# Real-Time Charging Scheduling and Optimization of Electric Buses in a Depot

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## Abstract

**:**

## 1. Introduction

## 2. High-Level Charging Management System

## 3. Methodology

#### 3.1. Problem Formulation and Assumptions

#### 3.2. Real-Time Scheduling and Optimization Algorithm

#### 3.3. Objective Function

#### 3.4. Initial Population

#### 3.5. Parameters

## 4. Results and Discussions

#### 4.1. Simulation Results

#### 4.1.1. Overnight Charging at Depot

#### 4.1.2. Charging at the Depot during the Day

#### 4.2. Experimental Results

- ChargePointMaxProfile, where the charger has one or more local charging profiles that limit the current to be shared by all connectors.
- TxDefaultProfile, where the default schedules for new transactions are used as the charging profiles.
- TxProfile, where the schedule constraints that apply to a transaction are determined by merging the ChargePointMaxProfile with the TxProfile or the TxDefaultProfile.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BEB | battery electric bus |

B2G | bus to grid |

DSO | distribution system operator |

ESS | energy storage system |

EV | electric vehicle |

GA | genetic algorithm |

GHG | greenhouse gas |

HL-CMS | high-level charging management system |

IoT | internet of things |

MILP | mixed-integer linear programming |

OCPP | open charge point protocol |

PEC | power electronic converter |

PTO | public transport operator |

PV | photovoltaic |

RER | renewable energy resource |

RL | reinforcement learning |

RTSO | real-time scheduling and optimization |

SLAC | signal level attenuation characterization |

SoC | state of charge |

TCO | total cost of ownership |

TOU | time of use |

## References

- European Environment Agency (EEA). Decarbonising Road Transport—The Role of Vehicles, Fuels and Transport Demand. 2022. Available online: https://www.eea.europa.eu/publications/transport-and-environment-report-2021 (accessed on 6 July 2022).
- UITP. ZeEUS eBus Report #2: An Updated Overview of Electric Buses in Europe. 2017. Available online: https://zeeus.eu/publications (accessed on 6 July 2022).
- Verbrugge, B.; Hasan, M.M.; Rasool, H.; Geury, T.; el Baghdadi, M.; Hegazy, O. Smart integration of electric buses in cities: A technological review. Sustainability
**2021**, 13, 12189. [Google Scholar] [CrossRef] - Xylia, M.; Leduc, S.; Patrizio, P.; Kraxner, F.; Silveira, S. Locating charging infrastructure for electric buses in Stockholm. Transp. Res. Part C Emerg. Technol.
**2017**, 78, 183–200. [Google Scholar] [CrossRef] - 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. [Google Scholar] [CrossRef] [Green Version] - Rinaldi, M.; Picarelli, E.; D’Ariano, A.; Viti, F. Mixed-fleet single-terminal bus scheduling problem: Modelling, solution scheme and potential applications. Omega
**2020**, 96, 102070. [Google Scholar] [CrossRef] - Liu, T.; Ceder, A. Battery-electric transit vehicle scheduling with optimal number of stationary chargers. Transp. Res. Part C Emerg. Technol.
**2020**, 114, 118–139. [Google Scholar] [CrossRef] - 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. [Google Scholar] [CrossRef] - Lajunen, A. Lifecycle costs and charging requirements of electric buses with different charging methods. J. Clean. Prod.
**2018**, 172, 56–67. [Google Scholar] [CrossRef] - Mohamed, M.; Farag, H.; El-Taweel, N.; Ferguson, M. Simulation of electric buses on a full transit network: Operational feasibility and grid impact analysis. Electr. Power Syst. Res.
**2017**, 142, 163–175. [Google Scholar] [CrossRef] - Rupp, M.; Rieke, C.; Handschuh, N.; Kuperjans, I. Economic and ecological optimization of electric bus charging considering variable electricity prices and CO
_{2}eq intensities. Transp. Res. Part D Transp. Environ.**2020**, 81, 102293. [Google Scholar] [CrossRef] - Leou, R.C.; Hung, J.J. Optimal charging schedule planning and economic analysis for electric bus charging stations. Energies
**2017**, 10, 483. [Google Scholar] [CrossRef] [Green Version] - Gao, Y.; Guo, S.; Ren, J.; Zhao, Z.; Ehsan, A.; Zheng, Y. An electric bus power consumption model and optimization of charging scheduling concerning multi-external factors. Energies
**2018**, 11, 2060. [Google Scholar] [CrossRef] [Green Version] - Raab, A.F.; Lauth, E.; Strunz, K.; Göhlich, D. Implementation schemes for electric bus fleets at depots with optimized energy procurements in virtual power plant operations. World Electr. Veh. J.
