{"id":3968,"date":"2021-06-24T11:27:44","date_gmt":"2021-06-24T11:27:44","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=3968"},"modified":"2025-05-27T12:31:11","modified_gmt":"2025-05-27T12:31:11","slug":"alpha-beta-zero-to-abc","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/software\/alpha-beta-zero-to-abc","title":{"rendered":"Alpha-Beta-Zero to abc"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-right-text counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/imperix.com\/doc\/software\/alpha-beta-zero-to-abc\/#Simulink-block\" >Simulink block<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/imperix.com\/doc\/software\/alpha-beta-zero-to-abc\/#Signal-specification\" >Signal specification<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/imperix.com\/doc\/software\/alpha-beta-zero-to-abc\/#Parameters\" >Parameters<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/imperix.com\/doc\/software\/alpha-beta-zero-to-abc\/#PLECS-block\" >PLECS block<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/imperix.com\/doc\/software\/alpha-beta-zero-to-abc\/#C-functions\" >C++ functions<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>The &#8220;Alpha-Beta-Zero to abc&#8221; block computes a three-phase (<em>abc<\/em>) signal from a space vector in a stationary reference frame (<em>\u03b1\u03b20<\/em>).<\/p>\n\n\n\n<p>The transformation is performed using the following equation:<\/p>\n\n\n\n<p>$$ \\begin{bmatrix} V_a\\\\V_b\\\\V_c\\end{bmatrix}<br>= \\begin{bmatrix} 1 &amp; 0 &amp; 1\\\\-1\/2 &amp; \\sqrt{3}\/2 &amp; 1\\\\ -1\/2 &amp; -\\sqrt{3}\/2 &amp; 1\\end{bmatrix}\\cdot<br>\\begin{bmatrix} V_\\alpha\\\\V_\\beta\\\\V_0\\end{bmatrix}$$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Simulink-block\"><\/span>Simulink block<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Signal-specification\"><\/span>Signal specification<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<ul class=\"wp-block-list\" id=\"block-a7a1f238-46fb-44ff-bfab-355768550388\"><li>The input is a vector of dimension 3, containing the <em><em>\u03b1\u03b20<\/em> <\/em>components of the three-phase signal in the stationary reference frame.<\/li><li>The output is a vector of dimension 3, containing the <em>abc <\/em>components of the three-phase signal.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/06\/ABG-abc.png\" alt=\"Alpha-beta-zero to abc Simulink block\" class=\"wp-image-3971\" width=\"118\" height=\"84\"\/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Parameters\"><\/span>Parameters<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p><em>None.<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"PLECS-block\"><\/span>PLECS block<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><em>None<\/em>. The PLECS block <em>Transformation SRF-&gt;3ph<\/em> can be used instead.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"C-functions\"><\/span>C++ functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The user template located in the installation folder of CPP SDK contains an API folder with implementations of the coordinate transformation functions. The <em><em><em>\u03b1\u03b20<\/em><\/em><\/em> <em>to abc<\/em> function is the following:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-1\" data-shcb-language-name=\"C++\" data-shcb-language-slug=\"cpp\"><span><code class=\"hljs language-cpp\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">void<\/span> <span class=\"hljs-title\">ABG2abc<\/span><span class=\"hljs-params\">(TimeDomain *physical, <span class=\"hljs-keyword\">const<\/span> SpaceVector *fixed)<\/span><\/span>;\n<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-1\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">C++<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">cpp<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p><strong>Parameters<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><code>physical<\/code>: pointer on the time domain <em>abc<\/em> data that will be updated. The <code>TimeDomain <\/code>structure is defined below.<\/li><li><code>fixed<\/code>: pointer on the <em><em>\u03b1\u03b20<\/em><\/em> space vector that will be transformed. The <code>SpaceVector <\/code>structure is defined below.<\/li><\/ul>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-2\" data-shcb-language-name=\"C++\" data-shcb-language-slug=\"cpp\"><span><code class=\"hljs language-cpp\"><span class=\"hljs-keyword\">typedef<\/span> <span class=\"hljs-class\"><span class=\"hljs-keyword\">struct<\/span>{<\/span>\n\t<span class=\"hljs-keyword\">float<\/span> real;       <span class=\"hljs-comment\">\/\/ alpha-axis component<\/span>\n\t<span class=\"hljs-keyword\">float<\/span> <span class=\"hljs-built_in\">imaginary<\/span>;  <span class=\"hljs-comment\">\/\/ beta-axis component<\/span>\n\t<span class=\"hljs-keyword\">float<\/span> offset;     <span class=\"hljs-comment\">\/\/ homopolar component<\/span>\n} SpaceVector;\n\n<span class=\"hljs-keyword\">typedef<\/span> <span class=\"hljs-class\"><span class=\"hljs-keyword\">struct<\/span>{<\/span>\n\t<span class=\"hljs-keyword\">float<\/span> A;\n\t<span class=\"hljs-keyword\">float<\/span> B;\n\t<span class=\"hljs-keyword\">float<\/span> C;\n} TimeDomain;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-2\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">C++<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">cpp<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>","protected":false},"excerpt":{"rendered":"<p>The &#8220;Alpha-Beta-Zero to abc&#8221; block computes a three-phase (abc) signal from a space vector in a stationary reference frame (\u03b1\u03b20). The transformation is performed using&#8230;<\/p>\n","protected":false},"author":2,"featured_media":33315,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[16],"tags":[],"software-environments":[105,103],"provided-results":[],"related-products":[50,31,32,92,166,51,113,114,112,111,110],"guidedreadings":[],"tutorials":[],"user-manuals":[],"coauthors":[63],"class_list":["post-3968","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-software","software-environments-c-plus-plus","software-environments-matlab","related-products-acg-sdk","related-products-b-board-pro","related-products-b-box-rcp","related-products-b-box-micro","related-products-b-box-rcp-3-0","related-products-cpp-sdk","related-products-mmc","related-products-motor","related-products-peb","related-products-pm","related-products-tpi"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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