Tower Oscillations Research Articles

RETRACTED: Maximizing output power and reducing tower oscillations: Controller design for a gearbox-free wind turbine

This study focuses on the development of a dynamic wind turbine system without a gearbox, with the primary objectives of adjusting output power, and generator torque and reducing tower oscillations through the design of an effective controller. The design of the controller faces challenges in selecting an appropriate mathematical model that strikes a balance between simplicity and comprehensiveness while accounting for the essential physical phenomena affecting the system. Enhancing the accuracy of the system model is crucial to improve the controller's efficiency and achieve a better approximation of the system dynamics. Therefore, this study addresses the two-fold problem of maximizing modeling accuracy while maintaining model simplicity. To capture the dynamic behavior of the wind turbine, the analysis considers three degrees of freedom: rotor rotation, kinetic pitch chain, and reciprocating motion of the tower. The tower and kinetic chain are modeled as flexible components to accurately represent their behavior. The objectives of designing controllers for wind turbines encompass maximizing output power and reducing structural vibrations, aiming to minimize the total cost associated with energy generation and turbine maintenance. To achieve this, the mathematical models developed for turbine modeling need to account for the flexibility of components that exhibit high flexibility in practical scenarios. Notably, the tower is modeled as a separate flexible object, considering its degrees of freedom, while the kinetic chain is modeled as a flexible object due to the high damping coefficient and flexibility of the shaft in a gearbox-free wind turbine. In addition to maximizing output power, ensuring system stability is of paramount importance in the absence of a gearbox. Fluctuations in generator rotational speed can escalate rapidly, leading to system instability. Therefore, precise adjustment of generator speed and torque plays a critical role in maintaining system stability. The results show that the proposed method could model the wind turbine in a better way that the maximum error of rotational speed in comparison with the real data is about 3.4%. In addition, the oscillation speed error of the tower top is about 2.3%.

In situ estimation of effective rock elastic moduli by seismic ambient vibrations

In this study, we performed a non-invasive ambient noise investigation of unsaturated rock structures in the Bohemian Paradise (Bohemian Cretaceous Basin, Czech Republic). Our study focused on two key topics: 1) An in situ elastic moduli estimate of competent, horizontally deposited sandstone layers using ambient noise array measurements. Recordings were processed using an f-k array analysis, from which frequency-dependent Love and Rayleigh wave dispersion curves, as well as Rayleigh wave ellipticity, were retrieved. Data were inverted for the P- and S-wave velocity profiles, from which Young's and shear moduli were successfully estimated. 2) A study of the local response of the Kapelník rock tower. We analysed a dataset of ambient noise recordings obtained from the top of the tower and its foot. Information regarding tower oscillation frequencies and directions, together with amplification ratios, were retrieved from a particle motion polarisation analysis and from site-to-reference spectral ratios. Euler-Bernoulli beam theory was also employed for interpreting measured data using elastic moduli estimated from noise array measurements.

A multi-stable ultra-low frequency energy harvester using a nonlinear pendulum and piezoelectric transduction for self-powered sensing

This paper presents the design, theoretical modelling and experimental validation of a quad-stable energy harvester for harnessing ultra-low frequency random motions using a nonlinear pendulum and piezoelectric transduction. The multi-stable pendulum is created by the magnetic forces between magnets on the pendulum and a tip magnet on a piezoelectric cantilever beam. Two attractive and one repulsive magnetic forces in combination with the gravitational force of the pendulum create multiple stable positions for the pendulum. The multi-stable dynamics allow the pendulum to effectively convert low-frequency random kinetic motions from the host, e.g. human motion or wind turbine tower oscillation into the pendulum oscillation, enabling effective plucking of the piezoelectric beam with enhanced output power. A theoretical model, including the magnetic interaction, piezoelectric conversion and pendulum dynamics, is established to describe the electromechanical dynamics of the whole harvester. A prototype is fabricated and tested on a linear shaker at ultra-low frequencies (1–3 Hz) to showcase the capability of the harvester and to validate the theoretical results. Around 8 μW Root-Mean-Square output power was obtained at 2.5 Hz and 0.8 g of excitation. Using the experimentally validated theoretical model, a parametric study was carried out to examine the influence of different structural and operating parameters, such as pendulum mass and length, magnetic coupling strength, excitation frequency and amplitude, on the output power and operating frequency range of the energy harvester. The operation frequency range and output power can be effectively adjusted by changing the above-mentioned parameters. The self-powered sensing capability is then illustrated by integrating the harvester with an off-the-shelf power management circuit and a 22 μF storage capacitor. The capacitor was charged from 2.8 V to 4 V in 90 s, showing its capability of implementing battery-free wireless sensing for different Internet of Things (IoT) applications.

