Abstract
In an offshore wind farm (OWF), the turbines are connected to a transformer by cable routes that cannot cross each other. Finding the minimum cost array cable layout thus amounts to a vehicle routing problem with the additional constraints that the routes must be embedded in the plane. For this problem, both exact and heuristic methods are of interest. We optimize cable layouts for real-world OWFs by a hop-indexed integer programming formulation, and develop a heuristic for computing layouts based on the Clarke and Wright savings heuristic for vehicle routing. Our heuristic computes layouts on average only 2% more expensive than the optimal layout. Finally, we present two problem extensions arising from real-world OWF cable layouts, and adapt the integer programming formulation to one of them. The thus obtained optimal layouts are up to 13% cheaper than the actually installed layouts.
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References
Arapogianni A, Moccia J, Williams D and Phillips J (2011). Wind in our sails. Technical Report, European Wind Energy Association.
Clarke G and Wright J (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research 12 (4): 568–581.
Dong Energy (2010). Walney Offshore Wind Farm Layout, http://www.dongenergy.com/Walney/News/data/Documents/WOW_I_grid.pdf, accessed 15 March 2013.
Dong Energy (no date). Barrow Windfarm Field Layout, http://www.lorc.dk/handlers/dh.ashx?id=32, accessed 15 March 2013.
Fosse T (2010). Optimizing the infield cable layout in offshore wind farms with network design algorithms. Master thesis, Bergen University College.
The Gas and Electricity Markets Authority (2011). Notice under Section 8A(3) of the Electricity Act 1989, http://www.ofgem.gov.uk/Networks/offtrans/rott/w1/Documents1/ NOTICE_UNDER_SECTION_8A_(W1).pdf, accessed 15 March 2013.
Godinho MT, Gouveia L and Magnanti TL (2008). Combined route capacity and route length models for unit demand vehicle routing problems. Discrete Optimization 5 (2): 350–372.
Gouveia L and Moura P (2010). Spanning trees with node degree dependent costs and knapsack reformulations. Electronic Notes in Discrete Mathematics 36: 985–992.
Hadley G (1964). Nonlinear and Dynamic Programming. Addison-Wesley Publishing Company: Reading, MA.
Laporte G and Semet F (2002). Classical Heuristics for the Capacitated VRP. In: Toth P and Vigo D (eds). The Vehicle Routing Problem. Society for Industrial and Applied Mathematics: Philadelphia, PA, pp. 109–128.
Letchford AN, Lysgaard J and Eglese RW (2007). A branch-and-cut algorithm for the capacitated open vehicle routing problem. Journal of the Operational Research Society 58 (12): 1642–1651.
Li F, Golden B and Wasil E (2007). The open vehicle routing problem: Algorithms, large-scale test problems, and computational results. Computers & Opererations Research 34 (10): 2918–2930.
LORC (2011a). Sheringham Shoal Offshore Wind Farm ∣ LORC Knowledge, http://www.lorc.dk/offshore-wind-farms-map/sheringham-shoal, accessed 15 March 2013.
LORC (2011b). Walney 1 Offshore Wind Farm ∣ LORC Knowledge, http://www.lorc.dk/offshore-wind-farms-map/walney-1, accessed 15 March 2013.
Lumbreras S and Ramos A (2013). Offshore wind farm electrical design: A review. Wind Energy 16 (3): 459–473.
Lysgaard J, Letchford AN and Eglese RW (2004). A new branch-and-cut algorithm for the capacitated vehicle routing problem. Mathematical Programming 100 (2): 423–445.
Pessoa A, Poggi de Aragão M and Uchoa E (2008). Robust branch-cut-and-price algorithms for vehicle routing problems. In: Golden B, Raghavan S and Wasil E (eds). The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces, Vol. 43. Springer: USA, pp 297–325.
Réthoré P-E, Fuglsang P, Larsen GC, Buhl T, Larsen TJ and Madsen HA (2013). TOPFARM: Multi-fidelity optimization of wind farms. Wind Energy, published online, 15 November, doi:10.1002/we.1667.
Sariklis D and Powell S (2000). A heuristic method for the open vehicle routing problem. Journal of the Operational Research Society 51 (5): 564–573.
Sheringham Shoal (2012). http://www.scira.co.uk/construction/foundationsmap.php, accessed 15 March 2013.
Subramanian A (2012). Heuristic, exact and hybrid approaches for vehicle routing problems. PhD thesis, Universidade Federal Fluminense.
Voß S (2009). Capacitated minimum spanning trees. In: Floudas CA and Pardalos PM (eds). Encyclopedia of Optimization. Springer: USA: pp 347–357.
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Bauer, J., Lysgaard, J. The offshore wind farm array cable layout problem: a planar open vehicle routing problem. J Oper Res Soc 66, 360–368 (2015). https://doi.org/10.1057/jors.2013.188
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DOI: https://doi.org/10.1057/jors.2013.188