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Optimizing cable routes in offshore wind farms Arne Klein Dag - - PowerPoint PPT Presentation
Optimizing cable routes in offshore wind farms Arne Klein Dag - - PowerPoint PPT Presentation
Optimizing cable routes in offshore wind farms Arne Klein Dag Haugland Department of Informatics, University of Bergen, Norway Energy lab, January 17th 2017 Offshore wind farm cabling Motivation High cabling and trenching costs offshore
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Given data
◮ Wind turbine positions ◮ Substation position(s) ◮ Max. energy output of turbines ◮ Obstacles ◮ (Available cable types) ◮ (Cable paths for comparison)
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Wind farm data
◮ Turbine and substation position data of offshore wind farms
◮ Barrow ◮ Sheringham Shoal ◮ Walney 1 ◮ Walney 2 Sheringham Shoal Walney 2
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Problem properties
Basics
◮ Cable capacity ◮ Connectivity
◮ turbines to substations
◮ Non-crossing
Possible additions
◮ Branching ◮ Different cable types ◮ Obstacles ◮ Parallel cables ◮ Energy losses
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Problem properties
Basics
◮ Cable capacity ◮ Connectivity
◮ turbines to substations
◮ Non-crossing
Possible additions
◮ Branching ◮ Different cable types ◮ Obstacles ◮ Parallel cables ◮ Energy losses
We want to
◮ Find optimal cable paths ◮ Minimize total cable
length/cost
◮ Satisfy constraints
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Optimization method and solution method
◮ Mathematical model describing the problem
◮ Integer linear programming (ILP) ◮ Linear constraints ◮ Binary decision variable ◮ yij = 1 means that there is a cable between turbine j and i
◮ Implemented using Python, solved by IBM CPLEX
- ptimization library
◮ Non-crossing constraints (O(|N|4)) only added if solution
violates them
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Experimental results - one cable type
◮ Relative improvement from branching below 1% for all test
cases
◮ Example Sheringham Shoal with C = 5
◮ relative improvement 0.72%
No branching Branching
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Experimental results - two cable type (1)
◮ Cable capacity C > Q, cable cost cij = 1.7qij
2 3 4 5 6 2 4 6 8 10 12 14
- rel. difference [%]
Walney 1 C = 5 C = 6 C = 7
2 3 4 5 6 Q 1 2 3 4 5 6 7 8 9
- rel. difference [%]
Walney 2 C = 5 C = 6 C = 7
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Experimental results - two cable type (2)
◮ Walney 1, C = 7, Q = 2
No branching Branching
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Parallel cables
3 2 1 0 1 2 3 1 2 3 4 5 3 2 1 0 1 2 3 1 2 3 4 5 3 2 1 0 1 2 3 1 2 3 4 5 ◮ Can improve solutions in some special cases ◮ Same mechanism in model allows to handle obstacles better
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Parallel cables example, Walney 1
463000 464000 465000 466000 467000 468000 469000 470000 471000 1000 2000 3000 4000 5000 6000 7000 +5.985e6
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Challenges
◮ Does not scale well with number of nodes ◮ High computational costs ◮ Information on cable cost hard to obtain
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