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A Simulated-Annealing-Based Approach for Wind Farm Cabling ACM e-Energy 2017 May 19, 2017 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner I NSTITUTE OF T HEORETICAL I NFORMATICS A LGORITHMICS G ROUP Denmark Baltic Sea

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SLIDE 1

The Netherlands Belgium

Baltic Sea North Sea

M¨ unster/Hafen Voerde Herdecke Huckingen Sintfeld

Denmark TenneT 50Hertz

Flensburg Arneburg Putlitz Grapzow B¨ utzfleth Wedel Reußenk¨

  • ge

Fehmarn Thyrow Dahme Bitterfeld Senftenberg Sch¨

  • newalde

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  • ser

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  • rbelitz

Druxberge S¨ ulzetal Hannover Heyden Hamburg Huntorf Bremen Marl Westfalen Bergkamen Gersteinwerk Hamm-Uentrop L¨ unen Herne

Poland

Rostock Kiel Emsland Ibbenb¨ uren Schwedt Uckermark Neuhardenberg Eisenh¨ uttenstadt J¨ anschwalde Boxberg Schwarzheide Leipzig Esperstedt-Obhausen Schkopau Hagen-Kabel Gelsenkirchen-Scholven Rheinberg Wilhelmshaven Ostermarsch Wybelsumer Polder Holtriem-Dornum

A Simulated-Annealing-Based Approach

ACM e-Energy 2017 · May 19, 2017 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner

for Wind Farm Cabling

INSTITUTE OF THEORETICAL INFORMATICS · ALGORITHMICS GROUP

Czech Republic Belgium France

KIT – The Research University in the Helmholtz Association

www.kit.edu

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SLIDE 2

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Motivation

Stribog II Stribog I Osters Bank 4 Osters Bank 3 Osters Bank 2 Ruyter West Cornelia Uthland Riffgrond Horns Rev Reserved Area Weiße Bank Horns Rev B HR7 Horns Rev B HR6 Horns Rev B HR5 Ruyter Oost Clear- camp Oost Friesland Ameland Potentiele Zoekgebieden PNE Atlantis III PNE Atlantis II Austern- grund Witte Bank Meerwind West Euklas Diamant Jules Verne Nautilus I HTOD 5 HTOD 4 HTOD 3 HTOD 2 HTOD 1 Concordia I Concordia II Gaia I Gaia II Gaia III Gaia IV Aiolos Apollon Horizont I Horizont II Horizont III SeaStorm II Seewind III Seewind IV AreaC III AreaC II AreaC I Skua Bight Power I Bight Power II Global Tech 2 Kaskasi Kaskasi II Nordpassage H2-20 Gode Wind III Borkum Riffgrund West II EnBW He dreiht II Sandbank 24 extension Sandbank 24 extension ? ProWind 3 ProWind 2 ProWind 1 Neptune I Neptune II Neptune III HTOD 6 Nemo Enova Offshore NSWP 8 Enova Offshore NSWP 10 Enova Offshore NSWP 12 Enova Offshore NSWP 14 Enova Offshore NSWP 15 Enova Offshore NSWP 13 Enova Offshore NSWP 11 Gaia V Norderland Norderland DanTysk DK Petrel Seagull Heron Gannet SeaStorm I Nord-Ost Passat I Nord-Ost Passat II Nord-Ost Passat III Aquamarin Enova Offshore NSWP 9 Zee- Energie Buiten- gaats Gode Wind II Gode Wind I Sandbank 24 Borkum Riffgrund West OWP West Borkum- Riffgrund II Borkum-Riffgrund II Merkur (ehem. MEG Off- shore I) Innogy Nordsee 3 Innogy Nordsee 2 Innogy Nordsee 1 Delta Nordsee 1 Delta Nordsee 2 Gode Wind IV Deutsche Bucht Veja Mate EnBW He dreiht EnBW Hohe See Albatros Albatros FiT SeaWind 1 Kaikas Horizont IV N¨
  • rdlicher
Grund Horns Rev III Riffgat Borkum-Riffgrund I Trianel Windpark Trianel Windpark alpha ventus BARD Offshore 1 Global Tech 1 Nordsee Ost Meerwind S¨ ud/Ost Amrumbank West Butendiek DanTysk Horns Rev II Horns Rev

Schifffahrtsroute 10 S c h i f f f a h r t s r

  • u

t e 4 S c h i f f f a h r t s r

  • u

t e 4 S c h i f f f a h r t s r

  • u

t e 4 Schifffahrtsroute 6 Schifffahrtsroute 6 Schifffahrtsroute 5 G e r m a n B i g h t W e s t e r n A p p r

