Distributed flexible dispatch of heterogeneous thermostatically controlled loads with physically consistent neural ODEs

Thermostatically controlled loads (TCLs) are the major energy sources in buildings that provide flexible load adjustment in power systems. The flexible dispatch of TCLs requires modeling thermal dynamics to measure indoor temperature variations and optimizing power consumption to provide flexibility to power grids while satisfying occupant comfort preferences. However, when dispatching TCLs across multiple buildings, heterogeneous building structures and comfort preferences can lead to different model complexities in thermal dynamics and temperature regulation intervals, both of which can make traditional methods insufficient or even infeasible for problem-solving. To tackle this challenge, this work first develops a novel Physically Consistent Neural Ordinary Differential Equation (PC-NODE) model to represent thermal dynamics, integrating weight learning and physics-informed loss functions to ensure a unified model structure and physics consistency. The developed continuous model is then seamlessly transformed into discrete equation constraints to represent comfort preferences with different time intervals. Furthermore, an asynchronous Alternating Direction Method of Multipliers (ADMM)-based distributed optimization method is proposed to coordinate buildings with heterogeneous comfort preferences by differentiating the frequency of local variable updates across buildings based on the time interval. Simulation results for a 12-building dispatch case demonstrate that the single-zone model trained by PC-NODE significantly improves statistical accuracy, whereas asynchronous ADMM achieves near-optimal economic performance relative to ground-truth centralized optimization.