clbottasso scacciola acroce sgupta ewec2010
TRANSCRIPT
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POLI
diMI
te
cnico
la
no
te
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
2/19
DampingEs
timationofW
indTurbines
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
3/19
DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
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DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
5/19
DampingEs
timationofW
indTurbines
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
6/19
DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
7/19
DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
8/19
DampingEs
timationofW
indTurbines
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
9/19
DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
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DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
Wind
easurement
noise
Simulation Environment
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DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
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DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
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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DampingEs
timationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
Example: Damping Estimation of
Fore-Aft Tower Modes
First tower mode
Second tower mode1P
Verification of linearity of response and presence of modes
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DampingEstimationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
Example: Damping Estimation of
Fore-Aft Tower Modes
Time domain
Frequency domain
Excellent quality of identified models
(supports hypothesis
A() 0) Necessary for reliable estimation
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DampingEstimationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
Estimated damping ratios for varying wind speed
Example: Damping Estimation of
Fore-Aft Tower Modes
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DampingEstimationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
Excitation: doublet of In-plane blade tip force Generator torque
Example: Damping Estimation of
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
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DampingEstimationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
Example: Damping Estimation of
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
18/19
DampingEstimationofW
indTurbines
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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7/24/2019 CLBottasso SCacciola ACroce SGupta EWEC2010
19/19
DampingEstimationofW
indTurbines
POLITECNICO di MILANO Poli-Wind Research Lab
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)