{"id":38,"date":"2018-12-14T10:05:35","date_gmt":"2018-12-14T10:05:35","guid":{"rendered":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/?post_type=chapter&#038;p=38"},"modified":"2020-09-03T15:51:33","modified_gmt":"2020-09-03T14:51:33","slug":"task-1-title","status":"publish","type":"chapter","link":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/chapter\/task-1-title\/","title":{"raw":"Task 1. Energy conversion - energy from the wind","rendered":"Task 1. Energy conversion &#8211; energy from the wind"},"content":{"raw":"<h1>Aim of the task<\/h1>\r\nThe aim of the task is to learn about selected aspects of energy conversion. Considered problem regards\u00a0 the conversion of primary energy like a wind energy into electrical energy. The task includes the analysis of the following issues: efficiency of conversion, annual production, mean time of use.\r\n<h2><\/h2>\r\n<h1>Introduction<\/h1>\r\nNowadays wind energy has become an increasingly popular\u00a0 source of sustainable energy, mainly because of successful efforts to increase the efficiency conversion from wind energy into electricity. All an apparatus for converting the kinetic energy available in the wind to mechanical energy that can be used to power machinery and to operate an electrical generator is called wind energy conversion system (WECS). In the field of electrical power engineering, the wind energy conversion system\u00a0 is simply referred to as wind turbine. General practice is to use horizontal axis wind turbines with three blades. A schematic representation of the wind turbine is shown in Fig.\u00a01.1.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_543\" align=\"aligncenter\" width=\"282\"]<img class=\"wp-image-543 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2019\/04\/img_5cb590f72258d.png\" alt=\"\" width=\"282\" height=\"371\" \/> Fig. 1.1. A schematic representation of a wind turbine with the properties that influence the maximum amount of incoming wind energy.[\/caption]\r\n\r\nIn recent years, the development of wind turbine technologies has been observed. In the last 3\u20134 decades, the wind turbine capacity has been increased around 30\u2013100 times. Development of wind turbines has been shown in Fig.\u00a01.2.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_544\" align=\"aligncenter\" width=\"586\"]<img class=\"wp-image-544 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2019\/04\/img_5cb590ff3568e.png\" alt=\"\" width=\"586\" height=\"268\" \/> Fig. 1.2. Development of wind turbines..[\/caption]\r\n\r\n&nbsp;\r\n\r\nAn important factors related to the wind that influence the amount of generated electricity produced by wind turbines are:\r\n<ul>\r\n \t<li>mean wind-speed at tower height<img class=\"alignnone wp-image-902 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind.png\" \/>,<\/li>\r\n \t<li>variation in wind speed over time <img class=\"alignnone wp-image-903 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-1.png\" \/> ,<\/li>\r\n \t<li>mean air density <img class=\"alignnone wp-image-904 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-2.png\" \/> .<\/li>\r\n<\/ul>\r\nIf wind speeds throughout a year will be measured, it will be found that in most areas strong gale force winds are rare, while moderate and fresh winds are quite common. The wind variation for a typical site is usually \u00a0can described using the Weibull distribution, as shown in the Fig.\u00a01.3.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_545\" align=\"aligncenter\" width=\"606\"]<img class=\"wp-image-545 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2019\/04\/img_5cb59105dad32.png\" alt=\"\" width=\"606\" height=\"341\" \/> Figure 3: Characteristic of the wind speed.[\/caption]\r\n<h1>Power from the wind<\/h1>\r\n<h2>a) wind power\r\nThe power in the wind <img class=\"alignnone wp-image-905 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-3.png\" \/>which is available by a wind turbine with a rotor surface <img class=\"alignnone wp-image-906 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-4.png\" \/> (Fig.1 .4) can be determined using the following formula:<\/h2>\r\n<img class=\"alignnone wp-image-907 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-5.png\" \/>\r\nwhere\r\n\u2022 <img class=\"alignnone wp-image-908 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-6.png\" \/> is the power in the wind [W]\r\n\u2022 <img class=\"alignnone wp-image-909 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-7.png\" \/> is the density of dry air at sea level at mean [kg\/m3] (for atmospheric pressure and an air temperature of 