Optimal Kron-based Reduction of Networks (Opti-KRON) for Three-phase Distribution Feeders
For power system engineers, this provides a scalable and accurate network reduction technique for steady-state analysis and optimal power flow studies.
This paper introduces a structure-preserving Kron-based reduction method for unbalanced distribution feeders that aggregates electrically similar nodes to produce reduced networks with low voltage errors. On real feeders with 5,991 and 8,381 nodes, the method achieves up to 90% and 80% reduction, respectively, with maximum voltage-magnitude error below 0.003 p.u., and GPU acceleration yields up to 15x speedup over CPU.
This paper presents a novel structure-preserving, Kron-based reduction framework for unbalanced distribution feeders. The method aggregates electrically similar nodes within a mixed-integer optimization (MIP) problem to produce reduced networks that optimally reproduce the voltage profiles of the original full network. To overcome computational bottlenecks of MIP formulations, we propose an exhaustive-search formulation to identify optimal aggregation decisions while enforcing voltage margin limits. The proposed exhaustive network reduction algorithm is parallelizable on GPUs, which enables scalable network reduction. The resulting reduced networks approximate the full system's voltage profiles with low errors and are suitable for steady-state analysis and optimal power flow studies. The framework is validated on two real utility distribution feeders with 5,991 and 8,381 nodes. The reduced models achieve up to 90% and 80% network reduction, respectively, while the maximum voltage-magnitude error remains below 0.003 p.u. Furthermore, on a 1000-node version of the network, the GPU-accelerated reduction algorithm runs up to 15x faster than its CPU-based counterpart.