{"id":4953,"date":"2021-08-09T06:39:45","date_gmt":"2021-08-09T06:39:45","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=4953"},"modified":"2026-03-02T07:32:09","modified_gmt":"2026-03-02T07:32:09","slug":"space-vector-modulation","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/implementation\/space-vector-modulation","title":{"rendered":"Space Vector Modulation (SVM)"},"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\/implementation\/space-vector-modulation\/#Space-vector-modulation-for-two-level-inverters\" >Space vector modulation for two-level inverters<\/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\/implementation\/space-vector-modulation\/#Active-and-zero-space-vectors\" >Active and zero space vectors<\/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\/implementation\/space-vector-modulation\/#Voltage-synthesis-with-space-vector-modulation\" >Voltage synthesis with space vector modulation<\/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\/implementation\/space-vector-modulation\/#Space-vector-modulation-for-three-level-inverters\" >Space vector modulation for three-level inverters<\/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\/implementation\/space-vector-modulation\/#Experimental-validation-of-space-vector-modulation\" >Experimental validation of space vector modulation<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/imperix.com\/doc\/implementation\/space-vector-modulation\/#Implementation-using-MATLAB-Simulink\" >Implementation using MATLAB Simulink<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/imperix.com\/doc\/implementation\/space-vector-modulation\/#Experimental-setup\" >Experimental setup<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/imperix.com\/doc\/implementation\/space-vector-modulation\/#Academic-references\" >Academic references<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>What is the space vector modulation (SVM) technique and how does it work? To answer these questions, this article introduces first the notions of active and zero space vectors and their representation in the Clarke referential. It presents then how to use space vectors to synthesize any output voltage with two or three-level inverters.<\/p>\n\n\n\n<p>A demonstration code example is provided and freely available. It can be tested in simulation using imperix <a href=\"https:\/\/imperix.com\/software\/acg-sdk\/\">ACG SDK<\/a> and validated in the laboratory with a <a href=\"https:\/\/imperix.com\/products\/control\/rapid-prototyping-controller\/\">B-Box RCP<sup>3.0<\/sup><\/a> programmable controller and <a href=\"https:\/\/imperix.com\/products\/power\/sic-power-module\/\">PEB half-bridge power modules<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"377\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/DSC9574_TN145.png\" alt=\"Experimental setup to test space vector modulation with imperix products.\" class=\"wp-image-26773\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/DSC9574_TN145.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/DSC9574_TN145-300x145.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/DSC9574_TN145-768x371.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-space-vector-modulation-for-two-level-inverters\"><span class=\"ez-toc-section\" id=\"Space-vector-modulation-for-two-level-inverters\"><\/span>Space vector modulation for two-level inverters<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-active-and-zero-space-vectors\"><span class=\"ez-toc-section\" id=\"Active-and-zero-space-vectors\"><\/span>Active and zero space vectors<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Space vector modulation is an alternative to the<a href=\"https:\/\/imperix.com\/doc\/software\/carrier-based-pwm\"> Carrier-Based modulation technique<\/a> that is used in the <a href=\"https:\/\/imperix.com\/doc\/example\/three-phase-voltage-source-inverter\">Three-phase Voltage Source Inverter (VSI)<\/a> application note. Both methods are similar, in the sense that they transform a reference voltage into switching signals for the inverter. However, SVM operates in the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Alpha%E2%80%93beta_transformation\">Clarke referential<\/a> (\u03b1\u03b2) rather than the abc one [1]. The topology of a two-level three-phase inverter is presented in the figure below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"547\" height=\"181\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/schematic_AN002.png\" alt=\"Topology of a two-level inverter\" class=\"wp-image-5441\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/schematic_AN002.png 547w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/schematic_AN002-300x99.png 300w\" sizes=\"auto, (max-width: 547px) 100vw, 547px\" \/><figcaption class=\"wp-element-caption\">Topology of a two-level inverter with an RL load<\/figcaption><\/figure>\n<\/div>\n\n\n<p>In the \u03b1\u03b2 frame, each switching state of the inverter is represented by a space vector. Then, since the DC bus should not be short-circuited, the upper and lower switches of each leg must operate in a complementary way. As such, there are only eight possible switching states for the inverter. In this note, the state of a leg is &#8220;1&#8221; if the upper switch is conducting, and &#8220;0&#8221; if the lower switch is conducting.