  Linear system solving is a key tool for computational power system studies,
e.g., optimal power flow, transmission switching, or unit commitment. CPU-based
linear system solver speeds, however, have saturated in recent years. Emerging
research shows that GPU-based linear system solvers are beginning to achieve
notable speedup over CPU-based alternatives in some applications. Due to the
architecture of GPU memory access, numerical pivoting represents the new
bottleneck which prevents GPU-based solvers from running even faster.
Accordingly, this paper proposes a matrix perturbation-based method to induce
static pivoting. Using this approach, a series of perturbed, well-conditioned,
pivot-free linear systems are solved in parallel on GPUs. Matrix expansion
routines are then used to linearly combine the results, and the true solution
is recovered to an arbitrarily high degree of theoretical accuracy. We showcase
the validity of our approach on distributed-slack AC power flow solve
iterations associated with the PGLib 300-bus test case.
