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A Simulated-Annealing-Based Approach

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

for Wind Farm Cabling

INSTITUTE OF THEORETICAL INFORMATICS · ALGORITHMICS GROUP

Czech RepublicBelgiumFrance

KIT – The Research University in the Helmholtz Association www.kit.edu

Sebastian Lehmann, Ignaz Rutter, Dorothea Wagner and Franziska Wegner – A Simulated-Annealing-Based Approach for Wind Farm Cabling

Institute of Theoretical InformaticsAlgorithmics Group

Motivation

Stribog II

Stribog I

Osters Bank 4Osters Bank 3

Osters Bank 2

Ruyter West

Cornelia

Uthland

Riffgrond

Horns Rev Reserved Area

WeißeBank

Horns RevB HR7

Horns RevB HR6

Horns RevB HR5

RuyterOost

Clear-camp

OostFriesland

AmelandPotentiele Zoekgebieden

PNEAtlantis III

PNEAtlantis II

Austern-grund

WitteBank

MeerwindWest

Euklas Diamant

Jules Verne

Nautilus IHTOD 5

HTOD 4 HTOD 3

HTOD 2

HTOD 1

Concordia I

Concordia II

Gaia I

Gaia II

Gaia III

Gaia IV

AiolosApollon

Horizont IHorizont II

Horizont III

SeaStorm II

Seewind III

Seewind IV

AreaC IIIAreaC II

AreaC I

Skua

Bight Power I Bight Power II

Global Tech 2

Kaskasi

Kaskasi II

Nordpassage

H2-20

GodeWind III

BorkumRiffgrund West II

EnBWHe dreiht II

Sandbank 24extension


?

ProWind 3ProWind 2ProWind 1

Neptune I

Neptune II

Neptune III

HTOD 6 Nemo

Enova OffshoreNSWP 8







Gaia V

Norderland

Norderland

DanTysk DK

PetrelSeagullHeronGannet

SeaStorm I

Nord-OstPassat I

Nord-OstPassat II

Nord-OstPassat III

Aquamarin

EnovaOffshoreNSWP 9

Zee-Energie

Buiten-gaats

GodeWind II

GodeWind I

Sandbank 24

BorkumRiffgrund WestOWP

West

Borkum-Riffgrund II

Borkum-Riffgrund II

Merkur(ehem.

MEG Off-shore I)