<\/p>\n\n\n\n<p>The eight possible space vectors are summarized in the table below: V<sub>0<\/sub> and V<sub>7<\/sub> are called zero space vectors as they do not produce any phase voltage. By contrast, V<sub>1<\/sub> to V<sub>6<\/sub> produce non-zero phase voltages and are called active space vectors.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Space vector<\/strong><\/td><td><strong>State leg A<\/strong><\/td><td><strong>State leg B<\/strong><\/td><td><strong>State leg C<\/strong><\/td><td><strong>v<sub>a<\/sub><\/strong><\/td><td><strong>v<sub>b<\/sub><\/strong><\/td><td><strong>v<sub>c<\/sub><\/strong><\/td><\/tr><tr><td>V<sub>0<\/sub><\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>V<sub>1<\/sub><\/td><td>1<\/td><td>0<\/td><td>0<\/td><td>2 V<sub>DC<\/sub>\/3<\/td><td>-V<sub>DC<\/sub>\/3<\/td><td>-V<sub>DC<\/sub>\/3<\/td><\/tr><tr><td>V<sub>2<\/sub><\/td><td>1<\/td><td>1<\/td><td>0<\/td><td>V<sub>DC<\/sub>\/3<\/td><td>V<sub>DC<\/sub>\/3<\/td><td>-2 V<sub>DC<\/sub>\/3<\/td><\/tr><tr><td>V<sub>3<\/sub><\/td><td>0<\/td><td>1<\/td><td>0<\/td><td>V<sub>DC<\/sub>\/3<\/td><td>2 V<sub>DC<\/sub>\/3<\/td><td>&#8211; V<sub>DC<\/sub>\/3<\/td><\/tr><tr><td>V<sub>4<\/sub><\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>-2 V<sub>DC<\/sub>\/3<\/td><td>V<sub>DC<\/sub>\/3<\/td><td>V<sub>DC<\/sub>\/3<\/td><\/tr><tr><td>V<sub>5<\/sub><\/td><td>0<\/td><td>0<\/td><td>1<\/td><td>-V<sub>DC<\/sub>\/3<\/td><td>-V<sub>DC<\/sub>\/3<\/td><td>2 V<sub>DC<\/sub>\/3<\/td><\/tr><tr><td>V<sub>6<\/sub><\/td><td>1<\/td><td>0<\/td><td>1<\/td><td>V<sub>DC<\/sub>\/3<\/td><td>-2 V<sub>DC<\/sub>\/3<\/td><td>V<sub>DC<\/sub>\/3<\/td><\/tr><tr><td>V<sub>7<\/sub><\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><td>0<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Possible switching states of the inverter with the corresponding phase voltages<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-voltage-synthesis-with-space-vector-modulation\"><span class=\"ez-toc-section\" id=\"Voltage-synthesis-with-space-vector-modulation\"><\/span>Voltage synthesis with space vector modulation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The space vector modulation method has only eight space vectors at its disposal. However, other space vectors can be synthesized &#8211; on average &#8211; by alternating several active and zero vectors over a switching period \\(T_{sw}\\) of the modulator. For example, the active vectors V<sub>1<\/sub> and V<sub>2<\/sub> can be used to synthesize a reference space vector \\(V_{\\alpha\\beta}^*\\) with an angle between 0 and 60\u00b0 &#8211; see the figure below &#8211; while the zero vectors V<sub>0<\/sub> and V<sub>7<\/sub> allow reducing the amplitude of this reference vector. The amplitude of the average space vector is then expressed as<\/p>\n\n\n\n<p class=\"has-text-align-center\">$$\\vec{V}_{\\alpha\\beta}^* = \\frac{T_1\\vec{V}_1 + T_2\\vec{V}_2 + T_0\\vec{V}_0 + T_7\\vec{V}_7}{T_{sw}},$$<\/p>\n\n\n\n<p>with \\(T_1\\), \\(T_2\\), \\(T_0\\), and \\(T_7\\), the application times of each vector. In the literature, the application times are also referred to as <em>dwell times<\/em> [1].<\/p>\n\n\n\n<p>When synthesizing a space vector with SVM,  the feasible space in the \u03b1\u03b2 plane is a hexagon, as shown in the figure below. Then, the active space vectors divide the hexagon into six triangular sectors. In the first sector, the active vectors V<sub>1<\/sub> and V<sub>2<\/sub> are used. <\/p>\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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"410\" height=\"411\" src=\"https:\/\/cdn.imperix.com\/doc\/wp-content\/uploads\/2021\/08\/voltage-synthesis-1.png\" alt=\"Synthesis of reference with active and zero space vectors\" class=\"wp-image-6167\" style=\"width:315px;height:315px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/voltage-synthesis-1.png 410w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/voltage-synthesis-1-300x300.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/voltage-synthesis-1-150x150.png 150w\" sizes=\"auto, (max-width: 410px) 100vw, 410px\" \/><figcaption class=\"wp-element-caption\">Synthesis of a reference space vector with the active vectors V<sub>1<\/sub> and V<sub>2<\/sub>, and the zero vectors V<sub>0<\/sub> and V<sub>7<\/sub><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"465\" height=\"411\" src=\"https:\/\/cdn.imperix.com\/doc\/wp-content\/uploads\/2021\/08\/active_and_zero_vectors.png\" alt=\"Available vectors for space vector modulation\" class=\"wp-image-6068\" style=\"width:354px;height:312px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/active_and_zero_vectors.png 465w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/active_and_zero_vectors-300x265.png 300w\" sizes=\"auto, (max-width: 465px) 100vw, 465px\" \/><figcaption class=\"wp-element-caption\">Representation of the active and zero space vectors in the \u03b1\u03b2 plane, and division in six sectors<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>The <a href=\"https:\/\/imperix.com\/doc\/software\/space-vector-pwm\">SV-PWM modulator<\/a> from <a href=\"https:\/\/imperix.com\/software\/bbos\/\">imperix libraries<\/a> will automatically select the appropriate active vectors and choose the dwell times, based on the angle and the amplitude of the input reference space vector. The switching sequence is then made symmetrical in order to minimize switching losses. The figures below illustrate how the same active and zero space vectors can produce different switching patterns (or PWM signals) for sector I, which are either optimal or sub-optimal in terms of switching losses.