Gunjit Bir

Aeroelastic Instabilities of Large Offshore and Onshore Wind Turbines

Offshore turbines are gaining attention as means to capture the immense and relatively calm wind resources available over deep waters. This paper examines the aeroelastic stability of a three-bladed 5MW conceptual wind turbine mounted atop a floating barge with catenary moorings. The barge platform was chosen from the possible floating platform concepts, because it is simple in design and easy to deploy. Aeroelastic instabilities are distinct from resonances and vibrations and are potentially more destructive. Future turbine designs will likely be stability-driven in contrast to the current loads-driven designs. Reasons include more flexible designs, especially the torsionally-flexible rotor blades, material and geometric couplings associated with smart structures, and hydrodynamic interactions brought on by the ocean currents and surface waves. Following a brief description of the stability concept and stability analysis approach, this paper presents results for both onshore and offshore configurations over a range of operating conditions. Results show that, unless special attention is paid, parked (idling) conditions can lead to instabilities involving side-to-side motion of the tower, edgewise motion of the rotor blades, and yawing of the platform.

Computerized Method for Preliminary Structural Design of Composite Wind Turbine Blades

A computerized method has been developed to aid preliminary design of composite wind turbine blades. The method allows for arbitrary specification of the chord, twist, and airfoil geometry along the blade and an arbitrary number of shear webs. Given the blade external geometry description and its design load distribution, the Fortran code uses ultimate-strength and buckling-resistance criteria to compute the design thickness of load-bearing composite laminates. The code also includes an analysis option to obtain blade properties if a composite laminates schedule is prescribed. These properties include bending stiffness, torsion stiffness, mass, moments of inertia, elastic-axis offset, and center-of-mass offset along the blade. Nonstructural materials-gelcoat, nexus, and bonding adhesive-are also included for computation of mass. This paper describes the assumed structural layout of composite laminates within the blade, the design approach, and the computational process. Finally, an example illustrates the application of the code to the preliminary design of a hypothetical blade and computation of its structural properties.

A Comparison of Multi-Blade Coordinate Transformation and Direct Periodic Techniques for Wind Turbine Control Design

The inherent periodic behavior of an operating wind turbine is not well accommodated by common time-invariant analysis and control techniques. A multi-blade coordinate transformation (MBC) helps to overcome this issue for rotors with three or more blades by mapping the dynamic state variables into a non-rotating reference frame. A number of researchers have applied MBC for modal analyses and individual blade pitch controller designs. They do so by assuming the transformed system model from MBC is time-invariant, which is not often the case. The paper explores the validity of the time-invariant assumption by comparison to direct periodic techniques, which retain all periodic system information. In a modal analysis study, eigenvalues of a system after MBC are compared to direct Floquet modes. In an individual blade pitch control design study, a linear quadratic regulation (LQR) design after MBC is compared to direct periodic LQR. A 5-MW three-bladed wind turbine model is used to quantify performance differences. Normal operating conditions are considered as well as conditions selected to increase the harmonics that are unfiltered by MBC. It is found that the direct periodic methods produce almost identical results to timeinvariant methods after MBC under all conditions studied. MBC is recommended for threebladed turbines, which can be followed by Floquet analysis or periodic control design methods if necessary.

Structural Design of a Horizontal-Axis Tidal Current Turbine Composite Blade

This paper describes the structural design of a tidal composite blade. The structural design is preceded by two steps: hydrodynamic design and determination of extreme loads. The hydrodynamic design provides the chord and twist distributions along the blade length that result in optimal performance of the tidal turbine over its lifetime. The extreme loads, i.e. the extreme flap and edgewise loads that the blade would likely encounter over its lifetime, are associated with extreme tidal flow conditions and are obtained using a computational fluid dynamics (CFD) software. Given the blade external shape and the extreme loads, we use a laminate-theory-based structural design to determine the optimal layout of composite laminas such that the ultimate-strength and buckling-resistance criteria are satisfied at all points in the blade. The structural design approach allows for arbitrary specification of the chord, twist, and airfoil geometry along the blade and an arbitrary number of shear webs. In addition, certain fabrication criteria are imposed, for example, each composite laminate must be an integral multiple of its constituent ply thickness. In the present effort, the structural design uses only static extreme loads; dynamic-loads-based fatigue design will be addressed in the future. Following the blade design, we compute the distributed structural properties, i.e. flap stiffness, edgewise stiffness, torsion stiffness, mass, moments of inertia, elastic-axis offset, and center-of-mass offset along the blade. Such properties are required by hydro-elastic codes to model the tidal current turbine and to perform modal, stability, loads, and response analyses.

