# An Elastic Charging Service Fee-Based Load Guiding Strategy for Fast Charging Stations

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis of Charging Location Selection and Charging Service Fee Response Based on User Classification

#### 2.1. Standard Classification of EV Fast Charging Users' Charging Location

- Class I: In the absence of an ITS, users will choose the nearest FCS;
- Class II: With access to an ITS, cost-insensitive users' general choice will be the FCS where they can finish the charging process in the shortest time;
- Class III: With access to an ITS, cost-sensitive users will generally consider both the charging time and charging cost. When the charging time is within the affordable range, their priority will be the one where the charging cost is relatively low.

_{d}is the total charging time (hours); T

_{a}is the arrival time (hours), namely the time needed to travel to the FCS; T

_{q}is the queuing time (hours), and the detailed deduction is given in the Appendix A; T

_{c}is the charging time (hours)—the time from the start of charging to the end of charging.

_{d}is the total charging cost (China Yuan, CNY); C

_{a}is the arrival charging cost (CNY), that is, the charging cost when the vehicle reaches a charging station considering the electricity consumption during the driving process. C

_{s}is the cost of the charging service fee (CNY); C

_{t}is the cost of travel (CNY), which is the charging cost of the amount of electricity consumed by the vehicle in the process of traveling to the corresponding fast charge station; C

_{c}is the charging cost (CNY) in the charging station.

#### 2.2. User Charging Location Selection Probability Based on a MNL Model

_{i}be the probability for i-th selection criteria of a charging location. For the Class I, II and III charging location selection criteria described in Section 2.1, the probability are P

_{I}, P

_{II}and P

_{III}respectively, where the P

_{I}can be obtained directly by calculating the probability of installing ITS. If Class III is viewed as a reference, P

_{II}can be described according to a logistic formula:

_{i}is the constant term for i-th option; ${x}_{k}^{i}$ is k-th variable of i-th option is used; ${\beta}_{k}^{i}$ is the corresponding coefficient of ${x}_{k}^{i}$.

#### 2.3. Cost-Sensitive User's Response to Charging Service Fees

## 3. Pricing Strategy of Charging Service Fees Based on Grid Benefits and Customer Satisfaction

#### 3.1. The Adjustment of Charging Power Based on the Acceptable Node Voltage of FCS

_{m}. However, the power limit is often used to analyze the system’s voltage stability margin, and the system’s normal operation point is very far from the critical point of the PV curve, thus, the power limit P

_{m}cannot reflect the possible load access in the FCS. On the other hand, the normal operation of the distribution system needs to meets the constraints of power quality, and the load power corresponding to voltage amplitude limit (power quality constraint) can be obtained by PV curve, which is more stringent compared to the power limit P

_{m}and is more likely to reflect the actual access of loads in the FCS. Therefore, the upper limit power P

_{ssm}constrained by the power quality of distribution system can be defined as the node tolerability D of the node where the FCS is located:

_{max}is the maximum fast charge power that can be provided by fast filling piles.

#### 3.2 Analysis of Grid Benefit and Customer Satisfaction Under Coordinated Fast Charging

_{i}represents the occupancy of i-th fast-charge station.

_{i}

_{0}, C

_{i}, T

_{i}

_{0}, T

_{i}are the total cost of charging and the total charging time of user i before and after charging service fee adjustment; m is the total number of fast charging EV users.

_{t}and the user's overall charging time L

_{t}. Theoretically, the optimal scheme should maximize the charge balance degree E, minimize the relative value of user’s overall charging time ${T}_{i}^{\ast}$, and the relative value of user’s overall charging cost ${C}_{i}^{\ast}$ should be reduced due to the reimbursement of FCSs. Taking into account the profitability and the enthusiasm of the user response, the benefits obtained from charging balance degree are quantified and parts of the benefits are returned to the users proportionally. The benefits mainly come from the reduced network loss, power expansion cost and reactive power compensation costs.

_{t}, thus, the relative value of user’s overall charging time ${T}_{i}^{\ast}$ increases.

#### 3.3. The Charging Service Fee Pricing Mechanism Considering the Equilibrium of FCS Loads Access and User Satisfaction

## 4. Example Simulation

#### 4.1 Simulation Idea and Data Sources Explaination

#### 4.2. Parameters Setting and Simulation Calculation

_{k}is the probability of k-th (k = I, II and III) type of users; ${I}_{j,k,i}$ is the charging location selection coefficient, whose value is set as 1 when the j-th (j = 1, …, m) user is the k-th type of users, and its optimal charging location is charging station i, otherwise is set as 0; ${C}_{capj}$ is the battery capacity for the j-th user; $SO{C}_{j,i}$ is the remaining SOC when the j-th user arrives at charging station i.

