{"id":27003,"date":"2024-03-26T12:16:35","date_gmt":"2024-03-26T12:16:35","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=27003"},"modified":"2025-12-31T10:43:12","modified_gmt":"2025-12-31T10:43:12","slug":"parallel-operation-of-grid-forming-inverters","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters","title":{"rendered":"Parallel operation of Grid-Forming Inverters (GFMIs)"},"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\/parallel-operation-of-grid-forming-inverters\/#Introduction-to-parallel-operation-of-Grid-Forming-Inverters\" >Introduction to parallel operation of Grid-Forming Inverters<\/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\/parallel-operation-of-grid-forming-inverters\/#Pre-synchronization-of-Grid-Forming-Inverters\" >Pre-synchronization of Grid-Forming Inverters<\/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\/parallel-operation-of-grid-forming-inverters\/#Pre-synchronization-of-amplitude\" >Pre-synchronization of amplitude<\/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\/parallel-operation-of-grid-forming-inverters\/#Pre-synchronization-of-frequency-and-phase\" >Pre-synchronization of frequency and phase<\/a><\/li><\/ul><\/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\/parallel-operation-of-grid-forming-inverters\/#Power-sharing-between-droop-controllers\" >Power sharing between droop controllers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters\/#Implementation-with-imperix-ACG-SDK\" >Implementation with imperix ACG SDK<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters\/#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\/parallel-operation-of-grid-forming-inverters\/#To-go-further%E2%80%A6\" >To go further&#8230;<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters\/#Academic-reference\" >Academic reference<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>This note introduces the parallel operation of Grid-Forming Inverters (GFMIs) and provides an implementation example on <a href=\"https:\/\/imperix.com\/products\/power\/programmable-inverter\/\">TPI 8032<\/a> programmable inverter with the <a href=\"https:\/\/imperix.com\/software\/acg-sdk\/\">ACG SDK<\/a>.<\/p>\n\n\n\n<p>An overview of the hardware architecture and detailed instructions on how to program the device are addressed in&nbsp;<a href=\"https:\/\/imperix.com\/doc\/help\/tpi-quick-start-guide\">getting started with the TPI 8032<\/a>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"469\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_Setup_picture_not_annotated.png\" alt=\"parallel grid-forming inverter setup without annotation\" class=\"wp-image-27464\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_Setup_picture_not_annotated.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_Setup_picture_not_annotated-300x180.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_Setup_picture_not_annotated-768x462.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Introduction-to-parallel-operation-of-Grid-Forming-Inverters\"><\/span>Introduction to parallel operation of Grid-Forming Inverters<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><a href=\"https:\/\/imperix.com\/doc\/implementation\/grid-forming-inverter\">Grid-Forming Inverters (GFMIs)<\/a> and <a href=\"https:\/\/imperix.com\/doc\/implementation\/grid-following-inverter\">Grid-Following Inverters (GFLI)<\/a> are two basic categories of inverters widely used in microgrid systems. Essentially, GFLIs can be considered as current sources with fast dynamic response so that they can rapidly regulate the output to synchronize with the grid. Therefore, the parallel operation of GFLIs is usually simple and costless to achieve. On the other hand, GFMIs can be represented as voltage sources with relatively slow dynamics, and thus require additional considerations to operate in parallel. The parallel operation of GFMIs faces three main challenges:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>GFMIs have voltage controllers to regulate their output voltage. When multiple voltage controllers are connected in parallel to the point of common coupling (PCC), they can &#8220;fight&#8221; against each other by trying to adjust the voltage at PCC simultaneously, causing oscillations in the grid voltage.<\/li>\n\n\n\n<li>When operating in standalone mode, each GFMI can have a different output voltage in phase, frequency, and amplitude than the PCC, but this is not possible with parallel inverters. Therefore, a pre-synchronization process is required to match the inverters&#8217; voltages to the PCC voltage before a physical connection can be made. Connecting different voltages without pre-synchronization can cause a significant and potentially destructive overcurrent at the PCC and may cause instability of the voltage controller. Besides, a sudden change of the grid phase and frequency may exceed the allowed Rate of Change of Frequency (RoCoF), causing damage to other devices connected to the grid.