km)
(3) DC (300 km)
(4) OC (300 kW)
(5) OC (450 kW)
(6) DC (200 km), 60 kW
(7) OC (300 kW), 60 kW
(8) Diesel
0
1
2
3
4
5
TCO ( /km)
4.42
/km
116 S
188 A
4.58
/km
130 S
206 A
4.31
/km
94 S
143 A
4.26
/km
104 S
158 A
4.21
/km
100 S
154 A
4.67
/km
133 S
217 A
4.27
/km
105 S
159 A
3.74
/km
94 S
140 A
Vehicles
Batteries
Fast charging infrastructure
Depot charging infrastructure
Energy
Vehicle maintenance
Infrastructure maintenance
Staff
Vehicles
Batteries
Fast charging infrastructure
Depot charging infrastructure
Energy
Vehicle maintenance
Infrastructure maintenance
Staff
Figure 14. TCO results for all scenarios. S: standard bus; A: articulated bus.
6. Discussion
In this section, we will address the limitations of our methodology and critically evaluate
our results.
6.1. OC Infrastructure Optimisation
The result obtained by the charging infrastructure optimisation—42 stations in the 300 kW scenario
and 44 in the 450 kW scenario—appears counterintuitive at first. It would be expected that the lower
the charging power, the more charging stations have to be deployed. However, our result can be
explained by the behaviour of the scheduling algorithm: Dwell times are determined such that the
battery can be fully charged at every terminus with a charging facility. Due to this strict condition,
a lower charging power increases the chance of the algorithm skipping the next departure at a terminus,
as illustrated schematically in Figure 15. If departures are skipped, however, the dwell time increases
by a multiple of the headway—creating additional time available for charging. This can eliminate the
need for additional charging stations on the same line. A high charging power, on the other hand,
increases the chance of obtaining a full charge without skipping departures, thus requiring more
charging stations, but reducing vehicle demand.
In practice, it would be conceivable to adjust timetables in order to better accommodate
opportunity charging and further reduce charging infrastructure demand. For example, departure
times could be modified such that the resulting dwell times are shifted toward one terminus,
thus allowing operation of the respective line with only one charging station. However, this was
outside of the scope of this study.
World Electric Vehicle Journal 2020,11, 56 27 of 43
Terminus A
Terminus B
Low charging power High charging power
time time
Charging timePassenger trips Schedule
Figure 15.
Schematic illustration of the effect of charging power on charging station placement using
the greedy scheduling algorithm.
6.2. Scheduling
As illustrated in Section 5.4, the greedy scheduling algorithm does not construct schedules
with minimum vehicle demand, which can lead to unexpected results especially in the case of
DC. The algorithm is therefore of limited use for schedule planning in practical applications.
Optimisation-based approaches as introduced in Section 3.2 are better suited, but issues regarding the
implementation and the ability to solve large problem instances have to be considered. In the case of
OC, the algorithm cannot consider charging station capacity constraints. This also is an obstacle to
practical application as the physical space available at potential charging locations is usually limited
from the outset.
6.3. Vehicle and Infrastructure Demand (System Simulation)
The OC charging infrastructure demand determined in the simulation is comparatively high in
relation to the fleet size: In both OC scenarios (4 and 5), it amounts to one charging slot for every
two vehicles. This figure could be lowered significantly in two ways. Firstly, charging slots that are
only seldom occupied could be dispensed of. Figure 13 provides an example: The peak demand of
eight slots only occurs three times a day for short intervals. Because vehicles generally have an ample
SOC reserve in the simulation, eliminating the eighth charging slot should have no adverse effects
(but this would have to be confirmed by a separate simulation). Secondly, changing the queueing
strategy at charging stations could enable a major reduction in charging points: In an unpublished
study we conducted for a bus operator, enabling vehicles to release charging points once fully charged
reduced the number of required charging points by 17%. However, this may incur additional staff cost,
depending on the labour regulations. Generally, the effect of reducing the number of charging slots on
overall TCO is expected to be marginal as charging infrastructure contributes no more than 3.4% to the
TCO.
6.4. TCO calculation
Our TCO results presented in Section 5.5 are not directly comparable to values from the literature
because the majority of works does not consider staff cost (as outlined in Section 3.5). For better
comparability, Figure 16 shows the results including only the additional staff cost incurred by electric
bus operation compared to the diesel scenario (i.e., the staff cost in the diesel scenario is set to zero).
Because of the infeasible scheduling results, the medium-range DC scenarios were omitted.
Table 9shows the relative TCO differences between individual technologies (diesel, OC, DC)
determined from the literature as well as our results from Figure 16. There are considerable
discrepancies between the values. Some studies claim a cost advantage of electric over diesel buses at
recent prices; our findings disagree with this. Furthermore, some studies estimate a high cost difference
between DC and OC of up to 55%, which we also cannot confirm. This is due to the fact that none of
the studies consider the additional staff cost incurred by OC and that some studies assume charging
at intermediate stops (as outlined in Section 3.5), reducing the cost of the OC system. The results by
World Electric Vehicle Journal 2020,11, 56 28 of 43
Lajunen and Lipman
[11]
are closest to ours, but even here, considerable deviations remain due to
methodological differences.
(a) With battery renewal
(1) DC (120 km)
(3) DC (300 km)
(4) OC (300 kW)
(5) OC (450 kW)
(7) OC (300 kW), 60 kW
(8) Diesel
0.0
0.5
1.0
1.5
2.0
2.5
3.0
TCO ( /km)
2.14
/km
116 S
188 A
2.14
/km
94 S
143 A
1.95
/km
104 S
158 A
1.90
/km
100 S
154 A
1.96
/km
105 S
159 A 1.35
/km
94 S
140 A
Vehicles
Batteries
Fast charging infrastructure
Depot charging infrastructure
Energy
Vehicle maintenance
Infrastructure maintenance
Staff
(b) Without battery renewal
(1) DC (120 km)
(3) DC (300 km)
(4) OC (300 kW)
(5) OC (450 kW)
(7) OC (300 kW), 60 kW
(8) Diesel
0.0
0.5
1.0
1.5
2.0
2.5
3.0
TCO ( /km)
2.03
/km
116 S
188 A
1.92
/km
94 S
143 A
1.87
/km
104 S
158 A
1.82
/km
100 S
154 A
1.88
/km
105 S
159 A
1.35
/km
94 S
140 A
Vehicles
Batteries
Fast charging infrastructure
Depot charging infrastructure
Energy
Vehicle maintenance
Infrastructure maintenance
Staff
Vehicles
Batteries
Fast charging infrastructure
Depot charging infrastructure
Energy
Vehicle maintenance
Infrastructure maintenance
Staff
Figure 16.
TCO comparison after subtracting staff cost of diesel scenario. S: standard bus; A:
articulated bus.
Table 9. Comparison of TCO results from the literature.
