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The load flow equations for a 3-node electrical power system. (English) Zbl 0506.90023


MSC:

90B10 Deterministic network models in operations research
90B99 Operations research and management science
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
34C25 Periodic solutions to ordinary differential equations

Citations:

Zbl 0506.90024
Full Text: DOI

References:

[1] Arapostathis, A.; Sastry, S.; Varaiya, P., Analysis of the power flow equation, (Memorandum No. UCB/ERL M80/35 (August, 1980), Electronics Research Laboratory, College of Engineering, University of California: Electronics Research Laboratory, College of Engineering, University of California Berkeley) · Zbl 0494.70027
[2] Arapostathis, A.; Varaiya, P., The behavior of three node power networks, (Memorandum No. UCB/ERL 81/77 (September, 1981), Electronics Research Laboratory, College of Engineering, University of California: Electronics Research Laboratory, College of Engineering, University of California Berkeley) · Zbl 0494.70027
[3] Baillieul, J.; Byrnes, C. I., A geometric problem in electric energy system, (Int. Symp. on Mathematical Theory of Networks and Systems, Vol. 4 (August 1981), Western Periodicals Co: Western Periodicals Co N. Hollywood, CA) · Zbl 0506.90024
[4] Baillieul, J.; Byrnes, C. I.; Washburn, R. B., An algebraic-geometric and topological analysis of the solutions to the load-flow equations for a power system, (20-th IEEE Conference on Decision and Control (1981)), 1312-1320 · Zbl 0507.58032
[5] Baillieul, J.; Byrnes, C. I., Geometric critical point analysis of lossless power system models, IEEE Trans. Circuits and Systems (November, 1982), Special Issue on Power Systems · Zbl 0523.93046
[6] Baillieul, J.; Byrnes, C. I., The singularity theory of the load flow equations for a 3-node electrical power system, Syst. Control Lett., 2, 330-340 (1983), (this issue) · Zbl 0506.90024
[7] J. Baillieul and C.I. Byrnes, A Bezout theorem for intersections with linear components with applications to an electrical network problem, to appear.; J. Baillieul and C.I. Byrnes, A Bezout theorem for intersections with linear components with applications to an electrical network problem, to appear.
[8] Desoer, C.; Kuh, E., Basic Circuit Theory (1969), McGraw-Hill: McGraw-Hill New York
[9] Gross, G. A., Power Systems Analysis (1979), John Wiley and Sons: John Wiley and Sons New York
[10] Korsak, A. J., On the question of uniqueness of stable load flow solutions, IEEE Trans. Power Apparatus and Systems, 91, 1093-1100 (1972)
[11] Luders, G. A., Transient stability of multimachine power systems via the direct method of Lyapunov, IEEE Trans. Power Apparatus and Systems, 90, 23-36 (1971)
[12] Milnor, J., Morse Theory (1983), Princeton University Press: Princeton University Press Princeton, NJ
[13] Milnor, J., Topology from a Differentiable Viewpoint (1965), University Press of Virginia: University Press of Virginia Charlottesville, VA · Zbl 0136.20402
[14] Tavora, C. J.; Smith, O. J.M., Equilibrium analysis of power systems, IEEE Trans. Power Apparatus and Systems, 91, 1131-1137 (1972)
[15] Van der Waerden, B. L., Einfuhrung in die algebraische Geometrie, (Grundl. der math. Wissenschaften, 51 (1973), Springer: Springer New York) · Zbl 0061.32303
[16] Van der Waerden, B. L., (Modern Algebra, Vol. 1 (1950), Frederick Ungar: Frederick Ungar New York) · Zbl 0037.01903
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