<\/li>\n\n\n\n<li>Power-sharing between the GFMIs in the grid also needs to be considered, especially for the parallel operation of GFMIs with different output power ratings. In general, GFMIs can participate in power-sharing thanks to their ability to set the phase and amplitude of the output voltage. A possible solution to regulate power-sharing explicitly is to use communication between the inverters, but this comes at the cost of increased complexity.<\/li>\n<\/ol>\n\n\n\n<p>Historically, various solutions have been developed for the parallel operation of synchronous generators. These solutions can also apply to parallel grid-forming inverters. <a href=\"https:\/\/imperix.com\/doc\/implementation\/proportional-droop-control\">Droop control<\/a> [1] is a well-established communication-less control strategy that avoids the issue of parallel voltage controllers. Besides, the active and reactive power-sharing between GFMIs can be regulated by the selection of droop coefficients.<\/p>\n\n\n\n<p>In this technical note, the droop controller developed in <a href=\"https:\/\/imperix.com\/doc\/implementation\/proportional-droop-control\">TN169<\/a> will be further developed, with the addition of pre-synchronization of the GFMIs. The effect of droop coefficients on power-sharing will also be addressed.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Pre-synchronization-of-Grid-Forming-Inverters\"><\/span>Pre-synchronization of Grid-Forming Inverters<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>To introduce the process of pre-synchronization, a microgrid consisting of two grid-forming inverters and a load is considered. The grid voltage at the PCC is already established by GFMI0 at the moment when GFMI1 is connected to the grid. To connect GFMI1 properly, its voltage must be synchronized with the PCC voltage before the relay is closed. Indeed, the slow dynamics of the voltage controller do not allow GFMI1 to instantaneously adjust its output voltage to match the PCC voltage. The synchronization prosses taking place before the relay is closed is called pre-synchronization.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"587\" height=\"315\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-D.png\" alt=\"two parallel GFMIs with load\" class=\"wp-image-27523\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-D.png 587w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-D-300x161.png 300w\" sizes=\"auto, (max-width: 587px) 100vw, 587px\" \/><figcaption class=\"wp-element-caption\">System under study: two parallel GFMIs with load<\/figcaption><\/figure>\n<\/div>\n\n\n<p>To achieve pre-synchronization, the GFMI1 must measure the voltage at PCC \\(V_{pcc}\\), and regulate its output voltage \\(V^{*}\\) to match \\(V_{pcc}\\). This process can be divided into three different steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Pre-synchronization of the voltage amplitude<\/li>\n\n\n\n<li>Pre-synchronization of the voltage frequency<\/li>\n\n\n\n<li>Pre-synchronization of the voltage phase<\/li>\n<\/ol>\n\n\n\n<p>For each of the three steps, a proportional-integral (PI) controller is used to compute corrective terms. Thanks to the integral part, this method can achieve approximately zero error between \\(V^{*}\\) and \\(V_{pcc}\\) in a steady state.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Pre-synchronization-of-amplitude\"><\/span>Pre-synchronization of amplitude<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>With the help of droop control, the active and reactive power flows can be decoupled, by controlling the voltage amplitude \\(V^{*}\\) and frequency \\(\\omega ^{*}\\) independently. Therefore, the pre-synchronization of voltage amplitude can be considered decoupled from that of frequency and phase. [2] The voltage amplitude can be calculated in the <a href=\"https:\/\/imperix.com\/doc\/software\/abc-to-alpha-beta-zero\">stationary reference frame (\u03b1\u03b20)<\/a> without knowledge of the phase.<\/p>\n\n\n\n<p>The adjustment of the voltage reference can be realized by either directly adjusting the voltage reference \\(V^{*}\\) or adjusting the reactive power input \\(Q\\) of the droop controller. However, the latter method may lead to inaccurate reactive power sharing and may also become unusable in the case of a mainly resistive line (i.e. where the reactive power also depends on the frequency).<\/p>\n\n\n\n<p>The control diagram of amplitude pre-synchronization is shown below, with the PI output directly fed forward to the droop controller \\(Q-V^{*}\\). To avoid affecting the voltage controller when working in standalone mode, a switch is added before the PI controller to keep its input at 0 when pre-synchronization is disabled (<code>sync<\/code> = 0). Besides, a delay block is added to the feedback of \\(V^{*}\\) to avoid an algebraic loop.