  • a

c h East Friesland Terschelling - German Bight Jade Approach Weiße Bank Helgol¨ ander Bucht

Vorranggebiet 3 f¨ ur Schifffahrt Vorranggebiet Schifffahrtsroute 12 Tief- wasser- reede

Doggerbank

S¨ udlich Amrumbank Dollard Jade- busen S y l t e r A u ß e n r i f W e i ß e B a n k SylWin alpha SylWin beta DolWin delta DolWin beta DolWin alpha DolWin gamma BorWin alpha BorWin beta BorWin delta BorWin epsilon BorWin gamma HelWin alpha BorWin beta

Vorbehaltsgebiet f¨ ur Rohrleitungen BorWin 3,4 DolWin 3 B
  • r
W i n 1 , 2 D
  • l
W i n 1 , 2 BorWin 1,2 BorWin 3,4 SylWin 1,2 HelWin 1,2 SylWin 1,2 85 km 1 6 k m 60 km 45 km 75 km 8 3 k m 50 km 141 km 130 km 125 km 125 km

Emden Wilhelmshaven Bremerhaven Cuxhaven

Leer Norden Norden Aurich Esens Jever Varel Groningen Dokkum Brundb¨ uttel Heide Husum Nieb¨ ull Tondern Ribe Varde

Esbjerg

Endrup Karlsg˚ arde

B¨ uttel Diele D¨

  • rpen West
Hagermarsch Emden/Borssum

D¨

  • rpen West
Eemshaven

Ameland Schiermonnikoog Terschelling Vlieland Borkum Memmert Juist Norderney Baltrum Langeoog Spiekeroog Wangerooge Mellum Neuwerk Helgoland Pellworm Hooge Amrum F¨

  • hr

Sylt Sylt Rømø Mandø Fanø

Inhausen Nordergr¨ unde

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

https://upload.wikimedia.org/wikipedia/commons/a/a1/Map of the offshore wind power farms in the German Bight.png

1

slide-3
SLIDE 3

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Motivation

Stribog II Stribog I Osters Bank 4 Osters Bank 3 Osters Bank 2 Ruyter West Cornelia Uthland Riffgrond Horns Rev Reserved Area Weiße Bank Horns Rev B HR7 Horns Rev B HR6 Horns Rev B HR5 Ruyter Oost Clear- camp Oost Friesland Ameland Potentiele Zoekgebieden PNE Atlantis III PNE Atlantis II Austern- grund Witte Bank Meerwind West Euklas Diamant Jules Verne Nautilus I HTOD 5 HTOD 4 HTOD 3 HTOD 2 HTOD 1 Concordia I Concordia II Gaia I Gaia II Gaia III Gaia IV Aiolos Apollon Horizont I Horizont II Horizont III SeaStorm II Seewind III Seewind IV AreaC III AreaC II AreaC I Skua Bight Power I Bight Power II Global Tech 2 Kaskasi Kaskasi II Nordpassage H2-20 Gode Wind III Borkum Riffgrund West II EnBW He dreiht II Sandbank 24 extension Sandbank 24 extension ? ProWind 3 ProWind 2 ProWind 1 Neptune I Neptune II Neptune III HTOD 6 Nemo Enova Offshore NSWP 8 Enova Offshore NSWP 10 Enova Offshore NSWP 12 Enova Offshore NSWP 14 Enova Offshore NSWP 15 Enova Offshore NSWP 13 Enova Offshore NSWP 11 Gaia V Norderland Norderland DanTysk DK Petrel Seagull Heron Gannet SeaStorm I Nord-Ost Passat I Nord-Ost Passat II Nord-Ost Passat III Aquamarin Enova Offshore NSWP 9 Zee- Energie Buiten- gaats Gode Wind II Gode Wind I Sandbank 24 Borkum Riffgrund West OWP West Borkum- Riffgrund II Borkum-Riffgrund II Merkur (ehem. MEG Off- shore I) Innogy Nordsee 3 Innogy Nordsee 2 Innogy Nordsee 1 Delta Nordsee 1 Delta Nordsee 2 Gode Wind IV Deutsche Bucht Veja Mate EnBW He dreiht EnBW Hohe See Albatros Albatros FiT SeaWind 1 Kaikas Horizont IV N¨
  • rdlicher
Grund Horns Rev III Riffgat Borkum-Riffgrund I Trianel Windpark Trianel Windpark alpha ventus BARD Offshore 1 Global Tech 1 Nordsee Ost Meerwind S¨ ud/Ost Amrumbank West Butendiek DanTysk Horns Rev II Horns Rev

