Sway vibration control of floating horizontal axis wind turbine by modified spar-torus combination
Introduction
Spar-type floating offshore wind turbines consist of mooring supports, floating spar, a long and flexible tower supporting nacelle and rotor at the top. Unlike onshore turbines, which are exposed to turbulent wind, the primary source of vibration for offshore floating turbines is the hydrodynamic load. In this structural set-up, small vibration of spar (i.e. tower base) due to sea wave can cause an amplified response at the nacelle (i.e. tower top). It is more pronounced under wind-wave misalignment, which is often reflected in the side-to-side response of tower or nacelle. This unwanted side-wise vibration can cause significant damage to electro-mechanical systems (notably, the gearbox). In this context, gearbox maintenance costs maximum revenue loss and downtime for any operational wind turbine. Therefore, nacelle vibration, especially in the side-to-side direction, should be kept as minimum as possible.
Due to this reason, the research activities in the recent past have been focused on different aspects of efficient modelling, analysis and design of wind turbines. Among them, vibration control has remained an open problem for the wind turbine industry. Li et al. (2020) have explored the effects of the yaw error and wind-wave misalignment on the dynamics and power generation of floating turbines using FAST. Their study indicates that yaw error can result in reduced power generation without adverse effects, while wind-wave misalignment significantly affects the dynamics of the structure. Kyle et al. (2020) have investigated the propeller and vortex ring states of NREL 5 MW floating turbine when subjected to strong waves and low wind using CFD analysis. Their study has shown that negative thrust can occur in regions of high twist angles. Li et al. (2019) have also studied the dynamics of a semi-submerged offshore wind turbine subjected to turbulent wind flow to investigate the effects of wind shear, turbulence intensity and coherence on the responses of the turbine structure. They have noticed that increased turbulence can create violent shaking of the platform, which, in turn, increases structural loads on the turbine significantly. They have suggested the use of a partial coherence structure to ensure the safety of the wind turbine. Liu et al. (2019) have analysed the reliability of floating wind turbine considering wind and wave loads with no misalignment between them. They have observed that edgewise blade response can be considerably larger in offshore turbines compared to its onshore counterpart, thereby adversely affecting the fatigue life at the blade root.
Besides improved analysis and design of turbines, vibration control also plays a significant role in performance enhancement. Skaree et al. (Skaare et al., 2007) have studied the effects of conventional generator torque and blade pitch control strategies on fatigue life of floating wind turbines. In this context, both torque and pitch control reduce loads on the turbine, where torque control operates below the rated speed while pitch control works above it. But there are design limitations with these strategies, e.g. power output fluctuations and stress development in electro-mechanical components (Horiuchi and Kawahito, 2001). Other than these techniques, several studies have been carried out in the recent past on vibration control of wind turbine structures using different passive or semi-active devices (Lackner and Rotea, 2011a, 2011b). Sun (2018) has investigated the performance of semi-active tuned mass dampers for vibrations mitigation of floating turbines considering wind-wave misalignment. However, the tuned mass damper can create adverse effects and increase the response of several components, particularly under wind-wave misalignment. Also, one of the significant problems with tuned mass dampers is housing a large mass within the tower or nacelle, which has limited or no space. Other advanced methods like rotational inertia of double-tuned mass damper (Garrido et al., 2013), magneto-rheological tuned liquid column damper (Sarkar and Chakraborty, 2018), tuned mass-damper-inerter system (Marian and Giaralis, 2014; Sarkar and Fitzgerald, 2019) have been extensively studied for vibration control of turbines. Park et al. (2020) have suggested orthogonal tuned liquid column dampers inside the nacelle to control the fore-aft and side-to-side responses of floating turbines. Besides these passive devices, the performance of individual blade pitch control (IBP) and disturbance accommodating control (DAC) strategies for floating offshore wind turbines have been investigated by Namik and Stol, 2010, 2011. Their study has shown improvement of different structural performances (e.g. platform pitching motion, fatigue load on turbine blades and side-to-side motion of tower), thereby reducing power fluctuations.