Source Relative TCO Difference Comments
OC vs. Diesel DC vs. Diesel DC vs. OC
Bi et al. [13] −18% −12% 8% No staff cost
Kunith [5] 4 ... 18% 53 . .. 83% 47 ... 55%
Additional staff cost
(for DC only)
Lajunen and Lipman [11] 22 ... 29% 34 ... 44% 7 ... 18% No staff cost
Pihlatie et al. [26] 7 ... 25% 43 . .. 60% 26 ... 40% No staff cost
Vilppo and Markkula [21] −6% n/a n/a No staff cost
Ke et al. [16] n/a n/a 8% No staff cost
This work 35 ... 45% 42 ... 58% 6 ... 13% Additional staff cost
The cost for modifications to the bus depot was not considered in our study. It is expected to be
higher for DC than for OC because of the larger fleet size and more powerful grid connection required.
Thus, the cost gap between the two technologies could widen when considering depot construction.
On the other hand, the planning and operation of OC charging infrastructure on public roads may also
incur additional cost not considered in our model.
In light of the narrow cost difference observed between some scenarios, it must be noted
that cost parameters may be subject to high uncertainties. In particular, the cost of vehicles
and charging infrastructure is difficult to determine due to the scarcity of public data and the
highly individualised nature of bus procurements. Also, there seem to be large cost differences
between various manufacturers as vehicle prices determined from the literature show (Figure 17):
Cost differences of up to one-third are observed despite similar battery capacity.
World Electric Vehicle Journal 2020,11, 56 29 of 43
200
300
400
500
600
700
800
900
1000
0 50 100 150 200 250 300 350 400
Vehicle cost (1000 €)
Battery capacity (kWh)
Standard bus (DC) Articulated bus (OC)
VDL
Solaris
Mercedes
Sileo
Irizar
Figure 17. Comparison of vehicle cost reported in the literature [53,62,66,67].
7. Conclusions and Outlook
We developed a planning and simulation methodology for electric bus networks comprising an
object-oriented, discrete-event based simulation tool, a greedy bus scheduling algorithm, and a genetic
algorithm for charging infrastructure positioning wrapped around the scheduling algorithm and
simulation. The methodology was applied to assess the electrification of a real-world, metropolitan
bus network with 39 bus lines using depot charging (DC) and opportunity charging at terminal
stops (OC-T).
We first investigated the feasibility of operating existing diesel bus schedules with electric buses.
Five electric bus scenarios were evaluated: three DC scenarios with varying range (120, 200 and 300 km)
and two OC scenarios with varying charging power (300 and 450 kW). The analysis shows that none
of the scenarios permit the operation of unchanged schedules, owing to the limited range of DC buses
and the limited charging time available for OC. Delays exert a significant influence in the OC case and
must therefore be taken into account to obtain valid results.
In the second stage, a TCO evaluation was carried out for fully electrified scenarios and a diesel
reference scenario. New schedules were planned for each scenario using our scheduling algorithm.
For OC, TCO-optimised charging locations were obtained using the genetic algorithm. We found that
the smallest electric bus fleet size could be achieved by DC buses with a range of 300 km; otherwise,
the OC scenarios yielded smaller fleet sizes than DC. The charging process at the depot was identified
as a bottleneck for DC, but not for OC buses.
The TCO calculation reveals that OC has a slight cost advantage over DC in all scenarios, the TCO
of DC being 1–6% higher than OC. As depot construction cost was not considered, the cost gap between
DC and OC may turn out higher in practice. Compared to diesel systems, the TCO of OC was at least
13% higher and the TCO of DC was at least 15% higher. Contrary to other studies, these figures include
the full driver cost, allowing an assessment of the true additional cost of electric bus operation on a
system level.
Our analysis of a complete bus network confirms our previous finding for a single bus line
in [
6
]: On a system level, the cost difference between OC and DC can turn out very small. Given the
uncertainties of the inputs, it can be argued that de facto cost parity exists between the two systems
under some circumstances. Thus, no general recommendation for either of the technologies can
be given solely on a cost basis. In cases where the results of the TCO analysis are inconclusive,
other criteria must be defined to decide upon one of the two technologies.
Our methodology provides a framework for the planning and evaluation of electric bus systems
with a higher level of detail and less reliance on simplifying assumptions than approaches found in
the existing literature. Nonetheless, several aspects could be improved in further research:
•
The strict condition to fully charge at every charging station enforced by the scheduling algorithm
reduces the efficiency of the OC schedules.
World Electric Vehicle Journal 2020,11, 56 30 of 43
•
The objective of the scheduling algorithm—maximising the schedule length—does not concur
with the objective of minimum fleet size or minimum cost, leading to partly unexpected results
especially in the case of DC. Development of a refined algorithm is already underway. It takes
into account the concurrence of trips and leads to a more even distribution of depot trips over
time, potentially mitigating the adverse effect observed in this work.
• The scheduling algorithm currently does not support charging station capacity constraints.
•
In this study, we limited the duration of an operational day to 24 h. However, with OC, vehicles
could remain in service for several consecutive days without returning to the depot, reducing the
number of depot trips and, therefore, the TCO. This should be examined in future works.
•
We did not evaluate a mixed scenario of OC and DC lines, even though it is a likely option for
real-world application. Determining the best choice of technology on a per-line basis is, however,
an optimisation problem in itself, requiring the development of additional methodology.
•
The possibility of opportunity charging with central charging stations (OC-C) was not evaluated.
This would also require further development of the scheduling algorithm.
•
The schedule simulation currently relies on a simple, constant consumption vehicle model.
This should be improved especially if the topography of the bus network includes steep gradients.
•
The battery model currently does not consider variable charging power depending on the
current state of charge. Also, no evaluation of the battery lifetime based on the actual
charging/discharging cycle (e.g., as in [
68
]) is carried out. Both could be improved for
better accuracy.
Author Contributions:
Conceptualization, D.J. and D.G.; methodology, D.J.; software, D.J.; investigation, D.J.;
resources, D.G.; data curation, D.J.; writing—original draft preparation, D.J.; writing—review and editing, D.G.;
visualization, D.J.; supervision, D.G.; project administration, D.J. and D.G.; funding acquisition, D.G. All authors
have read and agreed to the published version of the manuscript.
Funding: The authors would like to thank BVG Berliner Verkehrsbetriebe AöR for funding this research.
