Real-Time Scheduling of V2G Electric Vehicles in Distribution Networks Using SDP-Based Rolling-Horizon Optimization

This paper develops a real-time rolling-horizon optimization framework based on semidefinite programming (SDP) for vehicle-to-grid (V2G)-enabled electric vehicle (EV) fleets in distribution networks. The model coordinates time-varying EV availability, departure energy requirements, and distribution-network operating constraints under alternating-current (AC) power flow. The objective integrates voltage-dependent network loss cost, load-dependent EV energy transaction cost, and throughput-based battery degradation cost, while asymmetric charging/discharging efficiencies, EV implementation errors, and load forecast errors are also considered. To address the nonconvexity caused by AC power-flow equations and voltage-dependent losses, Hermitian lifting is used to reformulate the problem into a rank-constrained SDP model, followed by a convex SDP relaxation. Numerical studies on IEEE 33-bus and IEEE 69-bus systems show that the proposed rolling SDP method reduces EV-induced load peaks, improves load-smoothing performance, satisfies network and EV-side constraints, and yields numerically rank-one solutions in the tested cases. Further tests on time-slot lengths, look-ahead horizons, EV penetration levels, benchmark methods, EV implementation errors, and load forecast errors further verify the effectiveness and practical robustness of the proposed framework.