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
INSTITUTEOF THEORETICAL INFORMATICS · ALGORITHMICS GROUP Denmark
Flensburg Baltic Sea Reußenkoge¨
Fehmarn
Kiel Rostock North Sea Brunsbuttel¨ Brockdorf Grapzow
Ostermarsch Holtriem-Dornum Butzfleth¨ Wedel Wilhelmshaven Hamburg Wybelsumer Polder Geesthacht/Elbe
Huntorf Putlitz Uckermark Schwedt Bremen TenneT 50Hertz
Arneburg Neuhardenberg Berlin Poland Emsland Hannover The Netherlands Heyden Wolfsburg Kirchmoser¨ Ibbenburen¨ Braunschweig Thyrow Eisenhuttenstadt¨ Kirschlengern Korbelitz¨ Buschhaus Druxberge Salzgitter-Hallendorf Munster/Hafen¨ Grohnde Sulzetal¨ Marl Dahme Janschwalde¨ Lunen¨ Straßfurt Gelsenkirchen-Scholven Gersteinwerk Bernburg Schonewalde¨ Westfalen Voerde Hamm-Uentrop Bergkamen Bitterfeld Rheinberg Sintfeld Senftenberg Herne Schwarzheide Herdecke Schkopau Boxberg Hagen-Kabel Esperstedt-Obhausen Huckingen Leipzig Großkayna KIT – The Research University in the Helmholtz Association www.kit.edu
France BelgiumBelgium Czech Republic Motivation
H2-20 Horns Rev Horns Rev B HR6 B HR5 Horns Rev Reserved Area Karlsgarde˚
Horns Rev III
Horns Rev Varde B HR7
Horns Rev II Endrup
Doggerbank Horns Rev Esbjerg
Fanø
Nord-Ost Passat III Enova Ribe Nord-Ost Offshore Concordia I Passat I NSWP 9 DanTysk DK Nord-Ost Enova Offshore Mandø Passat II Concordia II HTOD 1 NSWP 11 Sandbank 24 Enova Offshore Enova Offshore extension NSWP 8 Sandbank 24 NSWP 13 Sandbank 24 HTOD 2 Enova Offshore Norderland extension Nordpassage NSWP 10 Enova Offshore HTOD 3 NSWP 15 HTOD 4 Enova Offshore DanTysk Rømø HTOD 6 NSWP 12 Nemo Schifffahrtsroute 4 Enova Offshore Witte Norderland NSWP 14 Bank Nordlicher¨ SylWin alpha HTOD 5 Grund Vorbehaltsgebiet Gaia V SylWin beta Nautilus I Butendiek Jules Verne Weiße Gaia I S y l t e r A u ß e n r i f Bank W e i ß e B a n k Uthland Tondern Sylt Sylt Horizont I Horizont IV Neptune III Horizont II ? Gaia II Weiße Schifffahrtsroute 6 SylWin 1,2 Neptune II Schifffahrtsroute 5 Bank Horizont III Nieb ¨ull Gaia III Neptune I ProWind 3 Gaia IV fur¨ ProWind 2 Schifffahrtsroute 4 Aiolos ProWind 1 Schifffahrtsroute 10 Apollon 160 km Seewind IV Fohr¨ Stribog II Euklas Diamant Amrum Seewind III Kaikas SeaStorm I Stribog I Hooge Albatros FiT PNE SeaStorm II Global Sudlich¨ Amrumbank Amrumbank West Atlantis III Tech 1 SeaWind 1 Rohrleitungen Albatros Husum PNE Kaskasi II BorWin beta Pellworm Atlantis II EnBW Skua Schifffahrtsroute 4 HelWin alpha Austern- Hohe See Meerwind BARD Nordsee Ost grund West 85 km Offshore 1 BorWin BorWin epsilon Kaskasi BorWin beta EnBW gamma Gannet Heron Seagull Meerwind Schifffahrtsroute 6 He dreiht Petrel S ¨ud/Ost Cornelia BorWin alpha EnBW Deutsche He dreiht II Bucht Veja AreaC I Mate BorWin delta Global Tech 2 AreaC II AreaC III Aquamarin Bight Power II Bight Power I 141 km 130 km 125 km 125 km Vorranggebiet BorWin 1,2 Heide Schifffahrtsroute 12 German Bight Western Approach Jade Approach Helgoland SylWin 1,2 B ¨uttel East Friesland HelWin 1,2 BorWin 3,4 Merkur Borkum (ehem. Delta Innogy Gode Tief- Helgolander¨ Buiten- Trianel Osters Bank 2 Riffgrund West II MEG Off- Nordsee 2 Nordsee Wind II Gode gaats wasser- Bucht Zee- Clear- Borkum Windpark shore I) Delta 3 Gode Wind IV Osters Bank 3 Gode RuyterEnergie camp OWP Riffgrund West Nordsee 1 Innogy Wind I reede Osters Bank 4 Ruyter West Oost West alpha ventus Nordsee 2 Wind III DolWin alpha 75 km DolWin gamma Borkum- DolWin delta 45 km DolWin beta Riffgrund II Innogy Borkum-Riffgrund I 60 km Borkum-Riffgrund II Nordsee 1 Neuwerk Brundb ¨uttel Cuxhaven Vorranggebiet 3 DolWin 3 BorWin 3,4 Terschelling - German Bight fur¨ Schifffahrt Nordergr ¨unde BorWin 1,2 Wangerooge Spiekeroog DolWin 1,2 Riffgrond Langeoog 83 km Baltrum Mellum Oost Norderney Friesland Riffgat Juist