Acknowledgments:
We gratefully acknowledge the cooperation of BVG, in particular Daniel Hesse and Jing Hui
Denny Chen, in conducting this research. Jonas Schulte-Mattler, student research assistant at our Department,
provided valuable support in data preparation and visualisation. We also thank the Electric Transport Solutions
team at our Department for many fruitful discussions.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
API Application programming interface
CAPEX Capital expenditures
CCS Combined charging system
DC Depot charging
GA Genetic algorithm
HVAC Heating, ventilation and air-conditioning
IMC In-motion charging
MILP Mixed-integer linear programming
NPV Net present value
OC (OC-T, OC-I, OC-C) Opportunity charging (terminal stops, intermediate stops, central charging stations)
OPEX Operational expenditures
SOC State of charge
SOH State of health
TCO Total cost of ownership
VDV Verband deutscher Verkehrsunternehmen (German association of public
transport operators)
VSP Vehicle scheduling problem
World Electric Vehicle Journal 2020,11, 56 31 of 43
Appendix A. Scheduling Algorithm Flowcharts
Start Find first trip in timetable;
determine vehicle type
Start new schedule with this vehicle type
Add depot trip to beginning of schedule
Can we charge
at destination?
Simulate schedule
Vehicle
SoC
critical?
End schedule yes
no
yes no
Minimum dwell time
= max(charging time1;
global min. dwell time)
Minimum dwell time
= global min. dwell time
Find next trip from destination with matching vehicle type
Max. dwell time
exceeded?
End schedule yes
no
Add trip to schedule,
remove from timetable
Matching
trip
available?
yes
End schedule no
Schedule
OK
(no errors)?
Trips
left in
timetable?
no
yes
yes no End (error)
End schedule
Start
Add depot trip to
end of schedule Simulate schedule
Vehicle
SoC
critical?
yes
no
Save schedule
Remove last depot
and passenger trip
from schedule;
re-add passenger
trip to timetable End
No. of
passenger trips in
schedule ≥ 1?
no
End (error)
yes
1 Time to fully charge energy
storage; including additional
delay reserve if specified
Generate schedules (main algorithm)
End
Figure A1. Scheduling algorithm, stage I.
World Electric Vehicle Journal 2020,11, 56 32 of 43
Schedule 1 = first schedule from stack 1;
remove from stack 1
Copy stack 1 to stack 2
Sort stack 2 by first
departure2, ascending
Schedules
left in
stack 2?
New schedule = concatenate schedule 1 and 2
Concatenation
successful?
yes
Simulate new schedule
Vehicle
SoC
critical?
no
●
●
●
●
Set "save" flag
Remove schedule 1 from
original schedules3
Remove schedule 2 from
original schedules and stack 13
Schedule 1 = new schedule
no
yes
yes
"Save"
flag set?
yes
no
Save schedule 1
to new schedules
● Copy original schedules to stack 1
● Sort stack 1 by last arrival1, ascending
● Create empty stack (new schedules)
Start
Schedules
left in
stack 1?
yes
no
New schedule set =
original schedules
+ new schedules
no
1 Arrival of last passenger trip
2 Departure of first passenger trip
3 If it exists in the respective stack
Combine schedules
End
Schedule 2 = first schedule from stack 2;
remove from stack 2
Figure A2. Scheduling algorithm, stage II.
Appendix B. All Inputs to Schedule Simulation
A schedule simulation requires a grid
G= (P
,
A)
consisting of a set of points
P={p1
,
. . .
,
pNP}
and a set of arcs
A={a1
,
. . .
,
ai
,
. . .
,
aNA}
connecting the points. Each arc
ai= (po,i
,
pd,i
,
di)
has an
origin point po,i, destination point pd,iand distance di.
Furthermore, a set of schedules
U={U1
,
. . .
,
Ui
,
. . .
,
UNU}
is required. Each schedule
Ui= (Ti,vi)
is defined by a list of trips
Ti= (Ti,1
,
. . .
,
Ti,j
,
. . .
,
Ti,NT,i)
and a vehicle type
vi
. Each trip
Tij = (Li,j
,
tti,j)
is defined by a list of legs
Li,j= (Li,j,1
,
. . .
,
Li,j,k
,
. . .
,
Li,j,NL,i,j)
and a trip type
tti,je{passenger trip, empty trip}
. Legs represent movements between two stops, however, to account
for topographical changes (such as different slopes), legs can be further divided into segments.
After each leg, a planned pause may be introduced; usually, this is only the case after the last
leg of a trip, but it may also occur in between to allow waiting for other bus lines and enabling
passenger transfer. Each leg
Li,j,k= (Si,j,k
,
tdep,i,j,k
,
tpause,i,j,k)
is therefore defined by a list of segments
Si,j,k= (Si,j,k,1
,
. . .
,
Si,j,k,l
,
. . .
,
Si,j,k,NS,i,j,k)
, departure time
tdep,i,j,k
and pause duration succeeding the
leg
tpause,i,j,k
. Each segment
Si,j,k,l= (ai,j,k,l
,
ti,j,k,l
,
tdelay,i,j,k,l)
is defined by the grid arc
ai,j,k,l
it covers,
World Electric Vehicle Journal 2020,11, 56 33 of 43
the travel duration
ti,j,k,l
and a delay
tdelay,i,j,k,l
. Leg and trip durations and distances are obtained by
summing over their respective children.
A set of charging points
Cp={Cp,1
,
. . .
,
Cp,i
,
. . .
,
Cp,NCp}
and a set of charging arcs
Ca=
{Ca,1
,
. . .
,
Ca,i
,
. . . Ca,NCa}
may be defined, each consisting of a location (grid point
pi
or arc
ai
),
a capacity
ci
and a charging interface
Ii
:
Cp,i= (pi
,
cp,i
,
Ip,i)
and
Ca,i= (ai
,
ca,i
,
Ia,i)
. Several charging
facilities can exist at the same location: For example, it is conceivable to have both a fast-charging and
a slow-charging facility at the same grid point.
A charging interface
Ii= (mi
,
tdock,i
,
tundock,i
,
Pmax,i
,
imi)
is characterised by its medium
mie{electricity, diesel, hydrogen, .. . }
, docking time
tdock,i
, undocking time
tundock,i
, maximum power
(or flow)
Pmax,i
and a boolean value indicating whether the interface is capable of charging while in
motion, imie{0, 1}.
Furthermore, a schedule simulation requires a set of depots
D= (D1
,
. . .
,
Di
,
. . .
,
DND)
.
Each depot
Di= (pi
,
tdead,arr,i
,
tdead,dep,i)
is characterised by its grid point
pi
and the duration that
vehicles are blocked for upon arrival and before departure,
tdead,arr,i
and
tdead,dep,i
, respectively. If a
depot is to include charging facilities, a charging point must be defined at the corresponding grid point
as illustrated above.
Finally, the simulation requires a set of vehicle types
V={V1
,
. . .
,
Vi
,
. . .
