The modelling and design optimisation of tidal stream turbine arrays
Creators: name: Culley, Dave
Publisher: name: Imperial College London
Year: 2016

description: Tidal stream turbines are devices that convert the momentum of tidally induced marine currents to electricity. Individual turbines typically have a rated power of up to a few megawatts, and thus power may be extracted on an industrial scale by installing arrays of dozens to hundreds of such devices. Accurately modelling such large arrays presents a formidable computational challenge, as the length scale of the problem varies from tenths of a meter (the scale of an individual turbine blade) to several kilometres (the scale of an array) to hundreds of kilometres (the scale of the ocean currents that govern the flow). In addition to this, the sites under consideration are chosen for their highly energetic, advection-dominated flow regimes. Since the power extracted by a turbine is proportional to the cube of the flow speed into which it is placed, the interaction between the turbines and the flow is both highly coupled and highly non-linear. `Array design' concerns determining the array size -- the number of turbines comprising the array -- and the micro-siting -- the locations of the turbines within the turbine site that has been leased by the array developer. For large arrays in real-world domains the micro-siting designer is faced with hundreds or thousands of control parameters that impact the farm performance through hydrodynamic interactions. Non-hydrodynamic factors such as technical, financial and practical engineering constraints can also have a significant impact upon the design decision. Thus, going beyond modelling such arrays to optimising their design adds an additional dimension of complexity to the problem. Manual optimisation over such large parameter spaces with complex nonlinear constraints is difficult, and there is little practical industrial experience to guide designs. As such the array design problem requires the deployment of specially designed computational tools which can balance the need for accurate evaluation of the hydrodynamics of the interactions between the flow and the array with a suitable optimisation strategy to achieve an efficient and scalable array design paradigm. This thesis documents work to develop and expand the utility of one such software tool; OpenTidalFarm, with the goal of developing a practical approach to array design optimisation and constructing a framework for the inclusion of wide ranging and disparate design criteria. OpenTidalFarm solves the Shallow-Water and associated adjoint equations to evaluate the power extracted by the array and the sensitivity of that power to the posisitions of the turbines. This work is aimed demonstrating that industrial sized turbine arrays may be designed within a broad range of constraints and optimised for complex and occasionally conflicting objectives. This is achieved through exploration of a collection of optimisation approaches including mixed fidelity hybrid global/local schemes for turbine layout, variable fidelity Bayesian optimisation for array size and integrating integer, routing optimisation for inclusion of location-based costs. The first chapter of this thesis introduces the engineering and practical aspects of the problem, while in the second chapter the numerical methods and optimisation techniques through which the problem can be tackled are presented. A family of alternate modelling and optimisation approaches are developed, tested and compared in Chapter 4, to understand how alternate approaches to the problem can be formulated by limiting the complexity of the problem, analysis or optimisation, and how this may successfully be done to suit the designer's available computational budget. In Chapter 5, a framework is presented in which costs over the lifespan of the array may be modelled and considered as part of the design optimisation process. Idealised scenarios are used to demonstrate the effects of a financial-return optimising design approach as contrasted with a power maximisation approach. The impact of non-hydrodynamic considerations on array design is shown to be potentially high. In Chapter 6 the broader question of array sizing is presented and a surrogate model is used to efficiently determine the optimal number of turbines to install on a given site based, once again, on a simple financial model. It is demonstrated that lower turbine densities on sites (between 20 % and 40 % of the maximum density the site could support) maximises the developer's profit on the installation and prevents diminishing returns on investment of additional turbines.