# An Electric Bus Battery Swapping Station Location Method Based on Global Optimized Peak Traffic Flow

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Frank–Wolfe Method

#### 2.2. Modified Genetic Algorithm

- (1)
- Individual.

- (2)
- Optimization constraints.

- (3)
- Fitness.

- (4)
- Selection.

- (5)
- Crossing.

- (6)
- Mutation.

#### 2.3. Traffic Flow Assignment Based on GA-FW Method

## 3. Model

#### 3.1. Model

#### 3.2. Simulation

## 4. Result

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notations

$\left(i,j\right)$ | Road segment $\left(i,j\right).$ |

$A$ | The set of all road segments. |

$\eta $ | Iteration step size. |

${x}_{ij}$ | The flow at the road segment $\left(i,j\right)$. |

${t}_{ij}\left(\omega \right)$ | The traffic impedance on road segment $\left(i,j\right)$ when flow on the road is $\omega $. |

${x}_{ij}^{hat}$ | Flow of road segment $\left(i,j\right)$ obtained by all-or-nothing assignment. |

$T$ | The set of “terminals”. |

$S$ | The set of “stations”. |

$N$ | The set of “nodes”. |

$X$ | The vector represents the location of BSS. |

$J$ | The set of all bus lines. |

${J}^{\prime}$ | The matrix represents connectivity between nodes and bus lines. |

$C$ | The connectivity between “nodes” and “terminals”. |

${\overline{v}}_{h,k-1,k,m}$ | The average speed of a bus following line ${j}_{h}$ passing through road segment $m$ as it travels from station $k-1$ to station $k$. |

${{\overline{v}}^{\prime}}_{k-1,k,m}$ | The design rode speed of segment $m$ from station $k-1$ to station $k$. |

${q}_{k-1,k,m}$ | The design passing capacity of segment $m$ from station $k-1$ to station $k$. |

${c}_{k-1,k,m}$ | The actual traffic flow of segment $m$ from station $k-1$ to station $k$. |

${l}_{h,k-1,k,m}$ | The length of segment $m$ when a bus following line ${j}_{h}$ travelling from station $k-1$ to station $k$. |

${e}_{h,k}$ | The battery level of a bus following line ${j}_{h}$ at station $k$. |

${e}_{warning}$ | The battery warning level. |

${e}_{safety}$ | The battery safety level. |

${q}_{i}$ | The number of buses passing$\mathrm{node}{n}_{i}$. |

$l\left({n}_{i},{t}_{m}\right)$ | $\mathrm{The}\mathrm{distance}\mathrm{between}\mathrm{each}\mathrm{chosen}\mathrm{node}{n}_{i}$$\mathrm{and}\mathrm{its}\mathrm{connected}\mathrm{terminal}{t}_{m}$. |

$f({n}_{i},{t}_{m})$ | $\mathrm{The}\mathrm{flow}\mathrm{between}\mathrm{each}\mathrm{chosen}\mathrm{node}{n}_{i}$$\mathrm{and}\mathrm{its}\mathrm{connected}\mathrm{terminal}{t}_{m}$. |

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**Figure 4.**Traffic flow of two methods: (

**a**) Expressway; (

**b**) 8-Lane Arterial Road; (

**c**) 6-Lane Arterial Road.

Class: Station | Class: Node | Class: Terminal |
---|---|---|

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 | 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 | 24 |

Road ID | Road Name | Road Hierarchy | Number of Two-Way Lanes |
---|---|---|---|

1 | 1-2-3-4 | Expressway | 8 |

2 | 13-14-15-16 | Expressway | 8 |

3 | 16-17-5 | Arterial Road | 6 |

4 | 12-11 | Expressway | 8 |

5 | 11-24-22-23-18-5 | Arterial Road | 8 |

6 | 10-21-20-19-6 | Arterial Road | 6 |

7 | 9-8-7 | Arterial Road | 8 |

8 | 4-5-6-7 | Expressway | 8 |

9 | 4-17-18-19 | Arterial Road | 6 |

10 | 4-16 | Arterial Road | 6 |

11 | 16-23-20-8 | Expressway | 8 |

12 | 3-15-22-21 | Arterial Road | 6 |

13 | 2-14-11 | Arterial Road | 8 |

14 | 12-11-10-9 | Expressway | 8 |

15 | 1-13-12 | Arterial Road | 8 |

Line ID | Entry Station ID | Passing Nodes | Exit Station ID |
---|---|---|---|

101 | 1 | 14, 15, 16, 17 | 5 |

102 | 2 | 14, 15, 22, 21 | 9 |

103 | 3 | 15, 16, 23, 20 | 8 |

104 | 4 | 16, 18, 19 | 6 |

105 | 5 | 17, 18, 23, 22, 24 | 11 |

106 | 6 | 19, 20, 21 | 10 |

107 | 7 | 19, 18, 17, 16, 15 | 3 |

108 | 8 | 20, 23, 16 | 4 |

109 | 9 | 20, 19, 18, 17 | 5 |

110 | 10 | 21, 20, 23, 16, 15, 14 | 13 |

111 | 11 | 24, 22, 21 | 9 |

112 | 12 | 14, 15, 16, 23, 20 | 8 |

113 | 13 | 14, 15, 16, 17 | 5 |

114 | 4 | 16, 23, 20, 21 | 10 |

115 | 4 | 16, 23, 22, 24 | 11 |

116 | 3 | 15, 16, 17 | 5 |

117 | 5 | 18, 17, 16, 15, 14 | 2 |

118 | 6 | 19, 20, 23, 16 | 4 |

119 | 9 | 21, 22, 15 | 3 |

120 | 10 | 21, 20, 19, 18, 17 | 4 |

Assignment Method | BSS Node ID | Capacity | Covering Line |
---|---|---|---|

TransCAD | 16 | 24 | 101, −101, 103, −103, 104, −104, 107, −107, 108, −108, 110, −110, 112, −112, 113, −113, 114.−114 116, −116, 117, −117, 118, −118 |

18 | 3 | 109, −109, −120 | |

21 | 7 | 102, −102, 106, −106, 119, −119, 120 | |

24 | 6 | 105, −105, 111, −111, 115, −115 | |

GA-FW | 16 | 24 | 101, −101, 103, −103, 104, −104, 107, −107, 108, −108, 110, −110, 112, −112, 113, −113, 114, −114 116, −116, 117, −117, 118, −118 |

20 | 3 | 109, −109, −120 | |

21 | 7 | 102, −102, 106, −106, 119, −119, 120 | |

24 | 6 | 105, −105, 111, −111, 115, −115 |

^{1}Negative value indicates the reverse direction of the corresponding line.

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## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Lei, M.
An Electric Bus Battery Swapping Station Location Method Based on Global Optimized Peak Traffic Flow. *World Electr. Veh. J.* **2023**, *14*, 280.
https://doi.org/10.3390/wevj14100280

**AMA Style**

Wang Y, Lei M.
An Electric Bus Battery Swapping Station Location Method Based on Global Optimized Peak Traffic Flow. *World Electric Vehicle Journal*. 2023; 14(10):280.
https://doi.org/10.3390/wevj14100280

**Chicago/Turabian Style**

Wang, Yu, and Mingyu Lei.
2023. "An Electric Bus Battery Swapping Station Location Method Based on Global Optimized Peak Traffic Flow" *World Electric Vehicle Journal* 14, no. 10: 280.
https://doi.org/10.3390/wevj14100280