Lidar-assisted model predictive control of wind turbine fatigue via online rainflow counting considering stress history

Abstract. The formulation of parametric online rainflow counting implements the standard fatigue estimation process and a stress history in the cost function of a model predictive controller. The formulation is tested in realistic simulation scenarios in which the states are estimated by a moving horizon estimator and the wind is predicted by a lidar simulator. The tuning procedure for the controller toolchain is carefully explained. In comparison to a conventional model predictive controller (MPC) in a turbulent wind setting, the novel formulation is especially superior with low lidar quality, benefits more from the availability of wind prediction, and exhibits a more robust performance with shorter prediction horizons. A simulation excerpt with the novel formulation provides deeper insight into the update of the stress history and the fatigue cost parameters. Finally, in a deterministic gust setting, both the conventional and the novel MPC – despite their completely different fatigue costs – exhibit similar pitch behavior and tower oscillations.

On the dynamics of a model wind turbine under passive tower oscillations

Laboratory experiments were carried out to quantify the effect of small-amplitude, passive oscillations of a model wind turbine in the structure of the unsteady motions, wake statistics, and mean power output and associated fluctuations at various yawing β∈[0o,30o] every Δβ=5o. Planar particle image velocimetry was used to characterize the flow statistics, and power output was measured at high temporal resolution. Scenarios with a fixed turbine were included to aid insight into the coupled and separated effects of passive oscillations and yawing. Unsteady pitch motions, dominant of the system dynamics, were more predominant at small but non-zero yaw of β≈5o. The spectral structure of the oscillations showed that the unsteady roll motions contributed substantially under high yawing. Using basic concepts, we derived a formulation for the turbine oscillation spectrum that shows good agreement with measurements; it serves as a base to include other input modulation types. The power output decreased monotonically with β in the fixed and oscillating turbines, which was more distinct for β>15o. Passive oscillations produced higher power for given yaw. A simple yaw-correction of the structure of the power output also showed reasonable agreement with measurements. Finally, mean velocity in the wake of the fixed and oscillating turbines exhibited minor differences for a given yawing. However, the turbulence levels showed distinct changes of turbine motions in the degree of symmetry and magnitude for given yaw.

Wind Turbine Tower Deformation Measurement Using Terrestrial Laser Scanning on a 3.4 MW Wind Turbine

Wind turbine plants have grown in size in recent years, making an efficient structural health monitoring of all of their structures ever more important. Wind turbine towers deform elastically under the loads applied to them by wind and inertial forces acting on the rotating rotor blades. In order to properly analyze these deformations, an earthbound system is desirable that can measure the tower’s movement in two directions from a large measurement working distance of over 150 m and a single location. To achieve this, a terrestrial laser scanner (TLS) in line-scanning mode with horizontal alignment was applied to measure the tower cross-section and to determine its axial (in the line-of-sight) and lateral (transverse to the line-of-sight) position with the help of a least-squares fit. As a result, the proposed measurement approach allowed for analyzing the tower’s deformation. The method was validated on a 3.4 MW wind turbine with a hub height of 128 m by comparing the measurement results to a reference video measurement, which recorded the nacelle movement from below and determined the nacelle movement with the help of point-tracking software. The measurements were compared in the time and frequency domain for different operating conditions, such as low/strong wind and start-up/braking of the turbine. There was a high correlation between the signals from the laser-based and the reference measurement in the time domain, and the same peak of the dominant tower oscillation was determined in the frequency domain. The proposed method was therefore an effective tool for the in-process structural health monitoring of tall wind turbine towers.

