## 1 Introduction  
Energy consumption has gradually changed from fossil fuels and other traditional energy sources to renewable energy sources, such as wind farms (WF), photovoltaic (PV) energy, and nuclear energy [1; 2; 3; 4]. With the reform of the power market in China, distributed WF and PV generation are developing rapidly, and the penetration of distributed generation (DG) in the distribution networks is increasing. When the capacity of DG in traditional medium- and low-voltage distribution networks approaches a high proportion (i.e., high penetration), there are difficulties in ensuring the power balance and the safe operation of distribution networks, and the reliability and power quality for customers [5; 6]. On the one hand, the connection of DG into distribution networks helps to alleviate energy supply shortages, reduce network loss, and improve environmental benefits and the voltage quality of the distribution network. On the other hand, due to the randomness and fluctuation of DG,the connection of DG into distribution networks may cause many problems, such as power quality, relay protection, and flexibility, which will affect the secure and reliable operation of the distribution network [7]. The volatility, intermittency, and unpredictability of renewable energy influence the fluctuation in distribution networks under high penetration of DG, resulting in low efficiency and great investment in distribution network equipment [8]. Improving the flexibility of distribution networks and effectively reducing the adverse impact of the high penetration of DG have become global research hotspots in recent years [9; 10]. Many research works have studied the flexibility of distribution networks by considering DG connection. In [11], an intelligent distribution network optimization planning model aiming to minimize comprehensive costs is proposed. The influence of flexible resources and strategies such as operation control means and demand side management on the distribution network planning are comprehensively considered in the proposed model. In [12], a multi-objective optimization dispatching model considering interruptible loads and energy storage is constructed based on the five flexibility indices. It is proven that the optimal dispatching of flexible resources can effectively improve the flexibility of the distribution network, with high penetration of DG, and that the ability of the distribution network to accommodate DG can be assessed with the proposed model. In [13], the flexible planning for power systems with high penetration of renewable energy is reviewed and the quantitative evaluation index system for flexible planning is introduced. Then, the strategies and the key difficulties of flexible coordination planning for power systems are put forward. In [14], a dynamic reconfiguration model for a distribution network is proposed, which aims at improving the accommodation level of DG. Different characteristics of DG in different time periods are considered in the proposed time varying model. In [15], a method for evaluating the accommodation capacity of renewable energy based on the flexibility adequacy of the distribution system is proposed, and the flexibility of various resources in the distribution system is analyzed from the perspective of power regulation range. Energy hub and energy router components that allow exchange of renewable energy sources among energy users are basic technologies that enhance the flexibility of distribution networks with DG. In [16], the Duindam-Stramigioli energy router is studied and applied to realize the energy exchange using standard power electronic converter topologies. The energy hub in [17] is an interface between different energy infrastructures and is used to convert, condition, and store multiple energy carrier systems.