An adaptive tensor convolution-based method for calculating the density flexibility region of distribution systems

A calculation method based on adaptive tensor convolution is proposed for constructing and quantifying the density flexibility region of distribution systems in transmission-distribution coordinated dispatch. This density flexibility region is a two-dimensional power region integrating operational security constraints and feasible combination density, which can depict the adjustable power range of the system and quantify the flexibility redundancy at each operating point. Local aggregation of flexibility resources is achieved through convolution, and an adaptive weighting function constructed from electrical distance and power factor angle is introduced to characterize the nonlinear coupling relationships among flexibility resources. Furthermore, tensor convolution operation is employed to extend the high-dimensional combinatorial space. The feasible region distribution is obtained through constraint filtering and tensor summation operations, thereby forming a global density flexibility region encompassing multiple flexibility resources. Case studies are carried out on the IEEE 33-bus system and a 38-bus distribution network in Guizhou. The results show that the flexibility region area obtained by the proposed method is 1.17 times that obtained by Latin hypercube sampling, and the computation time is only 5% of that of Latin hypercube sampling. Moreover, the flexibility region composed of discrete flexibility resources features dual density centers.