{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T15:45:09Z","timestamp":1778168709872,"version":"3.51.4"},"reference-count":49,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T00:00:00Z","timestamp":1724803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52207212"],"award-info":[{"award-number":["52207212"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U2166202"],"award-info":[{"award-number":["U2166202"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZR2021QE158"],"award-info":[{"award-number":["ZR2021QE158"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["52207212"],"award-info":[{"award-number":["52207212"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["U2166202"],"award-info":[{"award-number":["U2166202"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2021QE158"],"award-info":[{"award-number":["ZR2021QE158"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Virtual synchronous generator (VSG) control has positive effects on the stability of microgrids. In practical power systems, both single-phase loads and three-phase unbalanced loads are present. The four-leg inverter is an alternative solution for the power supply of unbalanced loads and grid connections. The traditional VSG control strategy still faces challenges when using a four-leg inverter to provide a symmetrical voltage and stable frequency in the load power supply and pre-synchronization. This paper proposes a VSG-based control strategy along with a pre-synchronization method for four-leg inverters. An improved VSG control strategy is put forward for four-leg inverters. The improved virtual impedance control and power calculation methods are integrated into the control loop to suppress the voltage asymmetry and frequency ripples. Building on the improved VSG control strategy, a pre-synchronization control approach is proposed to minimize the amplitude and phase angle discrepancies between the inverter output voltage and the power grid voltage. In addition, an optimized design method for control parameters is presented to improve VSG dynamic performance. A hardware prototype of the four-leg inverter is built; the results show that the voltage unbalance ratio can be reduced by 89%, and the response time can be shortened by 50%.<\/jats:p>","DOI":"10.3390\/sym16091116","type":"journal-article","created":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T03:57:06Z","timestamp":1724817426000},"page":"1116","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Virtual Synchronous Generator-Based Control Strategy and Pre-Synchronization Method for a Four-Leg Inverter under Unbalanced Loads"],"prefix":"10.3390","volume":"16","author":[{"given":"Zhenshan","family":"Huang","sequence":"first","affiliation":[{"name":"The School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhijie","family":"Liu","sequence":"additional","affiliation":[{"name":"The School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Shen","sequence":"additional","affiliation":[{"name":"The School of Rail Transportation, Shandong Jiaotong University, Jinan 250357, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7255-9044","authenticated-orcid":false,"given":"Kejun","family":"Li","sequence":"additional","affiliation":[{"name":"The School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanzong","family":"Song","sequence":"additional","affiliation":[{"name":"The School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baihe","family":"Su","sequence":"additional","affiliation":[{"name":"The School of Electrical Engineering, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1692","DOI":"10.1109\/TSG.2022.3208752","article-title":"Review of impedance-reshaping-based power sharing strategies in islanded AC microgrids","volume":"14","author":"Deng","year":"2022","journal-title":"IEEE Trans. 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