Accelerated DC loadflow solver for topology optimization

Abstract: We present a massively parallel solver that accelerates DC loadflow computations for power grid topology optimization tasks. Our approach leverages low-rank updates of the Power Transfer Distribution Factors (PTDFs) to represent substation splits, line outages, and reconfigurations without ever refactorizing the system. Furthermore, we implement the core routines on Graphics Processing Units (GPUs), thereby exploiting their high-throughput architecture for linear algebra. A two-level decomposition separates changes in branch topology from changes in nodal injections, enabling additional speed-ups by an in-the-loop brute force search over injection variations at minimal additional cost. We demonstrate billion-loadflow-per-second performance on power grids of varying sizes in workload settings which are typical for gradient-free topology optimization such as Reinforcement Learning or Quality Diversity methods. While adopting the DC approximation sacrifices some accuracy and prohibits the computation of voltage magnitudes, we show that this sacrifice unlocks new scales of computational feasibility, offering a powerful tool for large-scale grid planning and operational topology optimization.