DOI: https://doi.org/10.61435/ijred.2025.60466

Analytical computation of arm inductor for minimizing MMC circulating current using passive method

Department of Electrical Engineering, Bahria University, Karachi Campus, 13, National Stadium Road, Karachi 75260, Pakistan

Received: 12 Jul 2024; Revised: 25 Oct 2024; Accepted: 16 Nov 2024; Available online: 24 Dec 2024; Published: 1 Jan 2025.
Editor(s): H Hadiyanto
Open Access Copyright (c) 2025 The Author(s). Published by Centre of Biomass and Renewable Energy (CBIORE)
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Citation Format:
Abstract

The study of circulating currents in modular multilevel converters is vital for improving their efficiency and reliability. The circulating current may arise from capacitor voltage unbalancing, modulation imperfections, load variations, and transient conditions. Such currents typically induce distortions in arm currents, exhibiting second-order harmonics that lead to power losses and negatively impact the ratings of converter components as well as the amplitudes of capacitor voltage ripples. Despite ongoing research, effective strategies to mitigate circulating currents are limited. This paper aims to systematically address this issue by selecting key design parameters specifically arm inductance and capacitor values, to suppress circulating currents. The methodology incorporates harmonic analysis and instantaneous power theory to derive expressions for arm inductance. Initial modelling includes common mode and differential mode analyses, leading to an examination of harmonic content. Analysis reveals that the selection of the arm inductor value is mainly influenced by the second-order harmonic component, whereas the capacitor value is determined by the fundamental harmonic component. By adopting this methodology, the boundary limit for arm inductor selection can be determined. This article proposes a novel expression for arm inductor selection. The proposed expression mainly depends on factors such as load, submodule capacitor voltages, submodule capacitor, and differential current. By selecting an appropriate inductor value based on converter-rated parameters, circulating current within the system can be effectively suppressed. The methodology offers a practical framework for arm inductor selection. Simulation results validation shows strong alignment with analytical results with the error margin of less than 1%, hereby the MMC parameter can be determined with better accuracy through analytic method.

Fulltext View|Download
Keywords: MMC, Converter Design; Arm inductance; Harmonic Analysis; Capacitance; Circulating Current; NLM; PSC

Article Metrics:

