The high penetration of distributed energy resources is accelerating the topology evolution of distribution systems

necessitating research on cost-effective dynamic evolution pathways. This paper introduces and develops percolation theory to address “where to start” and “how to evolve” in distribution system topology evolution. First

this paper establishes a heterogeneous percolation model coupled with electrical constraints to achieve dynamic coupling between topology configuration and power flow constraints. Then

by analyzing percolation thresholds and the electrical functional giant connected component

identification methods for structural and functional bottlenecks are proposed. On this basis

this paper develops a reverse percolation-guided evolution path optimization method to identify critical investment intervals that trigger performance transitions. Case studies on a Czech urban distribution network demonstrate that prioritizing functional bottleneck expansion effectively avoids performance degradation caused by blind investment. Results from the modified IEEE 37-node system show that the proposed method improves distributed generation hosting capacity by 11.36% compared to traditional approaches with the same number of added branches

validating the effectiveness of the proposed methodology.