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.

💡 Research Summary

The paper addresses the growing challenge of coordinating electric vehicles (EVs) and heat pumps (HPs) in active distribution networks (ADNs). While these assets provide valuable demand‑side flexibility, their operation creates tightly coupled thermal‑electrical dynamics that traditional OPF models fail to capture. The authors propose a unified co‑optimization framework that embeds a calibrated 3‑resistor‑2‑capacitor (3R2C) grey‑box building thermal model directly into a network‑constrained optimal power flow (OPF) problem.

Key technical contributions are threefold. First, the 3R2C model represents indoor air temperature, building envelope temperature, thermal capacitances, and resistances, together with solar gains. It yields a discrete‑time heat balance (equations 10‑11) and maps heating demand to electrical consumption through the coefficient of performance (COP) of the heat pump (equation 9). Comfort constraints enforce indoor temperature within user‑specified bounds. Second, the framework simultaneously schedules EV charging (including state‑of‑charge dynamics and binary connection status), HP operation, and photovoltaic (PV) generation, respecting DER active/reactive power limits, IEEE‑1547‑2018 reactive‑power modes, and transformer ampacity constraints. Third, the power‑flow equations are expressed using the DistFlow formulation for a radial low‑voltage feeder. The non‑convex quadratic relation between power flow and current magnitude (equation 16) is relaxed to a second‑order cone (SOCP), yielding a convex problem that can be solved in sub‑second time. Although classical exactness proofs require either no upper load bounds or no lower injection bounds—conditions violated in realistic feeders—the authors reference recent voltage‑based sufficient conditions and demonstrate empirically that the relaxation remains exact for virtually all time steps in their case study.

The case study uses a realistic Cyprus low‑voltage feeder with multiple transformers, 200 residential nodes, and calibrated building parameters derived from measured temperature, solar irradiance, and power data. EVs are modeled with 2 kW chargers, 10 kWh batteries, and realistic arrival/departure windows. HPs have temperature‑dependent COPs, and PV output follows measured solar profiles. Three OPF formulations are compared: (i) full nonlinear AC‑OPF, (ii) bus‑injection convex formulation, and (iii) the proposed convex DistFlow (SOCP). The convex DistFlow solves in an average of 0.78 s, while the AC‑OPF and bus‑injection models require 9.3 s and 12.1 s respectively, with optimality gaps below 0.3 %.

Operational results show that coordinated scheduling reduces transformer aging acceleration factor by 41 %, cuts total line and transformer losses by 54 %, and eliminates all voltage violations, even under high DER penetration (≥30 % PV, ≥20 % EV). The framework thus demonstrates that integrating detailed thermal dynamics with convex power‑flow relaxations enables scalable, near‑optimal real‑time control of future smart grids.

The paper concludes by highlighting the practical viability of the approach and suggests future extensions such as multi‑day stochastic planning, bidirectional V2G capabilities, and incorporation of probabilistic weather and occupancy forecasts.