Keywords
векторне полеорієнтоване керування
релейний регулятор
екстремальне керування
бездатчикова система керування
дискретний розширений спостерігач Калмана doubly fed machine
vector field-oriented control
relay controller
extremum control
sensorless control system
discrete extended Kalman observer
How to Cite
Abstract
In this paper for the control system of a doubly fed machine (DFM) previously proposed by the authors, a discrete extended Kalman observer is synthesized in order to develop a sensorless relay – vector control system for the DFM with two extremum regulation loops. The Kalman observer is of relatively high order because in addition to identifying the reference stator flux linkage vector and rotor angular speed – which is sufficient for induction machines (IM) with a squirrel-cage rotor controlled through the stator – this observer also estimates the rotor position angle and the external disturbance, represented by the static load torque applied to the DFM shaft. A second feature of the proposed Kalman observer lies in the inclusion of the stator voltage vector projections onto the orthogonal rotor-related axes within the observer’s state matrix. Thus, these projections are computed as state variables rather than external inputs, with the only external control actions being the voltages applied to the rotor circuit of the DFM. In the rotor and stator reactive power channels optimization of the DFM’s energy performance is achieved under steady-state operating conditions. The standard Kalman filtering algorithm is applied here to a deterministic system to enable the identification of all necessary process variables within a single observer. The Kalman observer operates stably because the measured rotor currents of the DFM, from whose estimation errors the corrective feedbacks are formed, contain high-frequency pulsations under direct relay control; these pulsations are perceived by the observer as random measurement noise. Through mathematical modeling of a DFM with a fan-type mechanical load on the shaft, the high quality of speed regulation and the achievement of extremal energy performance values in steady state have been theoretically confirmed for the sensorless control system based on the proposed Kalman observer. References 21, figure 1.
References
1. Kliuiev O.V., Sadovoi O.V., Sokhina Yu.V. Control systems for asynchronous valve cascades. Kamianske: DDTU, 2018. 294 p. DOI: https://doi.org/10.5281/zenodo.16887109. (Ukr)
2. Kliuiev O.V., Sadovoi O.V., Sokhina Yu.V. Sensorless control system by doubly fed machineon based the Kalman filter. Tekhnichni nauky ta tekhnologii. 2024. No 4(38). Pp. 270-281. DOI: https://doi.org/10.25140/2411-5363-2024-4(38)-270-281. (Ukr)
3. Sadovoi O. V., Kliuiev O.V., Sokhina Yu.V. Use of Kalman filter in vector system of extreme control of asynchronous machine. Tekhnichna Elektrodynamika. 2025. No 1. Pp. 47-56. DOI: https://doi.org/10.15407/techned2025.01.047. (Ukr)
4. Hicham Ben Sassi, Khadija Lahrech, Fatima Errahimi, Najia ES-Sbai, Mokhtar Ghodbane. Mechanical speed estimation of a DFIG based on the Unscented Kalman Filter (UKF). International Journal of Energetica (IJECA). 2022. Vol. 7. Issue 1. Pp. 9-17. DOI: https://doi.org/10.47238/ijeca.v7i1.191.
5. Djamila Cherifi, Yahia Miloud. Improved Sensorless Control of Doubly Fed Induction Motor Drive Based on Full Order Extended Kalman Filter Observer. Periodica Polytechnica Electrical Engineering and Computer Science. 2020. Vol. 64(1). Pp. 64-73. DOI: https://doi.org/10.3311/PPee.14245.
6. Ricardo Perez, Cesar Silva, Juan Yuz, Gonzalo Carrasco. Experimental Sensorless Vector Control Performance of a DFIG Based on an Extended Kalman Filter. 38th IEEE Annual Conference on Industrial Electronics Society (IECON). Montreal, QC, Canada, 25-28 October 2012. Pp. 1786-1792. DOI: https://doi.org/10.1109/IECON.2012.6388930.
7. Gerasimos Rigatos, Pierluigi Siano. DFIG control using Differential Flatness theory and Extended Kalman Filtering. Pro-ceedings of the 14th IFAC Symposium on Information Control Problems in Manufacturing, Bucharest, Romania, 23-25 May 2012. Vol. 45. Issue 6. Pp. 1763-1770. DOI: https://doi.org/10.3182/20120523-3-RO-2023.00015.
8. Mohamed Abdelrahem, Christoph Hackl, Ralph Kennel. Application of extended Kalman filter to parameter estimation of doubly-fed induction generators in variable-speed wind turbine systems. 5th International Conference on Clean Electrical Power (ICCEP 2015), Taormina, Italy, 16-18 June 2015. Pp. 226-233. DOI: https://doi.org/10.1109/ICCEP.2015.7177628.
