A Simplified Approach for Beat Frequency Oscillation Analysis in DC Microgrids

Debora P. Damasceno; José Carlos U. Peña; Mateus P. Dias; Danilo Iglesias Brandao; José A. Pomílio

doi:10.18618/REP.e202625

Authors

Debora P. Damasceno Federal University of Ceará
José Carlos U. Peña Flex Power Grid Lab
Mateus P. Dias Instituto Tecnológico de Aeronáutica - ITA https://orcid.org/0000-0002-1624-4582
Danilo Iglesias Brandao Universidade Federal de Minas Gerais
José A. Pomílio Universidade Estadual de Campinas https://orcid.org/0000-0001-5457-4438

DOI:

https://doi.org/10.18618/REP.e202625

Keywords:

beat frequency, dc microgrids, EMI filters, high-frequency model, long dc connections

Abstract

This paper investigates beat frequency oscillations in dc microgrids, which occur due to switching frequency mismatches between cascaded converters. These oscillations can be aggravated by non-synchronized sampling in control systems, leading to stability and performance issues. The study introduces a simplified transfer function model that relates beat frequency disturbances to output voltage oscillations. Unlike previous methods, this approach allows for systematic analysis using Bode diagrams, providing a clear understanding of the mechanisms behind these disturbances. The analysis evaluates three configurations—ranging from a baseline setup to one including EMI filters and long cable feeders—using a 4.75 kW experimental prototype. The proposed model demonstrates high accuracy, with a maximum magnitude deviation of less than 2 dB up to 20 kHz. Furthermore, the model successfully predicts a critical resonance at 19.4 kHz, which amplifies oscillations by 8 V peak-to-peak. The results confirm that beat-frequency gain remains near 0 dB for frequencies below 1 kHz, while high-frequency attenuation exceeds 40 dB. Ultimately, this work offers a computationally efficient tool for stability assessment and effective filter parameter tuning in dc microgrids.

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Author Biographies

Debora P. Damasceno, Federal University of Ceará

was born in 1994 in Fortaleza, Brazil. She received the B.S. and M.Sc. degrees in electrical engineering from the Federal University of Ceará (UFC) Fortaleza, Brazil, in 2019 and 2021, respectively. She received the Ph.D. degree in electrical engineering from the University of Campinas (UNICAMP), Campinas, Brazil, in 2025. As part of her doctoral studies, she was a visiting Ph.D. student at the Department of Information Engineering (DEI), University of Padova, Padova, Italy. She is currently a Substitute Professor with the Department of Electrical Engineering, Federal University of Ceará (UFC), Fortaleza, Brazil. Her research interests include power electronics, modeling and control of power converters, stability analysis of interconnected power converter systems, and dc microgrids. Dr. Damasceno is a member of the SOBRAEP and IEEE.

José Carlos U. Peña, Flex Power Grid Lab

was born in 1984 in Peru. He received the B.S. degree in electronic engineering from the National University of Engineering, Lima, Peru, in 2010, and the M.S. and Ph.D. degrees in electrical engineering from São Paulo State University, São Paulo, Brazil, in 2012 and 2016, respectively. From 2022 to 2025, he was a Researcher with the School of Electrical and Computer Engineering, University of Campinas. Currently he is a Researcher with the KEMA Laboratories, Arnhem, The Netherlands. His research interests include power electronics, modeling and control of power converters, microgrids, and power quality.

Mateus P. Dias, Instituto Tecnológico de Aeronáutica - ITA

was born in 1996 in Quixadá, Brazil. He received the B.S.degree in electrical engineering from the Federal University of Ceará, Fortaleza, Brazil in 2017. He received the M.Sc. degree in 2020 and the PhD degree in 2025 at the University of Campinas, Campinas, Brazil. He is currently a Professor with the Department of Energy Engineering, Instituto Tecnológico de Aeronáutica (ITA), Fortaleza, Brazil.His research interests include power electronics, more electric Aircraft and dc microgrids, bipolar dc microgrids, power quality, high frequency interactions, electrical machines. M.Sc. Dias is a member of the SOBRAEP and IEEE. Dr. Dias was the Chair of the UNICAMP IEEE Power Electronics Society Student Branch Chapter.

