{"id":1833,"date":"2022-04-08T12:43:57","date_gmt":"2022-04-08T12:43:57","guid":{"rendered":"http:\/\/www.vicoter.it\/?p=1833"},"modified":"2022-04-08T12:59:34","modified_gmt":"2022-04-08T12:59:34","slug":"design-of-a-solar-tracker-for-wind-loads","status":"publish","type":"post","link":"https:\/\/www.vicoter.it\/index.php\/design-of-a-solar-tracker-for-wind-loads\/","title":{"rendered":"Design of a solar tracker for wind loads"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The increasing demand of green energy brought to a request\nto improve the efficiency of solar panels and of their capability to generate\nelectricity. Among the various solutions studied and developed, the most\ndiffused one is, for sure, the solar tracker. Such device permits the\norientation of the panels towards the sun during its daily movement from east\nto west. The less the misalignment angle is, the more the effective collection\narea is and, consequently, the more the energy production is. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Despite the various models on the market, solar tracker structural layouts are all very similar. Solar panels are connected to a long horizontal tube hinged by bearings to a certain number of vertical poles inserted into the ground. An electrical actuator, generally located in the middle of the tracker, rotates the main tube by a leverage and works as constraint, once the wanted position is reached.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"708\" height=\"610\" src=\"https:\/\/i1.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM1.png?fit=1024%2C1024\" alt=\"\" class=\"wp-image-1834\" srcset=\"https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM1.png?w=708&amp;ssl=1 708w, https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM1.png?resize=768%2C661&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM1.png?resize=300%2C258&amp;ssl=1 300w\" sizes=\"auto, (max-width: 708px) 100vw, 708px\" \/><figcaption>Solar tracker layout.<br><\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Although the geometrical and technological simplicity\ncan be misleading, solar trackers require an extensive and careful design, in\norder to be able to withstand, not only the static, but even the dynamic loads\ninduced by the wind. Due to their shape, very similar to a thin flat plate,\nsolar panels work in an air flow that generates lift and drag, according to the\nrelative angle between them and the stream velocity. Therefore, they are\nsubjected to both a forced response generated by the wind and aeroelastic\ninstabilities. The estimation of the maximum dynamic pressure encountered by\nthe structure during its life and the calculation of the induced static\nstresses become, in this way, only the first step in the development of a\nreliable device.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The most probable dynamic effect encountered by solar\ntrackers in their life is generated by air turbulence inducing time variant\nloads, able to excite structural resonances. Due to their layout, solar\ntrackers generally have torsional modes at very low frequencies: the horizontal\ntube used to support the panels acts as the only torsional spring in the\nstructure. It is constrained on ground by the actuator and its stiffness decreases\nwhen the total span increases. A good design aims at raising the frequency of\nthe first mode to a value higher than the maximum harmonic contribution of the\nwind.&nbsp; Theoretical Kaimal and von Karman\nwind power spectrum densities show that such threshold depends on the height\nfrom the ground and on the mean speed. According to the several standards such as\nthe ASCE 7, a threshold of 1 Hz can be fixed without loss of generality. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vicoter (<a href=\"https:\/\/www.vicoter.it\">www.vicoter.it<\/a>) is an Italian consulting society dealing with the structural dynamics\nmainly in the aerospace and energy sectors. Its competences integrate the\nnumerical and experimental methods to provide its clients the most suitable\nsolution in the vibration field. Due to their approach, Vicoter\u2019s engineers\nwere entrusted by RCM (<a href=\"http:\/\/www.rcm-italia.com\">www.rcm-italia.com<\/a>) to develop a validated analytical model of its new prototype of solar\ntracker, so to verify its compatibility with resonance requests and to study\nthe possibility to build wider versions. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Three parameters must be experimentally identified to\nobtain a correlated model:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The stiffness\nof the actuator, influencing the first symmetric torsional mode.<\/li><li>The real\ntorsional stiffness of the main tube accounting for the joints among the\nvarious parts, influencing the second antisymmetric torsional mode.<\/li><li>The equivalent\nstiffness of the soil, influencing third lateral mode, induced by flexibility\nof the vertical pylons.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Moreover, an estimation of the modal damping is required if also analyses of dynamic response are planned.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"877\" height=\"552\" src=\"https:\/\/i1.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM2.png?fit=1024%2C1024\" alt=\"\" class=\"wp-image-1835\" srcset=\"https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM2.png?w=877&amp;ssl=1 877w, https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM2.png?resize=768%2C483&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM2.png?resize=300%2C188&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM2.png?resize=80%2C50&amp;ssl=1 80w\" sizes=\"auto, (max-width: 877px) 100vw, 877px\" \/><figcaption>Experimental setup.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">An on-field experimental test\ncampaign was carried out, to recover the needed information on the real dynamic\nbehaviour of the solar tracker installed as in operative conditions. Two configurations\nwere studied, with and without balancing masses. Studies were performed with\ntwo SIMO (Single Input Multi Output) tests, by installing fifteen accelerometers\nin two layouts, appropriately located to obtain an excellent spatial\nreconstruction of the modes. The solar tracker was excited in two locations by a\nlong stroke shaker, a special purpose device able to load adequately flexible\nstructures which present high displacements. &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The first\nthree vibration modes have been identified in terms of frequency, shape and\ndamping starting from FRFs (Frequency Response Functions) between all the outputs\nand the load cell.