{"id":592,"date":"2021-03-25T13:26:32","date_gmt":"2021-03-25T13:26:32","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=592"},"modified":"2025-06-24T14:46:56","modified_gmt":"2025-06-24T14:46:56","slug":"dual-active-bridge-control","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control","title":{"rendered":"Dual Active Bridge converter 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\/dual-active-bridge-control\/#Dual-Active-Bridge-converter-overview\" >Dual Active Bridge converter overview<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Modulation-techniques-for-Dual-Active-Bridge-converters\" >Modulation techniques for Dual Active Bridge converters<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Phase-shift-modulation\" >Phase-shift modulation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Triangular-modulation\" >Triangular modulation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Trapezoidal-modulation\" >Trapezoidal modulation<\/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\/dual-active-bridge-control\/#Combined-modulation\" >Combined modulation<\/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\/dual-active-bridge-control\/#References-on-dual-active-bridge-converters\" >References on dual active bridge converters<\/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\/dual-active-bridge-control\/#Dual-active-bridge-control-example\" >Dual active bridge control example<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Software-resources\" >Software resources<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Variable-phase-PWM-modulator\" >Variable-phase PWM modulator<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Phase-shift-modulation-using-Simulink\" >Phase-shift modulation using Simulink<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Dual-Active-Bridge-converter-simulation-results\" >Dual Active Bridge converter simulation results<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Experimental-operation-of-a-dual-active-bridge\" >Experimental operation of a dual active bridge<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Appendix\" >Appendix<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Triangular-modulation-with-Simulink\" >Triangular modulation with Simulink<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/imperix.com\/doc\/implementation\/dual-active-bridge-control\/#Trapezoidal-modulation-with-Simulink\" >Trapezoidal modulation with Simulink<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n\n<p>This note presents several modulation techniques to operate a Dual Active Bridge (DAB) converter. First, the topology and the theoretical aspects of the Dual Active Bridge converters are presented, including a short overview of the main modulation techniques. Then, a possible control implementation on the&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bbox\">B-Box RCP<\/a>&nbsp;or&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bboard\">B-Board PRO<\/a>&nbsp;is introduced using <a href=\"https:\/\/imperix.com\/software\/acg-sdk\/simulink\/\">ACG SDK on Simulink<\/a>, and simulation results are shown.<\/p>\n\n\n\n<p>A Dual Active Bridge converter prototype (image below) and its control are presented in more detail in <a href=\"https:\/\/imperix.com\/doc\/implementation\/dab-converter-control\">DAB converter control<\/a>.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"754\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2022\/03\/DAB_setup_photo_with_oscillo_v3-1-1024x754.png\" alt=\"\" class=\"wp-image-10897\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2022\/03\/DAB_setup_photo_with_oscillo_v3-1-1024x754.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2022\/03\/DAB_setup_photo_with_oscillo_v3-1-300x221.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2022\/03\/DAB_setup_photo_with_oscillo_v3-1-768x565.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2022\/03\/DAB_setup_photo_with_oscillo_v3-1.png 1297w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Dual Active Bridge converter prototype with imperix products<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Dual-Active-Bridge-converter-overview\"><\/span>Dual Active Bridge converter overview<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>A Dual Active Bridge is a DC\/DC converter offering galvanic isolation and bidirectional power flow. The galvanic isolation is ensured by a high-frequency intermediary transformer.<\/p>\n\n\n\n<p>The topology of the dual active bridge converter is shown in the following figure. This system can be easily implemented using four&nbsp;<a href=\"https:\/\/imperix.com\/products\/power\/peb\/\">PEB modules<\/a>, or two&nbsp;<a href=\"https:\/\/imperix.com\/products\/power\/peh\/\">PEH modules<\/a>.