<\/p>\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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"512\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SV-PWM_1-1.png\" alt=\"Optimal switching pattern for space vector modulation\" class=\"wp-image-6567\" style=\"width:350px;height:290px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SV-PWM_1-1.png 620w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SV-PWM_1-1-300x248.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><figcaption class=\"wp-element-caption\">Optimal switching pattern<\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"512\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SV-PWM_2-1.png\" alt=\"Sub-optimal switching pattern for space vector modulation\" class=\"wp-image-6568\" style=\"width:350px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SV-PWM_2-1.png 620w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SV-PWM_2-1-300x248.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><figcaption class=\"wp-element-caption\">Sub-optimal switching patterns<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>For reference, the optimal switching patterns for each sector are presented in the next figure.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"688\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Switching_pattern-1024x688.png\" alt=\"Summary of all space vector modulation switching patterns\" class=\"wp-image-7620\" style=\"width:800px;height:528px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Switching_pattern-1024x688.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Switching_pattern-300x201.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Switching_pattern-768x516.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Switching_pattern.png 1400w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Optimal switching patterns for each sector<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"h-space-vector-modulation-for-three-level-inverters\"><span class=\"ez-toc-section\" id=\"Space-vector-modulation-for-three-level-inverters\"><\/span>Space vector modulation for three-level inverters<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The space vector modulation technique for two-level inverters can be generalized to three levels [2]. A three-level converter has three possible switching states per leg, denoted P (positive output voltage), N (negative output), and 0 (zero output). In total, the converter has 27 possible switching states. <a href=\"https:\/\/imperix.com\/doc\/implementation\/neutral-point-clamped-inverter\" type=\"link\" id=\"https:\/\/imperix.com\/doc\/implementation\/neutral-point-clamped-inverter\">NPC inverters<\/a> are a typical example of three-level converters (see the topology below).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"243\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/Topology.png\" alt=\"Topology of a three-level inverter\" class=\"wp-image-6018\" style=\"width:621px;height:243px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/Topology.png 621w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/Topology-300x117.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><figcaption class=\"wp-element-caption\">Topology of a three-level Neutral Point Clamp (NPC) inverter with an RL load<\/figcaption><\/figure>\n<\/div>\n\n\n<p>As for the two-level inverter, each switching state is represented by a space vector in the Clarke referential. Similarly, the feasible space in the Clarke referential is also a hexagon, as shown below. In terms of voltage synthesis, a three-level converter has more degrees of freedom, since it has more space vectors at disposal. Nevertheless, the same basic concept as before applies: look for the closest active and zero vectors, and alternate between them to produce the reference space vector on average.