Efficient Modeling of Rotational Effects for Wind Turbine
Efficient Modeling of Rotational Effects for Wind Turbine Structural Dynamic Analysis Diederik den Dekker September 9 th 2010
U. S. President Obama visits Siemens rotor blade plant in the U. S. state of Iowa, april 28 th, 2010
Agenda Introduction Goal of Study Method Results Conclusions & Recommendations 3
Introduction
Horizontal Axis Wind Turbine 5
Wind industry is growing rapidly 6
Wind turbines can become a mayor energy source by reducing their costs 7 * U. S. estimate for plants entering service in 2016
Structural dynamics is the cornerstone of cost reduction Turbine design Optimization Cost Reduction! Behavior prediction Dynamic analysis 8
Linear dynamic formulation Single Do. F system Multiple Do. F system 9
Linear dynamic formulation 10
Linear formulation: small body deformations No rotations No operational analyses 11
12
Floating Frame of Reference (FFR) 13
Floating Frame of Reference (FFR) 14
Floating Frame of Reference (FFR) 15
Floating Frame of Reference (FFR) 16
Floating Frame of Reference (FFR) Non-linear 17
FFR mass matrix 18
FFR mass matrix 19 36 Do. F System in 1 FFR
FFR mass matrix 20 36 Do. F System in 1 FFR
FFR adds rotational effects to a linear formulation Method Formulation Characteristics Linear Efficient FFR Rotations 21
Siemens Wind Power uses two tools for structural dynamic analysis BHaw. C Siemens DS Tool 22
Methodologies Rotations BHaw. C DS Rotating DS Simplified Rotating DS ✓ ✕ ✓ ✓ Model detail ? ? ? CPU Speed 23
Goal of Study
To what extent can the rotational effects be simplified. . . for various wind turbine operational analyses. . . without significantly impacting their dynamic characteristics? 25
Method
FFR simplification methodology Investigate which Do. F to fix Determine fixed position of Do. F Fix Do. F in equation of motion Simplified equations of motion 27
Investigation into the efficiency and accuracy of simplified models Load Cases BHaw. C model Referenc e model Simplified models Output Verification Output Accuracy and CPU speed Output
Siemens SWT-2. 3 -93 Nominal power: 2. 3 MW Rotor diameter: 93 m Operating wind speed: 4 - 25 m/s Rotor speed: Turbines in operation: 29 6 - 16 RPM 1, 374
Siemens FFR wind turbine (SFW) model x x x 30
Siemens FFR wind turbine (SFW) model • 1 FFR x 49 Do. F x • x
Three load cases are used to test the simplifications Steady State Wind Gust Emergency Shut Down 32
Steady State: Rotor speed: 16 RPM Wind speed: 14 m/s Extracted power: 2. 3 MW (blade deformation magnified 10 x) All units along axes in meters 33
Emergency Shut Down All units along axes in meters 34 Initial rotor speed: 16 RPM Wind speed: 14 m/s Shut down time: <10 s
Results
Three simplifications discussed today Deformation Do. F Fix Simplification one Rotation Do. F Fix Simplification Three Simplification two 36 Reference Model
Three simplifications discussed today Deformation Do. F Fix Simplification one Rotation Do. F Fix Simplification Three Simplification two 37 Fix Reference Model
Three simplifications discussed today Deformation Do. F Fix Simplification one Fix Rotation Do. F Fix Simplification Three Simplification two 38 Fix Reference Model
Three simplifications discussed today Deformation Do. F Simplification one Rotation Do. F Simplification Three Simplification two 39 Reference Model
Average CPU speed increase per time step* 40 *excluding overhead
Accuracy: Steady State Simplification one Simplification Three Simplification two 41 Reference Model
Accuracy: Steady State Simplification one Simplification Three Simplification two 42 Reference Model
Accuracy: Steady State Simplification one Simplification Three Simplification two 43 Reference Model
Accuracy: Wind Gust Simplification one Simplification Three Simplification two 44 Reference Model
Accuracy: Wind Gust Simplification one Simplification Three Simplification two 45 Reference Model
Accuracy: Wind Gust Simplification one Simplification Three Simplification two 46 Reference Model
Accuracy: Emergency Shut Down Simplification one Simplification Three Simplification two 47 Reference Model
Accuracy: Emergency Shut Down Simplification one Simplification Three Simplification two 48 Reference Model
Accuracy: Emergency Shut Down Simplification one Simplification Three Simplification two 49 Reference Model
Simplifications often show negligible differences with the reference model maximum relative difference in mean & standard deviation <10% <5% <1% Steady State Three Wind Gust Three Emergency Shut Down Two One 50
Conclusions & Recommendations
Main conclusions • • Simplifications prove that rotational effects can be simplified for dynamic wind turbine models at minimal accuracy loss: • The SFW model’s CPU speed can be increased up to 140 times in steady cases • The SFW model’s CPU speed can be increased up to 5 times in transient cases. Complete `linearization’ is not possible when external forces are defined in different axes w. r. t. the body they 52
Main recommendations • Apply FFR and its simplififcations to the Siemens DSTool • Investigate simplified FFR applied to models of other wind turbine types • Investigate simplified FFR for other applications with (‘axisymmetric’) rotating bodies 53
Efficient Modeling of Rotational Effects for Wind Turbine Structural Dynamic Analysis Diederik den Dekker September 9 th 2010
Quadratic velocity vector to ‘virtual dynamic properties’
Quadratic velocity vector to ‘virtual dynamic properties’
- Slides: 56