Balanced and unbalanced networks in offshore wind farms

The cable routing problem in offshore wind farms consists in designing a transportation network to transfer the electricity generated by wind turbines to a central hub (substation) which is connected to shore. The submarine electrical cables are expensive, comprising about 5% of the total capital expenditure (CAPEX) of an offshore wind farm (BVG Associates, 2019). For this reason, the optimization of cable routing has been investigated in literature, with the objective of finding the cable routing of minimum cost (Bauer & Lysgaard, 2015). One important constraint for the cable routing problem is that cable crossings are forbidden, due to the increased installation costs and difficult maintenance. Another constraint is that the routing must avoid all obstacles in the wind farm sea area. These obstacles may be due to unsuitable seabed conditions, to ship wrecks, and to regulations, such as fishing corridors and natural reserves. Cables must not cross any of these areas for the routing solution to be feasible. Acable routing allows only one electrical cable to exit from each turbine, and multiple cables to enter turbines and the substation. Each sub-tree leaving the substation is denoted a rootbranch. A property of cable routing solution is related to how many turbines are present in each root-branch. If the number of turbines in each root-branch is the same or differs at most by one, we denote the solution balanced. While literature mainly has focused on the general unbalanced cable routing problem, in industry the wind farm developers favor balanced cable routing solutions. As the solutions to the balanced problem are a subset of the solutions to the unbalanced formulation, unbalanced solutions may be cheaper than balanced. The drawbacks of the unbalanced routing are related to the additional electrical equipment cost that needs to be installed in the offshore substation. In particular, the cost of installing a spare Offshore Transformer Module (OTM) on the substation is about 5M€ (Walling & Ruddy, 2005), depending on its rating. In the case of a balanced cable routing, a single type of transformer is needed as spare in case of failures (online spare), since the transformer share the same electrical loads and can substitute any of the transformers in case of failure. For the unbalanced case instead, different transformer ratings and different spares would be needed, making this option less attractive in the industry. The contributions of this work are:

• Wedevelop a matheuristic that uses different neighborhoods to optimize the cable routing problem, for both balanced and unbalanced networks. • We present a technique to handle obstacles in the cable routing based on a visibility graph. 
• We quantify the difference between balanced and unbalanced cable routing on a set of realistic wind farm instances, taking into account the additional OTM costs.