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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

Procedia PDF Downloads 232

Authors: Swaleh Aboud, Mishal Gudka, David Obura

Abstract:

Background: Coral reefs are becoming increasingly vulnerable due to several threats ranging from climate change to overfishing. This has resulted in increased management and conservation efforts to protect reefs from degradation and facilitate recovery. Recruitmentof new individuals are isimportant in the recovery process and critical for the persistence of coral reef ecosystems. Local coral community structure can be influenced by successful recruit settlement, survival, and growth Understanding coral recruitment patterns can help quantify reef resilience and connectivity, establish baselines and track changes and evaluate the effectiveness of reef restoration and conservation efforts. This study will examine the abundance and spatial pattern of coral recruits and how this relates to adult community structure, including the distribution of thermal resistance and sensitive genera and their distribution in different management regimes. Methods: Coral recruit and demography surveys were conducted from 2020 to 2022, covering 35 sites in 19coral reef locations along the Kenyan coast. These included marine parks, reserves, community conservation areas (CMAs), and open access areas from the north (Marereni) to the south (Kisite) coast of Kenya and across different reef habitats. The data was collected through the underwater visual census (UVC) technique. We counted adult corals (>10 cm diameter)of23 selected genera using belt transects (25 by 1 m) and sampling of 1 m2 quadrat (at an interval of 5m) for all coloniesless than 10 cm diameter. The benthic cover was collected using photo quadrats. The surveys were only done during the northeast monsoon season. The data wereanalyzed using the R program to see the distribution patterns and the Kruskal Wallis test to see whether there was a significant difference. Spearman correlation was also applied to assess the relationship between the distribution of coral genera in recruits and adults. Results: A total of 44 different coral genera were recorded for recruits, ranging from 3at Marereni to 30at Watamu Marine Reserve. Recruit densities ranged from 1.2±1.5recruit m-2 (mean±SD) at Likoni to 10.3± 8.4 recruit m-2 at Kisite Marine Park. The overall densityof recruitssignificantly differed between reef locations, with Kisite Marine Park and Reserve and Likonihaving significantly large differences from all the other locations, while Vuma, Watamu, Malindi, and Kilifi had significantly lower differences from all the other locations. The recruit generadensity along the Kenya coastwas divided into two clusters, one of which only included sites inKisite Marine Park. Adult colonies were dominated by Porites massive, Acropora, Platygyra, and Favites, whereas recruits were dominated by Porites branching, Porites massive, Galaxea, and Acropora. However, correlation analysis revealed a statistically significant positive correlation (r=0.81, p<0.05) between recruit and adult coral densities across the 23 coral genera. Marereni, which had the lowest densityof recruits, has only thermallyresistant coral genera, while Kisite Marine Park, with the highest recruit densities, has over 90% thermal sensitive coral genera. A weak positive correlation was found between recruit density and coralline algae, dead standing corals, and turf algae, whereas a weak negative correlation was found between recruit density and bare substrate and macroalgae. Between management regimes, marine reserves were found to have more recruits than no-take zones (marine parks and CMAs) and open access areas, although the difference was not significant. Conclusion: There was a statistically significant difference in the density of recruits between different reef locations along the Kenyan coast. Although the dominating genera of adults and recruits were different, there was a strong positive correlation between their coral communities, which could indicate self-recruitment processes or consistent distance seedings (of the same recruit genera). Sites such as Kisite Marine Park, with high recruit densities but dominated by thermally sensitive genera, will, on the other hand, be adversely affected by future thermal stress. This could imply that reducing the threats to coral reefs such as overfishingcould allow for their natural regeneration and recovery.

Keywords: coral recruits, coral adult size-class, cora demography, resilience

Procedia PDF Downloads 103