15<sup>o<\/sup>C)\r\n\u2022 <img class=\"alignnone wp-image-910 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-8.png\" \/> is the mean wind speed at tower height [m\/s]\r\n\u2022 <img class=\"alignnone wp-image-906 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-4.png\" \/> is the surface area of the circle that is swept by the rotor blades with radius <img class=\"alignnone wp-image-911 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-9.png\" \/>\r\n\r\n[caption id=\"attachment_546\" align=\"aligncenter\" width=\"284\"]<img class=\"wp-image-546 \" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2019\/04\/img_5cb5910c66358.png\" alt=\"\" width=\"284\" height=\"207\" \/> Fig. 1.4: Illustration of the sweap area.[\/caption]\r\n<h2>b) available power<\/h2>\r\nNot all kinetic energy in a column of wind is extracted by a wind turbine. There is always some energy left in the wind behind the wind turbine. Therefore, one can conclude that only a certain fraction of the wind energy is extracted. This fraction is referred to as the conversion coefficient <img class=\"alignnone wp-image-912 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-10.png\" \/> . In theory, the highest possible value of <img class=\"alignnone wp-image-913 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-11.png\" \/> is <img class=\"alignnone wp-image-914 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-12.png\" \/> (Betz\u2019 law). In practice <img class=\"alignnone wp-image-912 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-10.png\" \/>\u00a0 usually is approximately 0.5.\r\n\r\nPart of the extracted wind power is subsequently lost by mechanical friction in the turbine and energy conversion in the generator. Hence the efficiencies of turbine and generator should be taken into consideration. Therefore, the maximal available power extractable from the wind can be estimated as follows:\r\n\r\n<img class=\"alignnone wp-image-915 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-13.png\" \/>\r\n\r\nwhere\r\n\r\n<img class=\"alignnone wp-image-916 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-14.png\" \/> \u2013 is wind conversion efficiency\r\n<img class=\"alignnone wp-image-917 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-15.png\" \/> \u2013 turbine mechanical efficiency\r\n<img class=\"alignnone wp-image-918 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-16.png\" \/> \u2013 generator conversion efficiency\r\n<h2>c) electric power<\/h2>\r\nWind turbine system is designed in specific manner. The typical wind turbine output electric power curve is shown in Fig. 1.5.\r\n<p style=\"text-align: justify\"><img class=\"wp-image-919 size-full aligncenter\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-17.png\" \/><\/p>\r\n<p style=\"text-align: center\"><em>Fig. 1.5. Wind turbine output power curve P<sub>e<\/sub> (v) (wind turbine output electric power as a\r\nfunction of wind speed).<\/em><\/p>\r\nThe wind turbine operates, with different dynamics, from the <em>cut-in wind speed <\/em>(usually 3\u20134 m\/s, for modern wind turbines) to the cut-out wind speed (around 25 m\/s), as shown in Fig. 1.5. The output power evolves until it reaches the wind turbine rated power. This happens at rated wind speed <em>v<\/em><sub>n<\/sub>, which splits the wind turbine operation range in two: below rated (also called partial load region) and full load region, where the captured power must be limited to rated. The <img class=\"alignnone wp-image-920 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-18.png\" \/>characteristic of the wind turbine is specified by the manufacturer.\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n<h1>Calculation<\/h1>\r\n<h2>a) Wind energy conversion efficiency<\/h2>\r\nThe efficiency of conversion of wind energy into electrical energy can be calculated as follows:\r\n\r\n<img class=\"alignnone wp-image-922 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-19.png\" \/>\r\n<h2>b) annual electrical energy production<\/h2>\r\nBasing on wind energy variability characteristic<img class=\"alignnone wp-image-923 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-20.png\" \/>, the annual electrical energy production <img class=\"alignnone wp-image-924 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-21.png\" \/> from the wind can be calculated as follows:\r\n\r\n<img class=\"alignnone wp-image-925 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-22.png\" \/>\r\n\r\n<img class=\"alignnone wp-image-926 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-23.png\" \/> - electric power generated wind turbine in case of wind speed equals to <img class=\"alignnone wp-image-927 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-24.png\" \/>,\r\n<img class=\"alignnone wp-image-928 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-25.png\" \/> - period of time corresponding to wind speed <img class=\"alignnone wp-image-929 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-26.png\" \/>, where <img class=\"alignnone wp-image-930 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-27.png\" \/>.