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1418\" height=\"362\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-67.png\" alt=\"Dual Active Bridge converter topology\" class=\"wp-image-621\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-67.png 1418w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-67-300x77.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-67-1024x261.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-67-768x196.png 768w\" sizes=\"auto, (max-width: 1418px) 100vw, 1418px\" \/><figcaption class=\"wp-element-caption\">Dual Active Bridge converter topology<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The power transfer inductance \\(L_{tot}\\) is the sum of the transformer leakage inductance and any additional inductance placed at the primary or secondary of the transformer.<\/p>\n\n\n\n<p>The simplified loss-less scheme of the Dual Active Bridge converter is shown below. It assumes that the magnetizing inductance is infinite, the switches and the voltage sources are ideal, and neglects the winding resistance and capacitance.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"810\" height=\"352\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/DAB_lossless.png\" alt=\"Simplified loss-less scheme of the dual active bridge converter.\" class=\"wp-image-2713\" style=\"width:491px;height:auto\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/DAB_lossless.png 810w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/DAB_lossless-300x130.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/DAB_lossless-768x334.png 768w\" sizes=\"auto, (max-width: 810px) 100vw, 810px\" \/><figcaption class=\"wp-element-caption\">Simplified loss-less scheme of the Dual Active Bridge converter<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The simplified model above shows that the power transfer between the primary and secondary sides is mainly governed by the current through the inductance&nbsp;\\(L_{tot}\\), which, in turn, derives from the voltage across the inductor \\(V^{sw}_2-V^{sw}_1\\). Therefore, a power flow control can be achieved by acting on the parameters defining the voltage across the inductor, namely:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The duty-cycle&nbsp;\\(D_1\\) of the 3-level switched voltage&nbsp;\\(V^{sw}_1\\)<\/li>\n\n\n\n<li>The duty-cycle&nbsp;\\(D_2\\) of the 3-level switched voltage \\(V^{sw}_2\\)<\/li>\n\n\n\n<li>The phase-shift&nbsp;\\(\\phi\\)&nbsp;between&nbsp;\\(V^{sw}_1\\) and&nbsp;\\(V^{sw}_2\\), relatively to the switching period&nbsp;\\(T_{sw}\\)<\/li>\n\n\n\n<li>The switching frequency&nbsp;\\(f_{sw}\\) of&nbsp;\\(V^{sw}_1\\) and&nbsp;\\(V^{sw}_2\\) (although generally kept constant)<\/li>\n<\/ol>\n\n\n\n<p>Although all 3 degrees of freedom can be combined and exploited in an optimization process, the most used method is to fix some of the parameters to reduce the problem complexity. This leads to 3 typical modulation techniques of different complexity, achieving different levels of performance.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-Principalmodulationtechniques\"><span class=\"ez-toc-section\" id=\"Modulation-techniques-for-Dual-Active-Bridge-converters\"><\/span>Modulation techniques for Dual Active Bridge converters<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The principal modulation techniques traditionally used are the 1) phase-shift, 2) triangular and 3) trapezoidal modulations. These techniques may also be 4) combined.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-1)Phase-shiftmodulation\"><span class=\"ez-toc-section\" id=\"Phase-shift-modulation\"><\/span>Phase-shift modulation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Phase-shift modulation is probably the simplest modulation technique for dual active bridge converters. It uses \\(D_1=D_2=0.5\\)&nbsp;(i.e. 2-level switched voltages), reducing the degrees of freedom to&nbsp;\\(\\phi\\)&nbsp;only.<\/p>\n\n\n\n<p>The switched voltage and inductor current waveforms are depicted below:<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2363\" height=\"1117\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-69.png\" alt=\"DAB converter switched voltage and inductor current waveforms\" class=\"wp-image-625\" style=\"width:631px;height:auto\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-69.png 2363w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-69-300x142.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-69-1024x484.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-69-768x363.