Improving Power Grid Network Robustness by Optimized Switch Allocation: A Large-Scale Case Study in Brazil

Radial distribution networks are inherently vulnerable to cascading outages: a single fault on an unprotected lateral can trip the feeder breaker and de-energize thousands of consumers. Optimally placing protective switches to segment these networks is an NP-hard combinatorial problem whose exact formulation scales at $O(2^N)$, making it intractable for real utility-scale grids. We propose a scalable graph-theoretic heuristic based on a Cumulative Downstream Load (CDL) metric that identifies the electrical backbone of each feeder through a two-pass tree traversal in $O(N)$ time. The method exploits a formal isomorphism between radial power flow and hydrological stream ordering (Horton-Strahler), treating the feeder as a ''reverse river'' where load accumulates from consumers to the substation. Applied to the full distribution network of COPEL, a major Brazilian utility encompassing approximately 3.8 million nodes and 2,415 feeders, the algorithm proposed 6,979 switch locations across 1,757 feeders in under five minutes on commodity hardware. Of these, 92.6\% correspond to genuinely unprotected locations, while the remaining 7.4\% independently confirm devices already placed by utility engineers. In aggregate, the proposed allocation would protect over 349,000 backbone consumer units from unnecessary cascading outages while isolating over one million lateral consumer units into properly segmented fault zones, with a highly skewed per-switch impact distribution that enables priority-based phased deployment. The results demonstrate that linear-time network science heuristics can deliver actionable infrastructure recommendations at scales where conventional optimization methods fail to converge.