Three-Time-Scale Singular Perturbation Stability Analysis of Three-Phase Power Converters
This paper analyzes the stability of the well‐known three‐phase two‐level power converter. Focusing on the rectifier operating mode, the dynamics of the system, when the instantaneous power and dc‐link voltage controllers are included, are described by a set of complex equations that results in a no...
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| Vydáno v: | Asian journal of control Ročník 16; číslo 5; s. 1361 - 1372 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Hoboken
Blackwell Publishing Ltd
01.09.2014
Wiley Subscription Services, Inc |
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| ISSN: | 1561-8625, 1934-6093 |
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| Abstract | This paper analyzes the stability of the well‐known three‐phase two‐level power converter. Focusing on the rectifier operating mode, the dynamics of the system, when the instantaneous power and dc‐link voltage controllers are included, are described by a set of complex equations that results in a nonlinear autonomous singularly perturbed system. Hence, the closed‐loop system can be studied under the assumption of separate time scales. The analysis proposed in this work follows a novel three‐time‐scale approach, where the fast time scale corresponds with the instantaneous power dynamics, the mid‐range time scale is related to the dc‐link voltage dynamics, and the slow time scale is associated with the dc‐link voltage regulator dynamics. In this way, the analysis leads to the decomposition of the closed‐loop system into three simpler subsystems: fast, medium, and slow subsystems. These subsystems approximate the closed‐loop system behavior over the three different time scales. Finally, since the equilibrium point of each subsystem is exponentially stable and some other conditions are satisfied, it is shown that the equilibrium point of the closed‐loop system also presents exponential stability. Experimental results for a synchronous three‐phase power rectifier prototype are included to corroborate the analysis carried out. |
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| AbstractList | This paper analyzes the stability of the well-known three-phase two-level power converter. Focusing on the rectifier operating mode, the dynamics of the system, when the instantaneous power and dc-link voltage controllers are included, are described by a set of complex equations that results in a nonlinear autonomous singularly perturbed system. Hence, the closed-loop system can be studied under the assumption of separate time scales. The analysis proposed in this work follows a novel three-time-scale approach, where the fast time scale corresponds with the instantaneous power dynamics, the mid-range time scale is related to the dc-link voltage dynamics, and the slow time scale is associated with the dc-link voltage regulator dynamics. In this way, the analysis leads to the decomposition of the closed-loop system into three simpler subsystems: fast, medium, and slow subsystems. These subsystems approximate the closed-loop system behavior over the three different time scales. Finally, since the equilibrium point of each subsystem is exponentially stable and some other conditions are satisfied, it is shown that the equilibrium point of the closed-loop system also presents exponential stability. Experimental results for a synchronous three-phase power rectifier prototype are included to corroborate the analysis carried out. [PUBLICATION ABSTRACT] This paper analyzes the stability of the well‐known three‐phase two‐level power converter. Focusing on the rectifier operating mode, the dynamics of the system, when the instantaneous power and dc‐link voltage controllers are included, are described by a set of complex equations that results in a nonlinear autonomous singularly perturbed system. Hence, the closed‐loop system can be studied under the assumption of separate time scales. The analysis proposed in this work follows a novel three‐time‐scale approach, where the fast time scale corresponds with the instantaneous power dynamics, the mid‐range time scale is related to the dc‐link voltage dynamics, and the slow time scale is associated with the dc‐link voltage regulator dynamics. In this way, the analysis leads to the decomposition of the closed‐loop system into three simpler subsystems: fast, medium, and slow subsystems. These subsystems approximate the closed‐loop system behavior over the three different time scales. Finally, since the equilibrium point of each subsystem is exponentially stable and some other conditions are satisfied, it is shown that the equilibrium point of the closed‐loop system also presents exponential stability. Experimental results for a synchronous three‐phase power rectifier prototype are included to corroborate the analysis carried out. |