50 km Hagermarsch Diele Memmert Dorpen¨ West Esens Inhausen
Ameland Borkum Norden Potentiele Zoekgebieden Jever Bremerhaven Schiermonnikoog Wilhelmshaven Aurich Jade- Ameland Emden/Borssum busen Terschelling Eemshaven Norden Dorpen¨ West Varel Emden https://upload.wikimedia.org/wikipedia/commons/a/a1/MapDokkum of the offshore wind power farms in the German Bight.png Vlieland Dollard Groningen Leer 1 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Motivation
H2-20 Horns Rev Horns Rev B HR6 B HR5 Horns Rev Reserved Area Karlsgarde˚
Horns Rev III
Horns Rev Varde B HR7
Horns Rev II Endrup
Doggerbank Horns Rev Esbjerg
Fanø
Nord-Ost Passat III Enova Ribe Nord-Ost Offshore Concordia I Passat I NSWP 9 DanTysk DK Nord-Ost Enova Offshore Mandø Passat II Concordia II HTOD 1 NSWP 11 Sandbank 24 Enova Offshore Enova Offshore extension NSWP 8 Sandbank 24 NSWP 13 Sandbank 24 HTOD 2 Enova Offshore Norderland extension Nordpassage NSWP 10 Enova Offshore HTOD 3 NSWP 15 HTOD 4 Enova Offshore DanTysk Rømø HTOD 6 NSWP 12 Nemo Schifffahrtsroute 4 Enova Offshore Witte Norderland NSWP 14 Bank Nordlicher¨ SylWin alpha HTOD 5 Grund Vorbehaltsgebiet Gaia V SylWin beta Nautilus I Butendiek Jules Verne Weiße Gaia I S y l t e r A u ß e n r i f Bank W e i ß e B a n k Uthland Tondern Sylt Sylt Horizont I Horizont IV Neptune III Horizont II ? Gaia II Weiße Schifffahrtsroute 6 SylWin 1,2 Neptune II Schifffahrtsroute 5 Bank Horizont III Nieb ¨ull Gaia III Neptune I ProWind 3 Gaia IV fur¨ ProWind 2 Schifffahrtsroute 4 Aiolos ProWind 1 Schifffahrtsroute 10 Apollon 160 km Seewind IV Fohr¨ Stribog II Euklas Diamant Amrum Seewind III Kaikas SeaStorm I Stribog I Hooge Albatros FiT PNE SeaStorm II Global Sudlich¨ Amrumbank Amrumbank West Atlantis III Tech 1 SeaWind 1 Rohrleitungen Albatros Husum PNE Kaskasi II BorWin beta Pellworm Atlantis II EnBW Skua Schifffahrtsroute 4 HelWin alpha Austern- Hohe See Merkur Meerwind BARD Nordsee Ost grund West 85 km Offshore 1 BorWin BorWin epsilon Kaskasi BorWin beta EnBW gammaTrianel Gannet Heron Seagull(ehem. Meerwind Schifffahrtsroute 6 He dreiht Petrel S ¨ud/Ost Cornelia BorWin alpha EnBW Deutsche He dreiht II Bucht Veja WindparkAreaC I MEG Off- Mate BorWin delta Global Tech 2 AreaC II AreaC III Aquamarin Bight Power II Bight Power I shore I) 141 km 130 km 125 km 125 km Vorranggebiet BorWin 1,2 Heide Schifffahrtsroute 12 German Bight Western Approach Jade Approach Helgoland SylWin 1,2 B ¨uttel East Friesland HelWin 1,2 BorWin 3,4 Merkur Borkum (ehem. Delta Innogy Gode Tief- Helgolander¨ Buiten- Trianel Osters Bank 2 Riffgrund West II MEG Off- Nordsee 2 Nordsee Wind II Gode gaats wasser- Bucht Zee- Clear- Borkum Windpark shore I) Delta 3 Gode alphaWind IV Ventus Osters Bank 3 Gode RuyterEnergie camp OWP Riffgrund West Nordsee 1 Innogy Wind I reede Osters Bank 4 Ruyter West Oost West alpha ventus Nordsee 2 Wind III DolWin alpha 75 km DolWin gamma Borkum- DolWin delta 45 km DolWin beta Riffgrund II Innogy Borkum-Riffgrund I 60 km Borkum-Riffgrund II Nordsee 1 Riffgrund II Borkum- Neuwerk Brundb ¨uttel Cuxhaven Vorranggebiet 3 DolWin 3 BorWin 3,4 Terschelling - German Bight fur¨ Schifffahrt Nordergr ¨unde BorWin 1,2 Wangerooge Spiekeroog DolWin 1,2 Riffgrond Langeoog 83 km Baltrum Mellum Oost Borkum-RiffgrundNorderney I Friesland Riffgat Juist
50 km Hagermarsch Diele Borkum-RiffgrundMemmert II Dorpen¨ West Esens Inhausen
Ameland Borkum Norden Potentiele Zoekgebieden Jever Bremerhaven Schiermonnikoog Wilhelmshaven Aurich Jade- Ameland Emden/Borssum busen Terschelling Eemshaven Norden Dorpen¨ West Varel Emden https://upload.wikimedia.org/wikipedia/commons/a/a1/MapDokkum of the offshore wind power farms in the German Bight.png Vlieland Dollard Groningen Leer 1 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
