An augmented Lagrangian method on GPU for security-constrained AC optimal power flow

We present a new algorithm for solving large-scale security-constrained optimal power flow in polar form (AC-SCOPF). The method builds on Nonlinearly Constrained augmented Lagrangian (NCL), an augmented Lagrangian method in which the subproblems are solved using an interior-point method. NCL has two key advantages for large-scale SCOPF. First, NCL handles difficult problems such as infeasible ones or models with complementarity constraints. Second, the augmented Lagrangian term naturally regularizes the Newton linear systems within the interior-point method, enabling solution of the Newton systems with a pivoting-free factorization that can be efficiently parallelized on GPUs. We assess the performance of our implementation, called MadNCL, on large-scale corrective AC-SCOPFs, with complementarity constraints modeling the corrective actions. Numerical results show that MadNCL can solve AC-SCOPF with 500 buses and 256 contingencies fully on the GPU in less than 3 minutes, whereas Knitro takes more than 3 hours to find an equivalent solution.