One of the key factors in the establishment of power plants is proper location, which entails addressing various criteria. Power plant establishment operations are included in the fundamental designs; in turn, comprehensive studies in this field seem to be a prerequisite. The most important innovation of the present study consists of applying the robust bi-level programming technique and game theory (Stackelberg competition) for locating renewable energy sites. Robust stochastic method is implemented for the robustification of the model against variations (eg, noise and perturbation) and uncertain conditions. The Karush-Kuhn-Tucker (KKT) method is used for solving bi-level programming. The obtained results reveal that the incorporation of uncertainties can enhance energy generation and supplier's profit. Furthermore, the objective functions of the proposed model are compared with those under conditions without uncertainties. A sensitivity analysis of major parameters is performed to validate the proposed model. By increasing uncertainty, generated energy decrease, and supplier's profit increase. The supplier's profit gradually diminishes by raising the discounting rate. Moreover, as scale of problems increases, the generated energy and supplier's profit are boosted.