,
VNV}
. Each vehicle type
Vi= (vai
,
Ii
,
etraction,i
,
Paux,i
,
Hi
,
NHVAC,i
,
UAi
,
Asol,i
,
mkerb,i
,
Enom,i
,
SOHi
,
SOCmin,i
,
SOCmax,i
,
Ccharge,i
,
Cdischarge,i)
is defined by a vehicle architecture
vaie{electric bus, diesel bus, . . . }
,
a list of charging interfaces
Ii
, specific traction consumption
etraction,i
,
auxiliary power
Paux,i
(excluding HVAC), the choice of HVAC system
Hie{AC+HP+electric backup, AC+HP+diesel backup, AC+electric heater, AC+diesel heater}
,
the number of HVAC units
NHVAC,i
, the vehicle’s heat transmittance
UAi
, the surface area used for
solar gain calculation
Asol,i
and kerb weight
mkerb,i
. Also, energy storage parameters have to be set;
for a battery, these are: nominal battery capacity
Enom,i
, state of health
SOHi
, operational SOC window
defined by
SOCmin,i
and
SOCmax,i
and charge/discharge limits defined by
Ccharge,i
and
Cdischarge,i
.
Some storage parameters may be omitted for vehicle types without a battery (e.g., diesel buses).
Appendix C. Equations for Vehicle Model
In the following, the model equations related to energy flow and energy consumption of the
vehicle are reproduced.
Appendix C.1. Energy Flow and Energy Storage Model
The total power of all loads is evaluated for each energy subsystem whenever a state
change occurs:
Ploads(t) = ∑
i
Pload,i(t). (A1)
For the primary subsystem of an electric bus, this equation typically evaluates to
Ploads(t) = Ptraction(t) + PHVAC(t) + Paux,other(t). (A2)
If
Ploads >
0, energy is consumed by the loads; if
Ploads <
0, energy is recuperated. In the following,
only the primary energy subsystem is considered, and the time argument
f(t)
is dropped for the sake
of readability. Generally, all variables in the model are time-dependent except for static parameters.
The following equations describe the energy routing logic applied by the charge controller, using
the terminology defined in Figure A3. Let
Pcharge,max
and
Pdischarge,max
be the current charge/discharge
limits of the energy storage. Also, let
Psupply,max
and
Pfeed-in,max
be the current limits for drawing
power from and feeding power back to a charging interface, respectively; if no interface is connected,
both are zero. (Feeding energy back to the grid can be of relevance in trolleybus and train operations
for which our model was also designed.)
World Electric Vehicle Journal 2020,11, 56 34 of 43
Energy
storage
Loads Charging
interface
Pinterface,loads
Ploads,interface
Pinterface,storage
Pstorage,loads
Ploads,storage
Energy subsystem
Figure A3. Energy flow model within energy subsystem.
If energy is consumed (
Ploads ≥
0), Equations
(A3)
through
(A8)
apply. In this case, there is no
flow from the loads:
Ploads,interface =0 (A3)
Ploads,storage =0 . (A4)
If power is available from the interface, it is preferentially routed to the loads:
Pinterface,loads =(Ploads,Ploads ≤Psupply,max
Psupply,max,Ploads >Psupply,max.(A5)
If the interface cannot supply all the power required, the remaining power must come from the
energy storage:
Pstorage,loads =Ploads −Pinterface,loads. (A6)
If
Pstorage,loads
exceeds the discharge limit
Pdischarge,max
, a warning is issued but simulation continues.
If the power available from the interface is greater than the load, the excess power can be used to
charge the energy storage. The maximum power available from the interface for charging is
Pinterface,storage,max =Psupply,max −Pinterface,loads. (A7)
To determine the actual flow from interface to storage, the charge limit must be observed (note that
if the storage is fully charged, Pcharge,max =0):
Pinterface,storage =(Pinterface,storage,max,Pinterface,storage,max ≤Pcharge,max
Pcharge,max,Pinterface,storage,max >Pcharge,max.(A8)
If energy is recuperated (
Ploads <
0), energy flow is governed by Equations
(A9)
through
(A15)
.
There is no flow to the loads:
Pinterface,loads =0 (A9)
Pstorage,loads =0. (A10)
Recuperation power is first routed to the energy storage:
Ploads,storage =(|Ploads|,|Ploads|≤Pcharge,max
Pcharge,max,|Ploads|>Pcharge,max.(A11)
World Electric Vehicle Journal 2020,11, 56 35 of 43
If there is still excess recuperation power that cannot be fed into the storage, the charge controller
attempts to route it to the interface. The maximum power available is:
Ploads,interface,max =|Ploads|−Ploads,storage. (A12)
The actual flow to the interface is then given by
Ploads,interface =(Ploads,interface,max,Ploads,interface,max ≤Pfeed-in,max
Pfeed-in,max,Ploads,interface,max >Pfeed-in,max.(A13)
Any power remaining in excess of
Pfeed-in,max
must be dissipated through a braking resistance,
which is not modelled.
If the recuperation power does not exceed the charge limit of the energy storage and an interface
is connected, there is power available to charge the storage from the interface. At most,
Pinterface,storage,max =Pcharge,max −Ploads,storage (A14)
can be transferred to the storage. Observing the power limit of the interface, the actual power transfer is:
Pinterface,storage =(Pinterface,storage,max,Pinterface,storage,max ≤Psupply,max
Psupply,max,Pinterface,storage,max >Psupply,max.(A15)
The net flows to the interface and storage are, respectively:
Pinterface =Pinterface,loads +Pinterface,storage −Ploads,interface, (A16)
where
Pinterface >
0 indicates power flowing from and
Pinterface <
0 indicates power flowing into the
interface, and
Pstorage =Pstorage,load −Pload,storage −Pinterface,storage, (A17)
with Pstorage >0 indicating discharging and Pstorage <0 indicating charging of the storage.
The energy flow entering or leaving the storage is now known at every time
t
. Let
t0
be the last
point in time at which the state was updated by the storage. The energy content of the storage at time
t
is then
E(t) = E(t0)−Pstorage(t0)·(t−t0). (A18)
The energy storage has a nominal capacity Enom. In the case of a simple tank, the state of charge
is determined relative to this nominal capacity:
SOC =E
Enom . (A19)
A battery has an additional attribute
SOH
defining its state of health, i.e., the fraction of the
nominal capacity still usable. The state of charge of a battery is determined relative to the real,
usable capacity
SOC =E
Ereal
, (A20)
which in turn is defined by
Ereal =SOH ·Enom. (A21)
Furthermore, the battery’s operational SOC range is defined by the values
SOCmin
and
SOCmax
.
Charge and discharge limits were already introduced above.
World Electric Vehicle Journal 2020,11, 56 36 of 43
Appendix C.2. Traction Model
The constant consumption traction model determines the mean traction power for each interval
based on a specific consumption etraction (in kWh/km, L/km etc.):
Ptraction(t) = etraction L
∆t,te[t0,t0+∆t](A22)
where Lis the distance of the arc, t0the departure time and ∆tthe travel duration.
