Comparing Machine Learning and Optimization Approaches for the N − k Interdiction Problem Considering Load Variability

Power grids must be operated, protected, and maintained such that a small number of line failures will not result in significant load shedding. To identify problematic combinations of failures, we consider an N-k interdiction problem that seeks the set of k failed lines (out of N total lines) that result in the largest load shed. This is naturally formulated as a bilevel optimization problem with an upper level representing the attacker that selects line failures and a lower level modeling the defender's generator redispatch to minimize the load shedding. Compounding the difficulties inherent to the bilevel nature of interdiction problems, we consider a nonlinear AC power flow model that makes this problem intractable with traditional solution approaches. Furthermore, since the solutions found at a particular load condition may not generalize to other loading conditions, operators may need to quickly recompute these worst-case failures online to protect against them during operations. To address these challenges, we formulate and compare the performance of three simplified methods for solving the N-k interdiction problem: a state-of-the-art optimization approach based on a network-flow relaxation of the power flow equations and two newly developed machine learning algorithms that predict load sheds given the state of the network