استفاده از شبکه های بیزی کلاس بندی ​​برای محاسبه توربین بادی خروجی انرژی متوسط طولانی مدت در یک سایت تبدیل انرژی بادی بالقوه

Due to the interannual variability of wind speed a feasibility analysis for the installation of a Wind Energy Conversion System at a particular site requires estimation of the long-term mean wind turbine energy output. A method is proposed in this paper which, based on probabilistic Bayesian networks (BNs), enables estimation of the long-term mean wind speed histogram for a site where few measurements of the wind resource are available. For this purpose, the proposed method allows the use of multiple reference stations with a long history of wind speed and wind direction measurements. That is to say, the model that is proposed in this paper is able to involve and make use of regional information about the wind resource. With the estimated long-term wind speed histogram and the power curve of a wind turbine it is possible to use the method of bins to determine the long-term mean energy output for that wind turbine. The intelligent system employed, the knowledgebase of which is a joint probability function of all the model variables, uses efficient calculation techniques for conditional probabilities to perform the reasoning. This enables automatic model learning and inference to be performed efficiently based on the available evidence. The proposed model is applied in this paper to wind speeds and wind directions recorded at four weather stations located in the Canary Islands (Spain). Ten years of mean hourly wind speed and direction data are available for these stations. One of the conclusions reached is that the BN with three reference stations gave fewer errors between the real and estimated long-term mean wind turbine energy output than when using two measure–correlate–predict algorithms which were evaluated and which use a linear regression between the candidate station and one reference station.

