This paper is the second of a series dedicated to the mathematical study of very high voltage power networks, based on an asymptotic analysis, in which the square root of one of the small parameters is the inverse of the reference voltage of the network. We call this scheme the very high voltage approximation. We show that the active and reactive parts of the limit problem are decoupled. We give an analytic expansion for the solution of the problem, and prove the convergence of two decoupled numerical algorithm.