| Author | Umbría, Francisco Gordillo, Francisco Salas, Francisco Aracil, Javier Sánchez, Juan Antonio |
| Author_xml | – sequence: 1 givenname: Francisco surname: Umbría fullname: Umbría, Francisco – sequence: 2 givenname: Javier surname: Aracil fullname: Aracil, Javier – sequence: 3 givenname: Francisco surname: Gordillo fullname: Gordillo, Francisco – sequence: 4 givenname: Francisco surname: Salas fullname: Salas, Francisco – sequence: 5 givenname: Juan Antonio surname: Sánchez fullname: Sánchez, Juan Antonio |
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| Cites_doi | 10.1109/TPEL.2008.2004272 10.1109/TIE.2010.2049719 10.1016/S0378-4754(03)00069-7 10.1109/TIE.2008.917113 10.1016/j.conengprac.2011.05.008 10.1109/TPEL.2003.810862 10.1137/1.9781611971118 10.1111/j.1934-6093.2005.tb00390.x 10.1109/TIA.1984.4504460 10.1002/asjc.586 10.1109/TIE.2006.882025 10.1109/TCST.2010.2043105 10.1109/63.554176 10.1109/MED.2010.5547605 10.1109/TIE.2007.893162 10.1109/TIE.2004.825278 10.1007/BF01599620 10.1109/TII.2011.2134856 |
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Eck, "A hierarchical controller for miniature VTOL UAVs - design and stability analysis using singular perturbation theory," Control Eng. Pract., Vol. 19, No. 10, pp. 1099-1108 (2011). Karimi, H. R. and M. J. Yazdanpanah, "Robust control for a class of uncertain state-delayed singularly perturbed systems," Asian J. Control, Vol. 7, No. 2, pp. 202-208 (2005). Kouro, S., M. Malinowski, K. Gopakumar, J. Pou, L. G. Franquelo, B. Wu, J. Rodríguez, M. A. Pérez, and J. I. León, "Recent advances and industrial applications of multilevel converters," IEEE Trans. Ind. Electron., Vol. 57, No. 8, pp. 2553-2580 (2010). Desoer, C. A. and S. M. Shahruz, "Stability of nonlinear systems with three time scales," Circuits Syst. Signal Process, Vol. 5, No. 4, pp. 449-464 (1986). Blasko, V. and V. Kaura, "A new mathematical model and control of a three-phase ac-dc voltage source converter," IEEE Trans. Power Electron., Vol. 12, No. 1, pp. 116-123 (1997). Tikhonov, A. N., "Systems of differential equations containing small parameters in the derivatives," Matem. Sb., Vol. 31-73, No. 3, pp. 575-586 (1952). Esteban, S., Three-Time-Scale Nonlinear Control of an Autonomous Helicopter on a Platform, Ph.D. Thesis, University of Seville, Seville, Spain (2011). Mohan, N., T. M. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications, and Design (3rd edition), John Wiley & Sons, Hoboken, NJ (2003). Vázquez, S., J. A. Sánchez, J. M. Carrasco, J. I. León, and E. Galván, "A model-based direct power control for three-phase power converters," IEEE Trans. Ind. Electron., Vol. 55, No. 4, pp. 1647-1657 (2008). Portillo, R. C., M. M. Prats, J. I. León, J. A. Sánchez, J. M. Carrasco, E. Galván, and L. G. Franquelo, "Modeling strategy for back-to-back three-level converters applied to high-power wind turbines," IEEE Trans. Ind. Electron., Vol. 53, No. 5, pp. 1483-1491 (2006). 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(e_1_2_10_4_1) 1967 e_1_2_10_2_1 e_1_2_10_19_1 e_1_2_10_6_1 e_1_2_10_16_1 e_1_2_10_5_1 e_1_2_10_14_1 e_1_2_10_7_1 Mohan N. (e_1_2_10_13_1) 2003 e_1_2_10_15_1 e_1_2_10_9_1 e_1_2_10_10_1 e_1_2_10_11_1 Tikhonov A. N. (e_1_2_10_3_1) 1952; 31 Umbría F. (e_1_2_10_18_1) 2009 Esteban S. (e_1_2_10_12_1) 2011 e_1_2_10_27_1 Naidu D. S. (e_1_2_10_8_1) 2002; 9 e_1_2_10_25_1 e_1_2_10_26_1 |