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-69-1536x726.png 1536w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-69-2048x968.png 2048w\" sizes=\"auto, (max-width: 2363px) 100vw, 2363px\" \/><figcaption class=\"wp-element-caption\">Dual Active Bridge switched voltage and inductor current waveforms<\/figcaption><\/figure>\n<\/div>\n\n\n<p>With this method, the power transfer between the primary and secondary has the following simple expression and has a maximum for&nbsp;\\(\\phi=0.25\\).<\/p>\n\n\n\n<p>$$ P = \\displaystyle\\frac{nV_1 V_2}{f_{sw}L_{tot}}\\phi(1-2\\phi) $$<\/p>\n\n\n\n<p>Some of the benefits and drawbacks of this method are summarized in the following table:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th scope=\"col\"><strong>Benefits<\/strong><\/th><th scope=\"col\"><strong>Drawbacks<\/strong><\/th><\/tr><\/thead><tbody><tr><td>Simplicity (1-D of freedom)<\/td><td>Higher RMS transformer current<\/td><\/tr><tr><td>Highest achievable power flow<\/td><td>Limited operating range with low switching losses<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Due to a high RMS current (hence conduction losses), and high switching losses, phase-shift modulation cannot be used for high-efficiency applications. Nevertheless, the best ratio between transferred power and inductor RMS current is optimal when&nbsp;\\(V_1=nV_2\\), making phase-shift modulation attractive when operated close to that operating point.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-2)Triangularmodulation\"><span class=\"ez-toc-section\" id=\"Triangular-modulation\"><\/span>Triangular modulation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>In triangular modulation, 3-level switched voltage waveforms are generated by both the primary and the secondary H-bridges. The waveforms (see graph below) are such that the beginning of their pulses is aligned, and the secondary is switched off as soon as the inductor current reaches zero. In this case, the secondary H-bridge switches always under zero current (ZCS).<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2363\" height=\"1117\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-70.png\" alt=\"Waveforms of a dual active bridge under triangular modulation.\" class=\"wp-image-627\" style=\"width:645px;height:auto\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-70.png 2363w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-70-300x142.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-70-1024x484.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-70-768x363.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-70-1536x726.png 1536w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-70-2048x968.png 2048w\" sizes=\"auto, (max-width: 2363px) 100vw, 2363px\" \/><figcaption class=\"wp-element-caption\">Waveforms of Dual Active Bridge converter operation with triangular modulation<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The condition for ZCS of the secondary is&nbsp; \\((V_1-nV_2)D_1=nV_2(D_2-D_1) \\Rightarrow V_1 D_1=nV_2 D_2 \\). This also implies that no power transfer is possible when&nbsp;\\(V_1=nV_2\\).<\/p>\n\n\n\n<p>More generally, it can be shown that for&nbsp;\\(V_1&gt;nV_2\\)&nbsp;, the power transfer is limited to<\/p>\n\n\n\n<p>$$ P_{max}^{tri}=\\displaystyle\\frac{n^2 V_2^2 (V_1-nV_2)}{4f_{sw}L_{tot}V_1} $$<\/p>\n\n\n\n<p>Some of the benefits and drawbacks of this method are summarized in the following table:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th scope=\"col\"><strong>Benefits<\/strong><\/th><th scope=\"col\"><strong>Drawbacks<\/strong><\/th><\/tr><\/thead><tbody><tr><td>Secondary always switches under zero current<\/td><td>Increased complexity<\/td><\/tr><tr><td>Reduced RMS transformer current<\/td><td>Power transfer direction defined by voltage difference<\/td><\/tr><tr><td>Allows better converter efficiency<\/td><td>Limited achievable power flow (particularly when close to&nbsp;\\(V_1=nV_2\\))<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-3)Trapezoidalmodulation\"><span class=\"ez-toc-section\" id=\"Trapezoidal-modulation\"><\/span>Trapezoidal modulation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The limited maximum power transfer of triangular modulation can be increased by using trapezoidal modulation. With this technique, ZCS is achieved twice per period on both the primary and secondary H-bridges. Typical waveforms are shown below.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2363\" height=\"1117\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-71.png\" alt=\"Waveforms of a dual active bridge under trapezoidal modulation.