As stated by Hiester and Pennell [1], the interannual variability of wind speed at a potential wind energy conversion site is a very important issue. The energy that can be obtained with a wind turbine and, therefore, the economic feasibility of the project, will be very sensitive to the wind speed acting on the wind turbine over the working life of the facility. On occasions no historical series of wind data measurements for a potential candidate site are available that would enable an assessment of the economic feasibility of the investment planned for the installation of a Wind Energy Conversion System (WECS). One option that can be employed to make up for the drawback of a lack of such data is to undertake a wind data measurement campaign over a sufficiently long period of time. According to Hiester and Pennell [1], it is difficult to accurately estimate the mean values of the behaviour of the wind at a potential candidate site with less than 10 years worth of data. This option therefore entails an increase in costs to cover the measurement campaign and, importantly, postponing the decision-taking process for a normally unacceptably length of time. Another option entails the estimation by statistical methods of the interannual mean wind behaviour at the candidate site. Such methods rely on the existence of reference climatological stations installed at nearby sites, for which long-term wind resource measurements are available. These methods also require a wind data measurement campaign to be undertaken at the candidate site for a relatively short period of time (normally 1 year). Additionally, a portion of the reference station’s wind data has to coincide in terms of length of time and dates with the measurement period of the candidate site. For several authors [2], [3], [4], [5], [6], [7], [8] and [9], the first concern about a site under consideration for a wind power station is with the long-term (many years) mean wind speed. With this in mind, various methods have been proposed to estimate the long-term mean wind speed. Putnam [2] used a procedure that estimated the long-term mean wind speed View the MathML sourceV¯cLT at a candidate site that was based on knowledge of the mean wind speed determined over a short-term period View the MathML sourceV¯cST. This method is known as the method of ratios [3], [4] and [5] and is given by Eq. (1) equation(1) View the MathML sourceV¯cLT=V¯cSTV¯rLT/V¯rST Turn MathJax on View the MathML sourceV¯rLT is the long-term mean for the reference site and View the MathML sourceV¯rST is the short-term mean for the reference site (for the period coinciding with that of View the MathML sourceV¯cST. Conrad and Pollak [5] listed the requirements that need to be met so that the method of ratios can be applied. The main requirement is equivalent, from a mathematical point of view, to the demand for a high spatial correlation between the candidate and reference site wind speeds. Corotis [1], [3], [4], [6] and [7], using as a basis the hypothesis that the mean wind speeds at the candidate and reference site are distributed in accordance with a normal law, proposes a method that explicitly includes the spatial correlation coefficient (ρLT ) between both sites and the standard deviations for the candidate site View the MathML sourceσcLT and for the reference site View the MathML sourceσrLT, Eq. (2) equation(2) View the MathML sourceV¯cLT=V¯cST+ρLTV¯rLT-V¯rSTσcLT/σrLT Turn MathJax on The values of ρLT , View the MathML sourceσcLT are unknown and have to be estimated. Working on the hypothesis that the correlation varies little over time, the short-term rather than long-term correlation is normally used. Daniels and Schroeder [6] used a series of hypotheses to estimate View the MathML sourceσcLT. Other methods have been proposed in the scientific literature to tackle the problem arising from a site with few measurements of the wind resource [10], [11], [12] and [13]. However, the statistical method that has been most widely used over the last 20 years has been the measure–correlate–predict method (MCP) [14], [15], [16], [17] and [18]. There are several variants of the method, but they are all based on the existence of statistical relationships between two time-series data sets and try to model the relationship between wind data (speed and direction) measured at the candidate site over a short period of time (normally 1 year) and wind data simultaneously measured at a reference site. By introducing into the model the long-term wind data (normally from several years) measured at the reference site, the long-term wind data series are estimated for the candidate site. In the last few decades, the ‘data mining’ has become an increasingly common term [19] used to refer to the automatic or semi-automatic (assisted) process of extracting useful and understandable knowledge from a dataset [20]. Data mining incorporates numerous data analysis and model extraction techniques. This paper proposes the use of one of these techniques, probabilistic Bayesian networks (BNs) [19], [21], [22] and [23], to estimate the long-term mean wind speed frequency distribution (called a histogram) for a site with few measurements of the wind resource. The method proposed enables the use of multiple reference stations with a long history of wind speed and direction measurements. That is, the proposed model is able to make use of and involve regional information of the wind resource. The model has been implemented in Weka (Waikato Environment for Knowledge Analysis), free software available under the GNU General Public License [19] and developed by Waikato University (New Zealand). The intelligent system employed, the knowledgebase of which is a joint probability function of all the model variables, uses efficient calculation techniques for conditional probabilities to perform the reasoning. This enables automatic model learning and inference to be performed efficiently based on the available evidence. With the estimated long-term wind speed histogram and the power curve of a wind turbine it is possible to use the method of bins [24] or a probably density function that is fitted to the histogram [25], [26] and [27] to determine the long-term mean energy output for that wind turbine. The proposed model is applied in this paper to wind speeds and wind directions recorded at four weather stations located on the Canary Islands (Spain). Ten years of mean hourly wind speed and direction data are available for these stations. To estimate the goodness-of-fit of the proposed estimation models a comparison has been made between the errors generated with these models and those generated with two measure–correlate–predict (MCP) algorithms which have been evaluated [13] and [14]: a linear regression method and a vector regression method. For this purpose different metrics have been used. These metrics characterise the estimation of (1) the correct cumulative relative frequency histogram of the wind speed, (2) the correct mean wind power density and (3) the correct mean annual energy production. For this final analysis we have also used two commercial wind turbines of 330 and 800 kW rated power [28].

This paper has presented an application of probabilistic Bayesian networks to the estimation of long-term wind speed frequency histograms of stations with only short-term wind data measurements. The proposed Bayesian network models allow the use of multiple reference stations with a long history of wind speed and wind direction measurements. That is, they can involve and make use of regional information of the wind resource. This method, using graphic representation of the models, constitutes an attractive tool for the specification of the quantitative knowledge of those models. The graphs of the Bayesian networks express the dependency/independency relationships between the variables that make up the models. The proposed model can be an alternative to MCP models that employ linear regressions to relate the wind speeds between a candidate station and a reference station. As a result of the application of the Bayesian network model proposed in this paper to the data for wind speed and wind direction recorded at four weather stations in the Canarian Archipelago, the following conclusions are reached: (a) For the four stations analysed the BN models with three (BN-3) and two (BN-2) reference stations gave fewer errors than the reference MCPs used, independently of the metric employed in the estimation of the long-term cumulative wind frequency histograms. (b) The BN-3 and BN-2 models obtained display a high power of generalisation. The errors obtained in the training stage are very similar to the errors committed in the long-term prediction. (c) The Bayesian network models with three reference stations (BN-3) have provided for all the stations a better prediction of the mean electrical power obtainable from the wind with the two selected wind turbines than the other models used.