{"id":612,"date":"2022-09-20T09:13:00","date_gmt":"2022-09-20T14:13:00","guid":{"rendered":"https:\/\/demo.creativethemes.com\/blocksy\/homi\/?p=612"},"modified":"2024-06-14T22:59:59","modified_gmt":"2024-06-15T03:59:59","slug":"estimate-weibull-parameters","status":"publish","type":"post","link":"https:\/\/ienergyplus.com\/es\/estimate-weibull-parameters\/","title":{"rendered":"C\u00f3mo estimar los par\u00e1metros de Weibull para una distribuci\u00f3n de velocidades del viento"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The <strong><a href=\"https:\/\/iienergyplus.com\/weibull-and-rayleigh-distributions\/\" data-type=\"URL\" data-id=\"https:\/\/iienergyplus.com\/weibull-and-rayleigh-distributions\/\">Weibull distribution<\/a><\/strong> is widely used in wind energy to mathematically model the distribution of wind speeds at a study site. This distribution is characterized by two parameters, <strong>the scale factor (c) <\/strong>and <strong>the shape factor (k)<\/strong>. Accurately estimating these parameters is essential for predicting the energy generated by a wind farm and making informed decisions. In this article, <strong>we will explore how to estimate Weibull parameters<\/strong> from a wind speed distribution using different methods such as the maximum likelihood method, the energy pattern factor method method, moment method and others.<\/p>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-3911300806559936\"\n     crossorigin=\"anonymous\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-3911300806559936\"\n     data-ad-slot=\"9222947307\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<p class=\"wp-block-paragraph\">The scale parameters <img decoding=\"async\" class=\"wp-image-1490\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/scale-parameter-c.svg\" alt=\"\"> and <img decoding=\"async\" class=\"wp-image-1491\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/shape-parameters-k.svg\" alt=\"\"> can be estimated using the following methods:<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">1. Maximum likelihood method<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The application of the maximum likelihood method involves maximizing the probability that the observed data fits the Weibull distribution with the estimated parameters. This method provides accurate and reliable estimates of the Weibull parameters, which are essential for predicting the energy generated by a wind farm. On the other hand, it is difficult to solve, since numerical iterations are needed to determine the parameters k and c. To estimate the Weibull parameters, the following equations are used:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/1-1.svg\" alt=\"\" class=\"wp-image-1472\" style=\"width:416px;height:80px\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/2.svg\" alt=\"\" class=\"wp-image-1473\" style=\"width:184px;height:83px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Where <img decoding=\"async\" class=\"wp-image-1489\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/15.svg\" alt=\"\"> is the number of observations and <img decoding=\"async\" class=\"wp-image-1488\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/14.svg\" alt=\"\"> is the average wind speed recorded in time interval i.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. Energy pattern factor method <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This method is particularly useful when<strong> data availability is limited<\/strong>. The energy pattern factor is calculated from wind power and used to fit a wind speed distribution to the energy distribution. This method is related to averaged wind speed data and is defined by the following equations: <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/3-1.svg\" alt=\"\" class=\"wp-image-1475\" style=\"width:118px;height:68px\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/4.svg\" alt=\"\" class=\"wp-image-1476\" style=\"width:160px;height:63px\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/5.svg\" alt=\"\" class=\"wp-image-1477\" style=\"width:193px;height:69px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Where E<sub>pf<\/sub> is the energy pattern factor and is the gamma function <img decoding=\"async\" class=\"wp-image-1487\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/13.svg\" alt=\"\"> defined by: <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/6.svg\" alt=\"\" class=\"wp-image-1478\" style=\"width:260px;height:67px\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">3. Moment method<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This method involves equating the moments of the Weibull distribution with the moments of the observed wind speed data. The estimation of the parameters is done by solving a system of non-linear equations. In this method, information from the moments of the wind speed data is used to obtain accurate estimates of the Weibull parameters. The moment method can be used as an alternative to the maximum likelihood method. In this case, the parameters k and c are determined by the following equations:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/7.svg\" alt=\"\" class=\"wp-image-1480\" style=\"width:179px;height:64px\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/8.svg\" alt=\"\" class=\"wp-image-1482\" style=\"width:390px;height:70px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Where <img decoding=\"async\" class=\"wp-image-1485\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/11.svg\" alt=\"\"> is the mean wind speed and <img decoding=\"async\" class=\"wp-image-1486\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/12.svg\" alt=\"\"> is the standard deviation of the data of the wind speed. <\/p>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-3911300806559936\"\n     crossorigin=\"anonymous\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-3911300806559936\"\n     data-ad-slot=\"9222947307\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<h2 class=\"wp-block-heading\">4. Empirical method <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The empirical method is considered a special case of the moment method. It is a quick and simple method where the Weibull parameters k and c can be calculated by the following equations:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/9.svg\" alt=\"\" class=\"wp-image-1483\" style=\"width:176px;height:61px\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/10.svg\" alt=\"\" class=\"wp-image-1484\" style=\"width:193px;height:69px\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">5. Method of least squares<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This method is based on the Weibull cumulative distribution function. The wind speed values are interpolated by a straight line using the concept of least squares.