\" class=\"wp-image-629\" style=\"width:633px;height:auto\" title=\"Technical notes &gt; TN116: Operation of DAB-type converters &gt; modulation_trapezoidal.png\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-71.png 2363w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-71-300x142.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-71-1024x484.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-71-768x363.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-71-1536x726.png 1536w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-71-2048x968.png 2048w\" sizes=\"auto, (max-width: 2363px) 100vw, 2363px\" \/><figcaption class=\"wp-element-caption\">Waveforms of Dual Active Bridge converter operation under trapezoidal modulation<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The condition for ZCS at applicable times on primary and secondary sides is still&nbsp;\\(V_1D_1=nV_2D_2\\).<\/p>\n\n\n\n<p>It can be shown that:<\/p>\n\n\n\n<p>$$ P_{max}^{tra}=\\displaystyle\\frac{n^2V_1^2V_2^2}{4f_{sw}L_{tot}(V_1^2+nV_1V_2+n^2V_2^2)} &gt; P_{max}^{tri} $$<\/p>\n\n\n\n<p>Some of the benefits and drawbacks of this method are summarized in the following table:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th scope=\"col\"><strong>Benefits<\/strong><\/th><th scope=\"col\"><strong>Drawbacks<\/strong><\/th><\/tr><\/thead><tbody><tr><td>Higher achievable power than triangular<\/td><td>Cannot be applied for low power transfer<\/td><\/tr><tr><td>Still ZCS on some switching<\/td><td>Not always ZCS on the secondary<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-4)Combinedmodulation\"><span class=\"ez-toc-section\" id=\"Combined-modulation\"><\/span>Combined modulation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>For optimal converter efficiency over a large range of power, a combination of techniques can be used. In particular, a seamless transition between triangular and trapezoidal modulation can be achieved when the inductor current is zero. This allows benefiting from the high efficiency of triangular modulation at low power, and the higher power capabilities of trapezoidal modulation when required.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-Academicreferences\"><span class=\"ez-toc-section\" id=\"References-on-dual-active-bridge-converters\"><\/span>References on dual active bridge converters<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>F. Krismer, \u201c<em>Modeling and Optimization of Bidirectional Dual Active Bridge DC-DC Converter Topologies,\u201d&nbsp;<\/em>Ph.D. dissertation, ETH Zurich, 2010<\/li>\n\n\n\n<li>F. Jauch and J Biela, \u201c<em>Generalized Modeling and Optimization of a Bidirectional Dual Active Bridge DC-DC Converter Including Frequency Variation<\/em>,\u201d in IEEJ Journal of Ind. Appl., Vol. 4, N\u00b0 5, 2015, pp. 593-601<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-DABcontrolexample\"><span class=\"ez-toc-section\" id=\"Dual-active-bridge-control-example\"><\/span>Dual active bridge control example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Software-resources\"><\/span>Software resources<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The Simulink demo model can be downloaded below. It can be used for Simulink-based simulation or code generation for real-time execution on imperix controllers.<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-5a208991-86ea-4b11-8ad6-43cd9a552ccd\" href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2025\/06\/TN116_DAB_converter_control_Simulink.zip\">TN116_DAB_converter_control_Simulink<\/a><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2025\/06\/TN116_DAB_converter_control_Simulink.zip\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-5a208991-86ea-4b11-8ad6-43cd9a552ccd\">Download<\/a><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-B-Box\/B-Boardimplementation\"><span class=\"ez-toc-section\" id=\"Variable-phase-PWM-modulator\"><\/span>Variable-phase PWM modulator<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Thanks to the flexible <a href=\"https:\/\/imperix.com\/doc\/software\/carrier-based-pwm\">Carrier-Based PWM modulator<\/a> provided with imperix\u2019s library (CB-PWM), control over the duty-cycle and the phase-shift of the PWM signals can be achieved very easily:<\/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\">\n<p><strong>With imperix ACG SDK<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"109\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-72.png\" alt=\"\" class=\"wp-image-633\" title=\"Technical notes &gt; TN116: Operation of DAB-type converters &gt; CB_PWM_Simulink.png\"\/><figcaption class=\"wp-element-caption\">PWM modulator block in Simulink<\/figcaption><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"138\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-73.png\" alt=\"\" class=\"wp-image-634\" title=\"Technical