Contents
In this paper, orthogonalisation of sparse matrices by a modified Given's method is discussed, a reordering policy to minimize fill-in is postulated and Shamanski's method is extended to orthogonalisation. The method so defined is compared to “Optimally Ordered Factorisation” as used at present for load-flow, economic-dispatch, short-circuit and state-estimation calculations. The comparison of efficiency (time), storage space required and accuracy shows that the method advocated here is often better.
Übersicht
In diesem Aufsatz wird die modifizierte Methode der Orthogonalisierung von Givens beschrieben, eine Umordnungs-Strategie zur Minimierung der aufgefüllten Matrix-Elemente festgelegt und die Methode von Shamanski für die Orthogonalisierung erweitert. Die so definierte Methode wird verglichen mit der optimal gezielten Faktorisierung, wie sie heutzutage für Lastfluß, Verbundbetrieb-Optimierung, Kurzschluß-und Zustandsberechnungen benutzt wird. Der Vergleich von Berechnungszeit, Speicherbedarf und Genauigkeit zeigt, daß die hier vorgeschlagene Methode öfters besser als die Faktorisierung ist.
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References
Wallach, Y.; Even, R.: Application of Newton's method to load-flow calculations, Proc. IEE, 114 (1967) 372–374
Dommel, R.; Tinney, W.: Optimal power-flow solutions. Trans: IEEE PAS-87 (1968) 1866–1876
Brown, H. E.: Solution of large networks by matrix methods New York: J. Wiley Inc. 1975
Takahashi, K.; Fagan, J.; Chen, M. S.: Formation of a sparse, bus-impedance matrix and its applications. PICA-Conf. 1973, 63–69
Schweppe, F.; Handschin, E.: Static state-estimation in power-systems. Proc. IEEE 62 (1974) 972–982
Tinney, W. F.; Walker, B.: Direct solution of sparse network equations by optimally ordered factorization. Proc. IEEE 55 (1967) 1801–1805
Tinney, W. F.; Hart, C. E.: Power flow solution by Newton'-method. Trans. IEEE PAS-86 (1967) 1449–1456
George, A.; Liu, J. W.: Computer Solution of Large Sparse Positive Definite Systems. Hemel Hauptstadt: Prentice-Hall 1981.
Stoer, J.; Bulirsch, R.: Einführung in die Numerische Mathematik Berlin, Heidelberg, New York: Springer 1976
Sameh, A.; Kuck, D.: On stable parallel linear system solvers. Assoc. Comput. Mach. 25 (1978) 91–91.
Freris, L. L.; Sasson, A. M.: Investigations on the load-flow problem, Proc. IEEE 115 (1968) 1459–1469
Gentleman, W. M.: Least-squares computations by Given's transformations without square-roots. J. Inst. Math. Appl. 12 (1973), 329–336
Orthega and Rheinboldt: Iterative solutions of nonlinear equations in several variables. New York: Academic-Press 1970.
Simões-Costa, A.; Quintana, V. H.: A robust numerical technique for power-system state-estimation. Trans. IEEE PAS-100 (1981) 691–698
Simões-Costa, A.; Quintana, V. H.: An orthogonal row-processing algorithm for powersystem sequential state-estimation. PES Winter Meeting 1981, paper 81WM023-1
Daniel, J. W. et al: Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR-factorization. Math. Comp. 30 (1976) 772–795.
Rutishauser, H.: Vorlesungen über Numerische Mathematik. Basel Birkhäuser, 1976
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Wallach, Y. Orthogonalisation for power-system computations. Archiv f. Elektrotechnik 67, 57–64 (1984). https://doi.org/10.1007/BF01574732
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DOI: https://doi.org/10.1007/BF01574732