Danilo Iglesias Brandao, Universidade Federal de Minas Gerais

received the doctoral degree in electrical engineering from the State University of Campinas (Unicamp), Brazil, in 2015. He was visiting positions at Colorado School of Mines (2009 and 2013), Università degli Studi di Padova (2014) and Norwegian University of Science and Technology (2018 and 2020). He is currently an assistant professor at Federal University of Minas Gerais (UFMG), Brazil. His main research interests are control of grid-tied converters and microgrids. He is a member of SOBRAEP.

José A. Pomílio, Universidade Estadual de Campinas

was born in Jundiaí, Brazil, in 1960. He received his B.S., M.S., and Ph.D. in electrical engineering from the University of Campinas, Campinas, Brazil, in 1983, 1986, and 1991, respectively. From 1988 to 1991, he was the Head of the Power Electronics Group, Brazilian Synchrotron Light Laboratory. He was a visiting professor at the University of Padova in 1993 and 2015 and at the Third University of Rome in 2003 in Italy. He is a Professor at the School of Electrical and Computer Engineering, University of Campinas, where he has been teaching since 1984. His main interests are power electronics and power quality. Dr. Pomilio was the President of the Brazilian Power Electronics Society (SOBRAEP) in 2000–2002 and a member of the Administrative Committee of the IEEE Power Electronics Society in 1997–2002. He was an Associate Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS in 2003-2018.

References

M. Nasser, T. F. Megahed, S. Ookawara, H. Hassan, “A review of water electrolysis–based systems for hydrogen production using hybrid/solar/wind energy systems”, Environmental Science and Pollution Research, vol. 29, no. 58, pp. 86994–87018, 2022, doi:10.1007/s11356-022-23323-y.

W. Qi, J. Li, Y. Liu, C. Liu, “Planning of Distributed Internet Data Center Microgrids”, IEEE Transactions on Smart Grid, vol. 10, no. 1, pp. 762–771, 2019, doi:10.1109/TSG.2017.2751756.

C. C. Thompson, P. E. Konstantinos Oikonomou, A. H. Etemadi, V. J. Sorger, “Optimization of Data Center Battery Storage Investments for Microgrid Cost Savings, Emissions Reduction, and Reliability Enhancement”, IEEE Transactions on Industry Applications, vol. 52, no. 3, pp. 2053–2060, 2016, doi:10.1109/TIA.2016.2517149.

A. Micallef, J. M. Guerrero, J. C. Vasquez, “New Horizons for Microgrids: From Rural Electrification to Space Applications”, Energies, vol. 16, no. 4, 2023, doi:10.3390/en16041966.

M. Ali, J. C. Vasquez, J. M. Guerrero, Y. Guan, N. Bazmohammadi, “Microgrid an Energy Solution for Remote Islanded Communities in Indonesia”, in 2024 IEEE 10th International Power Electronics and Motion Control Conference (IPEMC2024-ECCE Asia), pp. 3799–3804, 2024, doi:10.1109/IPEMC-ECCEAsia60879.2024.10567531.

J. C. U. Pena, J. A. A. Silva, M. P. Dias, D. P. Damasceno, L. H. S. Santos, J. A. Pomilio, “Droop-based Control Strategy to operate a DC Nanogrid under the Net Zero Energy Concept”, Open Journal of Power Electronics, vol. 30, p. e202529, Mar. 2025, doi:10.18618/REP.e202529.

T. Dragičević, X. Lu, J. C. Vasquez, J. M. Guerrero, “DC Microgrids—Part II: A Review of Power Architectures, Applications, and Standardization Issues”, IEEE Transactions on Power Electronics, vol. 31, no. 5, pp. 3528–3549, 2016, doi:10.1109/TPEL.2015.2464277.

J. A. Pomilio, A. F. Hernandes, D. P. Damasceno, M. P. Dias, J. I. Yutaka Ota, G. Ortenzi, R. K. Carneiro, “High-Frequency Interactions Among Power Converters in Built-in dc Networks”, in 2023 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles International Transportation Electrification Conference (ESARS-ITEC), pp. 1–6, 2023, doi:10.1109/ESARS-ITEC57127.2023.10114908.

X. Yue, M. Högrud, “Beat Frequency Oscillation Analysis for Voltage Regulators in Telecom Power System”, in 2022 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 2135–2140, 2022, doi:10.1109/APEC43599.2022.9773498.

