Turbine wake and local blockage effects are known to alter wind farm power production in two different ways: (1) by changing the wind speed locally in front of each turbine; and (2) by changing the overall flow resistance in the farm and thus the so-called farm blockage effect. To better predict these effects with low computational costs, we develop data-driven emulators of the ‘local’ or ‘internal’ turbine thrust coefficient CT* as a function of turbine layout. We train the model using a multi-fidelity Gaussian Process (GP) regression with a combination of low (engineering wake model) and high-fidelity (Large-Eddy Simulations) simulations of farms with different layouts and wind directions. A large set of low-fidelity data speeds up the learning process and the high-fidelity data ensures a high accuracy. The trained multi-fidelity GP model is shown to give more accurate predictions of CT* compared to a standard (single-fidelity) GP regression applied only to a limited set of high-fidelity data. We also use the multi-fidelity GP model of CT* with the two-scale momentum theory (Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to demonstrate that the model can be used to give fast and accurate predictions of large wind farm performance under various mesoscale atmospheric conditions. This new approach could be beneficial for improving annual energy production (AEP) calculations and farm optimisation in the future.
Economic model predictive control (EMPC) has received increasing attention in the wind energy community due to its ability to trade off economic objectives with ease. However, for wind turbine applications, inherent nonlinearities, such as from aerodynamics, pose difficulties in attaining a convex optimal control problem (OCP), by which real-time deployment is not only possible but also a globally optimal solution is guaranteed. A variable transformation can be utilized to obtain a convex OCP, where nominal variables, such as rotational speed, pitch angle, and torque, are exchanged with an alternative set in terms of power and energy. The ensuing convex EMPC (CEMPC) possesses linear dynamics, convex constraints, and concave economic objectives and has been successfully employed to address power control and tower fatigue alleviation. This work focuses on extending the blade loads mitigation aspect of the CEMPC framework by exploiting its individual pitch control (IPC) capabilities, resulting in a novel CEMPC-IPC technique. This extension is made possible by reformulating static blade and rotor moments in terms of individual blade aerodynamic powers and rotational kinetic energy of the drivetrain. The effectiveness of the proposed method is showcased in a mid-fidelity wind turbine simulation environment in various wind cases, in which comparisons with a basic CEMPC without load mitigation capability and a baseline IPC are made. Results indicate that CEMPC-IPC can achieve better reduction in rotating blade loads, as well as similar performance in the mitigation of shaft and yaw bearing loads, with the added advantage of convenient economic objectives trade-off tuning.
In this paper, 3D reconstruction of the leading edge of wind turbine blades from images, also known as photogrammetry, is investigated. The technique was applied to a decommissioned blade with an eroded leading edge, with images captured by a smartphone. The reconstructed 3D surface was accurate, when compared to the captured images, despite the small number of images used. A solid model was then created and imported into a finite element modelling software for rain-droplet impact simulations. Photogrammetry is relatively cheap, when compared to other surface scanning techniques, and provides means of monitoring erosion damage when combined with drone imaging. Further investigations of the parameters which control the accuracy of the reconstructed surface must be performed, to fully explore the potential of photogrammetry for 3D reconstruction of leading edge erosion damage.
The filtered lifting line theory is an analytical approach to solving the equations of flow subjected to body forces with a Gaussian distribution, such as used in the actuator line model. In the original formulation 1, the changes in chord length along the blade were assumed to be small. This assumption can lead to errors in the induced velocities predicted by the theory compared to full solutions of the equations. In this work, we revisit the original derivation and provide a more general formulation, that can account for significant changes in chord along the blade. The revised formulation allows for applications to wings with significant changes in chord along the span, such as wind turbine blades.
Accurate assessment of wind energy potential can provide important implication regarding the optimalization of micro-siting of wind turbines and increase of wind power generation. It is, however, noteworthy that most previous studies on wind energy resource assessment focused solely on wind speed, whereas the dependence of wind energy on wind direction was much less considered and documented. In the current study, a copula-based method is proposed to better characterize the direction-related wind energy potential at six typical sites in Hong Kong. In the first step, several widely used statistical models are adopted to fit the marginal distributions of wind speed and direction. The joint probability density function (JPDF) of wind speed and wind direction is therewith constructed by various copula models. The goodness-of-fit evaluation indicates that Frank copula has the best performance to fit the JPDF at hilltop and offshore sites, while Gumbel copula outperforms other models at downtown sites. More importantly, the derived JPDFs are applied to estimate the direction-related wind power density at each of the considered sites, finding a maximum value of wind energy potential of 506.4 W/m2 at a hilltop site. In addition, site-to-site variability is also identified regarding the prevailing wind resource directions. The outcome of this study is expected to be useful for the site selection of wind turbines, as well as the strategic development of wind energy in Hong Kong. Notably, the proposed copula-based method can also be applied to characterize the direction-related wind energy potential somewhere other than Hong Kong.