Ultra-low frequency energy harvesting using bi-stability and rotary-translational motion in a magnet-tethered oscillator

Harvesting ultra-low frequency random vibration, such as human motion or turbine tower oscillations, has always been a challenge, but could enable many potential self-powered sensing applications. In this paper, a methodology to effectively harness this type of energy is proposed using rotary-translational motion and bi-stability. A sphere rolling magnet is designed to oscillate in a tube with two tethering magnets underneath the rolling path, providing two stable positions for the oscillating magnet. The generated magnetic restoring forces are of periodic form with regard to the sphere magnet location, providing unique nonlinear dynamics and allowing the harvester to operate effectively at ultra-low frequencies (< 1 Hz). Two sets of coils are mounted above the rolling path, and the change of magnetic flux within the coils accomplishes the energy conversion. A theoretical model, including the magnetic forces, the electromagnetic conversion and the occurring bi-stability, is established to understand the electromechanical dynamics and guide the harvester design. End linear springs are designed to maintain the periodic double-well oscillation when the excitation magnitude is high. Parametric studies considering different design factors and operation conditions are conducted to analyze the nonlinear electromechanical dynamics. The harvester illustrates its capabilities in effectively harnessing ultra-low frequency motions over a wide range of low excitation magnitudes.

In-phase and out-of-phase pitch and roll oscillations of model wind turbines within uniform arrays

We experimentally explored the impact of in-phase and complete out-of-phase pitch and roll oscillations on the mean power output and the structure of the power fluctuations of turbines within 3×2 uniform arrays. The flow past selected configurations was also characterized with hotwire anemometry. The parameter space included combinations of three amplitudes and two frequencies of the turbine oscillations, and two turbine layouts; measurements with fixed units are also included for comparison. Results show that the structure of the flow past the wind-turbine arrays was significantly affected by the frequency of the tower oscillations. The turbines under in-phase pitching induced a signature that extended in the intermediate wake, which was measured up to 7 rotor diameters downwind of the last row of turbines. The roll oscillations produced an increase of the combined power output independent of the amplitude and frequency of the oscillations, where the complete out-of-phase motions resulted in larger values with a maximum at the largest amplitude of oscillations (β=20°) of over than 10%. Opposite behavior occurred with the turbines under pitching, which led to negligible changes or decrease of the combined power with a maximum reduction of ~10%. The spacing of the turbines substantially affected the power from the roll motions; however, this was not the case for the pitching. Finally, an inspection of the cross-correlation of the instantaneous power output of the turbines in the first and second rows revealed the strong modulation of the induced motions on the structure of the power fluctuations.

Wake and power fluctuations of a model wind turbine subjected to pitch and roll oscillations

Wind-tunnel experiments were performed to inspect the impact of a variety of pitch and roll oscillations of a model wind turbine on the instantaneous power output and wake. Particle image velocimetry and hotwire anemometry were used to characterize the flow in the wake; instantaneous power output was also obtained in each of the configurations. For comparison, measurements were also performed in a fixed wind turbine. Results show that the wake at the turbine symmetry plane is significantly altered by the imposed motions, where rolling induced the lowest momentum deficit. The mean power output of the turbine increased with moderate tower oscillations, namely ≲10°, independent of the type of motion. We argue that this is due to, at least, two distinctive processes. Namely, a relative gain due to the cube of the relative incoming velocity impinging the rotor in the pitching, and a momentum replenish in the rolling motion The power fluctuations exhibited a peak on the spectral content of the spectrum ΦP coincident with the frequencies of the pitching and rolling. They also revealed the effects of the oscillation within the low-frequency content of ΦP, which was likely due to the oscillation-driven changes in the aerodynamics of the blades. In particular, the pitch reduced the energy of the power fluctuations within frequencies below that of the pitching frequency, with stronger effect at larger amplitude of oscillations, θ. However, the roll motions reduced the energy of the power fluctuations in a relatively narrow band, and notorious only with θ≳10°.