R. Erickson, D. Maksimovic, “Fundamentals of Power Electronics”, Jan. 2020, doi:10.1007/978-3-030-43881-4.

Y. Huangfu, S. Pang, B. Nahid-Mobarakeh, L. Guo, A. K. Rathore, F. Gao, “Stability Analysis and Active Stabilization of On-board DC Power Converter System with Input Filter”, IEEE Transactions on Industrial Electronics, vol. 65, no. 1, pp. 790–799, 2018, doi:10.1109/TIE.2017.2703663.

P. Sbabo, L. Stojanić, P. Mattavelli, G. Spiazzi, “Enhancing Stability of Dual Active Bridge Converters with a Long Input Cable”, in 2024 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 2697–2704, 2024, doi:10.1109/APEC48139.2024.10509055.

X. Yue, F. Zhuo, S. Yang, Y. Pei, H. Yi, “A Matrix-Based Multi-frequency Output Impedance Model for Beat Frequency Oscillation Analysis in Distributed Power Systems”, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 4, no. 1, pp. 80–92, 2016, doi:10.1109/JESTPE.2015.2468051.

X. Yue, D. Boroyevich, F. C. Lee, F. Chen, R. Burgos, F. Zhuo, “Beat Frequency Oscillation Analysis for Power Electronic Converters in DC Nanogrid Based on Crossed Frequency Output Impedance Matrix Model”, IEEE Transactions on Power Electronics, vol. 33, no. 4, pp. 3052–3064, 2018, doi:10.1109/TPEL.2017.2710101.

F. Li, Z. Lin, H. Xu, R. Wang, “A Review of DC Bus Signalling Control Methods in DC Microgrids”, in 2022 IEEE International Power Electronics and Application Conference and Exposition (PEAC), pp. 1286–1291, 2022, doi:10.1109/PEAC56338.2022.9959577.

J. Lin, M. Su, Y. Sun, X. Li, S. Xie, G. Zhang, F. Blaabjerg, J. Feng, “Accurate Loop Gain Modeling of Digitally Controlled Buck Converters”, IEEE Transactions on Industrial Electronics, vol. 69, no. 1, pp. 725–739, 2022, doi:10.1109/TIE.2021.3050389.

Y. Jiang, Y. Sun, J. Lin, S. Xie, M. Su, Y. Liu, “Unified Extended-Frequency Model of Buck Converters Under Different Carriers”, IEEE Transactions on Industrial Electronics, vol. 70, no. 4, pp. 4108–4119, 2023, doi:10.1109/TIE.2022.3179561.

J. K. Motwani, Y. Xue, A. Nazari, D. Dong, I. Cvetkovic, D. Boroyevich, “Modeling of Power Electronics Systems and PWM Modulators in Harmonic-State Space”, IEEE Open Journal of Power Electronics, vol. 3, pp. 689–704, 2022, doi:10.1109/OJPEL.2022.3205893.

D. P. Damasceno, P. Sbabo, M. P. Dias, J. C. U. Peña, J. F. Guerreiro, P. Mattavelli, J. A. Pomilio, “DC Bus Voltage High-Frequency Disturbances Analysis for DC Microgrids With Long Connections”, IEEE Open Journal of Power Electronics, vol. 6, pp. 371–382, 2025, doi:10.1109/OJPEL.2025.3540347.

D. P. Damasceno, J. C. Ugaz Peña, M. P. Dias, D. I. Brandao, J. A. Pomilio, “A Simplified Approach for High-Frequency Disturbance Propagation in DC Microgrids”, in 2025 Brazilian Power Electronics Conference (COBEP), pp. 1–6, 2025, doi:10.1109/COBEP66423.2025.11231631.

D. P. Damasceno, M. P. Dias, J. C. U. Peña, J. A. Pomilio, “Impedance-Based Stability Analysis of DC Microgrid Feedforward-Controlled Connected Converters”, in 2024 IEEE 9th Southern Power Electronics Conference (SPEC), pp. 1–6, 2024, doi:10.1109/SPEC62217.2024.10893257.

S. Buso, P. Mattavelli, “Digital Control in Power Electronics”, 2nd ed., Springer Cham, Padova, IT, 2015.