Reliable Power Grid Expansion Considering $N-1-1$ Contingencies

The N-1-1 contingency consists of the consecutive loss of two components in a power system with intervening time for system adjustments between failures. This paper considers the expansion of an electric power system to achieve the N-1-1 reliability criterion with operation compliance check on unit commitment, economic dispatch, and power flow under contingency states. The resulting problem yields a very large-scale mixed-integer optimization model. For an efficient solution, a two-level Lagrangian Benders decomposition algorithm is adapted. The model and algorithm are evaluated on modified versions of several IEEE test systems with different contingency state combinations to confirm the proposed method's effectiveness.