Reducing Tower Fatigue through Blade Back Twist and Active Pitch-to-Stall Control Strategy for a Semi-Submersible Floating Offshore Wind Turbine

The necessity of producing more electricity from renewable sources has been driven predominantly by the need to prevent irreversible climate chance. Currently, industry is looking towards floating offshore wind turbine solutions to form part of their future renewable portfolio. However, wind turbine loads are often increased when mounted on a floating rather than fixed platform. Negative damping must also be avoided to prevent tower oscillations. By presenting a turbine actively pitching-to-stall, the impact on the tower fore–aft bending moment of a blade with back twist towards feather as it approaches the tip was explored, utilizing the time domain FAST v8 simulation tool. The turbine was coupled to a floating semisubmersible platform, as this type of floater suffers from increased fore–aft oscillations of the tower, and therefore could benefit from this alternative control approach. Correlation between the responses of the blade’s flapwise bending moment and the tower base’s fore–aft moment was observed with this back-twisted pitch-to-stall blade. Negative damping was also avoided by utilizing a pitch-to-stall control strategy. At 13 and 18 m/s mean turbulent winds, a 20% and 5.8% increase in the tower axial fatigue life was achieved, respectively. Overall, it was shown that the proposed approach seems to be effective in diminishing detrimental oscillations of the power output and in enhancing the tower axial fatigue life.

Evolutionary Multiobjective Optimization with Fractional Order Integral Objectives for the Pitch Control System Design of Wind Turbines

Abstract Evolutionary multiobjective optimization with fractional order objective functions is used for the tuning of three coupled control loops, which are part of the pitch control system of three-bladed, variable-speed, horizontal-axis large-sized wind energy converters. The first control loop is the collective pitch control (CPC). The second one is the active tower damping control (ATDC), which is used to damp tower oscillation due to the pitching activity. Finally, the third one is the active blade tip deflection damping control (ABDC) in the edgewise direction, which is proposed to mitigate blade oscillations. Simulation results by using the software FAST of a 20 MW reference turbine show that the tuning approach yields satisfactory performance for all control loops.

Parameterized Disturbance Observer Based Controller to Reduce Cyclic Loads of Wind Turbine

This paper is concerned with bump-less transfer of parameterized disturbance observer based controller with individual pitch control strategy to reduce cyclic loads of wind turbine in full load operation. Cyclic loads are generated due to wind shear and tower shadow effects. Multivariable disturbance observer based linear controllers are designed with objective to reduce output power fluctuation, tower oscillation and drive-train torsion using optimal control theory. Linear parameterized controllers are designed by using a smooth scheduling mechanism between the controllers. The proposed parameterized controller with individual pitch was tested on nonlinear Fatigue, Aerodynamics, Structures, and Turbulence (FAST) code model of National Renewable Energy Laboratory (NREL)’s 5 MW wind turbine. The closed-loop system performance was assessed by comparing the simulation results of proposed controller with a fixed gain and parameterized controller with collective pitch for full load operation of wind turbine. Simulations are performed with step wind to see the behavior of the system with wind shear and tower shadow effects. Then, turbulent wind is applied to see the smooth transition of the controllers. It can be concluded from the results that the proposed parameterized control shows smooth transition from one controller to another controller. Moreover, 3p and 6p harmonics are well mitigated as compared to fixed gain DOBC and parameterized DOBC with collective pitch.

