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A novel design optimization model for placing frequencies of a wind turbine tower/nacelle/rotor structure in free yawing motion is developed and discussed. The main aim is to avoid large amplitudes caused by the yawing-induced vibrations in the case of horizontal-axis wind turbines or rotational motion of the blades about the tower axis in case of...
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... system to be analyzed is illustrated in Fig. 1. The rotor/nacelle combination is considered as a rigid body with mass polar moment of inertia I N spinning about the vertical axis, X, at an angular displacement c(t) relative to the top of the tower. The tower is in the state of free torsional vibration about its centroidal axis with an absolute angular displacement denoted by j(x, ...
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... a tapered, thin-walled tower, the various cross sectional parameters are defined by the following expressions (refer to Fig. ...
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... scope of the present work is to perform first the necessary exact dynamical analysis of a practical model of the wind turbine in order to be able to place the frequencies at their target values. Secondly, the behavior of the yawing fundamental frequency will be investigated in detail to see how it changes with the selected design variables. Cases of study include the locked and unlocked conditions of the yawing mechanism. Design variables encompass the cross- sectional properties of the tower and its tapering ratio, as well as the yawing stiffness and the rotor/nacelle inertia ratios. It is demonstrated that global optimality can be achieved from the proposed model and an accurate method for the exact placement of the system natural frequencies is deduced. The system to be analyzed is illustrated in Fig. 1. The rotor/nacelle combination is considered as a rigid body with mass polar moment of inertia I N spinning about the vertical axis, X , at an angular displacement c ( t ) relative to the top of the tower. The tower is in the state of free torsional vibration about its centroidal axis with an absolute angular displacement denoted by j ( x , t ). The yawing mechanism is assumed to have a linear torsional spring with a stiffness K y . Applying the classical theory of torsion [12], the governing equation of the motion is cast in the ...
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... boundary conditions are obtained by substituting for d 2 q = d t 2 1⁄4 À o 2 q in Eq. (2) to get: at x 1⁄4 0 F ð x Þ 1⁄4 0 GJ d F GJ d F at x 1⁄4 H c o d x À K y 1⁄4 0 ; c o 1⁄4 o 2 I N d x À F . ð 4 Þ Considering a tapered, thin-walled tower, the various cross sectional parameters are defined by the following expressions (refer to Fig. 1): mean radius : r 1⁄4 r o ð 1 À b x ^ Þ , wall thickness : h 1⁄4 h o ð 1 À b x ^ Þ , torsional constant : J 1⁄4 I p 1⁄4 2 p r 3 h . ð 5 Þ The variables r and h are assumed to have the same linear distribution, and x ^ and b are dimensionless quantities defined ...
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Citations
... This model results from the coupling of an existing aerodynamic model and a structural model based on a segregated formulation derived in an index-based notation that enables combining very different descriptions such as rigid-body dynamics, assumed-modes techniques and finite element methods. Also, a novel design optimization model for placing frequencies of a wind turbine tower/nacelle/rotor structure in free yawing motion was developed and discussed by Karam and Maalawi [2]. The main aim was to avoid large amplitudes caused by the yawing-induced vibrations in the case of horizontal-axis wind turbines or rotational motion of the blades about the tower axis in case of vertical-axis wind turbines. ...
Wind turbines are kinds of electricity generators, proliferating nowadays due to their consistency with the environment. The rotation of the wind turbine blades duo to wind, burdens some frequencies on the wind turbine tower. Therefore, in addition to common design due to service loads, the wind turbine tower should be checked in the frequency analysis so that its natural frequencies do not coincide with the frequencies caused by blades rotation, resulting in the resonance of the tower and its failure. This makes the design of these structures to be complex. In this research, the frequency analysis of the lattice tower of a three-blade horizontal-axis wind turbine including different sources of nonlinearities, i.e., geometric, material and joint slip effect is carried out and the natural frequencies are obtained using the developed Nonlinear Analysis Software for Towers -NASTower-. It is observed that the joint slip effect can substantially reduce the natural frequencies of the lattice tower, which are significant in the design of these structures. In addition, the wind turbine displacements due to different design load cases are investigated, indicating that incorporating the joint slip effect into the analysis substantially increases the wind turbine displacements, which could affect on its performance.
... It is crucial to perform the optimization procedure of the wind turbine design and especially wind turbine tower to minimize vibration-inducted forces [36]. Efficient model for optimizing frequencies of a wind turbine blade in pitching motion was presented in article [37] in order to avoid resonance of the wind turbine design. Reduction of vibration is a good measure for a successful design of blade structure [38]. ...
Wind energy using increased dramatically in the last years. Because of that wind turbine design should be improved to increase efficiency. To make wind turbine with the best characteristics and with the highest efficiency it is suitable to analyze factors that are truly relevant to the converted wind energy. Wind turbine innovative design is investigated in this paper by the theory of inventive problem solution (TRIZ) as a systematic methodology for innovation. TRIZ methodology should provide creative conceptual design ideas of wind turbine. The main aim of this work is to show a systematic methodology for innovation as an effective procedure to enhance the capability of developing innovative products and to overcome the main design problems. The TRIZ method will be used in order to eliminate the technical contradictions which appear in the wind turbine systems.
