Binomial Coefficients of the 11-Phase Electromechanical System Digital Codes and Space Vector Modulation Algorithms
DOI:
https://doi.org/10.24160/1993-6982-2026-1-16-24Keywords:
11-phase electromechanical system, space vector modulation algorithms, binomial coefficients of binary digital codesAbstract
The research is concerned with evaluating the binomial coefficients of the 11-phase electromechanical system digital codes, classifying the basic vectors, and studying one space vector modulation algorithm. In total, an 11-phase system has 93 space vector modulation algorithms, each shaping a symmetrical 11-phase voltage with a certain phase voltage waveform. Owing to a significant number of space vector modulation algorithms, there appear additional motor control capabilities. The aim of the research work is to develop and classify space vector modulation algorithms for an 11-phase electromechanical system in accordance with the equivalent circuits of an 11-phase motor winding. A relationship is established between the converter load equivalent circuits in the pulse mode that are produced in implementing the space vector modulation algorithms and the binomial coefficients of the 11-phase converter digital codes. The values of the binomial coefficients correspond to Pascal's triangle eleventh row. One of the space vector modulation algorithms of an 11-phase electromechanical system is investigated, in implementing of which the base vectors with a modulus equal to unity are generated (at the converter input voltage equal to unity). The algorithm is presented in matrix form. A symmetrical 11-phase voltage, which is generated in implementing the described algorithm, and which corresponds to the "star" of unit base vectors, is considered. In carrying out the research, the combinatorics and vector analysis methods were used. The study results can be used by developers of electric traction systems based on multiphase electric machines.
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Для цитирования: Терешкин В.М., Баландин С.П., Рафиков А.М., Гришин Д.А. Биноминальные коэффициенты цифровых кодов 11-фазной электромеханической системы и алгоритмы пространственно-векторной модуляции // Вестник МЭИ. 2026. № 1. С. 16—24. DOI: 10.24160/1993-6982-2026-1-16-24
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Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
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1. Duran M.J., Gonzalez-Prieto I., Gonzalez-Prieto A., Aciego J.J. The Evolution of Model Predictive Control in Multiphase Electric Drives: A Growing Field of Research. IEEE Industrial Electronics Magazine. 2022;16(4):29—39.
2. Gonzalez-Prieto A., González-Prieto I., Duran M.J., Aciego J.J. Dynamic Response in Multiphase Electric Drives: Control Performance and Influencing Factors. Machines. 2022;10(10):866.
3. Gonzalez O. e. a. Model Predictive Current Control of Six-Phase Induction Motor Drives Using Virtual Vectors and Space Vector Modulation. IEEE Trans. Power Electronics. 2022;37(7):7617—7628.
4. Fleitas, A. e. a. Winding Design and Efficiency Analysis of a Nine-phase Induction Machine from a Three-phase Induction Machine. Machines. 2022;10(12):1124.
5. Gonzalez-Prieto A. e. a. On the Advantages of Symmetrical over Asymmetrical Multiphase AC Drives with even Phase Number Using Direct Controllers. IEEE Trans. Industrial Electronics. 2022;69(8):7639—7650.
6. Yepes A.G. e. a. A Comprehensive Survey on Fault Tolerance in Multiphase AC Drives, Part 1: General Overview Considering Multiple Fault Types. Machines. 2022;10(3):208.
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8. Gonzalez-Prieto A. e. a. Symmetrical Six-phase Induction Machines: a Solution for Multiphase Direct Control Strategies. Proc. IEEE Intern. Conf. Industrial Technol. 2021:1362—1367.
9. Rubino S., Dordevic O., Bojoi R., Levi E. Modular Vector Control of Multi-three-phase Permanent Magnet Synchronous Motors. IEEE Trans. Industrial Electronics. 2021;68(10):9136—9147.
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For citation: Tereshkin V.M., Balandin S.P., Rafikov A.M., Grishin D.A. Binomial Coefficients of the 11-Phase Electromechanical System Digital Codes and Space Vector Modulation Algorithms. Bulletin of MPEI. 2026;1:16—24. (in Russian). DOI: 10.24160/1993-6982-2026-1-16-24
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Conflict of interests: the authors declare no conflict of interest
