# A Charging Planning Method for Shared Electric Vehicles with the Collaboration of Mobile and Fixed Facilities

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Can mobile charging services be introduced to solve the problem of the difficult and costly charging of free-floating SEVs?
- (2)
- How can operators plan flexible mobile charging vehicles and low-cost fixed charging stations to achieve the most economical charging scheme?
- (3)
- How can operators efficiently design a travel path of charging SEVs that provides two types of charging with the power distribution and location distribution characteristics of free-floating SEVs?

## 2. Literature Review

- (1)
- MCV is flexible but costly, while fixed charging is economical and relies on the manual transfer of the SEV to complete charging. A search of the literature shows that there is no published research on how to combine the two charging facilities to achieve the most economical and efficient charging scheme.
- (2)
- Existing studies on MCVs mainly focus on one-to-one charging, and such a charging service has relatively high costs and a low efficiency. The cluster distribution characteristics of free-floating SEVs make it possible to use MCVs for multi-user parallel charging, and research on matching MCVs with SEV clusters needs to be conducted in depth.
- (3)
- On the one hand, there is manual transfer SEV path planning, which is based on the location of fixed charging stations, and, on the other hand, there is MCV path planning, which takes into account SEV clusters. The coordination of fixed and mobile charging planning is worth investigating, based on the power distribution characteristics and location characteristics of SEVs.

## 3. Methodology

#### 3.1. Scenario Description

#### 3.2. Assumptions and Variables

- Speed and power consumption rate are constant. The SEV or MCV travel time is equal to the distance between nodes divided by the speed, and the travel power consumed between nodes is equal to the distance between nodes multiplied by the power consumption rate.
- The period of the charging scheme is fixed.
- The charging time of each SEV is fixed.
- The SEV charging threshold is a fixed value. SEVs with power below this threshold send a charging request, and SEVs with power below the requirement to reach the nearest fixed charging station stop their service to wait for MCV charging.

#### 3.3. The Bi-Level Programming Model for Cooperative Charging

#### 3.3.1. The Upper Model

- (1)
- Mobile charging costs;

- (2)
- Fixed charging cost.

#### 3.3.2. The Lower Model

- (1)
- Charge mode constraint;

- (2)
- Vehicle equilibrium constraint;

- (3)
- Time window constraint;

- (4)
- Fixed charging station constraint;

- (5)
- Related constraints of mobile charging mode.

#### 3.4. GASA Algorithm

- (1)
- Set the initial solution under the individual charging scheme with iteration number n = 0. The initial solution is obtained by continuously constructing the feasible route;
- (2)
- Calculate the broad charging costs $Y$;
- (3)
- Use genetic algorithms to find optimal populations $\left({x}_{ijk}^{m(g)},{x}_{ijk}^{s(g)},{f}_{m}^{(\mathrm{g})}\right)$;
- (4)
- Substitute the output population $\left({x}_{ijk}^{m(g)},{x}_{ijk}^{s(g)},{f}_{m}^{(g)}\right)$ into the upper model to find the value of the fitness function.

## 4. Numerical Example

#### 4.1. Data Source

#### 4.2. Parameter Setting

#### 4.3. Calculation Result

#### 4.4. Analysis of Results

#### 4.4.1. The Impact of Different Charging Modes on the Cost of Charging Schemes

#### 4.4.2. Sensitivity Analysis

- (1)
- Charging Price

- (2)
- MCV Charging Performance

- (3)
- Time Window Penalty Cost

## 5. Conclusions

#### 5.1. Contribution

- (1)
- MCVs serving the single charging demand will lead to a high charging cost. In this paper, MCVs are introduced to serve multiple SEVs, and the parallel mobile charging service is used in the free–mobile SEV charging, which expands the service scope and reduces the charging cost of MCVs.
- (2)
- Utilizing the complementary advantages of fixed charging mode and MCVs, we propose a bi-level programming model for fixed and mobile cooperative charging and solve the model, using the GASA algorithm, to derive the optimal charging scheme and the number of required MCVs, which solves the problems of charging difficulties for free-floating SEVs.
- (3)
- To solve the charging path problem of MCVs and SEVs, a fixed–mobile cooperative charging path planning model and related constraints are proposed, to compute the optimal paths for MCVs and SEVs to be transferred to a fixed charging station for charging.