**2019**, 10, 5. [Google Scholar] [CrossRef] [Green Version] - Zhou, G.J.; Xie, D.F.; Zhao, X.M.; Lu, C. Collaborative optimization of vehicle and charging scheduling for a bus fleet mixed with electric and traditional buses. IEEE Access
**2020**, 8, 8056–8072. [Google Scholar] [CrossRef] - Arif, S.M.; Lie, T.T.; Seet, B.C.; Ahsan, S.M.; Khan, H.A. Plug-in electric bus depot charging with PV and ESS and their impact on LV feeder. Energies
**2020**, 13, 2139. [Google Scholar] [CrossRef] - Jahic, A.; Eskander, M.; Schulz, D. Charging schedule for load peak minimization on large-scale electric bus depots. Appl. Sci.
**2019**, 9, 1748. [Google Scholar] [CrossRef] [Green Version] - Houbbadi, A.; Trigui, R.; Pelissier, S.; Redondo-Iglesias, E.; Bouton, T. Optimal scheduling to manage an electric bus fleet overnight charging. Energies
**2019**, 12, 2727. [Google Scholar] [CrossRef] [Green Version] - Liu, K.; Gao, H.; Liang, Z.; Zhao, M.; Li, C. Optimal charging strategy for large-scale electric buses considering resource constraints. Transp. Res. Part D Transp. Environ.
**2021**, 99, 103009. [Google Scholar] [CrossRef] - Frendo, O.; Gaertner, N.; Stuckenschmidt, H. Real-Time Smart Charging Based on Precomputed Schedules. IEEE Trans. Smart Grid
**2019**, 10, 6921–6932. [Google Scholar] [CrossRef] - Zheng, Y.; Shang, Y.; Shao, Z.; Jian, L. A novel real-time scheduling strategy with near-linear complexity for integrating large-scale electric vehicles into smart grid. Appl. Energy
**2018**, 217, 1–13. [Google Scholar] [CrossRef] - Zheng, Y.; Song, Y.; Hill, D.J.; Meng, K. Online Distributed MPC-Based Optimal Scheduling for EV Charging Stations in Distribution Systems. IEEE Trans. Ind. Inform.
**2019**, 15, 638–649. [Google Scholar] [CrossRef] - Yao, L.; Lim, W.H.; Tsai, T.S. A Real-Time Charging Scheme for Demand Response in Electric Vehicle Parking Station. IEEE Trans. Smart Grid
**2017**, 8, 52–62. [Google Scholar] [CrossRef] - Papadimitrakis, M.; Giamarelos, N.; Stogiannos, M.; Zois, E.N.; Livanos, N.A.I.; Alexandridis, A. Metaheuristic search in smart grid: A review with emphasis on planning, scheduling and power flow optimization applications. Renew. Sustain. Energy Rev.
**2021**, 145, 111072. [Google Scholar] [CrossRef] - Frendo, O.; Graf, J.; Gaertner, N.; Stuckenschmidt, H. Data-driven smart charging for heterogeneous electric vehicle fleets. Energy AI
**2020**, 1, 100007. [Google Scholar] [CrossRef] - Wan, Z.; He, H.L.H.; Prokhorov, D. Model-Free Real-Time EV Charging Scheduling Based on Deep Reinforcement Learning. IEEE Trans. Smart Grid
**2018**, 10, 5246–5257. [Google Scholar] [CrossRef] - Wang, S.; Bi, S.; Zhang, Y.A. Reinforcement Learning for Real-Time Pricing and Scheduling Control in EV Charging Stations. IEEE Trans. Ind. Inform.
**2021**, 17, 849–859. [Google Scholar] [CrossRef] - Cao, Y.; Wang, H.; Li, D.; Zhang, G. Smart Online Charging Algorithm for Electric Vehicles via Customized Actor-Critic Learning. IEEE Internet Things J.
**2022**, 9, 684–694. [Google Scholar] [CrossRef] - Jiang, W.; Zhen, Y. A Real-Time EV Charging Scheduling for Parking Lots with PV System and Energy Store System. IEEE Access
**2019**, 7, 86184–86193. [Google Scholar] [CrossRef] - Su, J.; Lie, T.T.; Zamora, R. A rolling horizon scheduling of aggregated electric vehicles charging under the electricity exchange market. Appl. Energy
**2020**, 275, 115406. [Google Scholar] [CrossRef] - Maier, H.R.; Razavi, S.; Kapelan, Z.; Matott, L.S.; Kasprzyk, J.; Tolson, B.A. Introductory overview: Optimization using evolutionary algorithms and other metaheuristics. Environ. Model. Softw.
**2019**, 114, 195–213. [Google Scholar] [CrossRef] - Reddy, A.K.V.K.; Narayana, K.V.L. Meta-heuristics optimization in electric vehicles -an extensive review. Renew. Sustain. Energy Rev.
**2022**, 160, 112285. [Google Scholar] [CrossRef] - García-Álvarez, J.; González, M.A.; Vela, C.R. Metaheuristics for solving a real-world electric vehicle charging scheduling problem. Appl. Soft Comput. J.
**2018**, 65, 292–306. [Google Scholar] [CrossRef] - Frendo, O.; Gaertner, N.; Stuckenschmidt, H. Open Source Algorithm for Smart Charging of Electric Vehicle Fleets. IEEE Trans. Ind. Inform.
**2021**, 17, 6014–6022. [Google Scholar] [CrossRef] - Khan, A.R.; Mahmood, A.; Safdar, A.; Khan, Z.A.; Khan, N.A. Load forecasting, dynamic pricing and DSM in smart grid: A review. Renew. Sustain. Energy Rev.
**2016**, 54, 1311–1322. [Google Scholar] [CrossRef] - Bluebus. The Bluebus 12 m. Available online: https://www.bluebus.fr/en/bluebus-12-m (accessed on 24 June 2022).
- Al-Saadi, M.; Patkowski, B.; Zaremba, M.; Karwat, A.; Pol, M.; Chelchowski, L.; van Mierlo, J.; Berecibar, M. Slow and Fast Charging Solutions for Li-Ion Batteries of Electric Heavy-Duty Vehicles with Fleet Management Strategies. Sustainability
**2021**, 13, 10639. [Google Scholar] [CrossRef] - Rafique, S.; Nizami, M.S.H.; Irshad, U.B.; Hossain, M.J.; Mukhopadhyay, S.C. A two-stage multi-objective stochastic optimization strategy to minimize cost for electric bus depot operators. J. Clean. Prod.
**2022**, 332, 129856. [Google Scholar] [CrossRef]