notes &gt; TN116: Operation of DAB-type converters &gt; CB_PWM_PLECS.png\"\/><figcaption class=\"wp-element-caption\">PWM modulator block in PLECS<\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><strong>With imperix CPP SDK<\/strong><\/p>\n\n\n\n<p><em>Configuration<\/em>:<\/p>\n\n\n<pre class=\"wp-block-code\"><span><code class=\"hljs\">CbPwm_ConfigureClock(PWM_CHANNEL_0, CLOCK_0);<\/code><\/span><\/pre>\n\n\n<p><em>Update<\/em>:<\/p>\n\n\n<pre class=\"wp-block-code\"><span><code class=\"hljs\">CbPwm_SetDutyCycle(PWM_CHANNEL_0, dutyCycle);\nCbPwm_SetPhase(PWM_CHANNEL_0, phase);<\/code><\/span><\/pre><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-Phase-shiftmodulationusingSimulink\"><span class=\"ez-toc-section\" id=\"Phase-shift-modulation-using-Simulink\"><\/span>Phase-shift modulation using Simulink<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>In phase-shift modulation, the switched waveforms&nbsp;\\(V^{sw}_1\\) and&nbsp;\\(V^{sw}_2\\)&nbsp;must be 2-level, i.e.&nbsp;\\(D_1=D_2=0.5\\). In order to generate them from the primary and secondary H-bridges, the switching state of each of the 8 transistors can be obtained with a <a href=\"https:\/\/imperix.com\/doc\/software\/carrier-based-pwm\">Carrier-Based PWM modulator<\/a> (CB-PWM), using the following configuration:<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"945\" height=\"707\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-74.png\" alt=\"Phase-shift modulation for a DAB converter in Simulink\" class=\"wp-image-636\" style=\"width:481px;height:auto\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-74.png 945w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-74-300x224.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-74-768x575.png 768w\" sizes=\"auto, (max-width: 945px) 100vw, 945px\" \/><figcaption class=\"wp-element-caption\">Phase-shift modulation for Dual Active Bridge converter in Simulink<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"604\" height=\"384\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms_phase-shift.png\" alt=\"Phase-shift modulation waveforms for DAB converter\" class=\"wp-image-2710\" style=\"width:338px;height:auto\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms_phase-shift.png 604w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms_phase-shift-300x191.png 300w\" sizes=\"auto, (max-width: 604px) 100vw, 604px\" \/><figcaption class=\"wp-element-caption\">Waveforms of phase-shift control of Dual Active Bridge converter<\/figcaption><\/figure>\n<\/div>\n\n\n<p>With Dual Active Bridge converters, one can be interested in controlling the secondary voltage to a fixed value. A simple way of achieving that is by acting on the angle&nbsp;\\(\\phi\\)&nbsp;to control the power transfer to charge\/discharge the secondary DC bus to the desired voltage.<\/p>\n\n\n\n<p>In a possible implementation depicted below, <a href=\"https:\/\/imperix.com\/doc\/implementation\/basic-pi-control\">PI controller<\/a> regulates the secondary voltage at the desired value by generating a phase-shift reference. In addition, a feedforward term can be added to the phase-shift reference for improved dynamics. In the case of phase-shift modulation, the required angle can be derived from the power transfer equation, considering&nbsp;\\(P^*\\)&nbsp;the required power to achieve the desired output voltage&nbsp;\\(V^*_2\\)&nbsp;on the load resistor&nbsp;\\(R_{out}\\):<\/p>\n\n\n\n<p>$$ P^*=\\displaystyle\\frac{{V^*_2}^2}{R_{out}} \\Rightarrow \\phi = \\displaystyle\\frac{1}{4}\\left(1-\\sqrt{1-\\frac{8f_{sw}L_{tot}V^*_2}{nV_1R_{out}}}\\right) $$<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1086\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-76.png\" alt=\"Implementation of phase-shift control a Dual Active Bridge Converter\" class=\"wp-image-638\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-76.png 1086w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-76-300x83.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-76-1024x283.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-76-768x212.png 768w\" sizes=\"auto, (max-width: 1086px) 100vw, 1086px\" \/><figcaption class=\"wp-element-caption\">Implementation of phase-shift control for the Dual Active Bridge converter<\/figcaption><\/figure>\n<\/div>\n\n\n<p>Thanks to imperix&nbsp;<a href=\"https:\/\/imperix.com\/software\/acg-sdk\/\">ACG SDK<\/a>, this control implementation can be tested using offline simulation. The corresponding results are presented in the next section. The controlled system (converter model) is shown below and was drawn using PLECS Blockset.