A Least-squares-based Iterative Method with Better Convergence for PF/OPF in Integrated Transmission and Distribution Networks

The limitations of the conventional master-slave-splitting (MSS) method, which is commonly applied to power flow and optimal power flow in integrated transmission and distribution (I-T&D) networks, are first analyzed. Considering that the MSS method suffers from a slow convergence rate or even divergence under some circumstances, a least-squares-based iterative (LSI) method is proposed. Compared with the MSS method, the LSI method modifies the iterative variables in each iteration by solving a least-squares problem with the information in previous iterations. A practical implementation and a parameter tuning strategy for the LSI method are discussed. Furthermore, a LSI-PF method is proposed to solve I-T&D power flow and a LSI-heterogeneous decomposition (LSI-HGD) method is proposed to solve optimal power flow. Numerical experiments demonstrate that the proposed LSI-PF and LSI-HGD methods can achieve the same accuracy as the benchmark methods. Meanwhile, these LSI methods, with appropriate settings, significantly enhance the convergence and efficiency of conventional methods. Also, in some cases, where conventional methods diverge, these LSI methods can still converge.