{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:10:43Z","timestamp":1760231443169,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T00:00:00Z","timestamp":1663545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universidad del B\u00edo-B\u00edo","award":["2160180 GI\/EF-UBB","2260136 IF\/R-UBB","ANID\/FONDECYT\/1191028","ANID\/FB0008"],"award-info":[{"award-number":["2160180 GI\/EF-UBB","2260136 IF\/R-UBB","ANID\/FONDECYT\/1191028","ANID\/FB0008"]}]},{"name":"Regular Internal project","award":["2160180 GI\/EF-UBB","2260136 IF\/R-UBB","ANID\/FONDECYT\/1191028","ANID\/FB0008"],"award-info":[{"award-number":["2160180 GI\/EF-UBB","2260136 IF\/R-UBB","ANID\/FONDECYT\/1191028","ANID\/FB0008"]}]},{"name":"Chilean Government","award":["2160180 GI\/EF-UBB","2260136 IF\/R-UBB","ANID\/FONDECYT\/1191028","ANID\/FB0008"],"award-info":[{"award-number":["2160180 GI\/EF-UBB","2260136 IF\/R-UBB","ANID\/FONDECYT\/1191028","ANID\/FB0008"]}]},{"name":"Advanced Center for Electrical and Electronics Engineering (AC3E)","award":["2160180 GI\/EF-UBB","2260136 IF\/R-UBB","ANID\/FONDECYT\/1191028","ANID\/FB0008"],"award-info":[{"award-number":["2160180 GI\/EF-UBB","2260136 IF\/R-UBB","ANID\/FONDECYT\/1191028","ANID\/FB0008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Distributed power generation, micro-grids, and networks working in islanding mode have strong deviations in voltage quantities. These deviations can be divided into amplitude and frequency. Amplitude deviations are well-known and studied, as they are common in small and big grids. However, deviations on the ac mains frequency have not been widely studied. The literature shows control schemes capable of bearing these variations, but no systematic analysis has been performed to ensure stability. As the majority of power converters are designed for big grids, their analysis and design neglect frequency disturbances, therefore those devices allow a very small frequency operating window. For instance, in power converters that need to be synchronized to the grid, the standard deviation does not go beyond 0.5 Hz, and for grid-tied inverters it does not go beyond 1 Hz, whereas variations of around 8 Hz can be expected in micro-grids. This work presents a comprehensive analysis of the control system\u2019s stability, where two different control schemes for a back-to-back static converter topology are implemented and studied under a wide variable grid frequency. Because the behavior of power converters is nonlinear and coupled, dynamic and static decouplers are usually introduced in the controller, being a key element on the scheme according to the findings. The results show that using just a static decoupler does not guarantee stability under frequency variations; meanwhile, when a dynamic decoupler is used, the operating window can be greatly extended. The procedure shown in this paper can also be extended to other control algorithms, making it possible to carefully choose the control system for a variable frequency condition. Simulated and experimental results confirm the theoretical approach.<\/jats:p>","DOI":"10.3390\/s22187078","type":"journal-article","created":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T04:28:55Z","timestamp":1663648135000},"page":"7078","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Stability Analysis of Two Power Converters Control Algorithms Connected to Micro-Grids with Wide Frequency Variation"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1377-7244","authenticated-orcid":false,"given":"Jaime","family":"Rohten","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Universidad del B\u00edo-B\u00edo, Av. Collao 1202, Concepci\u00f3n 4051381, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Felipe","family":"Villarroel","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Universidad de Concepci\u00f3n, E. Larenas 219, Concepci\u00f3n 4089100, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2349-4632","authenticated-orcid":false,"given":"Esteban","family":"Pulido","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Avenida Espa\u00f1a 1680, Valpara\u00edso 