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"635\" height=\"210\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-E.png\" alt=\"amplitude pre-synchronization diagram\" class=\"wp-image-27524\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-E.png 635w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-E-300x99.png 300w\" sizes=\"auto, (max-width: 635px) 100vw, 635px\" \/><figcaption class=\"wp-element-caption\">Control diagram of amplitude pre-synchronization<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Pre-synchronization-of-frequency-and-phase\"><\/span>Pre-synchronization of frequency and phase<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>To achieve pre-synchronization of frequency and phase, a PLL is required to measure the frequency and phase of \\(V_{pcc}\\). This note uses a <a href=\"https:\/\/imperix.com\/doc\/implementation\/sogi-pll\">DSOGI-PLL<\/a> for better immunity against grid voltage disturbance when the load changes. <\/p>\n\n\n\n<p>The pre-synchronizations of frequency and phase are not independent. In fact, the phase pre-synchronization can be realized by increasing or decreasing the GFMI&#8217;s frequency reference [3]. However, this imposes that the phase pre-synchronization can only be started after the frequency pre-synchronization has finished. Otherwise, if the frequency is not synchronized with the grid, both controllers will try to adjust the frequency reference, causing possible oscillation of the frequency.<\/p>\n\n\n\n<p>To avoid the oscillation issue, the frequency pre-synchronization is first activated, whereas the phase pre-synchronization only begins when the frequency error is less than a certain threshold \\(\\epsilon\\), which is here set at 0.2Hz. The block diagram of the frequency synchronization is presented below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"420\" height=\"162\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-F.png\" alt=\"\" class=\"wp-image-27525\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-F.png 420w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-F-300x116.png 300w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><figcaption class=\"wp-element-caption\">Control diagram of frequency pre-synchronization<\/figcaption><\/figure>\n<\/div>\n\n\n<p>For phase pre-synchronization, the phase error is calculated with the sine of the angle difference \\(\\theta_{pcc} &#8211; \\theta^{*} \\) to avoid discontinuities when either angle wraps to 0 or 2\u03c0. For small angle differences, the sine can be approximated to the angle. The block diagram for the phase synchronization is shown below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"445\" height=\"136\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/Schematic-TN172-G.png\" alt=\"phase pre-synchronization diagram\" class=\"wp-image-27551\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/Schematic-TN172-G.png 445w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/Schematic-TN172-G-300x92.png 300w\" sizes=\"auto, (max-width: 445px) 100vw, 445px\" \/><figcaption class=\"wp-element-caption\">Control diagram of phase pre-synchronization<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The frequency and phase corrective terms \\(\\Delta \\omega\\) and \\(\\Delta \\theta\\) are then fed forward to the droop controller \\(P- \\omega \\), as shown below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"312\" height=\"119\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-B.png\" alt=\"phase and frequency pre-synchronization\" class=\"wp-image-27528\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-B.png 312w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-B-300x114.png 300w\" sizes=\"auto, (max-width: 312px) 100vw, 312px\" \/><figcaption class=\"wp-element-caption\">Overall pre-synchronization of frequency and phase<\/figcaption><\/figure>\n<\/div>\n\n\n<p>Once the errors in voltage amplitude, frequency, and phase are equal to zero, the pre-synchronization is complete, and the relay can be closed. After the relay is closed, the pre-synchronization must be switched off, and the corrective terms must be kept constant and retain the value they had at the end of the pre-synchronization. This can be done by simply setting the input of the PI controllers to zero.