In this paper, the problem of distributed power losses minimization in islanded distribution systems is dealt with. The problem is formulated in a very simple manner and a solution is reached after a few iterations. The considered distribution system, a microgrid, will not need large bandwidth communication channels, since only closeby nodes will exchange information. The correction of generated active powers is possible by means of the active power losses partition concept that attributes a portion of the overall power losses in each branch to each generator. The experimental part shows the first results of the proposed method on an islanded microgrid. Simulation results of the distributed algorithm are compared to a centralized Optimal Power Flow approach and very small errors can be observed.