2340000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1508-5281","authenticated-orcid":false,"given":"Javier","family":"Mu\u00f1oz","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Universidad de Talca, Camino Los Niches Km. 1, Curic\u00f3 3340000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2242-6462","authenticated-orcid":false,"given":"Jos\u00e9","family":"Silva","sequence":"additional","affiliation":[{"name":"Department of Engineering Science, Universidad de Los Lagos, km. 6, Camino A Chinquihue, Puerto Montt 5480000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4166-448X","authenticated-orcid":false,"given":"Marcelo","family":"Perez","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Avenida Espa\u00f1a 1680, Valpara\u00edso 2340000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Young, K., and Dougal, R.A. (2009, January 9\u201311). SRF-PLL with Dynamic Center Frequency for Improved Phase Detection. Proceedings of the 2009 International Conference on Clean Electrical Power, Capri, Italy.","DOI":"10.1109\/ICCEP.2009.5212055"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1109\/TEC.2018.2867906","article-title":"A HESM-Based Variable Frequency AC Starter-Generator System for Aircraft Applications","volume":"33","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1109\/TIA.2013.2255575","article-title":"Iterative Learning Control With Variable Sampling Frequency for Current Control of Grid-Connected Converters in Aircraft Power Systems","volume":"49","author":"Zanchetta","year":"2013","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5827","DOI":"10.1109\/TIE.2016.2541625","article-title":"Enhanced Predictive Control for a Wide Time-Variant Frequency Environment","volume":"63","author":"Rohten","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"216018","DOI":"10.1109\/ACCESS.2020.3041528","article-title":"A Simple Self-Tuning Resonant Control Approach for Power Converters Connected to Micro-Grids With Distorted Voltage Conditions","volume":"8","author":"Rohten","year":"2020","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ntomalis, S., Iliadis, P., Atsonios, K., Nesiadis, A., Nikolopoulos, N., and Grammelis, P. (2020). Dynamic Modeling and Simulation of Non-Interconnected Systems under High-RES Penetration: The Madeira Island Case. Energies, 13.","DOI":"10.3390\/en13215786"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1109\/TPWRS.2019.2939411","article-title":"A Linear Inertial Response Emulation for Variable Speed Wind Turbines","volume":"35","author":"Malekpour","year":"2020","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2574","DOI":"10.1109\/TAES.2011.6034652","article-title":"Aircraft Power System Stability Study Including Effect of Voltage Control and Actuators Dynamic","volume":"47","author":"Areerak","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1016\/j.rser.2014.09.030","article-title":"Review of Grid Connection Requirements for Generation Assets in Weak Power Grids","volume":"41","author":"Etxegarai","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Luo, X., Wang, J., Wojcik, J., Wang, J., Li, D., Draganescu, M., Li, Y., and Miao, S. (2018). Review of Voltage and Frequency Grid Code Specifications for Electrical Energy Storage Applications. Energies, 11.","DOI":"10.3390\/en11051070"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Herrej\u00f3n-Pintor, G.A., Melgoza-V\u00e1zquez, E., and Ch\u00e1vez, J.D.J. (2022). A Modified SOGI-PLL with Adjustable Refiltering for Improved Stability and Reduced Response Time. Energies, 15.","DOI":"10.3390\/en15124253"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Aldbaiat, B., Nour, M., Radwan, E., and Awada, E. (2022). Grid-Connected PV System with Reactive Power Management and an Optimized SRF-PLL Using Genetic Algorithm. Energies, 15.","DOI":"10.3390\/en15062177"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112297","DOI":"10.1109\/ACCESS.2020.3003009","article-title":"A Simple Approach to Reject DC Offset for Single-Phase Synchronous Reference Frame PLL in Grid-Tied Converters","volume":"8","author":"Liu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/TPWRD.2017.2740440","article-title":"Effect of Control-Loops Interactions on Power Stability Limits of VSC Integrated to AC System","volume":"33","author":"Huang","year":"2018","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Liu, R., Wang, S., Liu, G., Wen, S., Zhang, J., and Ma, Y. (2022). An Improved Virtual Inertia Control Strategy for Low Voltage AC Microgrids with Hybrid Energy Storage Systems. Energies, 15.","DOI":"10.3390\/en15020442"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Bimarta, R., Tran, T.V., and Kim, K.