Derivative-Free Decoupling Method for Asymmetric Six-Phase PMSMs Based on the Dual dq Reference Frame

Letícia D. Giovannini; Arthur C. B. Dias; Lenin M. F. Morais; Gabriel A. Fogli

doi:10.18618/REP.e202629

Authors

Letícia D. Giovannini Aeronautics Institute of Technology https://orcid.org/0009-0007-5763-0176
Arthur C. B. Dias Universidade Federal de Minas Gerais
Lenin M. F. Morais Universidade Federal de Minas Gerais https://orcid.org/0000-0003-1680-0400
Gabriel A. Fogli Universidade Federal de Minas Gerais https://orcid.org/0000-0003-1940-4630

DOI:

https://doi.org/10.18618/REP.e202629

Keywords:

Six-phase PMSM, Machine drives, Control applied to power electronis, Decoupling Method

Abstract

This paper presents the modeling, control, and hardware-in-the-loop (HIL) evaluation of an asymmetric six-phase Permanent Magnet Synchronous Motor (6φ-PMSM) supplied by two three-phase Voltage Source Inverters (VSIs). The machine is modeled as two coupled three-phase subsystems using a dual dq representation. Based on this model, a cascade control structure composed of two parallel inner current loops and an outer speed loop is designed. A frequency-domain tuning methodology is also proposed, requiring only the selection of the inner closed-loop time constant and the desired phase margin of the outer loop, allowing all controller gains to be analytically obtained. To mitigate coupling effects between coordinates and subsystems and enable a single-input single-output (SISO) design approach, a decoupling strategy is proposed and comparatively analyzed. The proposed approach is directly derived from the state-space model and eliminates the need for state-variable derivatives, reducing sensitivity to switching noise and simplifying digital implementation. The control strategy is verified through HIL test bench, in which the plant is implemented in the HIL platform while the control algorithm is executed in a digital signal processor. Experimental results demonstrate accurate dynamic behavior, fast current response, reduced coupling effects, and low current harmonic distortion under different operating conditions.

Downloads

Download data is not yet available.

Author Biographies

Letícia D. Giovannini, Aeronautics Institute of Technology

received the B.S degree in Electrical Engineering from Universidade Federal de Minas Gerais (UFMG), Brazil, in 2025, and has been pursuing the M.Sc. degree in Electronic Engineering at Instituto Tecnológico da Aeronáutica (ITA), Brazil, since 2025. Her research interests include modeling and control of power electronic converters.

Arthur C. B. Dias, Universidade Federal de Minas Gerais

received the B.S. degree in control and automation engineering from Universidade Federal de Minas Gerais (UFMG), Brazil, in 2023, and is an graduate student in electrical engineering at UFMG, since 2024. His research interests include modeling and control of electronic converters applied to electrical drives.

Lenin M. F. Morais, Universidade Federal de Minas Gerais

received the bachelor’s degree, the master’s degree, and the doctor’s degree, all in electrical engineering from the Federal University of Minas Gerais, Belo Horizonte, Brazil, in 2000, 2002, and 2007, respectively. He is currently a Full Professor with the Electronics Engineering Department, Federal University of Minas Gerais. He was a Postdoctoral Intern with the Laboratoire Plasma et Conversion d’Energie - LAPLACE, Université Toulouse III Paul Sabatier, Toulouse, France, and with the Institut de Recherche Technologique - IRT Saint Exupéry, Toulouse, France. IEEE Senior Member and member of the IEEE Power Electronics Society, and Member of SOBRAEP (Brazilian Power Electronics Society) since 2005. He has experience in the field of electrical engineering, with emphasis on power electronics, industrial electronics, and electronic systems and controls. His research interests mainly include the following: projects of converters with high density of power/high performance, electronic reactors for high intensity discharge lamps, power LEDs, circuits for power factor correction, repetitive control, control based on passivity, PWM methods.

Gabriel A. Fogli, Universidade Federal de Minas Gerais

received the B.S. degree in electronics and telecommunication engineering from Pontifícia Universidade Católica de Minas Gerais (PUC Minas), Brazil, in 2011, and the M.Sc. and Ph.D. degrees in electrical engineering from the Universidade Federal de Juiz de Fora (UFJF), Brazil, in 2014 and 2018, respectively. He was a Professor with the Department of Electrical Engineering, Universidade Federal de Ouro Preto (UFOP), Brazil, from 2016 to 2019. Since 2019, he has been a Professor with the Universidade Federal de Minas Gerais (UFMG), Brazil. He is a member of the Brazilian Power Electronics Society (SOBRAEP) and the IEEE Power Electronics Society (PELS). His research interests include modeling and control of power electronic converters and distributed generation applications.