PCC (110 kV)
Grid Point
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
PCC (110 kV)
Grid Point
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
Wind Turbine (33 kV)
PCC (110 kV)
Grid Point
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
Wind Turbine (33 kV)
PCC (110 kV) Substation
Grid Point
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
Wind Turbine (33 kV)
PCC (110 kV) Substation
Grid Point
Transport Cable
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
Wind Turbine (33 kV)
PCC (110 kV) Substation
Grid Point Transmission Cables
Transport Cable
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
Circuit
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling
Circuit
Collector System
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling Full Farm
Circuit
Collector System
2 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Wind Farm Cabling Full Farm
Circuit ≤ 2 Wind Turbines; $ 100 ≤ 6 Wind Turbines; $ 140 Collector System ≤ 9 Wind Turbines; $ 162
Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling 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)
Full Farm
Circuit
Collector System
3 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling 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)
Full Farm
Circuit
Collector System
3 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling 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)
Full Farm
≤ 2 Wind Turbines; $ 100 Circuit ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162 Collector System
3 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling 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)
find for each edge: the cable type Full Farm
≤ 2 Wind Turbines; $ 100 Circuit ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162 Collector System
3 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling 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)
find for each edge: the cable type Full Farm
minimizing total cable cost
≤ 2 Wind Turbines; $ 100 Circuit ≤ 6 Wind Turbines; $ 140 ≤ 9 Wind Turbines; $ 162 Collector System
3 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling 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)
find for each edge: the cable type Full Farm
minimizing total cable cost
subject to cable capacity constraints ≤ 2 Wind Turbines; $ 100 Circuit ≤ 6 Wind Turbines; $ 140 substation capacity constraints ≤ 9 Wind Turbines; $ 162 Collector System flow conservation constraints
3 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling 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)
find for each edge: the cable type Full Farm
minimizing total cable cost
subject to cable capacity constraints ≤ 2 Wind Turbines; $ 100 Circuit ≤ 6 Wind Turbines; $ 140 substation capacity constraints ≤ 9 Wind Turbines; $ 162 Collector System flow conservation constraints
Wind farm planning problem ⇔ Minimum cost flow problem using [Leibfried et al., 2015] P P P OPT(NFFP) ≤ OPT(NSP(j)) ≤ OPT(NCP(j, i)) j∈VS j∈VS i∈N
3 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Simulated Annealing
Metropolis Algorithm Cooling Schedule
4 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Simulated Annealing
Metropolis Algorithm Cooling Schedule
many local optima
4 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Simulated Annealing
Metropolis Algorithm Cooling Schedule
local search
many local optima
4 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Simulated Annealing
Metropolis Algorithm Cooling Schedule escape local optimum
?