... Uys et al. [4] studied the problem of minimum cost design of steel wind towers where the optimum shell thickness, number of stiffeners and dimensions of the stiffeners were defined. Maalawi [5] presented a design optimization model for engaging wind tower structure frequencies (tower/nacelle/rotor) in free yawing motion. The objective of the work by Silva et al. [6] was to find optimized designs of reinforced concrete (RC) towers taking into consideration the cost, computational time, construction techniques and precision of structural models, when subjected to dynamic wind loads while considering the vibration effects of the wind energy generator's components. ...
The objective of this work is to propose a design procedure, formulated as a structural design optimization problem, for designing steel wind towers subject to constraints imposed by the Eurocode. For this purpose five test examples are considered, in particular steel wind towers varying on their height are optimally designed with minimum initial cost, while the wind load is calculated according to Eurocode 1 Part 2–4 and design constraints imposed by Eurocode 3 on shell buckling and local buckling of flat ring-stiffeners are implemented. Furthermore, two formulations are examined differing on the shape of the wind tower along the height. While, for the solution of the optimization problem the Optimization Computing Platform (OCP) was used.
... Studies have been done on optimising the dynamic behaviour of the yaw system during the wind turbine design phase by tuning turbine structural parameters [4], for instance by reducing the stiffness of the yaw drive [5]. The principle of achieving active yaw control by extending recent blade load reduction techniques such as Individual Pitch Control (IPC) has recently been described in [6]. ...
Individual pitch control (IPC) for reducing blade loads has been investigated and proven successful in recent literature. For IPC, the multi-blade co-ordinate (MBC) transformation is used to process the blade load signals from the rotating to a stationary frame of reference. In the stationary frame of reference, the yaw error of a turbine can be appended to generate IPC actions that are able to achieve turbine yaw control for a turbine in free yaw. In this paper, IPC for yaw control is tested on a high-fidelity numerical model of a commercially produced wind turbine in free yaw. The tests show that yaw control using IPC has the distinct advantage that the yaw system loads and support structure loading are substantially reduced. However, IPC for yaw control also shows a reduction in IPC blade load reduction potential and causes a slight increase in pitch activity. Thus, the key contribution of this paper is the concept demonstration of IPC for yaw control. Further, using IPC for yaw as a tuning parameter, it is shown how the best trade-off between blade loading, pitch activity and support structure loading can be achieved for wind turbine design.
... This would avoid resonance where large amplitudes of torsional vibration could severely damage the whole structure. The frequency-placement technique [7,8] is based on minimizing an objective function constructed from a weighted sum of the squares of the differences between each important frequency and its desired (target) value. Approximate values of the target frequencies are usually chosen to be within close ranges; sometimes called frequency windows; of those corresponding to a reference baseline design, which are adjusted to be far away from the critical exciting frequencies. ...
With the growing demand for cost-effective wind energy, optimization of wind turbine components has been gaining increasing attention for its acknowledged contributions made to design enhancement, especially in early stages of product development. One of the major design goals is the accurate determination of structural dynamics and control, which is directly related to fatigue life and, hence the cost of energy production. In case of stronger winds it is necessary to waste part of the excess energy of the wind in order to avoid damaging the wind generator. Therefore, modern wind turbines are designed with pitch-regulated rotor blades, which have to be able to turn around their longitudinal axis several times per second in order to face the rapidly changing wind direction. There are frequent pitch-control system failures world-wide on wind turbines, where some statistical studies indicated that such failures accounts for about 6-11% of breakdowns in any given year the wind plant is in operation. This fact emphasizes the need to improve the design of pitch mechanisms using optimization techniques in order to increase availability of the turbines and reduce their maintenance overheads.
This chapter presents a model for optimizing a pitch-regulated blade in torsional motion. Exact solutions of the resulting governing differential equation are given by utilizing analytical Bessel's functions of the first kind. Design variables encompass the tapering ratio, blade chord and skin thickness distributions, which are expressed in dimensionless form, making the formulation valid for a variety of blade configurations. The functional behavior of the frequency has been thoroughly examined and the developed exact mathematical model guarantees its full separation from the undesired range which resonates with the pitching frequencies. This may further other design objectives such as higher stability and fatigue life and lower cost and noise levels. Design constraints are imposed on the total structural mass in order not to violate other economic and performance requirements. In fact, the mathematical procedure implemented, combined with exact Bessel's function solutions, can be beneficial tool, against which the efficiency of approximate methods, such as finite elements, may be judged.
... It is concluded that as tapering increases, frequency decreases. The towers that have completely conical shapes may have the maximum frequencies; however, these types of formations are not serviceable for adequate space at the top of the tower in order support the rotor/nacelle combination [9]. ...