\r\n<h2>c) Mean power generated and mean time of use<\/h2>\r\nMean power generated by wind turbine can be calculated as follows:\r\n\r\n<img class=\"alignnone wp-image-931 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-28.png\" \/>\r\n\r\nMean time of use of rated power of wind turbine\r\n\r\n<img class=\"alignnone wp-image-932 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-29.png\" \/>\r\n\r\nwhere <img class=\"alignnone wp-image-933 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-30.png\" \/> is rated power of the wind turbine.\r\n<h2>Example:<\/h2>\r\nUsing a\u00a0 turbine with an 80 meter rotor diameter as an example, the amount of wind power <em>P<\/em><sub>wind<\/sub> available in a 20 mph (9,8 m\/s) wind for this turbine with 5027 m2 of swept area is:\r\n<em>P<\/em><sub>wind<\/sub> = \u00bd \u00d7 1,2 kg\/m3 \u00d7 \u03c0 \u00d7 (40 m)2 \u00d7 (8,9 m\/s)3 = 2,3 \u00d7 106 kg\u00b7m2\/s3 = 2,3 MW $.\r\n<h1>References<\/h1>\r\n[1] Machowski J, Bialek J, Bumby J. Power system dynamics: stability and control. New York, USA: John Wiley &amp; Sons; 2008.\r\n[2] Brendan Fox ; Leslie Bryans ; Damian Flynn ; Nick Jenkins ; David Milborrow ; Mark O'Malley ; Richard Watson ; Olimpo Anaya-Lara: Wind Power Integration: Connection and System Operational Aspects. IET London, 2007.\r\n<h1>Exercise<\/h1>\r\n<h2><span style=\"text-decoration: underline\">Content and input data:<\/span><\/h2>\r\nThe input data are as follows:\r\n<ol>\r\n \t<li>characteristic of the wind speed <img class=\"alignnone wp-image-934 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-31.png\" \/>,<\/li>\r\n \t<li>wind turbine parameters: rotor diameter <img class=\"alignnone wp-image-935 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-32.png\" \/>, rated power<img class=\"alignnone wp-image-936 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-33.png\" \/>, output power curve <img class=\"alignnone wp-image-937 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-34.png\" \/>,<\/li>\r\n \t<li>air density <img class=\"alignnone wp-image-938 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-35.png\" \/> kg\/m3.<\/li>\r\n<\/ol>\r\n<h2><span style=\"text-decoration: underline\">To do:<\/span><\/h2>\r\n<ol>\r\n \t<li>Calculate and plot the value of efficiency of energy conversion as a function of wind speed.<\/li>\r\n \t<li>Calculate and plot curves of the wind power and electrical power (at the same figure).<\/li>\r\n \t<li>Calculate the annual mean power generated by wind turbine.<\/li>\r\n \t<li>Calculate the annual mean time of use of rated power of wind turbine.<\/li>\r\n \t<li>Prepare a report and formulate brief conclusions.<\/li>\r\n<\/ol>","rendered":"<h1>Aim of the task<\/h1>\n<p>The aim of the task is to learn about selected aspects of energy conversion. Considered problem regards\u00a0 the conversion of primary energy like a wind energy into electrical energy. The task includes the analysis of the following issues: efficiency of conversion, annual production, mean time of use.<\/p>\n<h2><\/h2>\n<h1>Introduction<\/h1>\n<p>Nowadays wind energy has become an increasingly popular\u00a0 source of sustainable energy, mainly because of successful efforts to increase the efficiency conversion from wind energy into electricity. All an apparatus for converting the kinetic energy available in the wind to mechanical energy that can be used to power machinery and to operate an electrical generator is called wind energy conversion system (WECS). In the field of electrical power engineering, the wind energy conversion system\u00a0 is simply referred to as wind turbine. General practice is to use horizontal axis wind turbines with three blades. A schematic representation of the wind turbine is shown in Fig.\u00a01.1.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_543\" aria-describedby=\"caption-attachment-543\" style=\"width: 282px\" class=\"wp-caption aligncenter\"><img class=\"wp-image-543 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2019\/04\/img_5cb590f72258d.png\" alt=\"\" width=\"282\" height=\"371\" \/><figcaption id=\"caption-attachment-543\" class=\"wp-caption-text\">Fig. 1.1. A schematic representation of a wind turbine with the properties that influence the maximum amount of incoming wind energy.