robust data filtering in wind power systems by: andrés llombart-estopiñán circe foundation –...
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Robust data filtering in wind power systems
By: Andrés Llombart-EstopiñánCIRCE Foundation – Zaragoza University
Index
ObjectiveIntroduction: the need of filteringThe LMS fitting techniqueThe LMedS methodologyExperimental resultsConclusions
Index
ObjectiveIntroduction: the need of filteringThe LMS fitting techniqueThe LMedS methodologyExperimental resultsConclusions
Objective
To assess the performance of the Least Median of Squares method when it is used to filter wind power data
Index
Objective
Introduction: the need of filteringThe LMS fitting techniqueThe LMedS methodologyExperimental resultsConclusions
Introduction
Why it is needed?OperationMaintenanceProduction Control
Characterization of the P – v curves
High quality P – v data
Introduction
Circumstances that affect the data qualitySensor accuracyEMI Information processing errorsStorage faultsFaults in the communication systemsAlarms in the wind turbineetc
Introduction
An example of P – v data
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wind speed (m/s)
po
we
r (k
W)
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Introduction
P – v data after considering the SCADA alarms
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wind speed (m/s)
po
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Index
ObjectiveIntroduction: the need of filtering
The LMS fitting techniqueThe LMedS methodologyExperimental resultsConclusions
The LMS fitting technique
Gets the curve that minimizes the Mean Square Error
All measurements can be interpreted with the same model
Very sensitive to outliersBreakdown of 0% of spurious data
The LMS fitting technique
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LMS line
Index
ObjectiveIntroduction: the need of filteringThe LMS fitting technique
The LMedS methodologyExperimental resultsConclusions
The LMedS fitting technique
It is based in the existence of redundancyLMedS method uses the Median whereas
the LMS method uses the meanUnfortunately the LMedS method don’t
have analytical solution
The LMS fitting technique
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LMS line
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The LMedS fitting technique
ExampleFitting with a polynomial with 4 coefficientsn measurements
m possible solutions, where
!4!4
!
n
nm
The LMedS fitting technique
Steps to get the fitting:
1. Calculate the m subsets of the minimum number of measurements required to fit your curve
2. For each subset S, we compute a power curve in closed form PS
3. For each solution PS, the median MS of the squares of the residue with respect to all the measurements is computed
4. We store the solution PS which gives the least median MS
The LMedS fitting technique
Rejection of wrong data:Estimate de standard deviation
Probability of accepting a measure being good: 99 %
Threshold = 2.57
SMn 45148.1ˆ
Index
ObjectiveIntroduction: the need of filteringThe LMS fitting techniqueThe LMedS methodology
Experimental resultsConclusions
Experimental results
Methodology
A year of historical data 5 different tests
Alarm Records (AR) AR + classical
statistic method AR + robust statistic Classical statistic Robust statistic
Experimental results
Rough data Considered Alarms
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wind speed (m/s)
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Experimental results
AR + Class. Stat AR + Robust Stat.
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Experimental results
Classic Stat. Robust Stat.
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wind speed (m/s)
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Index
ObjectiveIntroduction: the need of filteringThe LMS fitting techniqueThe LMedS methodologyExperimental results
Conclusions
Conclusions
A robust filtering method has been proposed It has been proved successfullyThe method have shown a good
robustnessSome research is needed
Considering the wind direction
Robust data filtering in wind power systems
Thanks for your attention
The LMedS fitting technique
Example: fitting a polynomial of 4 coefficients for a 3 months period of data, that implies ~ 12.750 data
The computational cost is huge
151!4!4
!E
n
nm
The LMedS fitting technique
Solution: selecting randomly subsets Compromise:
Minimizing the number of subsetsWarranting a reasonable probability of not
failingSo, the first method step is substituted
by a Monte Carlo technique to randomly select k subsets of 4 elements
The LMedS fitting technique
How many subsets?A selection of k subsets is good if at least in
one subset all the measurements are goodPns is the probability that a measurement is
not spuriousPm is the probability of not reaching a good
solution
41log
log
ns
m
P
Pk
The LMedS fitting technique
In our example considering:Pns = 75 %Pm = 0,001
191log
log4
ns
m
P
Pk