# Two-Layer Routing for High-Voltage Powerline Inspection by Cooperated Ground Vehicle and Drone

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Problem Description and Model Development

#### 3.1. Problem Description

_{G}= (V

_{G}, E

_{G}) for the road network and G

_{D}= (V

_{D}, E

_{D}) for the powerline network. V

_{G}is the set of all parking nodes and V

_{D}is the set of all the vertices in the powerline network. E

_{G}is the set of edges on the road network while E

_{D}contains the edges that can be traveled by the drone.

_{g}only on the edges in E

_{G}, which are all located in the lower layer. Each edge e

_{g}$\in $ E

_{G}can be represented by < i, j > (i, j $\in $ V

_{G}), and its distance can be calculated as d

_{ij}

^{1}, which is not the Euler distance but the actual travelling distance for the ground vehicle on the road network.

_{R}$\subset $ E

_{D}be the set of edges required to be inspected, which is {<a, c>, <b, c>, <c, d>, <e, f>} in Figure 3. Represented by < i, j > (i, j $\in $ V

_{D}), the linear distance of any required edge e

_{r}$\in $ E

_{R}can be calculated as d

_{ij}

^{2}, and the edge is said to be served if and only if the drone traverses the arc for one time. Since the drone can fly into or out of the powerline at any node, each edge e

_{r}$\in $ E

_{R}can be served in one flight or several flights. For instance, Edges <a,c> and <b,c> are only included in one drone route while Edge <c,d> is divided into three segments: <c, g> inspected in the first flight, <g,h> inspected in the second flight and <h,d> inspected in the third flight. In one drone route, there are two flight modes, regular flight and inspection flight. The drone can fly quickly from the vehicle to the node on the transmission line (e.g., 7→a) or from one powerline node to another (e.g., b→c), and inspect the powerline with airborne sensors at a slow speed (e.g., a→b). We denote the inspection speed as v

_{d}

^{1}and the regular flight speed as v

_{d}

^{2}(v

_{d}

^{1}≤ v

_{d}

^{2}). Besides, the airborne sensors would not work and stay in standby state when the drone is in regular flight. Thus, the power consumption rate of the drone per unit time during inspection, denoted as p

^{1}, is assumed to be higher than that during regular flight, p

^{2}(p

^{1}> p

^{2}). The more detailed calculation for the energy consumption process of the drone is presented in Section 3.2. In addition, since in this problem we utilize the ground vehicle that equips automated systems for launching, recycling and exchanging battery for the drone, it would take only a few seconds for launching, recycling and preparing for the next flight. Thus, compared to the endurance time, over 20 min, the launching and recycling time of the drone can be neglected.

^{ij}

_{m}into the edge < i, j > (i, j $\in $ V

_{D}), representing node m on the edge, among which

_{1}: {7, a, c, b, c, g, 5}, s

_{2}:{5, g, h, 6} and s

_{3}:{6, h, e, f, 8} in Figure 3.

_{k}than the vehicle on the corresponding road route. Let t

_{1}(s

_{k}) denote the time that the drone finishes the drone flight s

_{k}, which also means the completing time for the sub-solution of s

_{k}. In some situations, flight s

_{k}is not connected with flight s

_{k+1}, and the ground vehicle has to recycle the drone at the end node of s

_{k}and carry the drone to the start node of s

_{k+1}to launch it. Let t

_{2}(s

_{k}, s

_{k+1}) denote the time that the vehicle travel from the end node of sub-solution s

_{k}to the start node of sub-solution s

_{k+1}.

- All the edges of the powerline network must be inspected by the drone, and each edge is visited only once.
- The ground vehicle should start at the deport and return to the deport at end.
- The ground vehicle has to arrive at the parking node before the drone to recycle it in time.
- The drone must return to the truck before its battery is power off.
- The route of the ground vehicle must be successive.
- Each route of the drone must be successive.

#### 3.2. Energy Consumption Model of the Drone

^{1}, and the regular flight time is t

^{2}. With the maximum capacity of the drone battery, D, the energy consumption in one drone route must satisfy the constraint:

_{d}

^{1}and the flying speed under regular state is denoted as v

_{d}

^{2}. According to D’Andrea [35], the powers power consumption rate of the drone per unit time under different states can be calculated as follows.