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/02\/4.svg\" alt=\"\" class=\"wp-image-927\" style=\"width:365px;height:66px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" class=\"wp-image-1494\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/wind-speed.svg\" alt=\"\">: Wind speed (m\/s).<br><img decoding=\"async\" class=\"wp-image-1495\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/Funcion-acumulado.svg\" alt=\"\">: Weibull cumulative distribution function.<br><img decoding=\"async\" class=\"wp-image-1490\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/scale-parameter-c.svg\" alt=\"\">: Scaling factor (m\/s), value close to the annual mean velocity.<br><img decoding=\"async\" class=\"wp-image-1491\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/shape-parameters-k.svg\" alt=\"\">: Shape factor characterizing the asymmetry or skewness of the F(v) function.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The above equation can be transformed linearly by taking the Neperian logarithm twice. This gives it:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/02\/5.svg\" alt=\"\" class=\"wp-image-929\" style=\"width:225px;height:49px\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/02\/6.svg\" alt=\"\" class=\"wp-image-932\" style=\"width:356px;height:24px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">We proceed to least squares fitting. By substituting the standard form of the linear regression equation can be obtained:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/02\/7.svg\" alt=\"\" class=\"wp-image-937\" style=\"width:124px;height:25px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Where &#8220;a&#8221; and &#8220;b&#8221; are calculated using linear regression of the cumulative distribution function.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The slope (k) can be calculated:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/02\/8.svg\" alt=\"\" class=\"wp-image-941\" style=\"width:405px;height:66px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The value of &#8220;b&#8221; can be calculated:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/02\/9.svg\" alt=\"\" class=\"wp-image-943\" style=\"width:433px;height:68px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The scale parameter (c) is equal to:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/02\/10.svg\" alt=\"\" class=\"wp-image-945\" style=\"width:93px;height:33px\"\/><\/figure>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-3911300806559936\"\n     crossorigin=\"anonymous\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-3911300806559936\"\n     data-ad-slot=\"9222947307\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<h2 class=\"wp-block-heading\">Comparison of Methods for Estimating Weibull Parameters: Which One is the Most Accurate?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">To determine which method is the most efficient for estimating the parameters <img decoding=\"async\" class=\"wp-image-1491\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/shape-parameters-k.svg\" alt=\"\"> and <img decoding=\"async\" class=\"wp-image-1490\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/scale-parameter-c.svg\" alt=\"\">, the following tests are used: chi-square <img decoding=\"async\" class=\"wp-image-1498\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/chi_square.svg\" alt=\"\">, root mean square error <img decoding=\"async\" class=\"wp-image-1500\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/RMSE.svg\" alt=\"\">, and squared multiple correlation coefficient <img decoding=\"async\" class=\"wp-image-1499\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/squared-multiple-correlation-coefficient.svg\" alt=\"\">. These tests are used as criteria to determine which method fits the actual wind speed data the best. These tests are defined by:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/Formula_chi_square.svg\" alt=\"\" class=\"wp-image-1501\" style=\"width:249px;height:64px\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/Formula_RMSE.svg\" alt=\"\" class=\"wp-image-1502\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2023\/04\/formula_squared-multiple-correlation-coefficient.svg\" alt=\"\" class=\"wp-image-1503\" style=\"width:407px;height:69px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Where <img decoding=\"async\" class=\"wp-image-1489\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/15.svg\" alt=\"\"> is the number of observations, <img decoding=\"async\" class=\"wp-image-1504\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/yi.svg\" alt=\"\"> is the frequency of observations, <img decoding=\"async\" class=\"wp-image-1505\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/xi.svg\" alt=\"\"> is the frequency of Weibull, <img decoding=\"async\" class=\"wp-image-1506\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/zi.svg\" alt=\"\"> is the mean wind speed, and <img decoding=\"async\" class=\"wp-image-1507\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/n.svg\" alt=\"\"> is the number of constants used.