By Andrew Williams, UK correspondent

Inaccuracies in the methodology used to calculate the long-term wind resource prior to construction often result in many wind farm projects failing to deliver the levels of energy production and revenue predicted pre-construction.

To address this issue, Sinclair Knight Merz (SKM) has developed a new model, the Weibull correlation, that could assist developers in more accurately estimating energy outputs and have significant benefits for developing preventative operation and maintenance (O&M) strategies.

Current weaknesses

The Annual Energy Production (AEP) of proposed wind farms is commonly calculated using a three-stage Measure, Correlate and Predict (MCP) methodology.  At stage one, wind speeds at the proposed site and a nearby weather station are measured simultaneously over a set period. 

Next, the relationship, or correlation, between the sites is established by plotting the two short-term data sets against each other.  The long-term site wind resource is then predicted using long-term data from the weather station together with the established relationship between the weather station and the site, forming the basis of AEP calculations.

At the correlation stage, developers choose between two different ‘mathematical curves’ to describe the relationship between weather station and site data. 

The first, based on a numerical analysis, often uses straight lines to depict the relationship.  The second, based on an analytical analysis, uses a mathematical function that actually describes the physical properties of the wind. 

Historically, developers have assumed a ‘straight-line’ relationship between site and nearby meteorological station data, meaning that site wind speed is either a direct function of met station wind speed (in effect a line through origin or a ratio) or a straight line with a slope and offset.  As an example, such correlations might suggest that the wind at a proposed site is always twice the speed of the wind at the met station.  

“However, neither method has a connection with the characteristics of the wind resource,” says Paul van Lieshout, Wind Power Group Manager at SKM Europe Ltd.

“This assumption is based on simple mathematical statistics - it does not include nor describe the physical properties of wind and hence it affects the accuracy of AEP results,” he adds.

The Weibull Correlation

SKM has devised an improved correlation methodology to establish better relationships between site and met station data.  This methodology, an analytical analysis using ‘Weibull’ parameters, establishes a long-term resource data set upon which the AEP of a proposed wind farm can be calculated with greater accuracy.

The SKM correlation is based on IEC 61400 defined Weibull distribution curves derived from short-term measurements at the site and the met station.  Weibull curves are defined by two parameters, the k-factor (or shape factor), and the A-parameter or scale parameter (also known as lambda (λ).  Graph 1 shows data simultaneously measured at a site and a met station (red dots - with met station data on the x-axis and site data on the y-axis).  It also shows three possible correlation curves:

The red curve in the image above is based on the Weibull correlation, which is a function of the four different Weibull parameters (kmet, λmet, ksite and λsite );

The black curve is based on the above mentioned ‘ratio’ analysis where, at higher wind speeds, the curve doesn’t fully describe the measured data (i.e. it over-estimates site wind speed);

The blue curve uses a straight line correlation function with a slope and offset, indicating that it is always windy at the site (no zero wind speeds).

Verifying the results 

Analysis shows that, whereas the ‘straight line forced through origin’ data is better than the ‘straight line with an offset’ methodology, both are less accurate than the Weibull methodology. 

The graph above shows a ‘normalised’ AEP (black vertical line) compared to each of the three correlation methodologies.  The red curve is based on the Weibull methodology, which clearly shows results closest to the actual levels.  The green curve is based on the straight line forced through zero correlation (which overestimates the site’s AEP) and the blue curve is based on the straight line correlation, which underestimates the wind resource.

Benefits for Developers and Operators

In both onshore and offshore assignments to calculate AEP values for developers, investors and financial institutions, SKM has found that the Weibull methodology yields higher accuracy and lower uncertainty whenever site and weather station data is of sufficiently high quality.

“The Weibull correlation function is more than just a ‘fitting of a curve through data.’  It provides a relationship that should also hold for future measurements, assuming that ‘surroundings’ don’t change,” says van Lieshout.

Although based on quite complicated statistical techniques, it seems that the claimed advantages of the Weibull correlation model are quite plain – more accurate knowledge of the predicted energy output of a site will provide developers with much more confidence in the continued success of their projects.

To respond to this article, please write to:

Andrew Williams: TheGreenExpert@btinternet.com

Or write to the editor:

Rikki Stancich: rstancich@gmail.com