#### 5.2. Discussion

- (1)
- In practice, fixed charging stations often face the problem of charging queues, which increases the cost of fixed charging stations. This article does not consider the queuing problem at fixed charging stations, and the impact caused by queuing should be considered in subsequent studies.
- (2)
- The road network and setup during driving are ideal. Shared electric vehicle networks of different sizes are not considered, nor are the energy consumption and environmental impacts of charging vehicles. These factors on the SEV charging scheme need to be considered and solved in future studies.
- (3)
- In subsequent studies, SEV networks of different sizes or characteristics can be analyzed to examine the environment in which the proposed methodology is applicable. The subsequent scheduling issues, as well as the impact of factors such as operating costs and energy expenditure in different regions on scheme planning, need to be investigated.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Guangnian, X.; Qiongwen, L.; Anning, N.; Zhang, C. Research on carbon emissions of public bikes based on the life cycle theory. Transp. Lett.
**2022**, 15, 278–295. [Google Scholar] [CrossRef] - Tan, Z.; Shao, S.; Zhang, X.; Shang, W.-L. Sustainable urban mobility: Flexible bus service network design in the post-pandemic era. Sustain. Cities Soc.
**2023**, 97, 104702. [Google Scholar] [CrossRef] [PubMed] - Zhang, H.; Sheppard, C.J.R.; Lipman, T.E.; Zeng, T.; Moura, S.J. Charging infrastructure demands of shared-use autonomous electric vehicles in urban areas. Transp. Res. Part D Transp. Environ.
**2020**, 78, 102–210. [Google Scholar] [CrossRef] - Wang, C.; Lin, X.; He, F.; Shen, M.Z.-J.; Li, M. Hybrid of fixed and mobile charging systems for electric vehicles: System design and analysis. Transp. Res. Part C Emerg. Technol.
**2021**, 126, 103068. [Google Scholar] [CrossRef] - Liang, Y.; Ding, Z.; Ding, T.; Lee, W.-J. Mobility-Aware Charging Scheduling for Shared On-Demand Electric Vehicle Fleet Using Deep Reinforcement Learning. IEEE Trans. Smart Grid
**2020**, 12, 1380–1393. [Google Scholar] [CrossRef] - Huang, S.S.; He, L.; Gu, Y. Design of a mobile charging service for electric vehicles in an urban environment. IEEE Trans. Intell. Transp. Syst.
**2015**, 16, 787–798. [Google Scholar] [CrossRef] - Raeesi, R.; Zografos, K.G. The electric vehicle routing problem with time windows and synchronised mobile battery swapping. Transp. Res. Part B Methodol.
**2020**, 140, 101–129. [Google Scholar] [CrossRef] - Tang, P.; He, F.; Lin, X. Online-to-offline mobile charging system for electric vehicles: Strategic planning and online operation. Transp. Res. Part D Transp. Environ.
**2020**, 87, 102522. [Google Scholar] [CrossRef] - Schmöller, S.; Weikl, S.; Müller, J.; Bogenberger, K. Empirical analysis of free-floating carsharing usage: The Munich and Berlin case. Transp. Res. Part C Emerg. Technol.
**2015**, 56, 34–51. [Google Scholar] [CrossRef] - Ciociola, A.; Cocca, M.; Giordano, D.; Mellia, M.; Morichetta, A.; Putina, A.; Salutari, F. UMAP: Urban mobility analysis platform to harvest car sharing data. In Proceedings of the 2017 IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computed, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI), San Francisco, CA, USA, 4–8 August 2017; pp. 1–8. [Google Scholar]
- Weikl, S.; Bogenberger, K. A practice-ready relocation model for free-floating carsharing systems with electric vehicles-Mesoscopic approach and field trial results. Transp. Res. Part C-Emerg. Technol.
