# Optimal Planning of Electric Vehicle Charging Station Considering Mutual Benefit of Users and Power Grid

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## Abstract

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## 1. Introduction

- (1)
- An optimal electric vehicle charging station location and capacity model is proposed, which considers the mutual benefit of users and the power grid.
- (2)
- Based on the Voronoi diagram and improved particle swarm optimization (IPSO), a solution model is developed to determine location, capacity, and service area of each charging station. The remainder of this paper is organized as follows. Section 2 presents the forecasting model of EV’s fast charging demand. Section 3 presents the location and capacity model of EV charging stations. Section 4 gives the solution method. Section 5 conducts case studies to verify the effectiveness of the proposed method. Section 6 summarizes the paper.

## 2. Forecasting of EV’s Fast Charging Demand

## 3. Location and Capacity Model

#### 3.1. Location Model

#### 3.2. Capacity Model

## 4. Solution of Model

- Step 1: Forecast the number of EVs at each fast charging demand point according to (1).
- Step 2: Randomly generate ${n}_{c}$ charging stations’ locations in the planning area, and use the locations of charging stations as the positions of particles.
- Step 3: Taking the position of particle as the growing point, then use Voronoi diagram to divide the service area of each charging station. Use (10) to determine the capacity of charging station.
- Step 4: Calculate the annual construction and operation cost of charging station, the annual loss cost of users on the way to the charging station, and the annual network loss cost of power grid respectively according to (3), (4), (5), and (6). Then use (2) to calculate the annual social cost of charging station and take it as the value of particle. Finally, find the individual optimal value ${P}_{best}$ and the global optimal value ${G}_{best}$ and use the penalty function to deal with the particles that do not meet the constraints.
- Step 5: Determine whether reach the maximum number of iterations. If not, go to step 6, otherwise go to step 7.
- Step 6: Update the speed and position of particles, go to step 3 and the number of iterations plus one.
- Step 7: Output each charging station’s optimal location and its service area, the planning costs, and the number of chargers in each charging station.

## 5. Case Study and Discussion

#### 5.1. Case Description

^{4}¥. The price of a charger is 5 × 10

^{4}¥. The auxiliary investment coefficient of a charger is 1.5 × 10

^{4}¥. The depreciation life of charging station is 20 years, and the discount rate is 0.08. The operation cost is 15% of the construction cost. EV’s battery consumption is 0.3 kWh/km. The charging price of EV is 1 ¥/kWh. The zigzag coefficient of road is 1.2. The daily work time of a charging station is 20 h a day. The copper loss and iron loss of the transformer is 0.04 ¥/kWh, the line loss and charging loss of charger is 0.05 ¥/kWh. The simultaneous arrival rate of EVs is 0.6, and the number of EVs in a queue that can be accepted by EV users is 3. The minimum number of chargers in the charging station is 10 and the maximum is 20. The maximum distance between fast charging demand point and charging station is 1.5 km. The minimum distance between charging stations is 0.5 km.

#### 5.2. Simulation Analysis and Discussion

^{4}¥, the costs and the number of chargers in each charging station are shown in Table 1.

#### 5.3. Comparison of Different Method

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Charging stations’ locations and their service areas obtained by IPSO and Voronoi diagram.

Charging Station No. | Number of Chargers | Number of EVs in Its Service Area | Annual Construction and Operation Cost (×10^{4} ¥) | Annual Loss Cost of Users (×10 ^{4} ¥) | Annual Network Loss Cost (×10 ^{4} ¥) |
---|---|---|---|---|---|

1 | 19 | 97 | 97.98 | 0.45 | 1.74 |

2 | 14 | 70 | 66.07 | 0.41 | 1.31 |

3 | 16 | 79 | 77.77 | 0.58 | 1.46 |

4 | 14 | 71 | 66.07 | 0.38 | 1.31 |

5 | 11 | 57 | 51.13 | 0.32 | 1.04 |

6 | 15 | 77 | 71.74 | 0.46 | 1.39 |

Algorithm | Number of Chargers in Each Charging Station | Annual Social Cost (×10 ^{4} ¥) | Annual Construction and Operation Cost (×10^{4} ¥) | Annual Loss Cost of Users (×10^{4} ¥) | Annual Network Loss Cost (×10 ^{4} ¥) |
---|---|---|---|---|---|

PSO | 19,14,14, 12,17,14 | 446.93 | 436.08 | 2.48 | 8.38 |

IPSO | 19,14,16, 14,11,15 | 441.59 | 430.75 | 2.59 | 8.25 |

Methods | Method 1 [3] | Method 2 [20] | Proposed Method |
---|---|---|---|

Objectives | Construction cost + power loss cost of vehicle + time loss cost of driver | Construction cost + operating profit | Construction and operation cost + loss cost of users + network loss cost |

Algorithm /Platform | Universal simulation platform | Genetic algorithm /MATLAB | IPSO + Voronoi diagram/MATLAB |

Results | Optimal location and size of charging station | Optimal location and size of charging station | Optimal location, capacity, and service area of charging station |

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**MDPI and ACS Style**

Hou, H.; Tang, J.; Zhao, B.; Zhang, L.; Wang, Y.; Xie, C.
Optimal Planning of Electric Vehicle Charging Station Considering Mutual Benefit of Users and Power Grid. *World Electr. Veh. J.* **2021**, *12*, 244.
https://doi.org/10.3390/wevj12040244

**AMA Style**

Hou H, Tang J, Zhao B, Zhang L, Wang Y, Xie C.
Optimal Planning of Electric Vehicle Charging Station Considering Mutual Benefit of Users and Power Grid. *World Electric Vehicle Journal*. 2021; 12(4):244.
https://doi.org/10.3390/wevj12040244

**Chicago/Turabian Style**

Hou, Hui, Junyi Tang, Bo Zhao, Leiqi Zhang, Yifan Wang, and Changjun Xie.
2021. "Optimal Planning of Electric Vehicle Charging Station Considering Mutual Benefit of Users and Power Grid" *World Electric Vehicle Journal* 12, no. 4: 244.
https://doi.org/10.3390/wevj12040244