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Power-sharing-between-droop-controllers\"><\/span>Power sharing between droop controllers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>To share active power between both grid-forming inverters, different coefficients \\(m_{0}\\) and \\(m_{1}\\) can be used in the frequency droop equations:<\/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>$$ \\omega_{0}^* = \\omega_{nom} &#8211; m_0 P_0 $$<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>$$ \\omega_{1}^* = \\omega_{nom} &#8211; m_1 P_1 $$<\/p>\n<\/div>\n<\/div>\n\n\n\n<p>In steady state, since the frequency references of both GFMIs are equal (\\(\\omega_{0}^*=\\omega_{1}^*\\)), the power-sharing \\(P_0\/P_1\\) is defined by \\(m_{1}\/m_{0}\\), as illustrated below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"181\" height=\"139\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-C-1.png\" alt=\"\" class=\"wp-image-27570\"\/><\/figure>\n<\/div>\n\n\n<p>On the other hand, having different droop coefficients can cause oscillations in the frequency in the case of a load step. Considering the active power flow in a transmission line<\/p>\n\n\n\n<p>$$ P\\approx3\\cfrac{V_1V_2}{X_{l}} \\delta, $$<\/p>\n\n\n\n<p>if a load step occurs at \\(t = 0\\), at \\(t = 0^+\\) both \\(P_0\\) and \\(P_1\\) step to a different value determined by the equation above, and slowly reach their steady-state values. During this transient, the two reference frequencies are different. As a consequence, a phase shift appears between the voltages set by the GFMIs, leading to oscillations of active power between the two inverters. This effect can be observed in the experimental results.<\/p>\n\n\n\n<p>A possible way to dampen the oscillations during the transient is to add a derivative term in the proportional droop controller [4], but this is outside the scope of this page.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Implementation-with-imperix-ACG-SDK\"><\/span>Implementation with imperix ACG SDK<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The control models available here after are implemented in Simulink using the imperix&nbsp;<a href=\"https:\/\/imperix.com\/software\/acg-sdk\/simulink\/\" target=\"_blank\" rel=\"noreferrer noopener\">ACG SDK<\/a>&nbsp;blockset. The models can both simulate the behavior of the system in an offline simulation and generate code for real-time execution on the <a href=\"https:\/\/imperix.com\/products\/power\/programmable-inverter\/\">TPI 8032<\/a>. An introductory guide regarding the TPI is addressed in&nbsp;<a href=\"https:\/\/imperix.com\/doc\/help\/tpi-quick-start-guide\" target=\"_blank\" rel=\"noreferrer noopener\">Getting started with the TPI 8032<\/a>. To run these models, the minimum requirements are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Imperix ACG SDK 2024.2 or newer.<\/li>\n\n\n\n<li>MATLAB Simulink R2016a or newer.<\/li>\n\n\n\n<li>For simulation only: Simscape Electrical<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/TN172_Parallel_operation_of_GFMIs.zip\" class=\"wp-block-file__button wp-element-button\" download>Download <strong>TN172_Parallel_operation_of_GFMIs<\/strong><\/a><\/div>\n\n\n\n<p>The pre-synchronization of the grid-forming inverters is shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1604\" height=\"1214\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_simulink_model.png\" alt=\"simulink model for pre-synchronization\" class=\"wp-image-27463\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_simulink_model.png 1604w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_simulink_model-300x227.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_simulink_model-1024x775.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_simulink_model-768x581.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_simulink_model-1536x1163.png 1536w\" sizes=\"auto, (max-width: 1604px) 100vw, 1604px\" \/><figcaption class=\"wp-element-caption\">Simulink model for pre-synchronization of GFMIs<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><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>The experimental validation of the parallel operation of grid-forming inverters is carried out with three TPIs used in a master-slave configuration (connected with <a href=\"https:\/\/imperix.com\/products\/control\/accessories\/#cables\" target=\"_blank\" rel=\"noreferrer noopener\">SFP cables<\/a>), meaning that they are programmed from the same Simulink model. Two TPIs running as GFMIs are connected in parallel to the PCC through inductors emulating an inductive transmission line. A relay controlled by a <a href=\"https:\/\/imperix.com\/doc\/software\/tpi-gpo-helper-block\">GPO port<\/a> is used to connect GFMI1. A third TPI running as GFLI is connected directly to the PCC as an active load. <\/p>\n\n\n\n<p>The required equipments are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3x&nbsp;<a href=\"https:\/\/imperix.com\/products\/power\/programmable-inverter\/\" target=\"_blank\" rel=\"noreferrer noopener\">TPI 8032<\/a>&nbsp;three-phase inverter<\/li>\n\n\n\n<li><a href=\"https:\/\/imperix.com\/software\/acg-sdk\" target=\"_blank\" rel=\"noreferrer noopener\">ACG SDK