clbottasso scacciola acroce sgupta ewec2010

7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010

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POLI

diMI

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cnico

la

no

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cnico

la

no

ESTIMATION OF DAMPING FOR

WIND TURBINES OPERATING IN

CLOSED LOOP

C.L. Bottasso, S. Cacciola, A. Croce

Politecnico di Milano, Italy

S. Gupta

Clipper Windpower Inc., USA

EWEC 2010

Warsaw, Poland, April 20-23, 2010


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POLITECNICO di MILANO Poli-Wind Research Lab

Outline

Introduction and motivation

Approach: modified Pronys method for linear time

periodic systems

Applications and results:

- Simulation models

- Library of procedures for modes of interest

- Examples: tower, rotor and blade modes

Conclusions and outlook


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Introduction and Motivation

Focus of present work: estimation of damping in a wind turbine

Applications in wind turbine design and verification:

Explaining the causes of observed vibration phenomena

Assessing the proximity of the flutter boundaries

Evaluating the efficacy of control laws for low-damped modes

Highlights of proposed approach:

Closed loop: damping of coupled wind turbine/controller system

Applicable to arbitrary mathematical models (e.g., finite element

multibody models, modal-based models, etc.)

In principle applicable to a real wind turbine in the field


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Introduction and Motivation

Previous work:

Linear Time Invariant (LTI) systems:

Hauer et al., IEEE TPS, 1990; Trudnowski et al., IEEE TPS 1999

However: wind turbines are characterized by periodic coefficients

(vertical/horizontal shear layer, up-tilt, yawed flow, blade-tower

interaction, etc.)

Linear Time Periodic (LTP) systems:

Bittanti Colaneri, Automatica 2000; Allen IDETC/CIE 2007

However: methods well suited only when

characteristic time

(time to half/double)

much larger than period T (1rev):

T

Typically not the case for WT problems

E.g.: damping of tower fore-aft modes

Proposed approach:

transform LTP in equivalent/approximate LTI, then use

Prony

s

method (standard for LTI analysis)

T 5.5 sec

1

3.45 sec, 1st fore-aft tower mode

2

0,96 sec, 2nd fore-aft tower mode


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Outline



periodic systems


- Simulation models





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Approach

LTP system:

x

.

= A()x + B()u

A() = closed-loop matrix (accounts for pitch-torque controller)

u = exogenous input (wind), constant in steady conditions

Fourier reformulation (Bittanti Colaneri 2000):

A() = A0+i(Aissin(i)+Aiccos(i))

B() = B0+i(Bissin(i)+Biccos(i))

1. Approximate state matrix: A() 0

2. Transfer periodicity to input term (remark: arbitrary amplitude)

Obtain linear time invariant (LTI) system:

x

.

= A0x + Ub()

where b() = exogenous periodic input

Remark: no need for model generality, just good fit with measures


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Approach

Given reformulated LTI system

x

.

= A0x + Ub()

use standard

Pronys

method (Hauer 1990; Trudnowski 1999):

1. Trim and perturb with doublet (or similar, e.g. 3-2-1-1) input

2. Identify discrete time ARX model (using Least Squares or Output

Error method) with harmonic input

3. Compute discrete poles, and transform to continuous time (Tustin

transformation)

4. Obtain frequencies and damping factors


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Outline



periodic systems


- Simulation models





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Cp-Lambda highlights:

Geometrically exact composite-ready

beam models

Generic topology (Cartesiancoordinates+Lagrange multipliers)

Dynamic wake model (Peters-He,yawed flow conditions)

Efficient large-scale DAE solver

Non-linearly stable time integrator

Fully IEC 61400 compliant (DLCs,wind models)

Rigid body

Geometrically exact beam

Revolute joint

Flexible joint

Actuator

ANBA (Anisotropic Beam Analysis)cross sectional model

Compute

sectionalstiffness

Recover crosssectional

stresses/strains

Simulation Models


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Wind

easurement

noise

Simulation Environment


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Excitations (inputs)

Applications and Results

Response (outputs)

Definition of best practices for the identification

of modes of interest:

For each mode:

Consider possible excitations (applied loads,

pitch and/or torque inputs) and outputs (blade,

shaft, tower internal reactions)

Verify presence of modes in response (FFT)

Verify linearity of response

Perform model identification

Verify quality of identification (compare

measured response with predicted one)

Compiled library of mode id procedures:

In this presentation:

Tower fore-aft mode

Rotor in-plane, blade first edge modes


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Excitation: doublet of hubforce in fore-aft direction

Example: Damping Estimation of

Fore-Aft Tower Modes

Output: tower rootfore-aft bending

moment

Verification of linearity of response

Doublets of varying intensity to verify linearity


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First tower mode

Second tower mode1P

Verification of linearity of response and presence of modes


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Time domain

Frequency domain

Excellent quality of identified models

(supports hypothesis

A() 0) Necessary for reliable estimation


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Estimated damping ratios for varying wind speed




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Excitation: doublet of In-plane blade tip force Generator torque


Blade Edge and Rotor In-Plane Modes

First blade

edgewise mode

Quality of identified model, using blade root bending

Rotor in-plane

mode

Rotor in-plane

mode

Quality of identified model, using shaft torque

Outputs: Blade root bending moment Shaft torque


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Blade Edge and Rotor In-Plane Modes

Little sensitivity to used output

(blade bending or shaft torque)

Rotor in-plane mode

Blade edge mode


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Outline



periodic systems


- Simulation models





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Conclusions

Proposed a method for the estimation of damping in wind turbines:

Modified Pronys method (accounts for periodic nature of wind turbine

models)

Good quality model identification is key for reliable damping

estimation

Compiled library of mode id procedures (need specific inputs/outputs

for each mode)

Fast and robust

Outlook:

Riformulation leading to Periodic ARX, and comparison

Effect of turbulence (simulation study):

- Turbulence as an excitation

- Turbulence as process noise (filter error method)

Verify applicability in the field (theoretically possible)

clbottasso scacciola acroce sgupta ewec2010

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