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

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, which was formulated as a mixed-integer linear program, to enhance the framework in three 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. A linearized voltage magnitude error constraint is incorporated to explicitly bound the difference between full and reduced networks. The model is validated through its application to the 533-bus distribution test system and a 3499-bus utility 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 per unit, while in the 3499-bus feeder, over 94% reduction was obtained with maximum voltage errors below 0.002 per unit. Additionally, we show that the radialization step accelerates the runtime of optimal voltage control problems when applied to Kron-reduced networks.