toolbox<\/a>&nbsp;for automated generation of the controller code from Simulink or PLECS<\/li>\n\n\n\n<li>1x bidirectional DC power supply (800V)<\/li>\n\n\n\n<li>6x inductors (here 2.2mH)<\/li>\n\n\n\n<li>1x three-phase relay<\/li>\n\n\n\n<li>All the necessary cables<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"473\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-A2.png\" alt=\"parallel grid-forming inverter wiring scheme\" class=\"wp-image-27529\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-A2.png 683w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/Schematic-TN172-A2-300x208.png 300w\" sizes=\"auto, (max-width: 683px) 100vw, 683px\" \/><figcaption class=\"wp-element-caption\">Wiring of the experimental setup<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"469\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_Setup_picture_annotated.png\" alt=\"parallel grid-forming inverter setup\" class=\"wp-image-27455\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_Setup_picture_annotated.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_Setup_picture_annotated-300x180.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_Setup_picture_annotated-768x462.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Experimental setup with imperix products<\/figcaption><\/figure>\n<\/div>\n\n\n<p id=\"h-the-validation-of-the-control-has-been-carried-out-with-two-tpis-with-a-shared-dc-source-the-wiring-scheme-and-the-experiment-setup-are-shown-below\">The following table summarizes the experimental conditions:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Parameter<\/th><th>Value<\/th><\/tr><\/thead><tbody><tr><td>Control and switching frequency<\/td><td>50 kHz<\/td><\/tr><tr><td>Maximum active power P<br>Maximum apparent power S<br>Maximum reactive power Q<\/td><td>16 kW<br>22 kVA<br>15.1 kVar<\/td><\/tr><tr><td>Grid Voltage<br>DC voltage<br>Maximum RoCoF \\(\\rho\\)<\/td><td>400 VRMS<br>800 V<br>1 Hz\/s<\/td><\/tr><tr><td>\\( \\Delta f \\)&nbsp;(1%)<br>\\( \\Delta V \\)&nbsp;(10%)<\/td><td>3.14 rad\/s<br>32.5 V<\/td><\/tr><tr><td>Line inductance<\/td><td>2.2 mH<\/td><\/tr><tr><td>APC droop coefficient \\(m\\)<br>APC \u2013 LPF cut-off frequency<br>APC \u2013 HPF cut-off frequency<br>RPC droop coefficient \\(n\\)<br>RPC \u2013 LPF cut-off frequency<\/td><td>1.9635e-04<br>0.3 Hz<br>0.1 Hz<br>0.0022<br>0.3 Hz<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Experimental conditions<\/figcaption><\/figure>\n\n\n\n<p>The experiment is performed by running GFMI0 while GFMI1 is still unconnected. Then the GFMI1 starts pre-synchronization with GFMI0. During pre-synchronization, the voltage of GFMI1 is progressively adapted to match that of GFMI0, as shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure1.png\" alt=\"Phase A voltage of GFMI0 and GFMI1 during pre-synchronization\" class=\"wp-image-27483\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure1.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure1-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure1-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Phase A voltage of GFMI0 and GFMI1 during pre-synchronization<\/figcaption><\/figure>\n\n\n\n<p>Once the pre-synchronization is done, the relay is closed to connect GFMI1. An active power step of 15kW is performed on the load (GFLI). With the same droop coefficients on GFMI0 and GFMI1, they share the same active power output of 7.5kW.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure2P.png\" alt=\"active power of grid-forming inverters with the same droop coefficients\" class=\"wp-image-27500\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure2P.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure2P-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure2P-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Active power of GFMIs with the same droop coefficients<\/figcaption><\/figure>\n\n\n\n<p>To study the effect of different droop coefficients on power-sharing, the droop coefficient \\(m\\) of GFMI1 is doubled. An active power step of 15kW is performed on the load (GFLI).<\/p>\n\n\n\n<p>For the active power sharing, when the system reaches the steady state, the active power of GFMI0 and GFMI1 approximately satisfy \\(P_0 = 2P_1 \\), which matches well with the theory. Besides, the oscillations discussed previously caused by different droop coefficients can be observed after the load step.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure3P.png\" alt=\"active power of grid-forming inverters with different droop coefficients\" class=\"wp-image-27506\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure3P.