Wind Farm Performance Monitoring with Exploratory Factor ...
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Wind Farm Performance Monitoring with
Exploratory Factor Analysis
Niko Mittelmeier, Katharina Neumann
Analysis of Operating Wind Farms, EWEA Workshop, Malmö 9.12.2014
2
Agenda
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Introduction
About Exploratory Factor Analysis
EFA applied to wind turbine data
A monitoring demonstration
Summary and Outlook
3
Introduction
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Objective:
Robust detection of changes in turbine behaviour
Massive amount of data is collected from each turbine
Proposal: Advanced statistical models
4
Agenda
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Introduction
About Exploratory Factor Analysis
EFA applied to wind turbine data
A monitoring demonstration
Summary and Outlook
5
About Exploratory Factor Analysis
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Reduce observed variables to fundamental underlying unobserved variables
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About Exploratory Factor Analysis
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
𝑋𝑖 = 𝑎1𝐹1 + 𝑎2𝐹2 + …𝑎𝑝𝐹𝑝 + 𝑒𝑖
𝑋𝑖 : ith observed variable
𝐹1−𝑝: common factors (underlying unobserved variable)
𝑎1−𝑝: loadings
𝑒𝑖: not explained by the common factors (error term)
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About Exploratory Factor Analysis
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Develop covariance matrix from raw data
No missing values are allowed
Kaiser-Harris criteria to estimate the number of common factors
(number of eigenvalues of cov. matrix > 0)
Estimate loadings (are not unique)
Rotate matrix (maximize one loading and minimize the others)
• Maximum likelihood
• Principal axis
• (generalized) weighted least square
• Minimum residual ( minimizes the square sum of the off diagonal )
8
Agenda
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Introduction
About Exploratory Factor Analysis
EFA applied to wind turbine data
A monitoring demonstration
Summary and Outlook
9
EFA applied to wind turbine data
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Choose the variables Xi to be observed:
Pitch
Power
Torque
Revolution speed
Wind speed
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EFA applied to wind turbine data
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
F1
F2
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EFA applied to wind turbine data
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Standardize Observations: 𝑋′𝑖 =𝑋𝑖−𝑋𝑖
𝑆𝑖
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EFA applied to wind turbine data
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
minimum residuals (method)
Oblique: correlation between the Factors has been allowed
F1
F2
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Agenda
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Introduction
About Exploratory Factor Analysis
EFA applied to wind turbine data
A monitoring demonstration
Summary and Outlook
14
A monitoring demonstration
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Turbine Data from different operational modes
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A monitoring demonstration
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
To cover the full turbine behaviour, at least five variables are necessary
torque
pitch
power
wind speed
revolution speed Wind speed
revolution speed
torque
pitch
power
Normal operation
Mode 1
Mode 2
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A monitoring demonstration
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
The correlation of the two common factors shows clearly a different
behavior
Normal operation
Mode 1
Mode 2
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EFA applied to wind turbine data
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Normal operation Mode 1
Mode 2
F2
F2
F2
F1F1
F1
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A monitoring demonstration
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Choosing a smaller sample from the data
No suspicious behaviour visible in this plot
Normal operation
Mode 1
Mode 2
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A monitoring demonstration
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
The correlation of the two common factors shows clearly a different
behavior but less samples reduce the clarity
Normal operation
Mode 1
Mode 2
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A monitoring demonstration – Wind Farm Scan
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
21
Agenda
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Introduction
About Exploratory Factor Analysis
EFA applied to wind turbine data
A monitoring demonstration
Summary and Outlook
22
Summary and Outlook
Wind Farm Performance Monitoring with Exploratory Factor Analysis · N. Mittelmeier, K. Neumman · SENVION · 09.12.2014
Summary:
Turbine behaviour can be expressed with two common factors
Exploratory factor analysis needs a certain sample size
With 10 min data, the time to detect changes would be to long
Higher frequency data (e.g. 30s data) needs more memory space
Factors can be used as statistical summary of high frequency data
Outlook:
Check minimal sample size
Check optimal data frequency
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SENVION SE
Mittelmeier Niko
Wind Farm Performance Specialist
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