Algoritmo Paralelo para o Cálculo de Autovalores Associado à Avaliação da Estabilidade a Pequenas Perturbações
Resumo
A avaliação da estabilidade a pequenas perturbações, em sistemas elétricos de potência de grande porte, é realizada pelo cálculo de autovalores dominantes de matrizes esparsas. Este trabalho apresenta melhorias significativas no algoritino paralelo, para o cálculo de autovalores dominantes, reportado em [1]. Os autovalores são calculados pelo algoritmo de Iterações Simultâneas, implementado num computador paralelo iPSC/860 da Intel. Resultados são apresentados para um modelo prático de sistema de potência, mostrando grandes “speed-ups” obtidos em computação paralela.
Referências
J.M. Campagnolo, N. Martins, J.L.R. Pereira, L.T.G. Lima, H.J.C.P. Pinto, and D.M. Falcão. Fast small-signal stability assessment using parallel processing. Paper No. 93 SM 481-2 PWRS,IEEE/PES, Winter Meeting, Vancouver, Canada, July 1993.
N. Martins. Efficient eigenvalue and frequency response methods applied to power system small-signal stability studies. IEEE Trans. on Power Systems, PWRS-1, No. 1:217-226, February 1986.
N. Martins, L.T.G. Lima, and H.J.C.P. Pinto. Efficient methods for finding transfer function zeros of power systems. IEEE Trans. on Power Systems, Vol.7, No. 3:1350-1361, August 1992.
P. Kundur, G.J. Rogers, D.Y. Wong, L. Wang, and M.G. Lauby. A comprehensive computer program package for small signal stability analysis of power systems. Paper No. 90 WM 007-5, IEEE/PES Winter Meeting, Atlanta; Georgia, 1990.
L. Wang and A. Semlyen. Application of sparse eigenvalue techniques to the small-signal stability analysis of large power systems. IEEE Trans. on Power Systems, PWRS-6, No. 6:635-642, May 1990.
L. Wang. Eigenvalue Analysis of Large Power Systems. PhD thesis, University of Toronto, 1991.
L.T.G. Lima. Estudo Comparativo dos Métodos Iterativos de Cálculo de Autovalores Aplicado ao Problema da Estabilidade a Pequenas Perturbações de Sistemas Elétricos de Potência. Master's thesis, COPPE/UFRJ, 1991.
An IEEE Committee Report by a Task Force of the Computer and Analytical Methods Subcommittee of the Power Systems Engineering Committee. Parallel processing in power systems computation. Paper No. 91 SM 503-3 PWRS, IEEE/PES, Summer Meeting, San Diego, CA, July 1991.
J.S. Chai and A. Bose. Bottlenecks in parallel algorithms for power system stability analysis. Paper No. 92 WM 285-7 PWRS, IEEE/PES, Winter Meeting, New York, NY, January 1992.
B.N. Datta. Parallel and large-scale matrix computations in control: some ideas. Linear Algebra and Its Applications, Vol.121:243-264, 1989.
H.Y. Chang and S. Utku. Applications of parallel processing in structural engineering. Parallel Processing in Computational Mechanics, Edited by Hojjat Adeli, Marcel Dekker Inc., 219-243, 1992.
A. Jennings and W.J. Stewart. Simultaneous iteration for partial eigensolution of real matrices. J. Inst. Maths. Applics., Vol.15:351-361, 1975.
W.J. Stewart and A. Jennings. A simultaneous iteration algorithm for real matrices. ACM Trans. on Mathematical Software, Vol.7, No.2:184-198, June 1981.
A. Jennings. Matriz Computation for Engineers and Scientists. Wiley, London, 1977.
J.H. Wilkinson. The Algebraic Eigenvalue Problem. Clarendon Press - Oxford, 1965.
B. Gao, G.K. Morison, and P. Kundur. Voltage stability evaluation using modal analysis. Paper No. 91 SM 420-0 PWRS, IEEE/PES, Summer Meeting, San Diego, CA, July 1991.
S. Utku, H.Y. Chang, M. Salama, and D. Rapp. Simultaneous iterations algorithm for general eigenvalue problems on parallel processors. In International Conference on Parallel Processing IEEE, pages 59-66, St. Charles, Illinois, August 1986.
U. Schendel. Introduction to Numerical Methods for Parallel Computers. Ellis Horwood Limited - Chichester, 1984.
B.T. Smith et al. Matriz Eigensystem Routines EISPACK Guide. Springer-Verlag, Berlin, 1974.
E. Anderson et al. LAPACK Users" Guide. Society for Industrial and Applied Mathematics, 1992.
G. Withers. Parallel programming on the iPSC/860 system. Proceedings of the fourth ISMM/IASTED International Conference on Parallel and Distributed Computing and Systems, ISBN: 0-88986-159-5:341-343, October 1991.
J. M. Ortega. Introduction to Parallel and Vector Solution of Linear Systems. Plenum Press, New York and London, 1988.
L.H. Bezerra. Andlise da Estabilidade de Sistemas de Potência de Grande Porte. PhD thesis, PUC/Rio de Janeiro, 1990.
