Improving tidal turbine array performance through the optimisation of layout and yaw angles

Tidal stream currents change in magnitude and direction during flood and ebb tides. Setting the most appropriate yaw angles for a tidal turbine is not only important to account for the performance of a single turbine, but can also be significant for the interactions between the turbines within an array. In this paper, a partial differentiation equation (PDE) constrained optimisation approach is established based on the Thetis coastal ocean modelling framework. The PDE constraint takes the form here of the two-dimensional, depth-averaged shallow water equations which are used to simulate tidal elevations and currents in the presence of tidal stream turbine arrays. The Sequential Least Squares Programming (SLSQP) algorithm is applied with a gradient obtained via the adjoint method in order to perform array design optimisation. An idealised rectangular channel test case is studied to demonstrate this optimisation framework. Located in the centre of the computational domain, arrays comprised of 12 turbines are tested in aligned and staggered layouts. The setups are initially optimised based on their yaw angles alone. In turn, turbine coordinates and yaw angles are also optimized simultaneously. Results indicate that for an aligned turbine array case under steady state conditions, the energy output can be increased by approximately 80\% when considering yaw angle optimisation alone. For the staggered turbine array, the increase is approximately 30\%. The yaw optimised staggered array is able to outperform the yaw optimised aligned array by approximately 8\%. If both layout and the yaw angles of the turbines are considered within the optimisation then the increase is more significant compared with optimising yaw angle alone.