The longitudinal dynamics model currently assumes a constant total drivetrain efficiency
ηtotal
,
however the model architecture also permits implementation of a motor efficiency map. Traction
power is obtained from the mechanical power at the wheels, Pwheels,
Ptraction(t) =
Pwheels(t)
ηtotal
,Pwheels(t)≥0
Pwheels(t)ηtotal Pwheels(t)<0,
(A23)
which itself is determined from the driving resistance consisting of rolling, climbing, air and
acceleration resistances:
Pwheels(t) = [Froll(t) + Fclimb(t) + Fair(t) + Facc(t)]v(t). (A24)
Herein,
Froll(t) = frmtotal(t)gcos (α(t))Fclimb(t) = mtotal(t)gsin (α(t))(A25)
Fair(t) = ρair
2cwAfront (v(t))2Facc(t) = hλmkerb +mpayload(t)ia(t)(A26)
with rolling resistance coefficient
fr
, total vehicle mass
mtotal =mkerb +mpayload
, constant of gravitation
g
, vehicle slope
α
, density of air
ρair
, drag coefficient
cw
, vehicle frontal projection area
Afront
,
vehicle velocity
v
, rotational mass factor
λ
, vehicle kerb weight
mkerb
, payload
mpayload
and vehicle
acceleration a.
Appendix C.3. HVAC Model
The steady state heating load—negative values indicating heat loss (heating case) and positive
values indicating heat gain (cooling case)—is given by
˙
QHVAC(t) = ˙
Qconv(t) + ˙
Qsol(t) + ˙
Qpassengers(t). (A27)
Once again, we will henceforth drop the time argument
f(t)
for readability. The convective heat
loss is determined from the heat transfer equation using the heat transmittance
UA
, the ambient
temperature Tambient and the cabin temperature Tcabin:
˙
Qconv =U A (Tambient −Tcabin). (A28)
The solar gain ˙
Qsol results from the insolation ˙
qsol and a surface area Asol:
˙
Qsol =˙
qsol Asol. (A29)
World Electric Vehicle Journal 2020,11, 56 37 of 43
Heat release by passengers is determined using correlations from [69] (activity level II):
˙
Qpassengers =˙
Qpassengers,sensible +˙
Qpassengers,latent (A30)
˙
Qpassengers,sensible
W= 166 −3.8 T
°C!Npassengers (A31)
˙
Qpassengers,latent
W= −41 +3.8 T
°C!Npassengers (A32)
T=
16 °C, Tcabin ≤16 °C
Tcabin, 16 °C <Tcabin ≤28 °C
28 °C, Tcabin >28 °C.
(A33)
The HVAC system consists of a cooling system with a maximum cooling capacity
˙
Qcooling,max
,
a heating system with a maximum heating capacity
˙
Qheating,max
, and a backup heater with a maximum
capacity ˙
Qbackup,max.
In heating mode (
˙
QHVAC ≤
0), the thermal power supplied by the heating unit (usually, a heat
pump) is
˙
Qheating =(˙
QHVAC,˙
QHVAC≤˙
Qheating,max
˙
Qheating,max,˙
QHVAC>˙
Qheating,max.(A34)
The thermal power delivered by the backup heater is
˙
Qbackup =
0, ˙
QHVAC≤˙
Qheating,max
˙
QHVAC−˙
Qheating,max,˙
QHVAC>˙
Qheating,max and
˙
QHVAC−˙
Qheating,max ≤˙
Qbackup,max
˙
Qbackup,max, otherwise.
(A35)
In the latter case, a warning is issued because the available heating capacity is not sufficient to
keep the desired cabin temperature. Cooling power is ˙
Qcooling =0 in heating mode.
In cooling mode ( ˙
QHVAC >0),
˙
Qcooling =(˙
QHVAC,˙
QHVAC ≤˙
Qcooling,max
˙
Qcooling,max,˙
QHVAC >˙
Qcooling,max,(A36)
where, in the latter case, a warning is generated because cooling load exceeds cooling system capacity.
˙
Qheating =0 and ˙
Qbackup =0 apply in cooling mode.
The electric power of the HVAC system (equations for a diesel heater are not reproduced here) is
determined through the coefficient of performance (COP) of each component:
PHVAC =˙
Qheating
COPheating
+˙
Qbackup
COPbackup
+˙
Qcooling
COPcooling
. (A37)
˙
Qheating,max
,
˙
Qcooling,max
and
˙
Qbackup,max
need not necessarily be constant. For the heat pump
modelled,
˙
Qheating,max
was implemented as a function of ambient temperature based on data provided
by a manufacturer:
˙
Qheating,max =
0, Tambient <−15 °C
Nunits · 0.27 Tambient
°C +18.2!kW, −15 °C ≤Tambient <0 °C
Nunits ·18.2 kW, Tambient ≥0 °C.
(A38)
World Electric Vehicle Journal 2020,11, 56 38 of 43
Nunits
specifies the number of HVAC units installed in the vehicle (typically 1 for a standard bus
and 2 for an articulated bus). Furthermore,
˙
Qbackup,max =Nunits ·20 kW and ˙
Qcooling,max =Nunits ·20 kW. (A39)
The COPs of all components are currently assumed constant:
COPheating =2, COPcooling =2, COPbackup =0.9. (A40)
Appendix D. Equations for TCO Model
From the simulation, the following quantities are determined: Number of vehicles of type
v
,
Nvehicles,v
, number of charging facilities of type
c
,
Nstations,c
, number of charging slots of type
c
,
Nslots,c
,
annual fleet mileage per vehicle type
v
,
Mfleet,v,a
, annual fleet energy demand per medium
m
,
Efleet,m,a
(possible media being electricity, diesel, etc.) and annual driver hours tdriver,a.
Let
tbase
be the base year for which all currency shall be adjusted,
tstart
the start year of the project,
∆tproject
the project duration and
tend =tstart +∆tproject
the end year of the project. In the following,
all cost elements are assigned a category
c
, for example, vehicle investment for each vehicle type,
charging infrastructure investment for each charging station type, vehicle maintenance, charging
station maintenance, energy for each medium, staff hours.
