On the solution of robust transmission expansion planning using duality theorem under polyhedral uncertainty set

Abstract

The solution techniques of tri-level robust optimization for large-scale power systems continue to remain as a great challenge. Existing techniques rely on using either Karush-Kuhn-Tucker (KKT) conditions or primal-dual (PD) formulation which leads to introduce new binary variables or bilinear terms. In doing so, a bilevel model is obtained which cannot be solved by KKT or PD due to the presence of binary variables and thus it is required to be solved using decomposition-based methods such as Benders decomposition or column-and-constraint generation algorithm. This paper aims at proposing a solution technique to deal with the robust transmission expansion planning problem where the lower level problem is replaced by its dual problem. The advantage of dualizing the lower level problem is that all the uncertain parameters are integrated into the objective function which can be further recast as a linear constraint. Afterwards, the polyhedron uncertainty set is handled using duality theory. Since neither binary variables nor bilinear terms are introduced in this approach, the lower level can be substituted using PD formulation rendering a single level mixed-integer linear programming problem. Numerical experiments on two test systems verify that the proposed model is superior compared with the existing techniques in terms of computational burden.