{"id":5624,"date":"2021-08-19T08:08:16","date_gmt":"2021-08-19T08:08:16","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=5624"},"modified":"2025-12-17T14:39:01","modified_gmt":"2025-12-17T14:39:01","slug":"svpwm-vs-spwm-modulation-techniques","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/implementation\/svpwm-vs-spwm-modulation-techniques","title":{"rendered":"SVPWM vs SPWM modulation techniques"},"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\/svpwm-vs-spwm-modulation-techniques\/#What-are-SVPWM-and-SPWM\" >What are SVPWM and SPWM?<\/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\/svpwm-vs-spwm-modulation-techniques\/#Limitation-of-the-DC-bus-utilization-with-SPWM\" >Limitation of the DC bus utilization with SPWM<\/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\/svpwm-vs-spwm-modulation-techniques\/#Minmax-injection-with-SVPWM\" >Min\/max injection with SVPWM<\/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\/svpwm-vs-spwm-modulation-techniques\/#Experimental-comparison\" >Experimental comparison<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/imperix.com\/doc\/implementation\/svpwm-vs-spwm-modulation-techniques\/#Simulink-implementation\" >Simulink implementation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/imperix.com\/doc\/implementation\/svpwm-vs-spwm-modulation-techniques\/#SVPWM-and-SPWM-waveforms\" >SVPWM and SPWM waveforms<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/imperix.com\/doc\/implementation\/svpwm-vs-spwm-modulation-techniques\/#Academic-references\" >Academic references<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>What is the difference between Space Vector (SVPWM) and Sinusoidal Pulse Width Modulation (SPWM)? This article presents the advantages of the SVPWM technique over SPWM in the case of a two-level three-phase inverter.<\/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<\/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_TN145-2.png\" alt=\"Experimental setup to compare SVPWM and SPWM with imperix products.\" class=\"wp-image-26792\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/DSC9574_TN145-2.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/DSC9574_TN145-2-300x145.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/DSC9574_TN145-2-768x371.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-are-svpwm-and-spwm\"><span class=\"ez-toc-section\" id=\"What-are-SVPWM-and-SPWM\"><\/span>What are SVPWM and SPWM?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>SVPWM and SPWM are two modulation techniques commonly used with power converters. The purpose of a modulation scheme is to translate a voltage reference into a sequence of switching signals, in order to produce that reference at the output of the converter. While both techniques share similar acronyms, they have fairly different approaches.<\/p>\n\n\n\n<p>On one hand, the <a href=\"https:\/\/imperix.com\/doc\/implementation\/space-vector-modulation\">SVPWM technique<\/a> represents each switching state of the converter by a space vector in the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Alpha%E2%80%93beta_transformation\">Clarke referential<\/a>. Then, the desired output voltage is synthesized on average, by alternating between multiple space vectors over each switching period. On the other hand, SPWM is a Carrier-Based PWM scheme (<a href=\"https:\/\/imperix.com\/doc\/software\/carrier-based-pwm\">CB-PWM<\/a>) with a sinusoidal reference (see the note on the <a href=\"https:\/\/imperix.com\/doc\/example\/three-phase-voltage-source-inverter\">voltage source inverter<\/a>). In order to simplify the comparison, only the case of two-level three-phase inverters is covered. The topology of the inverter is shown 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_AN002-1.png\" alt=\"Topology of a two-level inverter\" class=\"wp-image-5663\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/schematic_AN002-1.png 547w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/schematic_AN002-1-300x99.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<h3 class=\"wp-block-heading\" id=\"h-limitation-of-the-dc-bus-utilization-with-spwm\"><span class=\"ez-toc-section\" id=\"Limitation-of-the-DC-bus-utilization-with-SPWM\"><\/span>Limitation of the DC bus utilization with SPWM<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>While producing a sinusoidal phase voltage with a two-level inverter, the peak amplitude is limited by the DC bus voltage [1]. Based on the illustration below, each leg of the inverter can produce a leg voltage \\(v_{leg}\\) of amplitude \\(V_{DC}\/2\\).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"134\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_1-1.png\" alt=\"Limitation of the output voltage by the DC bus with SPWM\" class=\"wp-image-6229\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_1-1.png 418w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_1-1-300x96.png 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><figcaption class=\"wp-element-caption\">Limitation of the output phase voltage by the DC bus<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The relative amplitude of the output voltage is often referred to as the <em>modulation index<\/em>, denoted \\(m\\) [1], and the maximum amplitude of the sinusoidal voltage corresponds to \\(m = 1\\).<strong> <\/strong>Thus, the phase voltage can be expressed as a function of the modulation index \\(m\\), the angular frequency \\(\\omega\\), and the phase \\(\\phi\\):<\/p>\n\n\n\n<p class=\"has-text-align-center\">$$v_{phase}(t) = m \\, \\frac{V_{DC}}{2} \\, \\sin(\\omega \\, t + \\phi)$$<\/p>\n\n\n\n<p>If \\(m &gt; 1\\), the output voltage will be clipped to \\(\\pm V_{DC}\/2\\). As such, the distortion introduces low-order harmonics that can be difficult to filter out. If the voltage reference exceeds the DC bus capabilities, the converter is said to be in the overmodulation region.