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. 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 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 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 35%

Integration of cost modelling within the micro-siting design optimisation of tidal turbine arrays

AbstractThe location of individual turbines within a tidal current turbine array – micro-siting – can have a significant impact on the power that the array may extract from the flow. Due to the infancy of the industry and the challenges of exploiting the resource, the economic costs of realising industrial scale tidal current energy projects are significant and should be considered as one of the key drivers of array design. This paper proposes a framework for the automated design of tidal current turbine arrays in which costs over the lifespan of the array may be modelled and considered as part of the design optimisation process. To demonstrate this approach, the cost of sub-sea cabling is incorporated by implementing a cable-routing algorithm alongside an existing gradient-based array optimisation algorithm. Three idealised test scenarios are used to demonstrate the effects of a financial-return optimising design approach as contrasted with a power maximisation approach

Modeling ice-ocean interaction in ice-shelf crevasses

Ocean freezing within ice-shelf basal crevasses could potentially act as a stabilizing influence on ice shelves; however, ice-ocean interaction and ocean dynamics within these crevasses are as yet poorly understood. To this end, an idealized 2-D model of an ice-shelf basal crevasse has been developed using Fluidity, a finite-element ocean model using an unstructured mesh. A simple model of frazil ice formation and deposition has been incorporated into Fluidity to better represent the freezing process. Model results show two different flow regimes, dependent on the amount of freezing in the crevasse: one driven by freezing at the top of the crevasse and the other by the ingress of meltwater from outside the crevasse. In the first, freezing at the top of the crevasse leads to the formation of an unstable overturning circulation due to the rejection of dense, salty water. In the second, a buoyant layer is formed along the sides and roof of the crevasse, stratifying the water column. Frazil ice precipitation is found to be the dominant freezing process at the top of the basal crevasse in the freeze-driven case, with direct freezing being dominant in the melt-driven case. In both cases, melting occurs lower down on the walls of the crevasse due to the strong overturning circulation. The freezing in ice-shelf crevasses and rifts is found to be highly dependent upon ocean temperature, providing a stabilizing influence on ice shelves underlain by cold waters that is not present elsewhere

Shoreline and Bathymetry Approximation in Mesh Generation for Tidal Renewable Simulations

Due to the fractal nature of the domain geometry in geophysical flow simulations, a completely accurate description of the domain in terms of a computational mesh is frequently deemed infeasible. Shoreline and bathymetry simplification methods are used to remove small scale details in the geometry, particularly in areas away from the region of interest. To that end, a novel method for shoreline and bathymetry simplification is presented. Existing shoreline simplification methods typically remove points if the resultant geometry satisfies particular geometric criteria. Bathymetry is usually simplified using traditional filtering techniques, that remove unwanted Fourier modes. Principal Component Analysis (PCA) has been used in other fields to isolate small-scale structures from larger scale coherent features in a robust way, underpinned by a rigorous but simple mathematical framework. Here we present a method based on principal component analysis aimed towards simplification of shorelines and bathymetry. We present the algorithm in detail and show simplified shorelines and bathymetry in the wider region around the North Sea. Finally, the methods are used in the context of unstructured mesh generation aimed at tidal resource assessment simulations in the coastal regions around the UK

Spud 1.0: generalising and automating the user interfaces of scientific computer models

The interfaces by which users specify the scenarios to be simulated by scientific computer models are frequently primitive, under-documented and ad-hoc text files which make using the model in question difficult and error-prone and significantly increase the development cost of the model. In this paper, we present a model-independent system, Spud, which formalises the specification of model input formats in terms of formal grammars. This is combined with an automated graphical user interface which guides users to create valid model inputs based on the grammar provided, and a generic options reading module, libspud, which minimises the development cost of adding model options. <br><br> Together, this provides a user friendly, well documented, self validating user interface which is applicable to a wide range of scientific models and which minimises the developer input required to maintain and extend the model interface

Assessing erosion and flood risk in the coastal zone through the application of multilevel Monte Carlo methods

Coastal zones are vulnerable to both erosion and flood risk, which can be assessed using coupled hydro- morphodynamic models. However, the use of such models as decision support tools suffers from a high degree of uncertainty, due to both incomplete knowledge and natural variability in the system. In this work, we show for the first time how the multilevel Monte Carlo method (MLMC) can be applied in hydro-morphodynamic coastal ocean modelling, here using the popular model XBeach, to quantify uncertainty by computing statistics of key output variables given uncertain input parameters. MLMC accelerates the Monte Carlo approach through the use of a hierarchy of models with different levels of resolution. Several theoretical and real-world coastal zone case studies are considered here, for which output variables that are key to the assessment of flood and erosion risk, such as wave run-up height and total eroded volume, are estimated. We show that MLMC can significantly reduce computational cost, resulting in speed up factors of 40 or greater compared to a standard Monte Carlo approach, whilst keeping the same level of accuracy. Furthermore, a sophisticated ensemble generating technique is used to estimate the cumulative distribution of output variables from the MLMC output. This allows for the probability of a variable exceeding a certain value to be estimated, such as the probability of a wave run-up height exceeding the height of a seawall. This is a valuable capability that can be used to inform decision-making under uncertaint

On the potential of linked-basin tidal power plants: An operational and coastal modelling assessment

Single-basin tidal range power plants have the advantage of predictable energy outputs, but feature non-generation periods in every tidal cycle. Linked-basin tidal power systems can reduce this variability and consistently generate power. However, as a concept the latter are under-studied with limited information on their performance relative to single-basin designs. In addressing this, we outline the basic principles of linked-basin power plant operation and report results from their numerical simulation. Tidal range energy operational models are applied to gauge their capabilities relative to conventional, single-basin tidal power plants. A coastal ocean model (Thetis) is then refined with linked-basin modelling capabilities. Simulations demonstrate that linked-basin systems can reduce non-generation periods at the expense of the extractable energy output relative to conventional tidal lagoons and barrages. As an example, a hypothetical case is considered for a site in the Severn Estuary, UK. The linked-basin system is seen to generate energy 80–100% of the time over a spring-neap cycle, but harnesses at best 30% of the energy of an equivalent-area single-basin design