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure3P-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/04\/TN172_exp_fugure3P-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Active power of GFMIs with different droop coefficients<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"To-go-further%E2%80%A6\"><\/span>To go further&#8230;<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In the case of a mainly resistive line, the assumption of an inductive line for P and Q decoupling is no longer valid. To decouple P and Q, a droop control with virtual impedance can be implemented. This is addressed in <a href=\"https:\/\/imperix.com\/doc\/implementation\/virtual-impedance-for-droop-control\">Virtual impedance for droop control<\/a>.<\/p>\n\n\n\n<p>To address the lack of explicit inertia in the control, the inertial characteristics of synchronous generators can be emulated through a virtual synchronous generator control. This is addressed in <a href=\"https:\/\/imperix.com\/doc\/implementation\/virtual-synchronous-generator\">Virtual synchronous generator<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Academic-reference\"><\/span>Academic reference<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><a href=\"https:\/\/doi.org\/10.1109\/TPEL.2007.900456\" target=\"_blank\" rel=\"noreferrer noopener\">[1]<\/a>&nbsp;K. De Brabandere, B. Bolsens, J. Van den Keybus, A. Woyte, J. Driesen and R. Belmans, \u201cA Voltage and Frequency Droop Control Method for Parallel Inverters,\u201d in&nbsp;<em>IEEE Transactions on Power Electronics<\/em>, Jul. 2007.<\/p>\n\n\n\n<p><a href=\"https:\/\/doi.org\/10.1109\/TIA.2013.2242816\">[2]<\/a> C. -T. Lee, R. -P. Jiang and P. -T. Cheng, &#8220;A Grid Synchronization Method for Droop-Controlled Distributed Energy Resource Converters,&#8221; in <em>IEEE Transactions on Industry Applications<\/em>, Mar.-Apr. 2013.<\/p>\n\n\n\n<p><a href=\"https:\/\/doi.org\/10.1109\/ECCE.2012.6342714\">[3]<\/a> C. Jin, M. Gao, X. Lv and M. Chen, &#8220;A seamless transfer strategy of islanded and grid-connected mode switching for microgrid based on droop control,&#8221; in <em><em>2012 IEEE Energy Conversion Congress and Exposition (ECCE)<\/em><\/em>, Raleigh, USA, 2012.<\/p>\n\n\n\n<p><a href=\"https:\/\/doi.org\/10.1109\/TPEL.2008.2005100\">[4]<\/a> Y. A. -R. I. Mohamed and E. F. El-Saadany, &#8220;Adaptive Decentralized Droop Controller to Preserve Power Sharing Stability of Paralleled Inverters in Distributed Generation Microgrids,&#8221; in&nbsp;<em>IEEE Transactions on Power Electronics<\/em>, Nov. 2008.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This note introduces the parallel operation of Grid-Forming Inverters (GFMIs) and provides an implementation example on TPI 8032 programmable inverter with the ACG SDK. An&#8230;<\/p>\n","protected":false},"author":10,"featured_media":28701,"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":[50,110],"guidedreadings":[],"tutorials":[127],"user-manuals":[],"coauthors":[72],"class_list":["post-27003","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-tpi","tutorials-parallel-operation-of-grid-forming-inverters"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Parallel operation of Grid-Forming Inverters (GFMIs) - imperix<\/title>\n<meta name=\"description\" content=\"Parallel operation of Grid-Forming Inverters, an implementation example and validation on imperix TPI 8032 programmable inverter.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Parallel operation of Grid-Forming Inverters (GFMIs) - imperix\" \/>\n<meta property=\"og:description\" content=\"Parallel operation of Grid-Forming Inverters, an implementation example and validation on imperix TPI 8032 programmable inverter.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters\" \/>\n<meta property=\"og:site_name\" content=\"imperix\" \/>\n<meta property=\"article:published_time\" content=\"2024-03-26T12:16:35+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-31T10:43:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/3_2_ratio_TN172.png\" \/>\n\t<meta property=\"og:image:width\" content=\"450\" \/>\n\t<meta property=\"og:image:height\" content=\"300\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Shu Wang\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Shu Wang\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"13 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters\"},\"author\":{\"name\":\"Shu Wang\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#\\\/schema\\\/person\\\/e57025902e777170f33a7afa4a74afb7\"},\"headline\":\"Parallel operation of Grid-Forming Inverters (GFMIs)\",\"datePublished\":\"2024-03-26T12:16:35+00:00\",\"dateModified\":\"2025-12-31T10:43:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters\"},\"wordCount\":2134,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/imperix.com\\\/doc\\\/wp-content\\\/uploads\\\/2024\\\/03\\\/3_2_ratio_TN172.png\",\"articleSection\":[\"Technical notes\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters\",\"url\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters\",\"name\":\"Parallel operation of Grid-Forming Inverters (GFMIs) - imperix\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/imperix.com\\\/doc\\\/wp-content\\\/uploads\\\/2024\\\/03\\\/3_2_ratio_TN172.png\",\"datePublished\":\"2024-03-26T12:16:35+00:00\",\"dateModified\":\"2025-12-31T10:43:12+00:00\",\"description\":\"Parallel operation of Grid-Forming Inverters, an implementation example and validation on imperix TPI 8032 programmable inverter.