the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Probabilistic lifetime extension assessment using mid-term data: Lillgrund wind farm case study
Abstract. Estimating the site-specific fatigue reliability of wind turbines is an integral part of probabilistic lifetime extension assessment. Limitations in type, accuracy, and availability of site-specific data is one of the main challenges in such estimations. The present research tackles the challenge of estimating long-term fatigue loads using short-term strain gauge measurements via statistical extrapolation. The case study wind turbine is a Siemens 2.3 MW, in the Lillgrund wind farm, located in the Øresund strait between Denmark and Sweden. The turbine is heavily instrumented and Supervisory Control and Data Acquisition (SCADA) is also available. The study also reassesses the performance of the Frandsen model – as a simplified approach for estimating higher turbulence due to wakes – in a compact wind farm layout using aeroelastic simulations of the case study wind turbine. Furthermore, it shows the sensitivity of the site-specific reliability with respect to the uncertainty in material strength, fatigue load, and damage accumulation model.
The results reveal that for the case-study site, the Frandsen model underestimates turbulence in below-rated mean wind speeds and overestimates the turbulence in above-rated mean wind speeds. However, using the Frandsen model for estimating the long-term fatigue loads in the case study location leads to a 35 % lower reliability index than a site-specific assessment using data from the SCADA system and, thus, is relatively more conservative. The study reveals that the sensitivity of the fatigue reliability to the load’s uncertainty is negligible in assessment using site measurements and relatively high when using the Frandsen model.
The extrapolation approach used in the current study can facilitate the use of digital twins when strain gauge measurements are unavailable for a part or the whole span of the lifetime. In addition, the assessment of the Frandsen model in the case study wind farm, as an example of a wind farm with short spacing, adds valuable information to the ongoing studies in the literature about the performance of the model in intense and mixed-waked conditions. Finally, the provided information about robustness of the reliability based on the load estimation approach, is useful for considering uncertainty in the lifetime extension assessment.
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Status: final response (author comments only)
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RC1: 'Comment on wes-2024-68', Anonymous Referee #1, 19 Jul 2024
- AC1: 'Response letter (reviewer #1 comments)', Shadan Mozafari, 24 Aug 2024
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RC2: 'Comment on wes-2024-68', Anonymous Referee #2, 26 Jul 2024
Lifetime extension of wind turbines is a very important topic of high industrial relevance. Using a probabilistic approach is also very relevant. Therefore, the paper is of interest to be published. However, there are a number of unclear sections and missing explanations, see below. A major revision is recommended.
Detailed Comments:
Line 79
’ One must consider that the material properties are calibrated such that the target reliability level of 3.7 ISO-2394 (2015) is reached’: this is an annual reliability index? And why 3.7? which components are considered?
Line 80
‘the levels are not’: unclear – reformulate
Line 161
Which ‘exponent’? wind shear?
Table 2
Is full (Weibull) distribution of turbulence used as specified in IEC 61400-1:2019? And if not add a comment on the potential influence
Line 174
Rayleigh
Line 174 + 178
Why use two different editions. Use ed 4 in order to obtain up-to-date comparisons?
Line 190
Explain equation
Eq (4)
Missing m in eq?
Eq (6)
k ?
M to power m ?
for composites the mean stress level is important. How is that accounted for?
Line 213-215
Unclear – reformulate
Eq (8)
How is lifetime damage obtained from 10-min damage?
Line 218
‘probability of turbulence’: which turbulence (ambient, effective, …) is the probability linked to?
Line 221
Conditional probabilities?
Line 235
Explain why ‘log’ is used
Line 240
Describe what is 30-year return loads’. Is it 30-year extreme loads to account for the extreme loads being important due to the high Wohler exponent?
Line 240
‘Forming a database based on the distribution’: unclear – explain which distribution. If the realizations follow the distribution function how is new information obtained?
Eq (10)+(11)+(12)
Explain the probabilistic assumption behind eq (10)
Eq (1): Lr is not included in the right hand side of the equation?
Probabilities in eq (11) always between 0 and 1?
Explain reference times for the probabilities
Are the loads obtained ‘random point in time’ loads or maximum loads with a certain reference period?
Section 2.4.4
The Frandsen and IEC turbulence models together with partial safety factors are intended for deterministic design and not for probabilistic design and reliability analysis. This link should be included in the probabilistic formulations.
Line 268
‘probability of failure at time t and can be stated as the probability of exceeding a certain level’: this probability is the probability of failure at time t and not the accumulated probability of failure up to time t and also not the annual probability of failure?
Figure 2
The uncertainty of DEL is modelled by log(DELlifetime) ? add description of the uncertainty modelled by DELlifetime . How is this uncertainty quantified and does it include model uncertainty in estimating the stress ranges (obtained from a validation process)? This stochastic modelling assumes that strain gauge measurements are available for the fatigue detail considered?
Eq (14)
Where does the time t enter in the limit state equation?
Line 288
Explain how R=10 is used and why R=10 to account for mean stress level?
Table 3
How is the mean value calibrated?
Mean and standard deviation of log(DELlifetime) are missing in the table?
Line 295
‘based on survival in the year before’: not correct – reformulate
Figure 2
Add explanation of all symbols in the figure
Figure 3
Could a Weibull distribution (as used in IEC 61400-1:20+29) fitted to the upper tail be as representative as the distributions considered?
Line 336
‘extrapolate the distribution to a 30-year return load’: figure 3 shows random point in time observations of the turbulence level. Is this distribution used to estimate the load with a return period of 30 years? Or is the load with a return period of 30 years estimated using e.g. a peak-over-threshold technique considering the extreme, statistical independent loads observed during the measurement period (as in DLC 1.1 load extrapolation)? More explanation is needed.
And how to use the load with a return period of 30 years for fatigue assessment?
Line 357
The target annual reliability index in IEC 61400-1 Annex K is 3.3 (and not 3.7 as indicated in some DNV standards – assuming a ductile failure mode)
Figure 7
As mentioned above the IEC and Frandsen models are intended for deterministic design with safety factors, not for reliability analyses. Recommendation: use the same approach for reliability analysis as in papers and reports related to fatigue of welded steel details in wind turbines.
Table 4
How is sensitivity defined?
Citation: https://doi.org/10.5194/wes-2024-68-RC2 - AC2: 'Response letter (reviewer #2 comments)', Shadan Mozafari, 24 Aug 2024
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EC1: 'Comment on wes-2024-68', Raimund Rolfes, 29 Jul 2024
The scientific problem addressed by the paper is very relevant. However, the paper needs very substantial improvement of focus and of clarity. In its present form it does not meet the standards of WES.
Citation: https://doi.org/10.5194/wes-2024-68-EC1 - AC1: 'Response letter (reviewer #1 comments)', Shadan Mozafari, 24 Aug 2024
- AC2: 'Response letter (reviewer #2 comments)', Shadan Mozafari, 24 Aug 2024
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