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Cabling Optimization in a Wind Farm Heuristics Based on Simulated Annealing Masters Thesis Final Presentation May 31, 2016 Sebastian Lehmann I NSTITUTE OF T HEORETICAL I NFORMATICS A LGORITHMICS G ROUP KIT University of the State

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Cabling Optimization in a Wind Farm

Master’s Thesis · Final Presentation · May 31, 2016 Sebastian Lehmann

KIT – University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association

INSTITUTE OF THEORETICAL INFORMATICS · ALGORITHMICS GROUP

www.kit.edu

Heuristics Based on Simulated Annealing

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Components in a Wind Farm

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Components in a Wind Farm

Turbines

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Components in a Wind Farm

Grid Point Turbines

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Components in a Wind Farm

Grid Point Turbines 33 kV 155 kV

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Components in a Wind Farm

Grid Point Turbines Substations 33 kV 155 kV

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Components in a Wind Farm

Grid Point Turbines Substations Transport Cables 33 kV 155 kV

1

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Components in a Wind Farm

Grid Point Turbines Substations Transport Cables Export Cables 33 kV 155 kV

1

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Components in a Wind Farm

Grid Point Turbines Substations Transport Cables Export Cables 33 kV 155 kV

≤6 turbines, $140 ≤2 turbines, $100 ≤9 turbines, $160

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Transmission Network Expansion Planning

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Transmission Network Expansion Planning

... for a circuit Optimize Cabling Cost ...

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Transmission Network Expansion Planning

... for a substation ... for a circuit Optimize Cabling Cost ...

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Transmission Network Expansion Planning

... for a substation ... for a circuit ... for the full farm Optimize Cabling Cost ...

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Transmission Network Expansion Planning

... for a substation ... for a circuit ... for the full farm Optimize Cabling Cost ... single cable type Berzan et al. (2011): Algorithms for Cable Network Design on Large-scale Wind Farms

http://thirld.com/files/msrp techreport.pdf

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Transmission Network Expansion Planning

... for a substation ... for a circuit ... for the full farm Optimize Cabling Cost ... multiple cable types Berzan et al. (2011): Algorithms for Cable Network Design on Large-scale Wind Farms

http://thirld.com/files/msrp techreport.pdf

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given t turbines, s substations (each with capacity), for each edge: cable types (each with cost and capacity)

3

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given find t turbines, s substations (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type

3

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given find t turbines, s substations (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type their total cost minimizing

3

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Wind Farm Cable Layout Problem

Given find subject to t turbines, s substations (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type their total cost minimizing substation capacity constraints flow conservation constraints cable capacity constraints

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Integer Linear Programming

Given find subject to t turbines, s substations (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type their total cost minimizing substation capacity constraints cable capacity constraints flow conservation constraints

4

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Integer Linear Programming

Given find subject to t turbines, s substations (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type their total cost minimizing substation capacity constraints cable capacity constraints flow conservation constraints

inputs

4

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Integer Linear Programming

Given find subject to t turbines, s substations (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type their total cost minimizing substation capacity constraints cable capacity constraints flow conservation constraints

variables

binary variables

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Integer Linear Programming

Given find subject to t turbines, s substations (each with capacity), for each edge: cable types (each with cost and capacity) for each edge: the cable type their total cost minimizing substation capacity constraints cable capacity constraints flow conservation constraints

=

cable chosen? × cable cost

  • bjective

edges cable types

4

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Meta-Heuristic Optimization Techniques

Tabu Search Hill Climbing Simulated Annealing Ant Colony Optimization Evolutionary Algorithms Stochastic Tunneling Greedy

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Meta-Heuristic Optimization Techniques

Tabu Search Hill Climbing Simulated Annealing Ant Colony Optimization Evolutionary Algorithms Stochastic Tunneling Greedy

Swarm Intelligence Monte-Carlo Local Optimization

5

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Meta-Heuristic Optimization Techniques

Tabu Search Hill Climbing Simulated Annealing Ant Colony Optimization Evolutionary Algorithms Stochastic Tunneling Greedy

Swarm Intelligence Monte-Carlo Local Optimization

5

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily

6

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily

minimize height

6

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily

minimize height

many local optima

6

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily

minimize height

many local optima local search

6

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily

minimize height

many local optima escape local optimum ?

