Voltage stability-constrained robust transmission expansion planning using binary discretization technique

Due to a persistent increase in electricity demand and the growing integration of renewable energy sources (RESs), power systems are now operating with narrower stability margins. Consequently, it becomes imperative to consider security criteria in planning studies to maintain a sufficient loading margin. This paper presents a tri-level robust transmission expansion planning (TEP) problem, in which, unlike the existing robust models that only optimize the operation cost in the third level, both operation cost and voltage stability margin (VSM) are optimized simultaneously. The third level is formulated as a bi-level model with an upper level aimed at minimizing the operation cost minus the weighted VSM, while the lower level evaluates the VSM. The duality theorem transforms the bi-level model into a single-level one, leading to an adaptive robust optimization (RO) with bilinear terms in the third level. The binary discretization and big-M techniques are employed to linearize the third level, which yields an adaptive RO with mixed-integer recourse. Due to integer variables in the third level, a nested column and constraint generation (NCCG) is employed to solve the tri-level structure. The effectiveness of the proposed approach is demonstrated through an application on the two standard systems.