Analytical segmental holomorphic embedding power flow method for integrated transmission and distribution networks

This paper proposes a novel analytical segmental holomorphic embedding (ASHE) based power flow method for integrated transmission and distribution (ITD) systems. In this method, the power flow calculation for ITD system is split into a main part for transmission network (TN) and a number of sub-problems for distribution networks (DNs). First, the sub-problems of DNs power flow are addressed using a specially designed holomorphic embedding (HE) formulation using an embedding factor to represent the voltage fluctuation at the boundary buses. Subsequently, an analytical polynomial expression, representing the power consumption of the DNs with respect to the voltage magnitude at the boundary buses, is derived from a single power flow calculation. Next, the analytical polynomial expression is integrated into the TN power flow equations, which is also solved by the HE method. Particularly, the TN and DNs exchange information only once. Numerical experiments demonstrate that the proposed method maintains the same accuracy as the method based on the traditional global model. Furthermore, it achieves better convergence and efficiency compared to the master–slave-splitting method under various scenarios, including DNs with distributed generations, heavily loaded DNs and unbalanced three-phase condition, which is especially suitable for large-scale systems.