Emilio Di Lorenzo – Research engineer – Siemens Industry Software nv PhD candidate at KU Leuven and University of Naples "Federico II" emilio.dilorenzo@siemens.com

OFFSHORE WIND TURBINE MODELLING IN LMS SAMCEF TO DERIVE AND VALIDATE NEW PROCESSING APPROACHES

Optiwind Open Project Meeting, Leuven, Belgium 02/12/2015

E. Di Lorenzo, S. Manzato

Agenda

1. Introduction

2. Rotor analysis

1. MBC transformation

2. HPS method

3. Validation cases

4. Conclusions

3. Gearbox analysis

1. Operational Modal Analysis

2. Order-Based Modal Analysis

3. Validation cases

4. Conclusions

Objectives

• Understand the problems and limitations of applying Operational Modal Analysis (OMA) techniques to wind turbines in operation

Deal with the time-variant nature of the structure Deal with presence of harmonics components

• Development of methodologies for automated data

processing for online structural health monitoring (SHM) applications

Operational Modal Analysis - OMA

• Identification of modal parameters (natural frequencies, damping ratios, mode shapes) from response data measured in operating conditions

• Operational Modal Analysis = identifying H without knowing U (white noise assumption) based on Y

Unkown input Structure Measured output

U H

Y

310.000.00 s

0.34

-0.36

Rea

lg

1.00

0.00

Ampl

itude

OMA: Limitations and solutions

Agenda

1. Introduction

2. Rotor analysis

1. MBC transformation

2. HPS method

3. Validation cases

4. Conclusions

3. Gearbox analysis

1. Operational Modal Analysis

2. Order-Based Modal Analysis

3. Validation cases

4. Conclusions

Rotor analysis

• Analyze the modal behaviour of Linear Time Periodic (LTP) systems.

• Analyze data with an harmonic dominance which masks the structural dynamics.

• Find modal parameters sensitive to small structural damages for SHM purposes.

Multi-Blade coordinate transformation - MBC

• Method to describe the motions of individual blades in the same coordinate system as the structure supporting the rotor

• Offers physical insight into rotor dynamics and how rotor interacts with fixed-system entities

• Fundamental assumption: rotor must be isotropic

• Filters out all periodic terms except those which are integral multiples of ΩN, where Ω is the rotor angular speed and N is the number of blades G.S.Bir – Multiblade Coordinate Transformation and

its Application to Wind Turbine Analysis

Multi-Blade coordinate transformation - MBC

∑=

=N

bibi q

Nq

1,,0

1

( )b

N

bibic nq

Nq ψ∑

=

=1

,, cos2

)(sin21

,, b

N

bibis nq

Nq ψ∑

=

=

Mode animation

Mode shapes in physical coordinates

Inverse MBC transformation

OMA

Mode shapes in multiblade coordinates

Modal frequencies & damping ratios

Accelerations in multiblade coordinates

MBC transformation

Accelerations of points on the

blades

Data from measurement campaign/aeroelastic code

Accelerations of points on the tower/nacelle

RESULTS

)sin()cos( ,,,0, bisbiciib qqqq ψψ ++=

• Input at a single frequency will cause output at a single frequency

𝑢 𝑡 = 𝑢0 sin 𝜔𝑡

y 𝑡 = 𝑦0 sin 𝜔𝑡 − 𝜙

Harmonic Power Spectrum - HPS

Linear Time Invariant (LTI) system �̇� = 𝑨𝑥 + 𝑩𝑢 𝑦 = 𝑪𝑥 + 𝑫𝑢

Linear Time Periodic (LTP) systems �̇� = 𝑨(𝑡 + 𝑇𝐴)𝑥 + 𝑩(𝑡 + 𝑇𝐴)𝑢

𝑦 = 𝑪(𝑡 + 𝑇𝐴)𝑥 + 𝑫(𝑡 + 𝑇𝐴)𝑢

• Input at a single frequency will cause output at an infinite number of frequencies

