@misc{13319,
  author = {Stephan Kramer and Simon Funke and Matthew Piggott},
  title = {A continuous approach for the optimisation of tidal turbine farms},
  abstract = {The optimal placement of individual devices within a tidal turbine farm is                                                                                                                                                                     a challenging problem that may benefit greatly from automated optimisation methods.                                                                                                                                                            A previously published gradient-based approach for the optimal placement/arrangement                                                                                                                                                           of turbines significantly reduces the number of required iterations                                                                                                                                                                            over traditional optimisation methods. This allows for a higher level of computational cost,                                                                                                                                                   and hence realism, in the hydrodynamic model used in every optimisation iteration.                                                                                                                                                                                                                                                                                                                                                                                                            Here, we                                                                                                                                                                                                                                       introduce a closely related approach that optimises for a turbine density field                                                                                                                                                                (referred to here as the {\textquoteleft}{\textquoteleft}continuous{\textquoteright}{\textquoteright} approach) instead of the positions of individual turbines                                                                                                                                              (the {\textquoteleft}{\textquoteleft}discrete{\textquoteright}{\textquoteright} approach).  Its advantages are: (1) it requires less                                                                                                                                                                         mesh resolution than the discrete approach and hence has lower computational costs;                                                                                                                                                            (2) the number of turbines does not need to be chosen in advance -- this allows for                                                                                                                                                            the inclusion of per-turbine-costs to be included in the optimisation, and as a by-product                                                                                                                                                     returns an estimate for the optimal number of turbines on a site; (3) it allows for the                                                                                                                                                        inclusion of more complex site design constraints.                                                                                                                                                                                                                                                                                                                                                                                                                                            We present a number of cases to demonstrate the validity of the                                                                                                                                                                                method.  The optimal number of turbines predicted by the continuous approach is                                                                                                                                                                shown to agree well with the results of running several discrete optimisations                                                                                                                                                                 with different numbers of turbines, giving confidence to the validity of the new                                                                                                                                                               approach.                                                                                                                                                                                                                                      In a realistic case we show how non-convex domain sites can be optimised.                                                                                                                                                                      Furthermore, this approach naturally supports complex constraints such as                                                                                                                                                                      maximum bathymetry gradients above which turbines cannot be installed, and                                                                                                                                                                     the simultaneous optimisation of multiple, potentially interacting farms.},
  year = {2015},
  journal = {European Wave and Tidal Energy Conference 2015},
}