Price-Calibrated Network Loss–Carbon Emission Co-Optimization for Radial Active Distribution Networks via DistFlow-Based MISOCP Reconfiguration

Active distribution networks (ADNs) with high DER penetration require coordinated decisions to ensure voltage security, limit losses, and support low-carbon targets. However, most reconfiguration-centric studies prioritize loss/cost and rarely integrate carbon pricing and emission accounting into a unified framework with verifiable optimality. This study develops a DistFlow-based mixed-integer second-order cone programming (MISOCP) model that co-optimizes feeder reconfiguration and resource active/reactive dispatch under a price-calibrated loss–emission objective. The framework coordinates PV/WT generation, MTs, aggregated PHEVs (V2G), and reactive-support devices (SVCs and switched capacitor banks (CBs)) and is solved by commercial CPLEX to global optimality for the SOCP-relaxed problem. On the IEEE 33-bus feeder, device coordination reduces losses from 0.203 MW to 0.0382 MW (81.18%) and CO2 emissions from 2.3872 to 0.3433 tCO2 (85.62%), while reducing operating cost from CNY 354.9357 to CNY 56.6271 (84.05%). Enabling reconfiguration further reduces losses to 0.0205 MW (89.90%), emissions to 0.2580 tCO2 (89.19%), and operating cost to CNY 37.4677 (89.44%), while keeping voltages within 0.99–1.01 p.u. Relative to device-only operation, reconfiguration yields 46.34% loss reduction, 24.85% emission reduction, and 33.83% operating-cost reduction. The mixed-integer optimality gap is ~10−7, and the solution quality for the original non-convex model depends on the tightness of the SOCP relaxation, which is numerically tight in the cases we studied. These results show interpretable technical and environmental gains via coordinated dispatch and topology control in radial ADNs at scale.