This article addresses the optimal distributed energy resources (DER) allocation and sizing into an LV distribution network (DN) considering demand response (DR) and high penetration of plug-in electric vehicles (PEV) in a two-stage stochastic programming framework. The model includes (i) economic variables related to the capital cost of the DERs capacity installed with their respective operational costs and (ii) operational technical constraints based on the AC power flow equations. The formulation estimates the distributed generation (DG) capacity in terms of apparent power, i.e., the capacity found by the model relates the active and reactive power injected from DG to the DN simultaneously. A linearization and a modified version of the genetic algorithm (GA) solve the mix-integer non-linear problem (MINLP), and the backward algorithm is applied to reduce the number of scenarios. The model is tested in the IEEE 69-bus system under 18 different scenarios of 24 h to measure the DERs capacity installed variability. Finally, the results showed that (i) the set of scenarios selected are decisive for the optimal capacity installed affecting the investment and the Grid dependence, (ii) the PEVs affect the total DERs capacity installed and the operation costs, and (iii) the reactive power provided by the DERs might supply the total reactive power demand.