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

Technical Summary: A Thermal-Electrical Co-Optimization Framework for Active Distribution Grids

Problem Statement
The increasing electrification of residential heating and transportation via Heat Pumps (HPs) and Electric Vehicles (EVs) introduces significant flexibility to Active Distribution Networks (ADNs) but also creates tightly coupled thermal-electrical dynamics. Current literature faces three primary limitations: (1) a lack of rigorous integration between building thermodynamics and electrical optimization, often relying on oversimplified models; (2) fragmented treatment of Distributed Energy Resources (DERs), failing to coordinate HPs, EVs, and Photovoltaic (PV) systems simultaneously; and (3) computational scalability issues, where reliance on heuristic methods or non-convex solvers prevents global optimality and real-time application at the distribution scale.

Methodology
The paper proposes a unified co-optimization framework that integrates a calibrated 3R2C grey-box building thermal model directly into a network-constrained Optimal Power Flow (OPF) problem.

• Thermal-Electrical Modeling: A high-fidelity 3R2C model captures indoor air and building envelope dynamics, mapping thermal comfort constraints to HP electrical consumption via the Coefficient of Performance (COP). This model accounts for ambient temperature, solar irradiance, and building thermal inertia.
• Asset Coordination: The framework simultaneously schedules HPs, EVs, and PVs. EV constraints include state-of-charge (SoC) limits, arrival/departure times, and charging power bounds. HPs are modeled with explicit thermal-to-electrical mapping. PVs are subject to generation limits based on irradiance.
• Network Formulation: The power flow problem utilizes the Branch Flow Model (DistFlow) for radial networks. To ensure computational tractability, the non-convex AC power flow equations are relaxed into a Second-Order Cone Programming (SOCP) formulation.
• Objective Function: The optimization minimizes line and transformer losses while penalizing PV curtailment. A weighting coefficient prioritizes the reduction of curtailment over loss minimization.
• Case Study: The framework is tested on a realistic low-voltage (LV) feeder in Cyprus (61 nodes, 3 feeders) using real-world load profiles, driving patterns, and building thermodynamics data.

Key Contributions

1. Thermal-Electrical Coupling: The development of a unified framework that embeds calibrated 3R2C grey-box models into electrical optimization, enabling precise mapping from thermal comfort constraints to HP electrical flexibility.
2. Comprehensive Multi-Asset Coordination: The simultaneous scheduling of HPs, EVs, and PVs within a single network-constrained OPF, capturing realistic operational constraints and inter-asset dependencies.
3. Scalable Convex Formulation: A computational assessment of SOCP relaxation on realistic LV networks. The study demonstrates that the convex DistFlow formulation achieves sub-second runtimes and near-optimal performance even at high DER penetration levels, outperforming non-convex Bus Injection and DistFlow models.

Results
Simulations on the Cypriot LV network demonstrate the effectiveness of the coordinated scheduling strategy compared to uncontrolled operation:

• Efficiency: Total daily energy consumption for HPs decreased significantly (from 1227 kWh to 866 kWh) while maintaining indoor temperatures within comfort limits (21°C vs. 20.4°C).
• Losses: Coordinated control reduced total daily losses (transformer + line) by 54% (from 1.29% to 0.59%).
• Transformer Aging: The strategy reduced the equivalent aging factor of the transformer by 41%, extending equipment lifespan by smoothing thermal stress and avoiding peak loading surges.
• Voltage Stability: The coordinated approach eliminated voltage violations observed in the uncontrolled scenario (where voltages dropped to 0.92 p.u. during evening peaks), maintaining voltages closer to nominal values.
• Computational Performance: The convex DistFlow formulation maintained runtimes under 1 second (0.87s at 100% DER penetration), whereas non-convex formulations scaled poorly, reaching nearly 900 seconds.
• Exactness Analysis: While theoretical sufficient conditions for SOCP exactness were not fully met due to network heterogeneity (e.g., varying r/x ratios in service lines), the relaxation remained exact in practice for the studied case, likely due to the absence of voltage-rise phenomena driven by high baseline demand.

Significance and Claims
The paper claims that integrated thermal-electrical coordination is a critical enabler for future smart grids. By explicitly coupling building thermodynamics with network constraints, the proposed framework allows for the exploitation of thermal inertia to shift electrical demand, thereby enhancing grid reliability and energy efficiency without compromising user comfort. The study highlights that convex relaxations, despite theoretical limitations in heterogeneous networks, offer a practical and computationally efficient alternative to non-convex methods for real-time distribution network management. The work bridges the gap between academic modeling and practical grid management tools by demonstrating that scalable, global-optimal solutions are achievable for complex, multi-asset distribution systems.