Mathematical study of very high voltage power networks I: The optimal DC power flow problem

J. Frederic Bonnans (1)

1 PROMATH - Mathematical Programming

The optimal power flow problem consists in setting the voltage and power delivered at the nodes of an electrical network, in order to minimize the loss of power over the lines. This paper is the first of a series dedicated to the mathematical study of this problem, based on an asymptotic analysis, in which the small parameter is the inverse of the reference voltage of the network. We call this scheme the very high voltage approximation. Here we deal with the case of direct current. We obtain an analytic expansion for the optimal value and the solution.

Mots clés: ELECTRICAL NETWORKS; NONLINEAR OPTIMIZATION; ASYMPTOTIC ANALYSIS; SENSITIVITY ANALYSIS; EXPANSION OF SOLUTIONS; DIRECTIONAL CONSTRAINT QUALIFICATION

Domaines: Autre [cs.OH]; Optimisation et contrôle [math.OC]

J. Frederic Bonnans. Mathematical study of very high voltage power networks I: The optimal DC power flow problem. [Research Report] RR-2408, INRIA. 1994. ⟨inria-00074267⟩