Floquet Modal Analysis of a Teetered-Rotor Wind Turbine

This paper examines the operating modes of a two-bladed wind turbine structural model. Because of the gyroscopic asymmetry of its rotor, this turbines dynamics can be quite distinct from that of a turbine with three or more blades. This asymmetry leads to system equations with periodic coefficients that must be solved by the Floquet approach to extract the correct modal parameters. A discussion of results is presented for a series of simple models with increasing complexity. We begin with a single-degree-of-freedom system and progress to a model with seven degrees-of-freedom: tower fore-aft bending, tower lateral bending, tower twist, nacelle yaw, hub teeter, and flapwise bending of each blade. Results illustrate how the turbine modes become more dominated by the centrifugal and gyroscopic effects as the rotor speed increases. Parametric studies are performed by varying precone angle, teeter stiffness, yaw stiffness, teeter damping, and yaw damping properties. Under certain levels of yaw stiffness or damping, the gyroscopic coupling may cause yaw and teeter mode coalescence, resulting in self-excited dynamic instabilities. Teeter damping is the only parameter found to strictly stabilize the turbine model.

Full-scale modal wind turbine tests: comparing shaker excitation with wind excitation

The test facilities at the National Wind Technology Center (NWTC) of the National Renewable Energy Laboratory (NREL) include a three-bladed Controls Advanced Research Turbine (CART3). The CART3 is used to test new control schemes and equipment for reducing loads on wind turbine components. As wind turbines become lighter and more flexible to reduce costs, novel control mechanisms are necessary to stop high winds from damaging the turbine. However, wind turbines must also be designed to capture the maximum amount of energy from the wind, so engineers must devise new ways of achieving this while controlling wind loads that would cause the turbines to fatigue quickly. New control mechanisms and computer codes can help the wind turbine shed some loads in extreme or very turbulent winds. The special configuration of the CART3 allows researchers to analyze these diverse control schemes. This paper reports on the initial results of a major full-scale modal testing campaign to validate and refine simulation models. One model is a tailored multi-body dynamic simulation model that will be used to develop an advanced controller designed to optimize power and minimize structural loads. Researchers would also like to tune Finite Element Models of the blades, nacelle and tower assembly to predict the higher order rotating modes of the wind turbine for a range of inflow conditions. The paper will discuss an Experimental Modal Analysis approach where the wind turbine in parked condition is excited by shakers connected with cables. This approach will be compared to Operational Modal Analysis where the same structure is subjected to wind excitation without the shakers activated. These tests and data analyses will provide experience and increase confidence in the approach used for future tests in rotating conditions.

Modal Dynamics of Large Wind Turbines with Different Support Structures

This paper presents modal dynamics of floating-platform-supported and monopile-supported offshore wind turbines.

Linearized dynamics and operating modes of a simple wind turbine model

Modal analysis and the future design of control strategies for a wind turbine rely heavily on the development of system descriptive dynamics models. Until now, wind turbine models have focused only on turbine simulations and not system characterization, which is necessary for the evaluation of operating modes, parameterization of stability, and controI designs. This paper presents an explicit, descriptive model of a rigid component, generic horizontal axis wind turbine, from which the system parameters and operating modes are extracted. A four degree-offreedom two-bladed turbine under free vibration is analyzed in parts and then as a complete system, presenting physical insight into the dynamic coupling behavior. A study perfonned at different rotor azimuth positions exposes the importance of Floquet analysis to better understand rotor-nacelle dynamic interactions. Mode shapes are identified and results are presented for modal frequencies at different rotor speeds.

MODAL ANALYSIS OF A TEETERED-ROTOR WIND TURBINE USING THE FLOQUET APPROACH

This paper examines the operating modes of a twobladed teetered wind turbine modeled with seven degrees of freedom: nacelle yaw, hub teeter, flapping of each blade, tower fore-aft bending, tower lateral bending, and tower twist. Because of the gyroscopic asymmetry of its rotor, this turbine’s dynamics can be quite distinct from that of a turbine with three or more blades. This asymmetry leads to system equations with periodic coefficients that must be solved by the Floquet approach to extract the correct modal parameters. Results illustrate how the turbine modes become more dominated by the centrifugal and gyroscopic effects as the rotor speed increases. Under certain design conditions, the gyroscopic coupling may cause phase locking or frequency coalescence of the yaw and teeter modes resulting in self-excited dynamic instabilities.

VALIDATION OF A SYMBOLIC WIND TURBINE STRUCTURAL DYNAMICS MODEL

A computational structural dynamics model for a Horizon,tal Axis Wind Turbine is presented, referred to as SymDyn. The model is capable of providing system dynamics in explicit form as opposed to only time responses. Validation of the model is made by comparison to a model built in ADAMS, a commercial dynamics simulation code. Properties for the models are taken from a generic two-bladed, constant speed, teetered-rotor turbine. Aerodynamic loads are neglected but provision is made for user defined external loading on the blades. Simulation results show almost exact agreement for a number of different test cases. Minor differences are attributed to the different numerical integration schemes employed.