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

Abstract

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.

A BEM-Based Model of a Horizontal Axis Tidal Turbine in the 3D Shallow Water Code SHYFEM

“…θ is defined in Figure 1 for both rotational verses. The lift and drag coefficients C L and C D , respectively, are tabulated as functions of the angle of attack and the Reynolds number; we obtain them by means of interpolation using Re and α from Equations (4) and (5). Finally, the infinitesimal forces on the blade element are calculated as in Equations ( 6) and (7).…”

“…Many studies have dealt with tidal turbine farms performed using shallow water software, but most were 2D studies where the turbine was parameterized by an additional drag force [5][6][7][8][9]. This approximation is useful for saving time and making preliminary evaluations, but it completely neglects the three-dimensional effects, making the analysis incomplete.…”

Vertical-Axis Tidal Turbines: Model Development and Farm Layout Design

“…We can distinguish between two-dimensional and three-dimensional cases: two-dimensional cases adopt a turbine parametrization consisting of increasing the bed friction at the turbine sites, while three-dimensional cases use a momentum sink approach. Some examples of the first approach can be found in [1], where a bed friction model of the turbine was adopted to simulate 12 devices, or in [2], where up to 266 devices were simulated. As the number of devices increases, the turbines become a sub-grid element (i.e., more than one turbine is deployed in a grid element), such as in [3], where more than 8000 devices were analysed.…”

Physical Modelling of Tidal Stream Turbine Wake Structures under Yaw Conditions

“…This would be a common scenario when considering yaw angle control across a tidal stream turbine array. It would also be a vital component to inform the optimisation of tidal stream turbine array design [4,24,25]. Therefore, we experiment with yawed turbine configurations, covering both single-turbine and two-turbine scenarios.…”