Article Info
Section: Original Research Article
Language : EN
Recent articles
Consumer preferences for solid biomass fuels for energy purposes Unveiling the interactive effect of green technology innovation, employment of disabilities and sustainable energy: A new insight into inclusive sustainability Analytical computation of arm inductor for minimizing MMC circulating current using passive method Using hydrogen as potential fuel for internal combustion engines: A comprehensive assessment More recent articles
Most cited articles
Enhanced Grey Wolf Optimizer Based MPPT Algorithm of PV System Under Partial Shaded Condition Performance investigation of a gasifier and gas engine system operated on municipal solid waste briquettes Batch and Fed-Batch Fermentation System on Ethanol Production from Whey using Kluyveromyces marxianus Influence of the Rubber Seed Type and Altitude on Characteristic of Seed, Oil and Biodiesel Performance Analysis of Maximum Power Point Tracking Algorithms Under Varying Irradiation More cited articles
  1. António-Ferreira, A., Collados-Rodríguez, C., & Gomis-Bellmunt, O. (2018). Modulation techniques applied to medium voltage modular multilevel converters for renewable energy integration: A review. Electric Power Systems Research, 155, 21–39. https://doi.org/10.1016/j.epsr.2017.08.015
  2. Camurca, L., Pereira, T., Hoffmann, F., & Liserre, M. (2022). Analysis, Limitations, and Opportunities of Modular Multilevel Converter-Based Architectures in Fast Charging Stations Infrastructures. IEEE Transactions on Power Electronics, 37(9), 10747–10760. https://doi.org/10.1109/TPEL.2022.3167625
  3. Fan, Z., Wan, Z., Gao, L., Xiong, Y., & Song, G. (2023). A Multi-Objective Optimal Configuration Method for Microgrids Considering Zero-Carbon Operation. IEEE Access, 11, 87366–87379. https://doi.org/10.1109/ACCESS.2023.3303926
  4. Glinka, M., & Marquardt, R. (2005). A New AC/AC Multilevel Converter Family. IEEE Transactions on Industrial Electronics, 52(3), 662–669. https://doi.org/10.1109/TIE.2005.843973
  5. Hafeez, K., Khan, S. A., Van den Bossche, A., & Eddinne, K. D. (2020). Capacitor Energy Variations in MMC Using Harmonics Injection. Power Electronics and Drives, 5(1), 97–107. https://doi.org/10.2478/pead-2020-0007
  6. Hafeez, K., Khan, S. A., Van den Bossche, A., & Hasan, Q. U. (2019). Circulating Current Reduction in MMC-HVDC System Using Average Model. Applied Sciences, 9(7), 1383. https://doi.org/10.3390/app9071383
  7. He, L., Zhang, K., Xiong, J., & Fan, S. (2015). A Repetitive Control Scheme for Harmonic Suppression of Circulating Current in Modular Multilevel Converters. IEEE Transactions on Power Electronics, 30(1), 471–481. https://doi.org/10.1109/TPEL.2014.2304978
  8. Ilves, K., Harnefors, L., Norrga, S., & Nee, H. P. (2015). Analysis and operation of modular multilevel converters with phase-shifted carrier PWM. IEEE Transactions on Power Electronics, 30(1), 268–283. https://doi.org/10.1109/TPEL.2014.2321049
  9. Kouro, S., Malinowski, M., Gopakumar, K., Pou, J., Franquelo, L. G., Bin Wu, Rodriguez, J., Pérez, M. A., & Leon, J. I. (2010). Recent Advances and Industrial Applications of Multilevel Converters. IEEE Transactions on Industrial Electronics, 57(8), 2553–2580. https://doi.org/10.1109/TIE.2010.2049719
  10. Kouro, S., Rodriguez, J., Wu, B., Bernet, S., & Perez, M. (2012). Powering the Future of Industry: High-Power Adjustable Speed Drive Topologies. IEEE Industry Applications Magazine, 18(4), 26–39. https://doi.org/10.1109/MIAS.2012.2192231
