[MUSIC] My name Philippe Drobinski and I'm going to be your guide on this blog. I'm a former engineer, professor at the Ecole Polytechnique, and researcher at CNRS in atmospheric physics. Wind energy is referred as a variable generation source because its electricity production varies based on the availability of wind. Some aspects of wind variability are predictable. Other aspects, such as intermittent wind gusts, are much less so. To calculate the likely power output from a given wind turbine, it is necessary to characterize the wind energy available in a planned wind turbine farm location. And this is on what we will focus on this block, on the characterization of the available wind energy in a specific site. We will guide you to be able to classify a data set from a long series of measurements for further statistical analysis. Build a wind speed probability density function, also called PDF, from the data set. And model this data using a Weibull or Rayleigh distribution. Let's start by working at a 12 hour wind speed measurement series from. Some aspects of wind variability are predictable. Other aspects, such as intermittent wind gusts, are much less so. Focusing on the variability, the wind speed can change over seconds, minutes or hours. Most changes are generally small and caused by random events, also called turbulence. Over several hours however, these changes can be of much more importance and tend to be more predictable as related to meteorological changes or local events, as the wind breeze for example. The variability of wind speed is important to characterize the wind power, so statistical analysis will be necessary. As the average wind speed in a location only paints half of the picture, the full distribution of wind speed values might be necessary. This means we will use probability theory. In probability theory, a probability density function is a function that describes the relative likelihood for a random variable to take on a given value. In our case, the random variable is the wind speed. In our illustration, we have taken a one week measurement of wind speed. The wind energy assessment would need longer series of at least one year measurements in the location of interest. To compute the probability density function of a time series of wind speed values, we first compute the frequency distribution function. First, we will organize the data to convert our measurements into a sample data space. Then we select significant delta t, for our study, typically ten minutes, and average the wind values for each deltat, here, the points in red. Doing so, we will obtain and discrete wind averaged values. Those n averaged values will be our starting sample space for statistical analysis. Second, we will select the statistical classes, Vi, for each interval that will necessarily be the mean value of the interval itself, defining as well the width interval delta V. This way we will obtain m intervals defined by the formula on the screen. And also the range of the distribution, typically for wind measurements from 1 to 20 meters per second. On our screen example, we have chosen a 1 meter per second with interval ranging from 0 to 7 meter per second. And the defined classes are the natural numbers 0, 1, 2, etc. So a given class of 5 meter per second will represent values from 4.5 to 5.5 meter per second. The last step is counting the total number of occurrences for each interval. In the example, the numbers are in blue. Taking our example for velocities ranging from 1.5 to 2.5 meter per second, the number of measurements counted in interval, the red dots, is 196. The possible outcomes can now be classified for statistical analysis. For example, in a table the organized data table will look like this one. With intervals on the first column, the statistical classes on the second column and the number of occurrences on the third column. On the fourth column, we will include the absolute frequency defined as the number of occurrences in each class divided by the total number of outcomes. While the absolute frequencies and sample gives us the frequency distribution, the normalized frequency distribution or absolute frequency defines the probability density function. In this case, the discrete probability density function, or PDF. Histograms, as in this figure, is a usual graphical representation of this data. As you can see in the abscissa axis, the velocity classes, or the possible outcomes, are represented. And the probability outcome is represented by the ordinate axis. The zero wind speed values are excluded from from the distribution. The first class is the 1 meter per second mean value interval. For this example, the probability to have a wind speed ranging between 4.5 and 5.5 meter per second is about 5%. The most probable wind speed is around 7 meter per second. The right tail shows the frequency of extreme wind speed. Our focus will be now in deriving an analytical expression to fit the probability density function. This is a way to reduce the number of parameters to characterize the probability density function and the estimate wind power resource. And modeling the shape of the probability density function with a generic function opens the way to standardization. And of course, it is more convenient to work with a function rather than with just theta. A lot of different statistical and analytical functions are commonly used and fitted to data, as it's easier to work with a continuous probability density function equation than it is with one. Some of the most usual ones are listed here. In most cases, wind speeds can be modeled using the so-called viable distribution, which is an extremely commonly used paradigm used to model wind speed statistics. We will focus on these analytical functions and their parameters on the next video. Thanks for your attention and see you later.
