Integrated Optimal Power Flow of Transmission and Distribution Networks Based on Multiple Linear Regression Modified Heterogeneous Decomposition

Under the dual-carbon strategy and the increasing integration of distributed energy resources (DERs), conventional equivalent-load-based modeling methods for transmission and distribution (T&D) systems face significant accuracy and effi-ciency challenges. This paper proposes an integrated T&D optimal power flow (OPF) framework that addresses these challenges via a heterogeneous decomposition (HGD) algorithm. The method enables secure and independent optimization of transmission and distribution subsystems through boundary information exchange. To incorporate environmental considerations, a node-level carbon emission intensity model based on carbon flow theory is introduced. A multi-objective optimization problem is formulated to balance economic cost and carbon emissions, which is solved by transforming the max-min objective into a linear weighted form via satisfaction functions. Furthermore, a multivariate linear regression-based acceleration technique is embedded into the iterative HGD process, significantly improving convergence performance. Case studies on typical T&D systems verify that the proposed approach maintains solution accuracy, enhances convergence speed, and expands the convergence domain, even in scenarios with high DER penetration and complex grid structures.