optimizing investment of pumped hydro storage system for renewable energy future

Renewable energies are increasingly being considered for use in electricity networks. the high variability of consumption, and the instability of renewable energies, necessitate the use of energy storage systems. the problem of optimizing investment for an energy storage system is formulated here. the proposed model, in particular, determines the optimal size of the energy storage system based on maximizing social welfare. the problem is formulated as a mixed-integer linear programming (milp), and an equivalent mixed complementary problem (mcp) to solve a quadratic system of nonlinear equations. due to its high efficiency, the benders decomposition technique is used to solve the proposed model. the results of solving a 300-node system that cannot be solved by cplex using the benders decomposition technique are presented. the results demonstrate that the proposed method can efficiently find a solution while considering the network rsquo;s limitations, increasing social welfare. finally, the performance of the milp and mcp models for various numerical cases is compared. the findings of this paper indicate that by increasing the dimensions of the problem, the performance of the mcp model improves compared to the milp model in terms of computational time and the value of the objective function.