I. Introduction
The large-scale integration of distributed energy resources and charging loads poses significant challenges to the balance between power supply and demand in distribution networks (DNs) [1]. Limited by the acting frequency of the primary regulation equipment [2], conventional adjustment means have difficulties in responding to rapid fluctuations in power flows. This mismatch in time-scale has led to an increasing demand for flexible resources [3], which are highly effective in grid regulation [4]. Meanwhile, the novel power distribution devices based on power electronic technologies, represented by soft open points (SOPs), provide the fundamentals for the feasibility of flexible regulation [5]. By integrating the complementary benefits of multi-type resources in spatial and temporal aspects, the SOP is able to optimize power flows in real-time and improve the operation performance [6]. Thus, its role as an important flexible resource has been increasingly emphasized.