power curve evaluation from tests on multiple turbines
TRANSCRIPT
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Power curve evaluation from tests on multiple turbinesAxel Albers, Jochen Cleve
Vindkraftnet, 9. April 2018
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Agenda
▪ The problem of averaging multiple power curves and annex R of IEC 61400-12-1
▪ Three methods to average power curves
▪ Examples from power curve tests using nacelle lidars
▪ Conclusion
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Annex R of IEC 61400-12-1 Ed. 2 is ‘underdeveloped’
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Annex R states:
➢ Average AEP as average over individual test AEPs
➢ Reference to IEC 61400-12-2 (nacelle power curves) Annex I&J
➢ Uncertainty as simple average over individual uncertaintiesOR by means of error propagation (but method not specified).
➢ Correlation between uncertainty components mentioned and table given, but …
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Shortcomings of Annex R
– No clear recommendation which method to use for averaging power curves
– Texts mentions ‘… with minor adjustments in the handling of correlation’ but doesn’t explain these adjustments
– Table R.1 of correlation is incomplete
– Editorial errors
=> Ørsted asked Deutsche Windguard to work out a correct way to calculate the uncertainties of multiple power curve tests and include the use of nacelle lidars.
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Method 1: simple average of AEP & error propagation for uncertainties
𝐴𝐸𝑃AVG =
𝑚=1
𝐿1
𝐿𝐴𝐸𝑃𝑚
𝑢AEP,𝑘AVG =1
𝐿2
𝑚=1
𝐿
𝑛=1
𝐿
𝑢AEP,𝑚,𝑘𝑢AEP,𝑛,𝑘𝜌𝑚,𝑛,𝑘
𝑢𝐴𝐸𝑃AVE =
𝑘=1
𝑀
𝑢AEP,𝑘AVE2
These equations are basically the sophisticated option described in IEC – correlations 𝜌𝑚,𝑛,𝑘 have to be worked
out properly.
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M is the total number of uncertainty
components, containing both
category A and B uncertainties.
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Method 2: optimal weighting of power curves in terms of AEP
More accurate measurements should get higher weight on average!
𝐴𝐸𝑃weighted =
𝑚=1
𝐿
𝑡𝑚 𝐴𝐸𝑃𝑚
𝑚=1
𝐿
𝑡𝑚 = 1
𝐴𝐸𝑃weighted: weighted average annual energy production
𝐴𝐸𝑃𝑚: measured annual energy production of the m-th test turbine
𝑡𝑚: weighting factor of the m-th test turbine
L: total number of power curve tests
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Uncertainty of optimally weighted AEP
The uncertainty is calculated by error propagation of the relative uncertainties of the single power curve tests.
𝑢AEP,𝑘weighted =
𝑚=1
𝐿
𝑛=1
𝐿
𝑡𝑚𝑢AEP,𝑚,𝑘𝑡𝑛𝑢AEP,𝑛,𝑘𝜌𝑚,𝑛,𝑘
𝑢𝐴𝐸𝑃weighted =
𝑘=1
𝑀
𝑢AEP,𝑘weighted2
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Weighting factors 𝑡𝑚 are determined from minimising the total uncertainty in AEP
– 𝑢𝐴𝐸𝑃weighted 𝑡1, … , 𝑡𝐿 = 𝑢𝐴𝐸𝑃weighted = σ𝑘=1𝑀 𝑢AEP,𝑘weighted
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– minimise 𝑢𝐴𝐸𝑃weighted with boundary condition σ𝑚=1𝐿 𝑡𝑚 = 1
– minimisation problem is robust, the results converge quickly.
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Method 3: direct power curve averaging and weighting
Weighting and averaging of measured power and wind speed is performed in each wind speed bin:
𝑃weighted,i =
𝑚=1
𝐿
𝑡𝑚,𝑖 𝑃𝑚,𝑖
vweighted,i =
𝑚=1
𝐿
𝑡𝑚,𝑖 v𝑚,𝑖
𝑢𝑘,𝑖weighted =
𝑚=1
𝐿
𝑛=1
𝐿
𝑡𝑚,𝑖𝑢𝑚,𝑘,𝑖𝑡𝑛,𝑖𝑢𝑛,𝑘,𝑖𝜌𝑚,𝑛,𝑘,𝑖
𝑢𝑖weighted =
𝑘=1
𝑀
𝑢𝑘,𝑖weighted2
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𝑚=1
𝐿
𝑡𝑚,𝑖 = 1
Uncertainty component k:
Uncertainty in wind speed bin i:
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Example of combining three power curve tests
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Overview of power curve campaigns
– Three power curve tests have been conducted at undisclosed locations on an undisclosed turbine type
– Offshore wind farms
– Wind measured with nacelle lidars
– Measured power curves are close to each other (no outliers)
– Only changes in uncertainty will be shown here
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Reduction of uncertainty by combining three power curves
Mean annual wind speed
(Rayleigh distr.)
Reduction weighted
uncertainty compared to
average uncertainty
Reduction uncertainty optimal
weighting compared to equal
weighting
[m/s] [%] [%]
6.0 -11.2 -0.6
7.5 -10.5 -0.5
9.0 -9.8 -0.3
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• Error propagation of uncertainties leads to ~10% reduction in uncertainty compared to average uncertainty
• Optimal weighting yields minor improvement compared to equal weighting
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Comparison of uncertainties for direct power curve averaging
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– Direct weighting of power curvesenables to weigh individually in each wind speed bin.
– Additional advantage: problem of different wind range coverageis avoided.
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Reduction of uncertainty with direct weighting of power curves
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– Uncertainty reduction is also in the orderof 10%.
– At lower wind speeds a higheruncertainty reduction is achieved.
– Optimal weighting compared to equalweighting gives minor improvement of uncertainty.
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Reduction in uncertainty by direct power curve weighting
Mean annual wind speed
(Rayleigh distr.)
Reduction in uncertainty direct
power curve weighting
compared to AEP weighting
[m/s] [%]
6.0 -0.2
7.5 -0.8
9.0 -1.7
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Direct power curve weighting is a bit more complicated but leads to a (small) reduction in total uncertainty compared to AEP weighting.
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Topics not covered by this presentation
– Problem of different wind speed ranges covered by different tests
– Discussion of individual uncertainty components and their correlation
– Sampling uncertainty which is mentioned in Annex I&J of IEC 61400-12-2
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Conclusions
– With three tests a reduction of about 10% in uncertainty can be achieved.
– A weighted average of the power curve / AEP yields a slightly more accurate mean AEP / power curve.
– Direct power curve weighting offers only slight benefits over weighted AEP averaging but it is the most consistent approach.
– IEC should not allow to use a simple average of the uncertainty because the chief benefit from doing multiple tests would not be realised
– … and should state more clear recommendation, e.g. to always use weighted power curve averaging.
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