Each investment object of category
c
has a usage period
∆tdp,c
after which a new procurement is
due. The number of procurements for objects of category cis:
Nproc,c=&∆tproject
∆tdp,c'. (A41)
The years where a procurement takes place are then given by
Tproc,c=ntproc,c,i|tproc,c,i=tstart + (i−1)∆tdp,c∀ie{1, . . . , Nproc,c}o. (A42)
The investments for category cat any time t(illustrated in Figure 8a) are obtained from
CCAPEX,c(t) = (cc(t)QcteTproc,c
0 otherwise, (A43)
where
cc(t)
is the unit cost in year
t
and
Qc
is the quantity determined from the simulation. The unit
cost is determined for every year of the component lifetime from cost escalation/degression factors
ic(t)
(indicating the change of cost relative to the previous year) that may be defined for each individual
year per category. Assuming the unit cost is known at time tbase,
cc(t) = cc(tbase)
t=t
∏
t=tbase+1
(1+ic(t)). (A44)
Investments are assumed made from borrowed capital, which is repayed as an annuity over
the lifetime of the respective component. The resulting cash flow for each category
c
at any year
t—pictured schematically in Figure 8b—is:
CFCAPEX,c(t) = CCAPEX,c(tproc,c(t)) ·CRF(icapital,∆tdp,c), (A45)
where the capital recovery factor CRF is defined as
CRF(i,T) = i(1+i)T
(1+i)T−1. (A46)
World Electric Vehicle Journal 2020,11, 56 39 of 43
To convert all cash flows into the currency of the base year, they are discounted using the mean
inflation rate iinflation, yielding the cash flows pictured in Figure 8c:
CFCAPEX,NPV,c(t) = CFCAPEX,c(t)
(1+iinflation)t−tbase . (A47)
The operational expenditures for category
c
are obtained from unit cost
cc(t)
and the annual
quantities Qc,a determined in the simulation (cf. Figure 8d):
CFOPEX,c(t) = cc(t)Qc,a. (A48)
Converted to the currency of the base year, we obtain the cash flows as displayed in Figure 8e:
CFOPEX,NPV,c(t) = CFOPEX,c(t)
(1+iinflation)t−tbase . (A49)
The sum of all discounted CAPEX cash flows over the respective component lifetime is
CFCAPEX,NPV,sum,c=
tstart+Nproc,c∆tdp,c
∑
t=tstart
CFCAPEX,NPV,c(t). (A50)
Generally, the project duration should be a multiple of component lifetimes, such that
∆tproject =
tstart +Nproc,c∆tdp,c
. If, however,
∆tproject <tstart +Nproc,c∆tdp,c
(this is commonly the case for the
charging infrastructure of which the assumed usage period is longer than the project duration), there
are two possible strategies to reflect this in the TCO calculation: Truncate the cash flows occurring after
the end of the project, or scale down the sum of cash flows. We chose the latter, such that the TCO
contribution of capital expenditures for component cis:
CTCO,CAPEX,c=CFCAPEX,NPV,sum,c
∆tproject
∆tdp,c
. (A51)
The TCO contribution of operational expenditures is:
CTCO,OPEX,c=CFOPEX,NPV,sum,c=
tend
∑
t=tstart
CFOPEX,NPV,c(t). (A52)
They add up to the total system TCO
CTCO =∑
c
CTCO,CAPEX,c+∑
c
CTCO,OPEX,c. (A53)
The TCO values are divided by the total productive fleet mileage (i.e., the mileage spent on
passenger trips) to yield the specific TCO per unit of mileage (€/km in our case):
cTCO,CAPEX,c=CTCO,CAPEX,c
Lfleet,prod
cTCO,OPEX,c=CTCO,OPEX,c
Lfleet,prod
cTCO =CTCO
Lfleet,prod
. (A54)
World Electric Vehicle Journal 2020,11, 56 40 of 43
References
1.
ZeEUS Project. ZeEUS eBus Report #2: An Updated Overview of Electric Buses in Europe. Available
online: http://zeeus.eu/uploads/publications/documents/zeeus-report2017-2018-final.pdf (accessed on
25 June 2020).
2.
Verband deutscher Verkehrsunternehmen (VDV). E-Bus-Projekte in Deutschland. Available online: https:
//www.vdv.de/e-bus-projekt.aspx (accessed on 25 June 2020).
3.
Wilkens, A. Induktives Laden: Mannheim Will Keine Weiteren Primove-Elektrobusse. Available
online: https://www.heise.de/newsticker/meldung/Induktives-Laden-Mannheim-will-keine-weiteren-
Primove-Elektrobusse-4060084.html (accessed on 25 June 2020).
4.
Sommariva, R. Trolleybuses in Berlin, BVG is Considering Massive Deployment in Spandau District.
Available online: https://www.sustainable-bus.com/news/trolleybuses-in-berlin-bvg-is-considering-
massive-deployment-in-spandau-district/ (accessed on 25 June 2020).
5.
Kunith, A.W. Elektrifizierung des Urbanen öffentlichen Busverkehrs: Technologiebewertung für den
Kosteneffizienten Betrieb Emissionsfreier Bussysteme. Ph.D. Thesis, Technische Universität Berlin, Berlin,
Germany, 2017. [CrossRef]
6.
Jefferies, D.; Göhlich, D. Integrated TCO Assessment of Bus Network Electrification
Considering Rescheduling and Delays: Modelling Framework and Case Study. EVS31
International Electric Vehicle Symposium & Exhibition, Kobe, Japan, 2018. Available online:
https://www.researchgate.net/publication/329210166_Integrated_TCO_Assessment_of_Bus_Network_
Electrification_Considering_Rescheduling_and_Delays (accessed on 25 June 2020).
7.
Göhlich, D.; Fay, T.A.; Jefferies, D.; Lauth, E.; Kunith, A.; Zhang, X. Design of urban electric bus systems.
Des. Sci. 2018,4.[CrossRef]
8.
Fusco, G.; Alessandrini, A.; Colombaroni, C.; Valentini, M.P. A Model for Transit Design with Choice of
Electric Charging System. Procedia- Soc. Behav. Sci. 2013,87, 234–249. [CrossRef]
9.
Lajunen, A. Lifecycle costs and charging requirements of electric buses with different charging methods.
J. Clean. Prod. 2018,172, 56–67. [CrossRef]
10.
Gao, Z.; Lin, Z.; LaClair, T.J.; Liu, C.; Li, J.M.; Birky, A.K.; Ward, J. Battery capacity and recharging needs for
electric buses in city transit service. Energy 2017,122, 588–600. [CrossRef]
11.
Lajunen, A.; Lipman, T. Lifecycle cost assessment and carbon dioxide emissions of diesel, natural gas, hybrid
electric, fuel cell hybrid and electric transit buses. Energy 2016,106, 329–342. [CrossRef]
12.
Macedo, J.; Soares, G.; Kokkinogenis, Z.; Perrotta, D.; Rossetti, R.J.F. A Framework for Electric Bus Powertrain
Simulation in Urban Mobility Settings: Coupling SUMO with a Matlab/Simulink Nanoscopic Model, 1st ed.;
SUMO User Conference: Berlin, Germany, 2013.
13.
Bi, Z.; de Kleine, R.; Keoleian, G.A. Integrated Life Cycle Assessment and Life Cycle Cost Model for
Comparing Plug-in versus Wireless Charging for an Electric Bus System. J. Ind. Ecol.
2017
,21, 344–355.
[CrossRef]
14.
De Filippo, G.; Marano, V.; Sioshansi, R. Simulation of an electric transportation system at The Ohio State
University. Appl. Energy 2014,113, 1686–1691. [CrossRef]
15.
Sebastiani, M.T.; Luders, R.; Fonseca, K.V.O. Evaluating Electric Bus Operation for a Real-World BRT
Public Transportation Using Simulation Optimization. IEEE Trans. Intell. Transp. Syst.
2016
,17, 2777–2786.
[CrossRef]
16.