<\/figcaption><\/figure>\n<p>In recent years, the development of wind turbine technologies has been observed. In the last 3\u20134 decades, the wind turbine capacity has been increased around 30\u2013100 times. Development of wind turbines has been shown in Fig.\u00a01.2.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_544\" aria-describedby=\"caption-attachment-544\" style=\"width: 586px\" class=\"wp-caption aligncenter\"><img class=\"wp-image-544 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2019\/04\/img_5cb590ff3568e.png\" alt=\"\" width=\"586\" height=\"268\" \/><figcaption id=\"caption-attachment-544\" class=\"wp-caption-text\">Fig. 1.2. Development of wind turbines..<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p>An important factors related to the wind that influence the amount of generated electricity produced by wind turbines are:<\/p>\n<ul>\n<li>mean wind-speed at tower height<img width=\"21\" height=\"28\" class=\"alignnone wp-image-902 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind.png\" alt=\"image\" \/>,<\/li>\n<li>variation in wind speed over time <img width=\"47\" height=\"34\" class=\"alignnone wp-image-903 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-1.png\" alt=\"image\" \/> ,<\/li>\n<li>mean air density <img width=\"32\" height=\"31\" class=\"alignnone wp-image-904 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-2.png\" alt=\"image\" \/> .<\/li>\n<\/ul>\n<p>If wind speeds throughout a year will be measured, it will be found that in most areas strong gale force winds are rare, while moderate and fresh winds are quite common. The wind variation for a typical site is usually \u00a0can described using the Weibull distribution, as shown in the Fig.\u00a01.3.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_545\" aria-describedby=\"caption-attachment-545\" style=\"width: 606px\" class=\"wp-caption aligncenter\"><img class=\"wp-image-545 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2019\/04\/img_5cb59105dad32.png\" alt=\"\" width=\"606\" height=\"341\" \/><figcaption id=\"caption-attachment-545\" class=\"wp-caption-text\">Figure 3: Characteristic of the wind speed.<\/figcaption><\/figure>\n<h1>Power from the wind<\/h1>\n<h2>a) wind power<br \/>\nThe power in the wind <img width=\"57\" height=\"45\" class=\"alignnone wp-image-905 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-3.png\" alt=\"image\" \/>which is available by a wind turbine with a rotor surface <img width=\"28\" height=\"23\" class=\"alignnone wp-image-906 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-4.png\" alt=\"image\" \/> (Fig.1 .4) can be determined using the following formula:<\/h2>\n<p><img width=\"145\" height=\"69\" class=\"alignnone wp-image-907 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-5.png\" alt=\"image\" \/><br \/>\nwhere<br \/>\n\u2022 <img width=\"57\" height=\"35\" class=\"alignnone wp-image-908 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-6.png\" alt=\"image\" \/> is the power in the wind [W]<br \/>\n\u2022 <img width=\"19\" height=\"31\" class=\"alignnone wp-image-909 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-7.png\" alt=\"image\" \/> is the density of dry air at sea level at mean [kg\/m3] (for atmospheric pressure and an air temperature of 15<sup>o<\/sup>C)<br \/>\n\u2022 <img width=\"19\" height=\"22\" class=\"alignnone wp-image-910 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-8.png\" alt=\"image\" \/> is the mean wind speed at tower height [m\/s]<br \/>\n\u2022 <img width=\"28\" height=\"23\" class=\"alignnone wp-image-906 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-4.png\" alt=\"image\" \/> is the surface area of the circle that is swept by the rotor blades with radius <img width=\"26\" height=\"28\" class=\"alignnone wp-image-911 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-9.png\" alt=\"image\" \/><\/p>\n<figure id=\"attachment_546\" aria-describedby=\"caption-attachment-546\" style=\"width: 284px\" class=\"wp-caption aligncenter\"><img class=\"wp-image-546\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2019\/04\/img_5cb5910c66358.png\" alt=\"\" width=\"284\" height=\"207\" \/><figcaption id=\"caption-attachment-546\" class=\"wp-caption-text\">Fig. 1.4: Illustration of the sweap area.