_{s}is the energy consuming rate of the airborne sensors.

^{1}, and regular flight distance, d

^{2}, which is

## 4. Solution Algorithm

#### 4.1. Heuristic Based on “Cluster First, Route Second”

#### 4.1.1. Generating Sub-Solutions

Algorithm 1: Generating sub-solutions | |

1 | Divide the transmission lines into segments |

2 | WHILE (there exist unvisited line segments) DO |

3 | Select an unvisited line segment |

4 | Find two nearest road nodes as launching node and recycling node |

5 | IF drone route can be built without violating the constraints THEN |

6 | Construct the drone route |

7 | ELSE |

8 | Replace the segment with two new segments |

9 | END IF |

10 | END WHILE |

11 | Cluster some drone routes and form sub-solutions |

Algorithm 2: Merging drone routes | |

1 | m: the number of drone routes |

2 | FORi = 1 to m−1 DO |

3 | WHILE (1) DO |

4 | FOR j = i+1 to m DO |

5 | IF drone route i and drone route j can be merged THEN |

6 | Calculate the saving time (i, j) |

7 | END IF |

8 | END FOR |

9 | IF exists a drone route that can save time through merging THEN |

10 | Merge drone route i with the most saving drone route |

11 | ELSE |

12 | Break |

13 | END IF |

14 | END WHILE |

15 | END FOR |

#### 4.1.2. Constructing Vehicle Route

Algorithm 3: Constructing vehicle route | |

1 | m: the number of generated sub-solutions |

2 | INITIALIZE subsoluArray |

3 | FOR tempSubSolu = 2 to m DO |

4 | FOR i = 1 to length(subsoluArray)+1 DO |

5 | Calculate added time when putting tempSubSolu into subsoluArray at position i |

6 | END FOR |

7 | Choose the position with minimum add time to insert tempSubSolu |

8 | Update the subsoluArray |

9 | END FOR |

#### 4.2. Heuristic Based on “Route First, Split Second”

#### 4.2.1. Generating a Giant Drone Route

_{D}), the forward insertion (from i to j) and reverse insertion (from j to i) would both be considered due to the undirected segment. Then, the segment would be put into the array with the position of minimum adding cost and the corresponding inspection direction (Line 7). Finally, a giant drone route is found. The drone route for the example case is shown in Figure 6, which is {7, a, c, b, c, d, e, f, 8}. The main procedure is shown in Algorithm 4.

Algorithm 4: Generating a giant drone route | |

1 | m: the number of transmission line segments |

2 | INITIALIZE routeArray |

3 | FOR tempSegment = 2 to n DO |

4 | FOR i = 1 to length(routeArray)+1 DO |

5 | Calculate added time when inserting tempSegment into routeArray at position i |

6 | END FOR |

7 | Choose the position with minimum add time to insert tempSegment |

8 | Update the routeArray |

9 | END FOR |

#### 4.2.2. Splitting into Feasible Sub-Solutions

Algorithm 5: Splitting | |

1 | WHILE (the giant drone route has not been split into sub-solutions) DO |

2 | INITIALIZE interval = 0.8 * D/k |

3 | WHILE (1) DO |

4 | Cut the giant drone route to get a segment with the length of interval |

5 | Find two nearest road nodes as launching node and recycle node |

6 | IF drone route can be built without violating the constraints THEN |

7 | Construct the drone route and get a sub-solution |

8 | Update the giant drone route |

9 | BREAK |

10 | ELSE |

11 | interval = interval $-$ 0.1 * D/k |

12 | END IF |

13 | END WHILE |

14 | END FOR |

#### 4.3. Local Search Improvement

Algorithm 6: Local Search | |

1 | s: the initial solution given by the constructive heuristic |

2 | k = 1 |

3 | WHILEk ≤ N DO |

4 | Find the best neighbor s’ ∈ N(s) |

5 | IF s’ < s THEN |

6 | s ← s’ |

7 | Reinitialize N |

8 | k = 1 |

9 | ELSE |

10 | k = k + 1 |

11 | END IF |

12 | END WHILE |

#### 4.3.1. Neighborhood 1: Exchanging Sub-Solutions

#### 4.3.2. Neighborhood 2: Exchanging Powerline Segments

#### 4.3.3. Neighborhood 3: Splitting Powerline Segments

## 5. Case Study and Results

#### 5.1. Case Description

#### 5.2. Experiment Results and Analysis

#### 5.2.1. Experiment Results

#### 5.2.2. Sensitivity Analysis

**(1) Impact analysis of the inspection speed**

**(2) Impact analysis of the battery capacity**

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Aerial view of a solution for the example in Figure 2.