**2015**, 57, 206–223. [Google Scholar] [CrossRef] - Kypriadis, D.; Pantziou, G.; Konstantopoulos, C. Optimizing Relocation Cost in Free-Floating Car-Sharing Systems. IEEE Trans. Intell. Transp. Syst.
**2020**, 21, 4017–4030. [Google Scholar] [CrossRef] - Folkestad, C.A.; Hansen, N.; Fagerholt, K. Optimal charging and repositioning of electric vehicles in a free-floating carsharing system. Comput. Oper. Res.
**2020**, 113, 104771. [Google Scholar] [CrossRef] - Roni, M.S.; Yi, Z.; Smart, J.G. Optimal charging management and infrastructure planning for free-floating shared electric vehicles. Transp. Res. Part D Transp. Environ.
**2019**, 76, 155–175. [Google Scholar] [CrossRef] - Cocca, M.; Giordano, D.; Mellia, M. Free Floating Electric Car Sharing:A Data Driven Approach for System Design. IEEE Trans. Intell. Transp. Syst.
**2019**, 20, 4691–4703. [Google Scholar] [CrossRef] - Boyacı, B.; Zografos, K.G.; Geroliminis, N. An optimization framework for the development of efficient one-way car-sharing systems. Eur. J. Oper. Res.
**2015**, 240, 718–733. [Google Scholar] [CrossRef] - Boyacı, B.; Zografos, K.G.; Geroliminis, N. An integrated optimization-simulation framework for vehicle and personnel relocations of electric carsharing systems with reservations. Transp. Res. Part B Methodol.
**2017**, 95, 214–237. [Google Scholar] [CrossRef] - Boyacı, B.; Zografos, K.G. Investigating the effect of temporal and spatial flexibility on the performance of one-way electric carsharing systems. Transp. Res. Part B Methodol.
**2019**, 129, 244–272. [Google Scholar] [CrossRef] - Corinaldesi, C.; Lettner, G.; Auer, H. On the characterization and evaluation of residential on-site E-car-sharing. Energy
**2022**, 246, 123400. [Google Scholar] [CrossRef] - Brandstätter, G.; Kahr, M.; Leitner, M. Determining optimal locations for charging stations of electric car-sharing systems under stochastic demand. Transp. Res. Part B Methodol.
**2017**, 104, 17–35. [Google Scholar] [CrossRef] - Hua, Y.; Zhao, D.; Wang, X.; Li, X. Joint infrastructure planning and fleet management for one-way electric car sharing under time-varying uncertain demand. Transp. Res. Part B Methodol.
**2019**, 28, 185–206. [Google Scholar] [CrossRef] - Huang, K.; An, K.; Correia, G.H.D.A. Planning station capacity and fleet size of one-way electric carsharing systems with continuous state of charge functions. Eur. J. Oper. Res.
**2020**, 287, 1075–1091. [Google Scholar] [CrossRef] - Huang, K.; An, K.; Rich, J. Vehicle relocation in one-way station-based electric carsharing systems: A comparative study of operator-based and user-based methods. Transp. Res. Part E Logist. Transp. Rev.
**2020**, 142, 102081. [Google Scholar] [CrossRef] - Xu, M.; Meng, Q. Fleet sizing for one-way electric carsharing services considering dynamic vehicle relocation and nonlinear charging profile. Transp. Res. Part B Methodol.
**2019**, 128, 23–49. [Google Scholar] [CrossRef] - Gambella, C.; Malaguti, E.; Masini, F. Optimizing relocation operations in electric car-sharing. Omega
**2018**, 81, 234–245. [Google Scholar] [CrossRef] - Qi, B. Integrated Economic Dispatching on Electric Vehicle Mobile Charging Service. Master’s Thesis, Tianjin University, Tianjin, China, 2017. [Google Scholar]
- Atmaja, T.D.; Mirdanies, M. Electric vehicle mobile charging station dispatch algorithm. Energy Procedia
**2015**, 68, 326–335. [Google Scholar] [CrossRef] - Bao, Z.; Long, G.; Peng, C. Optimized design and simulation of mobile charging for electric vehicles. Syst. Simul. Technol.
**2020**, 16, 15–19. [Google Scholar] - Çalık, H.; Fortz, B. A Benders decomposition method for locating stations in a one-way electric car sharing system under demand uncertainty. Transp. Res. Part B Methodol.
**2019**, 125, 121–150. [Google Scholar] [CrossRef] - Xiao, G.; Chen, L.; Chen, X.; Jiang, C.; Ni, A.; Zhang, C.; Zong, F. A hbrid visualization model for knowledge mapping: Scientometrics, SAOM, and SAO. IEEE Trans. Intell. Transp. Syst.
**2023**, 1–14. [Google Scholar] [CrossRef] - Bao, Z.; Li, J.; Bai, X.; Xie, C.; Chen, Z.; Xu, M.; Shang, W.-L.; Li, H. An optimal charging scheduling model and algorithm for electric buses. Appl. Energy
**2023**, 332, 120512. [Google Scholar] [CrossRef] - Liu, W.M. Research on the solution algorithm of bi-level planning model based on hybrid optimization strategy. J. Civ. Eng.
**2003**, 27–32. [Google Scholar]

