Influence of grid topology on the operating envelope using relaxed three-phase OPF

Distribution System Operators face challenges in managing low-voltage networks due to increasing integration of photovoltaic systems, electric vehicles, and heat pumps. Operating Envelopes, which define the maximum and minimum power limits for end-users, offer a solution for congestion management and flexibility optimization . This paper uses a relaxed unbalanced three-phase Optimal Power Flow method with Second-Order Cone Programming relaxation to compute Operating Envelopes efficiently. By introducing a loss-minimization parameter, λ, the approach balances OE maximization and solution exactness. Case studies on the IEEE EU LV Testfeeder and 49 real LV feeders in Brussels highlight the impact of feeder topology and fairness constraints on OEs. Three feeder types are identified, demonstrating how grid characteristics influence individual and aggregated flexibility. Results confirm that optimal λ selection enhances grid flexibility while ensuring fair and practical OE allocation, supporting DSOs in adapting to evolving network demands.