InnogyNordsee

3Innogy

Nordsee 2

InnogyNordsee 1

DeltaNordsee 1

DeltaNordsee 2 Gode

Wind IV

DeutscheBucht Veja

Mate

EnBWHe dreiht

EnBWHohe See

Albatros

Albatros FiT

SeaWind 1

Kaikas

Horizont IV

NordlicherGrund

Horns Rev III

Riffgat

Borkum-Riffgrund I

TrianelWindpark

TrianelWindpark

alpha ventus

BARDOffshore 1

GlobalTech 1

Nordsee Ost

MeerwindSud/Ost

Amrumbank West

Butendiek

DanTysk

Horns Rev II

Horns Rev

Schif

ffahr

tsrou

te10

Schifffahrtsroute 4

Schifffahrtsroute 4

Schifffahrtsroute 4Schifffahrtsroute 6

Schifffahrtsroute 6

Sch

ifffa

hrts

rout

e5

German Bight Western ApproachEast Friesland

Terschelling - German Bight

JadeApproach

WeißeBank

HelgolanderBucht

Vorranggebiet 3fur Schifffahrt

VorranggebietSchifffahrtsroute 12

Tief-wasser-reede

Doggerbank

Sudlich 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 alphaSylWin beta

DolWin deltaDolWin beta

DolWin alphaDolWin gamma

BorWin alphaBorWin beta

BorWin delta

BorWin epsilonBorWingamma

HelWin alpha BorWin beta

Vorbehaltsgebiet

fur

Rohrleitungen

BorW

in3,4

DolW

in3 BorWin 1,2

DolWin 1,2

BorWin 1,2

Bor

Win

3,4

SylWin 1,2

HelWin 1,2

SylWin 1,2

85 km

160 km

60 km

45 km

75 km

83 km

50 km

141 km 130 km125 km 125 km

Emden

WilhelmshavenBremerhaven

Cuxhaven

Leer

Norden

Norden

Aurich

Esens

Jever

Varel

Groningen

Dokkum

Brundbuttel

Heide

Husum

Niebull

Tondern

Ribe

Varde

Esbjerg

Endrup

Karlsgarde

Buttel

DieleDorpen West

Hagermarsch

Emden/Borssum

Dorpen WestEemshaven

Ameland

Schiermonnikoog

Terschelling

Vlieland

Borkum

Memmert

Juist

NorderneyBaltrum

LangeoogSpiekeroog

Wangerooge

Mellum

Neuwerk

Helgoland

Pellworm

Hooge

Amrum

Fohr

Sylt Sylt

Rømø

Mandø

Fanø

Inhausen

Nordergrunde



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

1



Motivation

Stribog II

Stribog I

Osters Bank 4Osters Bank 3

Osters Bank 2

Ruyter West

Cornelia

Uthland

Riffgrond

Horns Rev Reserved Area

WeißeBank

Horns RevB HR7

Horns RevB HR6

Horns RevB HR5

RuyterOost

Clear-camp

OostFriesland

AmelandPotentiele Zoekgebieden

PNEAtlantis III

PNEAtlantis II

Austern-grund

WitteBank

MeerwindWest

Euklas Diamant

Jules Verne

Nautilus IHTOD 5

HTOD 4 HTOD 3

HTOD 2

HTOD 1

Concordia I

Concordia II

Gaia I

Gaia II

Gaia III

Gaia IV

AiolosApollon

Horizont IHorizont II

Horizont III

SeaStorm II

Seewind III

Seewind IV

AreaC IIIAreaC II

AreaC I

Skua

Bight Power I Bight Power II

Global Tech 2

Kaskasi

Kaskasi II

Nordpassage

H2-20

GodeWind III

BorkumRiffgrund West II

EnBWHe dreiht II



?

ProWind 3ProWind 2ProWind 1

Neptune I

Neptune II

Neptune III

HTOD 6 Nemo








Gaia V

Norderland

Norderland

DanTysk DK

PetrelSeagullHeronGannet

SeaStorm I

Nord-OstPassat I

Nord-OstPassat II

Nord-OstPassat III

Aquamarin

EnovaOffshoreNSWP 9

Zee-Energie

Buiten-gaats

GodeWind II

GodeWind I

Sandbank 24

BorkumRiffgrund WestOWP

West

Borkum-Riffgrund II

Borkum-Riffgrund II

Merkur(ehem.

MEG Off-shore I)

