Optimal Kron-based Reduction of Networks (Opti-KRON) for Three-phase Distribution Feeders

TL;DR

This paper introduces a scalable, GPU-accelerated Kron-based network reduction method that preserves voltage profiles in unbalanced distribution feeders, enabling efficient steady-state analysis.

Contribution

It develops a novel, structure-preserving reduction framework using mixed-integer optimization and exhaustive search, scalable via GPU parallelization.

Findings

Achieves up to 90% network reduction with less than 0.003 p.u. voltage error.

GPU implementation runs up to 15 times faster than CPU.

Validated on real utility feeders with thousands of nodes.

Abstract

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.