Recently, distributed generators (DGs) have been widely integrated into distribution network, so that the distribution network is gradually transforming into an active distribution network (ADN). Due to the influence of meteorological conditions, the output of DGs has high uncertainty. At the same time, considering the increasing variety of loads in ADNs, the uncertainty of load demand of user side is also increasing. In order to fully consider the uncertainty of measurement and quantitatively evaluate the operational status, this paper proposes a steady-state analysis method for ADNs under uncertain conditions. Firstly, this paper proposes a steady-state analysis method including power flow analysis model and evaluation indicators for the operation status from the perspectives of node and network. Secondly, the uncertainty factors are elaborated from three aspects: sources, impact on evaluation index and impact on scheduling. The evaluation indicators considering uncertain conditions, the impact on system security and scheduling of network are further discussed. Finally, through the simulation analysis of the modified IEEE 33-node test system, The effectiveness of the proposed method are verified.

After a fault occurs in the distribution network, the real-time balance between power supply and load demand must be met. Load can be restored through upper sources and the nearby power supply of distributed generators. Therefore, it is necessary to construct the power transmission path between each node, namely transmission matrix. Furthermore, the access of new controllable devices such as soft open point (SOP) makes it possible for power supply quickly by providing a path for power loss loads. In this paper, a fault recovery model of distribution network considering SOP is established. The dynamic balance of node power is firstly considered, then the the impact mechanism of SOP on fault recovery is elaborated. The cone relaxation process and the objective function of fault recovery is further introduced. Through the simulation analysis of the modified IEEE 33-node test system, scenarios of single fault and multi-point fault are built. The effectiveness of the proposed method and the improvement of load recovery after fault by SOP are verified.

With the widespread use of electric vehicles, the rapid development of power electronics and smart grids making more and more nonlinear devices connected to the grid, the power quality problem is becoming more and more prominent, and active power filters (APFs) are widely used to reduce the harmonic voltage and current in the grid. In this paper, the optimal configuration and dimensions of APFs for distribution networks based on the improved Beluga whale optimization (IBWO) are proposed. The IBWO algorithm proposed in this paper is characterized by fast convergence and high accuracy. The objective of the method proposed in this paper is to reduce the number of APFs used and the investment cost, while making the total voltage harmonic distortion rate (VTHD) and the individual VTHD of the grid meet the requirements. Finally, this paper verifies the effectiveness and feasibility of the proposed method by an example in an IEEE-18 bus test system, and the results show that the proposed method is effective in optimizing the location and capacity of multiple APFs.