# A Comprehensive TCO Evaluation Method for Electric Bus Systems Based on Discrete-Event Simulation Including Bus Scheduling and Charging Infrastructure Optimisation

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## Abstract

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## 1. Introduction

- 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.

## 2. General Workflow in Electric Bus System Planning and TCO Analysis

- Problem formulation and input data definition
- System design methods
- System simulation methods
- TCO calculation methods.

## 3. Literature Review

#### 3.1. Problem Formulation and Input Data Definition

- 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 [5,8,9,13,14,15]. (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.
- 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].

#### 3.2. System Design Methods

- 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 1 for 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).
- 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).

#### 3.3. System Simulation Methods

#### 3.3.1. Vehicle Modelling

#### 3.3.2. Fleet Modelling

#### 3.3.3. Depot Modelling

#### 3.4. TCO Calculation Methods

#### 3.5. Comparison 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.

## 4. Electric Bus System Simulation and Planning Tool

#### 4.1. Bus Scheduling Algorithm

#### 4.2. Schedule Simulation

- 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.

#### 4.2.1. Discrete-Event Simulation Framework

#### 4.2.2. Vehicle Model

#### 4.2.3. Depot Model

#### 4.3. Year Simulation and TCO Calculation

#### 4.4. Genetic Algorithm for Charging Infrastructure Optimisation

`multiprocessing`package.

## 5. Case Study: Electrification Scenarios for an Urban Bus Network

#### 5.1. Vehicle Specifications and Energy Consumption

#### 5.1.1. Parameterising the Longitudinal Dynamics Model

#### 5.1.2. Defining Vehicle Types for the Simulation

#### 5.2. Simulation of Existing Schedules With Electric Buses

#### 5.3. Fully Electrified Scenarios: Scheduling and Charging Infrastructure Optimisation

#### 5.4. Fully Electrified Scenarios: System Simulation

- 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.

#### 5.5. Fully Electrified Scenarios: TCO Comparison

- 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.
- 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.

## 6. Discussion

#### 6.1. OC Infrastructure Optimisation

#### 6.2. Scheduling

#### 6.3. Vehicle and Infrastructure Demand (System Simulation)

#### 6.4. TCO calculation

## 7. Conclusions and Outlook

- The strict condition to fully charge at every charging station enforced by the scheduling algorithm reduces the efficiency of the OC schedules.
- 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

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

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 |

## Appendix A. Scheduling Algorithm Flowcharts

## Appendix B. All Inputs to Schedule Simulation

## Appendix C. Equations for Vehicle Model

#### Appendix C.1. Energy Flow and Energy Storage Model

#### Appendix C.2. Traction Model

#### Appendix C.3. HVAC Model

## Appendix D. Equations for TCO Model

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**Figure 2.**Generalised workflow of electric bus system planning and TCO evaluation, including examples of methods and data commonly used in the literature.

**Figure 3.**Overview of eFLIPS (Electric Fleet and Infrastructure Planning/Simulation) main features and workflow.

**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.

**Figure 15.**Schematic illustration of the effect of charging power on charging station placement using the greedy scheduling algorithm.

**Figure 16.**TCO comparison after subtracting staff cost of diesel scenario. S: standard bus; A: articulated bus.

**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 | • | • | ∘ | ∘ | ∘ | ∘ |

**Table 2.**Comparison of electric bus system TCO studies. Legend: • yes; ∘ no; – not applicable; ? unclear.

Source | ChargingStrategies | Exact Timetables | Delays | Fleet SizeCalculation | ChargingInfrastructureDemand Calculation | Staff Demand Calc. | |
---|---|---|---|---|---|---|---|

E-Scheduling | Depot | ||||||

Fusco et al. [8] | OC-I, OC-T | ∘ | •${}^{a}$ | approx. | ∘ | heuristic | ∘ |

Bi et al. [13] | DC, OC-I | ∘ | ∘ | none | ∘ | ? | ∘ |

Jefferies and Göhlich [6] | DC, OC-T | • | • | exact | • | heuristic | • |

Kunith [5] | DC, OC-I | ∘ | ∘ | approx. ${}^{b}$ | approx. ${}^{c}$ | optimisation ${}^{d}$ | partly ${}^{e}$ |

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 | ∘ |

Quantity | Symbol | Value | Source |
---|---|---|---|

Rolling resistance coefficient | ${f}_{\mathrm{r}}$ | 0.0075 | [51] |

Drag coefficient | ${c}_{\mathrm{w}}$ | 0.66 | [34] |

Frontal projection area | ${A}_{\mathrm{front}}$ | 8.8 m${}^{2}$ | [34] |

Rotational mass factor | $\lambda $ | 1.1 | [5] |

**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 % |

**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 | [53,54,55] | ||||

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 (m${}^{2}$) | 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) ${}^{a}$ | 0.73/0.99 | 0.77/1.05 | 0.80/1.09 | 0.77/1.06 | Simulation | |

Total consumption (kWh/km) ${}^{a}$ | 1.51/2.12 | 1.55/2.18 | 1.58/2.22 | 1.55/2.18 | Simulation |

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 |

Scenario No. | Name | Fleet Size ${}^{\mathit{a}}$ | Fast 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 |

**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 [62,63,64] ${}^{a}$ |

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 |

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 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jefferies, D.; Göhlich, D.
A Comprehensive TCO Evaluation Method for Electric Bus Systems Based on Discrete-Event Simulation Including Bus Scheduling and Charging Infrastructure Optimisation. *World Electr. Veh. J.* **2020**, *11*, 56.
https://doi.org/10.3390/wevj11030056

**AMA Style**

Jefferies D, Göhlich D.
A Comprehensive TCO Evaluation Method for Electric Bus Systems Based on Discrete-Event Simulation Including Bus Scheduling and Charging Infrastructure Optimisation. *World Electric Vehicle Journal*. 2020; 11(3):56.
https://doi.org/10.3390/wevj11030056

**Chicago/Turabian Style**

Jefferies, Dominic, and Dietmar Göhlich.
2020. "A Comprehensive TCO Evaluation Method for Electric Bus Systems Based on Discrete-Event Simulation Including Bus Scheduling and Charging Infrastructure Optimisation" *World Electric Vehicle Journal* 11, no. 3: 56.
https://doi.org/10.3390/wevj11030056