**Figure 2.**Scenario description. Where K1–K6 is the number of the charging vehicle and F′1, F′2 are the number of trips to the stationary charging station in the representative scheme.

**Figure 3.**Path planning results for fixed and mobile co-charging, exemplified by a region in Nanjing.

**Figure 5.**The impact of charging price. The red dots here represent the total cost of charging when the fixed charging station charging price is 0.5, 0.8, 1.1, and 1.4 RMB/kWh respectively.

Parameter | Define |
---|---|

${f}_{m}$ | Number of mobile charging vehicles (veh) |

${\beta}_{1}$ | Charging price (RMB/kWh) |

${\beta}_{2}$ | Depreciation cost per MCV (RMB) |

${\beta}_{3}$ | Initial price of manually transferring SEV to fixed charging station (RMB) |

${\beta}_{4}$ | Mileage price per kilometer when manually transferring SEVs (RMB/km) |

$i,j$ | virtual node |

${x}_{ijk}^{m}$ | ${x}_{ijk}^{m}\in \left\{0,1\right\}$, indicates whether the virtual SEV node k is charged by MCV. ${x}_{ijk}^{m}=1$, indicates that SEV k is charged by MCV. |

${x}_{ijk}^{s}$ | ${x}_{ijk}^{s}\in \left\{0,1\right\}$, indicates whether the virtual SEV node k is charged in a fixed mode or not. |

$h$ | Power consumption per kilometer of MCV (kWh/km) |

${q}_{k}^{m}$ | Charging demand for virtual SEV node k, which is handled by a mobile charging vehicle(kWh). |

${q}_{k}^{s}$ | Charging demand for virtual SEV node k, which is covered by a fixed charging station (kWh). |

$P$ | Battery capacity of SEV (kWh) |

${p}_{ik}$ | Electricity of SEV node k (kWh) |

${y}_{i}$ | The remaining power when MVC reaches at node i (kWh) |

$Q$ | Battery capacity of MVC (kWh) |

${Y}_{i}$ | Charging quantity of MVC at fixed charging stations. $i\in {V}^{\prime}\cup \left\{0\right\}$ (kWh) |

${d}_{ij}$ | Path distance between nodes (i, j) (km) |

${\tau}_{i}$ | Time to start services for SEV on the virtual client node |

${e}_{i}$ | Start time of service time window |

${l}_{i}$ | End time of service time window |

${t}_{ij}$ | The travel time of a road segment, which is related to the distance of segment ${d}_{ij}$ and the fixed speed of MCV (min). |

${t}_{i}$ | The time that a mobile charging vehicle spends on charging a shared electric vehicle at node $i$ (min) |

M | The length of the longest link in the path set L (km) |

${s}_{ij}$ | ${s}_{ij}$ ∈ {0,1}, indicates whether the charging services at the virtual SEV cluster nodes can be performed at the same time. |

SEV (id) | Latitude | Longitude | Time Window (min) | Electricity (%) | |
---|---|---|---|---|---|