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"465\" height=\"411\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/vectors_Clarke-referential.png\" alt=\"Switching states of an NPC three-level converter\" class=\"wp-image-6180\" style=\"width:460px;height:405px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/vectors_Clarke-referential.png 465w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/vectors_Clarke-referential-300x265.png 300w\" sizes=\"auto, (max-width: 465px) 100vw, 465px\" \/><figcaption class=\"wp-element-caption\">Representation of the active and zero space vectors in the \u03b1\u03b2 plane for an NPC converter<\/figcaption><\/figure>\n<\/div>\n\n\n<p>In order to find appropriate active and zero vectors to apply, the <a href=\"https:\/\/imperix.com\/doc\/software\/space-vector-pwm\">SV-PWM modulator<\/a> from <a href=\"https:\/\/imperix.com\/software\/bbos\/\">imperix libraries<\/a> uses a hexagonal coordinate system, as presented in [2], rather than a division in six sectors. While the search method differs from the two-level variant of the algorithm, switching patterns are constructed with the same logic: commutations are avoided as much as possible to limit switching losses. The figure below illustrates an example of an optimal switching pattern generated by a three-level converter.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"304\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/PWM-1.png\" alt=\"Optimal switching pattern with three levels\" class=\"wp-image-6029\" style=\"width:349px;height:170px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/PWM-1.png 621w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/PWM-1-300x147.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><figcaption class=\"wp-element-caption\">Example of optimal switching pattern with three levels<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"h-experimental-validation-of-space-vector-modulation\"><span class=\"ez-toc-section\" id=\"Experimental-validation-of-space-vector-modulation\"><\/span>Experimental validation of space vector modulation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-implementation-using-matlab-simulink\"><span class=\"ez-toc-section\" id=\"Implementation-using-MATLAB-Simulink\"><\/span>Implementation using MATLAB Simulink<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The attached Simulink model provides an example of a current controller similar to the one presented in the <a href=\"https:\/\/imperix.com\/doc\/implementation\/vector-current-control\">vector current control<\/a> note. However, a space vector modulation technique is used instead of a carrier-based one. The power converter is a two-level three-phase inverter.<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2026\/03\/TN145_Space_Vector_Modulation_Simulink.zip\" class=\"wp-block-file__button wp-element-button\" download>Download SVM control model<\/a><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"353\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink-overview-1024x353.png\" alt=\"\" class=\"wp-image-7606\" style=\"width:768px;height:265px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink-overview-1024x353.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink-overview-300x103.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink-overview-768x265.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink-overview.png 1181w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Current controller implementation in Simulink, using space vector modulation to produce the PWM signals<\/figcaption><\/figure>\n<\/div>\n\n\n<p>As explained in <a href=\"https:\/\/imperix.com\/doc\/implementation\/svpwm-vs-spwm-modulation-techniques\">SVPWM vs SPWM modulation techniques<\/a>, the maximum amplitude of the reference space vector is limited by the DC bus voltage. When normalized with respect to the DC bus, the maximum output voltage can only reach \\(2\/\\sqrt{3} \\approx 1.15\\) p.u. before entering the overmodulation region. If this threshold is exceeded, the load currents would be distorted, which is undesired for current control. For this reason, the control should saturate the output voltage.<\/p>\n\n\n\n<p>Let us call \\(m_{\\alpha}\\) and \\(m_{\\beta}\\) the components of the reference space vector. If the norm is larger than 1.15, it exceeds the limit by a ratio<\/p>\n\n\n\n<p class=\"has-text-align-center\">$$ R = \\frac{\\sqrt{m_\\alpha ^2 + m_\\beta ^2}}{1.15}.$$<\/p>\n\n\n\n<p>In this case, the \\(\\alpha\\) and \\(\\beta\\) components should be reduced by a factor \\(R\\) to avoid entering the overmodulation region, as shown below. While saturating, the current controller cannot follow its d and q references, since it cannot produce the required output voltage [3]. As such, the integrator of each PI regulator should be disabled, to prevent accumulating the error. The <a href=\"https:\/\/imperix.com\/doc\/software\/space-vector-pwm\">SV-PWM modulator<\/a> from <a href=\"https:\/\/imperix.com\/software\/bbos\/\">imperix libraries<\/a> has a built-in saturation mechanism. However, by implementing the saturation externally &#8211; as shown below &#8211; one has access to a boolean signal that notifies the current controller if it operates in the saturation region. As such, the controller can conditionally disable its integrator.