# Dynamic-Area-Based Shortest-Path Algorithm for Intelligent Charging Guidance of Electric Vehicles

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Based on the charging request point and the users’ next destination, a dynamic-area model is proposed. The area extension algorithm (AEA) and the charging station attribution algorithm (CAA) are added to ensure validity and scalability of the model. The constructed model can intelligently match the charging station area in accordance with the direction of users’ destination and provide charging guidance.
- (2)
- The Dijkstra algorithm is improved based on the dynamic-area model by limiting the node searching area. The improved shortest-path algorithm divides the charging guidance problem into three steps. It not only guarantees the users-oriented shortest-path planning but also effectively reduces time complexity.

## 2. The Dynamic-Area Model

#### 2.1. Restricted Area Initialization

- The line segments of SP and HE show the symmetry of up-down and the symmetry of left-right, respectively.
- The number of nodes contained in the area is significantly smaller than that in the area ABCD.
- The charging station nodes C1 and C2 in the area match with the direction of the users’ next destination and also meet the users’ travel demand.

#### 2.2. Dynamic-Area Construction

## 3. Intelligent Charging Guidance Strategy

#### 3.1. CAA Description

- (1)
- The rays and the points are below the area;
- (2)
- The rays and the points are above the area;
- (3)
- Both the rays and the points are in the area;
- (4)
- The rays pass through the area and the points to the left of the area;
- (5)
- The rays are outside the area, and the points are at the area boundary;
- (6)
- The rays and the points are to the right of the area.

#### 3.2. Dijkstra for Improving Node Searching Area

- -
- Step 1: R-C (Request point to Charging station). R-C indicates the shortest-path guidance from the charging request point to the charging station. The shortest-path distance is ${l}_{RC}$ = $l\left({R}_{i},{C}_{\sigma}\right)$, and its corresponding node set is ${d}_{RC}=d\left({R}_{i},{C}_{\sigma}\right)$.
- -
- Step 2: C-N (Charging station to Next destination). C-N indicates the shortest-path guidance from the charging station to the next destination. The shortest-path distance is ${l}_{CN}=l\left({C}_{\sigma},{N}_{i}\right)$, and its corresponding node set is ${d}_{CN}=d\left({C}_{\sigma},{N}_{i}\right)$.
- -
- Step 3: R-N (Request point to Next destination). R-N indicates the process of the dynamic-area shortest-path algorithm from the charging request point to the next destination.

#### 3.3. Strategy Structure

- -
**Step 1:**Determine ${U}_{i}=\left({r}_{i},{t}_{i}\right)$ and set ${r}_{i}=S$; ${t}_{i}=P$, HE points were calculated by Equations (6) and (7). The dynamic area model was established with points HPES.- -
**Step 2:**Determine the list ${C}_{sta}$ of charging stations in the area. According to the CAA, traverse the charging stations to determine whether they are within the dynamic area.- -
**Step 3:**Determine the list ${C}_{end}$ of charging stations in the dynamic area; the list length is n. Set the sufficient number of charging stations in the dynamic area as 3. If $n\le 3$, execute the AEA and return Step 2; otherwise, execute Step 4.- -
**Step 4:**Calculate the R-C and C-N distance of each station in the dynamic area. Then, get the R-N calculation results and the list of charging station guidance strategies.- -
**Step 5:**Calculate the shortest-path charging station guidance strategy ${\eta}_{min\text{}}$.

## 4. Simulation and Results

#### 4.1. Road Network Model

#### 4.2. Results and Discussion

#### 4.3. Comparison of Execution Time

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 9.**Schematic diagram of $D$ and ${D}^{\prime}$. (

**a**) ${U}_{1}$’s dynamic area change diagram. (

**b**) ${U}_{2}$’s dynamic area change diagram. (

**c**) ${U}_{3}$’s dynamic area change diagram. (

**d**) ${U}_{4}$’s dynamic area change diagram. (

**e**) ${U}_{5}$’s dynamic area change diagram.

${\mathit{U}}_{\mathit{i}}\left({\mathit{r}}_{\mathit{i}},{\mathit{t}}_{\mathit{i}}\right)$ | ${\mathit{U}}_{1}$ | ${\mathit{U}}_{2}$ | ${\mathit{U}}_{3}$ | ${\mathit{U}}_{4}$ | ${\mathit{U}}_{5}$ |
---|---|---|---|---|---|

${r}_{i}$ | ${r}_{1}=7$ | ${r}_{2}=38$ | ${r}_{3}=51$ | ${r}_{4}=16$ | ${r}_{5}=29$ |

${t}_{i}$ | ${t}_{1}=56$ | ${t}_{2}=1$ | ${t}_{3}=11$ | ${t}_{4}=44$ | ${t}_{5}=34$ |