-H. (2018). Frequency-Adaptive Current Controller Design Based on LQR State Feedback Control for a Grid-Connected Inverter under Distorted Grid. Energies, 11.","DOI":"10.3390\/en11102674"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1049\/iet-gtd.2018.7058","article-title":"Enhancing Inertia of Solar Photovoltaic-based Microgrid through Notch Filter-based PLL in SRF Control","volume":"14","author":"Panda","year":"2020","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"106226","DOI":"10.1109\/ACCESS.2020.3000691","article-title":"All-Pass-Filter-Based PLL for Single-Phase Grid-Connected Converters Under Distorted Grid Conditions","volume":"8","author":"Xia","year":"2020","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1470","DOI":"10.1109\/TSTE.2019.2893679","article-title":"Harmonics and Stability Analysis of Single-Phase Grid-Connected Inverters in Distributed Power Generation Systems Considering Phase-Locked Loop Impact","volume":"10","author":"Xu","year":"2019","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"54145","DOI":"10.1109\/ACCESS.2020.2981426","article-title":"A Frequency-Adaptive Improved Moving-Average-Filter-Based Quasi-Type-1 PLL for Adverse Grid Conditions","volume":"8","author":"Luo","year":"2020","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2040","DOI":"10.1109\/TPWRD.2016.2607205","article-title":"Impact of Inertia and Effective Short Circuit Ratio on Control of Frequency in Weak Grids Interfacing LCC-HVDC and DFIG-Based Wind Farms","volume":"32","author":"Yogarathinam","year":"2017","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5838","DOI":"10.1109\/TIE.2016.2527732","article-title":"Model Predictive Control for Power Converters in a Distorted Three-Phase Power Supply","volume":"63","author":"Rohten","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"39939","DOI":"10.1109\/ACCESS.2021.3061354","article-title":"Photovoltaic Failure Detection Based on String-Inverter Voltage and Current Signals","volume":"9","year":"2021","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Est\u00e9vez-B\u00e9n, A.A., Alvarez-Diazcomas, A., and Rodr\u00edguez-Res\u00e9ndiz, J. (2020). Transformerless Multilevel Voltage-Source Inverter Topology Comparative Study for PV Systems. Energies, 13.","DOI":"10.3390\/en13123261"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Est\u00e9vez-B\u00e9n, A.A., Alvarez-Diazcomas, A., Macias-Bobadilla, G., and Rodr\u00edguez-Res\u00e9ndiz, J. (2020). Leakage Current Reduction in Single-Phase Grid-Connected Inverters\u2014A Review. Appl. Sci., 10.","DOI":"10.3390\/app10072384"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Alvarez-Diazcomas, A., L\u00f3pez, H., Carrillo-Serrano, R.V., Rodr\u00edguez-Res\u00e9ndiz, J., V\u00e1zquez, N., and Herrera-Ruiz, G. (2019). A Novel Integrated Topology to Interface Electric Vehicles and Renewable Energies with the Grid. Energies, 12.","DOI":"10.3390\/en12214091"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Est\u00e9vez-B\u00e9n, A.A., L\u00f3pez Tapia, H.J.C., Carrillo-Serrano, R.V., Rodr\u00edguez-Res\u00e9ndiz, J., and V\u00e1zquez Nava, N. (2019). A New Predictive Control Strategy for Multilevel Current-Source Inverter Grid-Connected. Electronics, 8.","DOI":"10.3390\/electronics8080902"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"62944","DOI":"10.1109\/ACCESS.2018.2873504","article-title":"Transformerless Common-Mode Current-Source Inverter Grid-Connected for PV Applications","volume":"6","author":"Lopez","year":"2018","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"122573","DOI":"10.1109\/ACCESS.2019.2938596","article-title":"Deloading Power Coordinated Distribution Method for Frequency Regulation by Wind Farms Considering Wind Speed