Towards Negative Cycle Canceling in Wind Farm Seminar Energieinformatik · December 11, 2018 Sascha Gritzbach , T. Ueckerdt, D. Wagner, F. Wegner, and M. Wolf KIT – The Research University in the Helmholtz Association I NSTITUTE OF T HEORETICAL I NFORMATICS · ALGORITHMICS GROUP www.kit.edu Cable Layout Optimization u 2 u 1 v 1 v 2 2 2 2 ∞ -3 3 2 -2 ∞ 0 ∞ 0 u 2 u 1 v 1 v 2 s [Gritzbach et al., 2018]
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Cable Layout Optimization Towards Negative Cycle Canceling in Wind Farm · 2018-12-11 · Towards Negative Cycle Canceling in Wind Farm Seminar Energieinformatik December 11, 2018
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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
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.