  11. Kumar, A. R., Bhaskar, M. S., Subramaniam, U., Almakhles, D., Padmanaban, S., & Bo-Holm Nielsen, J. (2019). An Improved Harmonics Mitigation Scheme for a Modular Multilevel Converter. IEEE Access, 7, 147244–147255. https://doi.org/10.1109/ACCESS.2019.2946617
  12. Li, M., Dong, N., Chang, X., Yang, H., & Zhao, R. (2023). Analysis and Suppression of Capacitor Voltage Ripple for Hybrid MMCs under Boosted AC Voltage Conditions. IEEE Journal of Emerging and Selected Topics in Power Electronics, 11(4), 3775–3787. https://doi.org/10.1109/JESTPE.2023.3268847
  13. Li, Q., Li, B., He, J., Prieto-Araujo, E., Westerman Spier, D., Lyu, H., & Gomis-Bellmunt, O. (2022). A novel design of circulating current control target to minimize SM capacitance in MMC. International Journal of Electrical Power & Energy Systems, 143, 108432. https://doi.org/10.1016/j.ijepes.2022.108432
  14. Li, S., Wang, X., Yao, Z., Li, T., & Peng, Z. (2015). Circulating Current Suppressing Strategy for MMC-HVDC Based on Nonideal Proportional Resonant Controllers Under Unbalanced Grid Conditions. IEEE Transactions on Power Electronics, 30(1), 387–397. https://doi.org/10.1109/TPEL.2014.2329059
  15. Li, X., Song, Q., Liu, W., Xu, S., Zhu, Z., & Li, X. (2016). Performance Analysis and Optimization of Circulating Current Control for Modular Multilevel Converter. IEEE Transactions on Industrial Electronics, 63(2), 716–727. https://doi.org/10.1109/TIE.2015.2480748
  16. Liu, X., Huang, J., Sun, Y., Gao, S., & Tong, X. (2019). Passive Control for the MMC-HVDC System Based on the Energy Function. 2019 14th IEEE Conference on Industrial Electronics and Applications (ICIEA), 2232–2237. https://doi.org/10.1109/ICIEA.2019.8834318
  17. Liu, Z., & Zhao, J. (2021). Disturbance Interaction Analysis and Suppression Strategy of MMC-HVDC Systems Considering Sub-Module Capacitor Voltage Ripples. IEEE Transactions on Power Systems, 36(1), 235–247. https://doi.org/10.1109/TPWRS.2020.3006234
  18. Lizana, R., Perez, M. A., Arancibia, D., Espinoza, J. R., & Rodriguez, J. (2015). Decoupled Current Model and Control of Modular Multilevel Converters. IEEE Transactions on Industrial Electronics, 62(9), 5382–5392. https://doi.org/10.1109/TIE.2015.2405900
  19. Lyu, J., Yin, J., Zhu, H., & Cai, X. (2023). Impedance Modeling and Stability Analysis of Energy Controlled Modular Multilevel Converter. IEEE Transactions on Power Delivery, 38(3), 1868–1881. https://doi.org/10.1109/TPWRD.2022.3225640
  20. Lyu, Y., Li, C., Hsieh, Y.-H., Lee, F. C., Li, Q., & Xu, R. (2017). Capacitor voltage ripple reduction with state trajectory analysis for modular multilevel converter. 2017 IEEE Applied Power Electronics Conference and Exposition (APEC), 1829–1836. https://doi.org/10.1109/APEC.2017.7930947
  21. Ma, Y., Lin, H., & Wang, Z. (2019). Equivalent Model of Modular Multilevel Converter Considering Capacitor Voltage Ripples. IEEE Transactions on Power Delivery, 34(6), 2182–2193. https://doi.org/10.1109/TPWRD.2019.2915820
  22. Malinowski, M., Gopakumar, K., Rodriguez, J., & Pérez, M. A. (2010). A Survey on Cascaded Multilevel Inverters. IEEE Transactions on Industrial Electronics, 57(7), 2197–2206. https://doi.org/10.1109/TIE.2009.2030767
  23. Moon, J-W, Kim, C-S., Park, J-W., Kang,D-W., Kim, J-M., (2013). Circulating Current Control in MMC Under the Unbalanced Voltage. IEEE Transactions on Power Delivery, 28(3), 1952–1959. https://doi.org/10.1109/TPWRD.2013.2264496
  24. Nguyen, M. H., & Kwak, S. (2020). Nearest-Level Control Method With Improved Output Quality for Modular Multilevel Converters. IEEE Access, 8, 110237–110250. https://doi.org/10.1109/ACCESS.2020.3001587