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The coefficient of determination<\/strong>, <img decoding=\"async\" class=\"wp-image-1499\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/squared-multiple-correlation-coefficient.svg\" alt=\"\">, is commonly used as a measure of goodness of fit, as it provides information on the amount of variability in the data that can be explained by the model. Therefore, <strong>higher values of<\/strong> <strong><img decoding=\"async\" class=\"wp-image-1499\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/squared-multiple-correlation-coefficient.svg\" alt=\"\"><\/strong> <strong>indicate a better fit of the model to the data<\/strong>. Generally, a value of <img decoding=\"async\" class=\"wp-image-1499\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/squared-multiple-correlation-coefficient.svg\" alt=\"\"> close to 1 indicates a good fit of the data model, while a value close to 0 indicates that the model does not explain the variability in the data well. However, in some research fields, it is common for models not to explain all of the variability in the data due to the complexity of the factors influencing the studied phenomenon. In these cases, an <img decoding=\"async\" class=\"wp-image-1499\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/squared-multiple-correlation-coefficient.svg\" alt=\"\"> value of 0.2 or 0.3 may be considered a good fit value.  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On the other hand, <img decoding=\"async\" class=\"wp-image-1498\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/chi_square.svg\" alt=\"\"> is a <strong>measure of the discrepancy<\/strong> between the observed values and the values expected according to the model. Therefore, lower values of <img decoding=\"async\" class=\"wp-image-1498\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/chi_square.svg\" alt=\"\"> indicate that the model fits the observed data better.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, the <img decoding=\"async\" class=\"wp-image-1500\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/RMSE.svg\" alt=\"\"> (Root Mean Squared Error) is a <strong>measure of the accuracy of the model<\/strong> in predicting the data. Lower values of RMSE indicate greater accuracy in prediction.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In conclusion, estimating the Weibull parameters for wind speed distribution is a crucial task for wind energy applications as it helps to understand the potential of wind resource at a specific site. The process involves using various statistical techniques to obtain the shape and scale parameters of the Weibull distribution. The accuracy of the estimated parameters can be evaluated using measures such as <img decoding=\"async\" class=\"wp-image-1499\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/squared-multiple-correlation-coefficient.svg\" alt=\"\">, <img decoding=\"async\" class=\"wp-image-1498\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/chi_square.svg\" alt=\"\"> and <img decoding=\"async\" class=\"wp-image-1500\" style=\"width: NaNpx;\" src=\"https:\/\/iienergyplus.com\/wp-content\/uploads\/2022\/09\/RMSE.svg\" alt=\"\">, which indicate the goodness of fit and the accuracy of the model in predicting the data. Overall, obtaining accurate estimates of the Weibull parameters is essential for optimizing the design and operation of wind energy systems.<\/p>\n\n\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-stackable-divider stk-block-divider stk-block stk-347e4ad\" data-block-id=\"347e4ad\"><style>.stk-347e4ad hr.stk-block-divider__hr{background:var(--theme-palette-color-3,#3f4245) !important;height:5px !important;width:100% !important}<\/style><hr class=\"stk-block-divider__hr\"\/><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Reference <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">[1] Costa Rocha, P. A., de Sousa, R. C., de Andrade, C. F., &amp; da Silva, M. E. V. (2012). Comparison of seven numerical methods for determining Weibull parameters for wind energy generation in the northeast region of Brazil.&nbsp;<em>Applied Energy<\/em>,&nbsp;<em>89<\/em>(1), 395\u2013400. <a href=\"https:\/\/doi.org\/10.1016\/j.apenergy.2011.08.003\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.1016\/j.apenergy.2011.08.003<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[2] Wang, W., Chen, K., Bai, Y., Chen, Y., &amp; Wang, J. (2022). New estimation method of wind power density with three\u2010parameter Weibull distribution: A case on Central Inner Mongolia suburbs.&nbsp;<em>Wind Energy<\/em>,&nbsp;<em>25<\/em>(2), 368\u2013386. <a href=\"https:\/\/doi.org\/10.1002\/we.2677\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.1002\/we.2677<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[3] Villarrubia L\u00f3pez M. (2012).&nbsp;Ingenier\u00eda de la Energ\u00eda E\u00f3lica. Facultad de F\u00edsica, Universidad de Barcelona. Alfaomega Grupo Editor, S.A. de C.V.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Weibull distribution is widely used in wind energy to mathematically model the distribution of wind speeds at a study site. This distribution is characterized by two parameters, the scale factor (c) and the shape factor (k). Accurately estimating these parameters is essential for predicting the energy generated by a wind farm and making informed [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":948,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-612","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-wind_resource"],"blocksy_meta":{"has_hero_section":"default"},"_links":{"self":[{"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/posts\/612","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/comments?post=612"}],"version-history":[{"count":36,"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/posts\/612\/revisions"}],"predecessor-version":[{"id":1838,"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/posts\/612\/revisions\/1838"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/media\/948"}],"wp:attachment":[{"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/media?parent=612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/categories?post=612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ienergyplus.com\/es\/wp-json\/wp\/v2\/tags?post=612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}