This paper approaches the minimal loss reconfiguration problem, taking into account the load variations of the systems, through a stochastic reconfiguration process. The Monte Carlo method is used to consider the natural load variation. A normal probability function is used to generate aleatory load levels in the nodes. The results of this work show the existence of a set of branches that are frequently eliminated. This generates a tree branch set that best represents the universal randomness of the load. We call it "Expected Branch Set (EBS)". The topology associated to the EBS coincides with that obtained using the average demand values. This makes it unnecessary to generate a considerable number of tests to find that topology that best considers the load variation. The proposed algorithm was applied to two test networks and to a large real network.