<\/figcaption><\/figure>\n<h2>b) available power<\/h2>\n<p>Not all kinetic energy in a column of wind is extracted by a wind turbine. There is always some energy left in the wind behind the wind turbine. Therefore, one can conclude that only a certain fraction of the wind energy is extracted. This fraction is referred to as the conversion coefficient <img width=\"29\" height=\"34\" class=\"alignnone wp-image-912 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-10.png\" alt=\"image\" \/> . In theory, the highest possible value of <img width=\"29\" height=\"34\" class=\"alignnone wp-image-913 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-11.png\" alt=\"image\" \/> is <img width=\"152\" height=\"39\" class=\"alignnone wp-image-914 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-12.png\" alt=\"image\" \/> (Betz\u2019 law). In practice <img width=\"29\" height=\"34\" class=\"alignnone wp-image-912 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-10.png\" alt=\"image\" \/>\u00a0 usually is approximately 0.5.<\/p>\n<p>Part of the extracted wind power is subsequently lost by mechanical friction in the turbine and energy conversion in the generator. Hence the efficiencies of turbine and generator should be taken into consideration. Therefore, the maximal available power extractable from the wind can be estimated as follows:<\/p>\n<p><img width=\"221\" height=\"70\" class=\"alignnone wp-image-915 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-13.png\" alt=\"image\" \/><\/p>\n<p>where<\/p>\n<p><img width=\"33\" height=\"34\" class=\"alignnone wp-image-916 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-14.png\" alt=\"image\" \/> \u2013 is wind conversion efficiency<br \/>\n<img width=\"34\" height=\"29\" class=\"alignnone wp-image-917 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-15.png\" alt=\"image\" \/> \u2013 turbine mechanical efficiency<br \/>\n<img width=\"45\" height=\"28\" class=\"alignnone wp-image-918 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-16.png\" alt=\"image\" \/> \u2013 generator conversion efficiency<\/p>\n<h2>c) electric power<\/h2>\n<p>Wind turbine system is designed in specific manner. The typical wind turbine output electric power curve is shown in Fig. 1.5.<\/p>\n<p style=\"text-align: justify\"><img width=\"590\" height=\"232\" class=\"wp-image-919 size-full aligncenter\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-17.png\" alt=\"image\" \/><\/p>\n<p style=\"text-align: center\"><em>Fig. 1.5. Wind turbine output power curve P<sub>e<\/sub> (v) (wind turbine output electric power as a<br \/>\nfunction of wind speed).<\/em><\/p>\n<p>The wind turbine operates, with different dynamics, from the <em>cut-in wind speed <\/em>(usually 3\u20134 m\/s, for modern wind turbines) to the cut-out wind speed (around 25 m\/s), as shown in Fig. 1.5. The output power evolves until it reaches the wind turbine rated power. This happens at rated wind speed <em>v<\/em><sub>n<\/sub>, which splits the wind turbine operation range in two: below rated (also called partial load region) and full load region, where the captured power must be limited to rated. The <img width=\"57\" height=\"35\" class=\"alignnone wp-image-920 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-18.png\" alt=\"image\" \/>characteristic of the wind turbine is specified by the manufacturer.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h1>Calculation<\/h1>\n<h2>a) Wind energy conversion efficiency<\/h2>\n<p>The efficiency of conversion of wind energy into electrical energy can be calculated as follows:<\/p>\n<p><img width=\"208\" height=\"83\" class=\"alignnone wp-image-922 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-19.png\" alt=\"image\" \/><\/p>\n<h2>b) annual electrical energy production<\/h2>\n<p>Basing on wind energy variability characteristic<img width=\"50\" height=\"36\" class=\"alignnone wp-image-923 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-20.png\" alt=\"image\" \/>, the annual electrical energy production <img width=\"83\" height=\"44\" class=\"alignnone wp-image-924 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-21.png\" alt=\"image\" \/> from the wind can be calculated as follows:<\/p>\n<p><img width=\"247\" height=\"69\" class=\"alignnone wp-image-925 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-22.png\" alt=\"image\" \/><\/p>\n<p><img width=\"70\" height=\"36\" class=\"alignnone wp-image-926 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-23.png\" alt=\"image\" \/> &#8211; electric power generated wind turbine in case of wind speed equals to <img width=\"209\" height=\"42\" class=\"alignnone wp-image-927 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-24.png\" alt=\"image\" \/>,<br \/>\n<img width=\"29\" height=\"35\" class=\"alignnone wp-image-928 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-25.png\" alt=\"image\" \/> &#8211; period of time corresponding to wind speed <img width=\"23\" height=\"38\" class=\"alignnone wp-image-929 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-26.png\" alt=\"image\" \/>, where <img width=\"221\" height=\"50\" class=\"alignnone wp-image-930 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-27.png\" alt=\"image\" \/>.