𝑢 𝑡 = 𝑢0 sin 𝜔𝑡

y 𝑡 = 𝑦0 sin 𝜔𝑡 − 𝜙 + 𝑦1 sin (𝜔 + 𝜔𝐴𝑡) − 𝜙 + ⋯

𝜔𝐴 =2𝜋𝑇𝐴

Harmonic Power Spectrum - HPS

Linear Time Invariant (LTI) system �̇� = 𝑨𝑥 + 𝑩𝑢 𝑦 = 𝑪𝑥 + 𝑫𝑢

Linear Time Periodic (LTP) systems �̇� = 𝑨(𝑡 + 𝑇𝐴)𝑥 + 𝑩(𝑡 + 𝑇𝐴)𝑢

𝑦 = 𝑪(𝑡 + 𝑇𝐴)𝑥 + 𝑫(𝑡 + 𝑇𝐴)𝑢

𝑢 𝑡 = 𝑢0 sin 𝜔𝑡

y 𝑡 = 𝑦0 sin 𝜔𝑡 − 𝜙 + 𝑦1 sin (𝜔 + 𝜔𝐴)𝑡 − 𝜙 + ⋯ y 𝑡 = 𝑦0 sin 𝜔𝑡 − 𝜙

u𝑛 𝑡 = � 𝑢(𝑡)𝑒 𝑖𝜔+𝑖𝑛𝜔𝐴 𝑡𝑑𝑡∞

−∞

y𝑛 𝑡 = � 𝑦(𝑡)𝑒 𝑖𝜔+𝑖𝑛𝜔𝐴 𝑡𝑑𝑡∞

−∞

Power Spectrum (LTI system) Harmonic Power Spectrum (LTP system)

𝑢 𝑡 = 𝑢0 sin 𝜔𝑡

M. S. Allen et al. – Output-Only Modal Analysis of Linear Time Periodic Systems with Application to Wind Turbine Simulation Data

EMP

Harmonic Power Spectrum - HPS

Mode animation

Time periodic mode shapes

Harmonic Power

Spectrum (HPS)

Modal frequencies & damping ratios

Exponentially Modulated

Periodic (EMP) signal

Accelerations of points on the wind turbine under random

excitation

Data from measurement campaign/aeroelastic code

RESULTS

OMA

Summation over the

harmonics

Mode shapes at different harmonics

Reference wind turbines

NREL 5-MW WIND TURBINE Rated rotor speed 12.1 rpm Generator rated power 5 MW Tower Height 87.6 m Tower Mass 347*103 kg Nacelle Mass 240*103 kg

NREL 5-MW Wind Turbine

DTU 10-MW WIND TURBINE Rated rotor speed 9.6 rpm Generator rated power 10 MW Tower Height 119 m Tower Mass 628*103 kg Nacelle Mass 446*103 kg

DTU 10-MW Wind Turbine

2D WIND TURBINE m1 = m2 = m3 41,7*103 kg mT 446*103 kg k1 = k2 = k3 2,006*108 Nm/rad kH 2,6*106 N/m kV 5,2*108 N/m

2D Wind Turbine

2D Wind Turbine

1.500.00 Hz

0.01e-3

1.00e-12Lo

g

g2

180.00

-180.00

°

Before MBC - bladeAfter MBC - bladeTower

1.500.00 Hz

0.01e-3

0.10e-12

Log

g2

180.00

-180.00

°

Before MBC - bladeAfter MBC - bladeTower

• Crosspower comparison before and after MBC transformation • Isotropic rotor vs. Anisotropic rotor (k3=0.85*k1) • Same considerations can be done by applying HPS method • Very good match between MBC and HPS results has been found

Isotropic rotor Anisotropic rotor

2D Wind Turbine

No transformation

• White noise input • Extract displacement from the model and

apply OMA technique • Estimate modal parameters by means of

Operational Polymax

MBC transformation

HPS method

MBC AutoMAC HPS AutoMAC

MAC: (MBC) vs. (HPS selection)

Mode #

Freq [Hz]

S2S 0,37

B_as 0,84

B_coll 0,84

B_as 0,92

Mode #

Freq [Hz]