InnogyNordsee

3Innogy

Nordsee 2

InnogyNordsee 1

DeltaNordsee 1

DeltaNordsee 2 Gode

Wind IV

DeutscheBucht Veja

Mate

EnBWHe dreiht

EnBWHohe See

Albatros

Albatros FiT

SeaWind 1

Kaikas

Horizont IV

NordlicherGrund

Horns Rev III

Riffgat

Borkum-Riffgrund I

TrianelWindpark

TrianelWindpark

alpha ventus

BARDOffshore 1

GlobalTech 1

Nordsee Ost

MeerwindSud/Ost

Amrumbank West

Butendiek

DanTysk

Horns Rev II

Horns Rev

Schif

ffahr

tsrou

te10

Schifffahrtsroute 4

Schifffahrtsroute 4

Schifffahrtsroute 4Schifffahrtsroute 6

Schifffahrtsroute 6

Sch

ifffa

hrts

rout

e5

German Bight Western ApproachEast Friesland

Terschelling - German Bight

JadeApproach

WeißeBank

HelgolanderBucht

Vorranggebiet 3fur Schifffahrt

VorranggebietSchifffahrtsroute 12

Tief-wasser-reede

Doggerbank

Sudlich 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 alphaSylWin beta

DolWin deltaDolWin beta

DolWin alphaDolWin gamma

BorWin alphaBorWin beta

BorWin delta

BorWin epsilonBorWingamma

HelWin alpha BorWin beta

Vorbehaltsgebiet

fur

Rohrleitungen

BorW

in3,4

DolW

in3 BorWin 1,2

DolWin 1,2

BorWin 1,2

Bor

Win

3,4

SylWin 1,2

HelWin 1,2

SylWin 1,2

85 km

160 km

60 km

45 km

75 km

83 km

50 km

141 km 130 km125 km 125 km

Emden

WilhelmshavenBremerhaven

Cuxhaven

Leer

Norden

Norden

Aurich

Esens

Jever

Varel

Groningen

Dokkum

Brundbuttel

Heide

Husum

Niebull

Tondern

Ribe

Varde

Esbjerg

Endrup

Karlsgarde

Buttel

DieleDorpen West

Hagermarsch

Emden/Borssum

Dorpen WestEemshaven

Ameland

Schiermonnikoog

Terschelling

Vlieland

Borkum

Memmert

Juist

NorderneyBaltrum

LangeoogSpiekeroog

Wangerooge

Mellum

Neuwerk

Helgoland

Pellworm

Hooge

Amrum

Fohr

Sylt Sylt

Rømø

Mandø

Fanø

Inhausen

Nordergrunde

TrianelWindpark

Borkum-Riffgrund II

Borkum-

Merkur(ehem.MEG Off-shore I)

alpha Ventus

Borkum-Riffgrund I

Riffgrund II



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

1



Wind Farm Cabling

2



Wind Farm Cabling

PCC (110 kV)

Grid Point

2



Wind Farm Cabling

PCC (110 kV)

Grid Point

Wind Turbine (33 kV)

2



Wind Farm Cabling

SubstationPCC (110 kV)

Grid Point


2



Wind Farm Cabling


Grid Point


Transport Cable

2



Wind Farm Cabling


Grid Point


Transmission Cables

Transport Cable

2



Wind Farm Cabling

Circuit

2



Wind Farm Cabling

Circuit

Collector System

2



Wind Farm Cabling

Circuit

Collector System

Full Farm

2



Wind Farm Cabling

Circuit

Collector System

Full Farm

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



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




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




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


3




Given

find



total cable costminimizing

Circuit

Collector System

Full Farm


3




Given

find

subject to




substation capacity constraintsflow conservation constraints

cable capacity constraints Circuit

Collector System

Full Farm


3




Given

find

subject to




substation capacity constraintsflow conservation constraints

cable capacity constraints Circuit

Collector System

Full Farm


Wind farm planning problem⇔ Minimum cost flow problem

OPT(NFFP) ≤∑

j∈VSOPT(NSP(j)) ≤

∑j∈VS

∑i∈N OPT(NCP(j , i))

using [Leibfried et al., 2015]

3



Simulated Annealing

Metropolis Algorithm Cooling Schedule



4



Simulated Annealing

many local optima




4



Simulated Annealing

many local optima

local search




4



Simulated Annealing

many local optima

escape local optimum

?




