cable layout optimization towards negative cycle canceling in wind farm · 2018-12-11 · towards...

Towards Negative Cycle Canceling in Wind Farm

Seminar Energieinformatik · December 11, 2018Sascha Gritzbach, T. Ueckerdt, D. Wagner, F. Wegner, and M. Wolf

KIT – The Research University in the Helmholtz Association

INSTITUTE OF THEORETICAL INFORMATICS · ALGORITHMICS GROUP

www.kit.edu

Cable Layout Optimization

u2

u1 v1

v2

2 2

2

∞

-3

3

2

-2 ∞0

∞0

u2

u1 v1

v2

s

[Gritzbach et al., 2018]

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Introduction

EU28 (2016): 30.2 % of grosselectricity generation fromrenewables, out of which 39.9 %from wind [1]

Offshore wind farm: 17 % of totalplanning and building cost forinternal cabling [2]

[1] Energy datasheets: EU28 countries. European Commission DGENER Unit A4, 2018.[2] P. Santos Valverde, A. J. N. A. Sarmento, M. Alves. Offshorewind farm layout optimization – state of the art. Journal of Oceanand Wind Energy, 1(1):23–29, 2014.

1

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Introduction

EU28 (2016): 30.2 % of grosselectricity generation fromrenewables, out of which 39.9 %from wind [1]

Offshore wind farm: 17 % of totalplanning and building cost forinternal cabling [2]

Our contribution:

Fast algorithm to find good windfarm cablings

[1] Energy datasheets: EU28 countries. European Commission DGENER Unit A4, 2018.[2] P. Santos Valverde, A. J. N. A. Sarmento, M. Alves. Offshorewind farm layout optimization – state of the art. Journal of Oceanand Wind Energy, 1(1):23–29, 2014.

1

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Outline

Wind Farm Cabling Problem

Network Flows and Negative Cycle Canceling

Our Algorithm

Evaluation

Outlook

2

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Optimization Problem

Given turbines (unit production)substations (each with capacity)edge set: possible connectionscable types (cost and capacity)

3 5

Production Units

Cost per Unit Length c

1

34

3

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Optimization Problem

Given

find

minimizing total cable cost

for each edge: the cable type

turbines (unit production)substations (each with capacity)edge set: possible connectionscable types (cost and capacity)

3 5

Production Units

Cost per Unit Length c

∑e : edge

c(e) · length(e)

1

34

3

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Optimization Problem

Given

find

minimizing

subject to cable capacity constraintssubstation capacity constraintsflow conservation constraints

total cable cost

for each edge: the cable type

turbines (unit production)substations (each with capacity)edge set: possible connectionscable types (cost and capacity)

3 5

Production Units

Cost per Unit Length c

∑e : edge

c(e) · length(e)

1

34

20

5

3

3

1

1

2

3

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

Find “good” pathto free substation

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

Find “good” pathto free substation

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

Update

Find “good” pathto free substation

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

Update

1

1

1

Find “good” pathto free substation

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

Update

1

1

1

Find “good” pathto free substation

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

Update

1

1

1

Find “good” pathto free substation

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

Update

1

1

2

1

1

Find “good” pathto free substation

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

1

2

3

1

2

5

1

2

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

1

2

3

1

2

5

1

23 5

Production Units

Cost per Unit Length c

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Network Flows and Wind Farm Cabling

1

2

3

1

2

5

1

23 5

Production Units

Cost per Unit Length c

4

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

1

2

1 2 3

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

u2

u1 v1

v2

Total Cost: 5

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

1

2

1 2 3u2

u1 v1

v2

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

u2

u1 v1

v2

s

Total Cost: 5

Find edge weights for change of flow ∆ = 1= old cost - new cost

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

1

2

1 2 3

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

u2

u1 v1

v2

3

u2

u1 v1

v2

s

Total Cost: 5

Find edge weights for change of flow ∆ = 1

old flow old cost new flow new cost

1 3 2 61 3 0 0

= old cost - new cost

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

1

2

1 2 3

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

u2

u1 v1

v2

3

u2

u1 v1

v2

s

Total Cost: 5

Find edge weights for change of flow ∆ = 1

old flow old cost new flow new cost

1 3 2 61 3 0 0

= old cost - new cost

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

1

2

1 2 3

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

u2

u1 v1

v2

Total Cost: 5

Find edge weights for change of flow ∆ = 1

old flow old cost new flow new cost

1 3 2 61 3 0 0

-3

3

u2

u1 v1

v2

s

= old cost - new cost

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

1

2

1 2 3u2

u1 v1

v2

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

2 2

2

∞

-3

3

2

-2 ∞0

∞0

u2

u1 v1

v2

s

Total Cost: 5

Find edge weights for change of flow ∆ = 1

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

1

2

1 2 3u2

u1 v1

v2

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

2 2

2

∞

-3

3

2

-2 ∞0

∞0

u2

u1 v1

v2

s

Total Cost: 5

edge weights for change of flow ∆ = 1= old cost - new cost

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

= old cost - new cost

1

2

1 2 3u2

u1 v1

v2

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

2 2

2

∞

-3

3

2

-2 ∞0

∞0

u2

u1 v1

v2

s

Total Cost: 5

edge weights for change of flow ∆ = 1

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Negative Cycle Canceling

= old cost - new cost

1

2

1 2 3

Substation capacity: 2

Edge lengths: 2 (edge u1v2: 3)

Cable types:

2 2

2

∞

-3

3

2

-2 ∞0

∞0

u2

u1 v1

v2

sTotal Cost: 4

edge weights for change of flow ∆ = 1

u2

u1 v1

v2

u2

u1 v1

v2

Total Cost: 5

5

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Algorithm

New Flow∆ = 1

StoppingCriterionFulfiled?