<\/p>\n<h2>c) Mean power generated and mean time of use<\/h2>\n<p>Mean power generated by wind turbine can be calculated as follows:<\/p>\n<p><img width=\"167\" height=\"75\" class=\"alignnone wp-image-931 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-28.png\" alt=\"image\" \/><\/p>\n<p>Mean time of use of rated power of wind turbine<\/p>\n<p><img width=\"170\" height=\"72\" class=\"alignnone wp-image-932 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-29.png\" alt=\"image\" \/><\/p>\n<p>where <img width=\"31\" height=\"43\" class=\"alignnone wp-image-933 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-30.png\" alt=\"image\" \/> is rated power of the wind turbine.<\/p>\n<h2>Example:<\/h2>\n<p>Using a\u00a0 turbine with an 80 meter rotor diameter as an example, the amount of wind power <em>P<\/em><sub>wind<\/sub> available in a 20 mph (9,8 m\/s) wind for this turbine with 5027 m2 of swept area is:<br \/>\n<em>P<\/em><sub>wind<\/sub> = \u00bd \u00d7 1,2 kg\/m3 \u00d7 \u03c0 \u00d7 (40 m)2 \u00d7 (8,9 m\/s)3 = 2,3 \u00d7 106 kg\u00b7m2\/s3 = 2,3 MW $.<\/p>\n<h1>References<\/h1>\n<p>[1] Machowski J, Bialek J, Bumby J. Power system dynamics: stability and control. New York, USA: John Wiley &amp; Sons; 2008.<br \/>\n[2] Brendan Fox ; Leslie Bryans ; Damian Flynn ; Nick Jenkins ; David Milborrow ; Mark O&#8217;Malley ; Richard Watson ; Olimpo Anaya-Lara: Wind Power Integration: Connection and System Operational Aspects. IET London, 2007.<\/p>\n<h1>Exercise<\/h1>\n<h2><span style=\"text-decoration: underline\">Content and input data:<\/span><\/h2>\n<p>The input data are as follows:<\/p>\n<ol>\n<li>characteristic of the wind speed <img width=\"46\" height=\"38\" class=\"alignnone wp-image-934 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-31.png\" alt=\"image\" \/>,<\/li>\n<li>wind turbine parameters: rotor diameter <img width=\"29\" height=\"27\" class=\"alignnone wp-image-935 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-32.png\" alt=\"image\" \/>, rated power<img width=\"28\" height=\"43\" class=\"alignnone wp-image-936 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-33.png\" alt=\"image\" \/>, output power curve <img width=\"58\" height=\"42\" class=\"alignnone wp-image-937 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-34.png\" alt=\"image\" \/>,<\/li>\n<li>air density <img width=\"97\" height=\"35\" class=\"alignnone wp-image-938 size-full\" src=\"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-content\/uploads\/sites\/9\/2018\/12\/Pasted-into-Title-of-project-task-t.-1-Energy-conversion-energy-from-the-wind-35.png\" alt=\"image\" \/> kg\/m3.<\/li>\n<\/ol>\n<h2><span style=\"text-decoration: underline\">To do:<\/span><\/h2>\n<ol>\n<li>Calculate and plot the value of efficiency of energy conversion as a function of wind speed.<\/li>\n<li>Calculate and plot curves of the wind power and electrical power (at the same figure).<\/li>\n<li>Calculate the annual mean power generated by wind turbine.<\/li>\n<li>Calculate the annual mean time of use of rated power of wind turbine.<\/li>\n<li>Prepare a report and formulate brief conclusions.<\/li>\n<\/ol>\n","protected":false},"author":7,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[47],"contributor":[],"license":[],"part":25,"_links":{"self":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters\/38"}],"collection":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/users\/7"}],"version-history":[{"count":19,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters\/38\/revisions"}],"predecessor-version":[{"id":988,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters\/38\/revisions\/988"}],"part":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/parts\/25"}],"metadata":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapters\/38\/metadata\/"}],"wp:attachment":[{"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/media?parent=38"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/pressbooks\/v2\/chapter-type?post=38"},{"taxonomy":"contributor","embeddable":true,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/contributor?post=38"},{"taxonomy":"license","embeddable":true,"href":"http:\/\/pb.ee.pw.edu.pl\/pb\/iepe\/wp-json\/wp\/v2\/license?post=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}