... 9 shows that the onshore wind turbine has 6.9 rpm cut in rotor speed and 12.1 rpm rated rotor speed. The main goal is to stay away from resonance. ...
... One of the most cost-effective solutions in designing efficient yaw mechanisms and reducing the produced vibrations is to separate the natural frequencies of the tower/nacelle/rotor structure from the critical exciting yawing frequencies. An optimization model was developed by (Maalawi, 2007) showing the necessary exact dynamical analysis of a practical wind turbine model, shown in Fig. 5, for proper placement of the system frequencies at their target values. The rotor/nacelle combination was considered as a rigid body with mass polar moment of inertia I N spinning about the vertical axis x at an angular displacement ψ(t) relative to the top of the tower,where t is the time variable. ...
... Several case studies were investigated and discussed in (Maalawi, 2007). A specific design case for locked yawing mechanism is shown in Fig. 6. ...
... This would avoid resonance where large amplitudes of torsional vibration could severely damage the whole structure. The frequency-placement technique [7,8] is based on minimizing an objective function constructed from a weighted sum of the squares of the differences between each important frequency and its desired (target) value. Approximate values of the target frequencies are usually chosen to be within close ranges; sometimes called frequency windows; of those corresponding to a reference baseline design, which are adjusted to be far away from the critical exciting frequencies. ...
This article presents a mathematical model for optimizing frequencies of a wind turbine blade in pitching motion. Related design problems include the excessive blade torsional vibrations induced by continuous pitching, which is necessary to limit the power output and protect generator from damages in severe wind conditions. This, in turn, can have adverse effects on the fatigue life of the blades and might cause catastrophic failures near the resonant frequencies. The study considers a blade tapered linearly towards the tip representing the effective aerodynamical surface for producing the needed power. The blade inboard portion is modelled by an equivalent torsional spring simulating the torsional stiffness near the root. The model provides exact solutions of the resulting governing differential equation by utilizing analytical Bessel's functions of the first kind, where the functional behaviour of the torsional frequency has been thoroughly examined. The associated optimization problem is formulated by considering two forms of the objective function. The first one is represented by a direct maximization of the fundamental frequency, while the second one considers minimization of the square of the difference between the fundamental frequency and its target or desired value. In both strategies, an equality constraint is imposed on the total structural mass in order not to violate other economic and performance requirements. Design variables encompass the blade tapering ratio, chord, and shear wall thickness distributions, which are expressed in dimensionless form, making the formulation valid for a variety of blade configurations. In fact, the mathematical procedure implemented can be regarded as a beneficial design tool, in which significant increase in the overall stiffness/mass ratio level of the blade structure combined with full separation of the frequency from the undesired range that resonates with the pitching frequencies can be achieved.
This paper presents the first investigation on a high-fidelity linear time-invariant aeroelastic model of multi-rotor wind turbines with three-bladed rotors. The modeling method developed in this work integrates the rotor model from the aeroelastic single-rotor wind turbine stability software HAWCStab2 with a model of the support structure in the aeroelastic multi-body tool HAWC2.
The method is used to analyze the linear aeroelastic response of the DTU 30 MW tri-rotor wind turbine to see if the system experiences any aeroelastic instabilities or has any critical low damped modes. Furthermore, a comprehensive aeroelastic analysis of the DTU 10 MW wind turbine is performed and used to compare rotor modes between the two types of wind turbines. The results from the aeroelastic analysis are visualized using a developed mode-clustering algorithm utilizing an extension of the modal assurance criterion.
The results show that the tri-rotor wind turbine does not have any aeroelastic instabilities. Comparing the rotor modes of the single-rotor and the tri-rotor wind turbine shows that the dynamics of the lower rotors change significantly both in natural frequencies and damping ratios. This means that it can be sub-optimal to use the rotor from a single-rotor on a multi-rotor configuration. It is found that for multi-rotor wind turbines with arm structures the vertical arm-bending modes are low damped and therefore at risk of aeroelastic instabilities in addition to the side-side tower modes.
The aeroelastic multi-rotor wind turbine modeling framework is verified by comparing frequency response functions with a nonlinear model in HAWC2.
The main aim of a conceptual design is to obtain the innovative projects or ideas to enable the products and designs with best performance, what is also including the materials especially ceramics optimal selection for the effective solutions. The theory of inventive problem solution (TRIZ) is a systematic methodology for innovation. The design of a wind turbine system as an engineering example is illuminated in this paper to show the significance and approaches of applying TRIZ in getting the creative conceptual design ideas. In recent years the use of renewable energy including wind energy has risen dramatically. Because of the increasing development of wind power production, improvement of the design and control of wind turbines is necessary. To optimize the power produced in a wind turbine, it is important to analyze the wind turbine designs and systems. To build a wind turbine model with the best features, it is desirable to analyze factors that are truly relevant to the converted wind energy. The main aim of this work is to show a systematic methodology for innovation as an effective procedure to enhance the capability of developing innovative products and to overcome the main design problems. The TRIZ method will be used in order to eliminate the technical contradictions which appear in the wind turbine systems.