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1429\" height=\"606\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/plant_model_DAB_v2-1.png\" alt=\"\" class=\"wp-image-33645\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/plant_model_DAB_v2-1.png 1429w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/plant_model_DAB_v2-1-300x127.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/plant_model_DAB_v2-1-1024x434.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/plant_model_DAB_v2-1-768x326.png 768w\" sizes=\"auto, (max-width: 1429px) 100vw, 1429px\" \/><figcaption class=\"wp-element-caption\">Electrical model of the dual active bridge converter<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-Simulationresults\"><span class=\"ez-toc-section\" id=\"Dual-Active-Bridge-converter-simulation-results\"><\/span>Dual Active Bridge converter simulation results<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The following results have been obtained with the provided Simulink file and the following simulation parameters:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Parameter<\/th><th>Value<\/th><\/tr><\/thead><tbody><tr><td>\\(f_{sw}\\)<\/td><td>20 kHz<\/td><\/tr><tr><td>\\(V_1\\)<\/td><td>50 V<\/td><\/tr><tr><td>\\(n\\)<\/td><td>1<\/td><\/tr><tr><td>\\(L_{tot}\\)<\/td><td>30 \u00b5H<\/td><\/tr><tr><td>\\(R_{out}\\)<\/td><td>1.1*10 \u03a9<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Dual Active Bridge converter parameters for simulation<\/figcaption><\/figure>\n\n\n\n<p>The graph on the left-hand side below shows the reference tracking and perturbation rejection ability of the proposed control algorithm. At t = 0.1 s, a reference step from 50 V to 40 V is generated, and at t = 0.2 s, a load step from 10 \u03a9 to 6.6 \u03a9.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"838\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-78.png\" alt=\"Simulation results of the operation of a dual active bridge\" class=\"wp-image-640\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-78.png 838w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-78-300x107.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-78-768x275.png 768w\" sizes=\"auto, (max-width: 838px) 100vw, 838px\" \/><figcaption class=\"wp-element-caption\">Results of Dual Active Bridge power converter simulation<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The plot on the right-hand side shows the imposed phase-shift&nbsp;\\(\\phi\\)&nbsp;(red), which is the combination of a PI term (blue &#8211;) and a feedforward term (blue -.-).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>During the time interval [0 to 0.2 s], the feedforward term provides a fair estimation of the required phase-shift, although not perfect. The slight error comes from the output resistor value, which has been deliberately increased to 11 \u03a9 (instead of 10 \u03a9), to highlight the sensitivity of the feedforward term to parameter estimation. This slight error is compensated by the PI regulator.<\/li>\n\n\n\n<li>During the time interval [0.2 to 0.3 s], the feedforward term becomes erroneous, since it relies on the load resistance value, which has been changed by the load step. It is, therefore, unable to provide a proper estimation of the required phase-shift, and its error is fully compensated by the PI regulator.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-Experimentalresults\"><span class=\"ez-toc-section\" id=\"Experimental-operation-of-a-dual-active-bridge\"><\/span>Experimental operation of a dual active bridge<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The note <a href=\"https:\/\/imperix.com\/doc\/implementation\/dab-converter-control\">DAB converter control<\/a> presents experimental results of a 1 kW Dual Active Bridge converter, built with <a href=\"https:\/\/imperix.com\/products\/power\/full-bridge-module\/\">full-bridge power modules<\/a> and controlled with phase-shift modulation.<\/p>\n\n\n\n<p>In <a href=\"https:\/\/imperix.com\/doc\/implementation\/input-series-output-parallel-dab\">TN151<\/a>, an input series output parallel DAB application is shown, where the DABs are also controlled with phase-shift modulation. <\/p>\n\n\n\n<p>A similar approach is used in the&nbsp;<a href=\"https:\/\/imperix.com\/doc\/example\/fast-ev-charger-with-intermediate-energy-storage\">Fast EV charger with intermediate energy storage (AN007)<\/a>, where phase-shift modulation is used to control the secondary bus voltages of a Triple Active Bridge converter. In particular, experimental results show how the battery-side bus voltage is controlled after a step-change in the battery charging current.