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"266\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/external_saturation.png\" alt=\"Saturation of the normalized reference space vector\" class=\"wp-image-7611\" style=\"width:626px;height:266px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/external_saturation.png 626w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/external_saturation-300x127.png 300w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><figcaption class=\"wp-element-caption\">Saturation of the normalized reference space vector<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"h-experimental-setup\"><span class=\"ez-toc-section\" id=\"Experimental-setup\"><\/span>Experimental setup<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-simple-alerts-for-gutenberg-alert-boxes sab-alert sab-alert-success\" role=\"alert\">General\u00a0<strong>safety-related recommendations<\/strong>\u00a0for operating power converters in a laboratory environment are given in\u00a0<a href=\"https:\/\/imperix.com\/doc\/implementation\/safety-and-protection-in-the-lab\">TN181<\/a>.<\/div>\n\n\n\n<p>During the experiments, the two-level converter was connected to a balanced three-phase RL load, under the following conditions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>DC bus voltage: 100 V<\/li>\n\n\n\n<li>Control frequency and sampling: 20 kHz<\/li>\n\n\n\n<li>Sampling phase: 0.5<\/li>\n\n\n\n<li>Load resistance: 8.5 \u03a9<\/li>\n\n\n\n<li>Load inductance: 2.5 mH<\/li>\n<\/ul>\n\n\n\n<p>The experimental setup is presented in the picture below. The power converter is built from 3x <a href=\"https:\/\/imperix.com\/products\/power\/sic-power-module\/\">PEB 8024 phase-leg modules<\/a> and is controlled by a <a href=\"https:\/\/imperix.com\/products\/control\/rapid-prototyping-controller\/\">B-Box RCP prototyping controller<\/a>. The current control is implemented graphically using the <a href=\"https:\/\/imperix.com\/software\/acg-sdk\/simulink\/\">ACG SDK library for Simulink<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"392\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/TN145_component_connection-1.png\" alt=\"\" class=\"wp-image-7718\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/TN145_component_connection-1.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/TN145_component_connection-1-300x147.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/TN145_component_connection-1-768x376.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental setup<\/figcaption><\/figure>\n\n\n\n<p>The performances of the current controller were validated experimentally by applying multiple steps on the d and q-axis current references. As illustrated below, the controllers of both axes manage to independently track their respective references, while rejecting perturbations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/current_control-2.png\" alt=\"Experimental performances of the current controller\" class=\"wp-image-6449\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/current_control-2.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/current_control-2-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/current_control-2-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental performances of the current control with space vector modulation<\/figcaption><\/figure>\n\n\n\n<p>For the sake of completeness, the experimental measurements of the three-phase load currents are also illustrated below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/abc_currents_experimental.png\" alt=\"Load currents in abc frame\" class=\"wp-image-7023\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/abc_currents_experimental.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/abc_currents_experimental-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/abc_currents_experimental-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental measurements of the three-phase load currents<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-academic-references\"><span class=\"ez-toc-section\" id=\"Academic-references\"><\/span>Academic references<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>[1] Slobodan N. Vukosavic, &#8220;Grid-Side Converters Control and Design&#8221;, Springer, 2018, ISBN: 978-3-030-10346-0<\/p>\n\n\n\n<p>[2] N. Celanovic and D. Boroyevich, &#8220;A fast space-vector modulation algorithm for multilevel three-phase converters,&#8221; in IEEE Transactions on Industry Applications, vol. 37, no. 2, pp. 637-641, March-April 2001, doi: 10.1109\/28.913731.<\/p>\n\n\n\n<p>[3] Karl J. \u00c5str\u00f6m and Tore H\u00e4gglund, \u201cPID Controllers: Theory, Design and Tuning\u201d, Instrument Society of America, 1995, ISBN:1-55617-516-7<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the space vector modulation (SVM) technique and how does it work? To answer these questions, this article introduces first the notions of active&#8230;<\/p>\n","protected":false},"author":8,"featured_media":7804,"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":[4],"tags":[],"software-environments":[103],"provided-results":[108],"related-products":[50,31,32,92,166,112,111,110],"guidedreadings":[],"tutorials":[],"user-manuals":[],"coauthors":[62],"class_list":["post-4953","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-implementation","software-environments-matlab","provided-results-experimental","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-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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