New tight expression of network radiality constraints using constant commodity flow equipped with the parent–child supply chain

Preserving radiality is essential in distribution networks and Microgrid (MG) formation to ensure cost efficiency, reliability, and resiliency. However, maintaining radiality poses significant challenges due to the complexity of large-scale networks. Most existing models rely on Mixed-Integer Linear Programming (MILP) formulations, which suffer from low tightness, limiting their optimality and scalability. This paper addresses these limitations by introducing highly compact and tight radiality constraints designed to enhance computational performance and accuracy in reconfiguration and MG formation problems. The proposed approach is built on the novel Parent–Child Supply Chain (PCSC) framework, which, combined with a Constant Commodity Flow (CCF) model, ensures binary-like behavior for radiality variables without enforcing integer constraints. This innovation reduces the complexity of the problem, requiring binary variables only for line-switching decisions. Implementations of the model demonstrate significant improvements in computational performance, achieving a reduction of up to 72.61% in solution time and 14.7% in error margin compared to conventional MILP formulations. Moreover, the high tightness of the proposed constraints enables the use of second-order conic programming for highly accurate Distribution Power Flow (DistFlow) modeling. This advancement empowers operators to make realistic and informed decisions. The findings highlight the model’s potential to transform industry practices by offering a robust and scalable solution for network reconfiguration and MG formation.