A game-theoretic model for wind farm planning problem: A bi-level stochastic optimization approach

As the electric network progressively shifts away from fossil fuel-fired generators to inverter-based generators, including most renewable energy sources (RESs), considering the system strength measure in the planning and operation problems is essential to maintaining the power system stability. To this end, this paper aims to introduce a new game-based bi-level framework for the wind farm planning problem (WFPP). The upper level seeks to maximize each investor's profit, and the lower level aims to clear the electricity market by considering the optimal investment decisions of investors. One innovative contribution of this paper is to incorporate the equivalent short circuit ratio (ESCR) as an indicator for the system strength measure in the WFPP. The bi-level model is converted into its equivalent single-level mixed-integer linear programming (MILP) employing the Karush-Kuhn-Tucker (KKT) conditions and strong duality theorem. This will yield a generalized Nash equilibrium problem (GNEP) containing binary decision variables, which is further transformed into a MILP. The intermittency of wind-demand scenarios is considered in the mathematical formulation of the presented bi-level model through scenario-based stochastic programming. Numerical studies are carried out to validate the effectiveness of the proposed model.