S2S 0,37

B_bw 0,74

B_coll 0,86

B_fw 1,06

Parked Operating (Ω=0.16 Hz)

2D Wind Turbine

Tower S2S mode Collective Edge mode

Backward Whirling

mode

Forward Whirling

mode

Backward Whirling Mode

f=0.37 f=0.74 f=0.86 f=1.06

2D Wind Turbine

Backward Whirling Mode

k1= 0.98*k1

• Isotropic conditions: Backward and forward whirling mode shapes have a constant amplitude for each blade and the phase lag between the blades is equal to 120°

• Anisotropic conditions: These properties are lost. The damaged blade amplitude is higher than the others. The phase lag is not anymore equal to 120°

DTU 10-MW wind turbine

10 MW HAWT vs

Antonov An-225 Mriya

Rotor Diameter 178.3 m vs

Wing Span 88.4 m

DTU 10-MW wind turbine: modeling

TOWER • 10 – segments tower • Steel S355 • Diameters linearly variable from the base to the top • Thickness constant in each segment.

BLADES • Bladed rotor concept • Distributed properties assigned along the blades.

DRIVETRAIN • A rigid drivetrain has been written in Samcef code • The rigid connection can be exchanged with a flexible one • Several kinematic chains have been investigated.

CONTROLLER Generator Torque Law • Below rated conditions

• Gain speed to reach the rated speed. • Above rated conditions

• Keep the power produced constant. Pitch controller law • Pitch to feather • Pitch to stall

FFA – W3 – xxx

NACA 0015 cylinder

DTU 10-MW wind turbine: OMA in parked conditions

Turbulence: Kaimal Model Turbine class: 1A Wind speed: 10 m/s

Turbine instrumented with virtual accelerometers

Mode DTU [Hz]

SWT [Hz]

Error [%]

1st Tower FA 0.249 0.247 < 1 %

1st Tower S2S 0.251 0.251 < 1 %

1st flap with yaw 0.547 0.549 < 1 %

1st flap with tilt 0.590 0.598 1.3 %

1st collective flap 0.634 0.636 < 1 %

1st edge with tilt 0.922 0.942 2.2 %

1st edge with yaw 0.936 0.959 2.4 %

2nd flap with yaw 1.376 1.413 2.7 %

2nd flap with tilt 1.550 1.573 1.5 %

2nd collective flap 1.763 1.812 2.7 %

DTU 10-MW wind turbine: OMA in parked conditions

Ice density

Ice but one Germanischer Lloyd WindEnergie GmbH: Guideline for the Certification of Wind Turbines, Edition 2010

5.000.08 Hz

-40.00

-100.00

dBg2

no iceice

5.000.00 Hz

-40.00

-100.00

dBg2

no iceice

5.000.00 Hz

-40.00

-90.00

dBg2

no iceice

DTU 10-MW wind turbine: OMA in power production

1st Backward Whirling Mode 1st Forward Whirling Mode 1st Tower modes

2nd Backward Whirling Mode

2nd Forward Whirling Mode

ROTATING – MBC

1st Flap Yaw

DTU 10-MW wind turbine: OMA in power production

3.500.00 Hz

0.01

0.01e-6

Log

g2

0.16

OperatingParked

1.400.10 Hz

3.36e-3

1.98e-6

Log

g23p 6p0.80 1.12

F Before MBCF After MBC

• Crosspower comparison: parked vs operating conditions • All pairs of asymmetric rotor edgewise modes in parked conditions become pairs of

rotor whirling modes owing to the rotation

Conclusions

Two methods for taking into account the time varying nature of the wind turbine have been implemented and applied to different test cases:

Multi-Blade Coordinate transformation (MBC) Harmonic Power Spectrum method (HPS)

Conventional OMA techniques can be applied to estimate the modal parameters

FUTURE DIRECTIONS • Further studies will be done regarding SHM techniques for wind turbine

blades • Applicability of the implemented methods will be tested in case of real

experimental data

Emilio Di Lorenzo – Research engineer – Siemens Industry Software nv PhD candidate at KU Leuven and University of Naples "Federico II" emilio.dilorenzo@siemens.com

Questions?