An optimization drone routing model for inspecting wind farms

Abstract

The use of wind turbines to generate electricity is growing worldwide. They comprise an extended area of hundreds of square miles, making the inspection process difficult and time-consuming. Recently, there has been an increasing interest in using a drone, or also known as unmanned aircraft systems, for inspecting wind turbines. Motivated by leveraging drone technology, this paper provides a routing optimization model to reduce the total operation time for inspecting a wind farm. We assume that one drone and one ground vehicle which carries the drone and extra batteries and charging equipment are available. The optimization model is solved in two steps. The first step clusters the wind turbines and optimizes the drone routing in each cluster by solving the classical traveling salesman problem using an integer linear programming model. The second step optimizes the ground vehicle routing by solving the equality generalized traveling salesman problem using an integer linear programming model. We test our proposed model using three case studies created by using actual wind farm locations. We compare the results with two models. One model assumes no clustering of the wind turbines, and the other model uses a greedy approach for determining the ground vehicle route. The results show that the proposed model is more efficient at different flight speeds and endurances. Also, we confirm that the efficiency increases as the drone flies faster or it has longer flight endurance.

Appendices

Appendix 1: nomenclature

Indices
i, j, l	Wind turbines
a,b	Clusters
Sets
N	Set of the wind turbines and depot
$N^{a}$	Set of the wind turbines in cluster a
S	Subset of $N^{a}$
K	Set of the clusters
Parameters
FS	Flying speed of the drone (mph)
FE	Flight endurance of the drone (min)
GS	Moving speed of the ground vehicle (mph)
U	Number of wind turbines
I	Inspection time for a wind turbine (min)
P	Time for conducting pre- and post-flight procedures (min)
$G_{ij}$	Moving time between wind turbine i to wind turbine j by the ground vehicle (min)
$F_{ij}$	Flight time between wind turbine i to wind turbine j by the drone (min)
Variables
C	Cluster assignment vector
T	Total operation time (min)
$T^{D}$	Total operation time of the drone (min)
$T^{G}$	Total operation time of the ground vehicle (min)
$T^{P}$	Total operation time for conducting pre- and post-flight procedures (min)
$t_{a}^{D}$	Total flight time of the drone between wind turbines in cluster a (min)
k	Number of clusters
$m_{a}$	Number of wind turbines in cluster a
$x_{ij}$	Binary decision variable that equals 1 if the ground vehicle moves from wind turbine i to wind turbine j, and 0 otherwise
$y_{ab}$	Binary decision variable that equals 1 if the ground vehicle moves from cluster a to cluster b, and 0 otherwise
$z_{ij}$	Binary decision variable that equals 1 if the drone flies from wind turbine i to wind turbine j, and 0 otherwise.
$u$	Integer variable representing the sequence number in which cluster is visited by the ground vehicle