Sarkar et al. (2020) have proposed a multi-resolution wavelet pitch controller for improving the dynamics of spar type offshore wind turbines. Their control algorithm has shown a reduction of aerodynamic loads and subsequent dynamic responses in all modes. Madsen et al. (2020) have experimentally studied different close and open-loop control strategies on the scaled model of a 10 MW turbine supported by tension leg platforms. They have noticed that surge motion of the turbine governs the tension in the mooring cables. At the same time, negative aerodynamic damping of the controller can increase the vibration leading to higher responses in the surge, which can cause increased stresses and failure of the supporting structures. Han and Nagamune (2019) have studied platform position control in offshore wind farms to mitigate the effect of aerodynamic wakes considering disturbances in the wind and wave loading. Their study has shown that with the use of linear quadratic integrator control algorithm adequately designed to achieve the targeted platform positions can maximize the power output by substantially reducing the wake effects.
As vibration control of wind turbine is currently an active area of research, new ideas and techniques are coming up very often, and the industries have also embraced some of these options for further development (Jensen, 2016; Smith, 2002). For example, Spar-Torus Combination (STC) has been proposed by Muliawan et al. (2012), where a donut-shaped Wave Energy Converter (WEC) is attached with the spar-type floating wind turbine (FWT). Although torus designed in this format does not help in controlling spar vibration, its performance in trapping additional wave energy is impressive. Later, other studies have investigated its effect on the structural responses and power generation in both operational and extreme sea conditions (Muliawan et al., 2013a, 2013b, 2013c). These studies have observed that combining torus with a spar can increase power production. However, it can also increase forces in mooring lines with additional bending moments in the tower, causing new challenges in design against ultimate limit state and fatigue. Wan et al. (2014) have conducted laboratory tests on possible slamming effect and green water effect of STC. Their studies have shown that submerging the torus in case of extreme sea conditions can reduce the forces induced in the mooring lines and also the bending moments in the tower. Ren et al. (2020) have developed a new concept by combining wave energy converters (WEC) in the tension leg platform (TLP) of a floating wind turbine. Dynamic responses of the combined system have been studied numerically and experimentally with a scaled model that has a fair agreement. Although the primary focus of these studies is on harnessing wave energy in operational sea states, the use of torus to control the response has not been investigated. Yue et al. (2020) have studied the positive effects of installing a heave plate in the spar of the floating offshore wind turbines. Ren et al. (2015) have estimated the long term performances and fatigue life of STC using a simplified thrust model of wind loading. They have also developed two different survival modes to reduce long term fatigue damage and extreme responses.
The literature review presented above clearly outlines the need for vibration control of a floating wind turbine under different operational conditions. In this context, spar type floating turbines have proved themselves as a viable option for deep-sea wind farms. Availability of strong wind for longer duration in the marine environment makes them more profitable in the long run. However, they are exposed to a significant level of vibration due to the combined action of aero-hydrodynamic loads. Although previous studies have proposed different strategies for vibration control, it has remained an open problem. In this context, STC shows promising results in terms of power generation due to wave energy conversion. However, STC, in its present form, does not offer significant vibration control. This motivates to investigate the design of spar type floater by modifying the torus to act as a vibration isolator. Thus, the objectives of this study are as follows.
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Develop the concept of modified spar-torus combination by introducing spring and dashpot for wave load isolation to improve the dynamics of spar type floaters. This spring and dashpot in between spar and torus have the potential to isolate hydrodynamic loads from the spar, thereby, reducing its response significantly. The energy is dissipated as the torus is allowed to vibrate in the surge (i.e. along-wind) and sway (i.e. side-to-side). As the wave loads are higher near the surface, an adequately designed torus is bound to provide significant vibration control, particularly under wind-wave misalignment.