Experimental and Numerical Vibrational Analysis of a Horizontal-Axis Micro-Wind Turbine

Micro-wind turbines are energy conversion technologies strongly affected by fatigue, as a result of their size and the variability of loads, induced by the unsteady wind conditions, and modulated by a very high rotational speed. This work is devoted to the experimental and numerical characterization of the aeroelastic behavior of a test-case horizontal-axis wind turbine (HAWT) with a 2 m rotor diameter and a maximum power production of 3 kW. The experimental studies have been conducted at the wind tunnel of the University of Perugia and consisted of accelerometer measurements at the tower and the tail fin. The numerical setup was the Fatigue, Aerodynamics, Structures, and Turbulence (FAST) code for aeroelastic simulations, which was fed as input with the same wind conditions employed in the wind tunnel tests. The experimental and numerical analyses were coupled with the perspective of establishing a reciprocal feedback, and this has been accomplished. On one hand, the numerical model is important for interpreting the measured spectrum of tower oscillations and, for example, inspires the detection of a mass unbalance at the blades. On the other hand, the measurements inspire the question of how to interpret the interaction between the blades and the tower. The experimental spectrum of tail fin vibrations indicates that secondary elements, in terms of weight, can also transmit to the tower, giving meaningful contributions to the vibration spectra. Therefore, an integrated numerical and experimental approach is not only valuable but is also unavoidable, to fully characterize the dynamics of small wind-energy conversion systems.

Integrated Pitch Control System Design of a Wind Turbine by Using Multiobjective Optimization

Abstract The integrated pitch control system of a three-bladed, variable-speed, horizontal-axis large-sized wind turbines consists of three coupled control loops. The first one is known as collective pitch control (CPC). The second one is the active tower damping control (ATDC), which is used to damp tower oscillation due to the pitching activity. Finally, the third one is the individual pitch control (IPC), which is used to mitigate loads on the blades. In the present work, the coupled controllers are jointly tuned by using multiobjective optimization. Simulation results show that the proposed tuning approach yields satisfactory performance for all control loops.

Passive Vibration Control of a Semi-Submersible Floating Offshore Wind Turbine

Floating offshore wind turbines have the potential to commercially convert the vast wind resource in deep-water area. Compared with fixed-bottom wind turbines, motions of the floating foundation complicate vibrations and loads of the wind turbine in offshore environment. To alleviate the responses of the wind turbine, this study investigates the use of fore–aft tuned mass damper (TMD) in nacelle/tower for passive control of a semi-submersible offshore wind turbine. A simplified structural model, considering the degree-of-freedom of platform pitch and surge, tower tilt and TMD translation, is proposed in the light of motion features of semi-submersible platform. After identifying ten unknown parameters, the correctness of the deterministic model is validated by pitch free decay responses. The mass, stiffness and damping of TMD are optimized using both method of exhaustion and genetic algorithm to avoid local minimum. Six optimized TMD devices are evaluated under three kinds of realistic environment conditions. The control effectiveness is assessed by the extreme and fatigue response reduction ratios. It is found that the high stiffness TMDs that directly dissipate the energy of tower oscillation exhibit an overall stable performance. Similar to the spar-type foundation, the TMDs in the nacelle/tower are capable of extending the service life of floating wind turbines.

Simulating the dynamic behavior of a vertical axis wind turbine operating in unsteady conditions

The present work aims at assessing the reliability of a simulation tool capable of computing the unsteady rotational motion and the associated tower oscillations of a variable speed VAWT immersed in a coherent turbulent wind. As a matter of fact, since the dynamic behaviour of a variable speed turbine strongly depends on unsteady wind conditions (wind gusts), a steady state approach can't accurately catch transient correlated issues.The simulation platform proposed here is implemented using a lumped mass approach: the drive train is described by resorting to both the polar inertia and the angular position of rotating parts, also considering their speed and acceleration, while rotor aerodynamic is based on steady experimental curves. The ultimate objective of the presented numerical platform is the simulation of transient phenomena, driven by turbulence, occurring during rotor operation, with the aim of supporting the implementation of efficient and robust control algorithms.

Active tower damping and pitch balancing – design, simulation and field test

The tower is one of the major components in wind turbines with a contribution to the cost of energy of 8 to 12% [1]. In this overview the load situation of the tower will be described in terms of sources of loads, load components and fatigue contribution. Then two load reduction control schemes are described along with simulation and field test results. Pitch Balancing is described as a method to reduce aerodynamic asymmetry and the resulting fatigue loads. Active Tower Damping is reducing the tower oscillations by applying appropiate pitch angle changes. A field test was conducted on an Areva M5000 wind turbine.