6

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily

minimize height

many local optima multiple mutations

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily temperature controls acceptance of worse solutions

6

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily temperature controls acceptance of worse solutions Time hot cool Temperature exponential cooling

6

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing

mutate solution candidates idea: allow worse solutions temporarily temperature controls acceptance of worse solutions Time hot cool Temperature exponential cooling likely unlikely

6

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing solution candidate

mutation

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Simulated Annealing indirect representation solution candidate

decoding mutation

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6 1 2 3 10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3 10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges Decoding each turbine: construct path

1 2 3 10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges Decoding each turbine: construct path

1 2 3 10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges Decoding each turbine: construct path

1 2 3 10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges Decoding each turbine: construct path

1 2 3 10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges Decoding each turbine: construct path

1 2 3

each edge: find suited cable

10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3

Mutation

10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3

Mutation swap node potentials

10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3

Mutation swap node potentials

10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3

Mutation swap node potentials

3 8 10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3

Mutation swap node potentials

3 8 10

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3

Mutation swap node potentials

3 8 10

forbid / allow an edge

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3

Mutation swap node potentials

3 8 10

forbid / allow an edge

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Our Representation

nodes: potential values (permutation of indices)

5 8 7 9 4 6

forbid some edges

1 2 3

Mutation swap node potentials

3 8 10

forbid / allow an edge

8

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Generating Instances

Turbines & substations evenly distributed (Poisson Disk Sampling) Edges: 6 nearest neighbors + shortcuts Substation capacities: tight vs. loose

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Observations & Problems

good results for medium-sized farms (t < 350: faster than Gurobi) long running time required for large farms

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Observations & Problems

good results for medium-sized farms (t < 350: faster than Gurobi) long running time required for large farms reference solution: run Gurobi for 1h

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Observations & Problems

good results for medium-sized farms (t < 350: faster than Gurobi) long running time required for large farms reference solution: run Gurobi for 1h better results after 30 min

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Observations & Problems

good results for medium-sized farms (t < 350: faster than Gurobi) long running time required for large farms reference solution: run Gurobi for 1h better results after 30 min converges slower than Gurobi

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Observations & Problems

good results for medium-sized farms (t < 350: faster than Gurobi) long running time required for large farms temperature curve: parameter tuning difficult

10

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Observations & Problems

good results for medium-sized farms (t < 350: faster than Gurobi) long running time required for large farms temperature curve: parameter tuning difficult result depends on random seed

10

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Observations & Problems

good results for medium-sized farms (t < 350: faster than Gurobi) long running time required for large farms temperature curve: parameter tuning difficult result depends on random seed bad results for tight substation capacities

10

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Observations & Problems

good results for medium-sized farms (t < 350: faster than Gurobi) long running time required for large farms temperature curve: parameter tuning difficult result depends on random seed bad results for tight substation capacities bad results for many substations

10

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

temperature curve: parameter tuning difficult

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

Observation: escaping deep local optimum takes long time temperature curve: parameter tuning difficult

11

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

Observation: escaping deep local optimum takes long time much higher cost somewhat higher cost deep: temperature curve: parameter tuning difficult

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

Observation: escaping deep local optimum takes long time temperature curve: parameter tuning difficult Time hot Temperature exponential cooling cool

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

Observation: escaping deep local optimum takes long time temperature curve: parameter tuning difficult Time hot Temperature exponential cooling Global exploration Local refinement cool

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

Observation: escaping deep local optimum takes long time temperature curve: parameter tuning difficult Time hot Temperature exponential cooling Global exploration Local refinement cool

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

Observation: escaping deep local optimum takes long time temperature curve: parameter tuning difficult Time hot cool Temperature exponential cooling Global exploration Local refinement “frozen”

11

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

adjust temperature drop velocity to activity activity = avg. probability for accepting worse solution Idea: Observation: escaping deep local optimum takes long time temperature curve: parameter tuning difficult Time hot cool Temperature exponential cooling Global exploration Local refinement “frozen”

11

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve

adjust temperature drop velocity to activity activity = avg. probability for accepting worse solution Idea: Observation: escaping deep local optimum takes long time temperature curve: parameter tuning difficult Time hot Temperature exponential cooling cool Global exploration Local refinement sub-

