Structure-preserving Optimal Kron-based Reduction of Radial Distribution Networks

Abstract: Network reduction simplifies complex electrical networks to address computational challenges of large-scale transmission and distribution grids. Traditional network reduction methods are often based on a predefined set of nodes or lines to remain in the reduced network. This paper builds upon previous work on Optimal Kron-based Reduction of Networks (Opti-KRON), which was formulated as a mixed-integer linear program (MILP), to enhance the framework in two aspects. First, the scalability is improved via a cutting plane restriction, tightened Big~M bounds, and a zero-injection node reduction stage. Next, we introduce a radiality-preservation step to identify and recover nodes whose restoration ensures radiality of the reduced network. The model is validated through its application to the 533-bus distribution test system and a 3499-bus realistic test feeder for a set of representative loading scenarios. In the 533-bus system, an 85% reduction was achieved with a maximum voltage error below 0.0025 p.u., while in the 3499-bus feeder, over 94% reduction was obtained with maximum voltage errors below 0.002 p.u. Additionally, we show that the radialization step accelerates the runtime of optimal voltage control problems when applied to Kron-reduced networks.