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Formulate detailed mathematical model using Kane's approach for a modified spar-torus combination attached to the mooring cables. This multi-body dynamic framework helps to reduce the degrees of freedom to its minimum while modelling the highly non-linear system of a floating turbine assembly.
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Demonstrate the performance of the proposed modified spar-torus combination under the different operational scenario in the marine environment to examine its performance envelope, particularly in sway (i.e. side-to-side) direction, which is the main objective of this work.
The spar-torus combination (Muliawan et al., 2012) has a light donut-shaped floating buoy (i.e. torus) as a wave energy converter. This combination is modified in this study, where the torus is used as a floater that isolates wave energy. As stated above, the modified spar-torus combination (MSTC) (refer Fig. 1) acts as a vibration absorber that primarily controls the response of a floating wind turbine in passive mode. Here, it may be noted that the magnitude of the hydrodynamic load is maximum near the surface and decreases with depth. Thus, torus encircling the part of the spar near the sea surface effectively isolates the incident hydrodynamic loads. Fig. 1 shows the modified spar-torus combination, which consists of the following key elements.
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A floating spar is used to support the wind turbine. The dimensions of the spar depend on the size of the turbine, its power rating, water depth and wind profile at the site. The spar is moored with the help of catenary, to support the turbine.
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A modified torus is a hollow cylindrical shaped floating buoy, encircling the spar up to a sufficient depth to effectively isolate wave loads. It can move in two orthogonal directions (i.e. surge and sway) relative to the spar.
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The ballast tanks inside the spar and torus bring their centre of gravity below their centre of buoyancy to provide sufficient stability to carry a heavy wind turbine on top of it.
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The bearing system along the outer periphery of the spar consists of flexible spring and dashpot, as shown in Fig. 1 to connect the torus with the spar and allowing it to have relative translations in surge and sway and no rotation.
Section snippets
Dynamics of spar-type floating wind turbine
In this section, the dynamics of a spar-type offshore wind turbine coupled with a modified torus system is formulated using Kane's approach (Kane and Levinson, 1985). It is based on the vector representation of forces for solving a multi-body dynamic problem, which provides significant computational advantages. In this approach, the offshore floating wind turbine is modelled by 22 degrees of freedom (DOFs) whose details are given in Table 1. The proposed modified torus can move in the surge and
External loads on floating wind turbine
Different external loads act on a floating wind turbine, namely, aerodynamic load on blades and tower, hydrodynamic load on spar and torus and mooring forces arising from the anchoring cables. For brevity, the detailed description for these loads is not presented in this paper. Only the necessary details of modelling these loads are discussed below for completeness.
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Aerodynamic Load: In general, aerodynamic lift and drag forces act on the blades and only the drag forces act on the tower. In this
Numerical results & discussion
This section presents the numerical analysis of the proposed MSTC to control the vibration of a spar-type FWT. Aerodynamic and hydrodynamic loads are simulated, considering wind-wave correlation and misalignment. For mathematical modelling of Spar-type FWT, the benchmark properties of NREL 5 MW wind turbine on the OC3-Hywind spar (Jonkman, 2010) is used here. Six different time histories [spar surge () and sway (), spar roll () and pitch (), tower top fore-aft () and
Conclusions
A new concept for vibration control of a spar-type floating wind turbine using modified torus is presented in this work. The proposed modification isolates wave energy, which ultimately affects the dynamics of spar supporting the blade-tower assembly. An aero-servo-elastic multi-body dynamic model using Kane's approach is developed to study the performance of the proposed system. Different aerodynamic and hydrodynamic loading conditions ranging from cut-in to cut-out wind speed with
CRediT authorship contribution statement
Arka Mitra: Methodology, Software, Development and, Writing - original draft. Saptarshi Sarkar: Methodology, and, Software, Development. Arunasis Chakraborty: Conceptualization, Investigation, Supervision, Writing - review & editing. Sourav Das: Software, Development and Numerical Analysis.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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