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters#primaryimage\",\"url\":\"https:\\\/\\\/imperix.com\\\/doc\\\/wp-content\\\/uploads\\\/2024\\\/03\\\/3_2_ratio_TN172.png\",\"contentUrl\":\"https:\\\/\\\/imperix.com\\\/doc\\\/wp-content\\\/uploads\\\/2024\\\/03\\\/3_2_ratio_TN172.png\",\"width\":450,\"height\":300},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/implementation\\\/parallel-operation-of-grid-forming-inverters#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Knowledge base\",\"item\":\"https:\\\/\\\/imperix.com\\\/doc\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Technical notes\",\"item\":\"https:\\\/\\\/imperix.com\\\/doc\\\/category\\\/implementation\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Parallel operation of Grid-Forming Inverters (GFMIs)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#website\",\"url\":\"https:\\\/\\\/imperix.com\\\/doc\\\/\",\"name\":\"imperix\",\"description\":\"power electronics\",\"publisher\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/imperix.com\\\/doc\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#organization\",\"name\":\"imperix\",\"url\":\"https:\\\/\\\/imperix.com\\\/doc\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/imperix.com\\\/doc\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/imperix_logo.png\",\"contentUrl\":\"https:\\\/\\\/imperix.com\\\/doc\\\/wp-content\\\/uploads\\\/2021\\\/03\\\/imperix_logo.png\",\"width\":350,\"height\":120,\"caption\":\"imperix\"},\"image\":{\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#\\\/schema\\\/logo\\\/image\\\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/imperix.com\\\/doc\\\/#\\\/schema\\\/person\\\/e57025902e777170f33a7afa4a74afb7\",\"name\":\"Shu Wang\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8c5195ad4fcc5844061b0229a4e67ac2916756927bc646fb6f6ff3dfb1bba140?s=96&d=mm&r=g4b86f01b045719d1dd14babc666c16ba\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8c5195ad4fcc5844061b0229a4e67ac2916756927bc646fb6f6ff3dfb1bba140?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8c5195ad4fcc5844061b0229a4e67ac2916756927bc646fb6f6ff3dfb1bba140?s=96&d=mm&r=g\",\"caption\":\"Shu Wang\"},\"description\":\"Shu is an experienced development engineer at imperix. He authored or co-authored numerous articles on the knowledge base, notably on FPGA-based control implementation and high-level synthesis tools and techniques.\",\"sameAs\":[\"https:\\\/\\\/www.linkedin.com\\\/in\\\/shu-wang-6581221b9\\\/\"],\"url\":\"https:\\\/\\\/imperix.com\\\/doc\\\/author\\\/wang\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Parallel operation of Grid-Forming Inverters (GFMIs) - imperix","description":"Parallel operation of Grid-Forming Inverters, an implementation example and validation on imperix TPI 8032 programmable inverter.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters","og_locale":"en_US","og_type":"article","og_title":"Parallel operation of Grid-Forming Inverters (GFMIs) - imperix","og_description":"Parallel operation of Grid-Forming Inverters, an implementation example and validation on imperix TPI 8032 programmable inverter.","og_url":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters","og_site_name":"imperix","article_published_time":"2024-03-26T12:16:35+00:00","article_modified_time":"2025-12-31T10:43:12+00:00","og_image":[{"width":450,"height":300,"url":"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/3_2_ratio_TN172.png","type":"image\/png"}],"author":"Shu Wang","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Shu Wang","Est. reading time":"13 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters#article","isPartOf":{"@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters"},"author":{"name":"Shu Wang","@id":"https:\/\/imperix.com\/doc\/#\/schema\/person\/e57025902e777170f33a7afa4a74afb7"},"headline":"Parallel operation of Grid-Forming Inverters (GFMIs)","datePublished":"2024-03-26T12:16:35+00:00","dateModified":"2025-12-31T10:43:12+00:00","mainEntityOfPage":{"@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters"},"wordCount":2134,"commentCount":0,"publisher":{"@id":"https:\/\/imperix.com\/doc\/#organization"},"image":{"@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters#primaryimage"},"thumbnailUrl":"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/3_2_ratio_TN172.png","articleSection":["Technical