Trusted Aggregation of Heterogeneous Thermostatically Controlled Loads via Geometric Deep Learning based Inner Approximation Approach

Thermostatically controlled loads possess significant flexibility potential. They can provide essential balancing services such as frequency regulation to the power grid. However, the economic management of massive heterogeneous resources imposes severe high-dimensional computational and decision-making burdens. To overcome this limitation, this paper proposes a real-time trusted aggregation method based on geometric deep learning and inner approximation. First, physical modeling of flexibility resources is established to construct precise feasible regions. Subsequently, a DeepSets architecture with sum-pooling is employed to handle dynamic and heterogeneous inputs, efficiently mapping micro-parameters to macro-boundary geometric transformations. Furthermore, to ensure calculation safety, a novel physics-guided safety loss is introduced to enforce strict inner approximation of the feasible region. Simulation results demonstrate that, compared with traditional optimization methods, the proposed approach enables millisecond-level inference speed while drastically minimizing boundary violation risks, thereby ensuring both the computational efficiency and physical safety required for virtual power plant dispatch.