Enhancing Scalability of Optimal Kron-based Reduction of Networks (Opti-KRON) via Decomposition with Community Detection

TL;DR

This work tackles the scalability challenge of optimal Kron-based network reduction for large transmission systems by introducing a DC power-flow formulation and embedding community detection to partition the network for parallel MILP solving. The proposed DC Opti-KRON uses a cluster-based representation with a MICE-focused objective, Big-M linearization, and a cutting-plane to prune the feasible set, enabling scalable reductions. Empirical results on the IEEE RTS96 and 2383-bus Polish networks demonstrate substantial reductions in node count (enabled by partitioning) while achieving lower maximum intra-cluster error compared to CD- and Kron-based baselines; the approach preserves key electrical characteristics in the reduced models. The method’s significance lies in enabling scalable, accurate network reductions suitable for large-scale planning and operation analyses, with potential extensions to AC reductions and distribution-transmission co-reduction in future work.

Abstract

Electrical networks contain thousands of interconnected nodes and edges, which leads to computational challenges in some power system studies. To address these challenges, we contend that network reductions can serve as a framework to enable scalable computing in power systems. By building upon a prior AC "Opti-KRON" formulation, this paper presents a DC power flow formulation for finding network reductions that are optimal within the context of large transmission analysis. Opti-KRON previously formulated optimal Kron-based network reductions as a mixed integer linear program (MILP), where the number of binary variables scaled with the number of nodes. To improve the scalability of the Opti-KRON approach, we augment the MILP formulation with a community detection (CD) technique that segments a large network into smaller, disjoint, but contiguous sub-graphs (i.e., communities). For each sub-graph, we then (in parallel) apply MILP-based along with a new cutting plane constraint, thus, enhancing scalability. Ultimately, the new DC-based Opti-KRON method can achieve a 80-95\% reduction of networks (in terms of nodes) while statistically outperforming other CD- and Kron-based methods. We present simulation results for the IEEE RTS-96 and the 2383-bus Polish networks.

Figures (6)

• Figure 1: Decomposing the full network (left) with community detection to detect each disjoint community (colored sub-graphs in middle), and reconstructing the Kron-reduced network based on applying DC Opti-KRON to each community in parallel (right).
• Figure 2: Distribution of Maximum Intra-Cluster Error (MICE) with different reduction levels of RTS96 73 bus system.
• Figure 3: Visualization of the 2383-bus Polish transmission network with community detection.
• Figure 4: Distribution of MICE with different reduction levels of Polish transmission network with unweighted community detection.
• Figure 5: MICE distribution for network reduction of a 90% reduced Polish network.