notes"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters#respond"]}]},{"@type":"WebPage","@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters","url":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters","name":"Parallel operation of Grid-Forming Inverters (GFMIs) - imperix","isPartOf":{"@id":"https:\/\/imperix.com\/doc\/#website"},"primaryImageOfPage":{"@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters#primaryimage"},"image":{"@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters#primaryimage"},"thumbnailUrl":"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/3_2_ratio_TN172.png","datePublished":"2024-03-26T12:16:35+00:00","dateModified":"2025-12-31T10:43:12+00:00","description":"Parallel operation of Grid-Forming Inverters, an implementation example and validation on imperix TPI 8032 programmable inverter.","breadcrumb":{"@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters#primaryimage","url":"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/3_2_ratio_TN172.png","contentUrl":"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/03\/3_2_ratio_TN172.png","width":450,"height":300},{"@type":"BreadcrumbList","@id":"https:\/\/imperix.com\/doc\/implementation\/parallel-operation-of-grid-forming-inverters#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Knowledge base","item":"https:\/\/imperix.com\/doc\/"},{"@type":"ListItem","position":2,"name":"Technical notes","item":"https:\/\/imperix.com\/doc\/category\/implementation"},{"@type":"ListItem","position":3,"name":"Parallel operation of Grid-Forming Inverters (GFMIs)"}]},{"@type":"WebSite","@id":"https:\/\/imperix.com\/doc\/#website","url":"https:\/\/imperix.com\/doc\/","name":"imperix","description":"power electronics","publisher":{"@id":"https:\/\/imperix.com\/doc\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/imperix.com\/doc\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/imperix.com\/doc\/#organization","name":"imperix","url":"https:\/\/imperix.com\/doc\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/imperix.com\/doc\/#\/schema\/logo\/image\/","url":"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/imperix_logo.png","contentUrl":"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/03\/imperix_logo.png","width":350,"height":120,"caption":"imperix"},"image":{"@id":"https:\/\/imperix.com\/doc\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/imperix.com\/doc\/#\/schema\/person\/e57025902e777170f33a7afa4a74afb7","name":"Shu Wang","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/8c5195ad4fcc5844061b0229a4e67ac2916756927bc646fb6f6ff3dfb1bba140?s=96&d=mm&r=g4b86f01b045719d1dd14babc666c16ba","url":"https:\/\/secure.gravatar.com\/avatar\/8c5195ad4fcc5844061b0229a4e67ac2916756927bc646fb6f6ff3dfb1bba140?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8c5195ad4fcc5844061b0229a4e67ac2916756927bc646fb6f6ff3dfb1bba140?s=96&d=mm&r=g","caption":"Shu Wang"},"description":"Shu is an experienced development engineer at imperix. He authored or co-authored numerous articles on the knowledge base, notably on FPGA-based control implementation and high-level synthesis tools and techniques.","sameAs":["https:\/\/www.linkedin.com\/in\/shu-wang-6581221b9\/"],"url":"https:\/\/imperix.com\/doc\/author\/wang"}]}},"_links":{"self":[{"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/posts\/27003","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/comments?post=27003"}],"version-history":[{"count":55,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/posts\/27003\/revisions"}],"predecessor-version":[{"id":39481,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/posts\/27003\/revisions\/39481"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/media\/28701"}],"wp:attachment":[{"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/media?parent=27003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/categories?post=27003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/tags?post=27003"},{"taxonomy":"software-environments","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/software-environments?post=27003"},{"taxonomy":"provided-results","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/provided-results?post=27003"},{"taxonomy":"related-products","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/related-products?post=27003"},{"taxonomy":"guidedreadings","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/guidedreadings?post=27003"},{"taxonomy":"tutorials","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/tutorials?post=27003"},{"taxonomy":"user-manuals","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/user-manuals?post=27003"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/imperix.com\/doc\/wp-json\/wp\/v2\/coauthors?post=27003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}