# Location of Electric Vehicle Charging Stations Based on Game Theory

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## Abstract

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## 1. Introduction

## 2. Analytic Hierarchy Process

- The main factors affecting user arrival rate have been determined by consulting relevant information. The qualitative process is completed. On this basis, the quantitative process is completed to quantify the factors involved in the qualitative process by forming a decision-making team. The hierarchical analysis ladder structure of electric vehicle charging stations has been constructed. The target layer of this ladder structure is for electric vehicle users to charge the most at the charging station. The four standards of charging convenience, self-location, service capability, and surrounding environment are established in the guideline layer. The waiting points for electric vehicle charging stations and the locations of existing charging stations are considered as the most solution layer.
- The importance of each standard in the criterion layer is measured based on the target layer. Then, based on the criterion layer, measure the importance of each point in the solution layer. The judgment matrix is established by using a 1–9 level scaling method [37].
- The constructed $n$th order judgment matrix is processed through normalization. The maximum eigenvalue of the judgment matrix is ${\lambda}_{max}$. The maximum eigenvector corresponding to ${\lambda}_{max}$ is determined. The consistency index of the judgment matrix is calculated as Equations (1) and (2).$$CI=\frac{{\lambda}_{max}-n}{n-1}$$$$CR=\frac{CI}{RI}$$
- Using the eigenvectors of Target Layer–Criteria Layer and Criteria Layer–Scheme Layer, the combined weight value ${q}_{i}$ of each electric vehicle charging station and the constructed charging station is calculated in the scheme layer. If the combination weight value of the charging station is large, the arrival rate is high.

## 3. Charging Station Location Model Based on Game Theory

#### 3.1. Electric Vehicle Queue Waiting Time

#### 3.2. Assumptions

- The principle of proximity is that users prefer to go to charging stations closer to their own location.
- The demand point is an area with a constant area.
- The same performance and constant driving speed for all EVs.
- The service rate of all charging stations in the station is equal.
- Each waiting point is a queuing system with a constant daily arrival rate.
- Within the research area, the everyday requirements at the demand points are the similar and the demand relates only with the population.
- The arrival rate of electric vehicle users follows the Poisson distribution, and is only related to the conditions of the charging station itself and its surrounding environment.

#### 3.3. Objective Function Construction and Constraint Conditions

#### 3.3.1. Objective Function One: Minimize User Costs

#### 3.3.2. Objective Function Two: Minimizing the Cost of Charging Stations

#### 3.4. Mathematical Model Description

## 4. Model Solving and Artificial Bee Colony Algorithm Design

## 5. Simulation

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Influencing Factor | Convenience of Charging | Self-Position | Service Capability | Surrounding Environment | Weight |
---|---|---|---|---|---|

Convenience of charging | 1 | 2 | 3 | 3 | 0.46 |

Self-position | 1/2 | 1 | 1/2 | 1/2 | 0.13 |

Service capability | 1/3 | 2 | 1 | 1/2 | 0.17 |

Surrounding environment | 1/3 | 2 | 2 | 1 | 0.24 |

Optimal Solution | Optimal Solution | Standard Deviation | |
---|---|---|---|

Artificial Bee Colony Algorithm 1 | 0.0340 | 0.0343 | $5.231\times {10}^{-4}$ |

Artificial Bee Colony Algorithm 2 | 0.0244 | 0.0246 | $3.078\times {10}^{-4}$ |

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## Share and Cite

**MDPI and ACS Style**

Ma, H.; Pei, W.; Zhang, Q.; Xu, D.; Li, Y.
Location of Electric Vehicle Charging Stations Based on Game Theory. *World Electr. Veh. J.* **2023**, *14*, 128.
https://doi.org/10.3390/wevj14050128

**AMA Style**

Ma H, Pei W, Zhang Q, Xu D, Li Y.
Location of Electric Vehicle Charging Stations Based on Game Theory. *World Electric Vehicle Journal*. 2023; 14(5):128.
https://doi.org/10.3390/wevj14050128

**Chicago/Turabian Style**

Ma, Hao, Wenhui Pei, Qi Zhang, Di Xu, and Yongjing Li.
2023. "Location of Electric Vehicle Charging Stations Based on Game Theory" *World Electric Vehicle Journal* 14, no. 5: 128.
https://doi.org/10.3390/wevj14050128