caa a22 4500 475750292 CHVBK 20180406123521.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1023/A:1008781604329 doi (NATIONALLICENCE)springer-10.1023/A:1008781604329 Bonnans J. INRIA, B.P. 105, 78153, Rocquencourt, France aut Mathematical Study of Very High Voltage Power Networks III: The Optimal AC Power Flow Problem [Elektronische Daten] [J. Bonnans] This paper shows how to apply the perturbation theory for nonlinear programming problems to the study of the optimal power flow problem. The latter is the problem of minimizing losses of active power over a very high voltage power networks. In this paper, the inverse of the square root of the reference voltage of the network is viewed as a small parameter. We call this scheme the very high voltage approximation. After some proper scaling, it is possible to formulate a limiting problem, that does not satisfy the Mangasarian-Fromovitz qualification hypothesis. Nevertheless, it is possible to obtain under natural hypotheses the second order expansion of losses and first order expansion of solutions. The latter is such that the computation of the active and reactive parts are decoupled. We also obtain the high order expansion of the value function, solution and Lagrange multiplier, assuming that interactions with the ground are small enough. Finally we show that the classical direct current approximation may be justified and improved using the framework of very high voltage approximation. Kluwer Academic Publishers, 2000 electrical networks nationallicence very high voltage nationallicence active-reactive decoupling nationallicence asymptotic analysis nationallicence optimization with perturbations nationallicence sensitivity analysis nationallicence expansion of solutions nationallicence critical point nationallicence constrained optimization nationallicence Computational Optimization and Applications Kluwer Academic Publishers 16/1(2000-04-01), 83-101 0926-6003 16:1<83 2000 16 10589 https://doi.org/10.1023/A:1008781604329 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008781604329 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bonnans J. INRIA, B.P. 105, 78153, Rocquencourt, France aut NATIONALLICENCE 773 0- Computational Optimization and Applications Kluwer Academic Publishers 16/1(2000-04-01), 83-101 0926-6003 16:1<83 2000 16 10589 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer