Parallel LLC resonant converters are suitable for low-voltage and high-current applications. However, deviations in the resonant inductor, resonant capacitor, and magnetizing inductor cause gain differences among phases, resulting in output-current imbalance. To address the difficulty of achieving satisfactory multi-condition dynamic performance with a dual-loop controller under unknown resonant-parameter deviations, this paper proposes a multi-condition particle swarm optimization fractional-order proportional-integral (PSO-FOPI) current-sharing control method. The proposed method adopts a common-mode/differential-mode frequency dual-loop structure, in which common output-voltage regulation and interphase current-sharing regulation are mapped to the common-mode and differential-mode frequencies, respectively. Meanwhile, the worst-case time-domain performance over typical parameter-deviation conditions is used as the fitness function, and particle swarm optimization (PSO) is employed to offline tune the dual-loop FOPI controller parameters. Simulation results show that, under six typical parameter-deviation conditions and within a ±15% Monte Carlo random parameter-deviation range, the controller maintains favorable voltage and current-sharing dynamic performance. Hardware experiments further verify the practical operating feasibility of the proposed control method.
- Open Access
- Article
Multi-Condition PSO-FOPI Current-Sharing Control for Parallel LLC Resonant Converters under Parameter Deviations
Author Information
Received: 08 Aug 2026 | Revised: 07 Sep 2026 | Accepted: 09 Sep 2026 | Published: 21 Sep 2026
Abstract
Keywords
parallel LLC | current-sharing control | parameter deviation | FOPI | PSO
References
- 1.
Zeng, J.; Zhang, G.; Yu, S.S.; et al. LLC Resonant Converter Topologies and Industrial Applications—A Review. Chin. J. Electr. Eng. 2020, 6, 73–84. https://doi.org/10.23919/cjee.2020.000021.
- 2.
Guimarães França, J.V.; Costa, L.F.; Papafotiou, G. A Highly Modular Interphase Solid-State Transformer Architecture. In Proceedings of the 2025 IEEE Energy Conversion Conference Congress and Exposition (ECCE), Philadelphia, PA, USA, 19–23 October 2025; pp. 1–8. https://doi.org/10.1109/ecce58356.2025.11259843.
- 3.
França, J.V.G.; Christou, I.; van de Zanden, M.; et al. A Highly Modular LLC-based Interphase Solid-State Transformer Architecture for Smart-Grid Applications. IEEE Trans. Power Electron. 2026. 1–15. https://doi.org/10.1109/tpel.2026.3716728.
- 4.
Dong, H.; Xie, X. Review of Current-Sharing Schemes for Multiphase LLC Resonant Converter. IEEE Trans. Power Electron. 2025, 40, 1322–1345. https://doi.org/10.1109/tpel.2024.3447047.
- 5.
Shah, S.S.; Rastogi, S.K.; Bhattacharya, S. Paralleling of LLC Resonant Converters. IEEE Trans. Power Electron. 2021, 36, 6276–6287. https://doi.org/10.1109/tpel.2020.3040621.
- 6.
Sun, Z.; Wu, Q.; Wang, Q.; et al. An Improved Grouping Transformer’s Secondary Windings Current-Sharing Method for Multiphase LLC Converter. IEEE Trans. Power Electron. 2023, 38, 9872–9884. https://doi.org/10.1109/tpel.2023.3271351.
- 7.
Sun, Z.; Wang, Q.; Wu, Q.; et al. A Unified Common Inductor and Common Capacitor Current Sharing Method for Multiphase LLC Converter. IEEE Trans. Power Electron. 2022, 37, 12182–12196. https://doi.org/10.1109/tpel.2022.3178497.
- 8.
Kim, T.; Choi, D.; Choi, S.H.; et al. Improved Natural Current Sharing and Phase-Shedding Operation in LLC Resonant Converters with Voltage-Doubler Rectifier. IEEE Trans. Power Electron. 2024, 39, 13401–13412. https://doi.org/10.1109/tpel.2024.3422316.
- 9.
Sun, Z.; Yang, Y.; Zeng, J.; et al. Coupled Resonant Tank Current-Sharing Topology for Multiphase LLC-DCX Converter with Phase-Shedding Ability. IEEE J. Emerg. Sel. Top. Power Electron. 2025, 13, 7297–7313. https://doi.org/10.1109/jestpe.2025.3607893.
- 10.
Hu, Z.; Qiu, Y.; Wang, L.; et al. An Interleaved LLC Resonant Converter Operating at Constant Switching Frequency. IEEE Trans. Power Electron. 2014, 29, 2931–2943. https://doi.org/10.1109/tpel.2013.2273939.
- 11.
Zhou, X.; Yu, X.; Li, C.; et al. A Reduced-Switch-Count Two-Phase Interleaved Switch-Control-Capacitor LLC Converter with Accurate Current Balancing. IET Power Electron. 2024, 17, 1163–1175. https://doi.org/10.1049/pel2.12467.
- 12.
