Power networks - Methods for solving equations

Solving the equations of a power network, known as network calculation or distribution calculation, makes it possible to determine the state of this network, given the power injected. On the face of it, it's a very simple problem: solving a system of non-linear equations whose statement can be condensed into three lines.

The reality is quite different: we're only interested in one of the system's solutions, which, when it exists, is located in a restricted domain that can be practically applied; numerous automatic processes complicate modeling; above all, high execution speed is essential, as we can have a very large number of problems to solve in real time within very tight deadlines. On this last point, as luck would have it, the system is very hollow, so that the techniques for calculating networks and hollow matrices have evolved together, helping each other.

The interpenetration of these techniques is evident throughout this presentation, which has been ordered progressively, in order of increasing difficulty: after situating the problem 1 , we present its statement and the principle of its solution 2 , disregarding the complexity just mentioned. Next, a reminder of the main results of hollow matrix techniques 3 introduces the central part of the presentation: the algorithms for solving the classical distribution calculus