## 5. Conclusions

- Energy storage devices must be implemented to deal with the stochasticity and fluctuation of renewable energy resources. By making cascade utilization of the lithium batteries of EV, we can minimize the cost of the acquisition cost and discard cost of lithium batteries. Therefore, it’s worthy to research the collaborative planning of charging service fees and battery exchange fees setting.
- To encourage more EV users to adopt renewable energy resources, the charging fees at the renewable energy charging stations can be more favorable or free at specific moments. Thus, it’s worthy to study the charging fee setting of ordinary charging stations and renewable energy charging stations by considering the generation cost of thermal and hydro units and output characteristics of new energy resources at different moments.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

EV Num. | EV Location | Battery Parameter | EV Num. | EV Location | Battery Parameter | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

The Previous Intersection Numbers | The Next Intersection Numbers | Distance from the Next Intersection/km | Battery Capacity/kWh | State of Charge | The previous Intersection Numbers | The Next Intersection Numbers | Distance from the Next Intersection/km | Battery Capacity/kWh | State of Charge | ||

1 | 2 | 3 | 0.91 | 18 | 0.39 | 41 | 18 | 19 | 0.12 | 42 | 0.34 |

2 | 5 | 4 | 0.73 | 33 | 0.50 | 42 | 20 | 19 | 0.82 | 33 | 0.33 |

3 | 1 | 6 | 0.96 | 12 | 0.17 | 43 | 19 | 20 | 0.24 | 15 | 0.38 |

4 | 3 | 8 | 0.52 | 26 | 0.42 | 44 | 19 | 20 | 0.63 | 18 | 0.38 |

5 | 3 | 8 | 1.05 | 38 | 0.38 | 45 | 19 | 20 | 0.78 | 38 | 0.28 |

6 | 9 | 4 | 0.98 | 26 | 0.25 | 46 | 21 | 20 | 0.44 | 15 | 0.35 |

7 | 7 | 11 | 1.20 | 15 | 0.32 | 47 | 21 | 20 | 0.87 | 15 | 0.34 |

8 | 8 | 12 | 0.64 | 18 | 0.38 | 48 | 21 | 20 | 0.93 | 12 | 0.40 |

9 | 12 | 8 | 0.53 | 12 | 0.64 | 49 | 20 | 21 | 0.74 | 26 | 0.44 |

10 | 12 | 8 | 0.74 | 18 | 0.57 | 50 | 22 | 16 | 0.78 | 42 | 0.44 |

11 | 9 | 13 | 0.48 | 26 | 0.24 | 51 | 23 | 17 | 0.43 | 15 | 0.28 |

12 | 9 | 13 | 1.31 | 12 | 0.59 | 52 | 23 | 17 | 0.54 | 33 | 0.36 |

13 | 10 | 11 | 1.27 | 90 | 0.41 | 53 | 18 | 24 | 0.27 | 70 | 0.25 |

14 | 10 | 11 | 0.93 | 26 | 0.34 | 54 | 18 | 24 | 0.82 | 26 | 0.26 |

15 | 11 | 12 | 0.69 | 42 | 0.41 | 55 | 24 | 18 | 0.85 | 15 | 0.35 |

16 | 13 | 12 | 0.65 | 15 | 0.33 | 56 | 19 | 25 | 0.83 | 18 | 0.47 |

17 | 12 | 13 | 0.38 | 15 | 0.34 | 57 | 25 | 19 | 0.85 | 42 | 0.29 |

18 | 14 | 13 | 0.81 | 33 | 0.47 | 58 | 25 | 19 | 0.93 | 38 | 0.38 |

19 | 13 | 14 | 0.22 | 18 | 0.46 | 59 | 20 | 26 | 0.22 | 15 | 0.33 |

20 | 13 | 14 | 0.75 | 15 | 0.46 | 60 | 20 | 26 | 0.89 | 26 | 0.44 |

21 | 15 | 14 | 0.64 | 42 | 0.40 | 61 | 26 | 20 | 0.73 | 12 | 0.26 |

22 | 10 | 16 | 0.38 | 18 | 0.25 | 62 | 26 | 20 | 0.64 | 15 | 0.35 |

23 | 11 | 17 | 0.62 | 15 | 0.41 | 63 | 21 | 27 | 0.42 | 26 | 0.39 |

24 | 17 | 11 | 0.88 | 33 | 0.48 | 64 | 22 | 23 | 1.15 | 26 | 0.44 |

25 | 18 | 12 | 0.80 | 26 | 0.39 | 65 | 23 | 24 | 1.09 | 15 | 0.47 |

26 | 13 | 19 | 0.37 | 12 | 0.43 | 66 | 25 | 24 | 0.68 | 42 | 0.36 |

27 | 13 | 19 | 0.49 | 26 | 0.41 | 67 | 24 | 25 | 0.43 | 15 | 0.23 |

28 | 13 | 19 | 0.92 | 18 | 0.33 | 68 | 26 | 25 | 0.47 | 15 | 0.29 |

29 | 19 | 13 | 0.17 | 12 | 0.37 | 69 | 26 | 25 | 0.58 | 33 | 0.27 |

30 | 19 | 13 | 0.86 | 18 | 0.29 | 70 | 25 | 26 | 0.30 | 26 | 0.54 |

31 | 14 | 20 | 0.53 | 15 | 0.42 | 71 | 27 | 26 | 0.27 | 12 | 0.30 |

