The probability density function (PDF) of wind speed is important in numerous wind energy applications. A large number of studies have been published in scientific literature related to renewable energies that propose the use of a variety of PDFs to describe wind speed frequency distributions. In this paper a review of these PDFs is carried out. The flexibility and usefulness of the PDFs in the description of different wind regimes (high frequencies of null winds, unimodal, bimodal, bitangential regimes, etc.) is analysed for a wide collection of models. Likewise, the methods that have been used to estimate the parameters on which these models depend are reviewed and the degree of complexity of the estimation is analysed in function of the model selected: these are the method of moments (MM), the maximum likelihood method (MLM) and the least squares method (LSM). In addition, a review is conducted of the statistical tests employed to see whether a sample of wind data comes from a population with a particular probability distribution. With the purpose of cataloguing the various PDFs, a comparison is made between them and the two parameter Weibull distribution (W.pdf), which has been the most widely used and accepted distribution in the specialised literature on wind energy and other renewable energy sources. This comparison is based on: (a) an analysis of the degree of fit of the continuous cumulative distribution functions (CDFs) for wind speed to the cumulative relative frequency histograms of hourly mean wind speeds recorded at weather stations located in the Canarian Archipelago; (b) an analysis of the degree of fit of the CDFs for wind power density to the cumulative relative frequency histograms of the cube of hourly mean wind speeds recorded at the aforementioned weather stations. The suitability of the distributions is judged from the coefficient of determination R2. Amongst the various conclusions obtained, it can be stated that the W.pdf presents a series of advantages with respect to the other PDFs analysed. However, the W.pdf cannot represent all the wind regimes encountered in nature such as, for example, those with high percentages of null wind speeds, bimodal distributions, etc. Therefore, its generalised use is not justified and it will be necessary to select the appropriate PDF for each wind regime in order to minimise errors in the estimation of the energy produced by a WECS (wind energy conversion system). In this sense, the extensive collection of PDFs proposed in this paper comprises a valuable catalogue.

A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands

A review of wind speed probability distributions used in wind energy analysis: case studies in the canary islands: case studies in the canary islands

We consider estimation of the long term average power output from a wind turbine generator at a site for which few data on wind speeds are available. Long term records of wind speeds at the 12 synoptic meteorological stations are also used. Inference is based on a simple and parsimonious approximating model which accounts for the main features of wind speeds in Ireland, namely seasonal effects, spatial correlation, short-memory temporal autocorrelation and long-memory temporal dependence. It synthesizes deseasonalization, kriging, ARMA modelling and fractional differencing in a natural way

https://rss.onlinelibrary.wiley.com/doi/pdf/10.2307/2347679

Space-time modelling with long-memory dependence assessing Ireland's wind power resource

An assessment of wind energy potential as a power generation source in the capital of iran, tehran

A 100% renewable electricity generation system for New Zealand utilising hydro, wind, geothermal and biomass resources

A method is presented for estimating the probability distribution of wind power from a dispersed array of wind turbine sites where the correlation between wind speeds at distinct sites is less than unity. The distribution is obtained from a model for the joint probability distribution of wind speeds. This is able to incorporate arbitrary inter-site correlations. It is shown that this joint distribution reduces in the single site case to a wind speed distribution closely approximating the widely used Weibull; the multiple site power distribution is also shown to fit adequately to data on wind speeds from four sites in Western Australia. Results presented in graphical and tabular form for a range of representative cases show that a significant reduction in the variability of total wind power output may result from dispersion of aerogenerator sites; a quantitative guide to the magnitude of these effects is also provided.

John Carlin

Papers

The Probability Distribution of Wind Power From a Dispersed Array of Wind Turbine Generators

A theoretical model for estimating the capacity credit of wind power in the presence of correlation between wind speed and electricity demand