Schifffahrtsroute 10 S c h i f f f a h r t s r

  • u

t e 4 S c h i f f f a h r t s r

  • u

t e 4 S c h i f f f a h r t s r

  • u

t e 4 Schifffahrtsroute 6 Schifffahrtsroute 6 Schifffahrtsroute 5 G e r m a n B i g h t W e s t e r n A p p r

  • a

c h East Friesland Terschelling - German Bight Jade Approach Weiße Bank Helgol¨ ander Bucht

Vorranggebiet 3 f¨ ur Schifffahrt Vorranggebiet Schifffahrtsroute 12 Tief- wasser- reede

Doggerbank

S¨ udlich Amrumbank Dollard Jade- busen S y l t e r A u ß e n r i f W e i ß e B a n k SylWin alpha SylWin beta DolWin delta DolWin beta DolWin alpha DolWin gamma BorWin alpha BorWin beta BorWin delta BorWin epsilon BorWin gamma HelWin alpha BorWin beta

Vorbehaltsgebiet f¨ ur Rohrleitungen BorWin 3,4 DolWin 3 B
  • r
W i n 1 , 2 D
  • l
W i n 1 , 2 BorWin 1,2 BorWin 3,4 SylWin 1,2 HelWin 1,2 SylWin 1,2 85 km 1 6 k m 60 km 45 km 75 km 8 3 k m 50 km 141 km 130 km 125 km 125 km

Emden Wilhelmshaven Bremerhaven Cuxhaven

Leer Norden Norden Aurich Esens Jever Varel Groningen Dokkum Brundb¨ uttel Heide Husum Nieb¨ ull Tondern Ribe Varde

Esbjerg

Endrup Karlsg˚ arde

B¨ uttel Diele D¨

  • rpen West
Hagermarsch Emden/Borssum

D¨

  • rpen West
Eemshaven

Ameland Schiermonnikoog Terschelling Vlieland Borkum Memmert Juist Norderney Baltrum Langeoog Spiekeroog Wangerooge Mellum Neuwerk Helgoland Pellworm Hooge Amrum F¨

  • hr

Sylt Sylt Rømø Mandø Fanø

Inhausen Nordergr¨ unde

Trianel Windpark Borkum-Riffgrund II

Borkum-

Merkur (ehem. MEG Off- shore I) alpha Ventus Borkum-Riffgrund I Riffgrund II

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

https://upload.wikimedia.org/wikipedia/commons/a/a1/Map of the offshore wind power farms in the German Bight.png

1

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SLIDE 4

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling

2

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SLIDE 5

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling PCC (110 kV) Grid Point

2

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SLIDE 6

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling PCC (110 kV) Grid Point

2

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SLIDE 7

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling PCC (110 kV) Grid Point Wind Turbine (33 kV)

2

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SLIDE 8

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling Substation PCC (110 kV) Grid Point Wind Turbine (33 kV)

2

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SLIDE 9

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling Substation PCC (110 kV) Grid Point Wind Turbine (33 kV) Transport Cable

2

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SLIDE 10

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling Substation PCC (110 kV) Grid Point Wind Turbine (33 kV) Transmission Cables Transport Cable

2

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SLIDE 11

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling Circuit

2

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SLIDE 12

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling Circuit Collector System

2

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SLIDE 13

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling Circuit Collector System Full Farm

2

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SLIDE 14

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cabling Circuit Collector System Full Farm

≤ 2 Wind Turbines; $ 100 ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162

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SLIDE 15

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given VS set of substations, VT set of turbines (each with capacity), for each edge: cable types (each with cost and capacity)

Circuit Collector System Full Farm 3

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SLIDE 16

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given VS set of substations, VT set of turbines (each with capacity), for each edge: cable types (each with cost and capacity)

Circuit Collector System Full Farm 3

slide-17
SLIDE 17

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given VS set of substations, VT set of turbines (each with capacity), for each edge: cable types (each with cost and capacity)

Circuit Collector System Full Farm

≤ 2 Wind Turbines; $ 100 ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162

3

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SLIDE 18

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given find VS set of substations, VT set of turbines (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type

Circuit Collector System Full Farm

≤ 2 Wind Turbines; $ 100 ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162

3

slide-19
SLIDE 19

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given find VS set of substations, VT set of turbines (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type total cable cost minimizing

Circuit Collector System Full Farm

≤ 2 Wind Turbines; $ 100 ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162

3

slide-20
SLIDE 20

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given find subject to VS set of substations, VT set of turbines (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type total cable cost minimizing substation capacity constraints flow conservation constraints cable capacity constraints