  25. Nguyen, M. H., & Kwak, S. (2021). Predictive Nearest-Level Control Algorithm for Modular Multilevel Converters With Reduced Harmonic Distortion. IEEE Access, 9, 4769–4783. https://doi.org/10.1109/ACCESS.2020.3048156
  26. Perez, M. A., Bernet, S., Rodriguez, J., Kouro, S., & Lizana, R. (2015). Circuit Topologies, Modeling, Control Schemes, and Applications of Modular Multilevel Converters. IEEE Transactions on Power Electronics, 30(1), 4–17. https://doi.org/10.1109/TPEL.2014.2310127
  27. Picas, R., Pou, J., Ceballos, S., Zaragoza, J., Konstantinou, G., & Agelidis, V. G. (2013). Optimal injection of harmonics in circulating currents of modular multilevel converters for capacitor voltage ripple minimization. 2013 IEEE ECCE Asia Downunder, 318–324. https://doi.org/10.1109/ECCE-Asia.2013.6579115
  28. Pou, J., Ceballos, S., Konstantinou, G., Agelidis, V. G., Picas, R., & Zaragoza, J. (2015). Circulating Current Injection Methods Based on Instantaneous Information for the Modular Multilevel Converter. IEEE Transactions on Industrial Electronics, 62(2), 777–788. https://doi.org/10.1109/TIE.2014.2336608
  29. Raza, M., Aslam, A., & Aamir, T. (2023). Performance Analysis of Half-Bridge Commutation Cells of a Modular Multilevel Voltage Source Converter. IEEC 2023, 32. https://doi.org/10.3390/engproc2023046032
  30. Reddy, G. A., & Shukla, A. (2019). Arm current sensor-less control of MMC for Circulating current suppression. 2019 IEEE Energy Conversion Congress and Exposition (ECCE), 6905–6910. https://doi.org/10.1109/ECCE.2019.8913028
  31. Reddy, G. A., & Shukla, A. (2021). Circulating Current Optimization Control of MMC. IEEE Transactions on Industrial Electronics, 68(4), 2798–2811. https://doi.org/10.1109/TIE.2020.2977565
  32. Ren, J., Li, W., & Zhang, S. (2021). Study on AC Harmonic Characteristics of Netherland ±525kV/2GW MMC-HVDC System for Offshore Wind Farms Integration. 2021 International Conference on Power System Technology (POWERCON), 1534–1541. https://doi.org/10.1109/POWERCON53785.2021.9697553
  33. Ronanki, D., & Williamson, S. S. (2018). Modular Multilevel Converters for Transportation Electrification: Challenges and Opportunities. IEEE Transactions on Transportation Electrification, 4(2), 399–407. https://doi.org/10.1109/TTE.2018.2792330
  34. Sang, Y., Yang, B., Shu, H., An, N., Zeng, F., & Yu, T. (2019). Passive Current Control Design for MMC in HVDC Systems through Energy Reshaping. Electronics, 8(9), 967. https://doi.org/10.3390/electronics8090967
  35. Song, Q., Liu, W., Li, X., Rao, H., Xu, S., & Li, L. (2013). A steady-state analysis method for a modular multilevel converter. IEEE Transactions on Power Electronics, 28(8), 3702–3713. https://doi.org/10.1109/TPEL.2012.2227818
  36. Spier, D. W., Prieto-Araujo, E., Gomis-Bellmunt, O., & Mestre, J. L. (2021). Analytic estimation of the MMC sub-module capacitor voltage ripple for balanced and unbalanced AC grid conditions. https://doi.org/10.48550/arXiv.2109.00310
  37. Thakur, S., Odavic, M., Allu, A., Zhu, Z. Q., & Atallah, K. (2022a). Analytical Modelling and Optimization of Output Voltage Harmonic Spectra of Full-Bridge Modular Multilevel Converters in Boost Mode. IEEE Transactions on Power Electronics, 37(3), 3403–3420. https://doi.org/10.1109/TPEL.2021.3108877
  38. Thakur, S., Odavic, M., Allu, A., Zhu, Z. Q., & Atallah, K. (2022b). Analytical Modelling and Optimization of Output Voltage Harmonic Spectra of Full-Bridge Modular Multilevel Converters in Boost Mode. IEEE Transactions on Power Electronics, 37(3), 3403–3420. https://doi.org/10.1109/TPEL.2021.3108877