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The finite element model was then updated according to the experimentally obtained information, resulting in an optimal match of the data.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"957\" height=\"748\" src=\"https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM3.png?fit=1024%2C1024\" alt=\"\" class=\"wp-image-1836\" srcset=\"https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM3.png?w=957&amp;ssl=1 957w, https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM3.png?resize=768%2C600&amp;ssl=1 768w, https:\/\/i0.wp.com\/www.vicoter.it\/wp-content\/uploads\/2022\/04\/RCM3.png?resize=300%2C234&amp;ssl=1 300w\" sizes=\"auto, (max-width: 957px) 100vw, 957px\" \/><figcaption>Experimental (left) and numerical (right) modes comparison.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Solar trackers are also affected by other wind induced dynamic effects:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Vortex shedding. It is the alternating detachment of the vortices at the ends of the\npanels. This phenomenon creates forces that generate an alternating torsion of\nthe panel plane. If the shedding frequency of these vortices, and, therefore,\nthe resulting torsional loads, assumes the same value of a torsional natural\nfrequency of the structure, the response is amplified and potentially\ndisruptive. Vortex shedding frequency can be estimated quite simply assuming an\nadequate Strouhal number: it grows linearly with the average wind speed and diminish\nas the orientation angle increases. Also in this case, a possible solution\nwould be to raise the torsional natural frequency of the system above the\nmaximum achievable by such loads. Anyway, the satisfaction of such requirement\neven at angles below 15\u00b0, would require a torsional stiffness which is not\nreasonable for the single-axis tracker case.<\/li><li>Divergence. Unlike\nthe previous phenomena, divergence and torsional flutter are instabilities related\nto aeroelastic problems. Simplifying, it can be said that the torsional dynamic\nbehaviour of the solar tracker is forced by a twisting moment due to the wind and\nit can be decomposed \/ linearized into two contributions: one proportional to\nthe rotation angle and one proportional to the rotation speed. Being the former\nproportional to the rotation, it can be interpreted as an equivalent\naerodynamic torsional stiffness, while the latter, being proportional to the\nrotation speed, can be interpreted as an equivalent aerodynamic torsional\ndamping. In a flat plate at low angles of incidence, the aerodynamic stiffness\nterm works as a negative torsional stiffness. It is proportional to the square\nof the speed and therefore, at a certain speed, it equals the structural\ntorsional stiffness, cancelling the overall one. In this situation, the torsional\nequilibrium is not reacted with any stiffness and the shaft twists until it\nbreaks. This disruptive phenomenon is a static instability occurring in a not-oscillatory\nway. The divergence speed can be estimated starting from the correlated finite\nelement model, introducing the aerodynamic part which, in this situation, is\nwell approximated by the VLM (Vortex Lattice Method).<\/li><li>Torsional flutter (Torsional galloping, SDOF flutter). This instability is very similar\nto the divergence one, but here, the aerodynamic damping term deletes the\nstructural damping. Solar tracker acquires energy from the air flow and vibrates\nin torsion, until it breaks. This aeroelastic problem is much more complicated\nthan divergence: the flutter derivative of the torsional velocity (a term that\nmultiplies the angular velocity to give the torque) is, indeed, non-linear and\ndepending both on the angle of the follower and on the velocity itself. The\ntrend of these derivatives can be known through wind tunnel tests or through\nCFD studies and they can be found in literature.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Based on the obtained correlated\nfinite element model, Vicoter continues its collaboration with RCM to study the\nimpact of the various wind-induced effects on the of solar tracker prototype,\nso to design a safety strategy based on structural strength and adequate stow\nposition.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vicoter thanks RCM for the trust\nreceived in the development of this project and the opportunity to publish this\narticle, Dr. Umberto Bellotti of Bellum Laboratories for sharing of his wide on-field\nexperience on the behaviour of solar trackers subjected to wind and Prof. Marco\nMorandini of Politecnico di Milano for the long and vibrant discussions about\nthe best method to obtain reliable and cost-effective solutions to aeroelastic\nproblems.<\/p>\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>The increasing demand of green energy brought to a request to improve the efficiency of solar panels and of their capability to generate electricity. Among the various solutions studied and developed, the most diffused one is, for sure, the solar &hellip; <a href=\"https:\/\/www.vicoter.it\/index.php\/design-of-a-solar-tracker-for-wind-loads\/\">Continua<\/a><\/p>\n","protected":false},"author":1,"featured_media":1834,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[16,15],"tags":[71,164,133,165,166,87,98,157,160,163,159,158,161,162],"class_list":["post-1833","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news","category-portfolio","tag-analisi-modale","tag-divergence","tag-flutter","tag-galloping","tag-instability","tag-modal-analyses","tag-modal-analysis","tag-pannelli-solari","tag-renewable-energy","tag-shedding","tag-solar-energy","tag-solar-panels","tag-solar-plant","tag-turbolence"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Design of a solar tracker for wind loads - VICOTER<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.vicoter.it\/index.php\/design-of-a-solar-tracker-for-wind-loads\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Design of a solar tracker for wind loads - VICOTER\" \/>\n<meta property=\"og:description\" content=\"The increasing demand of green energy brought to a request to improve the efficiency of solar panels and of their capability to generate electricity. 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