{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T14:53:24Z","timestamp":1773154404113,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,26]],"date-time":"2023-12-26T00:00:00Z","timestamp":1703548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National High-Tech ship research project","award":["MC-202025-S02"],"award-info":[{"award-number":["MC-202025-S02"]}]},{"name":"National High-Tech ship research project","award":["U1966213"],"award-info":[{"award-number":["U1966213"]}]},{"name":"National Natural Science Foundation of China\u2014State Grid Corporation Joint Fund for Smart Grid","award":["MC-202025-S02"],"award-info":[{"award-number":["MC-202025-S02"]}]},{"name":"National Natural Science Foundation of China\u2014State Grid Corporation Joint Fund for Smart Grid","award":["U1966213"],"award-info":[{"award-number":["U1966213"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The recent oscillation events in offshore wind farms (OWFs) connected via a modular multilevel-converter-based HVDC (MMC-HVDC) system are developing towards a wider frequency band, which causes complex a small-signal interaction phenomenon and difficulties in the stability analysis and control. In this paper, the wideband dynamic interaction mechanism is investigated based on the impedance analysis method and an improved control strategy using an optimization algorithm is proposed to improve the small-signal stability and reduce the oscillation risks. First, the detailed impedance models of the grid-connected system are established considering the distribution characteristics of the submarine cable, control delay and frequency coupling effect. Then, combined with the active damping control method, the wideband resonance mechanism is analyzed, and the stability constraints of controller parameters are obtained using the impedance stability criterion. Finally, an improved multi-objective slime mold algorithm (MOSMA)-based coordinated optimization control strategy is proposed to enhance the adaptability of the controller parameters and the wideband damping ability of a grid-connected system, which can improve the wideband stability of the system. The simulation and experimental results verify the proposed control strategy.<\/jats:p>","DOI":"10.3390\/s24010139","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T02:58:12Z","timestamp":1703645892000},"page":"139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Small-Signal Stability Analysis and MOSMA-Based Optimization Control Strategy of OWF with MMC-HVDC Grid Connection"],"prefix":"10.3390","volume":"24","author":[{"given":"Jie","family":"Zheng","sequence":"first","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security and New Technology, School of Electrical Engineering, Chongqing University, Chongqing 400044, China"},{"name":"CSSC Haizhuang Windpower Co., Ltd., Chongqing 400044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6890-2583","authenticated-orcid":false,"given":"Hui","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security and New Technology, School of Electrical Engineering, Chongqing University, Chongqing 400044, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-8039-0576","authenticated-orcid":false,"given":"Bo","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security and New Technology, School of Electrical Engineering, Chongqing University, Chongqing 400044, China"}]},{"given":"Qinghe","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Transmission Equipment and System Security and New Technology, School of Electrical Engineering, Chongqing University, Chongqing 400044, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.ijepes.2019.04.004","article-title":"Identification of resonance interactions in offshore-wind farms connected to the main grid by MMC-based HVDC system","volume":"111","author":"Beza","year":"2019","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"7278","DOI":"10.1109\/JESTPE.2020.3017896","article-title":"Generalized Impedance Analysis and New Sight at Damping Controls for Wind Farm Connected MMC\u2013HVdc","volume":"9","author":"Ji","year":"2021","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2963","DOI":"10.1109\/TPWRD.2020.3022504","article-title":"Frequency-coupling impedance model based analysis of a high-frequency resonance incident in an actual MMC-HVDC system","volume":"35","author":"Man","year":"2020","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1109\/JESTPE.2016.2620378","article-title":"Understanding the origin of oscillatory phenomena observed between wind farms and HVdc systems","volume":"5","author":"Amin","year":"2017","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/TPWRS.2019.2924412","article-title":"Wind in weak grids: Low-frequency oscillations, subsynchronous oscillations, and torsional interactions","volume":"35","author":"Li","year":"2020","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_6","first-page":"226","article-title":"Dynamics and small signal stability analysis of PMSG-based wind farm with an MMC-HVDC system","volume":"6","author":"Wang","year":"2020","journal-title":"CSEE J. Power Energy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1109\/JESTPE.2014.2361290","article-title":"Voltage stability and control of OWFs with AC collection and HVDC transmission","volume":"2","author":"Liu","year":"2014","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/JESTPE.2015.2498182","article-title":"Frequency domain stability analysis of MMC-based HVDC for wind farm integration","volume":"4","author":"Lyu","year":"2016","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4060","DOI":"10.1109\/JESTPE.2019.2911654","article-title":"Impedance-based stability analysis of voltage-controlled MMCs feeding linear AC systems","volume":"8","author":"Wu","year":"2020","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_10","first-page":"558","article-title":"Harmonic impedance model of DFIG considering dynamic coupling effect of DC link","volume":"46","author":"Wang","year":"2022","journal-title":"Power Syst. Technol."