Application of an offshore wind farm layout optimization methodology at Middelgrunden wind farm

This article explores the application of a wind farm layout evaluation function and layout optimization framework to Middelgrunden wind farm in Denmark. This framework has been built considering the interests of wind farm developers in order to aid in the planning of future offshore wind farms using the UK Round 3 wind farms as a point of reference to calibrate the model. The present work applies the developed evaluation tool to estimate the cost, energy production, and the levelized cost of energy for the existing as-built layout at Middelgrunden wind farm; comparing these against the cost and energy production reported by the wind farm operator. From here, new layouts have then been designed using either a genetic algorithm or a particle swarm optimizer. This study has found that both optimization algorithms are capable of identifying layouts with reduced levelized cost of energy compared to the existing layout while still considering the specific conditions and constraints at this site and those typical of future projects. Reductions in levelized cost of energy such as this can result in significant savings over the lifetime of the project thereby highlighting the need for including new advanced methods to wind farm layout design.


Introduction
As offshore wind farms continue to grow it has become increasingly im-2 portant to ensure that these projects are managed as efficiently as possible. 3 With this in mind, the field of offshore wind farm layout optimization has 4 grown to include sophisticated methodologies for the evaluation of the lev-5 elized cost of energy (LCOE) of offshore wind farms which includes both the 6 lifetime energy production and lifetime costs of the wind farm. The LCOE, is 7 frequently used by project developers to evaluate the impact a change in de-8 sign might have on a project. This metric is also preferred as it is technology 9 agnostic and therefore gives a basis by which projects of different technology 10 types can easily be compared against one another.

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The present work expands on the standard paradigm for the optimization 12 of offshore wind farm layouts in which wake and cost models are integrated 13 as the evaluation function for an optimization algorithm. This work shows 14 that a sophisticated and detailed LCOE evaluation tool can successfully be 15 included in the optimization process accounting for realistic constraints faced 16 by a wind farm developer. Taking the UK Round 3 wind farms as a point 17 of reference, the present tool built in partnership with wind farm developers, 18 has been developed to aid in the planning of these wind farms allowing the 19 developer to explore wind farm layout alternatives. Given the future applica-20 tion to UK Round 3 sites, much of the tool has been calibrated to these sites 21 and sites of similar site characteristics. Extending the previous work of the 22 authors [1], the present work allows the wind farm to be designed considering 23 different degrees of layout restriction which may potentially be imposed by 24 regulatory bodies. 25 This article explores Middelgrunden wind farm, a wind farm off the Dan-26 ish coast, as a test case to both verify the full LCOE evaluation function 27 and highlight potential improvements that could have been achieved through 28 more optimal turbine placement using either a genetic algorithm (GA) or a 29 particle swarm optimizer (PSO). By applying the layout optimization frame-30 work to a real wind farm site rather than to fictional cases the capabilities and 31 applicability of the present wind farm layout optimization tool are demon- 32 strated.
and Herbert-Acero et al. [19]. 48 As the original work by Mosetti et al. [2] explored the applicability of 49 the genetic algorithm to this problem, it ignored the layout dependent costs. 50 Many of the developed tools following this have also focused on the appli-51 cability and development of the optimization and have therefore opted to 52 use cost functions that either omit important layout dependent factors or 53 which ignore the layout all together thereby only considering the impact 54 the layout has on the energy produced. The work by Elkinton [4] repre-55 sents an exception in which a detailed cost model was built and verified. 56 This, however, was developed based on published data at the time and has 57 limited applicability to new projects. As the aim of the existing tools has 58 been to further develop the optimizers rather than industrial applications 59 of the methods, it remains challenging for the developed wind farm layout 60 optimization tools and methodologies to be deployed in the design of real off-61 shore wind farms. Focusing more on the potential industrial applications, the 62 present work therefore both represents a more detailed evaluation function 63 over previous work and also applies the full methodology to a more complex 64 wind farm site with realistic constraints faced by developers. Furthermore, 65 the development of the present framework has allowed two of the leading 66 metaheuristic optimization algorithms applied to offshore wind farms to be 67 deployed on the same framework allowing a direct comparison. 68 Through the deployment of this tool for an existing wind farm it is pos-69 sible to gauge the tool's suitability to future wind farms and identify areas 70 in which the tool will need to be further developed in order for the results to 71 be of use to a site developer.  The LCOE is defined to be a function of both the total energy generated 91 and the costs over the lifetime of the wind farm: where C t is the total costs incurred in year t, n is the project lifetime, and this therefore represents the case in which the wind farm devel-123 oper is free to develop the site as they see best. As part of the development of this layout optimization framework, a sub-126 tool has been developed to address the optimization of an offshore wind 127 farm's electrical infrastructure. This is fully presented by in Pillai et al. [21].

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This sub-tool implements a heuristic approach and is therefore not guar-129 anteed to find the proven optimal solution, however, it takes a pragmatic   wind farm layout optimization problem has previously not been undertaken, however, is a feature sought by wind farm developers.  From this, the wind turbine power curve is used to convert the wake affected 185 incident wind speed to the energy produced under these conditions [33,34].
where θ i is the wind direction; v i is the wind speed; P (θ i , v i ) is the joint   The turbine supply costs are determined based on the price per turbine in-   included in this step rather than the foundation supply costs. In some condi-304 tions, the scour protection will not be necessary, however, for the time being 305 this model has assumed that all turbines will require scour protection.     The genetic algorithm represents a metaheuristic algorithm commonly 385 deployed to aid in decision making and engineering design. In existing work, 386 the GA has been frequently applied to wind farm layout design [19].

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The GA is so named because it borrows principles from biology and evo-    The below formulations ensure that as the population converges, as mea- where p c and p m are respectively the probability of crossover and muta-427 tion. The constants are defined such that k 1 = k 3 = 1 and k 2 = k 4 = 1 2 .

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The use of adaptive parameters like this has been found to both aid in the 429 rate at which the process converges as well as its ability to avoid local solu-  This process is shown in fig. 3. The particles' change in position within the search space is given each 440 iteration by the velocity. A particle's velocity in iteration i, v i is given by: where, w is an inertia weight determined by tuning the PSO; C 1 , C 2 , C 3 , 442 and C 4 are coefficients representing the weighting of each of the contributors 443 determined by tuning the PSO; p is the best position that the particle has 444 historically occupied within the search space; g is the best historical position 445 that the swarm as a whole has ever occupied; x is the solution under con-446 sideration; η is the best historical position that the neighborhood as a whole 447 has ever occupied; and rand is random number between 0 and 1. With this 448 velocity the particle's position the next iteration is given by:              ×10 6 (f) PSO -Continuous