The widespread adoption of electric buses (EB) is hampered by battery degradation. Battery degradation refers to the phenomenon of lithium batteries shrinking in capacity and eventually becoming unusable due to the extensive charging and discharging behavior. This paper proposes a joint optimization of EBs vehicle scheduling and charging strategies that considers both explicit charging cost and implicit battery degradation cost. First, we construct a mathematical optimization model through the graph theory. Then, the battery degradation cost is computed by investigating the relationship between battery degradation and state of charge (SoC) during charging/discharging. Finally, the proposed model is linearized and solved efficiently. Numerical results show that 7.45% of the battery degradation cost and 6% of the total cost can be saved just by simply adjusting the vehicle scheduling and charging strategies. The battery degradation cost is much larger than the charging cost, which emphasizes the need to consider battery degradation. The results also provide some practical suggestions for operators. The lowest possible initial SoC can reduce battery degradation, while increasing the number of buses has little impact.
REFERENCES
1.
K.
Jin
et al, “
Energy-optimal speed control for connected electric buses considering passenger load
,” J. Cleaner Prod.
385
, 135773
(2023
).2.
Ó.
García-Afonso
et al, “
On the road to a sustainable transport mobility in isolated power systems: The role of light-duty powertrain electrification
,” J. Cleaner Prod.
320
, 128646
(2021
).3.
https://www.globenewswire.com/news-release/2022/03/14/2402293/0/en/The-global-electric-bus-market-size-is-projected-to-grow-from-112-041-units-in-2022-to-reach-671-285-units-by-2027-at-a-CAGR-of-43-1.html for
ReportLinker,
“
The global electric bus market size is projected to grow from 112,041 units in 2022 to reach 671,285 units by 2027, at a CAGR of 43.1%
,” 2022
.4.
M.
Li
et al, “
Data-driven predictive energy management and emission optimization for hybrid electric buses considering speed and passengers prediction
,” J. Cleaner Prod.
304
, 127139
(2021
).5.
X.
Li
et al, “
A blockchain-enabled personalized charging system for electric vehicles
,” Transp. Res. Part C
161
, 104549
(2024
).6.
K.
Liu
et al, “
Optimal charging strategy for large-scale electric buses considering resource constraints
,” Transp. Res. Part D
99
, 103009
(2021
).7.
K.
Liu
et al, “
Robust charging strategies for electric bus fleets under energy consumption uncertainty
,” Transp. Res. Part D
104
, 103215
(2022
).8.
M.
Schneider
,
A.
Stenger
, and
D.
Goeke
, “
The electric vehicle-routing problem with time windows and recharging stations
,” Transp. Sci.
48
(4
), 500
–520
(2014
).9.
O. J.
Ibarra-Rojas
et al, “
Planning, operation, and control of bus transport systems: A literature review
,” Transp. Res. Part B
77
, 38
–75
(2015
).10.
L.
Desfontaines
and
G.
Desaulniers
, “
Multiple depot vehicle scheduling with controlled trip shifting
,” Transp. Res. Part B
113
, 34
–53
(2018
).11.
X.
Xu
,
Y.
Yu
, and
J.
Long
, “
Integrated electric bus timetabling and scheduling problem
,” Transp. Res. Part C
149
, 104057
(2023
).12.
L.
Lam
and
P.
Bauer
, “
Practical capacity fading model for Li-ion battery cells in electric vehicles
,” IEEE Trans. Power Electron.
28
(12
), 5910
–5918
(2013
).13.
S.
Han
,
S.
Han
, and
H.
Aki
, “
A practical battery wear model for electric vehicle charging applications
,” Appl. Energy
113
, 1100
–1108
(2014
).14.
S.
Pelletier
et al, “
Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models
,” Transp. Res. Part B
103
, 158
–187
(2017
).15.
L.
Zhang
,
S.
Wang
, and
X.
Qu
, “
Optimal electric bus fleet scheduling considering battery degradation and non-linear charging profile
,” Transp. Res. Part E
154
, 102445
(2021
).16.
S. S. G.
Perumal
,
R. M.
Lusby
, and
J.
Larsen
, “
Electric bus planning & scheduling: A review of related problems and methodologies
,” Eur. J. Oper. Res.
301
(2
), 395
–413
(2022
).17.
R.-C.
Leou
and
J.-J.
Hung
, “
Optimal charging schedule planning and economic analysis for electric bus charging stations
,” Energies
10
(4
), 483
(2017
).18.
C.
Yang
et al, “
On charging scheduling optimization for a wirelessly charged electric bus system
,” IEEE Trans. Intell. Transp. Syst.
19
(6
), 1814
–1826
(2018
).19.
A.
Bagherinezhad
et al, “
Spatio-temporal electric bus charging optimization with transit network constraints
,” IEEE Trans. Ind. Appl.
56
(5
), 5741
–5749
(2020
).20.
A.
Abdelwahed
et al, “
Evaluating and optimizing opportunity fast-charging schedules in transit battery electric bus networks
,” Transp. Sci.
54
(6
), 1601
–1615
(2020
).21.
B.-R.
Ke
et al, “
Battery charging and discharging scheduling with demand response for an electric bus public transportation system
,” Sustainable Energy Technol. Assess.
40
, 100741
(2020
).22.
C. H.
Häll
et al, “
Adjustments of public transit operations planning process for the use of electric buses
,” J. Intell. Transp. Syst.
23
(3
), 216
–230
(2019
).23.
K.
Jin
et al, “
Cost-optimal charging strategies for electric bus fleets considering battery degradation and nonlinear charging
,” IEEE Trans. Intell. Transp. Syst.
25
, 6212
(2023
).24.
K.
Jin
et al, “
Identifying the critical road combination in urban roads network under multiple disruption scenarios
,” Physica A
607
, 128192
(2022
).25.
S.
Pelletier
,
O.
Jabali
, and
G.
Laporte
, “
Charge scheduling for electric freight vehicles
,” Transp. Res. Part B
115
, 246
–269
(2018
).26.
L. C.
Coelho
and
G.
Laporte
, “
Improved solutions for inventory-routing problems through valid inequalities and input ordering
,” Int. J. Prod. Econ.
155
, 391
–397
(2014
).27.
R.
Lahyani
,
L. C.
Coelho
, and
J.
Renaud
, “
Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem
,” OR Spectrum
40
(1
), 125
–157
(2018
).28.
A.
Lajunen
, “
Energy consumption and cost-benefit analysis of hybrid and electric city buses
,” Transp. Res. Part C
38
, 1
–15
(2014
).29.
K.
Jin
et al, “
Sharing the electric bus charging stations by scheduling the charging strategy
,” J. Renewable Sustainable Energy
14
(4
), 045701
(2022
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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