Circuit Collector System Full Farm

≤ 2 Wind Turbines; $ 100 ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162

3

slide-21
SLIDE 21

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given find subject to VS set of substations, VT set of turbines (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type total cable cost minimizing substation capacity constraints flow conservation constraints cable capacity constraints

Circuit Collector System Full Farm

≤ 2 Wind Turbines; $ 100 ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162

Wind farm planning problem ⇔ Minimum cost flow problem OPT(NFFP) ≤

j∈VS OPT(NSP(j)) ≤ j∈VS

  • i∈N OPT(NCP(j, i))

using [Leibfried et al., 2015]

3

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SLIDE 22

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing Metropolis Algorithm Cooling Schedule

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group 4

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SLIDE 23

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

many local optima

Metropolis Algorithm Cooling Schedule

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group 4

slide-24
SLIDE 24

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

many local optima local search

Metropolis Algorithm Cooling Schedule

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group 4

slide-25
SLIDE 25

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

many local optima escape local optimum ?

Metropolis Algorithm Cooling Schedule

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group 4

slide-26
SLIDE 26

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

many local optima multiple mutations

Metropolis Algorithm Cooling Schedule

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group 4

slide-27
SLIDE 27

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

many local optima multiple mutations

Metropolis Algorithm Cooling Schedule

0.004 0.002 0.006 0.008 0.01 Temperature 5 10 15 20 25 30

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

activity µ dynamic, τ = 4 · 10−5 standard, τ = 4 · 10−7 Time in min

4

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SLIDE 28

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

many local optima multiple mutations

Metropolis Algorithm Cooling Schedule

0.004 0.002 0.006 0.008 0.01 Temperature Diversification Intensification 5 10 15 20 25 30

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Diversification activity µ dynamic, τ = 4 · 10−5 standard, τ = 4 · 10−7 Time in min

4

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SLIDE 29

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Benchmark Sets

21 21 21 21 21

5

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SLIDE 30

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Benchmark Sets

21 21 21 21 21

5

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SLIDE 31

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Benchmark Sets

21 21 21 21 21

5

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SLIDE 32

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Benchmark Sets

Substation Turbine Cable type 1 Cable type 2 Cable type 3

21 21 21 21 21 21

5

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SLIDE 33

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Benchmark Sets

Substation Turbine Cable type 1 Cable type 2 Cable type 3

21 21 21 21 21 21

5

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SLIDE 34

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Benchmark Sets

Substation Turbine Cable type 1 Cable type 2 Cable type 3

21 21 21 21 21 21

5

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SLIDE 35

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Multiple Instances of Simulated Annealing

100 200 300 400 500 0.4

−0.4 −0.8

0.8 1 Instance 2 Instances 4 Instances Number of Turbines

better

than Gurobi

worse

than Gurobi

6

slide-36
SLIDE 36

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Multiple Instances of Simulated Annealing

100 200 300 400 500 0.4

−0.4 −0.8

0.8 1 Instance 2 Instances 4 Instances Number of Turbines

better

than Gurobi

worse

than Gurobi

Results depend on a random seed. Multiple instances reduce the overall computation time. This causes a reduced time spend for the intensification phase.

6

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SLIDE 37

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Performance Influence of the

200 300 400 500 1 2 3

−1

4 5 6

τ = 1 · 10−5 τ = 2 · 10−5 τ = 4 · 10−5 τ = 8 · 10−5 τ = 16 · 10−5

Number of Turbines

better

than Gurobi

worse

than Gurobi

Thermal Conductivity and Capacity τ

7

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SLIDE 38

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Performance Influence of the

200 300 400 500 1 2 3

−1

4 5 6

τ = 1 · 10−5 τ = 2 · 10−5 τ = 4 · 10−5 τ = 8 · 10−5 τ = 16 · 10−5

Number of Turbines

better

than Gurobi

worse

than Gurobi

Thermal Conductivity and Capacity τ

Parameter tuning is difficult for the cooling schedule.

7

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SLIDE 39

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Cooling Schedule Performance

0.2 0.4

−0.2 −0.4 −0.8

Standard Cooling Schedule Dynamic Cooling Schedule 100 200 300 400 Number of Turbines

−0.6

worse

than Gurobi

better

than Gurobi

8

slide-40
SLIDE 40

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Cooling Schedule Performance

0.2 0.4

−0.2 −0.4 −0.8

Standard Cooling Schedule Dynamic Cooling Schedule 100 200 300 400 Number of Turbines

−0.6

worse

than Gurobi

better

than Gurobi

The dynamic outperorms the standard one without parameter tuning. Parameter tuning improve the standard one for larger instances.