Differences","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Mujcinagic, A., Kusljugic, M., and Nukic, E. (2020). Wind Inertial Response Based on the Center of Inertia Frequency of a Control Area. Energies, 13.","DOI":"10.3390\/en13236177"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, T., Li, Y., Yang, J., Ge, W., and Hu, B. (2019). A Modified DSC-Based Grid Synchronization Method for a High Renewable Penetrated Power System Under Distorted Voltage Conditions. Energies, 12.","DOI":"10.3390\/en12214040"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"121781","DOI":"10.1109\/ACCESS.2019.2931747","article-title":"Improved Current Decoupling Method for Robustness Improvement of LCL-Type STATCOM Based on Active Disturbance Rejection Control","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1763","DOI":"10.1109\/TPWRD.2009.2028795","article-title":"Design of a Modular UPQC Configuration Integrating a Components Economical Analysis","volume":"24","author":"Munoz","year":"2009","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Rohten, J.A., Espinoza, J.R., Munoz, J.A., Melin, P.E., and Espinosa, E.E. (2011, January 7\u201310). Discrete Nonlinear Control Based on a Double Dq Transform of a Multi-Cell UPQC. Proceedings of the IECON 2011\u201437th Annual Conference of the IEEE Industrial Electronics Society, Melbourne, VIC, Australia.","DOI":"10.1109\/IECON.2011.6119989"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5588","DOI":"10.1109\/TSG.2017.2691707","article-title":"Robust Nonlinear Controller Design for On-Grid\/Off-Grid Wind Energy Battery-Storage System","volume":"9","author":"Housseini","year":"2018","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"56925","DOI":"10.1109\/ACCESS.2022.3178425","article-title":"Implementation of Exact Linearization Technique for Modeling and Control of DC\/DC Converters in Rural PV Microgrid Application","volume":"10","author":"Aliaga","year":"2022","journal-title":"IEEE Access"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"162157","DOI":"10.1109\/ACCESS.2019.2951753","article-title":"Control Strategy Based on $\\text{H}\\infty$ Repetitive Controller With Active Damping for Islanded Microgrid","volume":"7","author":"Ma","year":"2019","journal-title":"IEEE Access"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Rohten, J., Espinoza, J., Villarroel, F., Perez, M., Munoz, J., Melin, P., and Espinosa, E. (2012, January 25\u201328). Static Power Converter Synchronization and Control under Varying Frequency Conditions. Proceedings of the IECON 2012\u201438th Annual Conference on IEEE Industrial Electronics Society, Montreal, QC, Canada.","DOI":"10.1109\/IECON.2012.6388651"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Munoz, J., Baier, C., Espinoza, J., Rivera, M., Guzman, J., and Rohten, J. (2013, January 10\u201313). Switching Losses Analysis of an Asymmetric Multilevel Shunt Active Power Filter. Proceedings of the IECON 2013\u201439th Annual Conference of the IEEE Industrial Electronics Society, Vienna, Austria.","DOI":"10.1109\/IECON.2013.6700565"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Munoz, J.A., Reyes, J.R., Espinoza, J.R., Rubilar, I.A., and Moran, L.A. (2007, January 5\u20138). A Novel Multi-Level Three-Phase UPQC Topology Based on Full-Bridge Single-Phase Cells. Proceedings of the IECON 2007\u201433rd Annual Conference of the IEEE Industrial Electronics Society, Taipei, Taiwan.","DOI":"10.1109\/IECON.2007.4459988"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1109\/OJIA.2020.3044810","article-title":"Decentralised Optimal Controller Design of Variable Frequency Three-Phase Power Electronic Networks Accounting for Sub-System Interactions","volume":"1","author":"Dewar","year":"2020","journal-title":"IEEE Open J. Ind. Appl."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/7078\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:34:13Z","timestamp":1760142853000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/7078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,19]]},"references-count":41,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["s22187078"],"URL":"https:\/\/doi.org\/10.3390\/s22187078","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,9,19]]}}}