},{"key":"ref_11","first-page":"2230","article-title":"Sub-synchronous oscillation suppression of modular multilevel converter based on capacitance energy and its impedance analysis","volume":"41","author":"Zhu","year":"2021","journal-title":"Proc. CSEE"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10157","DOI":"10.1109\/TPEL.2018.2809705","article-title":"Analysis of resonance between a VSC-HVDC converter and the AC grid","volume":"33","author":"Zou","year":"2018","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.epsr.2016.09.001","article-title":"Harmonic resonance characteristics of large-scale distributed power plant in wideband frequency domain","volume":"143","author":"Chen","year":"2017","journal-title":"Electr. Power Syst. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1036","DOI":"10.1109\/TEC.2018.2794367","article-title":"Analysis of high-frequency resonance in DFIG-based OWF via long transmission cable","volume":"33","author":"Song","year":"2018","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_15","first-page":"5169","article-title":"Analysis on high frequency resonance of collector network in OWF","volume":"42","author":"Qin","year":"2021","journal-title":"Proc. CSEE"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1606","DOI":"10.1109\/TPWRD.2019.2948489","article-title":"A strictly sufficient stability criterion for grid-connected converters based on impedance models and Gershgorin\u2019s theorem","volume":"35","author":"Ren","year":"2020","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_17","first-page":"81","article-title":"Impedance modeling and system stability analysis of MMC with double closed-loop AC voltage control","volume":"44","author":"Nian","year":"2020","journal-title":"Autom. Electr. Power Syst."},{"key":"ref_18","first-page":"5281","article-title":"Broadband oscillation mechanism and analysis for wind farm integration through MMC-HVDC system","volume":"39","author":"Li","year":"2019","journal-title":"Proc. CSEE"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1109\/JETCAS.2022.3147197","article-title":"High-frequency stability analysis and impedance optimization for an MMC-HVDC integrated system considering delay effects","volume":"12","author":"Huang","year":"2022","journal-title":"IEEE J. Emerg. Sel. Top. Circuits Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3867","DOI":"10.1109\/TPWRD.2021.3049973","article-title":"Analysis and suppression control of high frequency resonance for MMC-HVDC system","volume":"36","author":"Li","year":"2021","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Bostani, Y., Jalilzadeh, S., Mobayen, S., Rojsiraphisal, T., and Bartoszewicz, A. (2022). Damping of Subsynchronous Resonance in Utility DFIG-Based Wind Farms Using Wide-Area Fuzzy Control Approach. Energies, 15.","DOI":"10.3390\/en15051787"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6086","DOI":"10.1109\/JESTPE.2020.3044561","article-title":"Active\/passive method-based hybrid high-frequency damping design for MMCs","volume":"9","author":"Ji","year":"2021","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"20469","DOI":"10.1109\/ACCESS.2021.3054370","article-title":"Observer-Based Predictive Control of Nonlinear Clutchless Automated Manual Transmission for Pure Electric Vehicles: An LPV Approach","volume":"9","author":"Akbari","year":"2021","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/JESTPE.2017.2759096","article-title":"Optimal design of controller parameters for improving the stability of MMC-HVDC for wind farm integration","volume":"6","author":"Lyu","year":"2018","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"key":"ref_25","first-page":"623","article-title":"High frequency stability constraints based MMC controller design applying NSGA-III algorithm","volume":"9","author":"Ji","year":"2021","journal-title":"CSEE J. Power Energy Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3229","DOI":"10.1109\/ACCESS.2020.3047936","article-title":"MOSMA: Multi-objective slime mold algorithm based on elitist non-dominated sorting","volume":"9","author":"Premkumar","year":"2021","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zubaidi, S.L., Abdulkareem, I.H., Hashim, K.S., Al-Bugharbee, H., Ridha, H.M., Gharghan, S.K., Al-Qaim, F.F., Muradov, M., Kot, P., and Al-Khaddar, R. (2020). Hybridised artificial neural network model with slime mould algorithm: A novel methodology for prediction of urban stochastic water demand. Water, 12.","DOI":"10.3390\/w12102692"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","article-title":"An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints","volume":"18","author":"Deb","year":"2014","journal-title":"IEEE Trans. Evol. Comput."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/1\/139\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:42:18Z","timestamp":1760132538000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/1\/139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,26]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["s24010139"],"URL":"https:\/\/doi.org\/10.3390\/s24010139","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,26]]}}}