Old Flow∆++

Output

InitializeFlow, ∆ = 1

Y NNCC

Current FlowCurrent ∆

Wind FarmCable Types Cycle

Canceled?

Y

N

6

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Algorithm

New Flow∆ = 1

StoppingCriterionFulfiled?

Old Flow∆++

Output

InitializeFlow, ∆ = 1

Y N

1

1

2

1

1

NCC

Current FlowCurrent ∆

Wind FarmCable Types Cycle

Canceled?

Y

N

6

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Algorithm

New Flow∆ = 1

StoppingCriterionFulfiled?

Old Flow∆++

Output

InitializeFlow, ∆ = 1

Y N

2 2

2

∞

-3

3

2

-2 ∞0

∞0

u2

u1 v1

v2

s

u2

u1 v1

v2

1

1

2

1

1

NCC

Current FlowCurrent ∆

Wind FarmCable Types Cycle

Canceled?

Y

N

6

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Simulations

Code in C++14

Gurobi 7.0.2

Benchmark sets by Lehmann et al. [3]:

Benchmark Set |VT | |VS||VT ||VS|

|Ni |

N1 single 10–79 1 500N2 small 20–79 2–7 10–20 500N3 medium 80–180 4–9 10–20 1000N4 large 200–499 10–39 10–50 1000

Running times – Gurobi: 1 hour, our algorithm: until termination

[3] S. Lehmann, I. Rutter, D. Wagner, F. Wegner. A Simulated-Annealing-Based Approach for Wind Farm Cabling. Proceedings ofthe 8th ACM e-Energy International Conference on Future Energy Systems (ACM eEnergy ’17), p. 203–215, ACM Press, 2017.

7

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Evaluation

NiTime in ms

(min) (avg) (max)

1 0.72 40.63 293.422 3.77 51.72 220.923 157.69 575.02 2 968.564 2 815.12 149 209.92 440 235.07

1 2 3 4

85

90

95

100

105

0 100 200 300 400 500

90

95

100

105

Comparison to Gurobi:

Number of Turbines

Infeasible instancesInfeasible instances

Rel

ativ

eC

osti

n%

Rel

ativ

eC

osti

n%

BenchmarksetsNi with 1 ≤ i ≤ 4

Running times:

8

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Conclusion and Outlook

Summary:

Very fast heuristic to solve the Wind Farm Cabling Problem

Works very well on large instances

Allows various strategies for improvement

0 100 200 300 400 500

90

95

100

105

Number of Turbines

Infeasible instances

Rel

ativ

eC

osti

n%

New Flow∆ = 1

StoppingCriterionFulfiled?

Old Flow∆++

Output

InitializeFlow, ∆ = 1

Y NNCC

Current FlowCurrent ∆

Wind FarmCable Types Cycle

Canceled?

Y

N

9

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Conclusion and Outlook

Summary:

Very fast heuristic to solve the Wind Farm Cabling Problem

Works very well on large instances

Allows various strategies for improvement

Future Work:

Implement and test strategies

Give Gurobi more time

Compare to metaheuristics

0 100 200 300 400 500

90

95

100

105

Number of Turbines

Infeasible instances

Rel

ativ

eC

osti

n%

Escape local minima

Find more complex structures

Electrical constraints

New Flow∆ = 1

StoppingCriterionFulfiled?

Old Flow∆++

Output

InitializeFlow, ∆ = 1

Y NNCC

Current FlowCurrent ∆

Wind FarmCable Types Cycle

Canceled?

Y

N

9

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

Conclusion and Outlook

Summary:

Very fast heuristic to solve the Wind Farm Cabling Problem

Works very well on large instances

Allows various strategies for improvement

Future Work:

Implement and test strategies

Give Gurobi more time

Compare to metaheuristics

0 100 200 300 400 500

90

95

100

105

Number of Turbines

Infeasible instances

Rel

ativ

eC

osti

n%

Thank you!

Escape local minima

Find more complex structures

Electrical constraints

New Flow∆ = 1

StoppingCriterionFulfiled?

Old Flow∆++

Output

InitializeFlow, ∆ = 1

Y NNCC

Current FlowCurrent ∆

Wind FarmCable Types Cycle

Canceled?

Y

N

9

Sascha Gritzbach – Negative Cycle Canceling for Wind Farm Cabling Institute of Theoretical InformaticsAlgorithmics Group

References

[0] S. Gritzbach, T. Ueckerdt, D. Wagner, F. Wegner, M. Wolf. Towards egative cyclecanceling in wind farm cable layout optimization. Energy Informatics, 1 (Suppl 1) :51,2018

[1] Energy datasheets: EU28 countries. European Commission DG ENER Unit A4, 2018.

[2] P. Santos Valverde, A. J. N. A. Sarmento, M. Alves. Offshore wind farm layout opti-mization – state of the art. Journal of Ocean and Wind Energy, 1(1):23–29, 2014.

[3] S. Lehmann, I. Rutter, D. Wagner, F. Wegner. A Simulated-Annealing-Based Approachfor Wind Farm Cabling. Proceedings of the 8th ACM e-Energy International Confer-ence on Future Energy Systems (ACM eEnergy ’17), p. 203–215, ACM Press, 2017.

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