**Figure 4.**Simulation results of three BEBs charging overnight with (

**a**) electricity tariff, (

**b**–

**d**) charging current of each BEB and (

**e**) total charging current and grid limitation.

**Figure 6.**Simulation results of three BEBs charging during the day with (

**a**) electricity tariff, (

**b**–

**d**) charging current of each BEB and (

**e**) total charging current and grid limitation.

**Figure 7.**Sequence of the OCPP communication protocol between the EV, the charging point and the HL-CMS.

Parameter | Value |
---|---|

Population size | 100 × number of decisions variables |

Elite count | 0.05 × population size |

Crossover ratio | 0.8 |

Mutation rate | 0.02 |

Stopping criteria | 50 |

(Number of iterations without improvement in the cost function) |

BEB | Arrival Time (h) | Departure Time (h) | Range (km) |
---|---|---|---|

BEB 1 | 21:00 | 05:00 | 180 |

BEB 2 | 19:30 | 04:00 | 180 |

BEB 3 | 00:15 | 06:30 | 180 |

BEB | Arrival Time (h) | Departure Time (h) | Range (km) |
---|---|---|---|

BEB 1 | 12:15 | 15:30 | 100 |

BEB 2 | 11:30 | 14:40 | 100 |

BEB 3 | 13:00 | 16:45 | 100 |

Element | Details | |
---|---|---|

DC charger | Nexxtender Direct | 45 kW |

Measurement unit | comemso charging analyzer | / |

EV | BMW i3 | 42 kWh |

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## Share and Cite

**MDPI and ACS Style**

Verbrugge, B.; Rauf, A.M.; Rasool, H.; Abdel-Monem, M.; Geury, T.; El Baghdadi, M.; Hegazy, O.
Real-Time Charging Scheduling and Optimization of Electric Buses in a Depot. *Energies* **2022**, *15*, 5023.
https://doi.org/10.3390/en15145023

**AMA Style**

Verbrugge B, Rauf AM, Rasool H, Abdel-Monem M, Geury T, El Baghdadi M, Hegazy O.
Real-Time Charging Scheduling and Optimization of Electric Buses in a Depot. *Energies*. 2022; 15(14):5023.
https://doi.org/10.3390/en15145023

**Chicago/Turabian Style**

Verbrugge, Boud, Abdul Mannan Rauf, Haaris Rasool, Mohamed Abdel-Monem, Thomas Geury, Mohamed El Baghdadi, and Omar Hegazy.
2022. "Real-Time Charging Scheduling and Optimization of Electric Buses in a Depot" *Energies* 15, no. 14: 5023.
https://doi.org/10.3390/en15145023