  39. Tu, Q., & Xu, Z. (2011). Impact of sampling frequency on harmonic distortion for modular multilevel converter. IEEE Transactions on Power Delivery, 26(1), 298–306. https://doi.org/10.1109/TPWRD.2010.2078837
  40. Tu, Q., Xu, Z., Huang, H., & Zhang, J. (2010a). Parameter design principle of the arm inductor in modular multilevel converter based HVDC. 2010 International Conference on Power System Technology: Technological Innovations Making Power Grid Smarter, POWERCON2010, 0–5. https://doi.org/10.1109/POWERCON.2010.5666416
  41. Tu, Q., Xu, Z., Huang, H., & Zhang, J. (2010b). Parameter design principle of the arm inductor in modular multilevel converter based HVDC. 2010 International Conference on Power System Technology: Technological Innovations Making Power Grid Smarter, POWERCON2010, 0–5. https://doi.org/10.1109/POWERCON.2010.5666416
  42. Uddin, W., Hussain, S., Zeb, K., Khalil, I. U., Ullah, Z., Dildar, M. A., Adil, M., Ishfaq, M., Khan, I., & Kim, H. J. (2018). Effect of Arm Inductor on Harmonic Reduction in Modular Multilevel Converter. 2018 International Conference on Power Generation Systems and Renewable Energy Technologies (PGSRET), 1–5. https://doi.org/10.1109/PGSRET.2018.8685973
  43. Vasiladiotis, M., Cherix, N., & Rufer, A. (2014). Accurate Capacitor Voltage Ripple Estimation and Current Control Considerations for Grid-Connected Modular Multilevel Converters. IEEE Transactions on Power Electronics, 29(9), 4568–4579. https://doi.org/10.1109/TPEL.2013.2286293
  44. Wang, Y., Huang, Z., Yuan, Y., Gao, L., & Li, P. (2016). Harmonics analysis and simulation of NLM in MMC. 12th IET International Conference on AC and DC Power Transmission (ACDC 2016), 3 (6 .)-3 (6 .). https://doi.org/10.1049/cp.2016.0383
  45. Xi, Q., Tian, Y., & Fan, Y. (2024). Capacitor Voltage Balancing Control of MMC Sub-Module Based on Neural Network Prediction. Electronics, 13(4), 795. https://doi.org/10.3390/electronics13040795
  46. Xiao, H., Xu, Z., Xue, Y., & Tang, G. (2013). Theoretical analysis of the harmonic characteristics of modular multilevel converters. Science China Technological Sciences, 56(11), 2762–2770. https://doi.org/10.1007/s11431-013-5331-1
  47. Xu, C., Lin, L., Yin, T., & Hu, J. (2020). An Improved Phase-Shifted-Carrier Technique for Hybrid Modular Multilevel Converter with Boosted Modulation Index. IEEE Transactions on Power Electronics, 35(2), 1340–1352. https://doi.org/10.1109/TPEL.2019.2921202
  48. Xu, Z., Xiao, H., & Zhang, Z. (2016). Selection methods of main circuit parameters for modular multilevel converters. IET Renewable Power Generation, 10(6), 788–797. https://doi.org/10.1049/iet-rpg.2015.0434
  49. Yuan, Y., Li, P., Kong, X., Liu, J., Li, Q., & Wang, Y. (2016). Harmonic influence analysis of unified power flow controller based on modular multilevel converter. Journal of Modern Power Systems and Clean Energy, 4(1), 10–18. https://doi.org/10.1007/s40565-015-0175-2
  50. Yuvaraja, T., & Mazumder, S. (n.d.). Performance and Analysis of Modular Multilevel Converter. American Journal of Engineering Research, 2014. https://www.ajer.org
  51. Zhang, B., & Nademi, H. (2020). Modeling and Harmonic Stability of MMC-HVDC With Passive Circulating Current Filters. IEEE Access, 8, 129372–129386. https://doi.org/10.1109/ACCESS.2020.3009331
  52. Zhang, H., Belhaouane, M. M., Colas, F., Kadri, R., Gruson, F., & Guillaud, X. (2021). On Comprehensive Description and Analysis of MMC Control Design: Simulation and Experimental Study. IEEE Transactions on Power Delivery, 36(1), 244–253. https://doi.org/10.1109/TPWRD.2020.2977470

Last update:

No citation recorded.

Last update: 2025-02-09 08:47:51

No citation recorded.