Dong, H.; Xie, X. A Novel Current Sharing Scheme for Multiphase Interleaved LLC Converter Based on Partial Energy Regulation of Resonant Capacitor. IEEE J. Emerg. Sel. Top. Power Electron. 2025, 13, 136–146. https://doi.org/10.1109/jestpe.2024.3480956.
- 13.
Liu, K.; Xiao, T.; Zhao, J.; et al. Differentiated-Gain-Regulation-Based Current Balancing Control for Multi-Phase Interleaved LLC Resonant Converters. IEEE Open J. Power Electron. 2025, 6, 1428–1437. https://doi.org/10.1109/ojpel.2025.3600380.
- 14.
Cheng, Z.; He, L.; Yang, H. Fewer-Sensors Current Balancing in LLC-DCX Converters Parallel System with Powerless Fractional-Order Capacitor. IEEE Trans. Transp. Electrif. 2026, 12, 464–473. https://doi.org/10.1109/tte.2025.3616127.
- 15.
Zong, S.; Luo, H.; Li, W.; et al. Theoretical Evaluation of Stability Improvement Brought by Resonant Current Loop for Paralleled LLC Converters. IEEE Trans. Ind. Electron. 2015, 62, 4170–4180. https://doi.org/10.1109/tie.2014.2385661.
- 16.
Murata, K.; Kurokawa, F. An Interleaved PFM LLC Resonant Converter with Phase-Shift Compensation. IEEE Trans. Power Electron. 2016, 31, 2264–2272. https://doi.org/10.1109/tpel.2015.2427735.
- 17.
Moreno, M.; Pereda, J.; Rojas, F.; et al. Decoupled PI Controllers Based on Pulse-Frequency Modulation for Current Sharing in Multi-Phase LLC Resonant Converters. IEEE Access 2021, 9, 15283–15294. https://doi.org/10.1109/access.2021.3053171.
- 18.
Wang, Y.; Ren, X.; Zhang, Z.; et al. Research on Current Sharing Strategy of Parallel LLC Resonant Converter. In Proceedings of the 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), Anaheim, CA, USA, 17–21 March 2019. https://doi.org/10.1109/apec.2019.8721775.
- 19.
Zhang, C.; Duan, B.; Song, J.; et al. A Modified Active Disturbance Rejection Control Strategy for Current Balance in Parallel LLC Resonant Converter. In Proceedings of the 2022 34th Chinese Control and Decision Conference (CCDC), Hefei, China, 15–17 August 2022; pp. 3077–3082. https://doi.org/10.1109/ccdc55256.2022.10033970.
- 20.
He, K.; Gao, L.; Han, L.; et al. A Variable-Frequency and Phase-Shifted Based Current Sharing Control for Parallel LLC Resonant Converters with Parameter Differences. In Proceedings of the 2024 27th International Conference on Electrical Machines and Systems (ICEMS), Fukuoka, Japan, 26–29 November 2024.
- 21.
Zhang, S.; Wang, C.; Li, X.; et al. Research on Reduced-Order Model Predictive Control and Parallel Current-Sharing System of LLC Resonant Converters. In Proceedings of the 2026 9th International Conference on Energy, Electrical and Power Engineering (CEEPE), Nanjing, China, 17–19 April 2026; pp. 236–241. https://doi.org/10.1109/ceepe69795.2026.11552125.
- 22.
Cobani, O.; Dimitriuc, C.; Zaman, M.S.; et al. Gradient-Descent Sensorless Current Balancing for Multiphase LLC Converters. In Proceedings of the 2026 IEEE Applied Power Electronics Conference and Exposition (APEC), San Antonio, TX, USA, 22–26 March 2026; pp. 1590–1597. https://doi.org/10.1109/apec51134.2026.11516741.
- 23.
Liu, K.; Xiao, T.; Chen, P.; et al. Virtual-Synchronizer-Based Current Sharing Scheme in m-Phase Resonant DC-DC Converters System. IEEE Trans. Circuits Syst. II Express Briefs 2025, 72, 853–857. https://doi.org/10.1109/tcsii.2025.3559142.
- 24.
Gao, T.; Sun, G.; Wang, H.; et al. Research on Current Sharing Control Method Based on Duty Cycle Regulation for Interleaved Parallel LLC Resonant Converters. IEEE J. Emerg. Sel. Top. Power Electron. 2024, 12, 3977–3985. https://doi.org/10.1109/jestpe.2024.3416749.
- 25.
Li, D.; Liu, C.; Wang, L.; et al. Enhanced Dynamic Performance of FSBB Converters Using EPSO-Tuned FOPI Control: From Simulation to Hardware Validation. IEEE Trans. Power Electron. 2026, 41, 12892–12905. https://doi.org/10.1109/tpel.2026.3665732.
- 26.
Podlubny, I. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications; Academic Press: San Diego, CA, USA, 1998.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Suite 4002 Level 4, 447 Collins Street, Melbourne, Victoria 3000, Australia
General Inquiries: info@sciltp.com