Nodal Invulnerability Recovery Considering Power Generation Balance: A Bi-Objective Robust Optimization Framework

Nodal invulnerability has broad application prospects because of its emphasis on the differences between buses. Due to their long-term exposure, transmission lines are inevitably susceptible to damage caused by physical attacks or extreme weather. Therefore, restoring nodal invulnerability through a remedial approach or the introduction of mobile generators (MGs) is pivotal for resisting subsequent damage after a system is attacked. However, the research devoted to this field is limited. In order to fill the gap, this study conducts research on the configuration of MGs considering power generation balance to recover nodal invulnerability. First, a defender-attacker-defender (DAD) model is established, corresponding to the bi-objective robust optimization problem. The upper-level model is formulated to obtain the optimal compromise configuration scheme, the uncertainties of the attacked lines are elucidated in the middle level, and the nodal N-k security criterion utilized for measuring nodal invulnerability cooperates in the lower level. Then, a modified column-and-constraint generation (C&CG) algorithm is developed to incorporate fuzzy mathematics into the solution framework. In addition, the nodal invulnerability settings are optimized under limited resources. Numerical experiments are executed on the IEEE 24-bus system to verify the effectiveness and rationality of the proposed method.