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"160\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_2-1.png\" alt=\"Clamping of the DC bus voltage with SPWM\" class=\"wp-image-6230\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_2-1.png 418w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_2-1-300x115.png 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><figcaption class=\"wp-element-caption\">Clamping of the output voltage in the overmodulation region<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"h-min-max-injection-with-svpwm\"><span class=\"ez-toc-section\" id=\"Minmax-injection-with-SVPWM\"><\/span>Min\/max injection with SVPWM<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>It can be demonstrated that SVPWM is equivalent to an SPWM with min\/max injection [1]. The idea behind the min\/max injection method is to add a triangular zero sequence component (triplen harmonics) to the sinusoidal reference, which distorts the phase voltage references. This way, the peak voltage of the reference is reduced in comparison to a pure sinusoidal reference, and the modulation index can be increased up to \\(m = 2 \/ \\sqrt{3} \\approx 1.15\\) before hitting the limits of the DC bus voltage.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"162\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_3-1.png\" alt=\"Reduction of the peak output phase voltage with SVPWM\" class=\"wp-image-6231\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_3-1.png 418w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/SVPWM_3-1-300x116.png 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><figcaption class=\"wp-element-caption\">Reduction of the peak output voltage with min\/max injection<\/figcaption><\/figure>\n<\/div>\n\n\n<p>If the inverter is connected to a load with a grounded star connection, the distortion of the phase voltages is propagated to the line-to-line voltages, as shown below in Fig. (a). As a result, the load currents are also distorted, and SVPWM is not a suitable modulation scheme in terms of harmonic content. Fortunately, it is possible to suppress the distortions in the line-to-line voltages by using different wiring of the load. If the star connection is floating &#8211; see Fig. (b) &#8211; the triplen harmonics of the zero-sequence will cancel each other out, and the line-to-line voltages remain unaffected. The situation is similar in the case of a delta-connected load &#8211; see Fig. (c) &#8211; since the phase voltages of the load are equal to the line-to-line voltages produced by the inverter. Thus, for delta or floating star connections, SVPWM allows increasing the maximum line-to-line voltage without distortion of the load currents.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"308\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/harmonics_3-1.png\" alt=\"Representation of the phase and line voltages with star and delta connections.\" class=\"wp-image-6678\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/harmonics_3-1.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/harmonics_3-1-300x116.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/harmonics_3-1-768x296.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">(a) Distortion of the line-to-line voltages when the star is grounded; (b) the triplen harmonics cancel each other out when the star is floating; (c) no triplen harmonics neither with a delta connection.<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"h-experimental-comparison\"><span class=\"ez-toc-section\" id=\"Experimental-comparison\"><\/span>Experimental comparison<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-simulink-implementation\"><span class=\"ez-toc-section\" id=\"Simulink-implementation\"><\/span>Simulink implementation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The model provided in this article executes a simple open-loop voltage control of a two-level three-phase inverter. For comparison purposes, both SVPWM and SPWM (with or without min\/max injection) techniques are implemented in parallel, and the user can select which switching signals will drive the converter.<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a href=\"https:\/\/cdn.imperix.com\/doc\/wp-content\/uploads\/2021\/08\/TN146_SVPWM_vs_SPWM.zip\" class=\"wp-block-file__button wp-element-button\" download>Download SVPWM vs SPWM control model<\/a><\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"348\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink_overview-2-1024x348.png\" alt=\"\" class=\"wp-image-7987\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink_overview-2-1024x348.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink_overview-2-300x102.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink_overview-2-768x261.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/simulink_overview-2.png 1226w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Overview of the open-loop voltage control in Simulink with SVPWM or SPWM<\/figcaption><\/figure>\n\n\n\n<p>The implementation of SVPWM with <a href=\"https:\/\/www.mathworks.com\/products\/simulink.html\">Simulink<\/a> and the <a href=\"https:\/\/imperix.com\/software\/acg-sdk\/simulink\/\">ACG SDK<\/a> can be found in the <a href=\"https:\/\/imperix.com\/doc\/implementation\/space-vector-modulation\">space vector modulation (SVM) note<\/a>. Similarly, the details on the SPWM implementation can be found in the <a href=\"https:\/\/imperix.com\/doc\/example\/three-phase-voltage-source-inverter\">three-phase inverter<\/a> note. Finally, the min\/max injection for a carrier-based PWM is illustrated in the figure below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"911\" height=\"249\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/min_max_injection-2.png\" alt=\"Min\/max injection in Simulink\" class=\"wp-image-6621\" style=\"width:585px;height:160px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/min_max_injection-2.png 911w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/min_max_injection-2-300x82.