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An affine geometrical approach to power systems problems
Power Plants and Power Systems Control, Volume # 5 | Part# 1
Location: Ecole Nationale Superieure en Genie des Systemes Industriels, Canada
National Organizing Committee Chair: Rosehart, W.,
Kennedy, W.
International Program Committee Chair: Malik, Om P.,
Lerch, Edwim
Conference Editor: Rosehart, W.,
Malik, Om P.
Authors
Crainic, Emmanuel D.; Petroianu, Alexander I.
Digital Object Identifier (DOI)
10.3182/20060625-4-CA-2906.00023
Page Numbers:
101-106
Index Terms
affine geometry,affine transformations,linear methods,algebraic and geometric invariants,power systems load flow
Abstract
The paper introduces modern concepts and tools from affine geometry into power system analysis. It is shown that such an approach allows: i) a new non linear formulation of such classical problems as load flow and state estimation, ii) a more efficient way of solving such problems through non iterative methods. The new approach is illustrated for a small but representative example of a load flow for a two-bus network.
References
[1] Beklémichev, D.V. (1988). Cours de géométrie
analytique et d'algèbre linéaire. Éditions Mir,
Moscou.
[2] Debs, A.S. (1988). Modern Power Systems Control
and Operation. Kluwer Academic, Boston.
[3] Delode, C. (2000). Géométrie affine et euclidienne.
Dunod, Paris.
[4] Eremia, M., J. Trecat and A. Germond (2000).
Réseaux Électriques: aspects actuels. Editura
Technique, Bucuresti.
[5] Klein, F. (1974). Le Programme d'Erlangen. Éditions
Jacques Gabay, Paris.
[6] Klein, F. (2004). Elementary Mathematics from an
Advanced Standpoint: Geometry". Dover
Publications, Mineola, New York.
[7] Möbius, A.F. (1827). Der barycentrische Calcül: ein
neues Hilfsmittel zur analytischen Behandlung
der Geometrie, Leipzig.
[8] Petroianu, P.I. (1969). A Geometrical Approach to
the Steady State Problem of Electrical Networks.
Rev. Roum. Sci. Techn.-Electrotechn. Et Energ.,
Vol. 14, No. 4, 623-630.