Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2009 | 19 | 4 | 661-673
Tytuł artykułu

The steady-state impedance operator of a Linear Periodically Time-Varying one-port network and its determination

Treść / Zawartość
Warianty tytułu
Języki publikacji
The main subject of the paper is the description and determination of the impedance operator of a linear periodically timevarying (LPTV) one-port network in the steady-state. If the one-port network parameters and the supply vary periodically with the same period, the network reaches a periodic steady state. However, the sinusoidal supply may induce a nonsinusoidal voltage or current. It is impossible to describe such a phenomenon by means of one complex number. A periodically time-varying one-port network working in a steady-state regime can be described with a circular parametric operator. Within the domain of discrete time, such an operator takes the form of a matrix with real-valued entries. The circular parametric operator can be transformed into the frequency domain using a two-dimensional DFT. This description makes it possible to quantitatively assess LPTV system input and output harmonics aliasing. The paper also presents the derivation and the proof of convergence of an iteration scheme for the identification of circular parametric operators. The scheme may be used to determine the impedance of an LPTV one-port network. Some results of computer simulations are shown.
Opis fizyczny
  • Institute of Electrical Metrology, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
  • Bittanti, S. and Colaneri, P. (1999). Periodic Control. John Wiley Encyclopedia of Electrical and Electronic Engineering, Wiley, New York, NY.
  • Bittanti, S. and Colaneri, P. (2000). Invariant representations of discrete-time periodic systems, Automatica 36(12): 1777-1793.
  • Bru, R., Romero, S. and Sanchez, E. (2004). Structural properties of positive periodic discrete-time linear systems: Canonical forms, Applied Mathematics and Computation 153(3): 697-719.
  • Chen, T. and Qiu, L. (1997). Linear periodically time-varying discrete-time systems: Aliasing and LTI approximations, Systems and Control Letters 30(5): 225-235.
  • Doroslovacki, M., Fan, H. and Yao, L. (1998). Wavelet-based identification of linear discrete-time systems: Robustness issue, Automatica 34(12): 1637-1640.
  • Hu, S., Meinke, K., Chen, R. and Huajiang, O. (2007). Iterative estimators of parameters in linear models with partially variant coefficients, International Journal of Applied Mathematics and Computer Science 17(2): 179-187.
  • Kaczorek, T. (2001). Externally and internally positive timevarying linear systems, International Journal of Applied Mathematics and Computer Science 11(4): 957-964.
  • Kłosiński, R. (2005). Application of an identification algorithm for optimal control of compensation circuits, Proceedings of the International Conference on Power Electronics and Intelligent Control for Energy Conservation, PELINCEC 2005, Warsaw, Poland, pp. 1-6.
  • Kłosiński, R. (2006). Periodically time-varying two-terminals at a steady state, description and identification, Proceedings of the 13th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2006, Nice, France, pp. 284-287.
  • Kłosiński, R. (2007). Periodically variable two-terminal impedance description and measuring methods, Metrology and Measurement Systems 14(2): 375-390.
  • Kłosiński, R. and Kozioł, M. (2007). Reconstruction of nonlinearly deformed periodic signals using inverse circular parametric operators, Proceedings of the IEEE Instrumentation and Measurement Technology Conference, IMTC 2007, Warsaw, Poland, pp. 1-6.
  • Liu, K. (1997). Identification of linear time-varying systems, Journal of Sound and Vibration 204(4): 487-505.
  • Liu, K. (1999). Extension of modal analysis to linear time-varying systems, Journal of Sound and Vibration 226(1): 149-167.
  • Liu, K. and Deng, L. (2005). Experimental verification of an algorithm for identification of linear time-varying systems, Journal of Sound and Vibration 279(1): 1170-1180.
  • Mehr, A. S. and Chen, T. (2002). Representations of linear periodically time-varying and multirate systems, IEEE Transactions on Signal Processing 50(9): 2221-2229.
  • Liu, M., Tse, C. K. and Wu, J. (2003). A wavelet approach to fast approximation of steady-state waveforms of power electronics circuits, International Journal of Circuit Theory and Applications 31(6): 591-610.
  • Meyer, C. D. (2000). Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, PA.
  • Meyer, R. A. and Burrus, C. S. (1975). A unified analysis of multirate and periodically time-varying digital filters, IEEE Transactions on Circuits and Systems 22(3): 162-168.
  • Mikołajuk, K. and Staroszczyk, Z. (2003). Time-frequency approach to analysis of time varying dynamic systems, Przegląd Elektrotechniczny 79(10): 764-767.
  • Mikołajuk, K. and Staroszczyk, Z. (2004). Periodical variability in power systems: Small-signal models, L'Energia Electtrica 81(5-6): 97-102.
  • Shenoy, R. G., Burnside, D. and Parks, T. (1994). Linear periodic systems and multirate filter design, IEEE Transactions on Signal Processing 42(9): 2242-2256.
  • Siwczyński, M. (1987). Analysis of nonlinear systems with concentrated and distributed parameters by a new numerical operator method in time and frequency domain, Proceedings of Internationales Wissenschaftliches Kolloquium 1987, Ilmenau, Germany, pp. 759-762.
  • Siwczyński, M. (1995). Optimization Methods in Power Theory of Electrical Networks, Monograph No. 183, Cracow University of Technology, Cracow, (in Polish).
  • Siwczyński, M. and Kłosiński, R. (1997a). Current and voltage wave-form optimization with non-linear deformations for real voltage sources, COMPEL 16(2): 71-83.
  • Siwczyński, M. and Kłosiński, R. (1997b). Synthesis of linear inertialless periodically time varying circuits for optimal compensation of non-linear distortions, Proceedings of the 9th International Symposium on Theoretical Electrical Engineering, ISTET'97, Palermo, Italy, pp. 560-563.
  • Siwczyński, M., Pasko, M. and Kłosiński, R. (1993). Current minimization of the non-ideal voltage source with periodically time-varying parameters by means of an active compensator, Applied Mathematics and Computer Science 3(2): 329-340.
  • Staroszczyk, Z. (2002). Power system nonstationarity and accurate power system identification procedures, Proceedings of the International Conference on Harmonics and Quality of Power, Rio de Janeiro, Brasil, pp. 1-8.
  • Staroszczyk, Z. and Mikołajuk, K. (2004). Periodically time variance power systems impedance-Description and identification, Przegląd Elektrotechniczny 80(6): 521-526.
  • Tam, K. C., Wong, S. C. and Tse, C. K. (2006). A wavelet-based piecewise approach for steady-state analysis of power electronics circuits, International Journal of Circuit Theory and Applications 34(5): 559-582.
  • Verhagen, M. and Yu, X. (1995). A class of subspace model identification algorithms to identify periodically and arbitrarily time-varying systems, Automatica 31(2): 201-216.
  • Zadeh, L. A. (1950). Frequency analysis of variable networks, Proceedings of the Institute of Radio Engineers 38: 291-299.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.