Low-rank corrections to a shared reference Jacobian for GPU-parallel AC $N\!-\!1$ contingency analysis
Marc Hunkemöller, Nico Westerbeck, Joost van Dijk, Lars Schewe, Dirk Witthaut
Contingency analysis repeatedly solves the power-flow equations under many single-element outages, an increasingly demanding workload as operating margins tighten and renewable variability grows. Graphics processing units (GPUs) are attractive for this task, but a change in topology alters the sparsity pattern of the Jacobian, preventing the uniform batched factorization on which efficient GPU solvers rely. This paper presents a GPU-parallel Newton--Raphson solver for $N\!-\!1$ contingency analysis that separates the change in operating state from the change in topology. A single reference Jacobian is inverted once and reused across all contingencies. Each topology change is expressed as a low-rank Woodbury correction, while the residual state-dependent perturbation is handled by an inner iterative solve, a truncated Neumann series or the biconjugate gradient stabilized method. We analyze the spectral radius and condition number of the resulting iteration matrices and show that the reference Jacobian is an effective preconditioner. On transmission-scale benchmarks, the method attains per-topology solve times competitive with an optimized 80-core central processing unit baseline, with the low-rank correction accounting for approximately 1--2\% of the workload. This makes GPU-parallel $N\!-\!1$ contingency analysis feasible at transmission scale without per-topology refactorization.
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