A Thermal-Electrical Co-Optimization Framework for Active Distribution Grids with Electric Vehicles and Heat Pumps

The growing electrification of transportation and heating through Electric Vehicles (EVs) and Heat Pumps (HPs) introduces both flexibility and complexity to Active Distribution Networks (ADNs). These resources provide substantial operational flexibility but also create tightly coupled thermal-electrical dynamics that challenge conventional network management. This paper proposes a unified co-optimization framework that integrates a calibrated 3R2C grey-box building thermal model into a network-constrained Optimal Power Flow (OPF). The framework jointly optimizes EVs, HPs, and photovoltaic systems while explicitly enforcing thermal comfort, Distributed Energy Resource (DER) limits, and full power flow physics. To maintain computational tractability, Second-Order Cone Programming (SOCP) relaxations are evaluated on a realistic low-voltage feeder. The analysis shows that, despite network heterogeneity violating some theoretical exactness conditions, the relaxation remains exact in practice. Comparative assessments of convex DistFlow, bus injection, and branch flow formulations reveal that convex DistFlow achieves sub-second runtimes and near-optimal performance even at high DER penetration levels. Simulations confirm the effectiveness of coordinated scheduling, yielding reductions of 41% in transformer aging, 54% in losses, and complete elimination of voltage violations, demonstrating the value of integrated thermal-electrical coordination in future smart grids.