Bi-level linear programming based interval optimization for SCED in the presence of wind power uncertainty

Security constrained economic dispatch (SCED) is widely used in recent day-ahead market, especially when there is a large penetration of wind power in the power grid. In this work the wind generation uncertainty is modeled as an interval number, which leads to an interval optimal objective value (fuel costs) of the original SCED, as well as its interval optimal solution (each unit´s generation). In order to obtain the true upper and lower bound of the interval optimal objective value and solution, a bi-level programming model is initialized so that the combinatorial nature of bi-level programming can be observed through the study of the single-level reformulation obtained in replacing the inner level problem with its KKT condition. Furthermore, an important global approach encompassing mixed integer linear programming (MILP) is captured by the complementarity slackness constraints resulting from the KKT condition. Numerical results from a 118-bus test system containing 24 time periods verifies the effectiveness of this proposed method.