Computationally Efficient Determination of Long Term Extreme Out-of-Plane Loads for Offshore Turbines Anand Natarajan Senior Scientist Wind Energy Department, Risø DTU Denmark
Introduction IEC 61400-1 load case 1.1 requires that extreme load predictions are made under operating normal turbulent wind. Edition 3 requires that the 50 year operating extreme load is determined under normal turbulence wind inputs A common methodology to determine the 50 year operating extreme is to extrapolate the stochastic distribution of extreme loads as determined from limited simulation data. Normal turbulent wind simulations need to be performed between cut-in to cut-out with minimum 15 seeds per mean wind speed from near rated till cut-out. For offshore turbines, the added load contributions from stochastic sea states are also considered. These requirements greatly increase the computational time.
Offshore Turbines DLC 1.1 IEC 61400-3 also describes the need for extreme loads extrapolation in DLC 1.1. Significant computational efforts and potential for increased component costs can result from need to extrapolate extreme loads. The investigation of the 50 year mud line extreme moments under operational conditions needs investigation Do the RNA extreme loads transmit to the tower base? *Extract from IEC 61400-3
Extrapolation of the Extreme Load The CDF of the extreme load is combined with wind probability and extrapolated to a 50 year probability of exceedance The fitted extreme load distribution of the form p( F e F) 1e e ( af bfc) a 0, b 0 Extrapolation is stable even at low probabilities Distribution is valid only for all values >= tail data considered Natarajan A. & Holley, W.E., Statistical Extreme Loads Extrapolation with Quadratic Distortions for Wind Turbines, ASME Journal of Solar Energy Engineering, Vol. 130, 031017, Aug 008
Simulation Details 1. The Upwind 5 MW offshore turbine with a monopile foundation is used.. HAWC is used for aeroelastic simulations 3. The turbine controller is a conventional PID control with symmetric blade pitching. 4. The turbulent wind is input using rectangular grids and the Mann wind model. 5. The mean water depth is 0m and irregular wave input is used based on the JONSWAP spectrum.
Comparison of Proposed Methodology with Existing Extrapolation Methods Conventional Method (Extrapolation) Limited number of normal turbulent wind aeroelastic simulations run from cut in to cut out (may not suffice to obtain all needed tail data) Extrapolation of extreme loads either locally (at one mean wind speed) or globally (over all mean wind speeds) Uncertainty of the 50 year extreme load level is dependent on the number of aeroelastic simulations and probabilistic extrapolation technique. May take several hours to obtain a sample of extreme loads that is to be extrapolated Proposed Method No full aeroelastic simulations, but an extreme load emulator that accounts for the physics of the extreme load to be determined No extrapolation. The code should output the 50 year extreme load level. Uncertainty dependent on the order of approximation in the physics emulated in the simplified code. Should compute the 50 year extreme load within a minute
Out of Plane Loads The peak extreme out of plane moments are seen to occur between rated mean wind speed (11.4m/s) and ~16 m/s for normal turbulence wind inputs. Extreme loads sampled from one seed at each mean wind speed
Extreme RNA loads transmitted to the Tower Base 1. 0 seeds of normal wind turbulence at each mean wind speed from 7m/s to 5m/s.. The overall maximum O/P extreme tower base moment in 0 seeds occurs at 15m/s and is 87000kNm 3. At the instant of the peak tower base moment, at least two of the blades also possess a local maximum out of plane root moment.
Extreme Tower Base Out of Plane Moment Effect of the Control System 1. Mean wind speed is above rated wind speed.. Conventional symmetric pitch controller tracks the rotor speed error which is oscillatory about the set point. 3. Pitch angle drops to zero. This is seen to occur for many extreme out of plane moments even at the blade root. 4. Generator torque triggers
Effect on Angle of Attack at Peak Out of Plane Tower Base Moment 1. The low pitch angle results in higher out board angle of attack on at least two blades.. At non extreme tower base moments, the angle of attack profile on the blade follows the inverse of the local tip speed ratio. 3. Hence peak angles of attack on the outboard blade is a probable cause for peak out of plane tower base moments.
Mechanics of a simplified extreme loads code The control system does not possess a wind observer (such as a LIDAR) and that monopile foundations are used. The lift, drag curves for the blade airfoils are used. The blade section that possesses the largest chord times lift coefficient is made to attain the maximum lift. Other blade station angles of attack are obtained from BEM theory and conforming to the max angle of attack at 1 station. The wind PSD, coherence function are used with the blade and tower mode shapes at the tower natural frequency. The tower top loading is modeled as an impulse. Irregular wave loading on the support structure is included.
Quick computation of the 50 year operating load without waves Mud line out of plane moment computed without including the wave loading. Extrapolated extreme load also computed without including waves Quick Computation of the mud line moment 50 year Extrapolated mud line moment Maximum quick simulation load is within 10% of the extrapolated 50 year load
Determination of Wave Height 1. Determine the 50 year wave significant height at each operating mean wind speed.. The environmental contour method is used : assuming Rayleigh mean wind speed and Weibull distributed wave heights
Wave Kinematics Frequency domain approach. 1. Linearized Morison Equation 1 df (z,t) CM d u dz C dld u dz 4. Airy Wave theory : conservative for high wave heights 3. Wheeler stretching used 4. Maximum wave drag moment at the mud line M Dmax (, y) C d 1 d S(H s, ) 5. Maximum wave inertial moment at the mud line Linearized drag coefficient for Gaussian waves is estimated for a prescribed std. deviation of velocity ( u ) as C dl 1.596. Cd. U ( d y)-d k Csch(dk) ( k( d y) Sinh(dk) 4 k (d y) M Im ax (, y) C M d 4 (Tanh( d k k ) - d k ) d y 4 S ( H s, )
Extrapolated Mud line O/P Moment Extrapolating the overall mud line out of plane moment including extreme wave loading causes conservative estimates of the 50 year moment ~34% higher than without including wave loads. Effect of irregular waves on the mud line out of plane extreme loads has a less severe impact on parametric fitting of distributions than the effect of turbulent wind speed variations. Extrapolation with 6 turbulent wind seeds and a) 4 wave seeds, b) 7 wave seeds
Quick computation of 50 year mud line moment for offshore turbine 1. The effect of wave loading is included in the simplified code in the frequency domain.. The maximum out of plane extreme moment at the mud line is determined as 147000 knm 3. Simplified extreme moment is only 7.5% less than extrapolated 50 year moment when the extreme wave loading is added to the extrapolated wind induced loads.
Summary 1. The reasons for the peak extreme out of plane load are seldom due to only wind/waves, but are dependent on the action of the controls system and rotor aerodynamics.. A low blade pitch angle, dropping generator torque and high angle of attacks on outboard blade sections of two or more blades is often encountered for the peak tower base moment. 3. A wind observer based control system may attenuate this extreme moment by limiting peak angle of attacks on the blade. 4. A simplified code emulating the physics of the tower base extreme moment was able to reproduce the magnitude of a 50 year mud line out of plane moment within 10% of the extrapolated extreme load. 5. The extreme wave loads were computed using a linearized Morison equation and Airy wave theory corrected for Wheeler stretching. 6. The effect of soil conditions can readily be considered using the modified tower mode shapes, damping and frequency.