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/min_max_injection-2-768x210.png 768w\" sizes=\"auto, (max-width: 911px) 100vw, 911px\" \/><figcaption class=\"wp-element-caption\">Min\/max injection for a carrier-based PWM<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"h-svpwm-and-spwm-waveforms\"><span class=\"ez-toc-section\" id=\"SVPWM-and-SPWM-waveforms\"><\/span>SVPWM and SPWM waveforms<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 control software is implemented graphically using the <a href=\"https:\/\/imperix.com\/software\/acg-sdk\/simulink\/\">ACG SDK library for Simulink<\/a>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"392\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/TN146_component_connection-1.png\" alt=\"\" class=\"wp-image-7774\" style=\"width:800px;height:392px\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/TN146_component_connection-1.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/TN146_component_connection-1-300x147.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/TN146_component_connection-1-768x376.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental setup<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The goal is to observe whether the line-to-line voltages are distorted or not, depending on the modulation scheme in use.<strong> <\/strong>Since the output line-to-line voltages of the converter are switched, it would require heavy filtering to extract sinusoidal waveforms. Instead, the line-to-line voltages can be observed indirectly through the load currents, since they are filtered by inductors. Then, in order to evaluate the impact of the modulation scheme, the modulation index is toggled between \\(m = 0.5\\) and \\(m = 1.15\\) each 60 ms.<\/p>\n\n\n\n<p>When the modulation index is \\(m = 1.15\\), the SPWM technique is in its overmodulation region. As a result, the output currents are flattened at their maximum, as shown in the figure below between \\(t = 0\\, ms\\) and \\(t = 60\\, ms\\). However, the currents are undistorted if the SPWM is used in combination with a min\/max injection, as observed after \\(t = 120\\, ms\\).<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"318\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/spwm-3.png\" alt=\"SPWM load currents\" class=\"wp-image-6699\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/spwm-3.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/spwm-3-300x119.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/spwm-3-768x305.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental results of the SPWM modulation with or without min\/max injection<\/figcaption><\/figure>\n\n\n\n<p>The absence of distortion at \\(m = 1.15\\) with min\/max injection &#8211; or SVPWM, since the methods are equivalent &#8211; is easier to observe by superimposing the experimental currents obtained with SPWM and SVPWM, as shown below. For \\(m = 0.5\\) though,  the output voltages are within the capabilities of the DC bus with both modulation techniques, and the currents are identical regardless of the zero-sequence injection.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"318\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/svpwm_vs_spwm-3.png\" alt=\"SVPWM vs SPWM in overmodulation range (experimental results)\" class=\"wp-image-6681\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/svpwm_vs_spwm-3.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/svpwm_vs_spwm-3-300x119.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/svpwm_vs_spwm-3-768x305.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental results illustrating the absence of distortion with SVPWM at m = 1.15, when compared to SPWM<\/figcaption><\/figure>\n\n\n\n<p>The equivalence between SVPWM and SPWM with min\/max injection was also verified experimentally, by using both methods with \\(m = 1.15\\) and superimposing the measured currents, as shown 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\/09\/equivalence_svpwm_zspwm.png\" alt=\"Superposition of current waveforms with SVPWM and SPWM (min\/max injection)\" class=\"wp-image-7790\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/equivalence_svpwm_zspwm.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/equivalence_svpwm_zspwm-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/equivalence_svpwm_zspwm-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Experimental results illustrating the equivalence between SVPWM and SPWM with min\/max injection<\/figcaption><\/figure>\n\n\n\n<p>While the voltage waveforms are challenging to measure experimentally (switched waveforms), their references can be observed directly from the control. The figure below illustrates side-by-side the sinusoidal voltage references and the corresponding min\/max zero-sequence, with its characteristic triangular shape [1].<\/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\/sinewave_minmax.png\" alt=\"Zero-sequence from min\/max injection\" class=\"wp-image-6636\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/sinewave_minmax.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/sinewave_minmax-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/sinewave_minmax-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Min\/max zero-sequence resulting from sinusoidal references (from simulation)<\/figcaption><\/figure>\n\n\n\n<p>By subtracting the zero-sequence from the sinusoidal waveforms, one can obtain the saddle-shaped voltage references from SVPWM.<\/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\/references_minmax.png\" alt=\"SVPWM waveforms with min\/max injection\" class=\"wp-image-6637\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/references_minmax.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/references_minmax-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/references_minmax-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\">Effect of the min\/max injection on the phase voltage references (from simulation)<\/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","protected":false},"excerpt":{"rendered":"<p>What is the difference between Space Vector (SVPWM) and Sinusoidal Pulse Width Modulation (SPWM)? This article presents the advantages of the SVPWM technique over SPWM&#8230;<\/p>\n","protected":false},"author":8,"featured_media":7809,"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-5624","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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