8

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SLIDE 41

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Performance Influence of the

0.85 0.9 0.95 1

−1.5 −1 −0.5

0.5 1 1.5 2 Substation Capacity Tightness

better

than Gurobi

worse

than Gurobi

Substation Capacity Tightness

9

slide-42
SLIDE 42

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Performance Influence of the

0.85 0.9 0.95 1

−1.5 −1 −0.5

0.5 1 1.5 2 Substation Capacity Tightness

better

than Gurobi

worse

than Gurobi

Substation Capacity Tightness

The tighter the substation capacity or the more substations the harder the instance is to solve. Thus, the solution quality reduces with same duration.

9

slide-43
SLIDE 43

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

Circuit Problem Substation Problem Full Farm Problem

10

slide-44
SLIDE 44

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

Circuit Collector System Full Farm

Circuit Problem Substation Problem Full Farm Problem

10

slide-45
SLIDE 45

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

Circuit Collector System Full Farm

P (MST) NP-hard (CMST) NP-hard (Heuristics) Circuit Problem Substation Problem Full Farm Problem

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SLIDE 46

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

Circuit Collector System Full Farm Circuit Collector System Full Farm

P (MST) NP-hard (CMST) NP-hard (Heuristics) Circuit Problem Substation Problem Full Farm Problem

10

slide-47
SLIDE 47

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

Circuit Collector System Full Farm Circuit Collector System Full Farm

NP-hard NP-hard NP-hard P (MST) NP-hard (CMST) NP-hard (Heuristics) Circuit Problem Substation Problem Full Farm Problem

10

slide-48
SLIDE 48

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

Circuit Collector System Full Farm Circuit Collector System Full Farm

(Clustering)

NP-hard NP-hard NP-hard P (MST) NP-hard (CMST) NP-hard (Heuristics) Circuit Problem Substation Problem Full Farm Problem

10

slide-49
SLIDE 49

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

}

Circuit Collector System Full Farm Circuit Collector System Full Farm

Simulated Annealing (Clustering)

NP-hard NP-hard NP-hard P (MST) NP-hard (CMST) NP-hard (Heuristics) Circuit Problem Substation Problem Full Farm Problem

10

slide-50
SLIDE 50

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

}

Circuit Collector System Full Farm Circuit Collector System Full Farm

Simulated Annealing (Clustering)

NP-hard NP-hard NP-hard P (MST) NP-hard (CMST) NP-hard (Heuristics) Circuit Problem Substation Problem Full Farm Problem

RESULTS

Number of Turbines

  • 0.2
  • 0.4
  • 0.8

Number of Turbines

  • 0.6

0.2 0.4 Standard Cooling Schedule Dynamic Cooling Schedule 100 200 300 400 100 200 300 400 500 1 Instance 2 Instances 4 Instances 0.4

  • 0.4
  • 0.8

0.8 200 300 400 500 1 2 3

  • 1

4 5

τ= 1·

10-5

τ= 1·

10-5

τ= 2·

10-5

τ= 4·

10-5

τ=16·

10-5 Number of Turbines 6

τ= 8·

10-5 0.85 0.9 0.95 1 0.5 1 1.5 2 Substation Capacity Tightness

  • 0.5
  • 1.5
  • 1

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slide-51
SLIDE 51

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Conclusion & Future Work

}

Circuit Collector System Full Farm Circuit Collector System Full Farm

Simulated Annealing (Clustering)

NP-hard NP-hard NP-hard P (MST) NP-hard (CMST) NP-hard (Heuristics) Circuit Problem Substation Problem Full Farm Problem

Number of Turbines

  • 0.2
  • 0.4
  • 0.8

Number of Turbines

  • 0.6

0.2 0.4 Standard Cooling Schedule Dynamic Cooling Schedule 100 200 300 400 100 200 300 400 500 1 Instance 2 Instances 4 Instances 0.4

  • 0.4
  • 0.8

0.8 200 300 400 500 1 2 3

  • 1

4 5

τ= 1·

10-5

τ= 1·

10-5

τ= 2·

10-5

τ= 4·

10-5

τ=16·

10-5 Number of Turbines 6

τ= 8·

10-5 0.85 0.9 0.95 1 0.5 1 1.5 2 Substation Capacity Tightness

  • 0.5
  • 1.5
  • 1

RESULTS&FUTURE WORK

10

slide-52
SLIDE 52

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Based Approach for Wind Farm Cabling Institute of Theoretical Informatics Algorithmics Group

Are you a metal fan, too?

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