Ke, B.R.; Chung, C.Y.; Chen, Y.C. Minimizing the costs of constructing an all plug-in electric bus
transportation system: A case study in Penghu. Appl. Energy 2016,177, 649–660. [CrossRef]
17.
Rogge, M.; van der Hurk, E.; Larsen, A.; Sauer, D.U. Electric bus fleet size and mix problem with optimization
of charging infrastructure. Appl. Energy 2018,211, 282–295. [CrossRef]
18.
Lindgren, L. Electrification of City Bus Traffic-A Simulation Study Based on Data from Linköping. Available
online: http://lup.lub.lu.se/record/d5834bb3-c0f0-4c7c-a493-69b10291d1f1 (accessed on 25 June 2020).
19.
Li, L.; Lo, H.K.; Xiao, F. Mixed bus fleet scheduling under range and refueling constraints. Transp. Res. Part
Emerg. Technol. 2019,104, 443–462. [CrossRef]
20.
Kovalyov, M.Y.; Rozin, B.M.; Guschinsky, N.N. Mathematical Model and Random Search Algorithm for the
Optimal Planning Problem of Replacing Traditional Public Transport with Electric. Autom. Remote Control.
2020,81, 803–818. [CrossRef]
World Electric Vehicle Journal 2020,11, 56 41 of 43
21.
Vilppo, O.; Markkula, J. Feasibility of electric buses in public transport. In Proceedings of the EVS28
International Electric Vehicle Symposium and Exhibition, Seoul, Korea, 3–5 May 2015.
22.
Kunith, A.; Mendelevitch, R.; Göhlich, D. Electrification of a city bus network-An optimization model for
cost-effective placing of charging infrastructure and battery sizing of fast charging electric bus systems.
DIW Discussion Papers, 2016. Available online: http://www.diw.de/documents/publikationen/73/diw_01.
c.534056.de/dp1577.pdf (accessed on 25 June 2020).
23.
Liu, Z.; Song, Z. Robust planning of dynamic wireless charging infrastructure for battery electric buses.
Transp. Res. Part Emerg. Technol. 2017,83, 77–103. [CrossRef]
24.
Berthold, K.; Förster, P.; Rohrbeck, B. Location Planning of Charging Stations for Electric City Buses.
In Operations Research Proceedings; Springer International Publishing: Cham, Switzerland, 2017; pp. 237–242.
[CrossRef]
25.
Xylia, M.; Leduc, S.; Patrizio, P.; Kraxner, F.; Silveira, S. Locating charging infrastructure for electric buses in
Stockholm. Transp. Res. Part Emerg. Technol. 2017,78, 183–200. [CrossRef]
26.
Pihlatie, M.; Kukkonen, S.; Halmeaho, T.; Karvonen, V.; Nylund, N.O. Fully electric city buses-The viable
option. In Proceedings of the 2014 IEEE International Electric Vehicle Conference (IEVC), Florence, Italy,
17–19 December 2014; pp. 1–8. [CrossRef]
27.
Paul, T.; Yamada, H. Operation and charging scheduling of electric buses in a city bus route network.
In Proceedings of the 17th International IEEE Conference on Intelligent Transportation Systems (ITSC),
Qingdao, China, 8–11 October 2014. [CrossRef]
28.
Wang, H.; Shen, J. Heuristic approaches for solving transit vehicle scheduling problem with route and
fueling time constraints. Appl. Math. Comput. 2007,190, 1237–1249. [CrossRef]
29. Li, J.Q. Transit Bus Scheduling with Limited Energy. Transp. Sci. 2014,48, 521–539. [CrossRef]
30.
Adler, J.D.; Mirchandani, P.B. The Vehicle Scheduling Problem for Fleets with Alternative-Fuel Vehicles.
Transp. Sci. 2017,51, 441–456. [CrossRef]
31.
Wen, M.; Linde, E.; Ropke, S.; Mirchandani, P.; Larsen, A. An adaptive large neighborhood search heuristic
for the Electric Vehicle Scheduling Problem. Comput. Oper. Res. 2016,76, 73–83. [CrossRef]
32.
Reuer, J.; Kliewer, N.; Wolbeck, L. The Electric Vehicle Scheduling Problem-A study on time-space network
based and heuristic solution approaches. In Proceedings of the Conference on Advanced Systems in Public
Transport (CASPT), Rotterdam, The Netherlands, 19–23 July 2015.
33.
van Kooten Niekerk, M.E.; van den Akker, J.M.; Hoogeveen, J.A. Scheduling electric vehicles. Public Transp.
2017,9, 155–176. [CrossRef]
34.
Sinhuber, P.; Rohlfs, W.; Sauer, D.U. Study on Power and Energy Demand for Sizing the Energy Storage
Systems for Electrified Local Public Transport Buses. In Proceedings of the IEEE Vehicle Power and
Propulsion Conference (VPPC), Seoul, Korea, 9–12 October 2012; pp. 315–320.
35.
Hegazy, O.; El Baghdadi, M.; Coosemans, T.; Van Mierlo, J. Co-design Optimization Framework for
Electrified Buses in Cities:Brussels Case Study. In Proceedings of the EVS31 International Electric Vehicle
Symposium & Exhibition, Kobe, Japan, 30 September–3 October 2018.
36.
Lajunen, A.; Kalttonen, A. Investigation of thermal energy losses in the powertrain of an electric city bus.
In Proceedings of the 2015 IEEE Transportation Electrification Conference and Expo (ITEC), Dearborn,
Michigan, 14–17 June 2015. [CrossRef]
37.
Jefferies, D.; Ly, T.; Kunith, A.; Göhlich, D. Energiebedarf Verschiedener Klimatisierungssysteme für
Elektro-Linienbusse; Deutsche Kälte- und Klimatagung: Dresden, Germany, 2015.
38.
Göhlich, D.; Ly, T.; Kunith, A.; Jefferies, D. Economic assessment of different air-conditioning and heating
systems for electric city buses based on comprehensive energetic simulations. In Proceedings of the EVS28
International Electric Vehicle Symposium and Exhibition, Seoul, South Korea, 3–5 May 2015.
39.
Jäger, B.; Wittmann, M.; Lienkamp, M. Agent-based Modeling and Simulation of Electric Taxi Fleets.
6. Conference on Future Automotive Technology, Fürstenfeldbruck, Germany 2017. Available online: https:
//mediatum.ub.tum.de/1378513 (accessed on 25 June 2020).
40.
Gacias, B.; Meunier, F. Design and operation for an electric taxi fleet. OR Spectrum
2014
,37, 171–194.
[CrossRef]
41.
Cheng, S.F.; Nguyen, T.D. TaxiSim: A Multiagent Simulation Platform for Evaluating Taxi Fleet Operations.
IEEE/WIC/ACM International Conference on Intelligent Agent Technology, 2011. Available online: https:
//works.bepress.com/sfcheng/1/ (accessed on 25 June 2020).