| References_xml | – reference: Kokotović, P., H. K. Khalil, and J. O'Reilly, Singular Perturbation Methods in Control. Analysis and Design, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (1999). – reference: Kazmierkowski, M. P., M. Jasinski, and G. Wrona, "DSP-based control of grid-connected power converters operating under grid distortions," IEEE Trans. Ind. Informat., Vol. 7, No. 2, pp. 204-211 (2011). – reference: Gusia, S., F. Labrique, D. Grenier, and H. Buyse, "Two time scale global dynamical modelling of power electronic systems," Math. Comput. Sim., Vol. 63, No. 3-5, pp. 225-236 (2003). – reference: Desoer, C. A. and S. M. Shahruz, "Stability of nonlinear systems with three time scales," Circuits Syst. Signal Process, Vol. 5, No. 4, pp. 449-464 (1986). – reference: Tikhonov, A. N., "Systems of differential equations containing small parameters in the derivatives," Matem. Sb., Vol. 31-73, No. 3, pp. 575-586 (1952). – reference: Chakrabortty, A. and E. Scholtz, "Time-scale separation designs for performance recovery of power systems with unknown parameters and faults," IEEE Trans. Control Syst. Technol., Vol. 19, No. 2, pp. 382-390 (2011). – reference: Kimball, J. W. and P. T. Krein, "Singular perturbation theory for dc-dc converters and application to PFC converters," IEEE Trans. Power Electron., Vol. 23, No. 6, pp. 2970-2981 (2008). – reference: Vázquez, S., J. A. Sánchez, J. M. Carrasco, J. I. León, and E. Galván, "A model-based direct power control for three-phase power converters," IEEE Trans. Ind. Electron., Vol. 55, No. 4, pp. 1647-1657 (2008). – reference: Escobar, G., A. M. Stanković, J. M. Carrasco, E. Galván, and R. Ortega, "Analysis and design of direct power control (DPC) for a three phase synchronous rectifier via output regulation subspaces," IEEE Trans. Power Electron., Vol. 18, No. 3, pp. 823-830 (2003). – reference: Malinowski, M., M. Jasinski, and M. P. Kazmierkowski, "Simple direct power control of three-phase PWM rectifier using space-vector modulation (DPC-SVM)," IEEE Trans. Ind. Electron., Vol. 51, No. 2, pp. 447-454 (2004). – reference: Khalil, H. K., Nonlinear Systems (3rd edition), Prentice Hall, Upper Saddle River, NJ (2002). – reference: Kouro, S., M. Malinowski, K. Gopakumar, J. Pou, L. G. Franquelo, B. Wu, J. Rodríguez, M. A. Pérez, and J. I. León, "Recent advances and industrial applications of multilevel converters," IEEE Trans. Ind. Electron., Vol. 57, No. 8, pp. 2553-2580 (2010). – reference: Portillo, R. C., M. M. Prats, J. I. León, J. A. Sánchez, J. M. Carrasco, E. Galván, and L. G. Franquelo, "Modeling strategy for back-to-back three-level converters applied to high-power wind turbines," IEEE Trans. Ind. Electron., Vol. 53, No. 5, pp. 1483-1491 (2006). – reference: Moreno-Valenzuela, J. and V. Santibáñez, "Robust saturated PI joint velocity control for robot manipulators," Asian J. Control, Vol. 15, No. 1, pp. 64-79 (2013). – reference: Kaplun, S., Fluid Mechanics and Singular Perturbations: a Collection of Papers, Academic Press, New York, NY (1967). – reference: Akagi, H., Y. Kanazawa, and A. Nabae, "Instantaneous reactive power compensators comprising switching devices without energy storage," IEEE Trans. Ind. Appl., Vol. IA-20, No. 3, pp. 625-630 (1984). – reference: Naidu, D. S., "Singular perturbations and time scales in control theory and applications: an overview," Dynam. Cont. Dis. Ser. B, Vol. 9, No. 2, pp. 233-278 (2002). – reference: Karimi, H. R. and M. J. Yazdanpanah, "Robust control for a class of uncertain state-delayed singularly perturbed systems," Asian J. Control, Vol. 7, No. 2, pp. 202-208 (2005). – reference: Bertran, S., N. Guénard, T. Hamel, H. Piet-Lahanier, and L. Eck, "A hierarchical controller for miniature VTOL UAVs - design and stability analysis using singular perturbation theory," Control Eng. 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| Snippet | This paper analyzes the stability of the well‐known three‐phase two‐level power converter. Focusing on the rectifier operating mode, the dynamics of the... This paper analyzes the stability of the well-known three-phase two-level power converter. Focusing on the rectifier operating mode, the dynamics of the... |
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| SubjectTerms | Closed loop systems Control systems singular perturbations Stability analysis three-phase two-level power converter three-time-scale approach |
| Title | Three-Time-Scale Singular Perturbation Stability Analysis of Three-Phase Power Converters |
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