<\/p>\n\n\n\n<p>Furthermore, the galvanic isolation provided by the transformer can also be used in grid-related applications, such as <a href=\"https:\/\/imperix.com\/doc\/example\/solid-state-transformer\">solid-state transformers (AN015)<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"TN116:OperationofDABtypeconverters-Appendix\"><span class=\"ez-toc-section\" id=\"Appendix\"><\/span>Appendix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>For those wanting to use a more advanced modulation technique, the illustrations below give a sneak peek of what can be easily done with <a href=\"https:\/\/imperix.com\/software\/acg-sdk\/simulink\/\">ACG SDK on Simulink<\/a>. As always, the exact same implementation is also possible with PLECS and with CPP SDK.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Triangular-modulation-with-Simulink\"><\/span>Triangular modulation with Simulink<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-vertically-aligned-bottom is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"931\" height=\"724\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-64.png\" alt=\"Simulink-based triangular modulation for a dual active bridge.\" class=\"wp-image-618\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-64.png 931w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-64-300x233.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-64-768x597.png 768w\" sizes=\"auto, (max-width: 931px) 100vw, 931px\" \/><figcaption class=\"wp-element-caption\">Implementation of triangular modulation in Simulink<\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"546\" height=\"346\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms-triangular.png\" alt=\"Triangular modulation waveforms for DAB converter\" class=\"wp-image-2711\" style=\"width:377px;height:auto\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms-triangular.png 546w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms-triangular-300x190.png 300w\" sizes=\"auto, (max-width: 546px) 100vw, 546px\" \/><figcaption class=\"wp-element-caption\">Triangular modulation &#8211; generated waveforms<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Trapezoidal-modulation-with-Simulink\"><\/span>Trapezoidal modulation with Simulink<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns are-vertically-aligned-top is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"961\" height=\"716\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-66.png\" alt=\"Simulink-based trapezoidal modulation for a dual active bridge.\" class=\"wp-image-620\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-66.png 961w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-66-300x224.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/image-66-768x572.png 768w\" sizes=\"auto, (max-width: 961px) 100vw, 961px\" \/><figcaption class=\"wp-element-caption\">Implementation of trapezoidal modulation in Simulink<\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"546\" height=\"334\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms-trapezoidal.png\" alt=\"Trapezoidal modulation waveforms for DAB converter\" class=\"wp-image-2712\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms-trapezoidal.png 546w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/switched_waveforms-trapezoidal-300x184.png 300w\" sizes=\"auto, (max-width: 546px) 100vw, 546px\" \/><figcaption class=\"wp-element-caption\">Trapezoidal modulation &#8211; generated waveforms<\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This note presents several modulation techniques to operate a Dual Active Bridge (DAB) converter. First, the topology and the theoretical aspects of the Dual Active&#8230;<\/p>\n","protected":false},"author":5,"featured_media":3039,"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":[21],"software-environments":[103],"provided-results":[],"related-products":[50,32,92,166,51,111],"guidedreadings":[121],"tutorials":[148],"user-manuals":[],"coauthors":[65],"class_list":["post-592","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-implementation","tag-dc-dc-converters","software-environments-matlab","related-products-acg-sdk","related-products-b-box-rcp","related-products-b-box-micro","related-products-b-box-rcp-3-0","related-products-cpp-sdk","related-products-pm","guidedreadings-solid-state-transformer-sst-for-mc-lv-smart-grid","tutorials-isop-operation-with-isolated-dc-dc-converter"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Dual Active Bridge converter modulation techniques - imperix<\/title>\n<meta name=\"description\" content=\"The note presents several modulation techniques fir controlling a Dual Active Bridge converter. 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