John Berner /President/Applications Research Inc./ jmb@applicationsresearch.com
A shape factor tells of the data’s distribution. A shape factor of 3 or more approaches a normal distribution.
One way to glean more information from wind data is to examine it with a Weibull routine. It is a fast and the most accurate way to analyze wind speed and energy data.
The Weibull distribution is unique in that it has the ability to reveal, rather than mask, the correct distribution of data. For example, a Weibull shape factor of 1.0 represents an exponential distribution. A shape factor of 2.0 is a Raleigh distribution, while a Weibull shape factor of about 3.0 or above represents an approximate normal distribution. If data you’ve assumed to be distributed exponentially comes out with a Weibull shape factor of about 3.0, you’d best revisit your assumption.
In addition, use of Weibull analysis routines to estimate a data set’s characteristics, simply recognizes the fact that data is rarely 100% normal, binomial, or exponential. The reason for this is because any reasonably complex relationship will never exhibit a distribution shape that exactly matches any one of the traditional shapes. Each data point is almost invariably due to multiple effects. For example, usable wind velocity is a function of both direction and speed. This is why Weibull works.
The figures are calculated by the software. When users apply a cut-in and cut-out speed, the software responds with the fractional period of useful wind.
The Weibull procedure represents your data as it is, rather than as you might guess (or even hope) it to be. Put another way: Weibull calculations fit the curve to the data, as opposed to fitting the data to the curve. In most instances, the Weibull fit will be the most accurate and dependable representation of data.
Most wind-data sets tend to hover around or above a Raleigh distribution. Some people simply fit the data to a Raleigh distribution to be done with it. This corresponds to a Weibull routine shape factor of exactly 2.0, and that is often acceptable. However, a more accurate analysis results from the actual Weibull curve-fit analysis. There are a number of programs available for fitting a curve to data by way of a Weibull routine. Weibull-Ease, however, carries the standard analysis a step further and it has a built-in routine dedicated to wind energy.
The program first calculates a fit to the wind velocity data. After correcting for offset, the Weibull shape factor for the applied data is 2.246.
After applying 213 data points of speed and direction, Weibull Ease returns this data. The shape figure of 2.246 tells that the input data is not quite a normal distribution.
Next, the program calculates energy levels as a density function of speed. This is by way of a routine based upon root-mean-cube of velocity.
Then, by using cut-in and cut-out speeds for a particular wind turbine, it modifies the root-mean-cube value to take those values into account. Default values are used for starters to show how it works.
Author John Berner
The program also lets users modify the cut-in and cut-out speeds to investigate how these values effect energy output. This is accomplished by re-calculating the root-mean-cube value based only upon values that fall in between the user-supplied cut-in and cut-out speeds.
Finally, this amounts to a clean, neat, and fast method for calculating the most critical variable for subsequent energy, load, or economic analyses – the root-mean-cube of velocity. WPE
Filed Under: News, Software, Turbines