many local optima
4 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Simulated Annealing
Metropolis Algorithm Cooling Schedule
multiple mutations
many local optima
4 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Simulated Annealing
Metropolis Algorithm Cooling Schedule
0.01 standard, τ = 4 · 10−7 multiple mutations 0.008 dynamic, τ = 4 · 10−5 activity µ 0.006
0.004
Temperature 0.002
0 many local optima 0 5 10 15 20 25 30 Time in min
4 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Simulated Annealing
Metropolis Algorithm Cooling Schedule
0.01 standard, τ = 4 · 10−7 multiple mutations 0.008 dynamic, τ = 4 · 10−5 activity µ 0.006
0.004
Temperature 0.002
0 many local optima 0 5 10 15 20 25 30 Time in min
Diversification Diversification Intensification
4 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Benchmark Sets
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5 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Benchmark Sets
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5 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Benchmark Sets
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5 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Benchmark Sets
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21 Substation Turbine 21 Cable type 1 21 Cable type 2 Cable type 3
5 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Benchmark Sets
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21 Substation Turbine 21 Cable type 1 21 Cable type 2 Cable type 3
5 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Benchmark Sets
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21 Substation Turbine 21 Cable type 1 21 Cable type 2 Cable type 3
5 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Multiple Instances of Simulated Annealing
0.8 1 Instance worse 2 Instances than Gurobi 0.4 4 Instances
0
−0.4 better than Gurobi −0.8
100 200 300 400 500 Number of Turbines
6 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Multiple Instances of Simulated Annealing
0.8 1 Instance worse 2 Instances than Gurobi 0.4 4 Instances
0
−0.4 better than Gurobi −0.8
100 200 300 400 500 Number of Turbines Results depend on a random seed. Multiple instances reduce the overall computation time. This causes a reduced time spend for the intensification phase.
6 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Performance Influence of the Thermal Conductivity and Capacity τ
6 τ = 1 · 10−5 5 τ = 2 · 10−5 4 τ = 4 · 10−5 −5 3 τ = 8 · 10 worse τ = 16 · 10−5 than Gurobi 2 1 0 −1 better 200 300 400 500 than Gurobi Number of Turbines
7 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Performance Influence of the Thermal Conductivity and Capacity τ
6 τ = 1 · 10−5 5 τ = 2 · 10−5 4 τ = 4 · 10−5 −5 3 τ = 8 · 10 worse τ = 16 · 10−5 than Gurobi 2 1 0 −1 better 200 300 400 500 than Gurobi Number of Turbines
Parameter tuning is difficult for the cooling schedule.
7 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Cooling Schedule Performance
worse 0.4 than Gurobi Standard Cooling Schedule 0.2 Dynamic Cooling Schedule 0
−0.2 better than Gurobi −0.4
−0.6
−0.8 100 200 300 400 Number of Turbines
8 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Cooling Schedule Performance
worse 0.4 than Gurobi Standard Cooling Schedule 0.2 Dynamic Cooling Schedule 0
−0.2 better than Gurobi −0.4
−0.6
−0.8 100 200 300 400 Number of Turbines
The dynamic outperorms the standard one without parameter tuning. Parameter tuning improve the standard one for larger instances.