1 | 118.385968 | 32.705249 | 211 | 247 | 0.32 |

2 | 118.170446 | 32.688855 | 50 | 90 | 0.27 |

3 | 118.238767 | 32.952442 | 59 | 79 | 0.18 |

4 | 118.003842 | 32.81767 | 103 | 133 | 0.23 |

5 | 118.093071 | 32.641006 | 35 | 61 | 0.34 |

6 | 118.057605 | 32.860424 | 190 | 208 | 0.20 |

…… | …… | …… | …… | …… | …… |

39 | 118.235922 | 32.8217 | 30 | 160 | 0.31 |

40 | 118.281175 | 32.938024 | 35 | 150 | 0.35 |

41 | 118.346757 | 32.704077 | 20 | 90 | 0.08 |

SEV (id) | Latitude | Longitude | Time Window (min) | |
---|---|---|---|---|

0 | 118.374992 | 32.674618 | 0 | 300 |

51 | 118.015484 | 32.871561 | 0 | 300 |

52 | 118.19667 | 32.618216 | 0 | 300 |

53 | 118.217592 | 32.871277 | 0 | 300 |

54 | 118.281175 | 32.938024 | 0 | 300 |

Mobile Charging Mode | Fixed Charging Mode | |
---|---|---|

SEV (id) | 1, 2, 3, 4, 7, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 32, 34, 35, 37, 38, 39, 40, 41 | 5, 6, 8, 10, 11, 27, 28, 30, 33, 36 |

Number of vehicles | 31 | 10 |

Charging Path | MCV1:0-(4,31)-(20,21)-16-26-(19,32)-17-(13,14)-(7,34)-(40,41)-0 MCV2:0-25-(1,2,3,15,37)-9-(12,29,38)-(18,39)-35-(22,23,24)-0 | 5-51-5, 6-51-6, 8-51-8, 10-52-10, 11-52-11, 27-52-27, 28-53-28, 30-54-30, 36-55-36 |

Total cost of charging (RMB) | 2094.8 |

MCV Battery Capacity (kWh) | Depreciation Cost (RMB) | Number of MCVs | Number of SEVs in Mobile Charging | Number of SEVs in Fixed Charging | Total System Cost (RMB) |
---|---|---|---|---|---|

600 | 80 | 3 | 37 | 4 | 2155.7 |

800 | 100 | 2 | 31 | 10 | 2094.8 |

1000 | 130 | 2 | 32 | 9 | 2046.5 |

1200 | 160 | 2 | 32 | 9 | 2067.3 |

MCV Charging Service Time (min) | Depreciation Cost (RMB) | Number of MCVs | Number of SEVs in Mobile Charging | Number of SEVs in Fixed Charging | Total System Cost (RMB) |
---|---|---|---|---|---|

10 min | 150 | 2 | 35 | 10 | 2056.3 |

20 min | 100 | 2 | 24 | 13 | 2094.8 |

30 min | 80 | 3 | 31 | 6 | 2227.5 |

Time Window Penalty Cost (RMB/h) | Number of MCVs | Number of SEVs in Mobile Charging | Number of SEVs in Fixed Charging | Total System Cost (RMB) |
---|---|---|---|---|

150 | 2 | 30 | 7 | 1976.3 |

300 | 2 | 24 | 13 | 2094.8 |

600 | 3 | 31 | 6 | 2323.5 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Luo, Q.; Ye, Z.; Jia, H.
A Charging Planning Method for Shared Electric Vehicles with the Collaboration of Mobile and Fixed Facilities. *Sustainability* **2023**, *15*, 16107.
https://doi.org/10.3390/su152216107

**AMA Style**

Luo Q, Ye Z, Jia H.
A Charging Planning Method for Shared Electric Vehicles with the Collaboration of Mobile and Fixed Facilities. *Sustainability*. 2023; 15(22):16107.
https://doi.org/10.3390/su152216107

**Chicago/Turabian Style**

Luo, Qingyu, Zhihao Ye, and Hongfei Jia.
2023. "A Charging Planning Method for Shared Electric Vehicles with the Collaboration of Mobile and Fixed Facilities" *Sustainability* 15, no. 22: 16107.
https://doi.org/10.3390/su152216107