Non‐linear pitch control of wind turbines for tower load reduction

As the modern wind turbines (WTs) become larger in size, the structural loads experienced by the WTs increase dramatically, which would shorten the working life of the WTs and increase the maintenance cost. To mitigate such problem, this study proposes a non-linear pitch control strategy including tower load reducing objective for the WTs operating in the above-rated wind speed region. The proposed non-linear controller consists of a rotor speed regulator, a tower oscillation damper and a lead compensator. The rotor speed regulator and tower oscillation damper are designed separately based on inverse system method, which is a powerful tool in solving the control problem of non-affine non-linear system. The lead compensator is utilised to compensate for the phase lag of the pitch angle command caused by the pitch actuator. Furthermore, light detection and ranging (LIDAR) preview measurements are introduced to provide wind information for the proposed controller in order to improve its control performance. The simulation results with the aero-elastic model of fatigue, aerodynamics, structures and turbulence (FAST) show that, the proposed non-linear controller outperforms the baseline gain-scheduled proportional-integral controller. The proposed non-linear controller can work well in the whole above-rated wind speed region, and is easy to implement for application.

Frequency domain design of gain scheduling control for large wind systems in full-load region

The paper presents the issue of power control law synthesis, in the case of a large wind system that operates under full-load regime, based on dynamic properties details in frequency domain. Solving this problem involves two phases: the establishment of a linearized model as faithfully as possible in various operating points of the full-load region, and synthesis of the power controller, considered with classic structure, taking into account frequency particularities of the obtained linearized model. Obtained linear model of the controlled process is of order 16 and encloses subsystems for tower fore-aft oscillations damping, and for drive-train torsion oscillations damping. The designed controller contains a PI component and a lag compensator for dynamic correction at high frequencies. It is known that the main features of wind system dynamics generated by the interaction of wind–tower–blade ensemble cause a gap in the gain characteristic of the model and complex conjugate zeros, which can move between right and left half-planes, depending on the average wind speed value. Consequently, for control law synthesis an interactive frequency solution is adopted. This is “transparent” in relation to particularities induced by wind–tower–blade interaction. This solution allows evaluation of the extent to which control law is affected by the subsystem for tower oscillations damping. Given the strong dependence between the model and the mean wind speed value, a gain scheduling control law is designed. At different values of average wind speed, controller synthesis is performed in two ways: one applying the desired values to the stability reserve, and the other requiring the minimization of a performance criterion, aimed at reducing mechanical stress, while the controller parameters are kept in an area that ensures admissible values to the stability reserve. This second way allows obtaining a solution for designing a simple classic controller, dedicated to large wind turbines, to which may be imposed requirements for mechanical fatigue mitigation. The proposed solutions are backed by numerical results obtained through numerical simulation.

Dynamic identification of historic masonry towers through an expeditious and no-contact approach: Application to the “Torre del Mangia” in Siena (Italy)

Abstract The paper presents a synergic and multidisciplinary approach where laser scanner survey, radar interferometric monitoring and finite element (FE) numerical modelling are used for expeditious and no-contact dynamic identification of monumental masonry towers. The methodology is applied to a real case of great historical interest: the “Torre del Mangia” (Mangia's tower) in Siena (Italy). The tower geometry was acquired through Terrestrial Laser Scanning (TLS) techniques. The tower oscillations were detected using an interferometric radar in “Piazza del Campo”, the square facing the Mangia's Tower, along three alignments, and movement of the structure at several heights were recorded. A FE model, built on the basis of the geometry acquired through the TLS, was used to interpret and verify the physical meaning of the experimental results. Through the discussion of the case study, the paper shows that the proposed approach can be considered as an effective and expeditious method for assessing the dynamic behavior of monumental buildings (and to plan interventions) on territorial scale.