References

N. Novas, R. M. Garcia Salvador, F. Portillo, I. Robalo, A. Alcayde, M. Fernández-Ros, J. A. Gázquez, “Global Perspectives on and Research Challenges for Electric Vehicles”, Vehicles, vol. 4, no. 4, pp. 1246–1276, 2022, doi:10.3390/vehicles4040066. DOI: https://doi.org/10.3390/vehicles4040066

V. H. K. Ries, G. Waltrich, A. Vaccari, “Estimativa de Mapa de Eficiência para Máquinas Elétricas Através do Método de Filtro de Kalman Estendido”, Eletrônica de Potência, vol. 29, pp. e202426–e202426, 2024, doi:10.18618/REP.2005.2.061068. DOI: https://doi.org/10.18618/REP.2005.2.061068

J. B. V. Neto, V. H. K. Ries, G. Waltrich, “Controle de velocidade de uma máquina de ímãs permanentes tolerante a falhas em conjunto com técnica de máximo torque por ampere”, Eletrônica de Potência, vol. 29, pp. e202434–e202434, 2024, doi:10.18618/REP.e202434. DOI: https://doi.org/10.18618/REP.e202434

Q. Wang, S. Wang, C. Chen, “Review of sensorless control techniques for PMSM drives”, IEEJ Transactions on Electrical and Electronic Engineering, vol. 14, no. 10, pp. 1543–1552, 2019, doi:10.1002/tee.22974. DOI: https://doi.org/10.1002/tee.22974

M. Furmanik, L. Gorel, D. Konvičný, P. Rafajdus, “Comparative Study and Overview of Field-Oriented Control Techniques for Six-Phase PMSMs”, Applied Sciences, vol. 11, no. 17, 2021, doi:10.3390/app11177841. DOI: https://doi.org/10.3390/app11177841

J. Shen, X. Wang, Z. Zhang, S. Ren, D. Ma, D. Xiao, “Research on the Application of Dual Three-Phase PMSM in Renewable Energy System”, in 2023 26th International Conference on Electrical Machines and Systems (ICEMS), pp. 3475–3479, 2023, doi:10.1109/ICEMS59686.2023.10344728. DOI: https://doi.org/10.1109/ICEMS59686.2023.10344728

S. Bharti, C. Bhende, O. Ray, “Control of Six-Phase Permanent Magnet Synchronous Motor for Electric Vehicle Application”, in 2022 IEEE 2nd International Conference on Sustainable Energy and Future Electric Transportation (SeFeT), pp. 1–6, 2022, doi:10.1109/SeFeT55524.2022.9908704. DOI: https://doi.org/10.1109/SeFeT55524.2022.9908704

H. Gao, Z. Zhang, Y. Liu, W. Huang, H. Xue, “Development and Analysis of Dual Three-Phase PMSM With Phase-Shifted Hybrid Winding for Aircraft Electric Propulsion Application”, IEEE Transactions on Transportation Electrification, vol. 10, no. 3, pp. 6497–6508, 2024, doi:10.1109/TTE.2023.3334026. DOI: https://doi.org/10.1109/TTE.2023.3334026

S. Hu, Z. Liang, W. Zhang, X. He, “Research on the Integration of Hybrid Energy Storage System and Dual Three-Phase PMSM Drive in EV”, IEEE Transactions on Industrial Electronics, vol. 65, no. 8, pp. 6602–6611, 2018, doi:10.1109/TIE.2017.2752141. DOI: https://doi.org/10.1109/TIE.2017.2752141

Y. Hu, Z. Q. Zhu, M. Odavic, “Comparison of Two-Individual Current Control and Vector Space Decomposition Control for Dual Three-Phase PMSM”, IEEE Transactions on Industry Applications, vol. 53, no. 5, pp. 4483–4492, 2017, doi:10.1109/TIA.2017.2703682. DOI: https://doi.org/10.1109/TIA.2017.2703682

Y. Hu, Z.-Q. Zhu, K. Liu, “Current Control for Dual Three-Phase Permanent Magnet Synchronous Motors Accounting for Current Unbalance and Harmonics”, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 2, no. 2, pp. 272–284, 2014, doi:10.1109/JESTPE.2014.2299240. DOI: https://doi.org/10.1109/JESTPE.2014.2299240

L. D. Giovannini, A. de Carvalho Batista Dias, L. M. F. Morais, G. A. Fogli, “Modeling and Control of a Six-Phase PMSM Using Two Three-Phase Inverters with Decoupling Influence Analysis”, in 2025 Brazilian Power Electronics Conference (COBEP), pp. 1–6, 2025, doi:10.1109/COBEP66423.2025.11231710. DOI: https://doi.org/10.1109/COBEP66423.2025.11231710

