Abstract: The thermostatically controlled loads (TCLs) on the demand side are dispersed across physical locations. Only the loads physically connected within the same regional power grid can provide effective power transfer. To meet the power transfer requirements, it is essential to aggregate as many adjustable TCLs within a region as possible. However, due to the variations in load parameters, the aggregated load system exhibits hybrid characteristics of randomness and disorder. It is challenging to directly and uniformly control the aggregated load system to output a stable response. Aiming at the issues of power transfer capacity effectiveness and the stable control in heterogeneous aggregation models, we propose a heterogeneous aggregation and stable control model for the regional distributed TCL hybrid system. Firstly, a hybrid TCL clustering algorithm based on the Kohonen neural network is developed. According to the similarity of geographical and physical parameters of TCLs, regional hybrid loads are aggregated into multiple heterogeneous clusters, which are taken as the aggregation units for collaborative control. Secondly, a control-oriented generalized heterogeneous aggregation model for TCLs is established. For the heterogeneity of TCL physical parameters, an aggregation parameter estimation model is constructed utilizing an augmented Kalman filter. Based on the parameter estimation results, a generalized heterogeneous aggregation model is constructed to ensure the model’s stability and controllability. Finally, a hybrid system control model for heterogeneous cluster collaboration is built, enabling unified control and ensuring stable power transfer capacity. In the simulation, the photovoltaic power generation data are used as the tracking target. By employing the proposed algorithm in this paper, the tracking errors of clean energy output in different scenarios are maintained within ±0.03%, which verifies the accuracy and applicability of the proposed algorithm.