Appendix 2: geographic locations of the wind turbines

Geographic locations of the wind turbines

No	Small-sized wind farm		Medium-sized wind farm		Large-sized wind farm
	Latitude	Longitude	Latitude	Longitude	Latitude	Longitude
1	35.2360	− 102.2494	32.7673	− 99.5048	31.0812	− 100.7139
2	35.2350	− 102.2463	32.7662	− 99.5021	31.0834	− 100.7090
3	35.2297	− 102.2419	32.7663	− 99.4990	31.0851	− 100.7048
4	35.2287	− 102.2391	32.7668	− 99.4961	31.0851	− 100.7015
5	35.2289	− 102.2350	32.7682	− 99.4936	31.0851	− 100.6981
6	35.2279	− 102.2321	32.7694	− 99.4910	31.0851	− 100.6950
7	35.2289	− 102.2282	32.7688	− 99.4882	31.0855	− 100.6889
8	35.2278	− 102.2253	32.7679	− 99.4853	31.0854	− 100.6864
9	35.2267	− 102.2224	32.7683	− 99.4824	31.0855	− 100.6838
10	35.2279	− 102.2138	32.7690	− 99.4796	31.0854	− 100.6814
11	35.2268	− 102.2110	32.7701	− 99.4770	31.0854	− 100.6789
12	35.2276	− 102.1973	32.7709	− 99.4741	31.0993	− 100.7264
13	35.2266	− 102.1944	32.7665	− 99.4711	31.0967	− 100.7218
14	35.2300	− 102.1869	32.7664	− 99.4683	31.0972	− 100.7181
15	35.2289	− 102.1840	32.7764	− 99.5046	31.0962	− 100.7140
16	35.2290	− 102.1799	32.7765	− 99.5015	31.0966	− 100.7093
17	35.2280	− 102.1771	32.7857	− 99.5020	31.0969	− 100.7045
18	35.2269	− 102.1743	32.7865	− 99.4993	31.0961	− 100.7007
19	35.2278	− 102.1697	32.7874	− 99.4964	31.0961	− 100.6980
20	35.2348	− 102.1606	32.7870	− 99.4935	31.1036	− 100.6983
21	35.2336	− 102.1574	32.7853	− 99.4901	31.1042	− 100.6956
22	35.2438	− 102.1605	32.7834	− 99.4864	31.1061	− 100.6930
23	35.2447	− 102.1629	32.7910	− 99.4838	31.0696	− 100.6904
24	35.2456	− 102.1652	32.7908	− 99.4796	31.0696	− 100.6880
25	35.2363	− 102.1924	32.7897	− 99.4763	31.0696	− 100.6851
26	35.2373	− 102.1952	32.7841	− 99.4746	31.0696	− 100.6820
27	35.2375	− 102.2030	32.7767	− 99.4681	31.0696	− 100.6795
28	35.2387	− 102.2063	32.7751	− 99.4650	31.1235	− 100.7310
29	35.2466	− 102.1996	32.7729	− 99.4616	31.1240	− 100.7283
30	35.2443	− 102.2074	32.7652	− 99.4579	31.1243	− 100.7252
31	35.2454	− 102.2103	32.7669	− 99.4525	31.1243	− 100.7211
32	35.2344	− 102.2171	32.7660	− 99.4495	31.1233	− 100.7177
33	35.2354	− 102.2200	32.7653	− 99.4466	31.1235	− 100.7141
34	35.2374	− 102.2224	32.7653	− 99.4410	31.1356	− 100.7369
35			32.7654	− 99.4379	31.1347	− 100.7340
36			32.7652	− 99.4266	31.1328	− 100.7315
37			32.7653	− 99.4235	31.1359	− 100.6885
38			32.7652	− 99.4197	31.1312	− 100.6810
39			32.7651	− 99.4167	31.1318	− 100.6786
40			32.7655	− 99.4137	31.1471	− 100.7127
41			32.7685	− 99.4102	31.1479	− 100.7097
42			32.7789	− 99.4537	31.1477	− 100.7073
43			32.7786	− 99.4501	31.1470	− 100.7042
44			32.7900	− 99.4625	31.1406	− 100.7047
45			32.7888	− 99.4592	31.1414	− 100.7023
46			32.7898	− 99.4567	31.1458	− 100.6982
47			32.7903	− 99.4538	31.1452	− 100.6949
48			32.7891	− 99.4507	31.1088	− 100.6612
49			32.7886	− 99.4476	31.1078	− 100.6579
50			32.7875	− 99.4444	31.1100	− 100.6541
51			32.7873	− 99.4414	31.1089	− 100.6513
52			32.7873	− 99.4385	31.1041	− 100.6460
53			32.7867	− 99.4355	31.1053	− 100.6433
54			32.7825	− 99.4307	31.1088	− 100.6301
55			32.7778	− 99.4255	31.1083	− 100.6264
56			32.7789	− 99.4073	31.1100	− 100.6236
57			32.7789	− 99.4043	31.1110	− 100.6198
58			32.8056	− 99.4684	31.1024	− 100.6143
59			32.8065	− 99.4656	31.1015	− 100.6114
60			32.8069	− 99.4626	31.1001	− 100.6090
61			32.8060	− 99.4597	31.0999	− 100.6066
62			32.8034	− 99.4567	31.1323	− 100.6519
63			32.8023	− 99.4538	31.1330	− 100.6492
64			32.8015	− 99.4475	31.1322	− 100.6463
65			32.8012	− 99.4447	31.1310	− 100.6434
66			32.8007	− 99.4409	31.1306	− 100.6407
67			32.8011	− 99.4364	31.1295	− 100.6373
68			32.8012	− 99.4324	31.1264	− 100.6334
69			32.7997	− 99.4292	31.1252	− 100.6309
70			32.7986	− 99.4265	31.1198	− 100.6265
71			32.7968	− 99.4238	31.1225	− 100.6194
72			32.7905	− 99.4204	31.1196	− 100.6152
73					31.1514	− 100.6559
74					31.1504	− 100.6532
75					31.1490	− 100.6496
76					31.1510	− 100.6464
77					31.1532	− 100.6433
78					31.1560	− 100.6404
79					31.1543	− 100.6367
80					31.1538	− 100.6317
81					31.1530	− 100.6285
82					31.1640	− 100.6378
83					31.1643	− 100.6353
84					31.1660	− 100.6325
85					31.1656	− 100.6299
86					31.1660	− 100.6274
87					31.1655	− 100.6248
88					31.1652	− 100.6222
89					31.1613	− 100.6194
90					31.1620	− 100.6156
91					31.1653	− 100.6114
92					31.1589	− 100.6122
93					31.1589	− 100.6083
94					31.1617	− 100.6012
95					31.1664	− 100.5965
96					31.1519	− 100.6105
97					31.1568	− 100.6036
98					31.1661	− 100.5925
99					31.1628	− 100.5890
100					31.1539	− 100.5877