4



Simulated Annealing

many local optima

multiple mutations




4



Simulated Annealing

many local optima

multiple mutations


0.004

0.002

0.006

0.008

0.01

0

Tem

pera

ture

0 5 10 15 20 25 30



activity µdynamic, τ = 4 · 10−5standard, τ = 4 · 10−7

Time in min

4



Simulated Annealing

many local optima

multiple mutations


0.004

0.002

0.006

0.008

0.01

0

Tem

pera

ture

Diversification Intensification

0 5 10 15 20 25 30



Diversification

activity µdynamic, τ = 4 · 10−5standard, τ = 4 · 10−7

Time in min

4



Benchmark Sets

21

21

21

2121

5



Benchmark Sets

SubstationTurbineCable type 1Cable type 2Cable type 3

21

21

21

2121

21

5



Multiple Instances of Simulated Annealing

100 200 300 400 500

0

0.4

−0.4

−0.8

0.8 1 Instance

2 Instances

4 Instances

Number of Turbines

betterthan Gurobi

worsethan Gurobi

6



Multiple Instances of Simulated Annealing

100 200 300 400 500

0

0.4

−0.4

−0.8

0.8 1 Instance

2 Instances

4 Instances

Number of Turbines

betterthan Gurobi

worsethan 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



Performance Influence of the

200 300 400 500

0

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

betterthan Gurobi

worsethan Gurobi

Thermal Conductivity and Capacity τ

7




200 300 400 500

0

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

betterthan Gurobi

worsethan Gurobi

Thermal Conductivity and Capacity τ

Parameter tuning is difficult for the cooling schedule.

7



Cooling Schedule Performance

0

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

worsethan Gurobi

betterthan Gurobi

8



Cooling Schedule Performance

0

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

worsethan Gurobi

betterthan Gurobi

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

8




0.85 0.9 0.95 1−1.5

−1

−0.5

0

0.5

1

1.5

2

Substation Capacity Tightness

betterthan Gurobi

worsethan Gurobi


9




0.85 0.9 0.95 1−1.5

−1

−0.5

0

0.5

1

1.5

2


betterthan Gurobi

worsethan Gurobi


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

duration.

9



Conclusion & Future Work

Circuit ProblemSubstation ProblemFull Farm Problem

10




Circuit

Collector System

Full Farm


10




Circuit

Collector System

Full Farm

P (MST)NP-hard (CMST)

NP-hard (Heuristics)


10




Circuit

Collector System

Full Farm

Circuit

Collector System

Full Farm




10




Circuit

Collector System

Full Farm

Circuit

Collector System

Full Farm

NP-hardNP-hardNP-hard




10




Circuit

Collector System

Full Farm

Circuit

Collector System

Full Farm

(Clustering)NP-hardNP-hardNP-hard




10




}

Circuit

Collector System

Full Farm

Circuit

Collector System

Full Farm

Sim

ulat

edA

nnea

ling(Clustering)NP-hard

NP-hardNP-hard




10




}

Circuit

Collector System

Full Farm

Circuit

Collector System

Full Farm

Sim

ulat

edA

nnea


NP-hardNP-hard




RESULTS

Number of Turbines

-0.2-0.4

-0.8

Number of Turbines

-0.6

00.20.4

Standard Cooling ScheduleDynamic Cooling Schedule

100 200 300 400 100 200 300 400 500

1 Instance2 Instances4 Instances

0

0.4

-0.4

-0.8

0.8

200 300 400 500

0123

-1

45

τ= 1·10-5τ= 1·10-5τ= 2·10-5τ= 4·10-5

τ=16·10-5

Number of Turbines

6

τ= 8·10-5

0.85 0.9 0.95 1

00.511.52


-0.5

-1.5-1

10




}

Circuit

Collector System

Full Farm

Circuit

Collector System

Full Farm

Sim

ulat

edA

nnea


NP-hardNP-hard




Number of Turbines

-0.2-0.4

-0.8

Number of Turbines

-0.6

00.20.4

Standard Cooling ScheduleDynamic Cooling Schedule

100 200 300 400 100 200 300 400 500

1 Instance2 Instances4 Instances

0

0.4

-0.4

-0.8

0.8

200 300 400 500

0123

-1

45

τ= 1·10-5τ= 1·10-5τ= 2·10-5τ= 4·10-5

τ=16·10-5

Number of Turbines

6

τ= 8·10-5

0.85 0.9 0.95 1

00.511.52


-0.5

-1.5-1

RESULTS&FUTURE WORK

10



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