${r}_{i}\left({x}_{i},{y}_{i}\right)$ | (−10, −5) | (−36, −8) | (−20, 30) | (0, 10) | (36, 0) |

${t}_{i}\left({x}_{i},{y}_{i}\right)$ | (−31, −20) | (0, 0) | (16, −5) | (31, −20) | (−18, 25) |

${\mathit{C}}_{\mathit{s}\mathit{t}\mathit{a}}$ | Charging Station Node List | Charging Station Coordinates |
---|---|---|

${c}_{1}$ | 2 | (10, 0) |

${c}_{2}$ | 18 | (−16, 10) |

${c}_{3}$ | 27 | (26, −15) |

${c}_{4}$ | 31 | (26, 15) |

${c}_{5}$ | 41 | (0, −25) |

${c}_{6}$ | 46 | (44, 0) |

${c}_{7}$ | 53 | (−44, 10) |

**Table 3.**Results of the intelligent charging guidance strategy. CAA: charging station attribution algorithm.

${\mathit{U}}_{\mathit{i}}\left({\mathit{r}}_{\mathit{i}},{\mathit{t}}_{\mathit{i}}\right)$ | $\mathit{D}{\prime}_{\mathit{i}}$ | $\left({\mathit{H}}_{\mathit{k}},{\mathit{E}}_{\mathit{k}},{\mathit{S}}_{\mathit{k}},{\mathit{P}}_{\mathit{k}}\right)$ | CAA | R | AEA |
---|---|---|---|---|---|

${U}_{1}\left(7,56\right)$ | $D{\prime}_{1}$ | ${H}_{1}$(7.11, −51.15) | n = 3 $C=\left[18,53,41\right]$ | 54.84 | Execute 3 times L = 7.83 |

${E}_{1}$(−48.11, 26.15) | |||||

${S}_{1}$(1.81, 3.44) | |||||

${P}_{1}$(−42.82, −28.44) | |||||

${U}_{2}\left(-36,-8\right)$ | $D{\prime}_{2}$ | ${H}_{2}$(−47.75, −10.61) | n = 3 $C=\left[18,53,41\right]$ | 74.58 | Execute 1 time L = 10.65 |

${E}_{2}$(−6.54, −55.53) | |||||

${S}_{2}$(−29.45, 47.53) | |||||

${P}_{2}$ (11.75, 2.61) | |||||

${U}_{3}\left(51,11\right)$ | $D{\prime}_{3}$ | ${H}_{3}$(7.11, −51.15) | n = 4 $C=\left[2,18,31,53\right]$ | 64.55 | Execute 2 times L = 9.22 |

${E}_{3}$(−48.11, 26.15) | |||||

${S}_{3}$ (1.81, 3.44) | |||||

${P}_{3}$(−42.82, −28.44) | |||||

${U}_{4}\left(16,44\right)$ | $D{\prime}_{4}$ | ${H}_{4}$(41.48,21.85) | n = 4 $C=\left[2,27,31,41\right]$ | 43.14 | No execution |

${E}_{4}$(−10.48, −31.85) | |||||

${S}_{4}$ (0, 10) | |||||

${P}_{4}$ (31, −20) | |||||

${U}_{5}\left(29,34\right)$ | $D{\prime}_{5}$ | ${H}_{5}$(30.65, 59.26) | n = 3 $C=\left[2,18,31\right]$ | 76.51 | No execution |

${E}_{5}$(−12.65, −34.26) | |||||

${S}_{5}$ (36, 0) | |||||

${P}_{5}$(−18, 25) |

${\mathit{U}}_{1}$ | ${\mathit{U}}_{2}$ | ${\mathit{U}}_{3}$ | ${\mathit{U}}_{4}$ | ${\mathit{U}}_{5}$ | TR | |
---|---|---|---|---|---|---|

K | 99.26 | 106.83 | 99.47 | 112.82 | 70.70 | 11.56 |

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**MDPI and ACS Style**

Cai, J.; Chen, D.; Jiang, S.; Pan, W. Dynamic-Area-Based Shortest-Path Algorithm for Intelligent Charging Guidance of Electric Vehicles. *Sustainability* **2020**, *12*, 7343.
https://doi.org/10.3390/su12187343

**AMA Style**

Cai J, Chen D, Jiang S, Pan W. Dynamic-Area-Based Shortest-Path Algorithm for Intelligent Charging Guidance of Electric Vehicles. *Sustainability*. 2020; 12(18):7343.
https://doi.org/10.3390/su12187343

**Chicago/Turabian Style**

Cai, Junpeng, Dewang Chen, Shixiong Jiang, and Weijing Pan. 2020. "Dynamic-Area-Based Shortest-Path Algorithm for Intelligent Charging Guidance of Electric Vehicles" *Sustainability* 12, no. 18: 7343.
https://doi.org/10.3390/su12187343