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve better worse

than Gurobi than Gurobi

0% +0.5%

−0.5%

100 200 300 400 Number of turbines t (grouped in steps of 50) standard temperature curve dynamic temperature curve

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Dynamic Temperature Curve better worse

than Gurobi than Gurobi

0% +0.5%

−0.5%

100 200 300 400 Number of turbines t (grouped in steps of 50) worse better standard temperature curve dynamic temperature curve

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Multiple Runs

result depends on random seed

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Multiple Runs

result depends on random seed start same algorithm multiple times each with different random seed Idea:

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Multiple Runs

result depends on random seed start same algorithm multiple times each with different random seed Idea: run 2 finishes here run 1 finishes here

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Multiple Runs

result depends on random seed start same algorithm multiple times each with different random seed Idea: run 2 finishes here run 1 finishes here final result = best run

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Multiple Runs

result depends on random seed start same algorithm multiple times each with different random seed Idea: final result = best run distribute available time evenly

13

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Multiple Runs better worse

than Gurobi than Gurobi

0% +0.5%

−0.5%

100 200 300 500 Number of turbines t (grouped in steps of 50) 400 1 run 2 runs 4 runs

14

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Multiple Runs better worse

than Gurobi than Gurobi

1 2 4

0% +0.5%

−0.5%

100 200 300 500 Number of turbines t (grouped in steps of 50) 400 1 run 2 runs 4 runs

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach

bad results for tight substation capacities / many substations Observation: has difficulties assigning turbines → substations

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach

bad results for tight substation capacities / many substations (1) partition into substation networks (2) optimize each separately Idea: Observation: has difficulties assigning turbines → substations

15

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach

bad results for tight substation capacities / many substations (1) partition into substation networks (2) optimize each separately Idea: Observation: has difficulties assigning turbines → substations in different ways for each partitioning

15

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach

15

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach

  • ptimize
  • ptimize
  • ptimize
  • ptimize
  • ptimize
  • ptimize
  • ptimize
  • ptimize

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach

  • ptimize
  • ptimize
  • ptimize
  • ptimize
  • ptimize
  • ptimize
  • ptimize
  • ptimize

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach

best final result

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: high potential

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: high potential lower potential

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

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SLIDE 104

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

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SLIDE 105

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

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SLIDE 106

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

16

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SLIDE 107

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But:

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SLIDE 108

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: using turbine paths

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SLIDE 109

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: cables using

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SLIDE 110

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: cables 15 12 using substation cap.: 15

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SLIDE 111

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: cables 15 12 using substation cap.: 15

16

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SLIDE 112

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: cables 15 12 16 11 using

!

substation cap.: 15

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SLIDE 113

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: cables 15 12 using 15 12 13 14 substation cap.: 15

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SLIDE 114

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: cables 15 12 using 15 12 13 14 substation cap.: 15 ... changed original assignment ...

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SLIDE 115

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: cables 15 12 using 15 12 13 14 substation cap.: 15 ... changed original assignment ...

16

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SLIDE 116

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: Alternatives: Fuzzy C-means using cables as metric use partitioning as representation in top level (decoding = optimize single substation networks)

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SLIDE 117

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Two-Level Approach — Partitioning

Our idea: use substation assignment based on turbine paths subgraphs often not connected! But: Alternatives: Fuzzy C-means using cables as metric use partitioning as representation in top level (decoding = optimize single substation networks)

Future Work

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SLIDE 118

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Other Tings We’ve Tried

Recover when caught in local optimum Problem: Recover to which state?

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slide-119
SLIDE 119

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Other Tings We’ve Tried

Cancel runs when caught in local optimum Problem: How detect this? Recover when caught in local optimum Problem: Recover to which state?

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SLIDE 120

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Other Tings We’ve Tried

Cancel runs when caught in local optimum Problem: How detect this? Hybrid Simulated Annealing & Evolutionary Algorithm Problem: How cross two solutions? Recover when caught in local optimum Problem: Recover to which state?

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SLIDE 121

Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

Related Problems (Future Work)

Optimize locations of substations Allow adding merge points (⇒ Steiner Tree) Avoid intersections Redundant cables for failure safety Optimize types of substations (similar to types of cables)

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