G. Meurant. The evolution of scientific computing on parallel computers. In I Workshop of High Performance Scientific Computation, Rio de Janeiro, Brasil, Agosto 1992.
N. Martins. Efficient eigenvalue and frequency response methods applied to power system small-signal stability studies. IEEE Trans. on Power Systems, PWRS-1, No. 1:217-226, February 1986.
N. Martins, L.T.G. Lima, and H.J.C.P. Pinto. Efficient methods for finding transfer function zeros of power systems. IEEE Trans. on Power Systems, Vol.7, No. 3:1350-1361, August 1992.
P. Kundur, G.J. Rogers, D.Y. Wong, L. Wang, and M.G. Lauby. A comprehensive computer program package for small signal stability analysis of power systems. Paper No. 90 WM 007-5, IEEE/PES Winter Meeting, Atlanta; Georgia, 1990.
L. Wang and A. Semlyen. Application of sparse eigenvalue techniques to the small-signal stability analysis of large power systems. IEEE Trans. on Power Systems, PWRS-6, No. 6:635-642, May 1990.
L. Wang. Eigenvalue Analysis of Large Power Systems. PhD thesis, University of Toronto, 1991.
L.T.G. Lima. Estudo Comparativo dos Métodos Iterativos de Cálculo de Autovalores Aplicado ao Problema da Estabilidade a Pequenas Perturbações de Sistemas Elétricos de Potência. Master's thesis, COPPE/UFRJ, 1991.
An IEEE Committee Report by a Task Force of the Computer and Analytical Methods Subcommittee of the Power Systems Engineering Committee. Parallel processing in power systems computation. Paper No. 91 SM 503-3 PWRS, IEEE/PES, Summer Meeting, San Diego, CA, July 1991.
J.S. Chai and A. Bose. Bottlenecks in parallel algorithms for power system stability analysis. Paper No. 92 WM 285-7 PWRS, IEEE/PES, Winter Meeting, New York, NY, January 1992.
B.N. Datta. Parallel and large-scale matrix computations in control: some ideas. Linear Algebra and Its Applications, Vol.121:243-264, 1989.
H.Y. Chang and S. Utku. Applications of parallel processing in structural engineering. Parallel Processing in Computational Mechanics, Edited by Hojjat Adeli, Marcel Dekker Inc., 219-243, 1992.
A. Jennings and W.J. Stewart. Simultaneous iteration for partial eigensolution of real matrices. J. Inst. Maths. Applics., Vol.15:351-361, 1975.
W.J. Stewart and A. Jennings. A simultaneous iteration algorithm for real matrices. ACM Trans. on Mathematical Software, Vol.7, No.2:184-198, June 1981.
A. Jennings. Matriz Computation for Engineers and Scientists. Wiley, London, 1977.
J.H. Wilkinson. The Algebraic Eigenvalue Problem. Clarendon Press - Oxford, 1965.
B. Gao, G.K. Morison, and P. Kundur. Voltage stability evaluation using modal analysis. Paper No. 91 SM 420-0 PWRS, IEEE/PES, Summer Meeting, San Diego, CA, July 1991.
S. Utku, H.Y. Chang, M. Salama, and D. Rapp. Simultaneous iterations algorithm for general eigenvalue problems on parallel processors. In International Conference on Parallel Processing IEEE, pages 59-66, St. Charles, Illinois, August 1986.
U. Schendel. Introduction to Numerical Methods for Parallel Computers. Ellis Horwood Limited - Chichester, 1984.
B.T. Smith et al. Matriz Eigensystem Routines EISPACK Guide. Springer-Verlag, Berlin, 1974.
E. Anderson et al. LAPACK Users" Guide. Society for Industrial and Applied Mathematics, 1992.
G. Withers. Parallel programming on the iPSC/860 system. Proceedings of the fourth ISMM/IASTED International Conference on Parallel and Distributed Computing and Systems, ISBN: 0-88986-159-5:341-343, October 1991.
J. M. Ortega. Introduction to Parallel and Vector Solution of Linear Systems. Plenum Press, New York and London, 1988.
L.H. Bezerra. Andlise da Estabilidade de Sistemas de Potência de Grande Porte. PhD thesis, PUC/Rio de Janeiro, 1990.
G. Meurant. The evolution of scientific computing on parallel computers. In I Workshop of High Performance Scientific Computation, Rio de Janeiro, Brasil, Agosto 1992.
Publicado
07/09/1993
Como Citar
CAMPAGNOLO, Jorge M.; MARTINS, Nelson; PEREIRA, José L. R.; FALCÃO, Djalma M..
Algoritmo Paralelo para o Cálculo de Autovalores Associado à Avaliação da Estabilidade a Pequenas Perturbações. In: INTERNATIONAL SYMPOSIUM ON COMPUTER ARCHITECTURE AND HIGH PERFORMANCE COMPUTING (SBAC-PAD), 5. , 1993, Florianópolis/SC.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
1993
.
p. 562-576.
DOI: https://doi.org/10.5753/sbac-pad.1993.23059.
