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

TL;DR

This work tackles the challenge of jointly optimizing heating, EV charging, PV, and network operation by embedding a calibrated $3R2C$ grey-box building model into a network-constrained OPF and solving a convex relaxation of DistFlow via SOCP. The approach enables simultaneous scheduling of HPs, EVs, and PVs while enforcing thermal comfort, DER limits, and full power-flow physics. Case studies on a realistic LV Cypriot feeder show that convex DistFlow achieves sub-second runtimes and the SOCP relaxation remains exact in practice, with controllable operation reducing transformer aging by up to 41%, lowering losses by 54%, and eliminating voltage violations. The results demonstrate the value of integrated thermal–electrical coordination for future smart grids and point to extensions in real-time MPC for receding-horizon optimization.

Abstract

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.

Figures (8)

• Figure 1: Thermal network representation of the 3R2C grey-box model.
• Figure 2: RC model tuning performance using the identified 3R2C grey-box model across three phases: training, validation, and testing.
• Figure 3: Single-line diagram of the suburban low-voltage distribution network, comprising three feeders connected to a 22/0.4 kV transformer.
• Figure 4: Time-series comparison of active power consumption and indoor temperature for controlled and uncontrolled operation of HPs and EVs.
• Figure 5: Time-series comparison of total losses (transformer + line) under controllable and uncontrollable operation. The green curve shows the percentage improvement achieved via coordinated scheduling.