Y. Luo, K. Yang, Y. Zheng, “Luenberger Observer-Based Model Predictive Control for Six-Phase PMSM Motor With Localization Error Compensation”, IEEE Transactions on Industrial Electronics, vol. 70, no. 11, pp. 10800–10810, 2023, doi:10.1109/TIE.2022.3229340. DOI: https://doi.org/10.1109/TIE.2022.3229340

Z. Song, C. Liu, Z. Dong, R. Huang, “Improved Multi-Stage Decoupling Space Vector Modulation for Asymmetrical Multi-Phase PMSM With Series Winding Connection”, IEEE Transactions on Power Electronics, vol. 37, no. 9, pp. 10951–10966, 2022, doi:10.1109/TPEL.2022.3163275. DOI: https://doi.org/10.1109/TPEL.2022.3163275

Y. He, Y. Wang, J. Wu, Y. Feng, J. Liu, “A simple current sharing scheme for dual three-phase permanent-magnet synchronous motor drives”, in 2010 Twenty-Fifth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 1093–1096, 2010, doi:10.1109/APEC.2010.5433366. DOI: https://doi.org/10.1109/APEC.2010.5433366

Y. Luo, X. Zhang, S. Niu, “A Hybrid Two-Stage Control Solution for Six-Phase PMSM Motor With Improved Performance”, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 10, no. 5, pp. 5435–5445, 2022, doi:10.1109/JESTPE.2022.3141487. DOI: https://doi.org/10.1109/JESTPE.2022.3141487

H. Yan, L. Liu, B. Ge, “Decoupling control of asymmetric Six-Phase PMSM two-motor series-connected system with harmonic compensation”, Journal of Physics: Conference Series, vol. 3043, no. 1, p. 012130, jun 2025, doi:10.1088/1742-6596/3043/1/012130. DOI: https://doi.org/10.1088/1742-6596/3043/1/012130

A. de Carvalho Batista Dias, L. D. Giovannini, G. M. Auler, G. A. Fogli, “Analysis and Design of State Observers Applied to a Six-Phase Permanent Magnet Synchronous Machine”, in 2025 Brazilian Power Electronics Conference (COBEP), pp. 01–07, 2025, doi:10.1109/COBEP66423.2025.11231507. DOI: https://doi.org/10.1109/COBEP66423.2025.11231507

J. Karttunen, S. Kallio, P. Peltoniemi, P. Silventoinen, O. Pyrhonen, “Dual three-phase permanent magnet synchronous machine supplied by two independent voltage source inverters”, pp. 741–747, 06 2012, doi:10.1109/SPEEDAM.2012.6264448. DOI: https://doi.org/10.1109/SPEEDAM.2012.6264448

J. Karttunen, S. Kallio, P. Peltoniemi, P. Silventoinen, “Current Harmonic Compensation in Dual Three-Phase PMSMs Using a Disturbance Observer”, IEEE Transactions on Industrial Electronics, vol. 63, no. 1, pp. 583–594, 2016, doi:10.1109/TIE.2015.2461519. DOI: https://doi.org/10.1109/TIE.2015.2461519

Y. Zhao, T. Lipo, “Space vector PWM control of dual three-phase induction machine using vector space decomposition”, IEEE Transactions on Industry Applications, vol. 31, no. 5, pp. 1100–1109, 1995, doi:10.1109/28.464525. DOI: https://doi.org/10.1109/28.464525

J. Karttunen, S. Kallio, P. Peltoniemi, P. Silventoinen, O. Pyrhönen, “Decoupled Vector Control Scheme for Dual Three-Phase Permanent Magnet Synchronous Machines”, IEEE Transactions on Industrial Electronics, vol. 61, no. 5, pp. 2185–2196, 2014, doi:10.1109/TIE.2013.2270219. DOI: https://doi.org/10.1109/TIE.2013.2270219

S.-K. Sul, Control of electric machine drive systems, John Wiley & Sons, 2011, doi:10.1002/9780470876541. DOI: https://doi.org/10.1002/9780470876541

G. A. Fogli, I. D. Souza, M. C. Fernandes, P. M. Almeida, P. G. Barbosa, “Dispatchable distributed generation using a back-to-back converter for grid-forming improvements based on feed-forward action with load current prediction”, IET Power Electronics, vol. 13, no. 16, pp. 3686–3696, 2020, doi:10.1049/iet-pel.2020.0215. DOI: https://doi.org/10.1049/iet-pel.2020.0215

M. Furmanik, P. Makys, P. Rafajdus, “Self-Sensing Six-Phase PMSM Drive Based on Back-EMF Measurement”, Applied Sciences, vol. 13, no. 2, 2023, doi:10.3390/app13021077. DOI: https://doi.org/10.3390/app13021077