Tidal turbine array optimisation using the adjoint approach

Abstract

Oceanic tides have the potential to yield a vast amount of renewable energy. Tidal stream generators are one of the key technologies for extracting and harnessing this potential. In order to extract an economically useful amount of power, hundreds of tidal turbines must typically be deployed in an array. This naturally leads to the question of how these turbines should be configured to extract the maximum possible power: the positioning and the individual tuning of the turbines could significantly influence the extracted power, and hence is of major economic interest. However, manual optimisation is difficult due to legal site constraints, nonlinear interactions of the turbine wakes, and the cubic dependence of the power on the flow speed. The novel contribution of this paper is the formulation of this problem as an optimisation problem constrained by a physical model, which is then solved using an efficient gradient-based optimisation algorithm. In each optimisation iteration, a two-dimensional finite element shallow water model predicts the flow and the performance of the current array configuration. The gradient of the power extracted with respect to the turbine positions and their tuning parameters is then computed in a fraction of the time taken for a flow solution by solving the associated adjoint equations. These equations propagate causality backwards through the computation, from the power extracted back to the turbine positions and the tuning parameters. This yields the gradient at a cost almost independent of the number of turbines, which is crucial for any practical application. The utility of the approach is demonstrated by optimising turbine arrays in four idealised scenarios and a more realistic case with up to 256 turbines in the Inner Sound of the Pentland Firth, Scotland.

Optimization of wind plant layouts using an adjoint approach

“…These approaches benefit from high-fidelity CFD and leverage the power of adjoint optimization but have only been applied for fixed layouts. Finally, Funke et al (2014) performed an adjoint optimization of ocean turbine layouts using an analysis based on the shallow water equations, with ocean turbines represented by increased bottom friction.…”

Towards a Low-Cost Modelling System for Optimising the Layout of Tidal Turbine Arrays

“…The force is distributed evenly over the area of the grid cell. A final approach uses increased bed roughness to simulate the drag induced by energy extraction on the flow (e.g., [19,20,30,31]). Disadvantages of this approach are that it cannot account for the dimensions or performance characteristics of the turbine and energy is always captured from the flow regardless of the flow direction; this is unrealistic in the case of horizontal axis turbines whose orientation is typically fixed.…”

“…This allows the flows around individual turbines and interactions between adjacent turbines in an array to be resolved. This approach is similar to those of [19,20] who also use selective high resolution around turbines in 2D, depth-averaged, far-field models to capture the hydrodynamic interactions between adjacent turbines in arrays, with a view to optimising array layouts. Reference [19] used an irregular mesh to obtain the higher resolution while reference [20] used a regularly-spaced adaptive mesh.…”

“…This approach is similar to those of [19,20] who also use selective high resolution around turbines in 2D, depth-averaged, far-field models to capture the hydrodynamic interactions between adjacent turbines in arrays, with a view to optimising array layouts. Reference [19] used an irregular mesh to obtain the higher resolution while reference [20] used a regularly-spaced adaptive mesh. In the present model, the optimisation of array layouts is not conducted directly during the simulation; rather a number of simulations of single and twin turbine deployments are used to investigate turbine interactions with regard to power capture and the results are used to inform the optimum placement and spacing of turbines in a multi-row array.…”

“…The model of [20] is also incapable of directly conducting optimisation of layouts and is used to compare the energy capture from arrays of different layouts. By comparison, reference [19] combined a gradient-based optimisation algorithm with a shallow water flow model to carry out optimisation in a single simulation whereby turbines are repositioned and flows recalculated in an iterative manner. The authors are currently working to develop such optimising functionality within our model.…”