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’