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

The optimal power flow problem involves 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. We use 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.