World Electric Vehicle Journal 2020,11, 56 42 of 43
42.
van Lon, R.R.S.; Holvoet, T. RinSim: A Simulator for Collective Adaptive Systems in Transportation
and Logistics. In Proceedings of the 2012 IEEE Sixth International Conference on Self-Adaptive and
Self-Organizing Systems, Lyon, France, 10–14 September 2012. [CrossRef]
43.
Meignan, D.; Simonin, O.; Koukam, A. Simulation and evaluation of urban bus-networks using a multiagent
approach. Simul. Model. Pract. Theory 2007,15, 659–671. [CrossRef]
44.
Cats, O.; Larijani, A.N.; Koutsopoulos, H.N.; Burghout, W. Impacts of Holding Control Strategies on Transit
Performance. Transp. Res. Rec. J. Transp. Res. Board 2011,2216, 51–58. [CrossRef]
45.
Lajunen, A. Energy consumption and cost-benefit analysis of hybrid and electric city buses. Transp. Res. Part
Emerg. Technol. 2014,38, 1–15. [CrossRef]
46.
Lauth, E.; Mundt, P.; Göhlich, D. Simulation-based Planning of Depots for Electric Bus Fleets Considering
Operations and Charging Management. In Proceedings of the 4th International Conference on Intelligent
Transportation Engineering (ICITE), Singapore, 7 September 2019. [CrossRef]
47.
Python Software Foundation. Python. Available online: https://www.python.org/ (accessed on
25 June 2020
).
48.
Scherfke, S. SimPy: Discrete Event Simulation for Python. Available online: https://simpy.readthedocs.io/
en/latest/ (accessed on 25 June 2020).
49.
Heidelberg Institute for Geoinformation Technology (HeiGIT). Openrouteservice. Available online: https:
//openrouteservice.org/ (accessed on 25 June 2020).
50. UITP. UITP Project “SORT”–Standardised on-Road Test Cycles; UITP: Brussels, Belgium, 2009.
51.
Mitschke, M.; Wallentowitz, H. Dynamik der Kraftfahrzeuge; Springer Fachmedien Wiesbaden: Wiesbaden,
Germany, 2014. [CrossRef]
52.
Verband Deutscher Verkehrsunternehmen (VDV). VDV-Schrift 236: Klimatisierung von Linienbussen der
Zulassungsklassen I und II, Für Konventionell Angetriebene Diesel- und Gasbusse Sowie Für Hybrid-, Brennstoffzellen-
und Elektrobusse; VDV: Cologne, Germany, 2015.
53. Bünnagel, C. Irizar ie bus-Power aus dem Baskenland. Verk. Tech. 2018,10, 363–369. [CrossRef]
54.
Ebusco. The New Ebusco 2.2. Available online: https://www.ebusco.com/wp-content/uploads/EBUSCO_
brochure_2-2_digi.pdf (accessed on 25 June 2020).
55. Hondius, H. Daimler Buses stellt vollelektrischen Mercedes-Benz Citaro vor. Stadtverkehr 2018,5, 10–15.
56.
Berliner Verkehrsbetriebe AöR (BVG). Die Omnibusflotte der BVG. Available online: https://unternehmen.
bvg.de/index.php?section=downloads&download=579 (accessed on 25 June 2020).
57.
Färber, F. Heizen im Elektrobus. In Proceedings of the 10. VDV-Konferenz Elektrobusse, Berlin, Germany,
5–6 February 2019.
58.
Akasol AG. Akasol Akasystem 15 AKM 64 CYC. Available online: https://www.akasol.com/library/
Downloads/Datenbl%C3%A4tter/02-05-2019/Data%20sheet-AKASOL-AKASystem-15AKM64CYC-
WEB.pdf (accessed on 25 June 2020).
59.
Impact Clean Power Technology S.A. UVES LTO Standard Battery Pack LTO 15.2 kWh. Available online: https:
//icpt.pl/wp-content/uploads/2018/07/ICPT_UVES_LTO_Standard_leaflet.pdf (accessed on 25 June 2020).
60.
Bundesinstitut für Bau-, Stadt- und Raumforschung. Aktualisierte und Erweitere Testreferenzjahre
(TRY) von Deutschland für Mittlere und Extreme Witterungsverhältnisse. Available online: http:
//www.bbsr-energieeinsparung.de/EnEVPortal/DE/Regelungen/Testreferenzjahre/Testreferenzjahre/
01_start.html?nn=739044¬First=true&docId=743442 (accessed on 25 June 2020).
61.
Statistisches Bundesamt. Genesis-Online: Die Datenbank des Statistischen Bundesamtes. Available online:
https://www-genesis.destatis.de/genesis/online (accessed on 25 June 2020).
62.
Fülling, T. Neue Berliner E-Busse können nur halben Tag fahren. Available online: https://www.morgenpost.
de/berlin/article226090187/Neue-E-Busse-in-Berlin-koennen-nur-halben-Tag-fahren.html (accessed on
25 June 2020).
63.
Fülling, T. BVG kauft 156 neue Busse im “Schweden-Design”. Available online: https://www.morgenpost.
de/berlin-aktuell/article122117680/BVG-kauft-156-neue-Busse-im-Schweden-Design.html (accessed on
14 July 2020).
64.
Sauer, D.U. Aktueller Stand der Entwicklungen von Batterietechnik und Batteriemarkt. In Proceedings of
the 11. VDV-Konferenz Elektrobusse, Berlin, Germany, 4–5 February 2020.
65.
Statistisches Bundesamt. Daten zur Energiepreisentwicklung-Lange Reihen bis März 2020.
Available online: https://www.destatis.de/DE/Themen/Wirtschaft/Preise/Publikationen/Energiepreise/
energiepreisentwicklung-pdf-5619001.html (accessed on 25 June 2020).
World Electric Vehicle Journal 2020,11, 56 43 of 43
66. Krämer, K.; Hanke, D. Lange Stille. Bozankaya Elektrobus Sileo S 12. Omnibusspiegel 2015,2, 5–9.
67.
Kölner Verkehrs-Betriebe AG. KVB stellt den Betrieb der Linie 133 auf E-Busse um: Zehnmonatiges
Testprogramm wurde erfolgreich abgeschlossen: Pressemitteilung. Available online: https://www.
presseportal.de/pm/122503/3501162 (accessed on 25 June 2020).
68.
Göhlich, D.; Fay, T.A.; Park, S. Conceptual Design of Urban E-Bus Systems with Special Focus on Battery
Technology. Proc. Des. Soc. Int. Conf. Eng. Des. 2019,1, 2823–2832. doi:10.1017/dsi.2019.289. [CrossRef]
69.
Verein deutscher Ingenieure (VDI). VDI-Richtlinie 2078: Berechnung von Kühllast und Raumtemperaturen von
Räumen und Gebäuden; VDI: Düsseldorf, Germany, 2012.
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