32 | 20 | 14 | 0.52 | 15 | 0.26 | 72 | 27 | 26 | 0.73 | 18 | 0.41 |

33 | 20 | 14 | 0.61 | 38 | 0.26 | 73 | 26 | 27 | 0.48 | 38 | 0.33 |

34 | 15 | 21 | 0.85 | 15 | 0.29 | 74 | 30 | 23 | 1.01 | 26 | 0.42 |

35 | 21 | 15 | 0.44 | 12 | 0.11 | 75 | 31 | 24 | 0.77 | 33 | 0.29 |

36 | 17 | 16 | 1.38 | 15 | 0.47 | 76 | 25 | 32 | 0.35 | 38 | 0.24 |

37 | 18 | 17 | 0.79 | 33 | 0.38 | 77 | 32 | 25 | 0.83 | 15 | 0.24 |

38 | 17 | 18 | 0.81 | 70 | 0.29 | 78 | 33 | 27 | 0.97 | 18 | 0.39 |

39 | 19 | 18 | 0.23 | 26 | 0.46 | 79 | 30 | 31 | 1.66 | 26 | 0.34 |

40 | 19 | 18 | 0.39 | 26 | 0.21 | 80 | 33 | 32 | 0.13 | 18 | 0.33 |

Distribution Voltage Level (kV) | SVG Capacity (MVar) | Rated Service Life (year) | Investment Costs (Ten Thousand CNY) | Annual Operation Cost (Ten Thousand CNY) | Industry Discount Rate (%) |
---|---|---|---|---|---|

3.8 | 0.3 | 18 | 7 | 0.8 | 15 |

3.8 | 1 | 18 | 50 | 2 | 15 |

10 | 2 | 18 | 70 | 5 | 15 |

- The arrival pattern of the cars waiting to be charged is subject to Poisson’s flow distribution with parameter $\lambda $ ($\lambda >0$);
- The charging service time required of each vehicle is independent and obeys a negative exponential distribution with parameter $\mu $ ($\mu >0$);
- The charging station has $c$ ($c\ge 1$) charging equipment which can provide service independently and concurrently;
- The first-come first-served rule is executed in the station.

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EV Users’ Personal Attributes and Vehicle Types | Is ITS Installed? | Cost Per Unit Charge (CNY/kWh) | Affordable Charging Time Range | |||
---|---|---|---|---|---|---|

Maximum Affordability | Charging Option Change Price | Remaining Capacity (%) | Maximum Charging Time (h) | |||

Gender | Male | |||||

Female | ||||||

Age | Youth (18–38) | |||||

Middle-aged (38–58) | ||||||

Elderly (>58) | ||||||

EV type | Small car | |||||

Medium-large car | ||||||

Small SUV | ||||||

Medium-large SUV | ||||||

Others |

Scenes | The Over-Limit Voltage Node | The Most Serious Voltage Offset Value (Per Unit Value) |
---|---|---|

Random access of charging load | 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 28, 29, 30, 31, 32, 33 | 0.919573 |

Change the charging fees to regulate EVs | 13, 14, 15, 16, 17, 18, 30, 31, 32, 33 | 0.921568 |

Scenes | Configuration Capacity of Reactive Power Compensation Device (Mvar) | Initial Investment Cost (Ten Thousand CNY) | Annual Operating Costs (Ten Thousand CNY) | The Most Serious Voltage Offset Value after Reactive Compensation (Per Unit Value) |
---|---|---|---|---|

Random access of charging load | 9.6 | 324 | 23.6 | 0.9373 |

Change the charging fees to regulate EVs | 7 | 220 | 18 | 0.9427 |

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## Share and Cite

**MDPI and ACS Style**

Su, S.; Zhao, H.; Zhang, H.; Lin, X.
An Elastic Charging Service Fee-Based Load Guiding Strategy for Fast Charging Stations. *Energies* **2017**, *10*, 672.
https://doi.org/10.3390/en10050672

**AMA Style**

Su S, Zhao H, Zhang H, Lin X.
An Elastic Charging Service Fee-Based Load Guiding Strategy for Fast Charging Stations. *Energies*. 2017; 10(5):672.
https://doi.org/10.3390/en10050672

**Chicago/Turabian Style**

Su, Shu, Hang Zhao, Hongzhi Zhang, and Xiangning Lin.
2017. "An Elastic Charging Service Fee-Based Load Guiding Strategy for Fast Charging Stations" *Energies* 10, no. 5: 672.
https://doi.org/10.3390/en10050672