9. Saidi Omar, Djadi Hammou, Yazid Krim, Menaa Mohamed. Application of the extended Kalman filter to the parameters estimation in the vector control of the BDFIG. IEEE Smart Energy Grid Engineering (SEGE), Oshawa, Ontario, Canada, 21-24 August 2016. Pp. 208-214. DOI: https://doi.org/10.1109/SEGE.2016.7589527.
10. Mohamed Abdelrahem, Christoph Hackl, Ralph Kennel. Sensorless control of doubly-fed induction generators in vari-able-speed wind turbine systems. 5th International Conference on Clean Electrical Power (ICCEP 2015), Taormina, It-aly, 16-18 June 2015. Pp. 406-413. DOI: https://doi.org/10.1109/ICCEP.2015.7177656.
11. Rui Fan, Zhenyu Huang, Shaobu Wang, Ruisheng Diao, Da Meng. Dynamic state estimation and parameter calibration of a DFIG using the ensemble Kalman filter. IEEE Power & Energy Society General Meeting, Denver, Colorado, USA, 26-30 July 2015. DOI: https://doi.org/10.1109/PESGM.2015.7285990.
12. Mridul Kanti Malakar, Praveen Tripathy, Srinivasan Krishnaswamy. State estimation of DFIG using an Extended Kalman Filter with an augmented state model. Eighteenth National Power Systems Conference (NPSC), Guwahati, India, 18-20 December 2014. DOI: https://doi.org/10.1109/NPSC.2014.7103891.
13. Sayyed Ali Akbar Shahriari, Mahdi Raoofat, Mohammad Mohammadi, Maryam Dehghani, Maarouf Saad. Dynamic state estimation of a doubly fed induction generator based on a comprehensive nonlinear model. Simulation Modelling Prac-tice and Theory. 2016. Vol. 69. Pp. 92-112. DOI: https://doi.org/10.1016/j.simpat.2016.09.005.
14. Shenglong Yu, Kianoush Emami, Tyrone Fernando, Herbert H.C. Iu, Kit Po Wong. State Estimation of Doubly Fed In-duction Generator Wind Turbine in Complex Power Systems. IEEE Transactions on Power Systems. 2016. Vol. 31. Issue 6. Pp. 4935-4944. DOI: https://doi.org/10.1109/TPWRS.2015.2507620.
15. Hossein Madadi Kojabadi, Liuchen Chang. Online induction motor rotor time constant estimation using perturbation-based extremum seeking control. International Journal of Power Electronics and Drive Systems (IJPEDS). 2022. Vol. 13. No 3. Pp. 1459–1468. DOI: https://doi.org/10.11591/ijpeds.v13.i3.pp1459-1468.
16. Diachenko G., Schullerus G., Dominic A., Aziukovskyi O. Energy-efficient predictive control for field-orientation induc-tion machine drives. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2020. Vol. 6. Pp. 61-67. DOI: https://doi.org/10.33271/nvngu/2020-6/061.
17. Mohammad Hazzaz Mahmud, Yuheng Wu, Yue Zhao. Extremum Seeking-Based Optimum Reference Flux Searching for Direct Torque Control of Interior Permanent Magnet Synchronous Motors. IEEE Transactions on Transportation Electri-fication. 2020. Vol. 6. Issue 1. Pp. 41-51. DOI: https://doi.org/10.1109/TTE.2019.2962327.
18. Nannan Wang, Chaoying Xia. Research on the Optimal Control Strategy for the Maximum Torque per Ampere of Brush-less Doubly Fed Machines. Machines. 2023. Vol. 11. P. 422. DOI: https://doi.org/10.3390/machines11040422.
19. Quan Chen, Yaoyu Li, John E. Seem. Dual-loop self-optimizing robust control of wind power generation with Doubly-Fed Induction Generator. ISA Transactions. 2015. Vol. 58. Pp. 409-420. DOI: https://doi.org/10.1016/j.isatra.2015.04.009.
20. Abdelfatah Khatir, Abdelhak Dida, Badreddine Babes, Fahad Albalawi, Yayehyirad Ayalew Awoke. Particle swarm op-timization of synergetic controller and sliding mode extreme seeking controller for wind power generation system. Scien-tific Reports. 2025. Vol. 15. Article no 39613. DOI: https://doi.org/10.1038/s41598-025-23291-6.
21. Kliuiev O.V., Sadovoi O.V., Sokhina Yu.V., Zhydko Yu.O. Statistical analysis of asynchronous machine current with relay-vector control system. Zbirnyk Naukovyh Prats Dniprovskogo Derzhavnoho Tekhnichnoho Universytetu (technical sciences). 2024. Vyp. 1(44). Pp. 99-108. DOI: https://doi.org/10.31319/2519-2884.44.2024.12. (Ukr)
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