8 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Performance Influence of the Substation Capacity Tightness 2
1.5 worse 1 than Gurobi 0.5 0 −0.5
better −1 than Gurobi −1.5 0.85 0.9 0.95 1 Substation Capacity Tightness
9 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Performance Influence of the Substation Capacity Tightness 2
1.5 worse 1 than Gurobi 0.5 0 −0.5
better −1 than Gurobi −1.5 0.85 0.9 0.95 1 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 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Circuit Problem Substation Problem Full Farm Problem
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Full Farm
Circuit
Collector System
Circuit Problem Substation Problem Full Farm Problem
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Full Farm
Circuit
Collector System
P (MST) Circuit Problem NP-hard (CMST) Substation Problem NP-hard (Heuristics) Full Farm Problem
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Full Farm Full Farm
Circuit Circuit
Collector System Collector System
P (MST) Circuit Problem NP-hard (CMST) Substation Problem NP-hard (Heuristics) Full Farm Problem
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Full Farm Full Farm
Circuit Circuit
Collector System Collector System
P (MST) Circuit Problem NP-hard NP-hard (CMST) Substation Problem NP-hard NP-hard (Heuristics) Full Farm Problem NP-hard
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Full Farm Full Farm
Circuit Circuit
Collector System Collector System
P (MST) Circuit Problem NP-hard (Clustering) NP-hard (CMST) Substation Problem NP-hard NP-hard (Heuristics) Full Farm Problem NP-hard
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Full Farm Full Farm
Circuit Circuit
Collector System Collector System
P (MST) Circuit Problem NP-hard (Clustering) NP-hard (CMST) Substation Problem NP-hard } Simulated NP-hard (Heuristics) Full Farm Problem NP-hard Annealing
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Full Farm Full Farm
Circuit Circuit
Collector System Collector System
P (MST) Circuit Problem NP-hard (Clustering) NP-hard (CMST) Substation Problem NP-hard } Simulated NP-hard (Heuristics) Full Farm Problem NP-hard Annealing
RESULTS 0.4 2 6 -5 Standard Cooling Schedule 0.8 1 Instance τ= 1·10 1.5 0.2 Dynamic Cooling Schedule 2 Instances 5 -5 τ= 2·10-5 0 0.4 4 Instances 4 τ= 4·10 1 3 -5 0.5 -0.2 0 τ= 8·10-5 2 τ=16·10 0 -0.4 -0.4 1 -0.5 -0.6 0 -1 -0.8 -1 -0.8 -1.5 100 200 300 400 100 200 300 400 500 200 300 400 500 0.85 0.9 0.95 1 Number of Turbines Number of Turbines Number of Turbines Substation Capacity Tightness
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Conclusion & Future Work
Full Farm Full Farm
Circuit Circuit
Collector System Collector System
P (MST) Circuit Problem NP-hard (Clustering) NP-hard (CMST) Substation Problem NP-hard } Simulated NP-hard (Heuristics) Full Farm Problem NP-hard Annealing
RESULTS&FUTURE WORK 0.4 2 6 -5 Standard Cooling Schedule 0.8 1 Instance τ= 1·10 1.5 0.2 Dynamic Cooling Schedule 2 Instances 5 -5 τ= 2·10-5 0 0.4 4 Instances 4 τ= 4·10 1 3 -5 0.5 -0.2 0 τ= 8·10-5 2 τ=16·10 0 -0.4 -0.4 1 -0.5 -0.6 0 -1 -0.8 -1 -0.8 -1.5 100 200 300 400 100 200 300 400 500 200 300 400 500 0.85 0.9 0.95 1 Number of Turbines Number of Turbines Number of Turbines Substation Capacity Tightness
10 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group Are you a metal fan, too?
https://s-media-cache-ak0.pinimg.com/originals/8f/51/d3/8f51d30e4e60a97fc5b2fada2ecacd85.jpg
11 Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing- Institute of Theoretical Informatics Based Approach for Wind Farm Cabling Algorithmics Group