The optimal management of distributed energy resources is one of theexisting challenges for the deployment of microgrids. When microgrids op-erate under feeder flow control mode, trying to maintain a constant self-consumption, generators adapt their output power to compensate load andnon-dispatchable generation variations. So, due to the uncertainty, findingthe optimal operation point is an important task that can become complex.This paper proposes an optimal power flow problem formulation for feederflow controlled microgrids. It is formulated as a mixed integer second ordercone program considering the optimal power flow equations in its relaxedform and uncertainty by means of stochastic formulation. In addition, analgorithm is developed in order to find a feasible optimum solution of theoriginal non-relaxed problem. The proposed algorithm can also be used inother optimal power flow problems with the condition that they must usethe same relaxation. The algorithm is validated through the IEEE 33-Busdistribution test system.