Operating-Point Selection for Linearized Power-Flow Models in Active Distribution Grids: Accuracy, Critical-State Performance, and Runtime

Active distribution grids require analysis methods that combine physical fidelity with low computational cost for repeated screening, optimization workflows, and operational decision support. Local linearized power-flow models can support these tasks, but their accuracy depends strongly on the operating point around which they are derived and on how the relevant operating range is represented. This paper benchmarks operating-point-dependent linearized power-flow models for active distribution grids across five SimBench networks. We compare operating-point selection strategies, library sizes, and targeted library extensions for three separate target quantities: voltage magnitude, line loading, and transformer loading. The evaluation combines equal-budget accuracy, critical- and near-limit operating states, post-action AC validation, and controlled runtime measurements. At an equal budget of 36 linearization points, k-medoids provides the most consistent general-purpose accuracy and achieves the first target-specific rank for all three quantities. Increasing the library size yields diminishing gains, with the largest improvement between 10 and 22 points. A k-medoids/k-center hybrid improves all six primary accuracy metrics relative to a common 28-point basis and provides the best upper-tail voltage accuracy in critical states. In post-action validation, nominal linear actions are AC-feasible in 31 of 35 cases, while adding a safety margin yields successful AC results in all 35 cases without new violations. Online evaluation requires about 3.5 ms per state and achieves a median speed-up of about 26–28 relative to AC power flow. The results show that operating-point libraries can provide a practical accuracy–runtime compromise when representative coverage, critical-state validation, and residual decision margins are considered jointly.