**Figure 4.**An illustration of the drone routes for the example case: (

**a**) drone routes before merging; and (

**b**) drone routes after merging.

**Figure 5.**An illustration of the feasible solution by Cluster First, Route Second (CFRS) for the example case.

**Figure 6.**An illustration of the feasible solution by Route First, Split Second (RFSS) for the example case.

**Figure 11.**The powerline network and the road network in Ji’an: (

**a**) the power grid in Ji’an; and (

**b**) the road network in Ji’an.

Powerline Network | Road Network | ||
---|---|---|---|

Electric Voltage (KV) | Total Length (km) | Number of Arcs | Number of Parking Nodes |

550 | 178.05 | 6 | 20 |

220 | 522.71 | 25 | 40 |

110 | 1228.29 | 71 | 100 |

Vehicle | Speed | 60 km/h |

Drone | general flying speed | 50 km/h |

inspection speed | 25 km/h | |

capacity of battery | 5000 mAh | |

rate of work for the sensors | 200 W | |

coefficient $\phi $ | 0.05 |

Case | Objective Value (h) | Computational Time (s) | ||||||
---|---|---|---|---|---|---|---|---|

CFRS | RFSS | CFRS-LS | RFSS-LS | CFRS | RFSS | CFRS-LS | RFSS-LS | |

small | 9.97 | 10.83 | 9.58 | 9.56 | 0.13 | 0.16 | 1.22 | 1.36 |

medium | 26.91 | 28.32 | 24.66 | 24.03 | 0.45 | 0.50 | 1.52 | 1.68 |

large | 63.06 | 62.04 | 56.11 | 55.06 | 1.23 | 1.30 | 4.33 | 5.19 |

Inspection Speed (km/h) | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | |
---|---|---|---|---|---|---|---|---|---|

Battery Power (mAh) | |||||||||

2000 | 111.05 | 60.77 | 43.20 | 35.84 | 32.30 | 27.21 | 24.94 | 23.56 | |

3000 | 107.31 | 57.73 | 41.36 | 32.50 | 29.75 | 24.64 | 22.36 | 20.84 | |

4000 | 102.98 | 55.63 | 38.91 | 30.12 | 26.78 | 22.53 | 20.29 | 18.69 | |

5000 | 100.41 | 53.22 | 36.98 | 28.59 | 24.03 | 20.77 | 18.50 | 16.80 | |

6000 | 99.40 | 52.06 | 35.47 | 27.51 | 22.86 | 19.47 | 17.20 | 15.50 | |

7000 | 98.88 | 51.15 | 34.25 | 26.96 | 22.29 | 18.21 | 16.31 | 14.29 | |

8000 | 98.33 | 50.67 | 33.69 | 26.62 | 21.86 | 17.80 | 15.52 | 13.82 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Shi, J.; Liu, Z.; Huang, J.; Zhou, T.
Two-Layer Routing for High-Voltage Powerline Inspection by Cooperated Ground Vehicle and Drone. *Energies* **2019**, *12*, 1385.
https://doi.org/10.3390/en12071385

**AMA Style**

Liu Y, Shi J, Liu Z, Huang J, Zhou T.
Two-Layer Routing for High-Voltage Powerline Inspection by Cooperated Ground Vehicle and Drone. *Energies*. 2019; 12(7):1385.
https://doi.org/10.3390/en12071385

**Chicago/Turabian Style**

Liu, Yao, Jianmai Shi, Zhong Liu, Jincai Huang, and Tianren Zhou.
2019. "Two-Layer Routing for High-Voltage Powerline Inspection by Cooperated Ground Vehicle and Drone" *Energies* 12, no. 7: 1385.
https://doi.org/10.3390/en12071385