Tidal turbine array optimisation using the adjoint approach (1304.1768v2)

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.

• The paper presents a novel adjoint approach combined with PDE-constrained optimization to efficiently determine the optimal configuration of large tidal turbine arrays for maximum power extraction.
• The method utilizes the adjoint of the nonlinear shallow water equations, solved with a finite element method, allowing gradient computation for turbine positions and tuning parameters with computational cost nearly independent of array size.
• Demonstrated through various scenarios, including a realistic Pentland Firth model, the optimization significantly increased energy extraction (22-96%), showing potential for economically viable, large-scale tidal energy deployment.

Tidal Turbine Array Optimisation Using the Adjoint Approach

This paper addresses the critical challenge of optimizing the configuration of tidal turbine arrays to maximize power extraction, leveraging a gradient-based optimization algorithm integrated with a physically-realistic model. When deploying hundreds of turbines, determining the optimal layout and tuning for individual turbines becomes notably complex. The authors propose a novel approach by formulating the optimization problem constrained by the nonlinear shallow water equations, solved with an adjoint technique.

A significant contribution of this research is the utilization of an adjoint method to compute the gradient of the power extracted concerning turbine positions and tuning parameters. The adjoint technique is computationally efficient, yielding the gradient at a cost nearly independent of the number of turbines, making it feasible for large-scale applications.

The numerical implementation involves a sophisticated finite element method, and the paper demonstrates the methodology across various idealized scenarios and a realistic simulation modeling the Inner Sound of the Pentland Firth, Scotland. In each scenario, the optimization significantly increased energy extraction—from 22% to 96% improvement depending on the specific setup and constraints.

One of the remarkable results is in the semi-idealized Pentland Firth case, where the method was applied to both 128 and 256 turbine scenarios. It showed potential for substantial power increase by building turbine 'barrages' and optimizing spatial distribution, all with a manageable computational expense using high-performance computing resources.

The implications of this research are profound both theoretically and practically. Theoretically, it advances PDE-constrained optimization practices, offering scalable solutions for renewable energy array optimization. Practically, it lays a foundation for the economic deployment of tidal energy resources, essential for transitioning to renewable energy infrastructures.

Future research directions will require extending these simulations to incorporate variable bathymetry, real-world tidal forcing, and advanced turbulence modeling, aligning model predictions closely with empirical observations. Moreover, optimizing using a realistic power curve including different stages of turbine operation—such as cut-in and cut-out speeds—is crucial for comprehensive industrial application.

Overall, this paper shows how integrating advanced computational techniques with thorough physical modeling can tackle the inherent complexities of large-scale renewable energy resource exploitation, markedly improving the feasibility and economic viability of tidal energy extraction projects. The research outcomes highlight optimism toward impactful renewable energy solutions, addressing intrinsic power and deployment challenges.