Hybrid global-local optimisation algorithms for the layout design of tidal turbine arrays

Tidal stream power generation represents a promising source of renewable energy. In order to extract an economically useful amount of power, tens to hundreds of tidal turbines need to be placed within an array. The layout of these turbines can have a significant impact on the power extracted and hence on the viability of the site. Funke et al. [15] formulated the question of the best turbine layout as an optimisation problem constrained by the shallow water equations and solved it using a local, gradient-based optimisation algorithm. Given the local nature of this approach, the question arises of how optimal the layouts actually are. This becomes particularly important for scenarios with complex bathymetry and layout constraints, both of which typically introduce locally optimal layouts. Optimisation algorithms which find the global optima generally require orders of magnitude more iterations than local optimisation algorithms and are thus infeasible in combination with an expensive flow model. This paper presents an analytical wake model to act as an efficient proxy to the shallow water model. Based upon this, a hybrid global-local two-stage optimisation approach is presented in which turbine layouts are first optimised with the analytical wake model via a global optimisation algorithm, and then further optimised with the shallow water model via a local gradient-based optimisation algorithm. This procedure is applied to a number of idealised cases and a more realistic case with complex bathymetry in the Inner Sound of the Pentland Firth, Scotland. It is shown that in cases where bathymetry is considered, the two-stage optimisation procedure is able to improve the power extracted from the array by as much as 25 % compared to local optimisation for idealised scenarios and by as much as 12 % for the more realistic Pentland Firth scenario whilst in many cases reducing the overall computation time by approximately 30 % to 40 %.